Copyright by Ximing Cai 1999 A Modeling Framework for Sustainable Water Resources Management by Ximing Cai, B. E., M. E. Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy The University of Texas at Austin May 1999 A Modeling Framework for Sustainable Water Resources Management Approved by Dissertation Committee: In memory of my grandfather i A Modeling Framework for Sustainable Water Resources Management Publication No._____________ Ximing Cai, Ph.D. The University of Texas at Austin, 1999 Supervisor: Daene C. McKinney A prototype modeling framework for quantitative analysis of sustainable water resources management at the river basin scale is developed and applied to the Syr Darya River basin in Central Asia to analyze long-term water resource system sustainability. The research problem is specified as long-term, sustainable water resources management in river basins that are characterized by (semi)-arid climate, a heavy dependence on irrigated agriculture, and possibly severe environmental degradation in the form of water and soil salinity. Sustainable water management is defined here as ensuring a long-term, stable and flexible water supply capacity to meet crop water demands, as well as growing municipal and industrial water demands, at the same time as keeping a stable relationship between irrigation practices and their associated environmental consequences. For this research, an innovative systems approach has been developed to model and analyze sustainability issues related to water resources management. ii The core of this modeling framework consists of an intra-year, short-term optimization model and an inter-year, long-term, dynamic model that combines simulation and optimization. In the intra-year model, essential hydrologic, agronomic, economic, and institutional relationships are integrated into a coherent analytical framework at the river basin scale to reflect the interdisciplinary nature of water resources problems. The inter-year model includes long-term changes and uncertainties in both water supply and demand, and incorporates prescribed sustainability principles for river basin system performance control. Relations between short-term irrigation practices and their long-term economic and environmental consequences are modeled and controlled in the inter-year modeling framework. The intra-year, or short-term, model is applied to the Syr Darya River basin to explore case-specific, in-depth hydrologic-agronomic-economic- institutional relationships. This application shows the power of this type of integrated optimization model. Moreover, the application of the long-term modeling framework to the case study area shows the effectiveness of this tool for sustainability analysis in this region. Three approaches based on decomposition analysis and newly developed genetic algorithms for solving highly complex water resources management models that are large, nonconvex, and nonlinear are presented and applied. The short-term model, which is a large and nonlinear model, is solved by a ?piece-by- piece? approach based on model decomposition. A new genetic algorithm ? linear programming approach is used to solve the long-term model. Throughout the study, both the feasibility and the effectiveness of incorporating the philosophy of sustainability into traditional water resources management modeling are addressed. It is argued that system modeling techniques, if well supported by relevant empirical studies, and if sufficient data iii are available, can promote the understanding of sustainability in water resources research, a concept of utmost importance that will strongly influence future research in water resources management. v Acknowledgments I would like to thank my supervising professor, Dr. Daene McKinney, not only for his support, encouragement and guidance throughout this research, but also for his optimism and kindness. I feel very lucky to work under his supervision in a couple of international projects that were closely related to this research. I would also like to thank the rest of my committee for their contributions to this work and to my education. In particular, Dr. Leon Lasdon was very generous with his time in helping me develop solution techniques, Dr. David Maidment taught and supported me to use GIS techniques, Dr. David Eaton led me to understand more about sustainable water resources management, and Dr. Neal Armstrong taught me skills in water quality modeling. I believe the education and research practices with the committee will continually benefit my future career. A number of people outside of the university helped to shape the ideas behind this research and contributed to its fruition. In particular, Dr. Ronald North encouraged and helped me in both study and life in the U.S. through all these years. The friendship with Dr. North and his family has been making the life of my family and mine more enjoyable. Dr. Mark Rosegrant contributed very useful advice pertaining to the economic?based river basin modeling analysis, and I deeply appreciate his support and guidance during my several research trips to his institute, the International Food Policy Research Institute (IFPRI). Dr. Andrew Keller in the International Water Management Institute (IWMI) was instrumental vi in providing technical support to irrigation management modeling. Ms. Claudia Ringler in IFPRI provided generous help through review of the proposal of this research, comment on the document of the dissertation, and numerous communications in our two-year research collaboration. I would like to thank several fellow graduate students for their generous help and thoughtful advice, including Mr. Kwabena Asante, Dr. Nicot Jean- Philippe, Dr. Seann Reed, Dr. David Watkins and Dr. Zichuan Yeh. I?m particularly indebted in Dave for all his help both when he was in and after he left the university. I must also thank Dr. Randall Charbeneau (and then Dr. David Maidment) and the staff at the Center for Research in Water Resources for their generous support. The help provided by staff members in the Department of Civil Engineering was also appreciated, especially the computer support provided by Ms. Laurie Wood. Finally, I wish to thank my family for their love, devotion, and support throughout my studies. I particularly want to thank my wife for her patience and understanding during all these years. Financing for this research was provided, in part, by grants from the US Agency for International Development (USAID) through the Environmental Policy and Technology (EPT) project and the International Food Policy Research Institute (IFPRI). Ximing Cai Austin, Texas Jan 1999 vii A Modeling Framework for Sustainable Water Resources Management Publication No._____________ Ximing Cai, Ph.D. The University of Texas at Austin, 1999 Supervisor: Daene C. McKinney A prototype modeling framework for quantitative analysis of sustainable water resources management at the river basin scale is developed and applied to the Syr Darya River basin in Central Asia to analyze long-term water resource system sustainability. The research problem is specified as long-term, sustainable water resources management in river basins that are characterized by (semi)-arid climate, a heavy dependence on irrigated agriculture, and severe environmental degradation in the form of water and soil salinity. Sustainable water management is defined here as ensuring a long-term, stable and flexible water supply capacity to meet crop water demands, as well as growing municipal and industrial water demands, at the same time as keeping a stable relationship between irrigation practices and their associated environmental consequences. For this research, an innovative systems approach has been developed to model and analyze sustainability issues related to water resources management. viii The core of this modeling framework consists of an intra-year, short-term optimization model and an inter-year, long-term, dynamic model that combines simulation and optimization. In the intra-year model, essential hydrologic, agronomic, economic, and institutional relationships are integrated into a coherent analytical framework at the river basin scale to reflect the interdisciplinary nature of water resources problems. The inter-year model includes long-term changes and uncertainties in both water supply and demand, and incorporates prescribed sustainability principles for river basin system performance control. Relations between short-term irrigation practices and their long-term economic and environmental consequences are modeled and controlled in the inter-year modeling framework. The intra-year, or short-term, model is applied to the Syr Darya River basin to explore case-specific in-depth hydrologic-agronomic-economic- institutional relationships. This application shows the power of this type of integrated optimization model. Moreover, the application of the long-term modeling framework to the case study area shows the effectiveness of this tool for sustainability analysis in this region. Three approaches based on decomposition analysis and newly developed genetic algorithms for solving highly complex water resources management models that are large, nonconvex, and nonlinear are presented and applied. The short-term model, which is a large and nonlinear model, is solved by a ?piece-by- piece? approach based on model decomposition. A new genetic algorithm ? linear programming approach is used to solve the long-term model. Throughout the study, both the feasibility and the effectiveness of incorporating the philosophy of sustainability into traditional water resources management modeling are addressed. It is argued that system modeling techniques, if well supported by relevant empirical studies, and if sufficient data ix are available, can promote the understanding of sustainability in water resources research, a concept of utmost importance that will strongly influence future research in water resources management. x Table of Contents List of Tables .....................................................................................................xvii List of Figures ..................................................................................................xxiv Chapter 1. Introduction........................................................................................1 1.1 Motivation ................................................................................................1 1.2 Background and the Case Study Area...................................................... 3 1.2.1 Background .................................................................................. 3 1.2.2 Case study area............................................................................. 6 1.3 Objectives and Scope .............................................................................13 Chapter 2. Sustainability - A Systems Approach for Water Resources Management ...............................................................................................19 2.1 Introduction ............................................................................................ 19 2.2 Sustainability in Irrigation-Dominated Water Management.................. 25 2.2.1 Irrigation and crop production ................................................... 25 2.2.2 Irrigation and environment......................................................... 26 2.2.3 Sustainable water management for irrigation ? an operational definition .................................................................................... 28 2.2.4 Modeling sustainability ? interconnected relationships............. 30 2.3 Sustainability Criteria............................................................................. 31 2.3.1 Reliability, reversibility and vulnerability of water supply system......................................................................................... 32 2.3.2 Environmental system integrity ................................................. 34 2.3.3 Equity criteria............................................................................. 35 2.3.4 Socio-economic acceptability .................................................... 35 xi 2.4 A Systems Approach for Sustainability Modeling................................. 36 Chapter 3. Integrated Hydrologic-Agronomic-Economic-Institutional Modeling......................................................................................................40 3.1 Introduction ............................................................................................ 40 3.2 Background ............................................................................................ 41 3.2.1 Water resources management modeling at the river-basin level ............................................................................................ 41 3.2.2 Irrigation and drainage management: short-term and long- term models ................................................................................ 50 3.2.3 Crop production functions: yield - water use relationships ....... 53 3.2.4 Economics of water management............................................... 59 3.2.5 Integrated hydrologic -economic models................................... 62 3.3 Developing Models for Sustainability Analysis - Research Needs ....... 65 3.4 A Prototype Model................................................................................. 67 3.4.1 Introduction ............................................................................... 67 3.4.2 Institutional assumptions............................................................ 70 3.4.3 Hydrologic processes ................................................................. 70 3.4.3.1 Water and salinity balances in rivers, reservoirs and aquifers ................................................................................. 74 3.4.3.2 Water allocation within a demand site .............................. 76 3.4.3.3 Water available to crops.................................................... 78 3.4.3.4 Flow and salt balance in the root zone .............................. 79 3.4.3.5 Salt transport in irrigated areas ......................................... 84 3.4.3.6 Return flow........................................................................ 85 3.4.4 Agronomic relationships ............................................................ 86 3.4.4.1 Crop production as a function of soil moisture and soil salinity .................................................................................. 86 3.4.4.2 Critical crop stage.............................................................. 87 3.4.5 Economic incentives .................................................................. 88 xii 3.5 Summary ................................................................................................96 Chapter 4. The Model Applied for Short-Term Analysis .....................................97 4.1 Data and Assumptions for the Case Study............................................. 98 4.1.1 Hydrologic data and assumptions .............................................. 98 4.1.2 Agronomic data and assumptions ............................................ 106 4.1.3 Data and assumption about on-farm irrigation and drainage infrastructure ............................................................................ 108 4.1.4 Economic data and assumptions .............................................. 110 4.1.5 Data availability and reliability................................................ 113 4.2 Model Verification: Compare Model Results to Other Studies ........... 114 4.3 Analytical Issues of the Integrated Model ........................................... 119 4.3.1 Implications for hydrologic system operations ........................ 120 4.3.1.1 Sensitivity analysis on major hydrologic parameters...... 120 4.3.1.2 Reservoir operation ......................................................... 123 4.3.1.3 Basin-wide salinity distribution analysis ........................ 131 4.3.2 Irrigation and drainage management........................................ 136 4.3.2.1 Blending irrigation water supplies .................................. 137 4.3.2.2 Irrigation efficiency......................................................... 138 4.3.2.3 Water distribution and delivery efficiency...................... 139 4.3.2.4 Drainage reuse and disposal............................................ 140 4.3.2.5 Salt leaching .................................................................... 142 4.3.3 Agronomic analysis.................................................................. 143 4.3.4 Economic Analysis................................................................... 144 4.3.4.1 Economic values of water with crops ............................. 145 4.3.4.2 Economic values of water with demand sites ................. 147 4.3.4.3 Crop prices ...................................................................... 150 4.3.4.4 Water prices..................................................................... 151 4.3.4.5 Tax on excessive salt discharge ...................................... 153 xiii 4.3.4.6 Irrigation vs. hydropower generation.............................. 156 4.3.4.7 Economic efficiency of infrastructure investment .......... 158 4.3.4.8 Effect of municipal and industrial (M&I) water demand 160 4.3.5 Uncertainty Analysis................................................................ 160 4.3.5.1 Risk from hydrologic uncertainty-chance-constrained models ................................................................................ 161 4.3.5.2 Risk from other uncertainties .......................................... 165 4.4 Conclusions .......................................................................................... 165 Chapter 5. Solving Large-Scale NLP Water Resources Management Models .......................................................................................................168 5.1 Background .......................................................................................... 168 5.1.1 Nonlinear water resources management models...................... 168 5.1.2 Genetic algorithms ................................................................... 170 5.1.3 Decomposition techniques in water resources modeling ......... 173 5.2 A Gbd -Based Approach ...................................................................... 176 5.2.1 Generalized Benders Decomposition....................................... 177 5.2.2 GBD based approach for solving nonlinear nonconvex models ...................................................................................... 181 5.2.3 Implementation of the GBD based approach ........................... 185 5.2.4 An example: solving a river basin water allocation model ...... 186 5.2.4.1 Model formulation........................................................... 186 5.2.4.2 Computational results...................................................... 189 5.2.5 Summary .................................................................................. 194 5.3 A Combined GA&LP Approach .......................................................... 194 5.3.1 Introduction .............................................................................. 194 5.3.2 A reservoir operation model with hydropower generation ...... 197 5.3.3 Application of the GA-LP approach ........................................ 201 5.3.4 Results analysis ........................................................................ 204 5.3.5 Discussion and conclusion ....................................................... 212 xiv 5.4 The ?Piece by Piece? Approach........................................................... 213 5.4.1 Procedures of the ?piece-by-piece? approach .......................... 213 5.4.2 An example for the ?piece-by-piece? approach ....................... 218 5.4.3 Summary and discussion.......................................................... 223 5.5 Summary .............................................................................................. 224 Chapter 6. The Long-Term Dynamic Modeling Framework for Sustainability Analysis.............................................................................225 6.1 Long-Term Water Resources Management Modeling......................... 225 6.1.1 Time scales............................................................................... 225 6.1.2 Long-term changes and uncertainties....................................... 226 6.1.2.1 Changes and uncertainties in water supply ..................... 227 6.1.2.2 Changes and uncertainties in water demand ................... 229 6.1.3 Complexity - tradeoff between short-term and long-term objectives.................................................................................. 230 6.2 Quantification of Sustainability Criteria .............................................. 231 6.2.1 Quantification of risk criteria: reliability, reversibility, and vulnerability ............................................................................. 231 6.2.2 Quantification of environmental integrity criterion ................. 236 6.2.3 Quantification of equity criteria and socio-economic acceptability ............................................................................. 237 6.3 Composition of the Long-Term Dynamic Modeling Framework........ 240 6.3.1 The inter-year control program (IYCP) ................................... 241 6.3.2 The yearly model: decomposition and approximation............. 242 6.4 Implementation of the Long-Term dynamic Modeling Framework .... 246 6.4.1 Procedure for solving the yearly model ................................... 247 6.4.2 Implementation of the connection between the yearly models 250 6.4.3 Solving the long-term dynamic modeling................................ 251 6.5 Summary ..............................................................................................260 xv Chapter 7. Sustainability Analysis ? An Application of the Long-Term Dynamic Modeling Framework ..............................................................262 7.1 Introduction .......................................................................................... 262 7.2 Data and Assumptions.......................................................................... 263 7.2.1 Data and assumptions in water demand ................................... 264 7.2.2 Data and assumptions in water supply ..................................... 266 7.2.3 Other data and assumptions...................................................... 271 7.3 Effectiveness and Limitations of the Modeling Approach................... 271 7.3.1 Solving the yearly model.......................................................... 272 7.3.2 Searching long-term solutions.................................................. 278 7.4 The Baseline Scenario.......................................................................... 287 7.4.1 Implications of the inter-year controls ..................................... 289 7.4.1.1 Reservoir operation ......................................................... 289 7.4.1.2 Salt discharge control...................................................... 294 7.4.1.3 Crop pattern change ........................................................ 296 7.4.1.4 Water use facility improvement ...................................... 300 7.4.2 Water uses and long-term consequences.................................. 306 7.4.2.1 Soil salinity...................................................................... 306 7.4.2.2 Waterlogging................................................................... 308 7.4.2.3 Water quality reduction................................................... 309 7.4.2.4 Environmental and ecological water depletion ............... 311 7.4.2.5 Irrigated area reduction and decline in crop yield........... 311 7.4.3 Long-term modeling output vs. short-term modeling output... 314 7.4.3.1 Crop patterns ................................................................... 314 7.4.3.2 Irrigation profit................................................................ 315 7.4.3.3 Water and soil salinity..................................................... 316 7.4.3.4 Reservoir operation ......................................................... 316 7.4.3.5 Irrigation and drainage infrastructure.............................. 317 xvi 7.5 Scenario Analysis................................................................................. 318 7.5.1 What if the current status continues ......................................... 319 7.5.2 What if the irrigated area decreases or increases by various rates .......................................................................................... 323 7.5.3 What if the I&M water demand increases rapidly ................... 328 7.5.4 What if both the irrigated area and the I&M water demand increase rapidly ........................................................................ 329 7.5.5 What if the target of release to the Aral Sea is fully satisfied.. 334 7.5.6 What if the first priority is put on hydropower generation ...... 335 7.6 Sustainability Analysis......................................................................... 339 7.6.1 Water supply reliability............................................................ 339 7.6.2 Equity ....................................................................................... 343 7.6.3 Environmental integrity............................................................ 348 7.6.4 Socio?economic acceptability.................................................. 349 7.6.5 Tradeoff between multiple criteria........................................... 351 7.7 Summary ..............................................................................................353 Chapter 8. Summary and Conclusion .............................................................356 Appendix A : Deterministic Form of a Chance-Constrained Model with Nonlinear Constraints.............................................................................. 374 Appendix B : Note on the Genetic Algorithm Program ...............................376 Appendix C Generic Analysis of the Network-Based Water Allocation System........................................................................................................379 Appendix D Glossary ........................................................................................391 Bibliography ...................................................................................................... 401 xvii List of Tables Table 1. 1. Salinity in the Syr Darya River basin (source: EC, 1995). ................... 8 Table 1. 2. Change of percentage of irrigated land with various groundwater table from 1970 to 1989 (source: EC, 1995)................................... 10 Table 4. 1. Long-term average monthly inflow (km 3 ) to the Syr Darya River basin (Raskin, et al., 1992)............................................................... 99 Table 4. 2. Standard deviation (km 3 ) of the monthly inflow to the Syr Darya River basin...................................................................................... 100 Table 4. 3. Average monthly local sources (km 3 ) (Raskin, et al., 1992). ........... 101 Table 4. 4. Major water storage facilities of the Syr Darya basin....................... 101 Table 4. 5. Hydropower Station Data for the Syr Darya River Basin................. 102 Table 4. 6. Aquifer characteristics. ..................................................................... 103 Table 4. 7. Monthly average reference evapotranspiration (ET 0 , in mm) (EC, 1995). ..................................................................................... 103 Table 4. 8. Long-term monthly average precipitation (TR in mm) (World Bank, 1996). ................................................................................... 104 Table 4. 9. Standard deviation of monthly average precipitation (mm) (World Bank, 1996). ................................................................................... 104 Table 4. 10. Available irrigated area (1000 ha.) with soil types. ........................ 105 Table 4. 11. Soil characteristics. ......................................................................... 105 Table 4. 12. Crop coefficient of evapotranspiration (k c ). ................................... 107 xviii Table 4. 13. Empirical salinity coefficients, slope and threshold (Mass and Hoffman, 1979)............................................................. 107 Table 4. 14. Crop yield response coefficients (k y ). ............................................. 108 Table 4. 15. Maximum crop productions (YM, dry matter in ton/ha). ................ 108 Table 4. 16. Estimated Water distribution & delivery efficiency and drainage fraction (base value)....................................................................... 109 Table 4. 17. Estimated irrigation application efficiency (EIR, base value). ....... 109 Table 4. 18. Surface and groundwater supply cost (cs and cg in US$/m 3 ). ........ 110 Table 4. 19. Crop prices (pcp) and fixed crop planting cost (fc). ....................... 110 Table 4. 20. Annual investment necessary for improved water distribution system and drainage collection system. ......................................... 111 Table 4. 21. Annual investment (ainv_ir, US$/m 3 ) for improved on-farm irrigation systems. .......................................................................... 111 Table 4. 22. Monthly industrial and municipal water demands in 1987 (km 3 )... 113 Table 4. 23. Comparison of flow diversions from rivers and reservoirs (km 3 )... 115 Table 4. 24. Comparison of water diversion to demand sites (km 3 )................... 115 Table 4. 25. Annual salt discharge (million tons). .............................................. 116 Table 4. 26. Comparison of annual average salt concentration (g/l) in drainage ........................................................................................................ 116 Table 4. 27. Comparison of salt concentration (g/l) in the Syr Darya River. ..... 117 Table 4. 28. Comparison of irrigated area (1000 ha). ......................................... 117 Table 4. 29. Comparison of water use rate (m 3 /ha) for selected crops. .............. 117 Table 4. 30. Sensitivity analysis of inflow to the basin (relative values)............ 122 xix Table 4. 31. Sensitivity analysis of reference ET 0 (relative values).................... 122 Table 4. 32. Sensitivity analysis on effective rainfall (relative values). ............. 123 Table 4. 33. Ratios of sources to total irrigation water application (under a normal hydrologic level). ............................................................... 137 Table 4. 34. Annual average salt concentration (g/L) in different sources (under a normal hydrologic level).................................................. 138 Table 4. 35. Analysis on irrigation efficiency (EIR): Economic benefit. ........... 139 Table 4. 36. Analysis on irrigation efficiency (EIR): Environmental problem (result from demand site Fergana, soil type is loam). .................... 139 Table 4. 37. Analysis on water distribution and delivery efficiency (based on a ?dry? hydrologic level)................................................................... 140 Table 4. 38. Drainage reuse scenario analysis: Short-term benefit (based on a ?dry? hydrologic level)................................................................... 141 Table 4. 39. Drainage reuse scenario analysis: Environmental problems (based on a ?dry? hydrologic level)........................................................... 141 Table 4. 40. Analysis on salt leaching: Wheat - maize. ...................................... 142 Table 4. 41. Analysis on salt leaching: Cotton - forage. .................................... 142 Table 4. 42. Economic value of water with crops (V c , $/m 3 ) (in a normal year).145 Table 4. 43. Irrigated area (1000 ha.).................................................................. 146 Table 4. 44. Ratios of calculated irrigated area to total available irrigated area. 149 Table 4. 45. Irrigation profit vs. crop prices (relative values)............................. 151 Table 4. 46. Irrigated area allocation (fraction) vs. wheat-maize prices............. 151 xx Table 4. 47. Ratios of calculated irrigated area to total available irrigated area with various wheat-maize prices.................................................... 151 Table 4. 48. Economic values of water ($/m 3 ) with demand sites with various wheat-maize prices......................................................................... 151 Table 4. 49. Analysis on water supply prices...................................................... 152 Table 4. 50. Water values for crops and demand sites under various water supply prices................................................................................... 152 Table 4. 51. Water values for crops in each demand site with high water supply prices................................................................................... 153 Table 4. 52. Economic efficiency of investment for water distribution and delivery systems. ............................................................................ 158 Table 4. 53. Economic efficiency of investment for irrigation systems. ............ 159 Table 4. 54. Effect of M&I water demand. ......................................................... 160 Table 4. 55. Reducing slope with reliability in the chance-constrained model (after Mays and Tung, 1992).......................................................... 163 Table 4. 56. Water values (US$/m 3 ) for demand sites under hydrologic reliability scenarios. ....................................................................... 163 Table 4. 57. Water values (US$/m 3 ) for crops under hydrologic reliability scenarios......................................................................................... 164 Table 5. 1. Water resources management models with bilinear relations........... 169 Table 5. 2. Performance of GBD, MINOS, and CONOPT using 4 different initial points.................................................................................... 193 xxi Table 5. 3. Model statistics of the six models for the test of the GA-LP approach. ........................................................................................ 207 Table 5. 4. Parameters used in the genetic algorithm......................................... 207 Table 5. 5. Results from the GA-LP approach and the comparison with CONOPT2...................................................................................... 208 Table 5. 6. Comparison of convergence speed of models with various sizes and structures.................................................................................. 208 Table 5. 7. Statistics of models at different steps................................................ 222 Table 6. 1. Calculation of risk criteria................................................................. 235 Table 6. 2. Coefficients in the linearized power generation equations ............... 245 Table 7. 1. Projections of total irrigated area and industrial and municipal water demand in the Syrdarya River Basin.................................... 265 Table 7. 2. Hydrological fluctuations from 1988 -2020, after Raskin et al. (1992) ............................................................................................. 267 Table 7. 3. Ratios of monthly inflow in different hydrologic years to those in the normal year, after Raskin et. al (1992)..................................... 268 Table 7. 4. Ratios of monthly precipitation in different hydrologic years to those in a normal year. ................................................................... 269 Table 7. 5. Example for iterations in solving the yearly model: irrigated area reduction due to water shortage. .................................................... 274 Table 7. 6. Example for iterations in solving the yearly model: irrigated area reduction due to water shortage. .................................................... 274 xxii Table 7. 7. Example for iterations in solving the yearly model: irrigated area reduction due to salinity. ................................................................ 275 Table 7. 8. Selected items from year by year modeling output........................... 276 Table 7. 9. Comparison of the best and the worst individuals within one generation ? groundwater salinity (g/l) .......................................... 281 Table 7. 10. Comparison of the best and the worst individuals within one generation ? reservoir salinity (g/l)................................................ 281 Table 7. 11. Comparison of the best and the worst individuals within one generation ? soil salinity (dS/m) .................................................... 281 Table 7. 12. Comparison of the best individual in the first and the 30 th generation ? groundwater salinity (g/l) ......................................... 286 Table 7. 13. Comparison of the best individual in the first and the 30 th generation ? reservoir salinity (g/l)................................................ 286 Table 7. 14. Comparison of the best individual in the first and 30 th generation ? soil salinity (dS/m) ...................................................................... 286 Table 7. 15. Percentages of irrigated area under the short-term and long-term modeling......................................................................................... 316 Table 7. 16. Reservoir utilization efficiencies with the short-term and long- term modeling. ............................................................................... 317 Table 7. 17. Indices of water supply reliability under various scenarios............ 342 Table 7. 18. Indices of equity: statistics of increasing rate of water use benefit under various scenarios .................................................................. 346 xxiii Table 7. 19. Indices of environmental integrity: maximum salt concentration in surface and ground water. .......................................................... 348 Table 7. 20. Indices of environment integrity: crop area weighted average soil salinity at each demand site in the first year and in the last year... 349 Table 7. 21. Indices of socio-economic acceptability: benefits and investments over all study years......................................................................... 350 Table 7. 22. Comparison of alternatives for tradeoff analysis ............................ 352 Table A.b1. Components of the genetic algorithm applied in the GA-LP approach ......................................................................................... 377 xxiv List of Figures Figure 1. 1. The Aral Sea basin in Central Asia...................................................... 4 Figure 1. 2. Irrigated area (million ha) in the Aral Sea Basin and surface area (sq. km.) of the Aral Sea (after Micklin, 1993).................................. 4 Figure 1. 3. The Syr Darya River basin network .................................................... 8 Figure 1. 4. Salinity at selected points in the Syr Darya River from 1950 to 1990 (Source: EC, 1995).................................................................. 10 Figure 3. 1. Schematic representation of river basin processes (adapted Daza and Peralta, 1993)............................................................................. 43 Figure 3. 2. A framework for river basin management modeling........................ 45 Figure 3. 3. Schematic view of the complementary application of basin-scale models .............................................................................................. 48 Figure 3. 4. Representative crop yield ? salinity relations................................... 59 Figure 3. 5. Hierarchical structure of a multi-level irrigation management model................................................................................................ 69 Figure 3. 6. Diagram of water balances in multiple levels.................................... 77 Figure 3. 7. Diagram of water balance in root zones. ........................................... 81 Figure 3. 8. Crop yield vs. soil moisture under various soil salinity..................... 88 Figure 4. 1. Relative frequency function of the monthly inflow to the Toktogul Reservoir. ....................................................................................... 100 Figure 4. 2. Relative frequency function of the monthly precipitation at middle stream of the Syr Darya River basin. ............................................. 104 xxv Figure 4. 3. Actual ET vs. relative crop (wheat) yield (in demand site Mid_Syd, and the soil type is loam). .............................................. 119 Figure 4. 4. Reservoir utilization efficiency........................................................ 125 Figure 4. 5. Storage of the Toktogul Reservoir under the three operational cases. .............................................................................................. 126 Figure 4. 6. Storage of the Kayrakum Reservoir under the three operational cases. .............................................................................................. 126 Figure 4. 7. Storage of the Chardara Reservoir under three operational cases. .. 127 Figure 4. 8. Releases of the Toktogul Reservoirs under three operational cases. .............................................................................................. 127 Figure 4. 9. Releases of the Kayrakum Reservoirs under three operational cases. .............................................................................................. 128 Figure 4. 10. Releases of the Chardara Reservoirs under three operational cases. .............................................................................................. 128 Figure 4. 11. Salt concentration along the Syr Darya River (in a normal year).. 131 Figure 4. 12. Average monthly salt concentration in mixed water supply. ........ 133 Figure 4. 13. Average monthly salinity affecting coefficients (ks) (soil: loam; crop pattern: wheat-maize). ........................................ 133 Figure 4. 14. Soil salinity change through irrigation periods (demand site: Fergana, soil type: loam; crop field: cot_foa). ............................... 135 Figure 4. 15. Average monthly salt concentration in reservoirs. ........................ 135 Figure 4. 16. Actual ET vs. relative crop(wheat) yield (in Mid_Syd, the soil type is loam)................................................................................... 144 xxvi Figure 4. 17. Water values with crops................................................................. 147 Figure 4. 18. Economic values (V d ) with demand sites. ..................................... 149 Figure 4. 19. Total-benefit vs. tax on salt discharge. ......................................... 154 Figure 4. 20. Irrigation profit vs. tax on salt discharge....................................... 154 Figure 4. 21. Instream water use benefit vs. tax on salt discharge...................... 155 Figure 4. 22. Excessive discharged salt mass vs. tax on salt discharge. ............. 155 Figure 4. 23. Hydropower generation vs. power price........................................ 157 Figure 4. 24. Hydropower profit vs. Irrigation profit.......................................... 157 Figure 4. 25. Irrigation profit & socio-benefit vs. Hydrologic reliability........... 164 Figure 5. 1. GBD Lower bound (LBD) and upper bound (UBD)...................... 190 Figure 5. 2. Procedures of the GA-LP approach................................................. 196 Figure 5. 3. A hypothetical multi-reservoir system............................................. 197 Figure 5. 4. Variable representation in the genetic algorithm............................ 200 Figure 5. 5. Two individuals used to evaluate the similarity between individuals ...................................................................................... 203 Figure 5. 6. Objective value vs generations, model_1, with 1 reservoir, 12 time periods............................................................................... 209 Figure 5. 7. Objective value vs generations, model_2, with 1 reservoir, 24 time periods............................................................................... 209 Figure 5. 8. Objective value vs generations, model_3, with 2 reservoirs, 12 time periods.................................................................................... 210 Figure 5. 9. Objective value vs generations, model_4, with 2 reservoirs, 24 time periods.................................................................................... 210 xxvii Figure 5. 10. Objective value vs generations, model_5, with 5 reservoirs, 12 time periods.................................................................................... 211 Figure 5. 11. Objective value vs generations, model_5, with 5 reservoirs, 48 time periods.................................................................................... 211 Figure 5. 12. Comparison of reservoir release from the models at different steps................................................................................................ 222 Figure 6. 1. A simple structure of the long-term modeling framework .............. 240 Figure 6. 2. Decomposition and integration of the long-term modeling framework ...................................................................................... 244 Figure 6. 3. Procedure to solve the yearly model................................................ 249 Figure 6. 4. Genetic algorithm implementation of the inter-year control program .......................................................................................... 255 Figure 6. 5. Genetic algorithm implementation sketch of the inter-year control program .......................................................................................... 256 Figure 6. 6. Procedure for the long-term dynamic modeling.............................. 257 Figure 7. 1. Long-term objective value for all individuals within one generation (Generation 1)............................................................... 279 Figure 7. 2. Values of indices for multiple criteria of the ?best? and ?worst? individuals in one generation. ........................................................ 280 Figure 7. 3. Annual irrigation profit (IP) of the ?best? and ?worst? individuals in one generation (Generation 1).................................................... 280 Figure 7. 4. Comparison of the total long-term objective values of generation 1, 15, and 30. .................................................................................. 283 xxviii Figure 7. 5. Comparison of long-term objective resulting from different generations. .................................................................................... 284 Figure 7. 6. Comparison of outputs of multiple criteria resulted from different generations. .................................................................................... 284 Figure 7. 7. Index values of multiple criteria from gen. 1 and gen. 30............... 285 Figure 7. 8. Annual irrigation profit (IP) resulting from gen. 1 and gen. 30. ..... 285 Figure 7. 9. Objective values of the best individual in each of 60 generations under the baseline scenario. ........................................................... 288 Figure 7. 10. Objective values of all individuals in generation 60 under the baseline scenario. ........................................................................... 288 Figure 7. 11. Water sustained for future use (wsu). ............................................ 290 Figure 7. 12. Water sustained for future use (wsu) ? relative values. ................. 290 Figure 7. 13. Relative values of the end-year storage to the maximum storage for the major reservoirs. ................................................................. 292 Figure 7. 14. Relative values of the end-year storage to the maximum storage for the major reservoirs. ................................................................. 292 Figure 7. 15. Annual average reservoir utility efficiency. .................................. 293 Figure 7. 16. Annual average reservoir utility efficiency. .................................. 293 Figure 7. 17. Penalty tax on excessive salt discharge vs. years. ......................... 295 Figure 7. 18. Excessive salt discharge vs. years. ................................................ 295 Figure 7. 19. Crop patterns in different periods for demand site Naryn. ............ 297 Figure 7. 20. Crop patterns in different periods for demand site Low_syd......... 298 Figure 7. 21. Crop patterns in different periods for demand site Artur. ............. 298 xxix Figure 7. 22. Crop patterns in different periods for demand site Chakir. ........... 299 Figure 7. 23. Crop patterns in different periods for demand site Fergana. ........ 299 Figure 7. 24. Crop patterns in different periods for demand site Mid_syd. ........ 300 Figure 7. 25. Water distribution efficiency (EDS) at each demand site.............. 301 Figure 7. 26. Drainage efficiency (EDN) at each demand site............................ 301 Figure 7. 27. Irrigation efficiency (EIR) at each demand site - in crop field cotton-forage. ................................................................................. 302 Figure 7. 28. Irrigation efficiency (EIR) at each demand site - in crop field wheat-maize. .................................................................................. 303 Figure 7. 29. Irrigation efficiency (EIR) at each demand site - in crop field alfalfa-alfalfa. ................................................................................. 303 Figure 7. 30. Irrigation efficiency (EIR) at each demand site - in crop field other-other. ..................................................................................... 304 Figure 7. 31. Drainage reuse in each of the 30 years .......................................... 305 Figure 7. 32. Amount of drainage disposal at the demand sites where waterlogging may occur................................................................. 306 Figure 7. 33. Soil salinity in crop field cot_foa (cotton?forage) at selected demand sites. .................................................................................. 307 Figure 7. 34. Soil salinity in crop field wht_maz (wheat-maize) at selected demand sites. .................................................................................. 308 Figure 7. 35. Salt concentration in groundwater at each demand site................. 310 Figure 7. 36. Salt concentration in reservoirs on the main river......................... 310 Figure 7. 37. Planned inflow to the Aral Sea vs. calculated inflow.................... 311 xxx Figure 7. 38. Irrigation profit at each demand site.............................................. 312 Figure 7. 39. Irrigation profit at each demand site.............................................. 313 Figure 7. 40. Irrigation profit in the basin........................................................... 313 Figure 7. 41. Total agricultural profits under the baseline and zero scenario..... 320 Figure 7. 42. Ratios of agricultural profit under the zero scenario to that under the baseline scenario....................................................................... 321 Figure 7. 43. Inflow to the Aral Sea under the baseline and the zero scenario... 321 Figure 7. 44. Salt discharge to the river under the baseline and the zero scenario........................................................................................... 322 Figure 7. 45 Agricultural profits under the baseline and the irrigation scenario 324 Figure 7. 46. Inflow to the Aral Sea under the baseline and the irrigation scenario........................................................................................... 325 Figure 7. 47. Excessive salt discharge to the river system.................................. 326 Figure 7. 48. Salinity in the groundwater at demand site Low_syd under the baseline and the irrigation scenarios .............................................. 327 Figure 7. 49. Salinity in the soil (demand site: Low_syd, and crop field cotton- forage) under the baseline and the irrigation scenario................... 327 Figure 7. 50. Comparison of total agricultural profit and Aral Sea inflow: ratios of the I&M scenario to the baseline scenario....................... 329 Figure 7. 51. Comparison of total agricultural profit under the irrigation scenario and the high demand scenarios: ratios relative to the baseline scenario............................................................................ 330 xxxi Figure 7. 52. Comparison of inflow to the Aral Sea under the baseline, the irrigation, and the high demand scenarios: ratios relative to the inflow target. .................................................................................. 331 Figure 7. 53. Comparison of water and soil quality under the baseline, the irrigation, and the high demand scenarios ? excessive salt discharge......................................................................................... 332 Figure 7. 54. Comparison of water and soil quality under the baseline, the irrigation, and the high demand scenarios ? groundwater salinity at demand site Low_syd.................................................................. 332 Figure 7. 55. Comparison of water and soil quality under the baseline, the irrigation, and the high demand scenarios ? surface water salinity of the Kaykum Reservoir ................................................................ 333 Figure 7. 56. Comparison of water and soil quality under the baseline, the irrigation, and the high demand scenarios ? soil salinity in field cotton-forage at demand site Low_syd........................................... 333 Figure 7. 57. Total agricultural profit under the baseline and the flow release scenario........................................................................................... 334 Figure 7. 58. Agricultural profit (IP) under the hydropower scenario and the baseline scenario............................................................................ 336 Figure 7. 59. Hydropower in non-vegetation months (Oct.-Mar.) under the hydropower scenario and the baseline scenario............................ 337 Figure 7. 60. The Toktogul Reservoir utilization coefficient under under the hydropower scenario and the baseline scenario............................ 338 xxxii Figure 7. 61. The Kayrakum Reservoir utilization coefficient under under the hydropower scenario and the baseline scenario............................ 338 Figure 7. 62. The Chardara Reservoir utilization coefficient under under the hydropower scenario and the baseline scenario............................ 339 Figure 7. 63. Ratios of computed irrigated area to the planned irrigated area, and ratios of computed flow to the Aral Sea to the flow target, under the baseline scenario. ........................................................... 340 Figure 7. 64. Numbers of consecutive failure years for both irrigated area and flow release to the Aral Sea............................................................ 341 Figure 7. 65 (1,2) Changing rate of water use benefit at each demand site. ....... 344 Figure 7. 66. Changing rate of water use benefit, average value over all demand sites. .................................................................................. 345 Figure A.b1. A List of the job file for running the long-term model in the UNIX system.................................................................................. 378 Figure A.c1. A simple diagram of the river basin network for water allocation 380 1 Chapter 1 Introduction 1.1 MOTIVATION Water scarcity, water pollution and other water related environmental and ecological problems in many areas have brought a water crisis to the world. The future water crisis seems to be more serious than that at present. "The real crisis in water is a ?creeping crisis'- it comes on slowly but it demands a response right now" (Grigg, 1996). What kind of response should we have right now? This ques- tion needs to be answered with information on both current and future water de- mand and supply. The concepts of sustainable development, a popular concept in planning since the Brundtland Commission report (WCED, 1987), brings some hope for water researchers and policy makers. Sustainable development was de- fined as: Development that meets the needs of the present without compromising the ability of the future generations to meet their own needs. In light of this philosophy, sustainable water resources development has become an important topic in many national and international agencies such as the United Nations (UN), the World Bank, the American Society of Civil Engineers, etc. (detailed work of these agencies will be discussed in the background review). The definition of sustainable water resource systems is given by ASCE (1997) as: 2 Sustainable water resource systems are those designed and managed to fully contribute to the objectives of society, now and in the future, while maintain- ing their ecological, environmental and hydrological integrity. We have already received many guidelines for water resources manage- ment in light of sustainable development; unfortunately, we still do not know how to achieve this goal even though we know something about what to do. Biswas (1994) commented that: Operationally it (sustainable development) has not been possible to iden- tify a development process which can be planned and then implemented, and which would be inherently sustainable. In the water resources literature, there are many studies that argue the im- portance of sustainability for water resources development, and that describe principles needed to direct water resources management in view of sustainability. But only a few studies (e.g., Simonovic, 1996a, b) can provide a systematic ap- proach to incorporate sustainability principles in an analytic framework of water resources management. This is why Simonovic (1996a, b) suggested finding a way to put principles into practices. Often hydrologists and water resources engineers focus on the operation of hydrologic systems (reservoir systems or aquifers) without considering economic principles, which are essential to sustainable development. On the other hand, natural resource economists have made significant contributions to modeling of sustainable development, but their work generally ignores the physical complexity which affects decisions placed on any natural resource system. To develop an 3 analytical framework for sustainable water resources management, it is necessary to bring the work of hydrologists and economists together. The following comments given by The World Engineering partnership for Sustainable Development (WEPSD) may be appropriate to express the motivation of this research: Engineers need to translate the dreams of humanity, traditional knowledge, and the concepts of science into action through creative application of technology to achieve sustainable development. 1.2 BACKGROUND AND THE CASE STUDY AREA 1.2.1 Background The background of this research is a research project on water allocation and environment protection in the Aral Sea basin of Central Asia (McKinney, et al., 1997). The Aral Sea, a land-locked lake (i.e. without surface outflow), is lo- cated among the deserts of Central Asia (Figure 1.1). Its level is determined by the inflow of two feeding rivers, the Amudarya River and the Syr Darya River. In the1960?s, this inland lake was the world?s fourth largest such lake, but now it is dying due to intensive irrigation water withdrawal from the two rivers of the ba- sin. The average inflow from the Amudarya River and the Syr Darya River once was 72 and 37 km 3 per year, respectively, and now has decreased to a mere trickle. Compared to the status in 1960, the Sea is now half the size, 16 meters lower and three times as salty (Micklin, 1993). Figure 1.2 shows surface area of the Aral Sea over years, as well as the irrigated area in the basin. 4 Figure 1. 1. The Aral Sea basin in Central Asia. 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Years square kilometers 0 1 2 3 4 5 6 7 8 million hectares Figure 1. 2. Irrigated area (million ha) in the Aral Sea Basin and surface area (sq. km.) of the Aral Sea (after Micklin, 1993). Area of Aral Sea Irrigated area 5 The impacts of unsustainable water management in the Aral Sea basin ex- tend far beyond the fate of the Sea. Thirty-five million people have been losing access to the use of the lake for its water, fish, reed beds and transport, and more extensive environmental and ecological problems, such as dust storms, erosion, soil waterlogging and salinity, and poor water quality for drinking and other pur- poses, are endangering the human health and economy in this region. The Aral Sea disaster presents a very serious lesson for unsustainable water development. The huge hydrogeological changes which Soviet engineers have unwit- tingly triggered in the Aral Sea basin will take decades to reverse (Micklin, 1993). To stop the catastrophe, reduction in the use of irrigation water will be unavoid- able. However, more sadly, the Aral Sea basin countries have become dependent on a specialized, but unsustainable, pattern of agriculture, and the room for ma- neuver is limited. ?Any rapid reduction in the use of irrigation water will reduce living standards further unless these economies receive assistance to help them diversify away from irrigated agriculture? (World Bank, 1992). The price to completely reverse the catastrophe caused by unsustainable water development in the Aral Sea basin may be too high to be paid by the new independent developing states in Central Asia. The environmental and ecological problems in the Aral Sea basin have at- tracted attentions from all round the world, and financial aid for research on water resources management in this region have been provided by many interna- tional/national agencies including the U.S. Agency for International Development (USAID), the World Bank, and the European Union. Among the research work, USAID supported the Center for Research in Water Resources (CRWR) of The University of Texas at Austin, and the local partner, Tashkent Institute of Engi- neers of Irrigation and Mechanization of Agriculture (IEI) to develop a new com- puter modeling system for regional water allocation and salinity control (McKin- 6 ney et al.,1997). This system is a geographic information system (GIS) based de- cision support system (DSS), which includes two major models: multiple objec- tive optimization model for the Amudarya River basin water management (McKinney and Cai, 1996), and an optimization model for negotiation between upstream hydropower generation and downstream irrigation in the Syr Darya River basin (McKinney and Cai, 1997). These models were also extended to in- corporate irrigation management, agronomic production functions and economic incentives by researchers in CRWR and International Food Policy Research Insti- tute (IFPRI). The extended model was applied to the Maipo River basin in Chile (Rosegrant et al., 1999). All these works form a basis for this research, which fo- cuses on the development of a modeling framework for sustainable water re- sources management in irrigation-dominated regions like the Aral Sea basin. 1.2.2 Case study area The case study area of this research is the Syr Darya River basin. The Syr Darya River is one of the two major feeding rivers of the Aral Sea. The river be- gins at the Pamir and Tienshan plateaus, crosses the territories of several Central Asia republics, Kirgizstan, Tajikistan, Uzebekistan, and Kazakhstan, and termi- nates in the Aral Sea. About 70% of the flow is generated in the upper parts of the basin. In the middle and lower reaches, considerable anthropogenic influence is found in the forms of water diversions from the river and the discharges of return flows. The total water resource of the basin is assessed at 37.14 km 3 of natural runoff in a normal hydrologic year, plus 15 to 17 km 3 of return flow from irri- gated fields (EC, 1995, Vol. II). Groundwater is an integral part of the basin water resources. Installed pumping capacity is about 8.3 km 3 per year, which covers about 30% of the natural recharge (EC, 1995, Vol. II). 7 The water quality of the natural flows meets all typical international water quality standards, but it is seriously affected by anthropogenic activities. Agricul- tural drainage is the major factor affecting water quality in middle and lower sec- tions. The mineralisation is 0.2 - 0.7 g/l in the upstream area, 0.7 - 2.3 g/l in the midstream area, and 9.0 -10.0 g/l in the downstream area (EC, 1995, Vol. II). Raskin et al. (1992) estimated the water demand in the Syr Darya River basin in 1987 as 43.77 km 3 per year, which was dominated by the agriculture sec- tor, accounting for 82% of the total demand. The total irrigated area was 3.3 mil- lion hectares in 1987, and the major crops were cotton, wheat, maize and alfalfa; rice was also a major crop in the downstream area. The annual withdrawal of wa- ter in the basin was 57 km 3 in 1987 (Raskin et al., 1992). The flow to the Aral Sea has varied from 1.8 to 9.0 km 3 annually since 1990. The Syr Darya basin's water supply system is one of the most complicated human water development systems in the world. There are 9 major tributaries, 11 reservoirs, 6 major water distribution systems and numerous distributing canals. Figure 1.3 shows a modeling network of the Syr Darya River basin, which fol- lows the sketch of Raskin et al. (1992). Records show that just downstream of the Fergana Valley, a major irriga- tion district in the basin, the average salinity of the river water has increased to 1.2 g/l from a concentration of less than 0.5 g/l entering the valley (Raskin et al., 1992), illustrating that return flow has a considerable impact on water quality in the river. Salinity conditions vary significantly along the river from upstream to downstream, as shown in Table 1.1. 8 Table 1. 1. Salinity in the Syr Darya River basin (source: EC, 1995). Items Upstream Midstream Downstream Salinity of water supplied to irrigation (g/l) 0.56 0.89 1.16 Salinity of drainage disposed from irrigation (g/l) 2.10 3.00 3.40 Ratio of salinity of driange disposal to water supplied 3.7 3.4 2.9 Karadarya R Figure 1. 3. The Syr Darya River basin network In the last 30 years, with the increase of irrigated area, the river diversion for irrigation has increased and through the return of saline drainage water into the rivers, the salinity of the water in the rivers has increased. The effects are most pronounced in the downstream reaches of the river basin. Figure 1.4 plots salinity 9 at selected points in the Syr Darya River from 1950 to 1990. The stability and even improvement of water quality over the last 10 years at all points has resulted from improved water distribution and irrigation and drainage facilities. Soil salinity in the Syr Darya River basin has increased with irrigation practices too. Currently only 50% of the land in the basin is classified as non- saline. The soil salinity problem varies along the river just like river water salinity does. In the upper reaches, less than 10% of the land has moderate to strong salin- ity, while in downstream areas over 50% of the irrigated lands are classified as moderately to strongly saline. Salinisation is rapidly increasing in the midstream areas that are irrigated with water from the Srydarya river. For example, the per- centage of moderately to strongly saline lands in the midstream area increased from approximately 26% in 1970 to 54% in 1995 (EC, 1995). Intensive irrigation practices in the river basin have affected groundwater levels by recharging aquifers through deep percolation, as well as by pumping from aquifers. Table 1.2 shows the percentage of irrigated land with a number of water table ranges. During the period from 1970 to 1989, there was a relative de- crease in the proportion of land with water table shallower than 1 meter, but the percentage of irrigated land with water table less 2, and 5 meters has increased. The decrease shows the benefit of new drainage schemes installed during this time. However, the large relative increases in the proportion of land with water table between 2 and 5 still show a threat of waterlogging at some areas in the ba- sin. 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 50/55 55/60 60/65 65/70 70/75 75/80 80/85 85/90 Years Salinit y ( g /l) Naryn Kal Nadjinski Kazalinsk Figure 1. 4. Salinity at selected points in the Syr Darya River from 1950 to 1990 (Source: EC, 1995). Table 1. 2. Change of percentage of irrigated land with various groundwater table from 1970 to 1989 (source: EC, 1995). Depth of water table in meter Locations <1 1-2 2-3 3-5 Upper Reaches 00-610 Fergana -441888-59 Middle region 91163741 Chakir -62 16 -22 139 Artur 0 0 20 460 Lower reaches 0 -65 1180 2088 Average -78 1 40 67 11 Facing these environmental impacts, the questions to be studied for this basin include: (1) whether the environmental problems related to water manage- ment in the basin, including contamination of water in the lower reaches, soil deg- radation due to intoxication, salinization, erosion and compaction and climatic consequences from the desiccation of the Aral Sea, will worsen. (2) whether the current irrigation system will be deteriorated in the future due to consecutive droughts, waterlogging, and high salinity in irrigation water and soil salinity ac- cumulation. This is a serious question for people living in the basin, since a large portion of the national economies are derived from irrigated agriculture. Actually these two aspects, irrigation system and the environment in the basin are closely interconnected. More water withdrawal for irrigation will lead to less inflow to the Aral Sea, and probably, more salt and other pollutants being discharged to the river system, which will increase pollutant concentration in the river downstream, and finally this will affect irrigation water quality. Consdiering these two ques- tions together, we want to know whether such a high level of irrigated agriculture can be sustained while preventing or minimizing adverse environmental and eco- logical impacts. The answer to this question is at the heart of what sustainable wa- ter resources management means for the basin, and it presents an important re- search topic for life and development in the basin. After the collapse of the former Soviet Union, the management of the basin, which crosses four independent republics, has become an international is- sue, and it has attracted extensive attention around the world. Many research pro- jects, supported by both international and national funds, have been searching for solutions to this well-known environmental problem. About ten years ago, the first systematic study on water management in the Aral Sea region which has been reported in the non-Soviet literature, began in the Stockholm Environment Institute (Raskin, et al., 1992). A detailed water demand and supply simulation 12 was performed for 1987-2020 period, assuming that the current agricultural prac- tices continue. Water demand and supply were treated in an integral fashion using the Water Evaluation and Planning System (WEAP), a simulation modeling sys- tem. Water balance scenarios were studied considering alternative development patterns and supply dynamics. More recently, the Water Resources Management & Agricultural Pro- duction (WARMAP) in the Central Asian Republics, supported by the European Union Technical Assistance to Common Wealth of Independent States Program, was reported (EC, 1995). This project (Phase 1) includes a comprehensive land and water resources survey and an evaluation of irrigated crop production sys- tems, as well as legal and institutional aspects. Data reported in this project pro- vide a basis for analysis of land and water resources management strategies. The World Bank, cooperating with other international agencies like EU and UNDP, has been developing strategies for attaining a sustainable manage- ment and development of water resources with regard to environmental require- ments. Their work includes the development of management information systems, and economic-hydrologic modeling analysis (World Bank 1996). Unfortunately, even after five years, this effort is still in the planning and preparation phase and no concrete results have been reported. USAID has supported the Environmental Policy and Technology (EPT) Project (1994-1998) and the Environmental Policies and Institutions for Central Asia (EPIC) Program (1998-2001) Under these programs, a series of regional wa- ter, energy, and environmental management projects have been carried out, in- cluding the new modeling system developed in the Center for Research in Water Resources (CRWR) of the University of Texas of Austin, as described before, which has served as the basis for this research. 13 These projects, especially the WARMAP project, provide an adequate base of data for further water resources management studies in this region. The countries in the Syr Darya basin have expressed a great need for water policy analysis tools of the type to be developed in this research. In fact, an early version of the Syr Darya basin model has been developed and distributed to water and energy officials in the region (McKinney and Cai, 1997) and the current ver- sion of the short-term model described in Chapter 3 below has been adopted by the countries for planning purposes in the Syr Darya basin. Ongoing work will continue this development and dissemination of the results of this research. 1.3 OBJECTIVES AND SCOPE Sustainable water resources management entails a fundamental shift from looking to construction as a means for solving water needs to looking to improved management (non-structural) as a means for solving such problems. Structural solutions are often necessary, however, the traditional emphasis on structural so- lutions is more expensive and often can result in greater environmental damage than nonstructural solutions. Increased consideration of non-structural measures may lead to reduced financial pressure and environmental damage (Zilberman, 1998). The goal of a sustainable water resources management approach is to achieve substantive improvements in water use efficiency and preservation of the environment and ecology associated with the water use. This goal presupposes detailed information about current conditions of water supply, accurate and timely forecasts of meteorological events, how water is presently used, and what the needs of individual water users are. Through both qualitative and quantitative analysis, the management approach proposes (1) operational rules for storage and delivery system operations, as well as operations of terminal water use systems; (2) institutional directives and economic incentives that might encourage water 14 users to use water more efficiently; (3) mechanisms for supporting decision mak- ing, including ?what-if? scenario analysis and alternatives for evaluation; and (4) evaluation of the potential possibility, necessity and effectiveness of structural measures. The viewpoint of this research is formed by such a management approach that combines the structural solutions and the non-structural measures to achieve sustainability in real world practices. The modeling framework developed here is built on an integral river basin system with arid or semi-arid climates and irriga- tion-dominated water supply, and where salinity control is a major water quality and environmental problem. The integrated hydrologic-agronomic-economic- institutional modeling framework includes the following considerations: (1) inte- grated regulation among hydrologic systems, irrigation systems and environment systems; (2) representation of spatial externalities resulting from spatially distrib- uted water supply and demand; (3) representation of temporal externalities result- ing from intergenerational water allocation tradeoffs, and (4) consideration of un- certainty and risk on both water supply and demand sides. The major relationships in the modeling are hydrologic continuity, crop production as a function of both water application and water and soil salinity, and economic incentives for salinity control, water conservation and irrigation system improvement. The core of the modeling framework is an intra-year, short-term optimiza- tion model and an inter-year, long-term, dynamic control model. The short-term model is an extended irrigation management model, including essential hydro- logic, agronomic, economic and institutional relationships, and the inter-year con- trol model includes long-term changes and uncertainties, and incorporates pre- scribed sustainability principles for river basin system performance control. The intra-year model and the inter-year model are integrated into a long-term model- ing framework, so that the tradeoff between short-term and long-term benefits can 15 be analyzed based on sustainability principles. The short-term model is also run separately to study the in-depth hydrologic-agronomic-economic relationships. Three approaches based on decomposition techniques and genetic algo- rithms (GAs) respectively, are developed to solve the large complex models de- veloped in this research. Three approaches can be generally used for solving other complex models with appropriate conditions. The major questions answered through this research include: ? For a sufficiently complex case study, such as the Syr Darya River basin in Central Asia, what are the important inter-connections among water management, agricultural production and environment for sustainable wa- ter management? To what extent is policy making in each sphere (water management, agriculture, and environment) influenced by policy making in the others? ? What is an effective expression of sustainability for the specific study area? That is to say, do the quantified criteria of sustainability used in the modeling effectively reflect reliability in water supply, equity in water al- location, environmental preservation and economic efficiency in water use? ? What potential conflicts are likely to arise between agriculture and other competing water uses, including environmental uses, industrial and mu- nicipal uses? ? How can we achieve sustainability in water resources management, spe- cifically in river basins where irrigation water use dominates other uses and salinity is a potential problem? What implications for sustaining the water management system and the environmental system can be derived from the model results? More specifically, what kind of rules should be defined for hydrological system operations under various uncertainties? 16 What is the scope for applying water-conserving and water pollution pre- vention techniques and practices? How effective are economic incentives like penalty taxes on salt discharge? ? How can we solve the large, complex optimization models for sustainable water resources management under the currently available computer hardware and software capacity? This research develops a general methodology for sustainability modeling in irrigation-dominated river basins. The methodology is applied to the case study area, the Syr Darya River basin of Central Asia, based on the data available. The problems in the case study area are specifically analyzed, and suggestions are pre- sented based on modeling results. However, due to the limited data and time dur- ing this research, the solutions found in this research may not be taken as the prac- tical solutions for the basin before further verification. The rest of the dissertation is organized as follows: Chapter 2 presents principles and guidelines for sustainable water re- sources management, especially in irrigation dominated river basins with arid or semi-arid climate. A summary of previous research on sustainable water resources management is presented. Emphasis is put on what is an operation concept of sus- tainable development for water resources engineers, and why traditional models for various purposes in water resources management should be updated based on the principles of sustainability. Chapter 3 discusses basic components and structure of an integrated hy- drologic-agronomic-economic-institutional model at the river basin scale. The Chapter begins with a review of the background for integrated hydrologic- agronomic-economic-institutional modeling at the river basin scale, and then de- scribes the essential hydrologic, agronomic, and economic components and the inter-connections between these components. 17 Chapter 4 presents a short-term analysis based on the output from the short-term model applied to the case study area. This chapter demonstrates the performance of the complex, integrated hydrologic-agronomic-economic model by showing useful modeling output for sustainability analysis and decision- making. The outcomes of water uses under various scenarios are examined in terms of economic efficiency, equity, environmental impact, as well as the risk from hydrologic uncertainties. Since the model is applied for short-term analysis, and results also show why the short-term model is not efficient for sustainability analysis. Chapter 5 develops three approaches for solving difficult water resources management models that are large, nonlinear and nonconvex: (1) the GBD (Gen- eral Bender?s Decomposition) based approach that can be used to search ap- proximate global optimal solution for large nonconvex nonlinear models, (2) the GA-LP approach (genetic algorithm ? linear programming) that can be used to find approximate global solutions or feasible solutions for large models with high nonlinearity and nonconvexity, and (3) the ?piece-by-piece? approach that can be applied to solve large nonlinear models with multiple compartments. Each ap- proach is applied to an example that shows its effectiveness and limitations. Chapter 6 develops a long-term, dynamic modeling framework for sus- tainability analysis. The critical issue for this modeling is to trace and control long-term consequences resulting from short-term ?wait-and-see? actions, with predicted changes and uncertainties on both water demand and supply in the fu- ture. Sustainability criteria with respect to risk, equity, environmental impacts and social-economic acceptability are quantified and incorporated into the long-term modeling framework. The GA-LP approach is used to solve the long-term dy- namic modeling. 18 Chapter 7 applies the long-term model for sustainability analysis in water resources management. The issues of sustainability are discussed based on the long-term modeling results under various scenarios for the case study area. Through this analysis, we demonstrate the use of the analytical tool to evaluate sustainability with respect to the specific water management problems in the case study area, and also explore some policy implications for sustaining both the wa- ter resource and the environment of the basin. Chapter 8 presents summaries, conclusions and recommendations for fu- ture work. 19 Chapter 2 Sustainability - A Systems Approach for Water Resources Management 2.1INTRODUCTION For water resources management, sustainability implies a notion of equi- librium that simultaneously satisfies the needs of water uses and the preservation of the water resources system. The question of sustainable water resources man- agement then becomes: by what development strategies, management policies, or operational rules, can water uses still maintain long-term stable relationships with the water resources system and not deteriorate the recycling nature and potential sources of the system? On the other hand, facing uncertainties and fluctuations in the future, can the water resources system supply water with required quantity and quality at required times to satisfy various water demands? Sustainable water re- sources management should deal with these two inter-connected questions in an integrated framework. Based on some general concepts and principles of sustainability, this chap- ter focuses on the operational aspects of sustainable water resources management within a specific scope, and presents a systems approach for implementing sus- tainability analysis of water resources management in irrigation dominated river basins. We start this chapter by introducing the previous studies, which have fo- cused on two aspects: (1) what are the guidelines for water resources management in light of sustainability? And (2) what should we do according to the guidelines? Many guidelines for sustainable water resources management have been identified by various agencies. Bruce and Shrubsole (1994) presented "steward- 20 ship" for Canadian water management. Stewardship directs attention not only to the necessity to manage water to meet basic needs for a variety of interests, but also to ensure that water is protected and conserved, and its uses and values are sustained. Some activities were proposed to realize stewardship, which included maintaining ecological integrity and diversity, merging environment and econom- ics in decision making, building comprehensive water resources information sys- tems, and conducting public education. The World Bank (Serageldin, 1995) has adopted a new policy for water resources management that takes a comprehensive approach, emphasizing eco- nomic behavior, the overcoming of market and policy failures, more efficient use of water, and greater protection of the environment. This approach moves atten- tion away from the past approaches that tended to center on developing new sources of water - a "supply" focus, and puts emphasis on a "demand" focus, which implies so called "demand management". Demand management is an ap- proach that leads to water conservation, water protection and efficient use of wa- ter through pricing mechanisms, regulatory measures, and technology updating. To implement these objectives, the Bank, working actively with its partner coun- tries, has supported capacity building, promoted the creation of hydrologic, hy- drogeologic, water quality, and environmental data bases, and financed many waste treatment and water conservation projects. The United Nations Conference on the Environmental and Development (UNECD) in Rio de Janeiro in 1992 made a very impressive contribution to sus- tainable water resources management. In that conference, a number of countries came to a common perception that water should be taken as an integral part of the ecosystem, "a natural resource and social and economic good" (Chapter 18, Re- port of the UNCED, 1992). The major issues of water management were ad- dressed, including drinking water supply, water and urban development, water and food production, and impacts of climate changes on water resources. A com- 21 prehensive analytical framework was suggested and encouraged (1) to take into account interdependencies among sectors; (2) to create incentives for financial accountability and improved performance through greater use of pricing, and de- centralization of administration; (3) to realize consistent regulations and coordina- tion among agencies on different levels; (4) to use new technical measures in waste treatment, water recycling and polluted groundwater remediation; (5) to promote water use efficiency, optimal water allocation, extreme event (flood and drought) control; and (6) to build comprehensive data bases. Institutional weakness is thought to be one of the major obstacles to im- plementing sustainable water management. Therefore "capacity building", as an institutional activity for water management, has been encouraged (Alaerts et al., 1991). Three elements are involved in improving institutions: (1) creating an ena- bling environment with appropriate policy and legal frameworks; (2) institutional development, including community participation; and (3) human resources de- velopment and strengthening of managerial systems. Biswas (1996) argued that for effective capacity building, the first and the most essential requirement is hav- ing a good cadre of capable senior managers, and the appropriate institutions, policies or laws. More recently, the American Society of Civil Engineers (ASCE), associ- ated with United Nation?s International Hydrologic Program (UN/IHP), organized a special committee on sustainable water resources development and manage- ment. The committee conducted a comprehensive study of the definitions, guide- lines, applications, and research potentials of sustainability in water resources de- velopment and management, and published a monograph of their findings (ASCE and UN/IHP, 1998). The authors outlined some approaches for measuring and modeling sustainability and illustrated ways in which these measures and models might be used when evaluating alternative designs and operating policies. 22 Of all water use sectors, agriculture uses the largest amount of water in the world. Globally, 70 percent of freshwater diverted for human purposes goes to agriculture. On the other hand, low efficiency in agricultural water use causes more stress of water shortage, and non-point pollution carried in irrigation return flow often threatens the environment more seriously than other water uses. There- fore, sustainable water resources management in agriculture has been identified as very important by scientists and engineers. Very recently, the Organization for Economic Co-Operation and Development (OECD) hosted a workshop on issues and policies related to the sustainable management of water in agriculture (OCED, 1998). The workshop helped to illustrate what needs to be done to man- age water sustainably in agriculture, in particular through reviewing the experi- ence in OECD countries. The main conclusions include improving the transpar- ency of water management policies, taking into account environmental considera- tions and implementing economic incentives. As a summary, documents resulting from various national and interna- tional conferences, working grouping or committees have identified some broad guidelines and principles for sustainable water resources management. These guidelines may be briefly summarized as follows: Successful accomplishment of beneficial objectives This is the first and the most important principle for water resources man- agement. The successful services of water resources systems should meet multiple objectives in domestic and municipal water supply, economic development, and environmental maintenance. Adequate water quantity and quality should be con- sidered for various water demands. We should not only provide successful ser- vices for the current generation, but also leave options for the future generations. Minimization of negative impacts Potential negative impacts to health, environmental systems should be carefully studied in every step of water resources system planning, design and op- 23 eration. The long-term cumulative negative impacts should be forecast and be mitigated to the lowest possible level. Stability and flexibility Any system failure including system structural failure and operational er- ror should be controlled to the lowest possible frequency, in order to maintain sta- ble services. On the other hand, the system should be resilient enough to recover to normal status in case of system failure. Water resources systems should also be flexible enough to deal with various extreme events such as flooding, drought, excessive waste discharge, and other anticipated stochastic events. Realization of equity Water available in a basin may unevenly distribute. People in the upstream of a river may hold back too much water, or they discharge an excessive amount of pollutants into the river, which hinders people in the basin from sharing water rights. Both structural and non-structural measures should be implemented to make equitable water rights possible. Optimal system operations Under the physical constraints and policy limits, optimization of social, environmental and economical objectives should be sought through optimal sys- tem operations. Conjunctive use of surface and groundwater, and integral water quantity and quality management are often efficient methods for optimal system operations. Carefully planned structural measures like reservoirs may make up the integrity of the physical system, while non-structural measures through current facilities may bring additional benefit and avoid environmental damage. Financial feasibility and economic efficiency To increase water availability and maintain water quality, construction is often necessary. One problem is whether there is sufficient investment capital; another problem is that whether the investment is economically efficient. The in- 24 vestment limit and the requirement of economic efficiency form some external constraints to water resources planning and development. Another aspect of economic efficiency is related to water allocation. In some regions, water is limited, and appropriate strategies of water allocation among various water users are necessary to lead to high level of economic effi- ciency. Adaptation to new technology "... sustainable development is an effort to use technology to help clean up the mess it helped make, and engineers will be central players in its success or failures." (Prendergast, 1993). Engineers make new technology and apply it to solve problems in the real world so that better service can be provided, and greater economic efficiency can be achieved. New technology in water resources is expected to find more efficient methods of water conservation, sea water de- salination, greater water reuse and recycling, waste minimization, more compre- hensive economic/environmental assessments, and more effective operation of water resources systems. These principles and guidelines reflect some of the important aspects of sustainability in water resources management. There is no doubt that they would provide some assistance and guidance to those who are actually involved in plan- ning and decision making in specific regions. However, we still need to translate these broad guidelines into operational concepts that can be applied to the design- ing, operating and maintaining of water resources systems in specific regions. Another observation about these guidelines is that all of them mainly address the qualitative aspects of sustainable water resources management. How can we translate those qualitative descriptions into quantitative analysis that can provide more exact information for specific decisions in water management? An analyti- cal framework that combines water resource systems modeling with newly de- fined sustainability criteria is a meaningful research topic. 25 In this research, we examine sustainable water resources management spe- cifically for river basins like the Syr Darya, the study area introduced in Chapter 1. In those basins, the weather is arid or semi-arid, and water quantity is at a criti- cal level especially in dry years. Irrigation is currently the major water use, how- ever, instream and ecological water requirements are competing with irrigation water use, and the necessity for transferring water from irrigation to other off- stream water uses such as industrial and municipal water uses also emerges. Cur- rent irrigation practices already bring adverse environmental impacts such as wa- terlogging, soil salinization, and water quality reduction, which may finally de- stroy current irrigation effectiveness. For the study area, we translate the broad sustainability guidelines into op- erational concepts for water management. In the rest of this chapter, we first dis- cuss sustainability issues of water management in agriculture. Following that, we define some criteria that can be applied to measure sustainability in quantitative forms. Finally, a systems approach based on the concepts and principles of sus- tainability is described, which forms the backbone of this research. 2.2 SUSTAINABILITY IN IRRIGATION-DOMINATED WATER MANAGEMENT 2.2.1 Irrigation and crop production Over the last 30 years, irrigation has contributed a great deal to the in- creases in food production that have made it possible to feed the world?s growing population. There has been a continuos upward trend in the irrigated area for most countries, and the ratio of the irrigated to total cultivated area has also risen (Bon- nis and Steenblik, 1998). Clearly, irrigation has played a major role in boosting agricultural yields and output. However, because of high losses through evaporation and transpiration, ir- rigation uses the largest fraction of water in almost all countries, and globally, ir- rigation water demand is still increasing due to the expanding of irrigated area. In 26 some countries, the expansion of surface water use appears to be approaching the physical limits, and groundwater abstractions are increasingly exceeding rates of replenishment. Crop production has had a major impact on water uses. In many countries or regions, conflicts have already appeared in transferring irrigation wa- ter to other uses. 2.2.2 Irrigation and environment Although the achievements of irrigation in ensuring food security and im- proving rural welfare have been impressive, past experience also indicates prob- lems and failures of irrigated agriculture mostly related to environmental issues. Water depletion Water depletion is the most immediate effect of irrigation. Hydrological records over a long period (more than 50 years) have shown a marked reduction in the annual discharge on some of the world?s major rivers (OECD, 1998). Ex- cessive diversion of river water has brought environmental and ecological disas- ters in downstream areas, like the Aral Sea. Pumping groundwater at unsustain- able rates has contributed to the lowering of groundwater tables and to saltwater intrusion in some coastal areas. For example, excessive and inefficient irrigation has substantially reduced storage of the Ogallala Aquifer situated in the mid- western USA, and the water table has dropped more than 15m over 25 percent of the area since 1940 (ASCE, 1998). In arid or semi-arid geographic regions, depletion is more serious when ir- rigation is concentrated in a few months of the year when river water levels are low. Peak irrigation diversion usually exceeds naturally low water volumes, which leads to a deficit of minimum required flow for ecological uses. Water quality reduction Many water quality problems have also been created or aggravated by changes in stream flows associated with agriculture's consumptive uses. Generally 27 return flow and deep percolation from irrigated fields lead to concentrated pollut- ants such as pesticides and nutrients, and raise the average temperature of water bodies. Key water quality issues related to irrigation include eutrophication, con- tamination, turbidity, deoxygenation, acidification and salinisation. Waterlogging and salinisation Inappropriate irrigation practices, accompanied by inadequate drainage, have often damaged soils through over-saturation and salt build-up. In arid and semi-arid regions, less leaching water is often the main cause for soil salinity ac- cumulation. The United Nations Food and Agriculture Organization (FAO) esti- mates that over 20 million irrigated hectares are seriously affected, and that 60 to 80 million hectares are affected to varying degrees by water waterlogging and sa- linity (FAO, 1996). Threats to natural life systems Changes in flow rates and seasonal variations may lead to wetland loss and alter the biological cycles of aquatic and riparian plants and animals. Con- tamination of surface water from agricultural pollutant runoff causes death and deformities in fish and other life forms, and destroys possible sources of drinking water. Crop production depends on water and soil quality, as well as water quan- tity. For example, when the salt concentration in irrigation water, or soil salinity in the crop root zone, exceeds crop salinity tolerance thresholds, crop production is affected, and to a serious extent, crop growth will stop. Therefore, the environ- mental impacts resulting from inappropriate irrigation practices can deteriorate crop production. Certain effects of irrigation are indirectly beneficial to the environment. These include recharge of groundwater, regulation of runoff, and reuse of waste- water. However, today?s irrigation practices seem to impose more negative im- pacts on the environment as discussed above. 28 2.2.3 Sustainable water management for irrigation ? an operational defini- tion Now, people realize that irrigation, crop production and environment are parts of an integrated system. The purpose of irrigation is to increase crop produc- tion, however, its by-products may be environmental problems which reduce the quality of irrigation water sources, reduce the soil quality in the crop field, and may finally decrease crop production. Sustainable water management in irrigated agriculture has to employ appropriate irrigation practices that simultaneously sat- isfy the needs of crop water demands and environmental preservation, both now and in the future. Actually, humans have kept a stable relationship between these two conflicting aspects and formed the foundation of civilization for millennia. Only recently, over the last 30-50 years, the resonant relationship has been de- stroyed in some regions due to inappropriate irrigation practices such as excessive river and groundwater depletion, poor drainage, reuse of untreated field drainage, and use of polluted water from industrialization and urbanization. Further, some environment problems such as groundwater quality reduc- tion, and soil salinity accumulation have resulted from inappropriate, long-term irrigation practices. In some regions, these inappropriate practices may not impose immediate problems today, however, they may contribute to long-term environ- mental disasters, which will be suffered for generations. A two-part objective is defined for sustainable water resources manage- ment within the scope of this research. One is to sustain the environment includ- ing water and soil systems, and this part implies ?preservation? or ?conserva- tion?. The other aspect is to sustain crop production systems, on which people are assumed to depend. This is true in the Aral Sea basin since millions of people in the basin depend on irrigated agriculture for their economic livelihood, and desic- cation of the Aral Sea, due to the extensive irrigation system, has caused tremen- 29 dous social, environmental and economic impacts. This aspect implies ?develop- ment?. Protecting environment is critical to the ?preservation? side, and it is also important to the ?development? side, since environmental damage, such as pol- luted water and soil, diminishes opportunities for development of the crop produc- tion system. For the ?development? side, however, actions needed are more than ?defensive?. For planned crop water demands, is there sufficient and timely water supply? This question relates to water storage capacity (reservoirs, groundwater storage) facility, water delivery facilities (water distribution system), and field water application facilities (irrigation systems). Adequate capacity and efficiency of these facilities are necessary to maintain the development of irrigated agricul- ture. Another question is that under some extreme conditions like consecutive years of drought, how will water supply and crop production be affected? Sus- tainable water resources management requires a stable water supply with enough flexibility to deal with various extreme conditions. Based on the discussion above, we give a definition to sustainable water resources management, which is applied to the specific scope of this research: In river basins where irrigation is the major water use, sustainable water management should ensure a stable and flexible water supply capacity for crop water demands, and at the same time keep a stable relationship between irriga- tion practices and the associated environment. This definition raises questions about water supply and water demand, as well as management policy to achieve the two-side objective of sustainability. These questions require decisions such as: Decisions for water supply and water use: 30 ? Long-term reservoir and groundwater storage capacity and operations; ? Water distribution facility capacity and efficiency; ? Level of irrigation system (water use efficiency); ? Level of drainage system; ? Level of drainage disposal and treatment; and ? Level of drainage reuse. Decisions for water demands ? Irrigated area; ? Crop pattern; ? Water allocation among demand sites; ? Water allocation among crops; and ? Non-irrigation water supply for industrial, municipal, and ecological uses. Decisions on management policy ? Water prices; ? Tax on pollutant discharge; ? Water rights and water markets (water right exchange), and ? Management institutions. Based on the above definition, a modeling framework which includes both engineering and economic measures becomes both necessary and possible to inte- grate all these decisions, and search for sustainability through quantitative analy- sis. 2.2.4 Modeling sustainability ? interconnected relationships Within the scope of this research, modeling sustainability presupposes es- sential hydrologic, agronomic, economic and institutional relationships, and the integration of these relationships. Hydrologic flow and contaminant balance and distribution from crop field to river network, from short term to long term, pro- vides a physical basis to evaluate water availability and water quality conditions. Appropriate estimation of deep percolation, return flow and their contaminant concentrations, as well as groundwater levels, are essential to evaluate the envi- 31 ronmental impacts of irrigation. Long-term simulations of these processes are necessary to trace the dynamic consequences such as waterlogging, soil salinisa- tion, and groundwater water quality reduction. A crop production function that includes water and soil variables is an ap- propriate connection between water, soil quality and crop production. Based on this function, appropriate water supply capacity and soil quality to sustain the crop production can be determined. Economic relationships, i.e., water use benefits or profit and water pricing and taxing systems, provide incentives for making various decisions so as to achieve more efficient water development and use. An assessment of the envi- ronmental damage from the depletion of water over time is critical to evaluating the environmental impacts of irrigation. Institutional relationships present direc- tives aimed at achieving equity in water resources management. Modeling sustainability also presupposes a decision process that will in- clude decision-maker?s preference. Through modeling the integrated hydrologic, agronomic, economic and institutional relationships, we can compute the benefit of water uses and the environmental damage associated with them, and we can also compute the benefit and damage of both current and future water uses. Tradeoffs between benefit and damage, and between the current and the future should be considered in the modeling. How do we know the modeling outputs reflect sustainability or not? For this we need a measure of sustainability, which will be set up as the objective of the modeling. This is further elaborated through the sustainability criteria dis- cussed in the following. 2.3 SUSTAINABILITY CRITERIA Sustainable water resources management criteria reflect the principles and guidelines of sustainability. In this context, we assume that the objectives for 32 achieving sustainability are (1) water supply system reliability, reversibility and vulnerability; (2) environmental system integrity, (3) equity in water allocation and (4) socio-economic acceptability. Other objectives are possible and may be more appropriate in some situations. However, for the purposes of this research, this limited and quantifiable set has been selected. In this section, we review the definitions of these items, followed by a brief introduction to the current research. 2.3.1 Reliability, reversibility and vulnerability of water supply system Water supply systems, in a long-term view, are subject to substantial risk due to inherent stochastic variability and a fundamental lack of knowledge. Risk is identified as one of the key sustainability issues in water resources management (Simonovic, 1997). The traditional measures of system performance (mean value or variance of some variables) are insufficient to capture risk behavior, and addi- tional criteria must be used to quantify recurrence, duration, severity and other consequences of the non-satisfactory system performance. These criteria include reliability, reversibility and vulnerability (Kundzewicz and Kindler, 1995). Reliability represents the probability of a system success state, and it is a complimentary item to risk, which represents the frequency of system failure. The definitions of reliability used in water resources management include: ? Occurrence reliability, calculated as the ratio of the number of periods of sys- tem success to the number of periods of operation; ? Temporal reliability, determined as the ratio of time the system is in a success state to the total time of operation; and ? Volumetric reliability, often defined as the ratio of the volume of supplied wa- ter to the total demanded volume. Reversibility, also called resilience, is the probability of recovery of the system from failure to some acceptable state within a specified time interval. Fier- ing (1982) proposed several alternative indices of resilience, including the dura- 33 tion of the system's residence in the satisfactory state, steady state probability of the system being in the satisfactory state, and some other indices. Hashimoto et al. (1982a, b) developed a mathematical definition of resilience, suggesting that resil- ience could be a measure of the probability of being in a period of no failure in the current period when there was a failure in the last period. Moy et al. (1986) incorporated a formulation of resilience into mathematical programming for res- ervoir operation where resilience was measured as the maximum number of con- secutive periods of shortages that occur prior to recovery. Vulnerability represents the severity or magnitude of a system failure. Ha- shimoto et al. (1982a, b) developed a metric for overall system vulnerability as the expected maximum severity of a sojourn into the set of unsatisfactory states. Emphasis was placed on the maximum severity (how bad things are) for each un- satisfactory state, and the probability that the failure with the maximum severity would occur. Moy et al. (1986) defined a vulnerability criterion as the magnitude of the largest water supply deficit during the period of operation. Kundzewicz and Kindler (1995) used a reciprocal of vulnerability measured by the mean maximum deficit. Reliability, resilience and vulnerability of a system are not independent, and Moy et al. (1986), Hashimoto et al. (1982a, b), and Kundzewicz and Kindler (1995) considered tradeoffs among them. These criteria may be insufficient for non-stationary and uncertain conditions due to changing economic and social con- texts, and therefore, the appropriate treatment of the uncertain and the unknown is imperative (Kundzewicz and Kindler, 1995). In this research, in order to include these criteria in the measurement of sustainability, reliability, resilience and vulnerability are quantified with respect to water supply for irrigation and for environmental use. This is described in Chapter 6, Section 6.2.1 after we elaborate more details about this research. 34 2.3.2 Environmental system integrity As discussed in section 2.2.2, environmental impacts often put the sustain- ability of water resources systems at risk. A guiding criterion for sustainable wa- ter resources management is to make a water resource system interfere as little as possible with the integrity of the associated environmental system. To meet this criterion, we must at least ensure the following: (1) Sufficient water regimes to maintain and restore, if applicable, the health of aquatic and floodplain ecosystems; (2) No long-term irreversible or cumulative adverse effects on the envi- ronment and ecosystems; (3) Water quality that meets certain minimum standards that may vary over time and space; and (4) Integrated consideration of water quality and quantity when designing and operating water resource systems. To reflect the environmental system integrity in a modeling framework, first the environmental impacts, especially the long-term environmental conse- quences resulting from water uses, must be simulated and expressed in some quantitative forms, for example, salt concentration in groundwater, soil salinity in the crop field. Second, those environmental impacts need to be assessed in some forms that can be comparable with other criteria. One of the common direct forms is economic damage from environmental degradation, which, is often difficult to evaluate. Generally, indirect forms are used to calculate these effects, including normative forms related to water quality standards or institutional environment water supply quantum. The specific form of environmental system integrity for the purposes of this research is discussed in Chapter 6, Section 6.2.2. 35 2.3.3 Equity criteria Equity is one of the basic concepts within the primary definition of sus- tainable development (WCED, 1987). In view of equity, sustainable water re- sources systems must allow people, "now and then" and "here and there" to share the water use right (both benefit and cost) in such a way that no one should be disadvantaged or inadequately compensated (ASCE, 1998). Factors that affect either temporal equity or spatial equity in water resources development can be either anthropogenic or natural, or both. Temporal equity is associated with long- term cumulative consequences, which may lead to damages or even disasters in the future. One typical case related to spatial equity is the conflict between up- stream and downstream areas in a river basin. Conflict may arise when people in the upstream area want to use water during different periods than people in down- stream reaches. This is the case in the Syr Darya basin where upstream power generation demands in winter are in conflict with downstream irrigation demands in summer. Conflict may also arise when upstream users release excessive pollut- ants into the river, and downstream users suffer damage due to the poor water quality. This is the case in the Syr Darya basin, where return flows from the Fer- gana valley in Uzbekistan impact water quality downstream in Kazakstan. Since equity in water resources management involves complex natural, political and socio-economical factors, there is no general expression for this term. In this research we describe equity as an even distribution of beneficial wa- ter use related benefits in both spatial and temporal domains. Some statistical forms to represent both temporal and spatial distribution of water use benefit are described in Chapter 6, Section 6.2.3. 2.3.4 Socio-economic acceptability To determine the optimal scale of a sustainable economy, economists sug- gest the metric natural capital (Daly and Cobb, 1989), and the growth of the 36 economy should proceed to the point at which the marginal costs associated with natural capital depletion just equal the marginal benefits. In the field of water re- sources planning and management, we propose a similar concept called socio- economic acceptability. When the marginal cost associated with water resources development and management is greater than the marginal benefit, the water re- sources development activities lose their socio-economic acceptability, and the water resources system enters an unsustainable state at this point. An example would be the water resources management problem in the Aral Sea basin in Central Asia. The withdrawal of water for irrigation has created great profits for that region, but at the same time the environmental disaster due to excessive water withdrawal has caused huge damage. The environmental costs due to the excessive irrigation are so high that they go beyond the economic ca- pacity of the newly independent republics in Central Asia (World Bank, 1992). The marginal cost from the irrigation activities is much higher than the marginal benefit. This might be an economic explanation of the unsustainable state of water management in the basin. 2.4 A SYSTEMS APPROACH FOR SUSTAINABILITY MODELING For water resources management, the concept of sustainability needs to be addressed with an innovative systems approach. In this research we develop such an approach to model and analyze sustainability in irrigation-dominated river ba- sins. The major issues of this approach are described in the following. Multidisciplinary data requirement Modeling sustainability requires multidisciplinary data. Within the scope of this research, the modeling framework includes hydrologic, agronomic, eco- nomic and institutional relationships, and data related to each of these components are needed. For long-term modeling, required data include changes from year to year in both water demand and water supply. This research uses data from previ- 37 ous research projects, as well as data from related literatures. However, compre- hensive data collection and verification are beyond the scope of this research. Integrating hydrologic-agronomic-economic-institutional modeling at a river basin scale Representations of hydrologic processes at scales ranging from single reser- voir to multiple reservoir systems, from separate surface and groundwater systems to conjunctive systems, and from the soil profile to the cropped field, are impor- tant precursors to understanding and describing the mass balances at the river ba- sin scale. Sustainability needs an integrated basin system to reflect the integrality of the real world. It is at the basin level that hydrologic, agronomic and economic relationships can be integrated into a comprehensive modeling framework, and as a result, policy instruments designed to make more rational economic use of water resources are likely to be applied at this level. This research develops an inte- grated hydrologic-agronomic-economic-institutional model at the basin scale, which has the following characteristics: (1) representation of an integral river ba- sin network which includes the water supply system (surface and groundwater), the delivery system (canal network), the water users system (agricultural and non- agricultural), the drainage collection system (surface and subsurface drainage), and a waste water disposal and treatment system, as well as the connections be- tween these sub-systems; (2) representation of the spatial distribution of water flow and pollution, and water demand; (3) integrated water quantity and quality management, including flow and pollutant (salinity in this research) transport and mass balance, and regulation between required quantity and quality standards; and (4) integration of hydrologic, agronomic, economic and institutional relationships in an endogenous system that will adapt to environmental, ecological, and socio- economic status related to the river basin domain. 38 Connecting short-run and long-run models Short-term modeling and long-term modeling, apart from different time ho- rizons, have different purposes. Short-term modeling is used to calculate immedi- ate profits and operations, ignoring temporal externalities, while long-term model- ing is applied to search social benefits, considering both spatial and temporal ex- ternalities. For long-term modeling, two issues have to be taken into account: first, the conditions for future years can only be predicted with potential errors; and second, if something in the short-term is done inappropriately, then long-term benefits might be affected. Taking these factors into account, in a combined short- term and long-term model, the short-term decisions are directed by both short- term desires and long-term adjustments, and the long-term decisions try to reach a long-term optimality: satisfying the immediate demands and desires without com- promising those of future years, which reflects the spirit of sustainability. System performance control System performance control is based on the sustainable water resources management criteria described qualitatively in section 2.4 and described quantita- tively below. The risk criteria describe how often system failures occur, how long periods of unsatisfactory performance are likely to last and how severe a failure might be. Additional criteria for system performance are needed for control of negative environmental impacts, the consideration of equity, and socio-economic acceptability. These criteria are incorporated into the modeling so that system per- formance can be forecast, evaluated, analyzed and controlled based on these crite- ria. Combining sustainability criteria with water resources systems modeling is one of the major efforts of this research. 39 Solution techniques for large complex systems A complex system model is necessary for sustainability analysis. In this re- search, a basin-wide model that integrates hydrologic, agronomic, economic and institutional components is applied for long-term sustainability analysis. Such large-scale complex modeling can not be solved by currently available algorithms and computing capacity. New algorithms are developed in this research to solve the complex large-scale system modeling. 40 Chapter 3 Integrated Hydrologic-Agronomic-Economic-Institutional Modeling 3.1 INTRODUCTION Integrated water resources management arises as a new direction in sustain- able water resources management. The interdisciplinary nature of water resources problems requires new attitudes towards integrating the technical, economic, en- vironmental, social and legal aspects into a coherent analytical framework. Water resources development and management should incorporate environmental, eco- nomic and social considerations based on the principles of sustainability. They should include the requirements of all users as well as those relating to the pre- vention and mitigation of water-related hazards, and constitute an integral part of the socio-economic development planning process (Booker and Young, 1994). Comprehensive discussions of this topic are provided in UNECD (1992) and Serageldin (1994) and these issues have been reviewed in Chapter 2. To bring the concept of integrated water resources management into an ana- lytical framework, modeling techniques for integrating hydrologic, agronomic, economic and institutional components were studied and found to present oppor- tunities for the advance of water resources management in this new direction. In this chapter we first review the related background for the integrated hydrologic- agronomic-economic-institutional modeling, and then describe the basic compo- nents and structure of a prototype model that is able to provide capability for de- termining rational and effective water management strategies at river basin scales. 41 3.2 BACKGROUND Modeling methodologies in water resources management are reviewed in this section in order to find implications for modeling sustainability at the river basin scale. We focus on water management in irrigation-dominated river basins. Irrigation and drainage management is reviewed as part of integrated river basin modeling; empirical crop productions (crop yield vs. water use) are shown to pro- vide a critical linkage between hydrologic, agronomic, and economic compo- nents; the economics of water management are illustrated as incentives for effec- tive water use and salinity control in river basins where salinity presents a serious problem. Finally, with these basic approaches, previous integrated models are discussed, and the general modeling methodologies are addressed. 3.2.1 Water resources management modeling at the river-basin level A river basin is a natural unit for water resources planning and manage- ment, in which water interacts with and to a large degree controls the extent of other natural components in the landscape such as soils, vegetation and wildlife. Human activities, too, so dependent on water availability, might best be organized and coordinated within the river basin unit. Thus, water planners often utilize the river basin as the basic planning area. A river basin system is made up of three components (1) source components such as rivers, canals, reservoirs, and aqui- fers; (2) demand components such as irrigation fields, industrial plants, and cities; and (3) intermediate components such as treatment plants and water reuse and re- cycling facilities. Figure 3.1 shows a schematic diagram of the components of a river basin system, which includes the water supply system (ground and surface water), the delivery system (canal network), the water use system (agricultural, municipal, and industrial), and the drainage collection system (surface and subsur- face). The atmosphere forms the river basin?s upper bound, and mass and energy 42 exchange through this boundary determines the hydrologic characteristics within the basin. However, the state of the basin (for example reservoir and aquifer stor- age, and water quality), and the physical processes within the basin (for example stream flow, evapotranspiration, infiltration and percolation), are also character- ized by human actions, including impoundment, diversion, irrigation, drainage, and discharges from urban areas. Therefore, water resources management model- ing of a river basin system should not only include natural and physical processes, but it must also include artificial ?hardware? (physical projects) and ?soft- ware?(management policies). The essential relations within each component and the interrelations between these components in the river basin can be considered in an integrated modeling framework. As an example, Figure 3.2 presents a framework for river basin manage- ment modeling, including relationships and decision items at various levels. Wa- ter can be used for instream purposes including hydropower generation, recrea- tion, waste dilution, as well as offstream purposes that are differentiated into agri cultural water uses and municipal and industrial (M&I) water uses. Socio- benefits of the river basin area are an important component of a water manage- ment strategy of the basin. These include the positive contribution from the eco- nomic value of municipal and industrial (M&I) water use, profit from irrigation water use, and benefits from instream water uses, as well as environmental dam- age due to such things as M&I waste discharge and irrigation drainage. The top control for the system is assumed to be the institutional directives like water rights, and economic incentives such as water price, crop price, and any penalty tax on waste discharge and irrigation drainage. The institutional directives and economic incentives constrain or induce hydrologic system operations and deci- sions within both M&I demand sites and agricultural demand sites. Water uses are 43 Industrial & municipal demand sites Consumptive use seepage Groundwater system River reaches & reservoirs instream uses : hydropower, recreation, and dilution Distribution system diversion offstream uses Groundwater pumping groundwater Agricultural demand sites surface water groundwater Drainage collection system return flow spillage loss seepage precipitation drainage deep percolation percolation return flow drainage disposal/ treatment drainage reuse outflow aquifer-river inter-flow evapotranspiration & other comsumptive use precipitation Downstream economic and environmental requirements Precipitation Other sources Runoff inflow Treatment surface waterindustry tail water Figure 3. 1. Schematic representation of river basin processes (adapted Daza and Peralta, 1993) 44 competitive among various water users, under prescribed institutional rules and economic incentives. The hydrologic system interacts with M&I water use system, irrigation and drainage system, and instream water use systems. The operation of hydro- logic system is driven by these water use systems and on the other hand, the water use systems are constrained by the hydrologic system. Combined Optimization and Simulation Models Of particular importance to basin-scale analyses are models of two funda- mental types: simulation models which simulate water resources behavior in ac- cordance with a set of rules (actual or hypothetical) governing water allocations and infrastructure operations, and optimization models which optimize allocations based on an objective function (economic or other) and accompanying con- straints. McKinney et al (1999) provided a comprehensive review of the simula- tion, optimization, and combined simulation-optimization models applied to inte- grated river basin management. Figure 3.3 presents a schematic view of the com- plementary application of basin-scale simulation and optimization models. Whereas the assessment of system performance can be best addressed with simu- lation models, optimization models serve best if improvement of the system out- comes is the main goal. Hydrologic interactions among principal water sources and their uses are often described in less detail than they would in models of the separate entities in order to capture the broader resource dynamics. 45 River Basin: flow and salt balance and transport Decisions on: ? Reservoir releases ? Groundwater pumping ? Withdrawal from river reaches/reservoirs ? Downstream flow requirement Irrigation Demand Sites : water-soil-plant relationships, crop production functions Decisions on: ?Distribution efficiency ?Drainage efficiency ?Drainage disposal/treatment ?Irrigation systems ?Drainage reuse and source blending ?Crop acreage and crop pattern Damage from irrigation drainage Instream uses: physical, environmental and institutional relations and constraints ?power generation ?ecological use ?recreation ?waste dilution Municipal &Industrial Demand Sites: socioeconomic relations between: ?population change ?industrial development ?technological change ( recycling, water treatment, etc.) ?rules and regulations Economic value from M&I water use Profit from irrigation Damage from M&I waste discharge Benefit from instream uses Institutional directives and economic incentives Socio -economic benefits Damage from power generation Figure 3. 2. A framework for river basin management modeling 46 Simulation and optimization models of river basin-scale water resource systems are complementary research tools to address problems related to the competition over water resources as well as to the design and assessment of alter- native systems of water allocation. Models can often simultaneously include simulation and optimization capabilities. Applied optimization models must be able to characterize the hydrologic regime in order to calculate the objective func- tion. Optimal water allocation must also be feasible, at a minimum from an infra- structure operations perspective, for policymakers and system managers to con- sider their adoption. In the following, several models that integrate simulation and economic optimization capabilities with the goal of policy analysis and rec- ommendations are reviewed. Louie et al. (1984) used a multi-objective simulation/optimization proce- dure to study unified basin-wide water resources management. Three major is- sues are simultaneously considered in the procedure: (1) water supply allocation; (2) water quality control; and (3) prevention of undesirable overdraft of ground- water. The optimization procedure is implemented by interactively solving sev- eral optimization and simulation models. Three optimization models, each corre- sponding to one of the three major simulation models, are solved separately. The optimization model for water quality control is solved combined with a ground- water quantity-and-quality model or a river flow-and-mass transport model through the influence coefficient method (Becker and Yeh, 1972). After the three optimization models are solved, payoff tables are created, and the original multi- ple objective problem is converted into a constrained problem involving the three objectives. Finally the multiobjective optimization problem is solved for non- inferior solutions. This procedure was applied to a small test problem. Labadie et al. (1994) extend MODSIM, a widely used simulation language for river basin network flow modeling to incorporate constraints on water quality 47 loading and concentrations. The new model, MODSIMQ directly includes water quality regulations as constraints. The assessment of risks and uncertainties asso- ciated with water quality predictions and projections is included through an inter- active linkage with the QUAL2E streamflow water quality model of the United States Environmental Protection Agency. QUAL2E is used to update water qual- ity coefficients in MODSIMQ, and MODSIMQ calculates both network flows and concentrations, which are then fed into QUAL2E for further simulation. This approach is similar to that of Dandy and Crawley (1992) but removes some of the limitations in that work. More recently, Lee and Howitt (1996) modeled water and salt balances in the Colorado River basin to determine salinity levels which maximize net returns to agricultural and municipal & industrial (M&I) water users at selected locations in the basin. Nonlinear crop production functions and M&I costs per unit of sa- linity are derived for inclusion in the objective function, which was solved using the GAMS/MINOS software. Three scenarios are considered: (a) economic op- timality; (b) no change in cropping patterns with subsidies for salinity control measures; and (c) cropping changes with subsidies to maintain agricultural prof- its. The first-best, economically optimal scenario indicates major declines in cropped area with significant returns to M&I uses. Of the two scenarios with sub- sidies, the cropping changes subsidized to maintain profits indicate marginally lower total subsidies with a minor, but significant reduction in salinity. The au- thors note that optimal solutions were modeled without consideration of transac- tion costs or equity criteria. 48 Develop Simulation Model Develop Optimization Model Define Problem Assemble Data Establish Flow Network Assess system performance or improve system outcomes? Apply Model Results Assess Performance Improve Outcome Figure 3. 3. Schematic view of the complementary application of basin-scale models (After McKinney et al., 1999). 49 A final example of integrated simulation-optimization modeling of water resource systems involves groundwater usage (Faisal et al., 1994). Faisal et al characterize the hydrologic flow regime using a linear response matrix, which al- lows the superposition of the effects of pumping at different aquifer locations on the particular location where drawdown is to be controlled. The location-to- location drawdown functions, however, are derived using the popular MOD- FLOW three-dimensional finite-difference groundwater model developed by the United States Geological Survey. The conjugate gradient method applied to solve the optimization of the nonlinear objective function produces results that are iden- tical with a GAMS/MINOS solution. Two scenarios are modeled: (a) the social optimum for the basin, and (b) the common pool problem consisting of self- interested farmers. While discounted net benefits for the two scenarios are not markedly different, the common pool results in significantly reduced aquifer lev- els. Decision Support Systems Decision support systems are proactive tools for sustainable river basin planning and management, which provide interactive, graphics-based users inter- faces, comprehensive data management techniques, complex modeling capabili- ties, and flexible strategy analysis functions. In the following, a few recent exam- ples are discussed to show the application of DSSs in integrated water manage- ment at the river basin scale. Fedra and Jamieson (1996) reported an on-going comprehensive decision- support system (DSS) for river basin planning, the 'WaterWare'. The analytical components comprise a geographic information system(GIS), geo-referenced da- tabase, groundwater pollution control, surface-water pollution control, hydrologi- cal processes, demand forecasting and water-resources planning. All these com- 50 ponents were integrated into a common executive environment and an analytical framework. Other similar DSSs include the Tennessee Valley Authority's Envi- ronment and Water Resource Aid (TERRA) (Reitsma et al., 1994), the Interactive Mass-Balance Simulator of River-Aquifer Systems (IRAS) (Loucks et al., 1994), and RAISON (Lam and Swayne, 1990). In Europe, a major five-year program was initiated in 1992 to develop a sophisticated decision support system for inte- grated river basin management. The purpose for this DSS is to assist managers in coping with the complexities of multi-objective sustainable planning within im- posed environmental, public acceptance and legal and administrative constraints (ASCE, 1998). 3.2.2 Irrigation and drainage management: short-term and long-term models Due to the increasing water scarcity and worsening salinity condition, greater attention has been given to integrated water quantity and quality manage- ment in irrigated agriculture. Inappropriate irrigation is often responsible for highly saline drainage returning to surface river systems and groundwater sys- tems, and for long-term salt accumulation in soil (Hanks and Anderson, 1979). The physical basis for integrated water quantity and quality management includes the dynamics of soil moisture and salt movement in the root zone, which is generally described by the Richard?s Equation. Apart from some detailed simu- lation models, e.g., DRAINMOD (Skaggs, 1980) and WATRCOM (Parsons et al., 1990). These physical relations, combined with management strategies and eco- nomic incentives have been extensively studied since 1970's. A distinction can be made among the models in terms of the range of time that they cover: short-term models, long-term models, and extended long-term models (Yaron et al, 1980). Short-term models 51 A short-term model is confined to one year or a single irrigation season. The model deals with the initial salinity of the soil profile; it analyzes the optimal combination of water quality and quantity for each initial state but does not take into account the effects of accumulation of salt over time. For example, Bresler and Yaron's (1972) model is a short-run model developed to obtain the optimal quantity-quality combination of irrigation water in a single irrigation season via linear programming. Yaron et al. (1980) presented a dynamic programming model for scheduling of irrigation with soil salinity parameters explicitly considered. Two discrete state variables, soil moisture and salinity level of the soil were used to characterize the modeling system. Gini (1984) developed a short-run model which simulates the dynamics of water allocation and salt movement in a two- layered soil column. Nonlinear differential equations performing water and salt balance in the unsaturated and saturated zones were included in the model. The critical salinity approach (Mass and Hoffman, 1977) was used to estimate yield reduction from excessiveive salinity in the root zone. Long-term models A long-run model accounts for the effects of salt accumulation in the soil profile over time. The model comprises a succession of short-run processes, the initial conditions of which are affected by salt accumulation in previous periods. The irrigation decision over a single season takes into account the resulting termi- nal conditions and the effects on succeeding periods. Yaron and Olian (1973) studied a long-run model for the analysis of a winter leaching policy on a peren- nial crop in a Mediterranean climate. In their model a stage was defined as a year consisting of a rainy season (winter) and a dry season (summer). The state vari- able was the mean chloride concentration in the soil profile at the end of a rainy season, and the decision variable was the quantity of water used to leach the soil profile at the end of a rainy season. Matanga and Marino (1979) modified this 52 model taking into account seasonal irrigation depth as another decision variable; they also extended this model from considering a single crop to multiple, and then optimal area-allocation among crops was considered. Bras and Seo (1987) devel- oped a conceptual model to describe the dynamics of water allocation and salt movement in the root zone of a crop. Moisture stress and osmotic stress were combined to obtain the integrated inhibitory effect of salinity on transpiration. The long-term prevention of salt accumulation was handled via probabilistic state constraints with impose desired salinity and moisture levels with a particular con- fidence level. Bresler et al. (1983) considered soil variability and uncertainty via stochastic modeling in a long-run mixed integer linear programming model. In their study, soil properties were regarded as random variables that were character- ized by their probability density function. Extended long-term models There has been considerable interest in evaluating long-term trends of groundwater quality within irrigated stream-aquifer systems by studying the rela- tionship between agricultural practices and water quality variations in the irrigated stream-aquifer systems. The extended long-term models, which take in account both salt accumulation into the soil profile and its accumulation in the under- ground water reservoirs, have been developed for this purpose. These models in- clude soil water flow and solute transport, groundwater flow and solute transport, stream aquifer interflow, water use decisions, and agronomic relationships be- tween crop production and the depth of applied irrigation water. Latif and James (1991) presented a conjunctive-use model used to maxi- mize a water user?s return under limited and dynamic water supply for long-term considerations. Salt distribution and transport in the crop root zone were modeled using the physical soil properties and mass balance, and a daily crop water stress index was used to quantify crop yield reduction due to water stress over the grow- 53 ing stages. The model was used to explore optimal groundwater extraction corre- sponding to the agronomic behavior. Daza and Peralta (1993) developed a conjunctive water management model for an irrigated area. The model utilized a transient multilayer groundwater hydraulic simulation/ optimization model, incorporating the irrigation technology explicitly. Irrigation inflow was taken as a decision variable, and deep percolation and runoff losses from irrigation were state variables. Similar studies include Peralta et al, (1988), Lefkoff and Gorelick, (1990a), Peralta et al. (1990), and Musharrafieh et al. (1995), all of which applied simulation/optimization models to determine an optimal irrigation strategy that would maximize crop yield while preventing groundwater contamination. Finally, an example of integrated short-term and long-term model was de- veloped by Feinerman and Yaron (1983) who used a linear programming model, deterministic in the short run and stochastic (random rainfall) in the long run. The short-run model, limited to a single year, incorporated the physical, biological, and economic relationships involved in one endogenous system. The long-run model considered the effects of short-run decisions on the stream of future profits and rainfall uncertainty, with several relationships incorporated exogenously. These relationships, including irrigation water mixing, soil salinity ranges, crop yields, and net profits, were pre-determined based on the short-run model?s re- sults. The hydrologic aspects were meaningful but highly simplified in this study. This study was limited to a single farm, and no externalities were considered. 3.2.3 Crop production functions: yield - water use relationships Existing modeling approaches to crop-water relationships (for example, surveys by Hanks (1983) and Vaux and Pruitt (1983) address economic, engineer- ing, and biological aspects of the production process. These surveys conclude that crop-water relationships are very complicated and that not all management 54 issues have been fully addressed in one comprehensive model. An ideal crop- water production model should allow the assessment of policy-related problems, and results should be transferable between locations. In addition, the model should be simple to operate, requiring a small data set; easily adjustable to various farming conditions; and sufficiently comprehensive to allow the estimation of ex- ternality effects. In addition, the interaction between water quantity and quality and the water input/production output should be clearly defined (Dinar and Letey 1996). Four broad approaches to production functions can be identified, evapo- transpiration models, simulation models, estimated models, and hybrid models (McKinney, et al., 1999). Among these model types, the simulation models either simulate in detail the production process of one crop, or focus on one production input or the subsystems associated with a particular production input, and the hy- brid models combine aspects of the other three types. In the following we do not go further with the simulation models and the hybrid models, but focus on the empirical evapotranspiration models and estimated models that are more related to this research. Evapotranspiration Models Evapotranspiration models predict the relationship between crop yield and crop evapotranspiration under varying conditions of salinity levels, soil moisture conditions, and irrigation strategies. De Wit (1958) found a linear relationship be- tween dry matter yield and cumulative transpiration by the crop. Hanks (1974) improved this relationship and derived the following crop yield function: st st TPM TP YMYA st ? ? ? ? ? ? = (3-1) where YA = actual yield 55 YM = maximum yield, TP = cumulative transpiration by the crop, and TPM = potential value of TP. and st represents a growth stage in the season. The total dry matter in a season is obtained by the following additive relation: ?? == ? ? ? ? ? ? == ST st st st ST st st TPM TP YMYAYA 11 (3-2) Jensen (1968) proposed the following multiplicative relation for estimat- ing grain yield of crops: ? = ? ? ? ? ? ? = ST st w st st ETM ETA YMYA 1 (3-3) where ETA = actual evapotranspiration, ETM = maximum crop evapotranspiration (eq. 3-5), and w st = a weighting factor for stage st. Hill et al. (1982), Dariane and Hughes (1991) used both relations with dif- ferent crops. In most cases, equation (3-2) has performed better than equation (3- 3). FAO (1979) recommended a relationship between relative yield decrease and relative evapotranspiration deficit given by the empirically-derived yield re- sponse factor (ky), or: )/1(/1 ETMETAkyYMYA ??=? (3-4) 56 The value of ky for different crops is based on experimental evidence, which covers a wide range of growing conditions. The relationship is given for the total growing period and the individual growth periods of the crops. The maximum evapotranspiration is calculated as (also see Chow et al., 1987): 0 ETkcETM ?= (3-5) where ET 0 is the reference evapotranspiration, which represents the rate of evapotranspiration of an extended surface of an 8 to 15cm tall green grass cover, actively growing, completely shading the ground and not short of water. The Penman method is widely used to calculate ET 0 . k c is the empirically-determined crop coefficient relating ET 0 to ETM. The value of kc varies with crop, develop- ment stage of the crop, and to some extent with wind speed and humidity. For most crops, the kc value increases from a low value at time of crop emergence to a maximum value during the period when the crop reaches full development, and declines as the crop matures. The actual evapotranspiration (ETA) is a function of both soil water con- tent and soil salinity. FAO (1979) provided an approach to estimate ETA based on only soil water content. Bras and Seo (1987) presented an example of determining ETA based on both soil water stress and salinity. Prajamwong et al. (1997) im- plemented a more empirical method to include soil salinity in calculation of ETA. Equation 3-4 is probably the most complete summary of available data, and has been widely used for planning, designing and operating irrigation supply system taking account of the effect of the different water regimes on crop produc- tion (Perry and Narayanamurthy, 1998). 57 As a summary, although evapotranspiration and transpiration models cap- ture important aspects of crop-water relationships, they have limited ability to capture the impacts of non-water inputs. The relationships refer to high producing variety, well-adapted to the growing environment, growing in fields where opti- mum agronomic and irrigation practices, except for water, are provided. Estimated Production Functions Estimated production functions are more flexible than other types of mod- els. Polynomial or quadratic functions are most widely used. Moore et al. (1993) used farm-level, census data from the western United States to estimate crop wa- ter production functions for 13 crops in Cobb-Douglas and quadratic forms. Van Liebig response functions for nutrients and water have been estimated using ex- perimental data, and likely outperform polynomial functional forms (Paris and Knapp 1986). However, they are rarely applied as they require detailed field- level data. Berck and Helfand (1990) found that crop yields were better approxi- mated by a smooth concave function. However, Dinar and Letey (1996) argued that the specification and esti- mation procedures of an estimated model must comply with plant-water relation- ships: (1) plant yield increases as water quantity increases beyond some minimum value; (2) yield possibly decreases in a zone of excessiveive water applications; (3) yields decrease as the initial level of soil salinity in the root zone or the salt concentration in the applied irrigation water increase beyond some minimum value; and (4) the final level of root zone soil salinity decreases with increasing irrigation quantities, except for possible increases, where relatively insufficient water quantities have been applied. In order to meet these requirements, polynomial functions have been ap- plied in many production functions. Dinar and Letey (1996) applied the follow- ing quadratic polynomial form in the case of 3 production inputs: 58 2 9 2 8 2 7 6543210 / uasawa usauwaswauasawaaYMYA ++ ?+?+?++++= (3-6) where: w = relative irrigation water (water application to potential evapotranspiration, s = salinity of the irrigation water, u = irrigation uniformity, and a i (i=1,..9) = estimated coefficients. The function can be estimated through regression method based on a number of simulations on the inputs. Salinity effect on crop production The salinity effect on crop production can be explained by the increase in the energy required by the plant to acquire water from the soil and to take make the biochemical adjustment necessary for crop growth under stress (Yaron and Frenkel, 1994). Maas and Hoffman (1977) expressed crop tolerance to salinity in terms of relative yield (YR), threshold (S?), and percentage decrement value per unit increase of salinity in excessive of the threshold (B), as follows: ( ) ' 100 SSeB YM YA YR ???== (3-7) where, Se is the average seasonal root zone salinity, expressed in electrical con- ductivity of saturated soil extract (in dS/m). Figure 3.4 from Mass and Hoffman shows a representative yield-salinity curve. 59 The tolerance to salinity varies from species to species, and among crop development stages. During emergence and the early stages of growth, the toler- ance limits are more restrictive. The tolerance is also affected by climatic condi- tions and soil fertility. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0246810121416 Se (dS/m) YA / YM cotton wheat maize rice Figure 3. 4. Representative crop yield ? salinity relations (after Maas and Hoffman, 1977) 3.2.4 Economics of water management Economists consider prices, permits, rights, and markets as a means to improve water allocation and water quality in an economically efficient way (Easter et. al., 1997). A given allocation of resources is said to be economically efficient if and only if no individual could be made better off without making someone else worse off (Pareto optimality). Apart from prices, permits and rights are alternatives for efficient water allocation and pollution control. Permits are used to control pollution, and substantial interest has arisen in the concept of transferable, marketable pollution permits. Water rights can be defined in terms of 60 a share of an uncertain streamflow, or a share of an aquifer or reservoir, and these rights can be granted as either the actual water right (ownership) or as a use right (the case in the western United States). In an irrigation-dominated river basin, the non-point pollution produced from irrigated fields has been the focus of several studies. Griffin and Bromley (1982) identified four types of policies that could be used to regulate nonpoint- source pollution. These are nonpoint incentives, nonpoint standards, management practice incentives, and management practice standards. Nonpoint incentives place a tax on estimated emissions from individual firms, whereas nonpoint stan- dards limit the total emissions from each firm. Management practice incentives impose a system of taxes and subsidies on inputs to the production process, while management practice standards specify the actual input levels to be used. Exam- ples for applying these policies include: Howe and Orr (1974), putting penalty cost to tons of salt load; Scherer (1977), placing an offer for leaving water in a diluting bank; and Dinar and Letey (1996), imposing a tax on the volume of drainage. Based on the development of a water rights system, water can be allocated through trading water rights among users in markets. The market approach may offer a number of potential advantages, including flexibility in responding to change in water value; empowerment of water users by requiring consent to any reallocation of water and compensation for any water transferred; security of wa- ter rights tenure, which improves incentives for investment in water-saving tech- nology; establishment of incentives for water users to consider the full opportu- nity cost of water, including its value in alternative uses; and reducing the pres- sure to degrade resources (Howe et al., 1986; Rosegrant and Binswanger, 1994). However, a number of possible problems are also identified (Howe et al., 1986): the "third-party" effects from externalities, obstacles to communication among 61 potential buyers and sellers that result from wide geographic separation; and un- derstating the value of instream flows. To strengthen these weaknesses of water markets, Howe et al. (1986) argued that a complete water right should be defined, which not only covered water quantity aspects (quantity diverted and consumed, timing, and places of diversion and application), but also included a description of the water quality. In this way, a water right entitles the owner to a certain quantity of water of a quality at a standard, and at specified periods. Integrated hydro- logic-economic modeling will be helpful to define this complete water right for water markets. Rosegrant and Meinzen-Dick (1996) identify some economic concepts and issues that need to be examined through integrated economic-hydrologic river ba- sin modeling, including Transaction Costs, Agricultural Productivity Effects, In- tersectoral Water Allocation, Environmental Impacts, and Property Rights in Wa- ter. For transaction costs, institutional mechanisms that are most effective in minimizing the associated costs should be studied. Impacts of alternative water allocation mechanisms should be evaluated with concerns on farmer water use, choice of inputs, investments, productivity of water, agricultural production and income in different agroeconomic and scarcity environments. Tradeoff between agriculture and non-agriculture water use should analyze for intersectoral water allocation, and allocative mechanisms and associated institutions are important to eliminate the conflicts in water use between sectors. To develop the relationship between allocation mechanisms and environmental externalities caused by water uses is an urgent task to capture environmental impacts, and so is to design ap- propriate economic incentives and institutional directives to prevent environment reduction caused by water uses. Finally, setting up appropriate property rights in water is important in the actual implementation of allocation mechanisms, espe- cially for the purpose of equity. 62 3.2.5 Integrated hydrologic -economic models Integrated hydrologic-economic models combine hydrologic components and economic incentives either in one consistent model or through a connection between these two components. There are two approaches to combine these two components. One is referred to as the "compartment modeling" approach, and the main question is which mathematical formats are available to transform informa- tion between the hydrologic model and the economic model. The other approach is often called "holistic modeling", in which the models are typically built as one consistent model, instead of being put together from separate, mono-disciplinary sub-models. To use the holistic approach, the modelers have to use one single technique (simulation, dynamic programming etc.) and use a single denominator for the variable quantities. In integrated hydrologic-economic models, the operation of hydrologic systems is driven by a socio-economic objective (or multiple objectives including socio-economic and environmental objectives), while economic incentives are conducted on the physical system which is simulated by hydrologic components. A notable research effort in integrating economic modeling and complex hydro- logic modeling was reported by Noel and Howitt (1982), who incorporated a quadratic economic welfare function (Takayama and Judge, 1964) in a multibasin conjunctive use model. A number of economic (derived demand, opportunity cost, and urban demand) and hydrologic (groundwater, and surface water poten- tially) auxiliary models were applied to derive linear sets of first-order difference equations which formed a so-called linear quadratic control model (LQCM). This model was then used to determine the optimal spatial and temporal allocation of a complex water resource system, and examine relative performances of social op- timal policy, pumping tax policy, and laissez-faire policy. 63 More recently, Lefkoff and Gorelick (1990a) reported another research us- ing the "compartment modeling" approach. Distributed parameter simulation of stream-aquifer interactions, water salinity changes, and empirical agronomic func- tions were combined into a long-term optimization model to determine annual groundwater pumping, surface water applications and planting acreage. Micro- economic theory of the firm, associated with agronomic functions related to water quantity and quality, was applied for each farm during each season for farmers to choose a level of production where marginal revenue equals marginal cost. This model was further extended to incorporate a rental market mechanism (Lefkoff and Gorelick, 1990b), considering annual water trading among farmers. Information transfer between hydrologic and economic components re- mains a technical obstacle in the "compartment modeling" approach, while in the "holistic modeling" approach, information transfer is conducted endogenously. Booker and Young (1994) presented a nonlinear optimization model for investi- gating the performance of alternative market institutions for water resources allo- cation at the river basin scale. This model was built on the optimization model of market transfer exemplified by Vaux and Howitt (1984), and extensions were made on both supply and demand side. On the supply side, flow balance and transfer, and salt balance were considered in a river (the Colorado River) basin network including river nodes, reservoir nodes, hydropower station nodes and demand site nodes; on the demand site, both offstream (irrigation, municipal, and thermal energy) and instream (hydropower and water quality) uses were repre- sented by empirical marginal benefit functions. This model was used to estimate impacts of alternative institutional scenarios, river flows, and demand levels. In a related work, Faisal et al. (1997) studied a problem of groundwater basin man- agement in which economic objectives were combined with realistic aquifer re- sponses through the use of discrete kernels. 64 3.2.6 Technical aspect of integrated hydrologic-economic modeling A comprehensive discussion about the technical aspects of economic- ecological modeling was given by Braat and Lierop (1987). The following dis- cussion heavily depends on their work. The modeled relationships in the integrated hydrologic-economic model should not only reflect the structure or function of the real-world relationships but also allow for effective transfer of information from one component to the other. Hydrologic models are mostly built for simulation experiments, while a majority of the economic ones use optimization techniques. These two kinds of models may be conducted in different spatial scales and temporal scales, and their re- quirements of data may be different too. These differences often bring difficulties in transferring information between the hydrologic and the economic component. In spatial aspects, the boundaries of the economic system considered in a resources problem analysis may not a priori be the same as those of the hydro- logic system. In economic models we generally have to consider the political and administrative boundaries, and in hydrologic models we generally consider water- shed boundaries. Another kind of problem is that the two models may have differ- ent spatial development horizons, which refer to the area (or volume) over which impacts and development extend, as well as the area (or volume) over which the model can be validated. The temporal aspects relate to two problems: different time intervals and different time horizon used in hydrologic models and economic models. Eco- nomic models generally use larger time intervals (seasonal or annual) and longer time horizon (e.g. in long-term forecast), while, in hydrologic models, the time interval should be small enough to reflect the real-world processes, and the time 65 horizon often can not be too long due to the computation capacity and data avail- ability. Data requirements relate to type of data and level of aggregation. Mixed types of data, including experiment data, statistical data, and empirically esti- mated data, are used in multidisciplinary models, and data desired and available may differ as to their temporal and spatial resolution. For the two approaches to develop an integrated river basin model, the "compartment modeling" approach is more widely used for large complex sys- tems, since it is relatively easy to solve each compartment instead of the whole system. However, the loose connection between compartments may not be effec- tive for information transform between the components. For the "holistic model- ing", modeling components are tightly connected in one consistent model, instead of being put together from separate, and thus no problem with information trans- form, but less complexity should be enclosed, otherwise, it will be very different, if not possible, to solve the model. 3.3 DEVELOPING MODELS FOR SUSTAINABILITY ANALYSIS - RESEARCH NEEDS White (1969) argued water resources management strategies could be ad- dressed according the following questions: who makes what choices (how deci- sions are made)? What is the effect upon the public welfare and what is the effect upon the natural environment (consequences of the choice)? For sustainable water resources management, we may need to ask two more questions: what is the inter- relation between the effect upon the public welfare the effect upon the natural en- vironment? How does this interrelation evolve with time, subject to the changes and uncertainties in the future? Integrated hydrologic-agronomic-economic- institutional models will provide a comprehensive framework to analyze these questions for river basins where irrigation dominates the water use. 66 In an integrated model built at a river-basin level, water management and policy solutions must be tailored to specific regions or districts, because of differ- ences in institutional capabilities, irrigation and urban water supply infrastructure, the structure of agriculture, and the degree of water scarcity. Moreover, because of the increasing competition for water resources, water use will include not only offstream consumption of water in agricultural, municipal and industrial produc- tion, but also instream non-consumptive water use such as hydropower, ecological maintenance, and recreational purpose. The outcomes of water use will be examined in terms of efficiency, equity, and environmental impact. Over time, these outcomes may change with climate and hydrologic fluctuations, man-made events such as flow regulation and pollut- ant discharges, technological change, institutional change, and other social and economic uncertainties and changes. The water policy research should seek to ad- dress these issues in ways that are directly relevant to water management authori- ties and policymakers in choosing appropriate water policies and establishing pri- orities for reform of institutions and incentives that affect water uses. In order to trace the complex relationships across water allocation mecha- nisms and policies, agroclimatic variability, and the different water uses and us- ers, it is necessary to consistently account for a large number of physical, eco- nomic, and behavioral relationships. To accomplish this, it is possible to develop an analytical modeling framework based on several elements as below: (1) a nec- essary unit for the physical and technical management of water resources due to new developments; (2) growing competition for water among agricultural, indus- trial, urban, and instream uses that can only be traced along the entire basin; (3) increased attention on environmental impacts of anthropogenic interventions that can only be managed at a basin scale, and (4) a necessary unit to trace the com- 67 plex relationships and implications of water allocation mechanisms and policies on economic efficiency. Such as a modeling framework can be applied to river basins with arid or semi-arid climates and irrigation-dominated water supply, and where salinity con- trol is a major water quality and environmental problem. The components of an prototype model will include (1) the hydrological components, which account for flow and pollutant transport and balance in the river basin network which is ex- tended to include crop root zone, (2) crop production functions of both water stress and soil salinity, and benefit functions for instream-water uses (3) irriga- tion and drainage management, (4) institutional rules and policies that govern wa- ter allocation; and (5) economic incentives for salinity control, water conservation and irrigation system improvement. The analytical issues based on the output of the model will then concentrate on searching management policies and rules to sustain growth in irrigated agricultural production, to satisfy growing municipal and industrial water demands, and to reverse the ongoing degradation of the water and soil resources systems. 3.4 A PROTOTYPE MODEL 3.4.1 Introduction Referring to the schematic diagram of an integral river basin system shown in Figure 3.1, the essential relations within each component and the inter- relations between these components are included in a prototype model developed in this research. The water users system is differentiated into agricultural demand sites and industrial and municipal demand sites. However, the emphasis in this research will be put on agricultural demand sites. We model each agricultural demand site as a farm, and within each farm, a number of areas with specific soil types will be 68 identified. An area can have several crop fields, corresponding to specific crop patterns. Therefore, the modeling framework has a hierarchical structure of com- bined macro and micro levels including the region, farm, area with a specific soil type, and the crop field (Figure 3.5 and Figure 3.6). The regional level is used for hydrologic systems operation and water allocation among demand sites (cities and farms) possibly under conditions of maximizing social benefit in the whole region of a river basin. At the farm level, water is allocated to areas with specific soil types, and the efficiency of water distribution and drainage in each farm is to be planned. Crop acreage and water allocations among crops are determined at the soil area level. Finally, water mixing for irrigation, irrigation scheduling among growing stages and the type of irrigation technology are determined at the crop field level. The relations of these decisions with institutional regulations and eco- nomic incentives are referred to Figure 3.2. Three components are included in the modeling framework: (1) hydro- logic components, including water and salt balance in reservoirs, river reaches, aquifers, and root zones. Deep percolation, stream-aquifer interaction, surface drainage and subsurface drainage, soil salt accumulation, and return flow will be calculated explicitly; (2) agronomic components, including crop yield response with both irrigation water quantity and salinity in soil and in irrigation water, and crop acreage allocation; (3) economic components, including benefit and cost cal- culation and tax/subsidy systems. A short-term model (also called yearly model in the long-term framework) includes all these components in a one-year time hori- zon with 12 modeling periods (months). The long-term model extends the yearly model to multiple years, and includes changes and uncertainties in both water supply and demand. 69 In the rest of this chapter, the essential hydrologic, agronomic and eco- nomic relationships, as well as the formulation of the objective function of the model are first described, and generic analysis of the river basin network based water allocation system is presented. River Basin (Region) Hydrologic system operation and water allocation to demand sites Decisions on: ? Reservoir release ? Groundwater pumping ? Withdrawal from river reaches/reservoirs ? Downstream flow Demand Sites (Farm) Decisions on: ?Water allocation to soil slots ?Distribution efficiency ?Drainage efficiency ?Drainage disposal/treatment Crop Field Decisions on: ?Water allocation to growing stages ?Irrigation method ?Sources blending Soil Area Decisions on: ?Water allocation to crops ?crop acreage Figure 3. 5. Hierarchical structure of a multi-level irrigation management model. 70 3.4.2 Institutional assumptions Optimal water management must be consistent with specified institutions. Brown et al (1982) recognized four social values embodied in water institutions: economic improvement, environmental preservation, maintenance of agricultural lifestyle, and equitable access to water. Young (1996) pointed out that the indi- vidually rational resource use might not be optimal when considered from the per- spective of society, if institutions are inadequate in the water use framework. Gardner et al. (1990) encouraged a collective management of a ?common pool resource? like water, which has many appropriators or users. Each individual user may only reach sub-optimal outcomes, while a collective institution is needed to catch a global optimality. In this research, we assume that there is such a central authority in the river basin who can make decisions for the operation of the river basin system, standing on the overall socio-economic and environmental benefits in the region of the river basin. Some economic incentives that are active within the proposed institution will be discussed later in the section on economic consid- erations. 3.4.3 Hydrologic processes Hydrologic processes include flow and salt balance in reservoirs, river reaches, aquifers, and root zones, and flow and salt transport between these enti- ties. The general mass balance equations are referred to Mays and Tung (1992) and Loucks (1996). Some of the processes specifically related to irrigation and drainage activities are described in this section, as well as the associated assump- tions. Before that we define some items that build connections between hydro- logic processes and anthropogenic controls, including irrigation and drainage technologies. Some indices commonly used in the following equations are: t: time periods (months), y : years, 71 st: crop growth stages, tst ? , dm: demand sites, riv: river reaches, rev: reservoirs, gw: aquifers, n : water supply or demand nodes in the river basin network, n ={riv, rev, gw, dm}, Further, n1 represents a from-node, and n2 represents a to- node. (n1, n) represents all links from n1 to n, and (n, n2) represents all links from n to n2. sa: areas with specific soil types, fd: crop fields, and cp: crop patterns. It is assumed that each crop field has a single crop pat- tern, and fd and cp has the one-to-one relation. For example, in a field, spring wheat (growth stages from Jan. to Jun.) is planted, and then late maize (growth stages from Aug. to Nov.) may be planted in the same field. Delivery and distribution efficiency (EDS), which is defined as the ratio of the water arriving at the crops fields to the total water diverted: t dm t dm dm WD WDA EDS = (3-8) where, WDA : diverted water available for use in demand site (eq. 3-17), and WD : total water diversion from rivers and reservoirs, including local sources. EDS depends on the condition of the canal lining. Here we assume even EDS within a demand site, but it can vary among demand sites. 72 Irrigation Efficiency (EIR), which is often referred to as application effi- ciency, is defined as (Clemmens and Dedrick, 1994): applieddepth average zoneroot in the stored water ofdepth average =EIR The numerator refers to water which is available for consumptive use by plants, and is eventually used for that purpose. To use this definition in the model, we make two assumptions: (1) no surface runoff from the crop field, and (2) EIR is the same over all growth stages. The first assumption may be only reasonable for large crop fields in arid or semi-arid area, and the second applies for the aver- age condition of large crop fields. With these assumptions, EIR is calculated as: ? ? ? ? = stagesgrowtht t fdsadm stagesgrowtht t fdsadm fdsadm WAF WEU EIR ,, ,, ,, (3-9) where, WEU : water effectively used by crops (equation 3-19), and WAF : total water applied to crop fields. WAF includes diversion, local surface source, groundwater pumping, and drainage reuse (eq. 3-19). It should be noted that EIR is a measure of the perform- ance of the conventional irrigation systems, and it is not related to runoff irriga- tion by rainfall. Therefore, neither WEU nor WAF includes rainfall. Drainage efficiency (EDN) is defined as the ratio of drainage over percola- tion from the root zone, 73 ??? ??? = tsafd t fdsadm tsafd t fdsadm dm PN DN EDN ,, ,, (3-10) where, DN : drainage from a crop field, including surface drainage and subsurface drainage, and PN : percolation in a crop field, the amount of water leaving root zones to downward soil layers. Part of the percolation is drained, and the rest, which is called deep perco- lation (DP), enters the groundwater. t fdsadm t fdsadm t fdsadm DPDNPN ,,,,,, += (3-11) An even EDN is assumed for one demand site and over all time periods. Drainage disposal/treatment ratio (EDP) is the ratio the magnitude of drainage disposal and treatment to drainage at each demand site, ??? ? = tslfd t fdsadm t t dm dm DN DT EDP ,, (3-12) where DT is the amount of drainage disposed (in an evaporation pond) or treated at a demand site. The four items defined above relate anthropogenic controls to hydrologic processes. Delivery and distribution efficiency (EDS), irrigation efficiency (EIR), and the drainage disposal and treatment ratio (EDN) are all determined in the model. The decisions on these variables are induced by irrigation profit, as well as 74 management policies for equity and environment protection. They are also con- strained by their current conditions, potential improving capacities, and economic efficiency of investment. 3.4.3.1 Water and salinity balances in rivers, reservoirs and aquifers Water balances in rivers, reservoirs, and aquifers can be simply repre- sented as: 1 )2,(2),1(1 )2,(),1( ? ?? ?=? ?? tt nnn t out nnn t in STSTnnQnnQ (3-13) where Q in : inflow during time period t, Q out : outflow during time period t, ST: storage at the end of a time period, (n1, n): inflow links to node n from node n1, (n, n2): outflow links from node n to node n2. For river reaches, since the time period is one month, the storage effect can be neglected (Loucks, 1996), i. e., 0 1 =? ?tt STST . The inflow includes (1) flow from upstream river reaches or reservoirs; (2) return flow (eq. 3-31) from demand sites; (3) discharge from aquifers (eq. 3-15); and (4) natural drainage. The outflow includes (1) flow diversion to demand sites; and (2) flow to downstream river reaches or reservoirs; and (3) evaporation loss. For reservoirs, the inflow comes from (1) upstream reservoirs or river reaches, and (2) natural drainage. The outflow goes to (1) demand sites; (2) downstream rivers or reservoirs; (3) evaporation loss; and (4) seepage to ground- water. 75 For aquifers, given the inherent complexity of the hydrologic-economic models considered here, we simply use a single-tank model (Bear, 1977) to simu- late flow and salt balance in aquifers. Assuming each demand site has one groundwater ?tank?, the inflow to the tank includes natural recharge (NR), artifi- cial recharge (AR), surface water leakage (SL) and deep percolation (DP) (related to drainage efficiency) from irrigation fields, and the outflow includes pumping (PM), groundwater extraction to root zones (GE) and discharge to surface water systems (DS), namely, []( ) ttt hghgsAADSPMGEDPSLARNRt ???=???+++? ?+ (3-14) in which AA is the horizontal area of the aquifer, s is the aquifer storativity, and hg is the average water table elevation in the cell. A linear relationship is assumed between the discharge DS, and the water table head hg (Smedema and Rycroft, 1983), hgDS ?=? (3-15) where the water table (hg) is a state variable in the model, and ? is a coefficient to be calibrated by local experiments. It is assumed that the groundwater table should not be above a critical threshold. The critical groundwater table mostly depends on the rooting depth of the crop, the efficiency of irrigation water use and on the hydraulic characteristics of the soil. This assumption drives sufficient field drainage so as to prevent water- logging in crop fields. The salinity balances in river reaches, reservoirs, and aquifers are based on the flow balances in each of these entities, which can be simply expressed as: 76 11 )2,(2),1(1 )()2,()1(),1( ?? ?? ???=??? ?? ttttt nnn t out t nnn t in CSCSnCnnQnCnnQ (3-16) where C is the salt concentration with various flows. For long-term assessment of groundwater salinity change, solute transport simulation is necessary. Ahlfeld et al. (1988) and other researchers directly incor- porated distributed parameter numerical simulations of solute transport into a nonlinear optimization problem. Alley (1986) and Lefkoff and Gorelick (1990a) developed regression equations to predict changes in groundwater salinity as a function of hydrologic conditions and water use decisions, by using Monte Carlo techniques. However, we simply use equation 3-18 for groundwater salinity com- putation, which still makes sense for the basin-wide integrated model developed in this research. 3.4.3.2 Water allocation within a demand site Within a demand site, water delivered from reservoirs, diverted from riv- ers, and local sources are mixed, and then allocated to areas with different soil types. Within each area, water is allocated to crop fields (Figure 3.6) () t dmdm t dm riv t rev t dmrev WDAEDSLSRIVDREVD dmriv =??? ? ? ? ? ? ++ ?? 1__ , , (3-17a) ?? = sa fd t fdsadm t dm WFLDWDA ,, (3-17b) 77 D_RIV Groundwater DEMAND SITE SOIL PLOTS CROP FIELDS reservoir river tributary D_REV Local surface water LS PE REUSE WD WDA (WDA*EDS) PM WD*(1-EDS) WA tail-water= (WFLD+REUSE+PM)* (1-EIR) WFLD Figure 3. 6. Diagram of water balances in multiple levels 78 in which, D_REV : delivery from reservoirs to a demand site [L 3 ], D_RIV : diversion from rivers to a demand site [L 3 ], LS : local surface water source [L 3 ], WFLD : surface water allocated to crop fields [L 3 ]. 3.4.3.3 Water available to crops The total water available to a crop includes irrigation water application and effective rainfall. Since different crops have different salt tolerances, the model allows a crop with a high salt tolerance to use water with high salt concen- tration. For each crop, we assume that the normal sources, including diversions and local sources, may be blended with local groundwater and reused drainage (Figure 3.6). A highly tolerant crop may reuse a larger amount of drainage. fdsadm t sadm t fdsadm t fdsadm IAERWEUWA ,,,,,,, ?+= (3-18) fdsadm t fdsadm t fdsadm t fdsadm t fdsadm EIRPMREUSEWFLDWEU ,,,,,,,,,, )( ?++= (3-19) in which, WA : water available to a crop [L 3 ], REUSE : drainage reuse [L 3 ], PM : groundwater pumped [L 3 ], ER : effective rainfall [L], and IA : irrigated area [L 2 ]. Effective rainfall ER is the rainfall infiltrated into the root zone and avail- able for crop use. ER depends on total rainfall (TR), soil moisture content (Z), ref- 79 erence crop evapotranspiration (ET 0 ), and soil characteristics (hydraulic conduc- tivity K, moisture content at field capacity Z s , etc). ER can be estimated by the evapotranspiration/precipitation ratio method (USDA, 1969). Given total rainfall (TR), ET 0 and soil characteristics, an empirical relationship between ER and Z can be developed as: ...),,,|( ,,0,,,, sadmsadm t dm t dm t fdsadm t fdsadm ZsKETTRZfER = (3-20) 3.4.3.4 Flow and salt balance in the root zone Soil water balance in the root zone is expressed as (see Figure 3.7): t fdsadm t fdsadm t fdsadm t fdsadmfdsadm t fdsadm t fdsadm t fdsadm t sa PNETAGE IRAFWAFZZRD ,,,,,, ,,,,,, 1 ,,,, /)( ??+ +=?? ? (3-21) in which, RD : root zone depth [L], Z : soil moisture content in root zone in percentage, GE : groundwater extraction by absorption [L] (eq. 3-11), ETA : actual evapotranspiration [L] (eq. 3-25 ), IR : infiltrated precipitation [L]. and all other items have been defined before. By the definitions of EIR and ER, we can split equation 3-21 into the fol- lowing two equations: 80 / )( ,,,,,,,, ,, 1 ,,,, t fdsadm t fdsadmfdsadm t fdsadm t fdsadm t fdsadm t fdsadm t GEERAFWA ETAZZRD sa ++ =+?? ? (3-22) ( ) t fdsadm t fdsadm fdsadmfdsadm t fdsadm t fdsadm ERIR EIRAFWAFPN ,,,, ,,,,,,,, )1(/ ?+ ??= (3-23) where equation 3-22 shows the sum of water for crop evapotranspiration in the current period and water stored in the root zone for that purpose in a later period is equal to the sum of irrigation water application, precipitation, and groundwater extraction that are effectively used for crop growth. Percolation is defined as the movement of water to a depth that is inaccessible to plant roots. Equation 3-23 shows percolation from the crop field includes excessive irrigation water and ex- cessive water from infiltrated precipitation. If we assume the infiltrated precipita- tion (IR) can all be effectively used by crops, then the last two items in equation 3-23 can be dropped. 81 Water table GE ground WAF ETA PN RD GD DN DP TR Figure 3. 7. Diagram of water balance in root zones. Assuming no large change in the water table, the monthly upward move- ment of water from the water table (GE) can be calculated based on the equation given by Eagleson (1978): t GD s cm KGE sadmsadm fdsadm fdsadm cm t sadm sadmsadm sadm t ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? += ? ,, ,, ,, , ,, , 1 5.1 1 (3-24) where K is the saturated hydraulic conductivity, c is a coefficient taken as the soil?s pore connectivity index, m is a parameter related to the soil connectivity and tortuosity, ?s is the saturated soil matric potential. All of these items are known parameters for a specific soil type. GD is the depth of water table, and ?t is the time duration of one period. 82 The actual evapotranspiration (ETA) is a function of both soil water con- tent (Z) and soil salinity (SS). The presence of excessive soil salinity leads to a high level of soil osmotic potential (? 0 , potential due to the presence of solved salts, ? 0 =0 for pure water). Osmotic potential inhibits the ?passive? entry of wa- ter into the roots in the same manner as does the soil matric potential (? m , result- ing exclusively from the soil matrix, varying with soil water content). We assume that the soil matric potential affects both the bare soil evaporation and plant tran- spiration, while the soil osmotic potential only reduces the plant transpiration. Another assumption is that the soil water content and the soil salinity have inde- pendent effects on crop yield. Based on these assumptions, combining the work of Jensen et al. (1971), Hanks (1985), and Prajamwong et al. (1997), we may write an expression of the actual evapotranspiration as: )]( )1[(0 ,,,, ,,,,,,, t fdsa t fdsa t fdsadm t fdsa t fdsadm t fdsadm t dm t fdsadm kctkckap kctkatksETETA ??+ ????= (3-25) where, ks : coefficient of soil salinity effect (eq. 3-26), k at : coefficient of soil water stress effect for transpiration (eq. 3-27), k ct : crop transpiration coefficient. According to Hanks (1985), kct=0 be- fore crop emergence, and after that, kckct ?= 9.0 , k ap : coefficient of soil water stress effect for soil evaporation (eq. 3-28), k c : crop evapotranspiration coefficient (Chow, et. al., 1988). k s is estimated based on the yield - seasonal root zone salinity relationship in equation 3-4 as: 83 () ? ? ? ? ? ??=? < = otherwise 100/1 , 0 ' ,, ,, cp t cpsadmcp ' t cpsadm SSeB YM YA Sif Se ks (3-26) k at is estimated by the following equation given by Jensen et al. (1971) )101ln(/]1)(100ln[ ,, ,, + ? ? ?= sasa sa t fdsadmt fdsadm ZwZs ZwZ kat (3-27) The following empirical equation (Prajamwong et al., 1997) is used to estimate kap: 5.0 ,, ,, 5.0 5.0 ? ? ? ? ? ? ? ? ?? ?? = sasa sa t fdsadmt fdsadm ZwZs ZwZ kap (3-28) where, Zs : saturated soil moisture, and Zw: soil moisture at the wilting point. The root zone salt balance equation is based on the following two equa- tions. Assuming no lateral flow in the root zone, Abdel_buyem and Skaggs (1993) gave an equation as: )( / 1 ,,,, ,,,, ,,,,,,,,,, ? ???? ?+ ?=? t fdsadm t fdsadm t fdsa t fdsadm t fdsadm t fdsadmfdsadm t fdsadm t fdsadm t fdsadm ECeECeRDZs ECgGE ECwAFWAFECpPN (3-29) 84 where ECp, ECw, and ECg are the salinity in the percolation, water application, and groundwater extraction, respectively, expressed as electric conductivity [dS/m = mmhos/cm, lmgmdS / 700/ 1 ? ]; ECe represents a salt extract of soil solution made when the soil is at saturation point, expressed as electric conductivity [dS/m]. A salt transport equation is given by Sharply and Williams (1990) as: ? ? ? ? ? ? ? ? ? ? ?? ? ? ?+??=? ? ] )( exp[1 )( ,, 1 ,,,,,,,, t fdsasa t fdsadm t fdsadm t fdsadm t fdsa t fdsadm t fdsadm RDZwZs PN ECeECeRDZsECpPN (3-30) where the left side of the equation represents the salt mass leaving the root zone with the water flow, which should include the surface runoff and the vertical per- colation, but it is assumed that no surface runoff in the crop field. The right side represents the salt mass in the root zone multiplied by a discounting factor deter- mined by the amount of the total outflow. 3.4.3.5 Salt transport in irrigated areas Four phenomena of salt transport in an irrigated area are considered. The first one is the salt accumulation in the root zone due to consumptive crop evapotranspiration; the second phenomenon that may occur in some irrigated ar- eas is the leaching or mining of indigenous salts from the soil. The third process, which is called ?groundwater displacement effect?, may occur if an irrigated area is underlain by an aquifer whose chemical composition permits very high leach- ing by salt pickup (Skogerboe and Walker, 1973). In this case the root zone water percolates through the aquifers, displacing water of salinity perhaps 3 or 4 times 85 that of the root zone drainage. A final consideration that is important in some irri- gated areas is the leaking of delivery canals. Some or all of the loss may leave the basin , or it may eventually return to the source river. At one extreme, this loss may percolate into an aquifer and emerge as the same salinity as that of the diver- sion canal. At the other extreme, it may enter the type of highly saline aquifer de- scribed above and displace very salty water to the river. In any event, lining the canal can essentially eliminate the effect of the leakage. 3.4.3.6 Return flow Control of irrigation return flow is necessary for maintaining water quality in a river system. Estimation of return flow is critical to the economic evaluation of externalities from irrigation water use. Generally, the irrigation return flow contains more salt than the water diverted from a river system, but the quantity is less than the primary diversion. Therefore, the return flow can bring high salt concentrations to the water in the river system. The irrigation return flow is re- lated to anthropogenic controls including improved distribution efficiency and drainage facility, and enlarged disposal and treatment capacity. Drainage reuse reduces return flow. Return flow from a demand site (dm) is the sum of calculated in the model as: [ ( ) ] () t dm sa fd t fdsadm t dm t dm sa fd t fdsadm t da t da t dm rfeRUSEDT DSDNcmpNIWRF ???? ++??= ?? ?? 1 1 ,, ,, (3-31) where NIW: non-irrigation water supply, cmp: consumptive use rate of the non-irrigation water supply, DS: discharge from the aquifer associated with the demand site (eq. 3-15), 86 RUSE: drainge reuse, rfe: evaporation loss rate of the return flow, and all other items have been defined before. Salt concentration in the return flow is computed by a salt balance equa- tions including salt mass carried with each item in equation 3-23. 3.4.4 Agronomic relationships 3.4.4.1 Crop production as a function of soil moisture and soil salinity The yield evapotranspiration relation (equation 3-4) and the yield-salinity relation (equation 3-7) are used to derive a yield - soil moisture - soil salinity rela- tion. Equation 3-4 shows crop yield is a function of actual crop evapotranspiration (ETA), and in equation 3-21 to 3-24, ETA is explicitly expressed as a function of soil moisture and soil salinity. The yield ? soil moisture - soil salinity relation can be described by the following generic equations: )( 1 ETAfYA = (= Equation 3-4) ),,( 2 katkapksfETA = (= Equation 3-25) )( 3 zfkap = (= equation 3-28) )( 4 sfks = (= Equation 3-26) )( 5 zfkat = (= Equation 3-27) Equations 3-4 and 3-7 show a linear relation between crop yield and evapotranspiration and soil salinity, respectively. However, the new relation based on these two linear relations is not a simple linear one. For example, Figure 3.8 87 presents the relative yield of cotton vs. soil moisture under various soil salinity conditions (represented by salinity effecting coefficient, ks). 3.4.4.2 Critical crop stage Critical crop stage is the stage in which the relative crop yield (YR) is the minimum among all crop growth stages. To account for water stress and salinity effect in individual crop growth stages (st), YR is calculated as: [ ] ? ? ? ? ? ? ? ? ? ? ?? ??? = )/(1 )/1(1min min seasonseasonseason ststst st ETMETAky CETMCETAky YR (3-34) where st CETA and st CETM are cumulative actual and maximum evapotranspira- tion in each growth stage, respectively. ? = st st stst ETACETA ' ' , and ? = st st stst ETMCETM ' ' . Finally, YRYMYA ?= (3-5) 88 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.15 0.2 0.25 0.3 0.35 soil moisture (Z) relat i ve yield ( Y R) ks=0 ks=0.1 ks=0.2 ks=0.3 ks=0.4 Figure 3. 8. Crop yield vs. soil moisture under various soil salinity Thus, the crop production function includes the effects of soil water mois- ture and soil salinity over all crop growth stages, which makes possible to connect the crop production to hydrologic system operation by setting the same manipu- lating period for crop growth and hydrologic system operation. In the case study of this research, we use month, which is normal for both hydrologic and agro- nomic system management modeling. 3.4.5 Economic incentives One of the important purposes in this research is to apply economic incen- tives to influence hydrologic system operations and water use so as to reach opti- mal and rational water management. These incentives can enable farms to invest in improved distribution facilities and irrigation technology, pay for the safe dis- posal of drainage produced on their fields, or divert less water and leave more wa- 89 ter in the ?dilution bank?. The institutions that allow these incentives to be real- ized have been discussed before (Section 3.4.2) and they are further stated here: (1) individual demand sites (like firms) obey a central regulatory authority; (2) each of them is assumed to maximize profits subject to regulations and charges imposed by the authority, and (3) the authority owns the right let demand sites to withdraw water or to keep water for instream use. The economic components included in the modeling framework represent: ? agricultural production as a function of the volume of water benefi- cially transpired, the soil salinity level that is contributed by both cur- rent irrigation and previous salt accumulation in the root zone, and the acreage of irrigated land (eq. 3-25, 3-26, 3-35); ? Municipal and industrial water demand function, and a crop price function (Rosegrant,1997, personal communication) (eq. 3-38 and 3- 39); ? infrastructure improvements, as functions of investment on an annual- ized basis (eq. 3-41 ? 44); ? instream water use value from hydropower generation and ecological maintenance (eq. 3-40); ? a tax applied to the excessive salt discharge load to both the surface and ground water system, and a subsidy applied to the improvements of infrastructure. (eq. 3-36, and 3-44); and ? representation of externalities resulted from excessive water diversion and salt discharge by upstream demand sites, producing negative ef- fects to crop production at downstream demand sites. Flow and salt balances through the river basin network with the extension to crop fields provide a basis to analyze the effects (Appendix C). 90 With these components integrated in the model, the objective of this re- search is limited to search for optimal management of the river basin, i.e. the ob- jective function is to maximize the overall returns to land and management from all subregions. The maximization of private profit will not be analyzed specifi- cally in this research, however, the equity among the subregions under the overall optimum will be analyzed in the long-term model. Howe and Orr (1974) had simi- lar considerations of economic incentives as those proposed here, but they did not consider any sort of river basin or hydrologic network. This research also builds an analytic framework that represents potential communication among demand sites through an integral river basin network, includes both in-stream and off- stream water uses, and embeds externalities of water allocation at the river basin scale. Instead of fixed-quantity proposals (prescribed water use rights), in this research, empirical demand functions for individual demand sites are specified, and a hypothetical water market mechanism is used to identify optimal inter- demand site and inter-crop water allocations. Brooke and Young (1994) provided a remarkable example along this line of analysis. This research seeks to extend the work of Brooke and Young (1994) with more detailed hydrologic, agronomic and economic relationships, so that (1) an integral river basin network including sur- face water, root zone soil water, and groundwater systems, is represented; (2) a production function which considers both water stress and soil salinity explicitly is developed; (3) a more exact expression of externalities is represented through simulating return flow from crop fields and introducing agronomic water-salinity- production functions; (4) irrigation management and planning decisions (water distribution efficiency, drainage facilities, and irrigation technology) are con- nected to both shot-term and long-term water allocation, (5) tax and subsidy sys- tems are used to induce efficient water allocation, improvement of irrigation- 91 related capacities, and protection of the environment, and (6) sustainability prin- ciples are used to account for tradeoffs between short-term and long-term benefits and costs. These sustainability principles have never been included in a model like this before. Tax and subsidy systems have been popular incentives for resource reser- vation and pollution control (Baumol and Oates,1992). Specific discussions of tax/subsidy effects on agricultural nonpoint pollution include Howe and Orr (1974), Griffin and Bromley (1982), and Dinar and Letey (1996). In this research, we assume that efficient water use is affected by excessive salt discharge; on the other hand, the negative effect might be mitigated by improvements in water dis- tribution capacity, drainage collection and disposal capacity, and irrigation sys- tems. A tax/subsidy system, consistent with this assumption, is implemented in the model so that excessive salt discharge is taxed, and the infrastructure im- provements are subsided. The tax on the net salt discharge is the so-called Pigou- vian tax. The principle of the Pigouvian tax is that for an optimal policy, the tax on pollution should be equal to the marginal damage due to the pollution (Baumol and Oates, 1992). For simplicity, the tax on salt discharge is set as a parameter in the model, and scenario analysis of this parameter is made for optimal policy analysis. However, for further research, it can be determined endogenously in the model. A subsidy is imposed on all factors that conserve water and/or reduce pro- duction of drainage directly and indirectly, including canal lining, improvement of drainage facilities, and use of advanced irrigation systems. The demand sites in the whole river basin share the subsidy, but the allocation of the subsidy among demand sites, and among these improved facilities is determined by the model so that an efficient allocation of the subsidy will be selected so as to approximate a socially optimal management. Because returns from irrigated agriculture can 92 rarely finance infrastructure development and improvement, generally, the gov- ernment has to provide the finance source. In this research, we assume the total subsidy is equal to the total tax plus input provided by the central authority, gen- erally funded by the government (see eq. 3-32). The function of irrigation profit in an individual irrigation demand site is formulated as: IP (dm) = income from all crops - fixed crop cost - groundwater pumping cost - surface water diversion and distribution cost - cost on drainage reuse (not including fixed investment) - cost on drainage pumping (not including fixed investment) - cost on drainage disposal (not including fixed investment) ,, ,,,,,, ,,,, ?? ???? ????? ?? ???? ???? ???? ??= ?? t t dmdm t dm t dm tsafd t fdsadmdm t dm t dm sp fd t t fdsadmdm sa fd fdsadmfdsadm sa fd fdsadmfdcpsadmfdcpdm WDTcdtWDNcdn RUSEcrWDcs PMcgAFfc AFYLDpcpIP (3-36) where, fc : fixed crop input cost per unit area, pcp : crop selling price, cg : groundwater pumping cost, cr : cost per unit of drainage reuse, 93 cdt : cost per unit of drainage disposal (not including fixed investments), cdn : cost per unit of drainage collection (not including fixed investments). The net revenue (NREV) from irrigation at a demand site is equal to the ir- rigation profit minus the tax on excessive salt discharge: ? ??= t t dmdmdmdm MEStaxIPNREV (3-37) where, tax : tax imposed on excessive salt discharge, MES : salt mass in return flow in excessive of what was presented in the original diversion, and all other items have been defined before. Crop prices can be determined through an inverse demand function (or price function, Rosegrant, personal communication, 1997) )ln()/1()ln( cpcp TYLDpcp ??+= ??? (3-38) where ? is the intercept calibrated to "normal" production, ? is the market share of the commodity, and ? is the price elasticity of demand. The term 1/? is called the price flexibility coefficient. TYLD is the total yield of crop cp from all fields at all demand sites in the river basin. The profit function of municipal and industrial water use (PTMI) in one demand site is given as (Rosegrant, personal communication, 1997): )'/11( ' 1 1 dm t dm t dmt dm dm dm t dm NMWD WSMI NMWDmvPMI ? ? + ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? +?= (3-39) 94 where, mv : marginal value of water, ?? : elasticity of demand of water, NMWD : normal demand, which is a function of population and industrial production, WSMI : water supply for municipal and industrial use. The total water use benefit (TWB) in the river basin includes off-stream bene- fits from irrigation, municipal & industrial water use, and in-stream benefits from power generation (HP) and ecological water use value (EB), which is expressed as: () WECOvecoPWcpwppw PMIPITWB t t tst t ststst dm t t dmdm ??? ?? ?+??+ ? ? ? ? ? ? += (3-40) where, PW : power generation from hydropower station st in month m, ppw : power selling price, cpw : power generation cost, WECO : water for ecological use, and veco : socio-economic value from per unit of ecological water use under the condition of water scarcity. The annual fixed investments on water delivery, irrigation and drainage, and drainage disposal are calculated as: ? ???= t t dmdmdmdm WDEDSdsinvDSAINV __ (3-41) 95 ??? ???= tsafd t fdsadmdmdmdm PNEDNdninvDNAINV ,, __ (3-42) ??? ???= tsafd t dm,sa,fddmdmdm DNEDPdpinvDPAINV __ (3-43) ??? ???= t t fdsadm sa fd t fdsadmdmfdsadm WFLDEIRirinvIRAINV ,,,,,, __ (3-44) where, AINV_DS : annual investment for improving water delivery & distribution systems, AINV_DN : annual investment for improving drainage collection systems, AINV_DP : annual investment for improving drainage disposal/treatment systems, AINV_IR : annual investment for improving irrigation system, inv_ds : annual investment for per unit of water saving from delivery & distribution systems, inv_dn : annual investment for increasing one unit of artificial drainage from the drainage collection system, inv_dp : annual investment for increasing one unit of drainage disposal in the drainage disposal systems, inv_ir : annual investment for per unit of water saving from irrigation systems. The total investment within the river basin is limited by total tax income and additional government payment, which is expressed as: 96 )1( )____( rgpMESTAX IRAINVDPAINVDNAINVDSAINV dm dm dm dmdmdmdm +?? ?+++ ? ? (3-45) where rgp is the ratio of government input to the local input, and all other items are defined as before. 3.5 SUMMARY The basic components and structure of an integrated hydrologic- agronomic-economic-institutional model at the river basin scale are discussed in this chapter. Beginning with a review of the background for integrated hydro- logic-agronomic-economic-institutional modeling at the river basin scale, the es- sential hydrologic, agronomic, and economic components and the inter- connections between these components are described. The next chapter is to apply this integrated model to the case study area for a one-year short-term analysis in water resources management. 97 Chapter 4 The Model Applied for Short-Term Analysis The integrated hydrologic-agronomic-economic-institutional model de- scribed in Chapter 3 is applied to the study area, the Syr Darya River basin of Central Asia, for water management analysis within a one-year time horizon. We define the model for this purpose as a short-term model. The short-term model is a large-scale, nonlinear optimization model, which includes all essential hydro- logic, agronomic, economic and institutional relationships in one endogenous sys- tem. The major state variables of the short-term model include monthly reservoir storage, soil moisture content, aquifer water table, soil salinity level, and salt con- centrations in rivers, reservoirs and aquifers. The major flow process variables include flow in the surface water system, evapotranspiration, deep percolation, drainage and return flow from irrigation fields, groundwater discharge, and salt concentration associated with all these processes. The decision variables are com- posed of the following four classes: ? Reservoir/aquifer operations, including reservoir release and groundwater pumping; ? Water uses, on-farm water allocation to specific crop fields, drainage re- use, and source blending for various crops; ? Infrastructure improvements, including improvements to water delivery and distribution efficiency, irrigation efficiency, drainage collection effi- ciency, and drainage disposal facilities; and ? Irrigated area, irrigated area for the major crops planted in the study area. 98 Economic parameters, such as crop prices, water supply price, and tax on salt discharge, and subsidies for infrastructure improvement are all taken in the model as external data. However, scenario analysis on each of these items is con- ducted to provide information for examining various policies for water resources management at the river basin scale. Further, and tax on salt discharge is used as a decision variable in the long-term model discussed later. The short-term model is used to study the performance of the complex, in- tegrated hydrologic-agronomic-economic river basin system, and then determine whether this type of model can provide useful information for sustainability analysis and decision-making in water resources management of irrigation- dominated river basins. In this chapter, data and assumptions are first described, then, in order to verify that the results from the model are reasonable, the results are compared to some published studies. Finally, the analytical issues are discussed to determine the capacity of the model for examining sustainable water resources management at the river basin scale. 4.1 DATA AND ASSUMPTIONS FOR THE CASE STUDY 4.1.1 Hydrologic data and assumptions As shown in Figure 1.3, the basin-wide node-link network of the study area includes 11 river reaches, 11 reservoirs, 6 aquifers, 5 hydropower stations, and 6 water demand sites, and return-flow linkages between these entities. The model is built on this network and the farm (demand site) ? soil plot ? crop field concept described in Chapter 3. The long-term average inflow to rivers and reservoirs is presented in Table 4.1, and the standard deviation of these flows is shown in Table 4.2. Analysis of a long flow record for the primary basin tributaries shows that a log-normal distri- 99 bution fits the inflow to the basin. Figure 4.1 shows the relative frequency func- tion of the log-inflow to Toktogul Reservoir (the largest reservoir in the basin), calculated from samples and the fitted distribution, respectively. A 2 ? test (Haan, 1977) shows that distribution can not be rejected at the 95% confidence level. Calculation of the relative frequencies is based on 84-year records of the inflow to the Toktogul Reservoir (Gidroproekt, 1976). The long-term average local source from runoff collection is given in Ta- ble 4.3. Table 4. 1. Long-term average monthly inflow (km 3 ) to the Syr Darya River basin (Raskin, et al., 1992). River/ Reserv. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total Right_in 0.012 0.012 0.019 0.074 0.184 0.192 0.141 0.124 0.079 0.036 0.032 0.027 0.932 Shimi_in 0.003 0.003 0.003 0.003 0.003 0.003 0.005 0.005 0.004 0.003 0.003 0.003 0.041 Aksu_in 0.015 0.015 0.013 0.015 0.018 0.03 0.044 0.026 0.017 0.021 0.016 0.014 0.244 Tok_rev 0.371 0.336 0.415 0.652 1.518 2.374 2.135 1.442 0.779 0.563 0.457 0.399 11.441 Kurp_rev 0.015 0.012 0.011 0.016 0.043 0.057 0.07 0.057 0.041 0.035 0.026 0.022 0.405 Sham_rev 0.043 0.052 0.062 0.233 0.369 0.292 0.18 0.1 0.07 0.066 0.064 0.054 1.585 Utch_rev 0.002 0.002 0.006 0.015 0.02 0.014 0.011 0.009 0.004 0.004 0.005 0.004 0.096 Andj_rev 0.183 0.206 0.476 1.206 1.856 1.91 1.534 0.846 0.411 0.387 0.44 0.393 9.848 Chakir_rev 0.254 0.249 0.383 0.999 1.922 2.283 1.955 1.341 0.691 0.45 0.358 0.339 11.224 Bugun_rev 0.164 0.131 0.179 0.409 0.348 0.315 0.261 0.171 0.106 0.093 0.081 0.086 2.344 Total 1.062 1.018 1.567 3.622 6.281 7.47 6.336 4.121 2.202 1.658 1.482 1.341 38.16 100 Table 4. 2. Standard deviation (km 3 ) of the monthly inflow to the Syr Darya River basin. River/Resv. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Right_in 0.001 0.001 0.003 0.009 0.033 0.037 0.029 0.028 0.014 0.005 0.005 0.003 Shimi_in 0.000 0.000 0.001 0.000 0.000 0.001 0.001 0.001 0.001 0.000 0.001 0.000 Aksu_in 0.001 0.001 0.002 0.002 0.003 0.006 0.009 0.006 0.003 0.003 0.003 0.001 Tokgul_rev 0.059 0.046 0.053 0.231 0.418 0.796 0.682 0.372 0.167 0.091 0.075 0.068 Kurp_rev 0.001 0.001 0.002 0.002 0.008 0.011 0.014 0.013 0.007 0.005 0.004 0.002 Sham_rev 0.002 0.004 0.010 0.030 0.066 0.056 0.037 0.023 0.012 0.009 0.010 0.005 Utch_rev 0.000 0.000 0.001 0.002 0.003 0.003 0.002 0.002 0.001 0.001 0.001 0.000 Andjan_rev 0.009 0.014 0.077 0.154 0.330 0.368 0.313 0.192 0.071 0.051 0.069 0.038 Chakir_rev 0.013 0.017 0.062 0.128 0.341 0.440 0.399 0.304 0.119 0.059 0.056 0.033 Bugun_rev 0.008 0.009 0.029 0.052 0.062 0.061 0.053 0.039 0.018 0.012 0.013 0.008 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 123456789101112131415161718192021222324 Range Numbers Relative Frequency sample, fs(xi) fitted, p(xi) Figure 4. 1 Relative frequency function of the monthly inflow to the Toktogul Reservoir. 101 Table 4. 3. Average monthly local sources (km 3 ) (Raskin, et al., 1992). Demand sites Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total Fergana 0.091 0.075 0.067 0.099 0.295 0.521 0.763 0.67 0.291 0.168 0.133 0.125 3.298 Mid_syd 0.003 0.002 0.005 0.016 0.015 0.007 0.005 0.003 0.002 0.003 0.005 0.005 0.071 Low_syd 0.055 0.043 0.085 0.145 0.059 0.018 0.015 0.01 0.007 0.009 0.006 0.008 0.46 Total 0.149 0.12 0.157 0.26 0.369 0.546 0.783 0.683 0.3 0.18 0.144 0.138 3.829 Table 4.4 shows the characteristics of the major reservoirs in the Syr Darya basin. The three reservoirs, Toktogul, Kayrakum, and Chardara, located at upstream, middle-stream, and downstream respectively, are the major reservoirs in this basin. Table 4. 4. Major water storage facilities of the Syr Darya basin. Reservoir Active storage capacity (km 3 ) Dead storage capacity (km 3 ) Toktogul 14.0 5.5 Chardara 4.7 1.0 Kayrakum 2.55 1.48 Chakir 2.08 0.35 Andjan 1.64 0.15 Bugun 0.37 0.007 Farhad 0.30 0.15 Kassan 0.25 0.02 Kurpskaya 0.029 0.341 Utchkurgan 0.012 0.04 Tashkumur 0.006 0.134 Shamdalsai 0.005 0.039 Hydropower stations are associated with five upstream reservoirs, Tok- togul, Utchkurgan, Kurpskaya, Tashkumur, and Shamdalsai. The characteristics of these stations are presented in Table 4.5. Currently the Toktogul hydropower station is the largest one. The water head for the four reservoirs downstream of Toktogul is kept constant throughout each year, and hydropower generation for 102 these stations only depends on the inflow to these reservoirs (McKinney and Cai, 1997). Table 4. 5. Hydropower Station Data for the Syr Darya River Basin. Station Production capacity (MW) Efficiency (%) Maximum pool eleva- tion (m) Tailwater elevation (m) Head on turbine (m) Toktogul 864 0.85 900 700 200 Kurpskaya 576 0.85 724 618 106 Tashkumur 162 0.85 628 568 60 Shamdalsai 69.12 0.85 572 540 32 Utchkurgan 129.6 0.85 540 504 36 Few data related to the aquifers in the study area were available for this research. Assuming each demand site has a single aquifer, all water distribution losses and deep percolation occurring at a demand site are assumed to go to the aquifer associated with the demand site. Pumping from an aquifer is limited by the pumping capacity. Table 4.6 gives, for each demand site, the pumping capac- ity in 1987 (Raskin, et al., 1992), water table depth (EC, 1995), estimated surface area and yield coefficient, and estimated ratio of aquifer discharge to water table ( hq /=? , eq. 3-28). As discussed in Section 3.4.3.6, ? is a coefficient to be calibrated by local experiments, which is not available for this case study. This value was estimated by trial-and-error, in which the calculated aquifer discharge is compared to the value provided by another study (EC, 1995). 103 Table 4. 6. Aquifer characteristics. Aquifers with demand sites Pumping capacity (10 9 m 3 ) Water table depth (m) Surface area (1000 ha) Yield coefficient Initial salt conc. (g/l) hq /=? (10 -5 ) Naryn_gw 1.00 10.0 163 0.35 0.9 1.4 Ferga_gw 4.80 2.0 1300 0.36 1.2 1.6 Midsyd_gw 1.00 3.5 690 0.32 1.3 1.7 Chakir_gw 1.00 5.5 400 0.30 1.2 1.8 Artur_gw 0.25 3.0 162 0.30 1.3 1.7 Lowsyd_gw 0.25 7.5 530 0.32 1.4 2.0 Following Raskin, et al. (1992), 6 demand sites are located according to the geographic, climatic and political conditions. Table 4.7 shows the monthly average reference evapotranspiration (ET 0 ); Table 4.8 gives the monthly average precipitation (estimated according to EC, 1995), and Table 4.9 presents the stan- dard deviation of the monthly average precipitation. Analysis of long precipitation records in the study area shows that a normal distribution fits the monthly average precipitation . Figure 4.2 shows the fitted relative frequency vs. relative frequency calculated from samples of precipitation data. Calculation of the relative frequen- cies is based on 92-year records of the precipitation observed at station Lenin at the middle stream of the Syr Darya River basin. Table 4. 7. Monthly average reference evapotranspiration (ET 0 , in mm) (EC, 1995). Demand sites Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fergana 12 24 51 99 141 174 180 150 99 51 21 12 Artur 20 30 36 40 158 188 226 220 138 75 45 40 Chakir 18 30 54 96 141 180 186 159 108 57 27 15 Mid_syd 21 30 51 99 168 243 285 252 177 102 45 24 Low_syd 25 35 50 73 192 344 347 290 150 87 60 40 Naryn 12 24 49 90 130 154 170 140 85 47 19 12 104 Table 4. 8. Long-term monthly average precipitation (TR in mm) (World Bank, 1996). Demand sites Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fergana 23.0 21.0 30.0 21.0 20.0 11.0 6.0 3.0 2.0 13.0 22.0 20.0 Artur 17.1 17.5 22.6 25.5 18.0 3.4 2.8 1.2 2.8 10.3 16.5 26.4 Chakir 35.5 36.4 57.2 49.6 26.9 6.1 3.5 0.7 2.6 22.1 27.0 32.2 Mid_syd 22.2 23.6 26.0 29.9 23.0 4.4 3.2 1.5 3.1 11.8 22.4 31.7 Low_syd 42.8 41.1 48.4 46.6 28.8 11.5 6.5 4.9 7.6 24.9 43.0 41.8 Naryn 24.0 20.0 26.0 25.0 16.0 8.0 5.0 10.0 6.0 12.0 20.0 25.0 Table 4. 9. Standard deviation of monthly average precipitation (mm) (World Bank, 1996). Demand site Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fergana 3.7 3.9 6.2 4.6 4.9 4.8 4 2 1 4.6 5.3 3.4 Low_syd 3.8 4.7 7.1 8.5 6.2 2.3 2 1.2 2 5.1 5.4 5.8 Mid_syd 6.8 6.4 11 10 7.1 2.2 4 0.5 1.3 8.4 7.7 6.7 Artur 3.4 4.3 5.8 7.1 5.5 2.1 2 1 1.7 4.4 4.7 4.7 Chakir 3.2 4.5 4.8 4.4 3.8 2.7 2 1.2 1.2 4 5.8 4.6 Naryn 3.9 3.7 5.4 5.5 3.9 3.5 3 6.6 2.8 4.2 4.8 4.3 0 0.02 0.04 0.06 0.08 0.1 0.12 12345678910112131415161718192021 Range Numbers Rel a ti ve Fr equency fs(xi) p(xi) Figure 4. 2. Relative frequency function of the monthly precipitation at middle stream of the Syr Darya River basin. 105 Three soil types, sandy clay (scl), loam (l), and sandy loam (sl) are classi- fied for each demand site. The available irrigated area with the soil types in each demand site is shown in Table 4.10, which is based on a soil distribution study by EC (1995). The physical characteristics of the three soil types are shown in Table 4.11, which are estimated based on Eagleson (1978). Table 4. 10. Available irrigated area (1000 ha.) with soil types. Demand sites Sand clay(scl) Loam (l) Sand loam(sl) Total Fergana 190.0 855.0 255.0 1300.0 Artur 15.6 106.4 40.0 162.0 Chakir 52.0 208.0 140.0 400.0 Mid_syd 71.5 398.5 220.0 690.0 Low_syd 82.0 260.0 188.0 530.0 Naryn 16.9 111.1 52.0 180.0 Total 428 1939 895 3262 Table 4. 11. Soil characteristics. Pore connectivity index (c) Connectivity and Tortuosity (m) Saturat. matric potential (?s) Demand sites scl l sl scl l sl scl l sl Fergana 9.4 9.0 8.2 0.457 0.546 0.686 55.4 83.6 86.4 Artur 8.8 8.6 8.2 0.457 0.546 0.686 55.4 83.6 86.4 Chakir 9.4 9.0 8.0 0.502 0.546 0.730 69.5 83.6 86.5 mid_syd 9.0 8.5 8.0 0.457 0.508 0.686 55.4 83.9 86.4 Low_syd 8.8 8.6 8.0 0.464 0.546 0.730 54.8 83.6 86.5 Naryn 9.3 9.0 8.2 0.502 0.546 0.686 69.5 83.6 86.4 Hydr. conductivity (K in cm/day) Satur. field capacity (Zs) Permanent wilting point (Zw) Demand sites scl l sl scl l sl scl l Sl Fergana 5.06 5.39 6.13 0.355 0.342 0.322 0.225 0.186 0.186 Artur 5.06 5.39 6.13 0.355 0.342 0.322 0.225 0.186 0.186 Chakir 4.90 5.39 6.58 0.348 0.342 0.315 0.212 0.186 0.182 mid_syd 4.87 5.40 6.13 0.355 0.342 0.322 0.225 0.186 0.186 Low_syd 5.06 5.39 6.58 0.347 0.342 0.315 0.218 0.186 0.182 Naryn 5.06 5.39 6.13 0.348 0.342 0.322 0.212 0.186 0.186 106 Salinity in the Syr Darya River increases from upstream to downstream. The ranges in 1987 are upstream: 0.36-0.6 S/dm, mid-stream: 1.40 ? 3.01 dS/m, and downstream 2.16 ? 2.81 dS/m (EC, 1995). Soil salinity in the basin demand sites has the similar spatial tendency as salinity in the Syr Darya River. In the upstream demand sites (Naryn and Fer- gana), the degree of soil salinity is low. At middle stream, the percent of land with moderate salinity (Sodium content, 3-6 me Na in100g soil) is about 30%, and the percent with severe salinity (Sodium content, 6-12 Me Na in100g soil) is about 11%. Downstream, over 50% of the land is has moderate salinity, and over 8% has severe salinity. 4.1.2 Agronomic data and assumptions Cotton dominates irrigated cropping throughout the basin, with more than 40% of irrigated land planted to cotton. Alfalfa and other forages are second in importance to cotton. The reason for this is the established rotation between cot- ton and forages, which maintains soil fertility and provides winter-feed for live- stock due to food security concerns. Cereal crops have increasingly replaced cot- ton in the area since the independence of the Central Asian republics in 1991. Of the cereals, the small grains like wheat have shown the greatest increase. In the middle stream and upstream of the basin, the percentage of irrigated land in small grains is over 20%. Maize is one of the crops most likely to be grown from mid- summer following winter wheat. Cotton, grains and forages account more than 85% of irrigated cropping except in downstream, where rice occupies more than 15% - 22% of irrigated land. The remainder is a wide variety of fruits and vegeta- bles grown largely for local consumption. 107 Five crops are considered in the research here: cotton, forage, wheat, maize, alfalfa (perennial forage), and all other crops are grouped into one single crop. The growth periods of these crops are: cotton (April - Sept.), forage (Oct. ? Mar.), wheat (Nov. ? May), maize (June - Sept.), alfalfa (perennial), and other (Mar. ? Nov). Considering the rotation relationships, these crops are grouped into four types of crop combinations, namely, cot-foa representing cotton and forage, wht-maz, representing wheat and maize, alf_alf, representing perennial alfalfa, and oth_oth representing all other crops. In a soil plot, four types of crop fields corresponding to the four crop combinations are defined. Soil water and salinity balance, and crop water application are modeled in each field. Crop coefficients of evapotranspiration ,k c , (FAO, 1977) are presented in Table 4.12. The empirical salinity coefficients (Mass and Hoffman, 1979) are shown in Table 4.13. Crop yield response coefficients (FAO, 1977) are shown in Table 4.14, and maximum crop productions (dry matter) are shown in Table 4.15. The maximum crop production is calculated by methods described in FAO (1979), in which the maximum crop production depends on solar radiation, tem- perature, and crop characteristics. Table 4. 12. Crop coefficient of evapotranspiration (k c ). Crop Fields Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec cot_foa 0.80 0.80 0.90 0.50 0.80 1.10 1.20 0.90 0.70 0.50 0.50 0.50 wht_maz 0.50 0.85 1.20 0.95 0.60 0.85 1.20 0.95 0.60 0.50 0.40 0.30 alf_alf 1.00 1.00 0.40 0.45 0.80 1.05 1.10 1.05 1.10 1.10 1.10 1.00 oth_oth 1.00 1.00 0.60 0.70 0.80 1.08 1.15 1.10 1.05 0.90 0.70 1.00 Table 4. 13. Empirical salinity coefficients, slope and threshold (Mass and Hoffman, 1979). Salinity coefficient. Cotton Forage Wheat Maize Alfalfa Other Slope (B) 0.139 0.08 0.132 0.083 0.14 0.095 Threshold (S?) 7.7 3 1.8 1.8 2 2.5 108 Table 4. 14. Crop yield response coefficients (k y ). Crops Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec cotton 0.00 0.00 0.00 0.20 0.30 0.75 0.60 0.30 0.25 0.00 0.00 0.00 wheat 0.40 0.90 1.10 0.70 0.50 0.00 0.00 0.00 0.00 0.20 0.10 0.10 maize 0.00 0.00 0.00 0.00 0.00 0.90 1.20 0.70 0.20 0.00 0.00 0.00 alfalfa 0.00 0.00 0.70 0.73 0.92 1.00 1.00 0.90 0.80 0.75 0.70 0.00 forage 0.70 0.80 0.80 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.20 0.20 other 0.00 0.00 0.30 0.40 0.45 0.60 0.75 0.70 0.60 0.40 0.30 0.00 Table 4. 15. Maximum crop productions (YM, dry matter in ton/ha). Demand sites Cotton Wheat Maize Alfalfa Forage Other Fergana 1.63 4.10 7.10 5.70 7.00 5.00 Artur 1.60 4.09 7.05 5.70 7.00 5.00 Chakir 1.60 4.10 7.03 5.70 7.00 5.00 Mid_syd 1.62 4.12 7.00 5.70 7.00 5.00 Low_syd 1.61 4.10 7.03 5.70 7.00 5.00 Naryn 1.60 4.05 7.00 5.70 7.00 5.00 4.1.3 Data and assumption about on-farm irrigation and drainage infrastruc- ture According to the investigation of EC (1995), the average length of canal per hectare of irrigated land in the basin is 33m, which is rather high in view of the large size farms. Three quarters of the canals in the area are unlined; the ma- jority of irrigated land, 56% overall, is served by furrow irrigation, and only 8% of land is under more sophisticated methods such as drip and sprinkler irrigation. Some 70% of irrigated land is artificially drained, about 62% is drained by grav- ity, with little or no sub-surface drainage. Table 4.16 shows the estimated average water delivery and distribution efficiency and drainage ratio (drained area to total irrigated area) for each demand site. Table 4.17 shows the estimated irrigation ap- 109 plication efficiency over all demand sites, soil types, and crop fields. All these efficiencies are based on EC (1995). Table 4. 16. Estimated Water distribution & delivery efficiency and drainage fraction (base value). Demand sites Water distribution and delivery efficiency (EDS) Drainage efficiency (EDN) Low_syd 0.64 0.67 Artur 0.65 0.66 Chakir 0.61 0.72 Mid_syd 57 0.5 Naryn 0.59 0.47 Fergana 0.56 0.8 Average 0.60 0.64 Table 4. 17. Estimated irrigation application efficiency (EIR, base value). Demand site &Soil type cot_foa Wht_maz alf_alf oth_oth Fergana.scl 0.57 0.5 0.63 0.64 Artur.scl 0.6 0.52 0.53 0.62 Chakir.scl 0.55 0.5 0.55 0.65 Mid_syd.scl 0.54 0.52 0.54 0.65 Low_syd.scl 0.61 0.54 0.53 0.62 Naryn.scl 0.54 0.48 0.5 0.55 Fergana.l 0.52 0.46 0.58 0.58 Artur.l 0.55 0.47 0.48 0.56 Chakir.l 0.5 0.46 0.5 0.59 Mid_syd.l 0.49 0.47 0.49 0.59 Low_syd.l 0.56 0.49 0.48 0.56 Naryn.l 0.49 0.44 0.46 0.5 Fergana.sl 0.6 0.42 0.53 0.62 Artur.sl 0.5 0.43 0.44 0.59 Chakir.sl 0.46 0.42 0.46 0.56 Mid_syd.sl 0.45 0.43 0.45 0.56 Low_syd.sl 0.51 0.45 0.44 0.6 Naryn.sl 0.45 0.4 0.42 0.46 Average 0.53 0.47 0.50 0.58 110 4.1.4 Economic data and assumptions The cost of surface water supply (cs) is 3-6 $ per 1000 m 3 , and groundwa- ter pumping cost (cg) is 5-8 $ per 1000 m 3 (EC, 1995), the estimated surface and groundwater prices are presented in table 4.18. Crop fixed cost (fc) and crop val- ues (vc) are estimated based on the World Bank?s Aral Sea Basin study report (World Bank, 1996), which are shown in Table 4.19 Table 4. 18. Surface and groundwater supply cost (cs and cg in US$/m 3 ). Items low_syd artur chakir mid_syd naryn fergana Surface water price (cs) 0.004 0.004 0.006 0.006 0.005 0.005 Groundwater price (cg) 0.006 0.006 0.006 0.006 0.005 0.006 Table 4. 19. Crop prices (pcp) and fixed crop planting cost (fc). Items cotton Wheat Maize forage alfalfa Other Prices (vc in $/ton) 767.5 181.4 140.1 134.6 110.5 240.0 Fixed cost (fc in $ /ha.) 393.3 200.3 287.8 165.1 156.2 350.0 Data for infrastructure investment are estimated based on the EC?s report (Annex 4.5, Vol. II, EC, 1995). Table 4.20 shows the annual investment (ainv_ds, $/m 3 ) necessary for improving canal lining, which is represented by annual in- vestment for one cubic meter of water saved through the improved system. The annual investment (ainv_dn, $/ha) necessary for improving the on-farm drainage system is shown in Table 4.20 too, which is represented by annual investment for one hectare of irrigated land. The annual investment (ainv_ir, $/m 3 ) necessary for improving on-farm irrigation methods, for different crop fields, is given in Table 111 4.21. This item represents the annual investment for one cubic meter of water saved through the improved irrigation system. Table 4. 20. Annual investment necessary for improved water distribution system and drainage collection system. Demand Sites Water distribution System (ainv_ds, $/m 3 ) Drainage collection System (ainv_dn, $/ha.) Low_syd 0.02 700 Artur 0.02 70 Chakir 0.016 750 Mid_syd 0.017 700 Naryn 0.012 650 Fergana 0.014 800 Table 4. 21. Annual investment (ainv_ir, US$/m 3 ) for improved on-farm irrigation systems. Demand sites cot_foa Wht_maz alf_alf oth_oth Fergana 0.03 0.03 0.03 0.02 Artur 0.03 0.03 0.03 0.023 Chakir 0.035 0.035 0.035 0.022 Mid_syd 0.04 0.04 0.04 0.02 Low_syd 0.045 0.045 0.045 0.022 Naryn 0.025 0.025 0.025 0.023 The cost of drainage water reused (cr) for irrigation purposes lies within the range of $54 - 73 per 1000m 3 , about ten times of the cost of supplying irriga- tion water from the river system. Drainage disposal to the desert is a popular method in the study area. The cost for this purpose (cdt) is about $0.1/m 3 (EC, 1995). Average hydropower power generation cost (cpw) is estimated as 0.05 $/kWh, and the economic value of power (ppw) is about 0.08 $/kWh (World Bank, 1996). Maintaining a required volume of inflow to the Aral Sea, the destination of the Syr Darya River is a main ecological concern in water resources manage- 112 ment in the study area. In order to consider the Aral Sea as a separate ?user? of water, the historic record of flows in the Syr Darya River at Kazalinsk, in the far downstream reach of the river, is used as a measure of the flows to the sea. The annual inflow to the sea is about 7.0 km 3 in a normal hydrologic year and 10.0 km 3 in a wet year. Anderson (personal contact, 1996) gave an estimation of the economic value of $0.1/m 3 water flowing into the Aral Sea. In this research, we assume an ecological benefit (or damage) expression as: )( low0inflow-infeveben ?= (4-1) where inflow: computed annual inflow to the Aral Sea, inflow0: normal annual inflow to the sea by historic records, ev: economic benefit (inflow ? inflow0 >0), or damage (inflow ? inflow0 <0), per unit of inflow. The ecological benefit calculated from equation 4-1 does not directly rep- resent the real ecological benefit. Formulating the ecological benefit in this way maintains downstream flow for ecological purposes to the extent normally re- quired, while presenting a measure of the tradeoff between the benefit from eco- logical water uses and that from other uses. However, this policy-based approach should be verified before it is applied for policy analysis in water resources man- agement in any area. Municipal and industrial (M&I) water use benefit is not explicitly consid- ered in the case study. Irrigation water demand covers more than 80% of the total water demand in the Syr Darya basin. Municipal and industrial water demand has the first water supply priority, and it will be satisfied in any analytical cases. 113 Therefore, the benefit of M&I water supply is assumed to be constant, and it is not included in the objective function of the optimization model. Table 4.22 shows the M&I water demand in 1987(Raskin, et al., 1992). The penalty tax on excessive salt discharge is initially assumed to be 10$/ton. The model is run under various values of this item so as to search for an appropriate value. Table 4. 22. Monthly industrial and municipal water demands in 1987 (km 3 ). Demand Sites Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Naryn 0.018 0.018 0.033 0.024 0.054 0.066 0.085 0.074 0.026 0.016 0.013 0.018 Fergana 0.112 0.113 0.211 0.151 0.342 0.424 0.542 0.473 0.169 0.104 0.080 0.114 Mid_syd 0.079 0.080 0.149 0.107 0.242 0.300 0.384 0.335 0.119 0.074 0.057 0.081 Chakir 0.071 0.072 0.133 0.096 0.217 0.269 0.344 0.300 0.107 0.066 0.051 0.072 Artur 0.020 0.021 0.038 0.028 0.063 0.078 0.099 0.086 0.031 0.019 0.015 0.021 Low_syd 0.046 0.046 0.086 0.062 0.139 0.173 0.221 0.192 0.069 0.042 0.033 0.046 4.1.5 Data availability and reliability As stated above, multi-disciplinary data are required for model. The data availability is a critical factor in successfully applying the model. The data for the case study were directly found or estimated from some previous studies (e.g., EC, 1995; World Bank, 1996, Raskin, et al., 1992, etc.), and other related literatures, or calculated based on some intermediate data. However, it is beyond the effort of this research to verify all the data. Therefore, the results presented in this re- search are limited to demonstrating the kind of information can be derived from the model for decision support in sustainable water resources management. How- ever, the results should not be taken as real solutions to the case study area with- out further data verification. 114 For future application of this model in any real study, data reliability will be a great challenge even it is possible to obtain all required data. Hydrologic data should be studied based on extensive historic climatic records (e.g., precipitation, flow, temperature) and appropriate hydrologic modeling (e.g., runoff and inflow, evaporation /evapotranspiration, effective rainfall). Agronomic data such as maximum crop yield, crop evapotranspiration coefficients, crop response coeffi- cients to water stress and soil salinity are mostly based on empirical studies and should be verified for the study area. Economic data such as water value, crop cost and price, infrastructure investment, penalty tax, are related to external eco- nomic analysis. Therefore, beyond the model developed in this research, far more work is needed, and without those supporting works, the results from this model may not be applied usefully. 4.2 MODEL VERIFICATION: COMPARE MODEL RESULTS TO OTHER STUDIES It is beyond the effort of this research to calibrate and verify the model to the study area due to limitations of time and resource (i.e., data) availability. However, in order to check if results from the model are reasonable, we can com- pare the modeling results to those published in other papers and reports. Raskin et al. (1992) applied a simulation model (Water Evaluation and Planning System, WEAP) to the study area, which presented outputs on water balance in the river basin network and water allocation among the demand sites. (EC, 1995, Vol. II and III) provided some data on flow and salinity balance, crop production, and economic outputs in the study area. Most of WARMAP?s data are from field ob- servation, survey, and empirical estimation. Based on these two sources, we can check the results of the model developed in this research. The base year is selected as 1987, since this is also the base year used in the simulation model of Raskin et al. The WARMAP?s outcomes are also around this year. Raskin et al defined 1987 as a wet year for the Syr Darya River basin, 115 and they provided the surface water sources and groundwater availability, as well as agricultural and non-agricultural water demands. The same data was used in the short-term model, and the following tables (Tables 4.23 ? 4.30) present the comparisons between the results of this model and those of WEAP and WAR- MAP. Table 4. 23. Comparison of flow diversions from rivers and reservoirs (km 3 ). River & Resv. WEAP This model Toktogul Resv. 1.83 1.39 Farhad Resv. 12.09 13.60 Kazah gate 7.00 8.10 Andjan Resv. 0.00 6.84 Karadar_in 9.57 1.20 Karadarya total 9.57 8.04 Chakir Resv. 10.76 9.83 Naryn gate 2.56 4.80 Artur gate 1.00 3.34 Bugun Resv. 2.13 0.09 TOTAL 47.00 49.70 Table 4. 24. Comparison of water diversion to demand sites (km 3 ). Demand sites WEAP This Model Naryn 1.83 1.39 Fergana 12.13 13.24 Mid_syd 12.10 13.68 Chakir 10.76 9.83 Artur 3.13 3.45 Low_syd 7.01 8.11 Total 46.95 49.71 The total water application (river diversion, pumping and local surface water) is 57.8 and 60.0 km 3 from WEAP and this model, respectively, and the flow to the Aral Sea is 2.51 and 3.36 km 3 , respectively, in the two models. The 116 total drainage is 18.6 km 3 from this model in a normal year, and WARMAP?s es- timation is 17-19 km 3 . Table 4. 25. Annual salt discharge (million tons). Ranges WARMAP 1 This Model 2 Upstream of Kayrakum Reservoir 14 12 Kayrakum to Chardara Reservoirs 10 11 Lower part of Syr Darya 1 1.5 Total 25 24.5 1 1983-1990 average; 2 with tax on salt discharge of 100 US$/ton Table 4. 26. Comparison of salt concentration (g/l) in drainage (annual average) * Demand sites WARMAP1 This model Naryn 0.35-1.5 1.28 Fergana 1-2.7 1.84 Mid_syd 1.9-5.6 2.78 Chakir 0.35-5.7 1.89 Artur 1.6-4.6 1.49 Low_syd 1.6-4.6 2.55 * Toryanikova (1998) showed the salt concentration in drainage as: in upstream river reaches, 1 ? 2.68 g/l; in midstream river reaches, 2.0 ? 5.6 g/l, and in downstream river reaches, 1.2 ? 5.2 g/l. 117 Table 4. 27. Comparison of salt concentration (g/l) in the Syr Darya River. Ranges WARMAP This model upstream 0.3 ? 0.5 0.36-0.57 middle 0.9-2.0 0.76-2.14 low 1.4 -1.9 0.89-2.01 Table 4. 28. Comparison of irrigated area (1000 ha). Demand sites WEAP This model Naryn 173.1 165.6 Low_syd 445.1 340.8 Artur 173.0 145.5 Chakir 462.0 462.0 Mid_syd 680.0 553.0 Fergana 1365.6 1238.5 TOTAL 3298.8 2905.4 Table 4. 29. Comparison of water use rate (m 3 /ha) for selected crops. Cotton and forage Wheat and maize Demand Sites WEAP 1 This model 2 WEAP 1 This model 2 Naryn 7542 8550 7008 7700 Low_syd 8653 8150 6960 7400 Artur 7347 8400 5536 7200 Chakir 9443 9850 7756 7700 Mid_syd 10901 9750 11802 8100 Fergana 9485 9850 9040 7700 Average 8895 9092 8017 7633 1 Estimated from the data used in the WEAP model (Raskin et al., 1992) 2 and the soil type is loam. 118 From the above comparisons, the results from this model, including flow, salinity distribution, and water use for irrigation are close to those from the other studies. However, from Table 4.23, we see this model results in quite different reservoir operation. For example, this model shows demand site Fergana with- draws 6.84 km 3 water from the Andijan Reservoir, but the withdrawal was 0 in 1987 from WEAP model. This model also shows too much water was applied at the midstream demand site in 1987. Furthermore, the model implicates that per- haps the irrigated area in 1987 should have been reduced by 12% in the basin based on the optimal objective and other all considerations in the model. The verification of the crop production function is addressed in the follow- ing. Based on FAO crop yield-water relationship (see eq. 3-4), crop yield has a linear relation with actual crop evapotranspiration (ETA). Running the model un- der various hydrologic levels, we get a set of values of (Yield, ETA). This set of values and those calculated directed from equation (3-4), are plotted in Figure 4.3. The results from the modeling experiments are well fitted with the FAO empirical equation. However, currently little information is available to check the economic outputs from the model. The feasibility of the economic incentives are need to be verified based on further study. 119 0.72 0.77 0.82 0.87 0.92 0.97 28 30 32 34 36 Actual ET (cm) Relative Yield (YR) from model experiments from FAO equation Figure 4. 3. Actual ET vs. relative crop (wheat) yield (in demand site Mid_Syd, and the soil type is loam). 4.3 ANALYTICAL ISSUES OF THE INTEGRATED MODEL The model output includes values for all state variables, process variables, and decision variables described at the beginning of this chapter, with spatial di- mensions (demand sites, soil plots, crop fields) and time dimensions (month and year). The model results are analyzed in this section in order to show the analyti- cal functions of the model. Based on the results, the major research questions in- clude: what policy implications does this model point out for sustainable water management in irrigation-dominated river basins? Why is the integration of hy- drologic, agronomic and economic components at the river basin scale necessary 120 for sustainability analysis? Finally, what are the limitations of the short-term model presented here? 4.3.1 Implications for hydrologic system operations In the integrated hydrologic-agronomic-economic-institutional modeling framework, hydrologic system operations are connected to (1) infrastructure fa- cilities (e.g., water distribution and delivery systems, irrigation and drainage sys- tems, drainage reuse, and drainage disposal and treatment facilities), (2) climatic conditions (e.g., precipitation and all factors related to crop evapotranspiration), (3) soil type and salinity condition, and (4) crop patterns. Since the model has multiple time periods, decision on hydrologic system operations will also be af- fected by the timely requirements of irrigation for various crops. At the river basin scale, spatial heterogeneity of water sources and water demands, and externalities due to upstream water diversion and return flow are considered for optimal social benefit of the river basin area through economic in- centives, as well as institutional directives (water rights). 4.3.1.2 Sensitivity analysis on major hydrologic parameters Various scenarios are defined for inflow, effective rainfall (ER), and refer- ence evapotranspiration (ET 0 ) for sensitivity analysis, and the results are shown in Table 4.30-32, respectively. All numbers in these tables are relative values. Under the scenarios of effective rainfall, we assume that the total rainfall does not change from what shown in Table 4.8, and the increase or decrease of ER is due to the status of runoff collection for irrigation. Runoff irrigation is an effective management measure for irrigation in arid and semi-arid areas (Ben-Ashir and Berliner, 1994). For simplicity in this case, we do not consider investment or O&M costs of runoff irrigation. 121 The profit from irrigation (IP) is very sensitive to the inflow and the ET 0 , especially when the inflow decreases (15% decrease in IP in a dry year) and the ET 0 increases, but the profit is less sensitive to the ER (lossing inly 5% when ER decreases by 25%). Since ER accounts for less than 15% of the total irrigation water in the basin, increasing or decreasing the ER by 25% does not have much effect on irrigation profit. Irrigated area has a similar sensitivity to these parame- ters with irrigation profit. When ET 0 decreases by 15%, irrigation area increases by 14%. However, when ET 0 increases by 15%, irrigation area decreases only by 3%. As expected, hydropower profit (HP) is very sensitive to inflow, but it is not sensitive to ET 0 or ER. Flow to the Aral Sea increases by 10% when ET 0 increases by 15%, and it increases by 6% when ET 0 decreases by 15%. When ET 0 increases, crop water demand increases, and irrigation water supply becomes less profitable, more flow stays in the river and goes to the Aral Sea; while, when ET 0 decreases, crop water demand decreases, and water going to irrigation or ecological use depends on the marginal value of water for irrigation and ecological use. When water supply for irrigation reaches a certain level, additional water supply to irrigation becomes less profitable or unnecessary, and then more water goes to the ecological use. Total water use benefit (TWB), including profits from irrigation (IP), power generation (HP) and benefits from ecological uses (EB), is not sensitive when ET 0 increases. The increase of ET 0 makes water for irrigation less profitable, and irrigation profit decreases; however, since more water goes to the ecological use (1.1 times of the normal value), benefit from this use increases. Finally the decrease of irrigation profit is offset by the increase in the ecological benefit. The same explanation can be given to the non-sensitivity of the total benefit to ER. 122 From these tables we can also make some observations about salinity. In- creased inflow results in a lower salt concentration in the surface water outflow of the basin, less salt mass entering the groundwater, and lower soil salinity. Higher ET 0 causes lower salt concentration in the surface water outflow of the basin, and more salt mass entering the groundwater, and higher soil salinity. High ER use results in higher salt concentration in the surface water outflow of the basin, higher salt mass entering the groundwater, and higher soil salinity, which shows that a high level of runoff irrigation may produce negative environmental effects, as well as a positive contribution to irrigation profit in a short-term analysis. Table 4. 30. Sensitivity analysis of inflow to the basin (relative values). Inflow (relative In- flow) Irrigation profit (IP) Hydro- power profit (HP) Flow- to-aral Total- benefit (TBEN) Salt conc. In downstr. (Ss) Salt. In percol. (Sp) Salinity in root zone (Sf) Irrigation Area (AF) Dry (0.80) 0.85 0.68 1.00 0.86 1.00 1.04 1.00 0.93 Normal (1.00) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Wet (1.17) 1.06 1.29 1.07 1.07 0.98 0.93 0.93 1.02 Table 4. 31. Sensitivity analysis of reference ET 0 (relative values). ET 0 (relat. Value) Irrigation profit (IP) Hydro- power profit (HP) Flow- to-aral Total- benefit (TBEN) Salt conc. In downstr. (Ss) Salt. In percol. (Sp) Salinity in root zone (Sf) Irrigation Area (AF) High (1.15) 0.87 1.01 1.10 0.99 0.95 1.02 1.02 0.97 Normal (1.00) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Low (0.85) 1.17 1.00 1.06 1.11 1.05 0.90 0.93 1.14 123 Table 4. 32. Sensitivity analysis on effective rainfall (relative values). Eff. Rainf. (re- lat. Value) Irrigation profit (IP) Hydro- power profit (HP) Flow- to-aral Total- benefit (TWB) Salt conc. In downstr. (Ss) Salt. In percol. (Sp) Salinity in root zone (Sf) Irrigation Area (AF) High (1.25) 1.08 1.00 0.94 1.01 1.02 1.01 1.02 1.01 Normal (1.00) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Low (0.75) 0.95 1.00 1.05 0.99 0.97 0.98 0.96 0.99 Notation Flow-to-aral = annual downstream flow to the Aral Sea; Conc. in downstr. = annual average salt concentration in downstream flow; Salt in percol. = salt mass in deep percolation to groundwater, result from demand site mid_syd; the soil type is loam; the crop field is cot-foa; and Salinity in root zone = result from demand site: mid_syd, soil type: loam; crop field: cot-foa. 4.3.1.2 Reservoir operation Eleven reservoirs are considered in the river basin network (See Figure 1.3). Among them, Toktogul, Kayrakum, and Chardara Reservoirs, located at up- stream, middle-stream, and downstream, respectively, provide the major flow regulation in this basin. Five upstream reservoirs, Toktogul, Utchkurgan, Kurp- skaya, Tashkumur, and Shamdalsai have hydropower stations. This section dis- cusses the combined operation of the three major reservoirs under three cases: (1) for irrigation water supply only; (2) for irrigation and hydropower generation; and (3) for irrigation, hydropower generation, and soil and water quality maintenance. It should be noted that two other large reservoirs exist in the basin but they are on the main tributaries to the main stem of the Syr Darya river; Andijan reservoir on the Karadarya River and Charvak reservoir on the Chirchik River, respectively. In case 1, the objective function of the model does not include profit from hydro- power generation (HP), and the constraints do not include salt balance or trans- port at any levels, i.e., there are no constraints on salt concentrations in any river, reservoir or aquifer, and there are no limits on soil salinity, and the effect of soil salinity to crop production is not considered. Case 2 is case 1 with the inclusion of 124 the hydropower generation profits. Case 3 is case 2 with the inclusion of the salin- ity balance and salinity effect to crop production. In each of the three cases the model is run with multi-year average inflow (Table 4-1) and current agricultural and economic data described in Section 4.1. We define reservoir utilization efficiency (RUE) as the ratio of actual util- ized storage to the total available storage. For a system including multiple reser- voirs, we define this ratio using the sum of the storage of all reservoirs. RUE shows how much of available storage capacity is used for flow control within a time period, and the high value of RUE shows more flow is effectively controlled by reservoirs. Figure 4.4 shows the RUE in each month under the three cases. The average annual RUE is 0.288 for case 1, 0.324 for case 2, and 0.329 for case 3. The RUE is increased from case 1 to case 2 due to additional reservoir storage used for hydropower generation, and the RUE is increased from case 2 to case 3 due to additional reservoir storage used for salinity control. The major reservoirs on the Syr Darya River were designed for multiple-year flow regulation, however, the time horizon of the short-term model is just one year, this is why the RUEs under various cases are low. The values of RUE also depend on the initial storage of reservoirs in this one-year model. We assume the initial storage for the major reservoirs is one-third of the full storage of those reservoirs, and the ending stor- age is equal to the initial storage for all these reservoirs. The long-term operation will be discussed in Chapter 7. One of the major sources of the Syr Darya River is the Naryn River in the mountainous Kyrgyz Republic. This source is controlled by the cascade of Tok- togul reservoir plus the four downstream constant volume reservoirs. The Tok- togul Reservoir controls more than 30% of the total inflow to the basin, and has the largest hydropower station in the area. The other four hydroelectric power sta- tions have relatively small and constant storage, and minor drainage inflow, and 125 they depend on the release from the Toktogul Reservoir for hydropower genera- tion. These five hydropower stations provide over 80% of the installed generating capacity in the Kyrgyz Republic, where the peak demand for domestic power oc- curs in winter. 0.15 0.2 0.25 0.3 0.35 0.4 12345678910112 Month RUE irri. irri.+hydropower irri.+hydropower+salt ctrl. Figure 4. 4. Reservoir utilization efficiency. However, the downstream countries (mainly Uzbekistan and Kazakstan), which do not have much local water source, but do have large irrigated lands, must rely on the water releases of the upstream reservoirs, and their peak demand for irrigation water occurs in the summer. Since the major runoff period occurs in the summer, the Kyrgyz Republic would like to release some water in the summer period, which helps to meet the downstream irrigation needs; but at the same time, they would like to store water for power generation in the winter when there is little runoff. The Kyrgyz Republic?s preferred release during April to Septem- 126 ber is generally expected to be less than the downstream irrigation requirement, except in a wet year. 0 1 2 3 4 5 6 7 12345678910112 Month Storage (km 3 ) irri. irri.+hydropower irri.+hydropower+salt ctrl. Figure 4. 5. Storage of the Toktogul Reservoir under the three operational cases. 0 0.5 1 1.5 2 2.5 3 12345678910112 Month S t orage (km 3 ) irri. irri.+hydropower irri.+hydropower+salt ctrl. Figure 4. 6. Storage of the Kayrakum Reservoir under the three operational cases. 127 0 0.5 1 1.5 2 2.5 3 3.5 12345678910112 Month Storage (km 3 ) irri. irri.+hydropower irri.+hydropower+salt ctrl. Figure 4. 7. Storage of the Chardara Reservoir under three operational cases. 0.15 0.65 1.15 1.65 2.15 2.65 12345678910112 month release (cubic km.) irri. irri.+hydropower irri.+hydropower+salt ctrl. Figure 4. 8. Releases of the Toktogul Reservoirs under three operational cases. Release in the vegetation period (Apr. ? Oct.) is 6.43, 3.77, 3.87 km 3 in the three cases, respec- tively. The total release in one year is 10.23, 10.34, 10.48 km 3 , respectively. 128 0 0.5 1 1.5 2 2.5 3 12345678910112 Month Release (km3) irri. irri.+hydropower irri.+hydropower+salt ctrl. Figure 4. 9. Releases of the Kayrakum Reservoirs under three operational cases. Release in the vegetation period (Apr. ? Oct.) is 11.37, 10.67, 11.23 km 3 in the three cases, respec- tively. The total release in one year is 14.95, 14.99, 15.94 km 3 , respectively. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 12345678910112 month Release (km 3 ) irri. irri.+hydropower irri.+hydropower+salt ctrl. Figure 4. 10. Releases of the Chardara Reservoirs under three operational cases. Release in the vegetation period (Apr. ? Oct.) is 7.33, 7.33, 7.47 km 3 in the three cases, respec- tively. The total release in one year is 10.18, 10.21, 10.28 km 3 , respectively. 129 Combined with Toktogul Reservoir, the other two major reservoirs, Kay- rakum and Chardara, have been utilized to solve the upstream and downstream conflict. The two reservoirs, located at midstream and downstream of the basin respectively, are designed for seasonal regulation of Toktogul release and flood- ing control. The results from the model developed in this research show that the combined utilization of the three reservoirs can also provide facilities for salinity control, as well as solving the timing problem between upstream hydropower generation and downstream irrigation. In winter periods, Toktogul releases water for power generation, and the released water can be stored in Kayrakum and Chardara Reservoirs for water supply to irrigation and salt dilution in summer pe- riods. Figures 4.5-4.7 show the reservoir active storages vs. months, and Figures 4.8-4.10 show reservoir releases vs. months, of the three major reservoirs under three cases. In Case 1, reservoir operation is only driven by water supply, which is mainly for irrigation. The releases of all reservoirs follow irrigation water de- mands, which increase in March, remain high from June to August, and decrease in non-irrigation periods (Oct. ? Mar.). In Cases2 and 3, the releases from Tok- togul Reservoir are higher in winter and other periods. The releases of the other two reservoirs are not very different from those in Case 1, because they are only driven by irrigation demand (an upper bound constraint is set for flooding con- trol). However, the storage behaviors of these two reservoirs are different for various purposes. The Kayrakum Reservoir stores water in non-irrigation periods and almost dries up in irrigation periods. From Case 1 to Case 3, the storage in the non-irrigation period is increased, due to (1) in Cases 2 and 3 Toktogul reservoir releases more in non-irrigation periods; (2) in Case 3 more storage is needed for salt dilution. For the downstream region, salt concentration in drainage and 130 groundwater is higher, and Chardara Reservoir keeps more water in storage in most periods in Case 3 than Cases 1 and 2 in order to avoid higher salinity. Figure 4.11 shows the salt concentration (at the end of a month) in flows along the Syr Darya River in months from June to September. The return flow inlets along the river are shown in the Figure. The drainage from upstream de- mand sites Naryn and Fergana causes the salt concentrations to increase in river reaches from Naryn_gate to Right_in. The natural inflow to Karadar_in and Right_in may dilute the drainage, therefore the increasing magnitude of salinity is not very significant. From Right_in to the Kayrakum Reservoir, the salt concen- trations decrease slightly in all the months except increasing lightly in August. Through the Kayrakum Reservoir the salt concentrations in all the months stay constant until river reach Shimi_in, where drainage from demand site Mid_syr causes an abrupt salinity increase. Inflow to Chakir_in, and the storage of the Chardara Reservoir dilute the drainage, and after the Chardara Reservoir, the salt concentrations show less fluctuation. In June and July, the Kayrakum and Chardara Reservoirs have more ca- pacity for salt dilution than in August and September. Salinity at the end of a month affects crop production in the next month, i.e., salinity at the end of June, July and August affect crop production in July, August and September, respec- tively. Since peak withdrawal for irrigation occurs in June, July and August, res- ervoir operation has a stronger influence on salt dilution in June and July than in August and September, in the peak irrigation demand periods the water with- drawal has lower salinity helping increase crop production. Unlike Kayrakum Reservoir located at the mid-stream, Chardara Reser- voir has to keep enough water in storage for downstream ecological release re- quirements in each month, and therefore no consecutive dry periods occur with this reservoir. 131 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 tokgul_re v tok_dow n n aryn _gat e ka radar_i n rig ht_i n kay kum _re v aks u_ in farhad shim i _i n chakir_ i n chard a_re v aris_in artur_gat e kazah_gat e Model nodes (upstream --> downstream) Concentration (g/l) Jun Jul Aug Sep nary n fergan a fer g an a c hak i r low_sy d mid_syd Figure 4. 11. Salt concentration along the Syr Darya River (in a normal year). 4.3.1.3 Basin-wide salinity distribution analysis Beside water shortage, salinity is another serious problem in the study area. In this section, we discuss both the spatial and the temporal distribution of salinity at a basin-wide scale. The ?third-party? effect of irrigation drainage is demonstrated through the modeling results. As discussed above, Figure 4.11 shows the salt concentration along the Syr Darya River. Neglecting other factors that may affect salinity distribution in 132 the study area, our modeling results show that the salinity change in the river is due to drainage from irrigation fields distributed along the river. The peak salt concentration happens in river reach Shimi_in, which is caused by drainage from demand site Mid_Syr. From the Farhad Reservoir to river reach Chakir_in, more than 80% of the river flow is diverted to Mid_Syr, the site of the major Uzkeb di- version for the ?hungry? steppe region, in the irrigation months (June, July, and August), and about 45% of the water withdrawn returns back to the river, with higher salinity (about 1.5 ? 2.5 times of the salinity in water withdrawn, depend- ing on the month). Even with the dilution from natural inflow and reservoir stor- age, the salinity with the water withdrawal is higher for the downstream demand sites than for the upstream demand sites. As described in Appendix D, the return flow from upstream demand sites is responsible for the salinity increase at down- stream river reaches. Figure 4.12 shows the average monthly salt concentration in water with- drawal for irrigation water supply in each demand site. The downstream demand sites Low_Syr and Artur have the highest salt concentration. Demand site Chakir is supplied by a local tributary, where the salt concentration is relatively low and constant. Figure 4.13 shows the salinity affecting coefficient (ks, eq. 3.22) for the same crop with the same soil type, at each demand site. Note that the salinity af- fecting coefficient in a period is a function of soil salinity, which is affected by soil salinity accumulation in the previous periods, and salinity in irrigation water in the current period. 133 0 0.2 0.4 0.6 0.8 1 1.2 1.4 12345678910112 Month Concentration (g/l) naryn fergana chakir mid_syd artur low_syd Figure 4. 12. Average monthly salt concentration in mixed water supply. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 12345678910112 Month salinity affecting coefficient naryn fergana chakir mid_syd artur low_syd Figure 4. 13. Average monthly salinity affecting coefficients (ks) (soil: loam; crop pattern: wheat-maize). 134 Salinity variation with time periods (months) depends on irrigation period scheduling, as well as the temporal distribution of natural sources. From Figure 4.13, we notice that the salinity at the end of September is higher than that of June, showing that the drainage effect is most significant just after the major irri- gation months. Soil salinity increases through the major irrigation months, and reaches its peak at the end of the season. Therefore, the salt concentration in drainage water is highest in September, a period just after the peak irrigation months. After the peak irrigation period, if there is considerable rainfall, the drain- age amount may have a high salt concentration since crops consume less water during this period. This process is called salt leaching, which can create better soil salinity conditions, but may also result in worse surface and ground water salinity if drainage is not well treated. Figure 4.14 shows soil salinity (saturated extrac- tion), salt mass entering the root zone and salt mass leaving the root zone. Obvi- ously, the salt leaching in this case is not enough, since the soil salinity increases. This figure also shows that if drainage is not appropriate, then irrigation moti- vated by a short-term objective may produce poor soil salinity conditions. Addi- tional issues about salt leaching will be discussed later in this chapter. Salt concentrations in the three major reservoirs vs. months are presented in Figure 4.15. In this model, the Toktogul Reservoir is not affected by drainage from crop fields, the salinity in this reservoir varies only with the salinity in natu- ral inflow. The salinity in Kayrakum and Chardara reservoirs reaches a peak in the late irrigation season (around Sept.), when the amount of drainage from crop fields is high. 135 0 0.5 1 1.5 2 2.5 3 3.5 12345678910112 Months Soil salinity (dM / S) / salt mass (million tons ) Soil salinity Salt in (million ton) Salt out (million ton) Figure 4. 14. Soil salinity change through irrigation periods (demand site: Fergana, soil type: loam; crop field: cot_foa). 0 0.2 0.4 0.6 0.8 1 1.2 1.4 12345678910112 Month Concentration (g/l ) tokgul_rev kaykum_rev charda_rev Figure 4. 15. Average monthly salt concentration in reservoirs. 136 Note that the salinity in reservoir storage (Figure 4.15) and the soil salinity (Figure 4.14) are significantly higher at the ending time period (Dec.) than those in the starting period (Jan.). This ending effect means the water use (mainly irri- gation) has imposed negative impacts to the environment, which is obviously not desirable. This effect can be managed in the long-term modeling that takes ac- count of salinity accumulation. Another problem that the short-term model can not deal with is the groundwater salinity. The model shows that the groundwater salinity does not change significantly in a one-year time horizon. This is normal since generally only a long-term percolation process may affect groundwater sa- linity significantly. 4.3.2 Irrigation and drainage management Irrigation and drainage management is a conjunctive part of basin-wide sustainable water resources management, especially in irrigation-dominated ba- sins. Once water withdrawn from surface water systems or pumped from ground- water sources are determined, irrigation and drainage management measures will be necessary to satisfy crop water demands, while conserving limited water re- sources and not producing any environmental problems. The main practical as- pects of irrigation are the determination of how much water to apply to a given crop and when to apply the water. The ideal situation would be avoidance of wa- ter stress throughout the growing season, yet having no losses. Basically, drainage systems are installed for (1) trafficability so that field operations such as seedbed preparation, planting and harvesting can be conducted in timely manner; (2) for protection of the crop from excessiveive soil water condition; and (3) for salinity control (Skaggs and Murugaboopathi, 1994). In this section we analyze some is- sues including irrigation water application and infrastructure improvements. 137 4.3.2.1 Blending irrigation water supplies Four kinds of sources for on-field irrigation water sources are considered in the model, including surface water (river and major canal diversion and local surface source), groundwater, drainage reuse, and effective rainfall. Table 4.33 shows the ratios of these sources for cotton and wheat under a normal hydrologic level, and Table 4.34 presents the seasonal average salt concentrations of these sources. The blending of these sources to a specific crop depends on the salinity of these sources, previous soil salinity, as well as crop salinity tolerance. The ac- cessibility of sources to a specific crop field is not yet considered in the model, but the total availability is limited. Cotton has much higher salinity tolerance than wheat so that more sources with higher salinity (groundwater and field drainage) can be used for cotton than for wheat in all demand sites. No drainage reuse is applied to cotton and wheat in demand site Mid_Syd, due to the high salt concentration in drainage. Downstream demand site Low_Syd reuses more field drainage for cotton. Demand site Mid_Syd has the lowest effective rainfall. This is another rea- son for the high salinity in the drainage from the demand site. Table 4. 33. Ratios of sources to total irrigation water application (Under a normal hydrologic level). Crops Cotton Wheat Demand Sites Surface water Groud water Drainage reuse Rainfall Total Surface water Ground water Drainage reuse Rainfall Total Naryn 0.103 0.700 0.057 0.140 1.000 0.413 0.413 0.020 0.153 1.000 Low_syd 0.175 0.492 0.112 0.220 1.000 0.776 0.000 0.028 0.196 1.000 Artur 0.588 0.237 0.083 0.137 1.000 0.748 0.029 0.038 0.143 1.000 Chakir 0.570 0.250 0.044 0.136 1.000 0.608 0.181 0.041 0.170 1.000 Mid_syd 0.185 0.708 0.000 0.107 1.000 0.869 0.032 0.000 0.099 1.000 Fergana 0.478 0.399 0.014 0.109 1.000 0.525 0.364 0.005 0.106 1.000 138 Table 4. 34. Annual average salt concentration (g/L) in different sources (Under normal hydrologic level). Demand Sites Naryn Fergana Chakir Mid_syd Artur Low_syd Surface water 0.541 0.572 0.692 0.793 0.945 0.917 Ground water 1.066 1.193 1.194 1.294 1.199 1.399 Drainage 1.159 1.871 1.146 2.15 1.99 2.12 Rainfall - - - - - - 4.3.2.2 Irrigation efficiency As defined in section 3.4.3, irrigation efficiency (EIR) used in the model is the ratio of water effectively used by crops to the total water application. The ad- vanced irrigation systems have higher irrigation efficiency. Therefore, high irriga- tion efficiency means more water conservation, which is very important for com- petitive water uses, and water storage for long-term risk aversion. On the other hand, irrigation systems with high irrigation efficiency produce less percolation, which is necessary for salt leaching in farms where soil salinity is a serious prob- lem. Soil salinity accumulation may result from long-term irrigation actions with- out sufficient leaching. Tables 4.35 and 4.36 show four modeling scenarios of EIR in a dry year. With the increase of EIR, both irrigation profit and total benefit increase. How- ever, as shown in Table 4.36, with the increase of irrigation efficiency, field per- colation decreases, and soil salinity increases. The determination of irrigation ef- ficiency should be studied in a long-term framework, considering both economic benefit and environment consequence. 139 Table 4. 35. Analysis on irrigation efficiency (EIR): Economic benefit. Ratio of Assumed to primary efficiency (R) Irrigation profit (IP) (billion $) ?(IP) 1 / ?(R) 2 Total bene- fit(TWB) (billion $) ?(TWB) 3 / ?(R) 1.00 1.604 2.289 1.15 1.808 1.36 2.460 1.14 1.30 1.924 0.77 2.526 0.44 1.40 1.937 0.13 2.559 0.33 1 ?(IP) change of irrigation profit 2 ?(R) change of ratio of assumed to primary efficiency 3 ?(TWB) change of total water use benefit. Table 4. 36. Analysis on irrigation efficiency (EIR): Environmental problem (Result from demand site Fergana, soil type is loam). Cotton-forage Wheat-maize Ratio of Assumed to primary efficiency (R) Percola- tion (cm) Soil sa- linity (dm/s) Water use per ha. (m 3 ) Percola- tion (cm) Soil sa- linity (dm/s) Water use per ha. (m 3 ) 1.00 47.2 1.657 12891 33.2 1.992 8612 1.15 43.1 1.777 11236 29.6 2.14 7286 1.30 34.1 1.989 10164 28.8 2.159 7310 1.40 29.2 2.033 8153 20.9 2.207 6846 4.3.2.3 Water distribution and delivery efficiency The current average water distribution and delivery efficiency (EDS) for each demand site is shown in Table 4.16. A model scenario with improved EDS is defined, in which EDS is increased to 0.8 for all demand sites (about 15% in- crease of the current value), and Table 4.37 compares this scenario to the scenario with the current EDS in a dry year. In the improved scenario, less total water di- version produces more irrigation profit and total benefit. The increase of total benefit (0.601) is larger than that of irrigation profit (0.423), which shows that less withdrawal for irrigation produces more hydropower or/and ecological bene- 140 fit, as well as irrigation profit. That is, a 5% decrease in total water diversion produces a 26% increase in total net benefits. Table 4. 37. Analysis on water distribution and delivery efficiency (based on a ?dry? hydrologic level). Water Diversion (WD, km 3 ) EDS Total Benfit (TWB) (billion $) Irri. Profit (IP) (billion $) Irrigated Area (10 3 ha.) (AF) Naryn Ferg- ana Mid- Syr Chakir Artur Low- syr Total Original 2.319 1.59 2105 0.92 9.87 5.69 5.02 2.48 3.23 27.21 Improved 2.919 2.01 2105 1.05 10.97 4.31 4.94 2.05 2.64 25.96 Ratio 1.26 1.27 1.00 1.14 1.11 0.76 0.98 0.83 0.82 0.95 4.3.2.4 Drainage reuse and disposal Drainage effluent currently accounts for about 35% of water available for use within the study area, and it is an important source in the area. However, its on-field reuse can be problematic, and is a contributory factor to soil and ground- water salinisation. Drainage disposal/treatment is thus necessary when drainage with high salinity seriously pollutes soil and water systems. Tables 4.38 and 4.39 show scenario analysis on drainage reuse. Table 4.38 shows positive contributions to irrigation profit and total benefit when the amount of drainage reuse is in- creased. However, these contributions are short-term values, the soil salinity prob- lem shown in Table 4.39 may ultimately decrease the positive contributions when accumulated soil salinity exceeds the crop salinity tolerance, and groundwater sa- linity exceeds its standard. Since more drainage is reused in fields, less drainage is disposed to the river system, the salt concentration in downstream flow decreases for the scenario of larger reuse amount, but this is also a short-term result. Modeling results show that drainage disposal to the desert can increase ir- rigation profit only in a wet year. For example, the model result shows 0.784 km 3 141 drainage disposal can increase irrigation profit $10 million, and total benefit $13 billion $. Again the short-term model is not able to deal well with the drainage disposal issue since it does not consider long-term environmental benefits. Table 4. 38. Drainage reuse scenario analysis: Short-term benefit (based on a ?dry? hydrologic level). Scenarios (reuse amount) (km 3 ) Irrigation profit (IP) (billion $) Total benefit (TWB) (billion $) 0 1.563 2.094 0.71 1.579 2.170 1.42 1.593 2.242 2.06 1.604 2.289 Table 4. 39. Drainage reuse scenario analysis: Environmental problems (based on a ?dry? hydrologic level). Scenarios (reuse amount) (km 3 ) Conc. in drainage 1 (g/l) Soil salinity 2 (dS/m) Conc. in downstr. 3 flow (g/l) 0.00 1.33 1.58 1.07 2.06 1.75 2.38 1.02 1,2 Seasonal average salt concentration 1 or saturated extract 2 in demand site fergana; soil type, loam; crop field: wht-maz. 3 Annual average salt concentration. 4.3.2.5 Salt leaching Salt leaching is often necessary to sustain crop production over time. The amount of leaching required depends upon the crop, the salinity of the irrigation water, soil characteristics, and management. The leaching fraction (LF) is defined 142 as the ratio of water that drains below the root zone to the volume of water ap- plied. Tables 4.40 and 4.41, show that (1) the LF for crop field wht-maz is larger than that for cot-foa, since wheat and maize have lower salinity tolerances than cotton and forage; (2) the LF values in winter are largest, because of less crop consumptive use in winter periods; and (3) in both cases of crop field, soil salinity in the last period is significantly higher than that in the first period, which may not be realistic. Higher LF may be needed to reduce soil salinity. A long-term model can deal with this problem. Table 4. 40. 1 Analysis on salt leaching: Wheat - maize. Items Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dev Annual Applied water (cm) 1.62 1.34 2.08 8.58 10.82 13.97 20.48 12.00 0.20 0.83 0.84 0.36 73.12 Drained water (cm) 0.68 0.64 0.38 2.24 3.14 3.65 5.45 3.09 0.04 0.15 0.36 0.17 20.44 LF 0.42 0.48 0.18 0.26 0.29 0.26 0.27 0.26 0.20 0.18 0.43 0.46 0.28 ECw (dS/m) 0.81 n/a N/a 0.81 0.90 0.87 0.84 1.79 1.78 n/a n/a n/a ECe (dS/m) 1.09 1.11 1.19 1.19 1.18 1.27 1.40 1.67 2.06 2.12 2.06 1.99 Table 4. 41 2 Analysis on salt leaching: Cotton - forage. Items Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec An- nual Applied water (cm) 1.98 1.28 1.74 1.68 15.52 18.34 20.53 12.26 7.76 1.49 0.95 0.60 84.14 Drained water (cm) 0.62 0.64 0.57 0.23 3.11 3.32 3.75 2.06 1.32 0.35 0.35 0.23 16.84 LF 0.31 0.50 0.33 0.14 0.20 0.18 0.18 0.17 0.17 0.23 0.37 0.38 0.20 3 ECw(dS/m) 0.81 n/a n/a n/a 0.90 0.93 1.75 1.25 1.52 0.45 N/a n/a 4 ECe (dS/m) 1.10 1.12 1.16 1.23 1.16 1.32 1.65 2.03 2.13 2.24 2.20 2.15 1 Result of demand site: Fergana; soil type: loam; crop field: wht-maz., in a normal hydrologic year; 2 Result of demand site: Fergana; soil type: loam; crop field: cot-foa, in a normal hydrologic year; 3 ECw: salinity of irrigation water in dS/m; 4 ECe: soil saturated extraction in dS/m. 143 4.3.3 Agronomic analysis Through the operation of hydrologic systems and irrigation and drainage management, the quantity and quality of water to be applied to specific crop fields in scheduled periods can be determined. The agronomic relationships included in the model determine the crop production. This section demonstrates crop yield as a function of both soil moisture and soil salinity. Figure 4.16 shows the crop yield (YR) vs. soil moisture (z) with the effect of soil salinity. Basically the relation of yield and soil moisture is nonlinear, and the non-linearity is affected by soil salinity. Define dy as the change of crop yield, ks as the salinity affecting coefficient, d(ks) as the change of ks, and dz as the change of the soil moisture. We have the following observations from Figure 4.16: (1) d(YR)/dz decreases as d(ks) increases; and (2) when ks is larger, d(ks) has larger effect on d(YR)/dz. 144 0.7 0.75 0.8 0.85 0.9 0.95 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 soil moisture (Z) Relative yield (YR) Figure 4. 16. Actual ET vs. relative crop(wheat) yield (in Mid_Syd, the soil type is loam). 4.3.4 Economic Analysis In the model presented here, hydrologic system operation and irrigation and drainage management are integrated with economic objectives to maximize the total benefit from irrigation (IP), hydropower generation (HP), and ecological water use (EB). Economic incentives such as water supply prices, crop prices, and taxes on excessive salt discharge are applied to search for more economic and ecological gains, and to avoid serious environmental damages. The economic value of water is evaluated with respect to water application to crops and water withdrawal to demand sites, respectively. Decisions on crop irrigation acreage, water application to crops, and water allocation among demand d(YR)/dz=4. ks=0.282 d(ks)=0.05 ks=0.214 d(ks)=0.224 ks=0.314 d(ks)=0.032 ks=0.560 d(ks)=0.246 d(YR)/dz=4. d(YR)/dz=1.84. d(YR)/dz=3. 145 sites are based on the water values with crops or with demand sites, as well as physical water availability constraints and institutional directives. 4.3.4.1 Economic values of water with crops The economic value of water with a crop (V c , $/m 3 ) is defined as: p fieldto the cror applied nt of watetotal amou tt - other er supply vest - watm crop harprofit fro V c coscos = (4-5) The numerator does not include infrastructure investment, and the de- nominator refers to water arriving to the crop field. Table 4.42 shows the values of V c in a normal year. Irrigation area for crops is determined according to the wa- ter values with crops, as well as some other factors formulated by lower and upper bounds to the irrigation area of a crop in the model. Table 4.43 shows the irrigated area for each crop combination at each demand site. Table 4. 42. Economic value of water with crops (V c , $/m 3 ) (in a normal year). Crop-patterns cot_foa wht_maz alf_alf Oth_oth Naryn 0.171 0.138 0.089 Low_syd 0.113 0.074 0.039 Artur 0.146 0.097 0.059 Chakir 0.152 0.129 0.055 0.084 Mid_syd 0.108 0.075 0.045 0.047 Fergana 0.154 0.119 0.051 0.084 Whole basin 0.141 0.103 0.041 0.081 146 Table 4. 43. Irrigated area (1000 ha.). Crop-patterns cot_foa wht_maz alf_alf oth_oth Naryn 130.5 32.6 16.9 Low_syd 48.6 48.6 12.3 Artur 117.1 15.4 2.3 Chakir 275.6 37.6 34.8 52.0 Mid_syd 490.4 66.3 61.9 10.7 Fergana 882.9 116.1 111.0 190.0 Total 1945.1 316.6 207.7 284.3 Figure 4.17 shows the average economic values for the four crop combina- tions in the whole basin, under three hydrologic levels (dry, normal, and wet). Cot_foa has the highest value (0.12 ? 0.15 $), while alf_alf has the lowest (0.038 ? 0.042 $). For all crop combinations cot_foa and wht_maz, the value in a dry year is the highest, while that in a wet year is the lowest. For alf_alf and oth_oth, the normal year has a highest water value. In a dry year, if the amount of water applied to a crop is too small then either crop yield (production per unit of planted area) or planted area will be sharply reduced due to water stress. Thus, crop profit, which is assumed to be linearly related to crop production, divided by the water applied will still be low. It seems that water application to alf_alf and oth_oth falls in this condition, and for all other crop combinations, reduction of water ap- plication in a dry year will not cause sharp reduction of crop yield or planted area. However, the result shown here is based on a given set of crop prices, and the changes of crop prices will significantly affect the water value with crops, which will be discussed later. 147 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 cot_foa wht_maz alf_alf oth_oth crop combinations V c ($ /m 3 ) dry normal wet Figure 4. 17. Water values with crops. 4.3.4.2 Economic values of water with demand sites Economic value of water with a demand site (V d , $/m 3 ) is defined as: . , , . coscos reusedandpumpednr withdrawnt of watetotal amou investtureinfrastructt - other ter supplycrops - waom revenue fr V d ? = (4-6) Figure 4.18 shows economic values with demand sites in a dry, normal or wet year. The upstream demand site Fergana has the highest value, while the most downstream demand site Low_syd has the lowest one. Water quantity and 148 quality are the two factors explicitly considered in the model, less quantity avail- able and worse water quality makes water less valuable downstream. Relatively high crop evapotranspiration downstream (see Table 4.8), resulting in higher con- sumptive water use, may make water less valuable at downstream demand sites. However, factors other than water, such as various soil capacity and farmer?s in- puts of labor and fertilizer also affect the crop yield, and the economic value of water with demand sites. In this case study, we simply assume that those condi- tions are the same for all demand sites. Hydrologic levels seem to affect downstream and upstream demand sites in different ways. At upstream demand sites, like Naryn and Fergana, where there is more water of better quality available, water value decreases with inflow avail- ability; while at downstream demand sites, where there is less water available and it has worse water quality, water value increases with inflow availability. Water value with demand site, as well as physical water availability and institutional constraints, could be used to determine water allocation among de- mand sites. However, existing agreed allocations of water among the nations of the river basin take precedence over economic allocation of water in the basin. The allocation of water among the basin states has not been considered in this model, but could be easily incorporated as these allocations represent an upper limit of the water that may be used in any demand site, since the demand sites, for the most part, are determined on national boundaries. Table 4.44 shows the ratios of calculated irrigated area to total available irrigated area for each demand site in a dry, normal or wet year. The ratio at the downstream demand site (low_syd) is only 0.21. The difference between demand sites will be addressed in the following sections. Clearly, the model results point out the need to reduce irrigated area un- der drought conditions and this reduction is on the order of 8-17% of irrigated lands in the basin. 149 Table 4. 44. Ratios of calculated irrigated area to total available irrigated area. Hydrologic level Naryn Low_syd Artur Chakir Mid_syd Fergana Dry 0.92 0.21 0.83 0.89 0.91 0.88 Normal 1.00 0.21 0.83 1.00 0.91 1.00 Wet 1.00 0.21 0.83 1.00 1.00 1.00 0 0.02 0.04 0.06 0.08 0.1 0.12 naryn fergana chakir mid_syd artur low_syd demand sites value ($ /m 3 ) dry normal wet Figure 4. 18. Economic values (V d ) with demand sites. 150 4.3.4.3 Crop prices Crop price is one of the economic incentives considered in the model. Ta- ble 4.45 shows results of three model scenarios: the first one used 75% of the primary crop prices (see Table 4.18 for the primary crop prices), the second used the primary prices for all crops, and the third used 125% of the primary prices for all crops. Irrigation profits at all demand sites, especially at the downstream de- mand sites are very sensitive to crop prices. The relative values of the total irri- gated areas are 0.956, 1.000, and 1.134, resulted from these scenarios, respec- tively. That is to say, increasing crop prices by 25% will increase irrigated area by 13.4%, while decreasing crop prices by 25% will decrease irrigated area by 4.6%. For the downstream demand site, Low_syd, when the crop prices increase by 25%, the irrigation profit (IP) increases by 7.26 times. Detailed result shows un- der this case, no irrigated area reduction at Low_syd, while the irrigated area is reduced by 75% with the normal crop prices. Therefore, crop price may be a strong incentive for water allocation and agricultural production in the basin. Wheat ? maize is a potential crop combination replacement for cotton- forage in the study area (EC, 1995). However, results from the model, clearly show that cotton-forage still dominates the crop pattern (Table 4.43). A potential solution to increase the irrigated area of wheat-maize is to increase the prices for wheat-maize. Table 4.46 shows that increasing wheat-maize prices by 25% will significantly increase the irrigated area of wheat-maize. Table 4.47 shows that increasing wheat-maize prices by 50% will make wheat-maize dominate the irri- gated area and significantly increase the irrigated area in demand site Low_syd, as well as the total irrigated area in the study area. Table 4.48 shows the economic values of water with demand sites (V d ) for the three scenarios. 151 Table 4. 45. Irrigation profit vs. crop prices (relative values). Crop price changes Naryn Low_syd Artur Chakir Mid_syd Fergana Total 25% decr. 0.613 0.521 0.120 0.626 0.602 0.640 0.556 Original 1.000 1.000 1.000 1.000 1.000 1.000 1.000 25% incr. 1.369 7.260 1.617 1.372 1.409 1.355 1.571 Table 4. 46. Irrigated area allocation (fraction) vs. wheat-maize prices. Wht_maz price Cot_foa wht_maz alf_alf oth_oth Total total area/ available area Original 0.71 0.11 0.08 0.10 1.00 0.84 25% incr. 0.16 0.58 0.07 0.09 1.00 0.85 50% incr. 0.11 0.73 0.07 0.01 1.00 0.94 Table 4. 47. Ratios of calculated irrigated area to total available irrigated area with various wheat-maize prices. Wht_maz price Naryn Low_syd Artur Chakir Mid_syd Fergana Original 1.00 0.21 0.83 1.00 0.91 1.00 25% incr. 1.00 0.21 0.92 1.00 0.92 1.00 50% incr. 1.00 0.79 0.92 1.00 0.91 1.00 Table 4. 48. Economic values of water ($/m 3 ) with demand sites with various wheat- maize prices. Wht_maz price naryn low_syd Artur chakir mid_syd fergana Original 0.103 0.023 0.068 0.065 0.048 0.086 25% incr. 0.123 0.035 0.083 0.079 0.062 0.098 50% incr. 0.135 0.084 0.103 0.096 0.077 0.118 4.3.4.4 Water prices The model was run under four scenarios of water prices (WP), and some re- sults are shown in Tables 4.49, 4.50 and 4.51. The first scenario uses the original surface and ground water supply prices (Table 4.18), and the other three apply 2, 152 4, and 8 times of the original prices. From Table 4.49, we find that d(IB)/d(WP) <0, d(HP)/d(WP)>0, d(EB)/d(WP)>0, and d(TWB)/d(WP)<0, where IB, HP, and EB are the net profits to irrigation and power production, and benefit to environ- ment, respectively and, TWB is the total net benefit. Total water withdrawal and irrigated area decrease with WP. Table 4.50 shows d(V c )/d(WP)<0 for all crops, and d(V d )/d(WP)<0 for all demand sites. When WP is increased to 8 times of the original value, alfalfa and ?other crops? have negative profit in some demand sites, and negative water value happens in low_syd. Water values for each crop in each demand site with high WP is presented in Table 4.51. Table 4. 49. Analysis on water supply prices 1 . Water prices Irri. Profit, IP (billion $) Hydro- Power Profit, HP (billion $) Ecological Benefit, EB (billion $) Total Benefit, TWB (billion $) Withdrawal (km 3 ) Irr. Area (1000 ha.) Original 2.755 0.187 1.160 4.102 31.70 2753.5 2* original 2.507 0.194 1.162 3.863 31.64 2703.5 4* original 2.002 0.200 1.238 3.439 30.75 2665.4 8* original 1.235 0.205 1.446 2.886 27.81 2600.0 Table 4. 50. Water values for crops and demand sites under various water supply prices 2 . Water values for crops Water values for demand sites Water supply prices Cot_foa wht_maz alf_alf oth_oth Naryn Low_syd Artur Chakir Mid_syd Fergana Original 0.141 0.103 0.041 0.081 0.103 0.023 0.068 0.065 0.048 0.086 2* original 0.133 0.095 0.033 0.073 0.096 0.017 0.06 0.059 0.042 0.08 4* original 0.119 0.081 0.02 0.058 0.084 0.008 0.049 0.047 0.03 0.071 8* original 0.097 0.054 -0.013 0.032 0.059 -0.009 0.026 0.025 0.008 0.054 153 Table 4. 51. Water values for crops in each demand site with high water supply prices 3 . 4 * original water supply price 8*original water supply price Demand sites Cot_foa wht_maz alf_alf oth_oth cot_foa wht_maz alf_alf oth_oth Naryn 0.128 0.115 0.071 0.117 0.083 0.049 Low_syd 0.091 0.051 0.021 0.066 0.027 -0.004 Artur 0.126 0.074 0.014 0.1 0.048 0.006 Chakir 0.131 0.107 0.035 0.062 0.11 0.08 0.008 0.035 Mid_syd 0.085 0.053 0.004 0.025 0.062 0.025 -0.03 -0.004 Fergana 0.132 0.097 0.029 0.062 0.11 0.073 -0.005 0.035 1,2,3 All scenarios are under the normal hydrologic year, all conditions except the water prices are the same for all scenarios. 4.3.4.5 Tax on excess salt discharge As discussed in Section 3.4.5, a tax on excess salt discharge (tax) is an- other economic incentive considered in the model. We consider a range of tax of $10 ? $400 per ton of excess salt mass discharge. Figures 4.19 ? 4.22 show the total benefit (TWB) vs. tax, irrigation profit (IP) vs. tax, total instream water use benefit INB (= hydropower profit (HP) + ecological water use benefit (EB)). vs. tax, and total excess salt mass discharged (SM) vs. tax, respectively. From these results, we have the following observations: 1) d(TWB)/d(tax) >0, and d(IP)/d(tax) >0, when tax? $50.0 per ton, d(TWB)/d(tax) <0, and d(IP)/d(tax) <0, otherwise; 2) d(INB)/d(tax) >0, when tax? $60.0 per ton, d(INB)/d(tax) <0, otherwise; and 3) d(SM)/d(tax)<0 for the whole range. From Figures 4.19 and 4.20, it is seen that a tax of $50 per ton of salt mass discharged appears to be optimal and that taxes above $50 do not improve bene- fits. However, this must be offset by the fact that the instream benefits increase 154 with the tax, as shown in Figure 4.21. Figure 4.22 indicates that a tax in excess of $100 per ton provides negligible decreases in salt mass discharge. 3.8 3.85 3.9 3.95 4 4.05 4.1 4.15 0 50 100 150 200 250 300 350 400 tax ($ /ton) total benefit (billion $ ) Figure 4. 19. Total-benefit vs. tax on salt discharge. 2.4 2.45 2.5 2.55 2.6 2.65 2.7 2.75 2.8 0 50 100 150 200 250 300 350 400 tax ($ /ton) irriga tion be ne fit (billion $ ) Figure 4. 20. Irrigation profit vs. tax on salt discharge. 155 1.34 1.345 1.35 1.355 1.36 0 50 100 150 200 250 300 350 400 tax ($ /ton) instream benefit (billion $) Figure 4. 21. Instream water use benefit vs. tax on salt discharge. 20 25 30 35 40 45 50 55 60 65 70 75 80 0 50 100 150 200 250 300 350 400 tax ($ /ton) salt mass( million t on) Figure 4. 22. Excess discharged salt mass vs. tax on salt discharge. 156 In reality it is difficult to measure return flow from irrigated fields, which is generally non-point flow. Therefore implementing the tax on salt discharge with the return flow may not be realistic. The model developed here can be used as an inexpensive tool to estimate return flow from irrigated fields at specific de- mand sites, and then provide a framework to analyze tax potentially applied for salinity control, as well as other management policies. 4.3.4.6 Irrigation vs. Hydropower generation There exists a tradeoff relationship between the water use for upstream hydropower generation and downstream irrigation. The hydropower sale price (ppw) was varied in a range from $0.08 (base value) to $0.32 per kWh, about 4 times the base value. The hydropower profit (HP) vs. ppw in a normal year is shown in Figure 4.23. From this we see that that d(HP)/d(ppw) >0, and ppw = $0.15 kWh is a critical point, d(HP)/d(ppw) is much larger before this point than that after this point. When ppw is increased from $0.08 to $0.32 kWh, in a normal year, irriga- tion profit decreases from $2.755x10 9 to $2.735x10 9 . It seems that changing the price has small effect on irrigation profit. Figure 4.24 shows a ?tradeoff? relation between hydropower generation and irrigation profit. 157 6200 6250 6300 6350 6400 6450 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 price ($/KWH) power (MWH ) Figure 4. 23. Hydropower generation vs. power price. 0.186 0.187 0.188 0.189 0.19 0.191 0.192 0.193 2.73 2.735 2.74 2.745 2.75 2.755 2.76 Irrigation profit (billion $) H y dropower profit (billion $) Figure 4. 24. Hydropower profit vs. Irrigation profit. 158 4.3.4.7 Economic efficiency of infrastructure investment The effect of infrastructure improvements have been discussed in Section 4.3.2.2?4. In this section, we analyze the economic efficiency of the investments (INV) on water distribution and delivery systems, irrigation and drainage systems, and drainage disposal systems, respectively. Water distribution and delivery systems Assume that the water distribution and delivery efficiency is increased from the base value (Table 4.16) to 0.8 in all demand sites. The ratio of total benefits (TWB) to invested amount for various hydrologic scenarios ?(TWB)/?(INV) and ?(IB)/?(INV) between the base scenario and the improved scenario are shown in Table 4.52. In both scenarios, irrigation and drainage effi- ciencies do not change. At all hydrologic levels, the investment on water distribu- tion and delivery systems is economically efficient. Table 4. 52. Economic efficiency of investment for water distribution and delivery systems. ?(TWB) 1 /?(INV) 2 ?(IP) 3 /?(INV) Dry Normal Wet Dry Normal Wet 6.0 2.0 2.3 3.1 3.7 3.6 1 ?(TWB) : change of total water use benefit (TWB), 2 ?(INV): change of infrastructure investment (INV), 3 ?(IP): change of irrigation profit (IP). 159 Irrigation systems Four scenarios of irrigation efficiency were considered. In the base scenario, irrigation efficiency takes the base value shown in Table 4.17. In the other three scenarios, the irrigation efficiency was 1.15, 1.30 and 1.40 times the base value, respectively. Values of ?(TWB)/?(INV) and ?(IB)/?(INV) for the dif- ferent scenarios are shown in Table 4.53. For example, if irrigation efficiency is increased from the base value to 1.15 times the base value, ?(TWB)/?(INV) is 7.0, 4.0, 3.5 in a dry, normal, or wet year, respectively. The table shows that invest- ment in irrigation systems is economically efficient in all cases and at all hydro- logic levels. The investment is most efficient with a ?dry? hydrologic level and less efficient with a wet level. In a wet year, in view of the irrigation profit, the investment is not attractive. In view of the total benefit, since saved water from irrigation can always be used for instream purposes, the investment is less sensi- tive to hydrologic levels. The incremental benefit to irrigation provides a measure of the amount of funding that might be used to finance irrigation system im- provements. Table 4. 53. Economic efficiency of investment for irrigation systems. ?(TWB)/?(INV) ?(IB)/?(INV) Irrigation System Effi- ciency Change Dry Normal Wet Dry Normal Wet 1.15* base value 7.0 4.0 3.5 5.9 2.8 0.9 1.30* base value 4.3 3.2 3.0 2.4 1.9 0.8 1.40* base value 1.4 1.2 1.2 1.9 0.9 0.6 Average 3.3 3.0 2.9 3.0 2.0 0.7 Results from the model show investment on drainage systems is not eco- nomically attractive. 160 4.3.4.8 Effect of municipal and industrial (M&I) water demand Municipal and industrial water demand accounts for less than 20% of the total water demand in the study area. In the model we assume the M&I water de- mand must be satisfied. However, with the increase of the M&I water demand in the study area, conflict will arise between the M&I water supply and water supply for other purposes such as irrigation and ecological use. To find the effect of the M&I water demand, four scenarios were considered in which the M&I water de- mand is 1.0, 1.25, 1.50, and 2.0 the base value (shown in Table 4.21), respec- tively. The hydrologic level considered is normal, and all other conditions are the same as the base model. Table 4.54 shows the results of these scenarios. Irrigation profit and ecological benefit will be affected, and no change of hydropower profit, when the M&I water demand increases. Table 4. 54. Effect of M&I water demand. Scenarios of M&I water demand (* base value) Irrigation profit IP (billion $) Ecological benefit EB (billion $) Power profit HP (billion $) Total benefit TWB (billion $) 1.00 2.7554 1.3466 0.1866 4.2886 1.25 2.6774 1.3164 0.1866 4.1804 1.50 2.5782 1.2904 0.1866 4.0551 2.00 2.3516 1.2248 0.1866 3.7629 4.3.5 Uncertainty Analysis In the integrated model presented here, uncertainties exist in hydrologic, agronomic, economic and institutional components. Considering the risks associ- ated with these uncertainties is necessary for appropriate decision-making. The integrated model provides a framework to analyze risks based on the inter- 161 relationships between the components considered in the model. In this section we mainly discuss the risks from hydrologic uncertainties, and the effects of hydro- logic uncertainties on agronomic and economic outputs are demonstrated. Due to data incompleteness, risks from agronomic and economic factors will only be ad- dressed normatively. 4.3.5.1 Risk from hydrologic uncertainty-chance-constrained models A large body of studies on stochastic water resources management has appeared in the literature. The models used in those studies include stochastic dy- namic programming models (Louck et al., 1981), chance-constrained models (Mays and Tung 1992), and recourse models (Watkins, 1997). Among these mod- els, chance-constrained models have the simplest structure. A chance-constrain model can be expressed as: abxAP cx ?? ) ~~ ( .. min ts (4-6) where both right hand side coefficient ~ b and technological coefficients ~ A can be random. a is a vector of specified reliability of compliance (or confidence). This kind of models accepts infeasibility, but only with ?small? probability. One of the advantages for the chance-constraint is that the model is not driven by the ?worst? scenario; and another advantage, maybe most advantageous to realistic applica- tion, is that the size of equivalent deterministic model is almost as large as the stochastic model. One of the disadvantages is that magnitude of violation is not captured. This disadvantage can be cleared by using a recourse model, in which infeasibility is corrected at a cost represented by a recourse function. The recourse models have been proved to be proactive methods for stochastic programming (Mulvey et al., 1994, Watkins, 1997). However, to use a recourse model, the 162 equivalent deterministic model has to incorporate a number of scenarios, and the model size is often proportional to the number of the scenarios, which will make the model very large. As described in Chapter 3, the deterministic short-term model is already a large model, and it is necessary to keep the model at an appro- priate size so that it can be solved efficiently. Based on this consideration, in this research, we only use the chance-constrained models to treat hydrologic uncer- tainties, including those of monthly inflow and precipitation. Equation (4-6) represents a linear model and the derivation of its determi- nistic form is given in Mays and Tung (1992). The integrated model described in Chapter 3 is a highly nonlinear model, and we treat the monthly inflow and pre- cipitation as the right hand side coefficient ~ b in water balance equations of reser- voirs, river reaches, and crop root zones. The reservoir and river reaches water balance equations are linear, but the soil water balance equations are nonlinear. However, as shown in Appendix I, if only the right hand side coefficient ~ b is ran- dom, a general stochastic model, linear or nonlinear has the same deterministic form with a linear model. As described in section 4.1.1, a log-normal distribution fits the monthly in- flow of the study area, and a normal distribution fits the monthly precipitation. The statistics of both inflow and precipitation are included in the chance- constrained model. We assume the monthly inflow and the monthly precipitation have the same reliability, i.e., the same vector of reliability (a) of compliance is applied in the right side of equations including the item of inflow or precipitation. For simplicity, the same reliability is applied in each month. We defined six sce- narios, corresponding to the values of reliability 1.00, 0.95, 0.85, 0.75, 0.65 and 0.50 respectively. Based on the above assumptions, a scenario with reliability 1.00 means the reliability of both the monthly inflow and the monthly precipita- 163 tion in all months is 1.00. The standard variates of the random item corresponding to above reliabilities are presented in Table 4.55. Table 4. 55. Reducing slope with reliability in the chance-constrained model (Mays and Tung, 1992). Reliability 50% 65% 75% 85% 95% 100% Reducing slope 0 -0.385 -0.675 -1.037 -1.645 -3.492 In Figure 4.25, we show the results from the six scenarios total benefit (TWB) vs. reliability and the irrigation profit (IP) vs. reliability are plotted. The range of TWB is $3.00-4.04 billion, and the range of IP is $1.91-2.68 billion. Water value for each demand site under the six hydrologic-reliability sce- narios is shown in Table 4.56. Water values for demand sites at downstream (Low_syd and Artur) and at tributaries (Chakir and Artur) are less sensitive to the hydrologic reliability; while for demand sites upstream, the values decrease when the reliability is reduced. Water value for each crop combination is shown in Table 4.57. The val- ues for the major crops decrease when the hydrologic reliability is reduced. Table 4. 56. Water values (US$/m 3 ) for demand sites under hydrologic reliability scenarios. Hydro. Reliability Naryn Low_syd Chakir Artur Mid_syd Fergana Average 100% 0.110 0.022 0.063 0.065 0.015 0.098 0.062 95% 0.110 0.022 0.063 0.066 0.042 0.095 0.066 85% 0.107 0.022 0.063 0.065 0.047 0.092 0.066 75% 0.105 0.022 0.063 0.065 0.048 0.09 0.066 65% 0.104 0.022 0.063 0.065 0.048 0.086 0.065 50% 0.103 0.023 0.068 0.065 0.048 0.086 0.066 164 Table 4. 57. Water values (US$/m 3 ) for crops under hydrologic reliability scenarios. Hydro. Reliability Cot_foa wht_maz alf_alf oth_oth 100% 0.179 0.103 0.041 0.058 95% 0.158 0.103 0.041 0.063 85% 0.149 0.103 0.041 0.065 75% 0.146 0.102 0.041 0.075 65% 0.144 0.102 0.040 0.078 50% 0.141 0.101 0.040 0.081 1.5 2 2.5 3 3.5 4 4.5 0.40 0.50 0.60 0.70 0.80 0.90 1.00 reliability benefit (billion $ ) irrigation benefit total benefit Figure 4. 25. Irrigation profit & socio-benefit vs. Hydrologic reliability. 165 4.3.5.2 Risk from other uncertainties Because of the data incompleteness, risk analysis of agronomic and eco- nomic factors could not be performed for this case study. However, risks from the uncertainties of these factors should have the same important impact to the out- comes of water uses, as hydrologic uncertainties do. Among the agronomic pa- rameters, the one with the largest uncertainty may be the maximum crop produc- tion (Table 4.15), which is the crop production under perfect conditions, water, soil, fertilizers, labor input, etc. Many factors may bring uncertainty to the estima- tion of this parameter. In economic parameters, crop prices and water supply prices, which are affected by many socio-economic factors, are most uncertain. Although no systematic risk analysis is presented for these parameters, results under various scenarios of these parameters are already shown above, which may help to understand the effect of the uncertainties associated with these parameters. If a probability distribution is available for any of these parameters, the chance-constrained model applied to handle hydrologic uncertainties could be effectively used for analyzing agronomic and economic uncertainties. 4.4 CONCLUSIONS The major purpose of this chapter is to answer the following two ques- tions: Why is the integrated hydrologic-agronomic-economic model recom- mended for sustainability analysis? Why is the short-term model not enough for sustainability analysis? Through the results from various scenarios of the short- term model, the performance of the integrated hydrologic-agronomic-economic model applied in irrigation dominated river basins has been demonstrated. We show that hydrologic system operations are derived by agricultural productivity and instream water use (hydropower and ecological use). Irrigation and drainage management, as a conjunctive part for basin-wide sustainable water resources management, has important contributions to the outcomes of water uses. Eco- 166 nomic analysis explores the economic values of water uses under various scenar- ios of hydrologic conditions and infrastructure status of irrigation and drainage management. Economic incentives, including water supply prices, crop prices and tax on excess salt discharge, are shown to have profound influences on the per- formance of integrated hydrologic-agronomic-economic systems. Finally, the ef- fects from hydrologic uncertainties on agronomic and economic outputs are demonstrated. The outcomes of water uses are examined in terms of economic efficiency, equity, environmental impact, as well as the risk from hydrologic uncertainties. Hydrologic system operation rules, irrigation and drainage infrastructure im- provements, and economic incentives are searched within an optimization frame- work to maximize the total benefit from irrigation, hydropower generation, and ecological water use. The main advantages from using the model for sustainability analysis at a river basin scale include: (1) system integration instead of fragmenta- tion provides an analytical framework to find both economic and environmental consequences from policy choices. This process represents a tradeoff between gains and losses and it is necessary to trace sustainability in water resources man- agement; and (2) alternative solutions can be searched based on hydrologic, agro- nomic, economic and institutional conditions within the integrated system. As we will show later, by extending this short-term model to a long-term model, we can have an inexpensive tool to analyze sustainability in water resources management at the river basin. This short-term model includes the basic components and rela- tionships of the modeling tool. Through the analytical issues discussed in this chapter, we also clearly demonstrate the limitations of using the short-term model for sustainability analy- sis. The problems are due to the fact that environmental impacts are not wholly connected to the utility of water uses. More specifically, groundwater quality deg- 167 radation could not be reflected in the short-term model; soil salinity ends with worse status, economic efficiency for drainage is under-evaluated. Therefore, the results from the model do not wholly reflect sustainability of water management in irrigation-dominated river basins. To solve these problems, a long-term model is a necessity. Finally, it should be noted that some technical difficulties exist in develop- ing and applying the large-scale model formulated in this research. The major dif- ficulty comes from data requirements and data processing. The model needs hy- drologic, agronomic, economic and institutional data, which may be available from experiments, statistics, and empirically estimation. Optimistically, assuming the availability of all the data, one should be careful when mixing data of different themes, different types, and different spatial and temporal scales. The difficulties on data preparation for integrated hydrologic-economic models are discussed in Chapter 3. Another technical difficulty is to solve the model. The short-term model is a large-scale, nonconvex, nonlinear optimization model written in the GAMS high level language (Brooke et al., 1988, 1996). The model statistics are as below: Number of equations: 9874 Number of variables: 13713 Number of non-zero elements: 57200 Number of nonlinear non-zero elements: 31099 Due to the size and complexity of the model, it is very difficult, to use any currently available solvers to solve the model. In this research, a piece-by-piece procedure was developed and applied to solve the model efficiently. 168 Chapter 5 Solving Large-Scale NLP Water Resources Management Models 5.1 BACKGROUND 5.1.1 Nonlinear water resources management models For many water resources management models, nonlinear programming (NLP) offers a general mathematical formulation for handling non-separable ob- jective functions and nonlinear constraints. Often, these models contain at most bilinear or quadratic objectives and constrains. Some of these models with bilin- ear items are summarized in Table 5.1. Yeh (1985) reviewed some traditional nonlinear programming (NLP) al- gorithms in surface water resources management, including the quasi-Newton method, the gradient projection method, the reduced gradient method and the La- grangian dual procedure. However, these calculus-based NLP algorithms are gen- erally suitable for convex problems, and they very often do not lead to the global solution of the nonconvex problems (Floudas et al.,1989). In addition, the compu- tational speed of these algorithms tends to be slow. Yeh argued that NLP gained its practical importance only in some cases, such as the following: (1) when ine- quality constraints can be dealt with by using an interior point barrier function and equality constraints can be dealt with using an exterior penalty function; (2) when nonlinear constraints can be linearized; and (3) when nonlinear problems can be decomposed into separable sub-problems, assuming the problems are convex. Obviously these conditions can often limit the application of NLP in water re- sources management modeling. 169 Table 5. 1. Water resources management models with bilinear relations Model types Nonlinear items References Reservoir operation with hydropower Generation release*head, and storage and surface area may be nonlinear function of head. Loucks et al., (1981) and this research Water distribution model with contaminant con- stituent balance flow * concentration McKinney and Cai (1997), and this research Irrigation cropping model Irrigated area * depth of water applied Kumar et al. (1998), and this research Groundwater quantity management model (unconfined aquifers) head * head Willis and Yeh (1987) Integrated Groundwater quantity and quality man- agement model velocity * concentration Willis and Yeh (1987), and Gorelick (1983) For groundwater management models, Gorelick (1983) found much work had been done for solving water quality management models with known groundwater velocity fields, while, for some cases, groundwater velocity fields might be unknown and should be considered explicitly within the management model. In these cases, the contaminant transport equation and the groundwater flow equation must be solved simultaneously, and nonlinearities arise as a result of products of unknown concentrations and unknown velocity components which occur in advective and dispersive transport terms. The tightest connection of wa- ter quantity and quality aspects exists in these nonlinear models. In many cases the NLPs in water resources management models are non- convex, but local solvers are applied. Methods for obtaining global solutions to 170 nonconvex mathematical programming problems have appeared rarely in the wa- ter resources literature, even though these problems are the rule more than the ex- ception. 5.1.2 Genetic algorithms In recent years, genetic algorithms (GAs) have been proposed as a promis- ing method to solve nonconvex NLP problems in water resources systems plan- ning. Genetics algorithms (GAs) are a subclass of general artificial-evolution search methods based on natural selection and the mechanisms of population ge- netics (Michalewicz, 1992). In this form of search the solution vector evolves throughout generations, improving the features of potential solutions by means of biologically inspired operations. GAs belong to a family of optimization tech- niques in which the solution space is searched by generating candidate solutions with the help of a pseudorandom number generator. As the run proceeds, the probability distribution by which new candidate solutions are generated may change, based on results of trials earlier in the run. The theory behind GAs was proposed by Holland (1975) and further developed by Goldberg (1989) and others in the 1980s. These algorithms rely on the collective learning process within a population of individual candidate solutions, each of which represents a search point in the space of potential solutions. The theoretical principle of implicit par- allelism (Holland, 1975) enables highly fit solution structures (schemata) to re- ceive increased numbers of offspring in successive generations and thus lead to better solutions. There are many variations of GAs but the important features are general. The analogy with nature is established by the creation within a computer of a set of candidate solutions called a population. Each individual in a population is repre- sented by a set of parameters that completely describe a solution. These are en- coded into chromosomes, which are, in essence, sets of character strings analo- 171 gous to the chromosomes found in DNA. Standard GAs use a binary alphabet (characters may be 0?s or 1?s) to form chromosomes. But not all GAs restrict rep- resentation to the binary alphabet, which makes them more flexible and applicable to variety of decision-making problems. The initial population of solutions is usually chosen at random, and then it is allowed to evolve over a number of generations. For each generation, a measure of how good each chromosome (or candidate solution) is with respect to an objec- tive function is calculated. This measure is called the fitness for each individual in a population. For each individual, its binary alphabet is decoded into parameter values, and then these values are substituted into a program that is used to calcu- late the value of the objective function, i.e., its fitness. Next, individuals are se- lected for ?mating? to produce offspring, and this process is called reproduction. The reproduction is based on probabilities calculated from the individual?s fitness value, which means that strings with a higher value have a higher probability of participating in reproduction and contributing one or more offspring in the next generation. Two important processes continue after the reproduction phase, namely crossover and mutation. In the process of crossover, genetic material crosses over from one chromosome to another. Reproduction and crossover com- bine to test and exchange high-performance notions in the search for potentially new ideas, which is the process of innovation. However, in the processes of re- production and crossover, some potentially useful genetic materials may be lost. The process of mutation, which is the occasional random alternation of the value of a string position, protects against such an irrecoverable loss. Crossover plays a primary role in GAs, and the probability of crossover is generally set high, while mutation plays a secondary role, and the probability mutation is set low. Using GAs for a particular problem, these probabilities need to be selected by trial-and- error, which is a drawback of using GAs. 172 GAs have clearly demonstrated their capability to yield robust and good approximate solutions even in cases of complicated multimodal, discontinuous, nondifferentiable functions (Savic and Walters, 1994). Because of their stochastic nature, there is no guarantee that the global optimum solution will be found, but a variety of applications have shown a high-level of performance across the spec- trum of the problems. Recently, there has been a significant growth of interest in using GAs for water resources planning and design. McKinney and Lin (1994) and Huang and Myer (1997) applied a binary-coded GA to the pump-and-treat groundwater remediation, Savic and Walters (1996) applied GAs for least-cost design of water distribution networks, and Halhal et al (1997) studied water net- work rehabilitation, replacement, and expansion by using a structured messy ge- netic algorithm. Oliveira and Loucks (1997) developed a GA-based approach to search effective operating policies for multipurpose multireservoir systems. All problems dealt with in these studies are basically nonlinear. Huang and Myer (1997), and Oliveira and Loucks (1997) included state transformation between discrete time periods. All others were static models. The advantage of GAs for a nonlinear problem comes from its stochastic search strategy: the optimal solution is searched for by testing solutions of the problem which are first created ran- domly within the solution space, and then induced by the ?fitness? of the model- ing output. The modeling method for each solution testing is generally simulation, which handles nonlinear relationships and large models easily. The major obstacle for using standard GAs in water resources designing, planning and management is the long computation time due to the global random search. For large-scale water resources models, a study on computation time with GAs has not yet appeared in the literature. 173 5.1.3 Decomposition techniques in water resources modeling If the size of NLP models (i.e. the number of variables and the number of equations) is large, solving them becomes difficult. Decomposition techniques are extensively used to handle large and complex models in water resources man- agement modeling. The most important factor encouraging the decomposition of a large water resource system into small systems, namely subsystems, is the diffi- culties faced in designing a large system as a single system. The difficulties come from two aspects: one is that, typically, the computing time required to solve a large model is not acceptable, given current computing capacity; the other is that for some large and complex systems, the traditional algorithms are not able to find satisfactory solutions (Yeh, 1985; Gorelick, 1983). Decomposition is generally applied for cases such as those described below: (1) Spatial decomposition, decomposing a hydrologic system into a num- ber of subsystems. This method is most often used in conjunctive surface water and groundwater use and multi-reservoir operation. River systems and aquifers are simulated separately, but both are regulated through the physical interactions between them (seepage, river depletion, groundwater discharge etc). For some multiple reservoir operation problems, reservoirs are first modeled individually, and then an inter-reservoir control program is used to regulate the relations be- tween reservoirs, arriving at an approximate global solution (Turgeon, 1981). (2) Temporal decomposition, decomposing a long-time horizon into a number of stages. Discrete-time modeling is based on this decomposition. The previous, current, and next stage are connected through physical transformation relations, respectively. Among these approaches, dynamic programming (DP) is popular in use (Augustine, 1989). 174 (3) Thematic decomposition, decomposing an integral problem into some sub-problems according to thematic characteristics. For example, separating water quantity and quality modeling. For all decomposition approaches, the critical step is to implement the in- teraction between the subsystems. Theoretical work on the decomposition tech- niques was introduced by Lasdon (1970). The most popular decomposition tech- niques include Dantzig-Wolfe Decomposition (1960), Bender's Decomposition (1962), and Generalized Bender's Decomposition (Geoffrion, 1972). Although these techniques are different in implementation, and are suitable for different problem structures, they are all based on the same idea: the initial problem is de- composed into smaller sub-problems, whose coordination is controlled by what is called the master problem. The master problem and the sub-problems are solved interactively: the master problem creates a proposal and sends it to the sub- problems, and the proposal is tested and information is sent back to the master problem. The master problem then creates a new proposal according to the ?feed- back?, and so on. On the practical side of water resources planning and management, devel- opment of general methods for decomposition does not seem to be feasible, due to the specific purposes and conditions of the problems studied. However, evidence of this kind of development can be found in the literature. Haimes (1977) devel- oped a multilevel decomposition technique for large water resources systems, in which the basic idea is the same as in the theoretical decomposition methods in the sense that the top level acts as a master problem. More recently, work to in- corporate general theoretical decomposition methods (e.g., Bender's Decomposi- tion ) into procedures to solve large-scale complex water resources management problems has been done. Watkins and McKinney (1997) used Generalized Bender's Decomposition (GBD) and Outer Approximation (OA) to solve a mixed- 175 integer nonlinear (MINLP) water resources optimization model with fixed costs. Cai et al. (1999) presented a global search approach to solve large-scale nonlinear nonconvex problems in water resources management. The approach was proved effective in solving two large water resources management models: a multi- reservoir operation model with nonlinear hydropower generation functions and a regional water allocation model with linear flow balance equations and nonlinear salt balance equations. 5.1.4 New approaches: extensions of GA and decomposition techniques This chapter presents three approaches to solve large NLP water resources management models. The first approach is based on Generalized Benders De- composition (GBD) algorithm, using an approximation to the GBD cuts proposed by Floudas et. al.(1989) and Floudas (1995). To insure feasibility of the GBD subproblem, we relax its constraints by introducing elastic slack variables, penal- izing these slacks in the objective function. This approach leads to solutions with excellent objective values in run times much faster than the GAMS NLP solvers MINOS (Murtagh and Saunders, 1987), and CONOPT (Drud, 1994). This ap- proach is especially useful for nonconvex NLP problems, and we apply it to a large nonconvex water allocation model involving flow and salinity balance at the river basin scale. The second approach presented in this chapter is based on the combination of a genetic algorithm (GA) and a linear programming (LP), and it is applied to solve a nonlinear reservoir operation model with nonlinear hydropower genera- tion relationships. As shown in Table 5.1, bilinear items (reservoir surface eleva- tion multiplying release) appear in the hydropower generation expression. The original model is reformulated as a linear program by fixing the reservoir surface elevation, which is treated as a variable vector in the genetic algorithm. The ge- 176 netic algorithm determines the values of the surface elevation, and these values are taken as parameters and substituted into the LP model. The solution from the LP model is used to calculate the fitness, which is fed back to the genetic algo- rithm for creating a new generation (a set of new values for reservoir elevations), and so on. The process of improved solution generating and evaluating is repeated until no further improvement in performance is obtained. The third approach is called the ?piece-by-piece? approach. It is assumed that a large model can be decomposed into several pieces, and the model is solved step by step with one more piece added in each step. At each step, solving the par- tial model is based on the solution found in the last step, and the solution from the current step is saved as a basis for the next step. At the final step, all pieces are added together, and the whole model is then solved. For a large model including nonlinear relationships, available solvers may not directly solve the model. This is the case for the short-term model described in Chapter 3. However, the model was successfully solved by the ?piece-by-piece? approach. Details about these approaches and their applications are described in the rest of this chapter. 5.2 A GBD -BASED APPROACH A more theoretical description of this approach should is given in Floudas et. al. (1989), and Cai et al. (1998). Here we put more emphasis on the implemen- tation and application of this approach to nonconvex nonlinear water resources management models. As an example, the approach is applied to solve a river ba- sin water allocation and salinity control model developed by McKinney and Cai (1997). Through the example, we demonstrate some advantages of this approach in (1) dealing with nonconvexity; (2) solving large models; and (3) searching for an approximate global optimal solution. 177 5.2.1 Generalized Benders Decomposition In the Benders? Decomposition method (BD) (Benders, 1962), the key procedure is to select complicating variables in the original problem, so that the original problem becomes a much easier problem to solve when the complicating variables are fixed. The procedure leads to the decomposition of an original prob- lem into a sub-problem (SP) and a master problem (MP), and the final solution of the original problem is reached through iterating between these problems. One limitation for BD is that the parameterized SP needs to be linear. Geoffrion (1972) generalized BD (GBD) to a broader class of problems in which the SP needs no longer be linear. The mathematical programming problem that Geoffrion defined is: Original problem (OP): Max f x y(,) subject to: (5-1) g x y(,)? 0 x X y Y? ?, If y is chosen as a class of complicating variables, then a SP is formulized as: Sub-problem (SP): Max f x y x (, ) * subject to: (5-2) gxy(, ) * ? 0 x X? 178 The SP has an optimal multiplier vector u for each y * ? Y? V, if X is convex, g and f are both concave on X for each y * , and {}VyyYxXgxy=??? ?|, ,(,)0?? (5-3) The derivation of the master problem begins with a partitioning of the original problem into an equivalent formulation featuring an inner and outer optimization problem: Equivalent problem to the original problem: Max v y() subject o (5-4) vy f xy gxy x X() {max (,)|(,) , }=>?0 y ? Y ? V The inner optimization problem over x ? X is simply the SP. The outer optimization problem seeks to maximize v(y) over all y ? Y ? V, defined as the set of all y that provides a feasible solution to the constraint set g(x, y). v(y) and V can be represented explicitly by dualizing the inner problem: { }vy MinMax f xy ugxy uxX T () (,) (,)=+ ??0 (5-5) 179 VyMaxgxy xX T =??? ? ? ? ? ? ? ? ? ? ? ? |(,),??0 ? (5-6) where, ?= ? ? = ? ? ? ? ? ?= = ? ?? ?R and m i i im :0 1 1 (5-7) If we define Lyu * (,)= { }Max f x y u g x y xX T ? +(,) (,) (5-8) Ly * (, )? = Max g x y xX T ? ? (,) (5-9) Then, the master problem (MP) can be written as: Master problem (MP): Max y 0 subject o: (5-10) yLyu u 0 0??? * (,) Ly j * (, )? ? 0 y ? Y 180 The master problem can be difficult to solve in its above form since it has an infinite number of constraints. This difficulty can be overcome by relaxing the formulation to form the following relaxed master program (RMP): Relaxed master problem (RMP): Max y 0 Subject to: (5-11) yLyui r i 0 12?= * (, ) ,.. Ly j p j * (, ) ,..? ?=012 y ? Y Testing the solution of the relaxed problem requires solving the SP. If this problem is feasible, then a new constraint (L * ) based on the optimal multiplier vector u is generated for the RMP to make it closer to the original problem. If the SP is infeasible, then a constraint of the form Ly j * (, )? ? 0 is violated for some ?. For that ?, the L * constraint is added to the RMP to keep it in the feasible range of the original problem. As the RMP contains fewer constraints than the equivalent of the original problem, its optimal value must be greater or equal to the optimal value of the original problem. Thus the RMP provides an upper bound on the final solution. Conversely, as the complicating variables are fixed in the SP, it contains more constraints than the equivalent of original problem, and thus the SP provides a lower bound to the final solution. 181 5.2.2 GBD based approach for solving nonlinear nonconvex models The approach was primarily proposed by Floudas et. al. (1989), who sug- gested a 4-stage approach: stage 1 - Identification of sources of nonconvexities. stage 2 - Transformations and partitioning of variable set and the nonconvex constraint set. stage 3 - Decomposition of the original nonconvex problem into two subproblems whose global solutions are attainable. stage4 - Iterations between the two subproblems to identify the optimal solution, using GBD. They claimed that ?the key idea in the partitioning and decomposition stages is to select the complicating variables and decompose the problem in such a manner that both the primary and the master problem can be solved for their respective global solutions at each iteration.? ?The complicating variables are defined as those variables which are responsible for nonconvexities and which when fixed at particular values, allow the resulting subproblem to be solved for its global solution?. If nonconvexities are bilinear in form, then fixing one vari- able (i.e. the complicating variable) will make the bilinear terms linear, making both the SP and the RMP linear programs (LPs), which can always attain their global solution if feasible solutions exist. If nonconvexities are in the form other than bilinear, then those items can be transformed into equivalent bilinear forms. Terms that do not have equivalent bilinear forms may be replaced by their ?linear underestimating functions? (Floudas et al., 1989). As noted by Floudas et. al., even though the SP and the RMP can attain their global solution in each iteration, there is no theoretical guarantee that the proposed approach will always identify 182 the global solution. Despite this limitation, Floudas et. al. found that the approach identified the global solution for several nonconvex nonlinear problems (NLP) and mixed-integer nonlinear problems (MINLP). During the iterations between the SP and the RMP, if SP is feasible, then an optimal multiplier vector u is generated, and an L * type constraint is added to the RMP. While, if for some y k , the SP is infeasible, Floudas et. al suggested solv- ing a relaxed sub-problem (RSP) to obtain the required Lagrangian multipliers ? . The RSP was defined as: Relaxed Sub-problem (SP): Min ? subject to: g x y k (, ) ? 0 (5-12) h x y k (, )+ ?? 0 ? + ?h x y k (, ) ? 0 x X? in which the function set h represents the equality constraints, and ? is a positive slack variable vector. It should be noted that all the examples which Floudas et al (1989) used in their paper are small NLP problems (at most 7 variables, and 10 constraint equa- tions). Although the approach was successfully applied to those examples, we may find it difficult to implement the approach to some large-scale NLP problems that have a large number of complicating variables, and constraints involving the complicating variables. We may need a method to simplify the model structure that includes the L * and L * constraints, and includes both the primary SP and the 183 relaxed SP. In our research, we introduce an alternative form of the RSP. For each of the tight constraints (generally equality constraints), a slack variable is added, and all slack variables are also penalized in the objective function. This RSP is formulated as: Alternative Relaxed Sub-problem (RSP): )(),( max * 21 sswyxf +?? subject to: 0),( * 1 ?yxg (5-13) 0),( * 2 =?+ 21 ssyxg Xx? where g 1 represents all inequality constraints, and g 2 represents all equality con- straints in the primary sub-problem, s 1 and s 2 are positive slack variables, and w is a weight assigned to the penalty item, which depends on the magnitude of the real objective value and the value of the penalty item. This new relaxed sub-problem (RSP) is then "feasible" for any values of the complicating variable y * . Therefore, the RMP will have one more L * function in each iteration, and the L * function is not needed since all proposals from the master problem will be feasible. The pri- mary SP (eq. 5-2) and the relaxed SP (eq. 5-12) are replaced by the single relaxed SP defined in (5-13).This alternative form makes the application of the approach to large models much easier than with the primary form. The iterations between the RMP and the RSP first drive all the slack vari- ables to zero, i.e. a feasible solution to the original problem, and further lead to the optimum solution. Since we put the slack variable in the RSP objective func- tion as a penalty, a straight conclusion is that if the original problem is feasible, 184 the slack variable should decrease to zero when the solution is reaching its opti- mum status, otherwise the non-zero slack will always penalize the objective. But this is not always the case. Assuming we add the slack variables to a reservoir storage balance equation, the model can consider the slack item (a 1 - a 2 ) as extra water in the reservoir, which may increase the objective value somehow, while simultaneously the nonzero slack variables penalize the objective value. Therefore the slack variable may bring an apparent, but fictitious, tradeoff into the model. Generally, we can give the penalty item a larger weight, so that the slack variable always penalizes the objective more than it improves the objective. Finally, to apply the GBD based approach proposed by Floudas et. al. for large water resources management problems, we recommend using the relaxed sub-problem (RSP) defined in equation (5-13). The steps of the GBD-based ap- proach are: 1. Initialize: == 0r iteration number, user 0 =?Yy supplied initial values for y, lbd (lower bound) ??= , ubd (upper bound) +?= , ?=convergence toler- ance. 2. Solve () r yRSP , obtaining an optimal solution r x objective value () r yv , and an optimal multiplier vector r u . If ( ) ,y r lbdv > set ( ) r y vlbd = . 3. Generate a closed form expression for ( ) r uyL , ? and add the constraint () r uyLy , 0 ? ? to RMP(r-1), creating RMP(r). 4. Solve RMP(r). The optimal solution is ( ) r r yy , 0 . Set r yubd 0 = . 5. If ?? INVSEA ; however, when the river basin system enters or is close to an unsustainable state, 0 / tol or 0 ET ETA < 0.5 or ks > 0.5 { (While the difference between the objective value of y FM in the current iteration and the last iteration is less than a pre-defined tolerance, or the salinity coefficient is less than 0.5, or the actual ET is less than half of the reference ET, do the loop) If ( 0 ET ETA < 0.5 ) then )1( ???= IAIA , ??+= IAIANIAN (Irrigated area is reduced by a fraction? ) If (K s > 0.5) then )1( ???= EIREIR (Field application efficiency is reduced by a fraction? ) Solve y FM by maximizing profit aflow = flow FM (Calculate the aggregated seasonal flow based on the solution of the y FM ) Solve y SM for calculating the salinity variable ks = ks SM EDS=EDS SM (Update the values of the soil salinity coefficients and the excessive salt discharge, and back to check the running condition for next iteration) } Figure 6. 3. Procedure to solve the yearly model 250 6.4.2 Implementation of the connection between the yearly models The connection between the yearly models maintains the dynamic relationships from year to year in the long-term modeling framework. Basically, the ending conditions of year y form the starting conditions of year y+1, and we need to set the status in the last period of the y YM as the initial condition of the first period of 1+y YM . With respect to flow, at the end of each year, some amount of water will be sustained for the use in the next year, which is specified by WSU y , an item from the IYCP. Further, the storage of reservoirs, the groundwater table, and the soil moisture in the root zone at the end of year y are set as the initial values of these items in year y+1, so that the surface water, groundwater storage and soil water storages can keep their continuity. With respect to salinity, the seasonal salt concentrations from y SM will be set as the initial salinity for 1+y SM . That is to say, the salt concentrations at the end of the nongrowing season of year y are the salt concentrations at the beginning of the growing season of year y+1. The connection between the yearly models is shown in Figure 6.3. The salt concentrations in surface and groundwater storage and the salinity in the soil of the root zone are transferred to the next year. The irrigated area from year to year should also keep its continuity in order to trace the waterlogging and salinity conditions in the long-term time horizon. Year by year, new area may be added to a crop, or part of the primary area of a crop may be cut due to many factors such as urbanization, crop rotation, as well as water shortage, excessive soil salinity, and waterlogging. We use the procedure described below to keep the continuity of irrigated area. For one year (y), irrigated area for one crop may be reduced due to water shortage and soil salinity, and we assume the reduced area (RIA) is left unplanted in that year, but the soil water and salinity balances are still determined for the area in the model. In year y+1, the initial irrigated area for that crop is equal to: 251 11 0 ++ ??+= y cp y cp y cp y cp IAIARIAIA (6-15) where 1 0 +y cp IA = Initial irrigated area of crop cp in year y+1, y cp RIA = Reduced irrigated area of crop cp in year y, y cp IA = Actual irrigated area of crop cp in year y, 1+ ? y cp IA = Planned added or cut area for crop cp in year y+1. The initial soil moisture and soil salinity for year y+1 are calculated as the area-weighted average value of the three components in the above equations, respectively. The soil moisture and salinity with y cp IAN and y cp IA are from the y FM and the y SM , respectively. For 1+ ? y cp IA , the soil moisture and salinity take the average values of the whole cropping area within one demand site. 6.4.3 Solving the long-term dynamic modeling The implementation of the long-term modeling includes (1) determining the inter-year control variables through the inter-year control program (IYCP); (2) solving the yearly models year by year; (3) calculating the the performance over the whole time horizon based on the results from all yearly models; and (4) executing iterations between the IYCP and the YMs. The GA & LP approach described in Chapter 5 is used to solve the long-term dynamic modeling framework. Figures 6.4 and 6.5 show diagrams of the implementation of the GA & LP program. The GA program starts the first generation by randomly creating a 252 prescribed number of individuals ( ng ni IND , ni=1, 2, ? NI), and each individual is represented as an alternate solution of the inter-year control variables: ng ni IND = (WSU y , y dm EDS , y dm EDN , y fddm EIR , , y fddm IA , , y dm tax ) (6-16) and each generation ( ng GEN , ng=1, 2, ? NG) is represented as a group of individuals: }ND ... ,,,{ 321 ng NI ngngngng IINDINDINDGEN = (6-17) Actually, the individual inter-year control variables should be indexed by generation number (ng) and individual number (ni), but the notation would be too cumbersome here so it is suppressed in eq. 6-16. Each individual represents an alternative solution of the inter-year decision variables. For each individual, the genetic algorithm selects values for the inter-year control variables within their prescribed ranges. These values with an index y = 1, 2, ? Y (number of years considered in the model) are then input into the corresponding yearly model )SMFM(YM yyy += (y=1, 2, ? Y), which is solved year by year with the year-to-year transitions described above. That is to say, with each individual, the modeling framework simulates the long-term system performance, while optimizing the decisions within each individual year under the given proposal from the inter-year variables. The results from the YMs are input into a fitness calculation program to determine the fitness of each individual in the current generation. The fitness calculation is based on the sustainability criteria expressed in equations 6-1 to 6- 253 10. Considering all these criteria, we have a multiple criteria evaluation problem. Some of the indices are to be maximized, and the others are to be minimized, according to their formulation (eq. 6-1 to 6-11), which is to: { SEAmaxSEQminTEmin ENVIminVUNminREVminRELmax and ; ;Q ; ; ; ; } (6-18) The objective function of the IYCP is formulated as a weighted sum of these multiple objectives, and the objective variable (OBJ) is to be minimized: 1 Q )-(1 ? ?+?+?+?+ ?+?+?= SEAwseaSEQwseqTEweqENVINwenv VUNwvunREVwrevRELwrelOBJ (6-19) where, wrel, wrev, wvun, wenv, weq, wseq, and wsea are weights (or scaling factors) assigned to corresponding criteria. The objective variable, OBJ, is set to be minimized, and the two items, ?1-REL? and ?SEA -1 ?, are used in the objective function to make the indices ?REL? and ?SEA? to be maximized. All other indices are directly minimized in the objective function. The genetic algorithm calculates this objective for each individual of one generation, and thus determines the fitness value of the individual, that is, )( 1 ng ni ng INDOBJFITNESS ind ? = (6-20) 254 where the value of fitness is equal to the inverse of the objective variable, obj, which is minimized in the long-term modeling, i.e., a lower value of obj corresponds to a higher value of fitness of an alternative solution. The best individual has the highest fitness. The fitness of an individual depends on the effects from the decisions in each year, and represents an evaluation of the individual according to the prescribed sustainability criteria. The GA searches the best individual from generation to generation. Based on the fitness for all individuals in one generation, the GA determines the probability for each individual to be selected to ?mate? for the creation of the individuals in the next generation that theoretically include better individuals than the prior generation. From generation to generation, the program will gradually approach the globally best individual which represents the optimal solution of the inter-year decision variables. This optimal solution will provide the best proposal for the yearly models with respect to the sustainability criteria discussed before. The optimal decisions within each year (i.e., short-term decisions) are searched by the procedure described in Figure 6.3. 255 GEN ng ng IND 1 ng ni IND ng NI IND y dm EDS y dm EDN y dm EIR y dm TAX y dm EDS y dm EDN y dm EIR y dm TAX y dm EDS y dm EDN y dm EIR y dm TAX ?... y=1 y=Yy=y ?... ?... ?... 1 dm EDS 1 dm EDN 1 dm EIR 1 dm TAX y=2 YM 1 YM 2 YM y YM Y IYCP 2 dm EDS 2 dm EDN 2 dm EIR 2 dm TAX y dm EDS y dm EDN y dm EIR y dm TAX y dm EDS y dm EDN y dm EIR y dm TAX GEN ng +1 ng = ng +1 y dm WSU y dm WSU y dm WSU 1 dm WSU 1 dm WSU 1 dm WSU 1 dm WSU Figure 6. 4. Genetic algorithm implementation of the inter-year control program 256 GEN1 (initial) GEN2 (good) (better) GENN (best) IND 1 IND 2 ... IND NI Yearly Model FM 1 & SM 1 y=1 y=2 y=Y Fitness Calculation Yearly Models Yearly Model FM 2 & SM 2 Yearly Model FM Y & SM Y New Generation Figure 6. 5. Genetic algorithm implementation sketch of the inter-year control program 257 Randomly create the first generation ) ... ,( 11 3 1 2 1 1 1 NI INDINDINDINDGEN = = { (WSU y , y dm EDS , y dm EDN , y fddm EIR , , y fddm IA , , y dm tax ) 1 1 , (WSU y , y dm EDS , y dm EDN , y fddm EIR , , y fddm IA , , y dm tax ) 1 2 , ... (WSU y , y dm EDS , y dm EDN , y fddm EIR , , y fddm IA , , y dm tax ) 1 NI , } For ng GEN ng = 1 ? NG { For each individual in } ... ,,,{ 321 ng NI ngngngng INDINDINDINDGEN = { Run the )SMFM(YM yyy += for each year (y=1, 2, ? Y) Calculate )( ng ni ng INDOBJFITNESS ind = based on outputs from all YM y } Create 1+ng GEN based on ng ind FITNESS with ng ni IND ni=1 to NI } Figure 6. 6. Procedure for the long-term dynamic modeling 258 The inter-year control variables, i.e., the decision variables in the IYCP, are limited by some bounds and constraints, which are described below. ? Water saved for future use at the end of year y is bounded by prescribed lower and upper bounds depending on the hydrologic condition of the year: y yy WSUWSUWSU ?? (6-21) where the upper bounds is the total available reservoir storage in the basin, and the lower bound is an empirical value depending on hydrologic condition of the year. The lower bound is smaller in dry years than in wet years. The determination of the lower bound is also related to reservoir operation rules set for specific purposes such as flooding control and emergency water supply. ? Since water delivery & distribution, irrigation and drainage are related to long-term permanent systems, and assuming that system maintenance is well done, then water delivery & distribution efficiency, irrigation efficiency, and drainage efficiency are not reduced over time. Therefore besides the lower bounds (current level) and upper bounds (a value less than 1.0), an inter-year relationship of these items is defined as: y dm y dm EDSEDS ? +1 (6-2) y dm y dm EDNEDN ? +1 (6-23) y dm y dm EIREIR ? +1 (6-24) 259 ? The irrigated area for each crop at a demand site is bounded by empirical ranges. However, the sum of crop areas over all crop fields must remain below the total available area in one demand site: y dm fd y fddm TIAIA ? ? , (6-25) ? the penalty tax rate on excessive salt discharge is constrained by ranges varying from year to year. y dm y dm y dm taxtaxtax ?? (6-26) where the lower and upper bounds for penalty tax rate are estimated based on the scenarios defined for short-term analysis, as presented in Chapter 4, Section 4.3.3.5. The variable bounds are directly implemented in the GA. When the GA chooses a value for a variable, it must be within the prescribed variable bound. However, the constraints other than direct bounds on the variables may not be automatically satisfied by the solution created by the genetic algorithm. For example, the genetic algorithm chooses the values of the irrigated area for all crops at one demand site within their prescribed ranges. However, the sum of these values may be above the total available irrigated area at the demand site. Generally a penalty is defined based on the magnitude of the violation of the constraint, and it is incorporated into the objective function (expression of the ?fitness?). In this research, we simply apply a post-modification to the solutions of the genetic algorithm, based on the relationships expressed in equation (6-19 to 6-22). For irrigated area (eq. 6-22), 260 If y dm fd y fddm TIAIA ? > , then ? ?= fd y dm y dmy fddm y fddm IA TIA IAIA ,, , thus y dm fd y fddm TIAIA ? = , (6-27) and for water distribution, irrigation and drainage efficiencies (eq 6-18 to 6-20 ), taking water distribution efficiency EDS as an example: If y dm y dm EDSEDS < +1 , then y dm y dm EDSEDS = +1 (6-28) The modified GA solutions satisfy all prescribed variables and relationships. However, for a general GA model, this post-modification may lose some useful ?genes?, and further research has to be done on this issue. 6.5 SUMMARY This chapter presents a viable modeling framework for sustainability analysis in long-term water resources management. concepts related to the long- term modeling for sustainability analysis in water resources management were discussed. The critical issue for this modeling is to trace and control long-term consequences resulting from short-term ?wait-and-see? decisions, with predicted changes and uncertainties on both water demand and supply in the future. The long-term system performance is controlled by specifically prescribed 261 sustainability criteria with respect to water supply risk, equity, environmental integrity, and socio-economic acceptability. A modeling framework is described to incorporate the quantified sustainability criteria into mathematical formulas. The modeling framework is composed of a series of yearly models (YM) and an inter-year control program (IYCP). The yearly model includes the essential hydrologic, agronomic, economic, and institutional relationships described in Chapter 3. However, for computing efficiency, it is formulated as a linear model by approximation and decomposition, and it is solved by an integrated simulation and optimization procedure. The inter-year control program is implemented by the GA-LP approach described in Chapter 5. An application of this modeling framework to the case study area is presented in the next chapter. 262 Chapter 7 Sustainability Analysis ? An Application of the Long-Term Dynamic Modeling Framework 7.1 INTRODUCTION In this chapter, the long-term dynamic modeling framework described in Chapter 6 is applied to water resources planning and management for the case study area, the Syrdarya River basin in Central Asia. The time horizon for the modeling is 30 years. First, the data required by the model for the case study, as well as the assumptions with regard to the case study are described. Emphasis is put on the appropriate prediction and expression of the long-term changes and uncertainties of both water supply and demand, which are essential to the long-term modeling analysis. It goes beyond the effort of this research to calibrate and verify the modeling framework for solving the problems in the study area. This will need further work in data collection and verification, as well as a more in-depth study of the water management problems in that area. However, based on the current data availability and the current understanding of the problems, the effectiveness of the modeling framework applied to the case study area is demonstrated i.e., how effectively it can be used to analyze sustainability in the river basin. The limitations of the modeling framework are also addressed. The modeling framework traces the long-term consequences resulting from year-to-year decisions, such as soil salinity accumulation, waterlogging, quality reduction in surface and ground water, irrigated area reduction, and 263 ecological water depletion due to excess water withdrawal. These consequences may put sustainability at risk in the study area, an irrigation-dominated river basin situated in an arid climate. Based on the modeling output, these consequences are displayed and analyzed. Since the sustainability of the irrigation and environmental systems is associated with long-term changes and uncertainties, scenario analysis based on possible changes and uncertainties in both water demand and water supply are conducted to ensure a robust modeling analysis. Based on the outputs from various scenarios, sustainability is analyzed with respect to the risk on water supply, environmental integrity, equity and socio-economic efficiency. The tradeoffs existing among these aspects are also discussed. Although the results from the modeling output may not provide really applicable solutions to the current problems experienced in the Syrdarya River basin, it is hoped that the modeling results provide timely information for informed decision-making for the long-term water resources management in the river basin, including the operations of hydrologic systems, improvements of irrigation and drainage facilities, and economic incentives and institutional directives. The purpose of this chapter is thus to demonstrate that the prototype long- term dynamic model can be used as an effective tool for sustainability analysis, and to search for potential solutions for long-term water resources management in the case study area. 7.2 DATA AND ASSUMPTIONS Data and assumptions described for the short-term model in Section 4.2 will be used for the yearly model in the long-term modeling framework, where appropriate. In this section, we describe the data that change from year to year in both water demand and supply. Some data related to scenario analysis, which are 264 required but currently not available, are estimated based on data available in the literature. The assumptions involved in the long-term modeling for the case study area are also addressed. 7.2.1 Data and assumptions in water demand Water demand considered in the modeling framework includes irrigation and non-irrigation water demand. Irrigation water demand depends on the irrigated area and the water requirement per unit of area. The total available irrigated area for each demand site and the irrigated area for various crops within each demand site will likely change in the next 30 years. Many experts suggest a reduction of the current irrigated area, or at least the abandonment of new irrigated area expansion. However, some districts are still developing new irrigated area in order to increase food supply security. The official plans for irrigated area in the study area are not available for this research. Therefore we simply project the total irrigated area in four scenarios based on different changing rates of the irrigated area in next 30 years, such as ?10%, 5%, 10% and 58%. An increase of the current total irrigated area by 5% in next 30 years is assumed to be the ?best estimation? (baseline). It seems to be impossible for the irrigated area in the basin to increase by 58% in next 30 years, and here we define an extreme case so as to study how severely the irrigation associated environment is affected. It is assumed that irrigated area increases evenly across all demand sites. The current irrigated area is presented in Table 4.10, and the projected irrigated area (relative value to the current value) of the scenarios defined above is shown in Table 7.1. The demand of hydropower in the upstream country in next 30 years is also shown Table 7.1. 265 Table 7. 1. Projections of total irrigated area and industrial and municipal water demand in the Syrdarya River Basin. Data are relative to the current values in Table 4.10 and Table 4.22. Year Irrigated Area Change in 30 years M&I Water Demand Hydropower Demand * -10% 5% (baseline) 10% 58% Normal High 1 1 1.00 1 1.00 1.00 1.00 1 2 0.993 1.01 1.003 1.02 1.01 1.03 1.005 3 0.992 1.01 1.006 1.04 1.01 1.06 1.009 4 0.99 1.01 1.009 1.06 1.02 1.09 1.014 5 0.988 1.02 1.012 1.08 1.02 1.12 1.017 6 0.986 1.02 1.015 1.1 1.02 1.16 1.021 7 0.983 1.02 1.018 1.12 1.03 1.2 1.025 8 0.981 1.03 1.021 1.14 1.04 1.24 1.029 9 0.978 1.03 1.024 1.16 1.05 1.28 1.033 10 0.977 1.03 1.027 1.18 1.06 1.32 1.037 11 0.975 1.03 1.035 1.2 1.07 1.35 1.041 12 0.972 1.04 1.039 1.22 1.08 1.38 1.045 13 0.968 1.04 1.042 1.24 1.09 1.41 1.049 14 0.964 1.04 1.046 1.26 1.1 1.45 1.054 15 0.96 1.04 1.05 1.28 1.11 1.49 1.058 16 0.958 1.04 1.054 1.3 1.12 1.53 1.062 17 0.956 1.04 1.058 1.32 1.13 1.57 1.067 18 0.954 1.04 1.061 1.34 1.14 1.61 1.072 19 0.952 1.04 1.065 1.36 1.15 1.64 1.078 20 0.95 1.05 1.07 1.38 1.16 1.67 1.081 21 0.944 1.05 1.074 1.4 1.17 1.7 1.087 22 0.942 1.05 1.078 1.42 1.18 1.74 1.092 23 0.938 1.05 1.082 1.44 1.19 1.78 1.097 24 0.932 1.05 1.085 1.46 1.2 1.82 1.102 25 0.928 1.05 1.088 1.48 1.21 1.85 1.107 26 0.922 1.05 1.091 1.5 1.22 1.88 1.113 27 0.916 1.05 1.093 1.52 1.23 1.91 1.119 28 0.91 1.05 1.095 1.54 1.24 1.94 1.124 29 0.905 1.05 1.098 1.56 1.25 1.97 1.129 30 0.9 1.05 1.1 1.58 1.25 2.00 1.135 * Estimated based on Harza (1995). The yearly hydropower demand in 1990 is 9500 MKW. The monthly distribution is 11%, 17%, 9%, 8%, 6%, 6%, 6%,6%, 6%, 8%,8%, and 11%, from Jan. to Dec. 266 As described in Chapter 6, irrigated area for different crops is determined by the inter-year control program (IYCP). Without much loss of reality, we assume that crop patterns change every five years. The IYCP reallocates irrigated area for each considered crop every five years. The projected total irrigated area forms an upper bound for the total irrigated area calculated from the modeling. The non-irrigation water demand includes industrial, domestic, and environmental water demands. Growth in population and incomes will be mainly responsible for increased domestic water requirements. Moreover, institutional, political, and technical factors can influence future water demand. We make a projection of the future 30 years? municipal and industrial (M&I) water demand based on the work of Raskin (1996). The projection includes a normal and a high scenario that are shown in Table 7.1. The ecological water demand, which is the annual inflow requirement of the Aral Sea, is estimated according to hydrologic conditions in each year. The requirement is set as 15.5, 12.0, 10.0, 7.0, and 5.0 km 3 in very wet, wet, normal, dry, and very dry years based on historical records. It is assumed that inflows below the corresponding requirement will cause environment damage in the form described in Chapter 4, Section 2. The definitions of these hydrologic years are discussed in the following section. 7.2.2 Data and assumptions in water supply Water supply in future years mainly depends on climatic changes, water storage and distribution capacities, as well as financial, institutional and political constraints. Hydrologic fluctuation patterns are important in estimating future water availability. Generally, historical fluctuations are used to represent future patterns, if time series data for many elements of the river basin are available. In the Syrdarya River basin, river flows have been altered with extensive irrigation 267 development and many hydrologic records cannot serve as proxies for historic patterns. Raskin et al. (1992) applied a simple method to project future hydrologic patterns for the Aral Sea basin, in which five categories of water-type years, Very Wet, Wet, Normal, Dry, and Very Dry, are used to represent hydrologic patterns. These five hydrologic-level years correspond to different hydrologic occurrence probabilities in conventional frequency analyses. The frequency analysis of an annual inflow record at a representative river point provides a sequence of hydrologic-level years. This sequence is then adjusted to explore alternative assumptions of future hydrologic patterns. The monthly inflow data of 1950-1982 at the Naryn gauging stations were used in estimating the basin?s hydrologic-level sequences during the 1988 ? 2020 period, which is shown in Table 7.2. Table 7. 2. Hydrological fluctuations from 1988 -2020, after Raskin et al. (1992) Years 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Hydrologic Levels N N VW N N W VW VD D N N Years 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Hydrologic Levels N N N W N W D N W N N Years 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Hydrologic Levels VD N D D D W N N N D D Notation: N: normal, D: dry; VD: very dry, W: wet, VW: very wet. The long-term model starts in 1991, covers 30 years, and ends in 2020. The method used by Raskin et al. assumed hydrological homogeneity across the basin. In this research we do not have time series data for many small tributaries, and the existing records for some tributaries are obviously affected by irrigation practices through return flow. In addition, insufficient data are available to separate return flow from the flow records. Because of these limitations, this research follows the simple method used by Raskin et al. (1992). 268 For every source, the monthly inflows in a normal year are taken as the base, and ratios of the inflows in other hydrologic-level years to the base were computed by Raskin et al., and shown in Table 7.3. Table 7. 3. Ratios of monthly inflow in different hydrologic years to those in the normal year, after Raskin et. al (1992). Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Very Wet 1.15 1.10 1.45 1.10 1.11 1.25 1.30 1.42 1.47 1.46 1.54 1.25 Wet 1.06 1.02 1.19 1.05 1.05 1.09 1.14 1.21 1.23 1.23 1.27 1.13 Normal 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Dry 0.99 0.89 0.83 0.76 0.70 0.70 0.70 0.70 0.94 0.99 0.95 0.92 Very Dry 0.90 0.81 0.76 0.69 0.50 0.50 0.50 0.50 0.60 0.90 0.87 0.83 The same method is applied to specify precipitation data. From the hydrologic fluctuation sequences in Table 7.2, the probability of the five hydrologic-level years is calculated as 3.3% (Very wet), 16.7% (Wet), 52.0% (Normal), 21.3% (Dry) and 6.7% (Very Dry), respectively. It is assumed that those probabilities also apply for precipitation at each demand site in the same period. A representative precipitation record (92 years) is selected at upstream, mid-stream, and downstream of the basin, respectively. The above probabilities are applied to each of the representative precipitation records to classify the record into the above five types of hydrologic years based on the amount of annual precipitation. In each class, the average monthly precipitation is calculated, and it is used to represent the monthly precipitation corresponding to the hydrologic types. The ratios of monthly precipitation in various hydrologic years to that in a normal year are shown in Table 7.4. 269 Table 7. 4. Ratios of monthly precipitation in different hydrologic years to those in a normal year. Hydrologic Levels Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Upstream Very Wet 1.21 1.21 1.25 1.20 1.19 1.25 1.34 1.36 1.38 1.40 1.45 1.23 Wet 1.10 1.06 1.24 1.09 1.09 1.13 1.19 1.26 1.28 1.28 1.32 1.18 Normal 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Dry 0.99 0.92 0.87 0.80 0.74 0.73 0.74 0.75 0.94 0.99 0.99 0.95 Very Dry 0.77 0.69 0.65 0.59 0.45 0.54 0.56 0.55 0.65 0.77 0.74 0.71 Midstream Very Wet 1.50 1.40 1.67 1.38 1.61 1.47 1.63 1.48 1.46 1.68 1.82 1.21 Wet 1.24 1.01 1.43 1.29 1.43 1.14 1.25 1.10 1.13 1.48 1.70 1.17 Normal 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Dry 0.80 0.73 0.65 0.69 0.67 0.48 0.65 0.42 0.54 0.64 0.96 0.79 Very Dry 0.29 0.57 0.46 0.34 0.26 0.27 0.35 0.30 0.39 0.51 0.73 0.82 Downstream Very Wet 1.72 1.61 1.92 1.59 1.85 1.60 1.78 1.61 1.59 1.83 1.99 1.32 Wet 1.43 1.38 1.61 1.42 1.42 1.47 1.54 1.55 1.53 1.66 1.72 1.25 Normal 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Dry 0.88 0.80 0.72 0.76 0.73 0.53 0.72 0.46 0.59 0.71 1.06 0.87 Very Dry 0.33 0.65 0.52 0.39 0.30 0.31 0.40 0.35 0.45 0.58 0.84 0.95 It is assumed that no new reservoirs will be built in the next 30 years. Moreover, it is expected that the current major reservoirs in the basin will be well maintained, and that their storage will keep the current conditions (Table 4.4). In this case study, we focus on the performance of the current reservoir systems, although new reservoirs and extended storage of existing reservoirs could be included in the modeling framework at specific stages. Groundwater is an important source in the basin, although the current groundwater pumping is far less than river water withdrawals. We assume that groundwater availability will increase by 20% of the current capacity during 1991-2020. The effective agricultural water supply depends on the overall water distribution and application efficiency, as well as on the water storage capacity. 270 As discussed before, water distribution efficiency (considering water loss from the outlet to the crop field), and irrigation application efficiency (considering water loss in the crop field) are related to canal lining and irrigation systems, respectively. We assume that these efficiencies, as well as the drainage efficiency that is critical to soil quality protection, will be improved in the coming years, and that the current status will be at least well maintained. As described in Chapter 6, these anthropogenic improvements will meet the investment constraint, and they are defined as inter-year control variables in the long-term modeling framework. That is to say, the long-term modeling will determine in which year and at what magnitude the water distribution and application efficiency related to permanent facilities should be chosen. The current values of water distribution efficiency, drainage efficiency, and irrigation efficiency are already shown in Table 4.16 ? 4.17, which are the lower bounds of these items in the long-term modeling. As various lower bounds for different demand sites and different crop fields, the upper bounds for these items may also vary spatially. Due to the insufficient data, we assume the upper bounds for these items are the same at all demand sites and crop fields for the long-term irrigation system planning. According to EC (1995), if the unlined canals, covering three quarters of the total canals, become lined, then the distribution efficiency will increase to 75%; if most farm canals are lined with concrete, then the distribution efficiency will increase up to 85%. Therefore, we set the upper bound of the water distribution efficiency as 85% in the next 30 years. In some area of the basin, the percentage of irrigated area that is drained is up to 85%, although large differences exist in different areas. We assume this percentage for the whole basin will not be over 85%. As for the irrigation efficiency, which is defined as the field application efficiency (eq. 3-9), EC (1995) estimated the overall field application efficiency in the basin will increase up to 70% if modern technologies are used to 271 the existing furrow systems. Clemmens and Dedrick (1994) showed that the typical potential application efficiencies for well-designed and managed irrigation systems could be up to 80 ? 90%. We assume that the irrigation efficiency is up to 85% in the next 30 years, which means some advanced irrigation systems such as drip and sprinkler irrigation systems are going to replace some of the furrow irrigation systems. Further, to reduce the computing work, we assume that the condition of water distribution and application may be improved every five years in during the next 30 years. 7.2.3 Other data and assumptions In the long-term modeling, the tax rate on excess salt discharge is chosen by the inter-year control program (IYCP) based on the lower and upper bounds ( $10.0 ? $300 per ton of salt mass) which are consistent with those used for the scenario analysis in Chapter 4, Section 4.3.3.5. Other economic data such as water supply prices, crop costs and prices may change considerably in the future. However, currently, we are not able to get enough information about these changes to include them. Therefore, we assume that there will be no changes of these items in the study time horizon. This limitation can be removed in the future through connecting economic forecasting to this modeling framework. 7.3 EFFECTIVENESS AND LIMITATIONS OF THE MODELING APPROACH As described in Chapter 6, the long-term modeling framework includes a procedure for solving the yearly model and a procedure to search for better solutions through the GA&LP approach described in Chapter 5. For this case study, the parameters used in the GA&LP approach are listed as follows: Number of Variables in GA 384 Number of Individuals 50 Length of substring 5 272 Probability of crossover 0.85 Probability of mutation 0.01 In the following we demonstrate the effectiveness and limitations of the modeling approach for the case study. 7.3.1 Solving the yearly model The procedure for solving the yearly model (YM) is shown in Figure 6.3. In the following a practical application of this approach is presented. Tables 7.5 and 7.6 present the iterations of the yearly model, including the objective values of the current and prior iterations (TWB, eq. 3.40). The index of water shortage (iws) is calculated as the sum of slack variables (?) in the root zone water balance. These slack variables act as ?additional water? supplied to the crop root zone, but they are penalized in the objective function, which can be described as: iwswpenobjobj ??= * max s.t. ??? = dm fd pd pd fddm iws , ? (7-1) pd fddm pd fddm pd fddm winwout ,,, ?+= where wpen = weight assigned for the penalty item, win = inflow to the root zone, and, wout = outflow from the root zone. Both win and wout are variables in the yearly models (YM). 273 With the slack variable defined in the model, the yearly model will be mathematically feasible in each iteration even water supply can not satisfy water demand (note: the relative crop yield must not be less than 0.5, see Figure 6.3). A positive value of a slack variable implicates water supply can not sustain the irrigated area pre-determined by the inter-year control variable, y fddm IA , . Therefore, in the next iteration, the irrigated area corresponding to positive ? pd pd fddm a , must be reduced. The index of excess soil salinity (iss) is defined as the maximum soil salinity coefficient (ks, eq 3-22 ) over all crop fields and all demand sites. In Table 7.5, the first four iterations result in negative objective values, because the values of some slack variables are positive and therefore they penalize the objective and cause it to be a negative value. Detailed output shows that water shortage occurs to two demand sites, Low_syd and Fergana, and Table 7.6 shows that for these two demand sites, the irrigated area is reduced until the water shortage index becomes zero. Although the indices of water shortage and soil salinity are zero in iteration 6 and 7, the difference between the objective value of the current iteration and that of the prior iteration is larger than the prescribed tolerance. Therefore, iterations continue until the difference is below the tolerance in iteration 8. 274 Table 7. 5. Example for iterations in solving the yearly model: irrigated area reduction due to water shortage. Iterations Objective values from prior iteration Objective value from current iteration Water shortage index (iws) Soil salinity index (iss) 1 -1637.091 -1269.66 25.394 0 2 -1269.661 -817.031 16.341 0 3 -817.032 -524.127 10.483 0 4 -524.132 -175.249 3.505 0 5 -175.251 0.672 0 0 6 0.672 0.654 0 0 7 0.654 0.627 0 0 8 0.627 0.631 0 0 Table 7. 6. Example for iterations in solving the yearly model: irrigated area reduction due to water shortage. water shortage irrigated area Iterations Low_syd fergana low_syd fergana 1 7.341 18.053 433.2 1356.1 2 4.003 12.338 420.4 1308.5 3 2.809 7.673 413.5 1261.2 4 0.837 2.667 408.2 1218.3 5 0 0 408.2 1218.3 6 0 0 408.2 1218.3 7 0 0 408.2 1218.3 8 0 0 408.2 1218.3 Table 7.7 shows the iterations for another run of the yearly model. Here, the soil salinity is so high that the crop yield-water coefficient is larger than 0.5. As we described in Figure 6.3, with this condition, both the irrigated area and the irrigation application efficiency will be reduced. Detailed output shows that excess soil salinity occurs in demand site Low_syd, i.e., KS('low_syd', 'other')=0.614 275 (?other? means a crop type, including crops other than cotton, wheat, maize forage, and alfalfa). Between iterations 1 and 2, the irrigated area is reduced from 472.8 to 442.4 thousand hectares, and the irrigation application efficiency is reduced from 0.835 to 0.801, for crop field (?oth_oth?) in demand site low_syd. Table 7. 7. Example for iterations in solving the yearly model: irrigated area reduction due to salinity. Iterations Obj. value from prior iteration Obj. value from current iteration Water shortage index (iws) Soil salinity index (iss) 1 -12.915 -10.189 0 0.614 2 -10.189 0.905 0 0.432 3 0.905 0.907 0 0.322 In the first iteration ks('low_syd', 'other') = 0.614, irrigated area is reduced from 472.8 to 442.4, and irrigation application efficiency, eff_irr, is reduced from 0.835 to 0.801. For each alternative of the long-term modeling solutions, the yearly model is run year by year for 30 years. As an example, Table 7.8 shows some items from the model output for each of the 30 years. 276 Table 7. 8. Selected items from the year by year modeling output. Year Hydrol. Level WSU 1 Irrigated Area (10 3 ha) Irrigation Profit (10 9 $) Aral Inflow (km 3 ) Ground water Salinity (g/l) Reserv. Salinity (g/l) Soil Salinity (dS/m) Tax Rate (100$/ton) Salt Discharge (10 6 tons) EDS at Low_syd EDN at Low_syd EIR 2 Low_syd (cot-foa) 1 normal 0.39 3250 1.562 8.0 1.1 0.9 0.7 1.0 53.4 0.67 0.7 0.64 2 normal 0.27 3282.5 1.543 9.5 1.1 1.1 0.6 0.83 50.1 0.67 0.7 0.64 3 normal 0.27 3282.5 1.5994 8.7 1.2 1.0 0.6 0.36 49.5 0.67 0.7 0.64 4 very wet 0.49 3282.5 1.605 12.3 1.2 1.0 0.5 0.25 47.3 0.67 0.7 0.64 5 very dry 0.03 3315 1.0075 4.5 1.3 1.1 0.6 0.45 26.2 0.67 0.7 0.64 6 dry 0.04 3315 1.1315 3.1 1.4 1.1 0.8 0.94 44.6 0.74 0.7 0.74 7 normal 0.3 3315 1.3152 4.9 1.4 1.1 0.8 0.22 52.1 0.74 0.7 0.74 8 normal 0.25 3347.5 1.3853 11.6 1.4 1.1 0.8 0.8 52.7 0.74 0.7 0.74 9 normal 0.28 3347.5 1.3479 11.1 1.5 1.1 0.8 0.27 48.3 0.74 0.7 0.74 10 normal 0.33 3347.5 1.3448 10.2 1.5 1.1 0.8 0.88 50.4 0.74 0.7 0.74 11 normal 0.25 3347.5 1.5424 11.4 1.5 1.2 0.8 0.42 61.0 0.74 0.7 0.74 12 wet 0.4 3380 1.705 12.1 1.6 1.3 0.8 0.51 68.6 0.74 0.7 0.74 13 normal 0.21 3380 1.5994 11.4 1.6 1.2 0.8 0.91 54.1 0.74 0.7 0.74 14 wet 0.51 3380 1.5514 10.7 1.6 1.1 0.8 0.88 77.4 0.74 0.7 0.74 15 dry 0.12 3380 1.5211 10.8 1.6 1.3 0.8 0.36 51.9 0.74 0.7 0.74 16 normal 0.23 3380 1.5613 6.7 1.6 1.2 0.9 0.1 61.3 0.74 0.74 0.76 17 wet 0.42 3380 1.6837 12.0 1.7 1.2 0.9 0.42 77.2 0.74 0.74 0.76 18 normal 0.34 3380 1.68 11.3 1.7 1.3 0.8 0.77 57.2 0.74 0.74 0.76 19 normal 0.47 3380 1.6032 8.9 1.7 1.2 0.9 0.68 62.7 0.74 0.74 0.76 20 very dry 0.03 3412.5 1.4638 6.2 1.7 1.4 1.0 0.39 49.2 0.74 0.74 0.76 21 normal 0.32 3412.5 1.5729 8.5 1.7 1.3 1.0 0.36 65 0.81 0.82 0.81 22 dry 0.1 3412.5 1.552 9.3 1.8 1.4 1.1 0.16 56.4 0.81 0.82 0.81 23 dry 0.15 3412.5 1.5363 3.3 1.8 1.4 1.1 0.25 65 0.81 0.82 0.81 24 dry 0.03 3412.5 1.5399 5.0 1.8 1.5 1.2 0.97 60 0.81 0.82 0.81 25 wet 0.27 3412.5 1.6848 12.4 1.8 1.4 1.0 0.13 79.2 0.81 0.82 0.81 277 Year Hydrol. Level WSU 1 Irrigated Area (10 3 ha) Irrigation Profit (10 9 $) Aral Inflow (km 3 ) Ground water Salinity (g/l) Reserv. Salinity (g/l) Soil Salinity (dS/m) Tax Rate (100$/ton) Salt Discharge (10 6 tons) EDS at Low_syd EDN at Low_syd EIR 2 Low_syd (cot-foa) 26 normal 0.26 3412.5 1.6314 10.9 1.8 1.3 1.0 0.27 67 0.81 0.82 0.84 27 normal 0.32 3412.5 1.6828 11.8 1.9 1.4 1.0 0.45 74.1 0.81 0.82 0.84 28 normal 0.34 3412.5 1.7107 11.8 1.9 1.4 1.1 0.22 77.6 0.81 0.82 0.84 29 dry 0.15 3412.5 1.5869 5.4 1.9 1.4 1.1 0.51 64.4 0.81 0.82 0.84 30 dry 0.02 3412.5 1.5735 4.4 1.9 1.5 1.2 0.45 69.3 0.81 0.82 0.84 Notations 1 Water saved for future use; 2 Field application efficiency in field cot-foa at demand site Low_syd. 278 7.3.2 Searching long-term solutions The GA&LP approach searches for improved solutions at two levels: the best solution among all the individuals within a generation, and improved solutions through generations. Since the objective of the long-term modeling is found by minimization, the ?best? solution is the one with the lowest objective value corresponding to the highest fitness. The objective of the long-term modeling includes multiple sub-objectives such as reliability, reversibility, vulnerability, equity, environmental integrity, and socio-economic acceptability, each with a pre-determined weight or a scaling coefficient in the objective function. (See eq. 7-2 for an example) Therefore, the ?best? solution reflects a decision preference and a compromise among multiple objectives. However, it may not be the best with regard to each individual aspect. 1 2 Q 2 2 )-(1 5 ? +?+?++ +?+?= SEASEQTEENVIN VUNREVRELOBJ (7-2) See eq. 6-28 for definitions of each items in this equation. Figure 7.1 shows the long-term objective value for all individuals within one generation. We choose two individuals which represent the ?best? and the ?worst? in the generation, respectively, according to the total objective. These individuals are compared in Figure 7.2 and Tables 7.9-11. Tables 7.9?11 show groundwater salinity, surface water salinity and soil salinity at the end of the modeling period, respectively. Figure 7.2 shows the indices corresponding to multiple criteria prescribed in the long-term modeling, and Figure 7.3 compares the annual water use benefit with the two individuals. The ?best? individual is better than the ?worst? for all items. The GA always chooses the better 279 individuals with a higher probability to create the next generation. The individual with the highest fitness in one generation represents the best solution in that generation. 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1 5 9 13 17 21 25 29 33 37 41 45 49 Individuals Objective Figure 7. 1. Long-term objective value for all individuals within one generation (Generation 1). 280 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 r i s k re s i l ie n c e vu ln e rb i li t y te m p . e q u it y s p a t ia l e q u i ty e n v i n . in t eg ri ty s - e c o n ac ce pt a b i l i t y Index value best ind. worst ind. Figure 7. 2. Values of indices for multiple criteria of the ?best? and ?worst? individuals in one generation. All the indices in this figure are by minimization as shown in eq. 6-28 or 7-2. Due to the difference among the magnitude of these indices, scaling coefficients are applied so that these items can be normalized in the long-term objective function (eq. 7-2). Figure 7. 3. Annual irrigation profit (IP) of the ?best? and ?worst? individuals in one generation (Generation 1) 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 nnwvvddnnnnnwnwdnwnnvdndddwnnndd Years Benefit (billion US $ gen 0: total 45.3 gen 30 total 45.9 281 Table 7. 9. Comparison of the best and the worst individuals within one generation ? groundwater salinity (g/l) Sites NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA worst ind. 0.6 1.7 1.9 1.3 1.4 2.4 best ind. 0.5 1.6 1.8 1.4 1.4 2.2 Table 7. 10. Comparison of the best and the worst individuals within one generation ? reservoir salinity (g/l) Reservoirs Chardara Reservoir Kayrakum Reservoir Farkhad Reservoir worst ind. 1.3 1.9 1.8 best ind. 1.3 1.7 1.7 Table 7. 11. Comparison of the best and the worst individuals within one generation ? soil salinity (dS/m) Crop Fields SITES Individuals Cot_foa Wht_maz Alf_alf Oth_oth NARYN Worst ind. 0.7 0.3 n/a 0.5 Best ind. 0.4 0.5 n/a 0.4 LOW_SYD Worst ind. 0.8 0.8 n/a 7.4 Best ind. 1.4 0.6 n/a 2.5 ARTUR Worst ind. 0.5 1.6 n/a 0.9 Best ind. 0.8 1.0 n/a 1.3 CHAKIR Worst ind. 1.0 0.6 0.8 0.8 Best ind. 0.5 0.7 0.9 1.0 MID_SYD Worst ind. 1.2 0.8 0.9 2.4 Best ind. 0.5 0.7 0.9 0.9 FERGANA Worst ind. 1.5 0.9 0.9 1.4 Best ind. 0.7 0.6 1.1 1.1 282 To show the improvement of the solution over generations, we compare the total long-term objective values for all individuals of generation 1, generation 15, and generation 30 in Figure 7.4. We have the following observations: (1) solutions in later generations are closer to better solutions than initial generations, that is to say, the average performance of a future generation is improved compared to the initial generations (as one would expect); and (2) the ?best? solution of the later generations is better than that of the initial generations. These observations clearly show that solutions converge to better ones over generations. Figure 7.5 shows the total objective value, and Figure 7.6 shows the values for reliability, reversibility, vulnerability, temporal equity, spatial equity, environmental integrity, and the socio-economic acceptability, of the ?best? solution in each of the 30 generations. The reduction of the value of the total objective shows the improvement of the minimizing objective. An improving tendency is also shown for all the sub-items. The fluctuations of these items from generation to generation shows the tradeoff among these items, which will be discussed in detail later. The improvement of the total objective, as well as its sub-items, shows that the solution is improved through generations. Tables 7.12-7.14 and Figures 7.7?7.8 further show the solution improvement by comparing two solutions, the best solution in generation 1, and the best solution in generation 30. Tables 7.12 ?7.14 present groundwater salinity, surface water salinity and soil salinity at the end of the modeling period, respectively. Figure 7.7 shows the indices corresponding to the multiple criteria prescribed in the long-term modeling, and Figure 7.8 compares the annual water use benefit of the two individuals. In all these aspects, the solution from generation 30 is better than that from generation 1. 283 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 individuals objective gen. 15 gen. 30 gen. 1 Figure 7. 4. Comparison of the total long-term objective values of generation 1, 15, and 30. Comparisons above show that the GA-LP approach not only searches for the best solution within one generation, but also searches for better solutions through generations. We define 50 individual solutions in each generation, and the search through 30 generations does not simply mean that a better solution is found among 50*30 =1500 alternatives, since in GA, the ?offspring? is always created with better ?genes? of the previous generation. That is to say, the average performance of the individuals in one generation is better than its previous generations, which is demonstrated above. We find the GA-LP approach is effective in searching better solutions of a large-scale, dynamic model like the one developed in this research. 284 0.6 0.65 0.7 0.75 0.8 0.85 0.9 gen01 gen04 gen07 gen10 gen13 gen16 gen19 gen22 gen25 gen28 objective Figure 7. 5. Comparison of long-term objective resulting from different generations. Figure 7. 6. Comparison of outputs of multiple criteria resulted from different generations. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 gen01 gen05 gen09 gen13 gen17 gen21 gen25 gen29 generations indic e risk resilence vulerability t-equity s-equity socio-econ envin. 285 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tota l-objective r e l i ab i l ity rever s i b i lity vulera b il ity te m p. eq u ity spatia l e quity envin i n tegrity s-e co n accep t . Index value gen01 gen30 Figure 7. 7. Index values of multiple criteria resulting from gen. 1 and gen. 30. Figure 7. 8. Annual irrigation profit (IP) resulting from gen. 1 and gen. 30. 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years I rri gati on profi t ( IP , 1 0 9 $) gen 0: total 45.3 gen 30 total 45.9 286 Table 7. 12. Comparison of the best individual in the first and the 30 th generation ? groundwater salinity (g/l) Sites NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA Gen 1 0.6 1.8 2 1.3 1.5 2.4 Gen 30 0.5 1.6 1.8 1.4 1.4 2.2 Table 7. 13. Comparison of the best individual in the first and the 30 th generation ? reservoir salinity (g/l) Reservoirs Chardara Reservoir Kayrakum Reservoir Farkhad Reservoir Gen 1 1.3 1.9 1.8 Gen 30 1.1 1.5 1.5 Table 7. 14. Comparison of the best individual in the first and 30 th generation ? soil salinity (dS/m) Crop Fields Demand Sites Individuals cot_foa wht_maz alf_alf Oth_oth NARYN Worst ind. 0.4 0.5 n/a 0.4 Best ind. 0.2 0.4 n/a 0.4 LOW_SYD Worst ind. 1.4 0.6 n/a 2.5 Best ind. 1.2 0.7 n/a 1.2 ARTUR Worst ind. 0.8 1 n/a 1.3 Best ind. 0.7 0.9 n/a 0.8 CHAKIR Worst ind. 0.5 0.7 0.9 1 Best ind. 0.4 0.9 0.8 0.6 MID_SYD Worst ind. 1.2 0.8 0.9 0.9 Best ind. 1 0.8 0.5 0.7 FERGANA Worst ind. 0.7 0.6 1.5 1.1 Best ind. 0.8 0.7 1.1 0.9 However, just as discussed in Section 5.3, the GA-LP approach has some limitations. For this case study, the major limitation is long computing time. Considering the procedures described in Section 6.4.1, for one generation, the 287 long-term model has to be run for each individual, and within each long-term model run, the yearly model will be run for each year. In this case study, the number of individuals is 50, and the long-term horizon is 30 years, therefore, in one generation the yearly model needs to run 50*30 =1500 times, although the grouping strategy and restarting facility described in Section 5.3 reduce the computation time in later generations. The average CPU for one generation with an Alpha Workstation UNIX 4.0D is 860 seconds. 7.4 THE BASELINE SCENARIO The baseline scenario corresponds to the hydrologic fluctuations and normal water demands presented in Section 7.2, with 5% increase of current irrigated area in the next 30 years, and 25% increase of M&I water demand. This section presents the output of the long-term modeling with the baseline scenario. The GA-LP approach is applied for the scenario through 60 generations. This number of generations is determined experimentally. The solution by the 60 th generation may not be the final global solution, however, it seems to be approximate to the final solution. Figure 7.9 shows the objective value of the best alternative in each of the 60 generations. As can be seen, (1) the curve of objective values vs. generations is almost flat in the last 10 generations, i.e. no significant changes occur in the last 10 generations; and (2) most alternatives in generation 60 are close to the best one, as shown in Figure 7.10. 288 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 1 101928374655 Generations Object ive values Figure 7. 9. Objective values of the best individual in each generations under the baseline scenario. 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 Individuals objective values Figure 7. 10. Objective values of all individuals in generation 60 under the baseline scenario. 289 7.4.1 Implications of the inter-year controls The inter-year control variables include water sustained for future use, tax rate on excessive salt discharge, irrigated area, and efficiency levels for water distribution, irrigation and drainage. Based on the values of these variables, in the following we discuss reservoir operation, salt discharge, crop pattern change, and water use facility improvement. 7.4.1.1 Reservoir operation In Chapter 4, we discussed reservoir operation based on the short-term model output. In the long-term modeling framework, reservoir operation is controlled by an inter-year control variable, namely water sustained for future year use (wsu), as well as being driven by maximizing benefits within individual years. As defined before, wsu is the sum of all reservoir storage at the last period of a study year, which will be the initial reservoir storage available in the next year. Figure 7.11 shows this item in each year labeled by its hydrologic level, and Figure 7.12 shows their values relative to the maximum reservoir storage. The ranges of the relative values for different types of hydrologic years are 0.53 or more (very wet), 0.40 ? 0.51 (wet), 0.20 ? 0.45 (normal) and 0.10 ? 0.17 (dry and very dry). However, the values for the same type of hydrologic years are also different, depending on the hydrologic fluctuations around the year. For a normal year, the value is around 0.2 if followed by a wet or very wet year, 0.3 ?0.4 if followed by a normal year, and 0.4 ?0.45 if followed by a dry or very dry year. 290 0 2 4 6 8 10 12 14 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd years storage (km 3 ) Figure 7. 11Water sustained for future use (wsu). 0 0.1 0.2 0.3 0.4 0.5 0.6 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd years with hydrologic levels Act u al reservoir st orage /max. st orage Figure 7. 12. Water sustained for future use (wsu) ? relative values. 291 The inter-year control variable, wsu, is not specified for individual reservoirs, but just presents a lower bound for the total reservoir storage at the last period of a study year. The end-year storage of each reservoir is determined within the yearly model (YM), subject to the constraint that the sum of the end- year storage of all reservoirs must not be lower than the prescribed wsu. The relative values of the ending storage to the maximum storage for the major reservoirs are shown in Figures 7.13-7.14. We can see that the major reservoirs on the main river, including the Toktogul Reservoir and the Kayrakum Reservoir, are not active in inter-year water flow control, compared to the reservoirs on the main tributaries including the Charvak and Andijan Reservoirs. That is to say, water saved for future use tends to be stored in reservoirs on the tributaries and the reservoir downstream of the main river, the Chardara Reservoir. The largest reservoir, the Toktogul Reservoir has a minimum storage (10% of the maximum active storage) for hydropower generation, and the ratio of its active storage to the maximum active storage reaches only 0.36 during 30 years considered in the case study. Figures 7.15?7.16 show the annual average reservoir utility efficiency (defined in Section 4.3.1.2) over all study years for five major reservoirs in the basin. The reservoirs on the tributary have higher values than those on the main river. However, Toktogul, which has a very large volume, exhibits smaller long- term fluctuations in filling and emptying, and it has the most consistent RUE (around 20%) of all the reservoirs. 292 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd years endingl storage/m ax. storage toktogul kaykum chadara Figure 7. 13. Relative values of the end-year storage to the maximum storage for the major reservoirs. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd years en d i n g l sto r ag e/ max. sto r ag e chakir andjan Figure 7. 14. Relative values of the end-year storage to the maximum storage for the major reservoirs. 293 0 0.1 0.2 0.3 0.4 0.5 0.6 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Reser vo ir Utilizatio n Efficien cy toktogul kaykum chadara Figure 7. 15. Annual average reservoir utility efficiency. 0 0.2 0.4 0.6 0.8 1 1.2 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Reservoir Utility Efficiency andjan chakir Figure 7. 16. Annual average reservoir utility efficiency. 294 7.4.1.2 Salt discharge control Salt discharge is related to many factors changing with years, including hydrologic level, water withdrawn for irrigation, drainage efficiency, drainage disposal (to a nearby desert), as well as the penalty tax on excess salt discharge that is an inter-year control variable in the model. Therefore, in the long-term modeling, a monotonic relationship between the penalty tax and the salt discharge over all the study years may not exist. Figure 7.17 shows the penalty tax over 30 years. Higher values are related to wet years, while lower values are related to dry years. One reason for this relationship is that more water is withdrawn for irrigation in wet years, and as a result there is increased return flow carrying more salt to the river system. The modeling output shows even in the wet years defined in Section 7.2.2, the crop yields do not reach their maximum, because the irrigation water demand can not be fully provided. Therefore, in the wet years with more water supply, more withdrawal occurs. The excessive salt discharge in different hydrologic years is presented in Figure 7.18. This figure shows an increasing tendency of salt discharge over the years (almost doubling over 30 years), which implies an increase of water and soil salinity in the basin. Clearly, this increasing salt discharge will lead to environmental unsustainability in the long run. 295 0 20 40 60 80 100 120 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels T a x r a te (US$ /to n ) Figure 7. 17. Penalty tax on excess salt discharge vs. years. 0 5 10 15 20 25 30 35 40 45 50 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic years Salt dis c harge (ton) Figure 7. 18. Excessive salt discharge vs. years. 296 7.4.1.3 Crop pattern change It is assumed that crop patterns may be changed every five years in the modeling period. The model determines crop patterns every five years, based on the possible range for each crop. Figures 7.19?7.24 present the crop patterns for different periods at each demand site, respectively. The crop pattern in 1987 (Raskin, 1992) is also shown in each of these figures, and then for each demand site, crop patterns from the model can be compared to the actual status in 1987. For all demand sites, these figures show that (1) crop patterns from the model are different from those in 1987; (2) irrigated area for cotton is significantly decreased and that for wheat-maize is significantly increased compared to the area in 1987; and (3) based on the model output, irrigated area is rotated between cotton and wheat over years. Compared to 1987, irrigated area for cotton in Fergana, Mid_syd, and Naryn decreases, while it increases in Chakir, Artur, and Low_syd. In Artur, and Low_syd, irrigated area for other crops (including rice) is significantly lower than the actual value in 1987. The crop pattern change shown by the model mainly reflects the requirements of water and soil quality conservation, ecological water release to the Aral Sea, and agricultural production enhancement. Cotton and wheat are the most attractive crops to produce in the basin. The long-term modeling result shows there are great changes for the irrigated area of these two crops, and field rotation is suggested between them. Cotton is more economically attractive than wheat. However, cotton needs more water for irrigation in the basin, especially in the summer season when peak irrigation withdrawal occurs. Also cotton has higher salinity tolerance, which allows water application (i.e., drainage reuse and 297 groundwater) with higher salinity. In a long-term frame, this leads to salinity accumulation in the soil. Therefore, the rotation of these two crops reflects the objective of this modeling: sustaining irrigation-based economy without deteriorating the environment. In order to study crop patterns in future years more comprehensively, extended work is needed to incorporate more factors, such as demands for various crops, crop cost and selling price, and the changes of these items over future years, into the modeling framework. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 cot-foa wht-maz alf-alf oth-oth crop fields area f o r a c r op/ t o t a l area in 1987 mod:1-5 th yr. mod:6-10 th yr. mod:11-15 th yr. mod:16-20 th yr. mod:21-25 th yr. mod:26-30 th yr. Figure 7. 19. Crop patterns in different periods for demand site Naryn. 298 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 cot-foa wht-maz alf-alf oth-oth crop fields ar ea for a c r op/total ar ea in 1987 mod:1-5 th yr. mod:6-10 th yr. mod:11-15 th yr. mod:16-20 th yr. mod:21-25 th yr. mod:26-30 th yr. Figure 7. 20. Crop patterns in different periods for demand site Low_syd. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 cot-foa wht-maz alf-alf oth-oth crop fields area f o r a crop/ t o t a l area in 1987 mod:1-5 th yr. mod:6-10 th yr. mod:11-15 th yr. mod:16-20 th yr. mod:21-25 th yr. mod:26-30 th yr. Figure 7. 21. Crop patterns in different periods for demand site Artur. 299 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 cot-foa wht-maz alf-alf oth-oth crop fields area of one crop/total are a in 1987 mod:1-5 th yr. mod:6-10 th yr. mod:11-15 th yr. mod:16-20 th yr. mod:21-25 th yr. mod:26-30 th yr. Figure 7. 22. Crop patterns in different periods for demand site Chakir. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 cot-foa wht-maz alf-alf oth-oth crop fields area for one crop/total area in 1987 mod:1-5 th yr. mod:6-10 th yr. mod:11-15 th yr. mod:16-20 th yr. mod:21-25 th yr. mod:26-30 th yr. Figure 7. 23. Crop patterns in different periods for demand site Fergana. 300 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 cot-foa w ht-maz alf-alf oth-oth crop fields area of one crop/total area in 1987 mod:1-5 th yr. mod:6-10 th yr. mod:11-15 th yr. mod:16-20 th yr. mod:21-25 th yr. mod:26-30 th yr. Figure 7. 24. Crop patterns in different periods for demand site Mid_syd. 7.4.1.4 Water use facility improvement Three inter-year variables, including the water distribution efficiency (EDS), the irrigation efficiency (EIR), and the drainage efficiency (EDN), are computed in the modeling framework in order to determine the appropriate water supply and application facility improvements for sustainable water management in the area. Water distribution efficiency vs. years is presented in Figure 7.25. For most demand sites, the value of this item in the next 30 years increases up to 0.75- 0.80, which is feasible in the basin according to EC (1995). This item increases particularly in later years. Figure 7.26 shows the drainage efficiency vs. years in each demand site. The upstream demand site, Naryn, has a relatively lower value over years, while all mid-stream and downstream demand sites have higher values, especially in later years. The numbers shown in this figure are within the possible ranges of the drainage improvement in the basin. Drainage is important in preventing soil salinity accumulation and waterlogging. 301 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 YR01 YR06 YR11 YR16 YR21 YR26 Years Distrib u t io n efficien cy ( EDS ) NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA Figure 7. 25. Water distribution efficiency (EDS) at each demand site. 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 YR01 YR06 YR11 YR16 YR21 YR26 Years Drainage efficiency ( EDN ) NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA Figure 7. 26. Drainage efficiency (EDN) at each demand site. 302 Irrigation efficiency is computed for the four types of crop fields at each demand site. Figures 7.27-7.30 show this item for all crop fields in each demand site, respectively. At all demand sites, except for the downstream demand site Low_syd, irrigation efficiency increases significantly. This is expected because in later years both irrigation water demand and non-irrigation water demand grow significantly. Demand sites Naryn and Mid_syd have a higher irrigation efficiency for all crops in later years, whereas demand site Low_syd has a much lower irrigation efficiency for all crops over most years. This may be due to the high leaching requirement to mitigate the soil salinity effect in this demand site. In the last 10 years, irrigation efficiencies increase up to 0.75-0.85, which means the current major irrigation system (furrow system) needs to be replaced by advanced systems such as drip or sprinkler systems. 0.5 0.55 0.6 0.65 0.7 0.75 0.8 YR01 YR06 YR11 YR16 YR21 YR26 Years Irrigation efficiency ( EIR ) NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA Figure 7. 27. Irrigation efficiency (EIR) at each demand site - in crop field cotton- forage. 303 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 YR01 YR06 YR11 YR16 YR21 YR26 Years Irrigation effic iency (EIR) NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA Figure 7. 28. Irrigation efficiency (EIR) at each demand site - in crop field wheat- maize. 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 YR01 YR06 YR11 YR16 YR21 YR26 Years Irrig a tio n efficien cy ( EIR ) CHAKIR MID_SYD FERGANA Figure 7. 29. Irrigation efficiency (EIR) at each demand site - in crop field alfalfa- alfalfa. 304 0.5 0.55 0.6 0.65 0.7 0.75 0.8 YR01 YR06 YR11 YR16 YR21 YR26 Years Irrigation efficiency ( EIR ) NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA Figure 7. 30. Irrigation efficiency (EIR) at each demand site - in crop field other- other. Drainage reuse is not defined as a variable in the inter-year control program (IYCP), but it is determined in the yearly models (YM) based on prescribed capacity limits and investment constraints. Figure 7.31 presents the total drainage reuse in each of the 30 years. The figure shows that drainage reuse basically occurs in very dry years and years after consecutive dry years. However, drainage reuse is recommended for the upstream demand site Naryn in all years. This is explainable because the salinity in drainage at this demand site is comparably low and the reuse will not create high salinity in the crop field. Demand site Fergana, which has the largest irrigation water demand among the demand sites has the largest amount of drainage reuse in very dry years. Drainage reuse tends to increase in later years due to increased water demands. In the long-term model, in addition to the normal drainage facility specified by the inter-year control variable, drainage efficiency, we assume that 305 additional drainage pumping and disposal to nearby deserts may be realized if the groundwater table rises over a critical level, to prevent waterlogging. This item is determined within individual years according to the groundwater table status in those years. Figure 7.32 shows the amount of drainage pumping and disposal at demand sites where waterlogging may occur. Referring to Figure 7.26, over the study years at demand site Mid_syd, the excess drainage pumping decreases with the increase in drainage efficiency in later years. The same shift occurs in demand site Low_syd. Improved drainage facilities are therefore necessary for preventing waterlogging problems at these sites. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Dr ai nage r e use (km^ 3) NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA Figure 7. 31. Drainage reuse in each of the 30 years 306 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels D r ainage disposal ( k m3) LOW_SYD ARTUR MID_SYD Figure 7. 32. Amount of drainage disposal at the demand sites where waterlogging may occur. 7.4.2 Water uses and long-term consequences The long-term model traces the economic and environmental consequences of the expected water use practices during 30 years, and controls these consequences according to the prescribed sustainability criteria. In the following, the relations between irrigation water use and the associated economic and environmental impacts are explored according to the long-term modeling output under the baseline scenario. 7.4.2.1 Soil salinity High salinity in irrigation water, poor field drainage, and a high groundwater table may lead to soil salinity accumulation over a long time. The baseline result shows that the crop fields in demand sites Naryn, and Chakir can avoid soil salinity accumulation, while demand sites Fergana, Mid_syd, and 307 Autur will experience increased soil salinity but no serious effects on crops occur. However, crop fields, especially the cotton fields of demand site Low_syd, will suffer a tremendous salinity increase, which will be above the crop salinity tolerance. Figure 7.33 shows the salinity in the crop field cot_foa (cotton ? forage) of demand sites Fergana, Mid_syd and Low_syd, and Figure 7.34 shows the salinity in crop field wht_maz (wheat-maize) of the three demand sites in each of the 30 years. Soil salinity in field wht_maz is lower than that in field cot-foa since cotton has a higher salt tolerance than wheat and maize. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd years Soil s a linity in r oot zone (dM/s ) LOW_SYD MID_SYD FERGANA Figure 7. 33. Soil salinity in crop field cot_foa (cotton?forage) at selected demand sites. 308 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years S a lt c o n c e n tr a tio n ( g /l) LOW_SYD MID_SYD FERGANA Figure 7. 34. Soil salinity in crop field wht_maz (wheat-maize) at selected demand sites. 7.4.2.2 Waterlogging Because of excess application of irrigation water (low application efficiency) and ineffective drainage, the groundwater table may rise into the root zone of irrigated crops, resulting in a waterlogging situation. In the long-term modeling, we assume that if waterlogging occurs in a demand site, then additional drainage pumping and disposal must be carried out to keep the groundwater table below the critical level. Therefore, the amount of additional drainage pumping and disposal at a demand site is an indication of a potential waterlogging status at that demand site. We can see in Figure 7.32 that waterlogging problems occur at the midstream and downstream area of the basin (demand sites Mid_syd and Low_syd). 309 7.4.2.3 Water quality reduction Figure 7.35 shows the salt concentration in the groundwater vs. years at each demand site. At the most upstream demand site, Naryn, salt concentration in the groundwater decreases, which may be due to a high initial salt concentration in the groundwater. However, all other groundwater sources are affected by the salt load from irrigation fields with deep percolation. High salt concentration (up to 2.1 g/l) occurs in the groundwater at the downstream demand site Low_syd, where the salt concentration in deep percolation is high. As can be seen in Figures 7.27-7.30, the irrigation efficiency in this demand site is relatively low in later years, which causes increased deep percolation and affects the groundwater quality in that region. A significant salinity increase in groundwater also occurs at demand sites Fergana and Mid_syd due to high salt concentration in deep percolation from the crop field. Figure 7.36 shows the possible salt concentration in reservoirs on the main river. The upstream reservoir, Toktogul, is not affected. For the other three reservoirs at the midstream and downstream, however, the salt concentration increases by 1.5 times the initial concentration at the end of the study period. 310 0 0.5 1 1.5 2 2.5 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Salt concentration (g/l) UP_GW FERGA_GW MIDSYN_GW CHAKIR_GW ARTUR_GW LOWSYN_GW Figure 7. 35. Salt concentration in groundwater at each demand site. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Sa lt c onc e n t r a t ion ( g /l) TOKGUL_REV CHARDA_REV KAYKUM_REV FARHAD Figure 7. 36. Salt concentration in reservoirs on the main river 311 7.4.2.4 Environmental and ecological water depletion The planned inflow to the Aral Sea based on the hydrologic level of each year and the calculated inflow are plotted in Figure 7.37. Generally, in dry and very dry years, the calculated inflow is below the planned flow; this occurs also in some wet years due to the high inflow target. In normal years, the required inflow is basically satisfied. Considering the total inflow over 30 years, the target of the inflow is 288 km 3 , while the computed inflow from the model is 258.4 km 3 , about 10% lower than the goal. This condition is closely related to river water withdrawal for irrigation. 0 2 4 6 8 10 12 14 16 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Fl ow rel ease to the Aral Sea (Km3) computed total =259.4 km^3 goal : total =288 km^3 Figure 7. 37. Planned inflow to the Aral Sea vs. calculated inflow 7.4.2.5 Irrigated area reduction and decline in crop yield In the baseline run, irrigated area only declines in very dry years. However, the price of sustaining the irrigated area is environmental problems, such as soil salinity accumulation (see Fig. 7.33) and water quality reduction in surface and groundwater (see Figs. 7.35 and 7.26), especially in the midstream 312 and downstream demand sites. As we will show later, any increase in irrigated area in these demand sites will worsen these problems. Figures 7.38-7.39 show the agricultural profit over years at each demand site, and Figure 7.40 shows the total agricultural profit in the basin over the years. The tendency of increasing agricultural profits results from the projected increase of irrigated area (Table 7.1), and possibly from improved water distribution, irrigation and drainage facilities. However, the effect from hydrologic fluctuation is obvious. In dry and very dry years, the crop yields decline. This causes a reduction of irrigation profit shown in these figures. This section presents the results from a baseline run that is defined according to the hydrologic fluctuations and normal water demands presented in Section 7.2. The ?baseline? is expected to provide a basic guess of the long-term consequences of water uses subject to the sustainability criteria. The uncertainty ranges of these consequences will be further addressed in the scenario analysis presented in Section 5. 0 0.05 0.1 0.15 0.2 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Irri g ation Profit ( billion US$ ) NARYN LOW_SYD ARTUR Figure 7. 38. Irrigation profit at each demand site. 313 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Irrigation profit (billion US $) MID_SYD FERGANA CHAKIR Figure 7. 39. Irrigation profit at each demand site 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with Hydrologic levels Total agricultural profit (109US$) Figure 7. 40. Irrigation profit in the basin 314 7.4.3 Long-term modeling output vs. short-term modeling output As mentioned before, the objective of the short-term model is to maximize benefit from water uses within a year with given hydrologic conditions and environmental constraints. This model does not take into account the criteria for sustainable water resources management that are included in the long-term modeling. The short-term modeling output has been discussed in Chapter 4, and here it is compared with the long-term modeling output. For convenience, the output from the short-term model under normal hydrologic conditions is compared to the average output of normal years from the long-term modeling. 7.4.3.1 Crop patterns The irrigated area resulting from the short-term modeling is shown in Table 4.43, which shows the irrigated area for the major crops at each demand site. The allocation of irrigated area resulting from the long-term modeling is presented in Figures 7.20-7.24. The short-term modeling shows that the crop field cotton-forage dominates the irrigated area at all demand sites except for the downstream demand site Low_syd. However, in the long-term modeling framework, irrigated area for wheat-maize increases significantly, the pattern cotton-forage no longer dominates the irrigated area, and irrigated area is rotated between cotton-forage and wheat-maize over the years. The short-term modeling also implies that the irrigated area at the downstream demand site Low_syd is reduced to 20% of total available irrigated area, which is not acceptable in the long-term modeling framework due to the equity concerns included in the sustainability criteria. Thus, due to the equity among demand sites, and due to even development of irrigation facilities, no 315 reduction of irrigated area at that demand site in normal hydrologic years is suggested in the long-term modeling framework. 7.4.3.2 Irrigation profit The total irrigation profit resulting from the short-term modeling reaches $2.75 billion in a normal year (Table 4.49). However, it is only between 1.25 to $1.64 billion in the long-term modeling (Figure 7.40). The difference is a result of several reasons. First, in the study area, cotton is the crop with the highest net profit under the given crop prices and costs (Table 4.19). From the short-term modeling, the cotton-forage area covers up to 70% of the total irrigated area, whereas in the long-term modeling, the percentage is only between 30% to 38%. Second, as shown in Table 7.15, the irrigated area is distributed differently among demand sites in the short-term and the long-term modeling. Compared to the long-term modeling, the percentages at the downstream demand sites are lower, and those at the upstream and mid-stream demand sites are higher in the short- term modeling. The downstream demand sites have lower water use benefit due to lower water quantity availability and higher water and soil salinity. Third, in the short-term modeling, we assume that the end-year reservoir storage is equal to the reservoir storage at the beginning of that period, and all inflows coming within one year can be used for water supply purposes in that year. However, for the long-term modeling, a long-term control variable, wsu constraints the end-year reservoir storage. Thus, some water coming in a normal years may not be used as it is saved for the following dry year. 316 Table 7. 15. Percentages of irrigated area under the short-term and long-term modeling NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA short-term 6.5% 4.0% 4.9% 14.5% 22.9% 47.2% long-term 5.2% 13.8% 5.5% 12.3% 19.9% 43.3% Actual percent. in 1987 5.2% 13.5% 5.2% 14.0% 21.6% 41.4% 7.4.3.3 Water and soil salinity High irrigation profits can lead to serious water and soil quality deterioration. As discussed in Chapter 4, Section 4.3.1.3, basin-wide salinity distribution analysis, with the short-term modeling, at the mid-stream and downstream sites, salinity in reservoirs in the last time period increases to about 1.5 times that at the first period. Groundwater salinity does not change significantly within the one-year time frame. However, soil salinity can increase to unacceptable levels in just one cropping season, not only at downstream demand sites, but also at mid-stream and upstream demand sites (see Figure 4.9). As discussed in Section 7.4.2.3, over 30 years, salinity in reservoirs increases up to 1.5 times of that in the beginning year, soil salinity increases slightly at all demand sites except for the downstream demand site where soil salinity increases more strongly. 7.4.3.4 Reservoir operation Reservoir operation with the short-term and the long-term modeling has been discussed in Section 4.3.1.2 and 7.4.1.1, respectively. Table 7.16 presents the reservoir utilization efficiency (RUE) computed based on the output from the short-term and long-term modeling, respectively. The reservoirs, Toktogul, Chardara, and Kayrakum are on the main river, and the other reservoirs presented 317 in Table 7.16 are on the tributaries. With the short-term modeling, the values of RUE of the reservoirs on the main river are higher, while the values of RUE of the reservoirs on the tributaries are higher in the long-term modeling. The time period for reservoir operation is one month for both the short-term and the long- term modeling, and the values of RUE shown in Table 7.11 are averaged over one year (short-term) and over multiple years (long-term). Therefore, the numbers shown in Table 7.11 do not reflect the exact reservoir utilization efficiency. However, at least the figures show that the reservoir operation is different for short-term and long-term river basin management purposes in the study area. Table 7. 16. Reservoir utilization efficiencies with the short-term and long term modeling. Toktogul Chardara Kayrakum Bugun Andijan Charvak short-trem 0.27 0.39 0.08 0.03 0.43 0.05 long-term * 0.16 0.12 0.01 0.38 0.56 0.38 * Average value over 30 years. 7.4.3.5 Irrigation and drainage infrastructure Both the short-term and the long-term modeling show the necessity of improvements to the irrigation and drainage infrastructure. However, some differences can be identified for them, such as (1) the short-term modeling shows the irrigation application efficiency (EIR) increases to its upper bound in each crop field at each demand site, while the long-term modeling shows that the irrigation application efficiency at the downstream demand sites increases much slower than at the other demand sites (Section 7.4.1.4); (2) the short-term modeling shows that the drainage efficiency improvements are not economically attractive, while it increases over the study years and is shown to be attractive to the long-term model; and (3) the short-term modeling shows positive 318 contributions to irrigation benefit and total benefit when drainage reuse is increased, without consideration of salinity accumulation due to drainage reuse, while the long-term modeling shows drainage reuse only take places in very dry years or consecutive dry years, and only the upstream demand site reuses drainage in all years. It becomes clear, through the comparisons between the short-term and the long-term modeling, that the long-term modeling performs according to the sustainability criteria defined before. With respect to water supply, the long-term modeling shows consideration of reliability and equity with regard to irrigation and the environment, the long-term modeling shows a balance between irrigation profits and their associated environmental consequences through crop pattern changes and appropriate irrigation and irrigation infrastructure improvements. In the rest of this chapter, the long-term modeling is further examined through the analysis of several scenarios considering various water demands, and through a specific sustainability analysis that discusses each aspect of the prescribed sustainability criteria. 7.5 SCENARIO ANALYSIS To explore robust relationships between water uses and associated economic and environmental consequences, we define several scenarios with specific changes in water demands: ? Zero scenario. This scenario assumes no change in irrigated area, crop pattern, non-irrigated water demand, water distribution facility, and irrigation and drainage facility. Put in another way, this scenario runs the current condition over 30 years only subject to hydrologic fluctuations; ? Irrigation scenarios. Four irrigation scenarios are defined, each of which is based on a projection of the increase rate of irrigated area (See table 7.1). 319 These scenarios range from low to high increase of the irrigated area by -10%, 5%, 10% and 58% in the next 30 years, respectively. ? I&M scenario. This scenario proposes a high increase of industrial and municipal (I&M) water demand (See table 7.1); ? High demand scenario. This scenario assumes both high irrigation and high industrial and municipal water demands; and ? Flow scenario. This scenario fully satisfies the environmental and ecological water demand. ? Hydropower scenario. This scenario put the highest priority on hydropower generation. That is to say, the power demand of Kyrgyzstan in winter months (October - March) will be satisfied at the greatest possibility. The model is run under these scenarios, respectively. As applied to the baseline scenario, the GA-LP approach runs over 60 generations for each of other scenarios. The best solution of the 60 th generation is taken as the final solution of each scenario for analysis. 7.5.1 What if the current status continues? In the following, the result from the zero scenario is presented and compared with the result from the baseline scenario. Figure 7.41 shows the comparison of total agricultural profit vs. years under the baseline and the zero scenario. Irrigation profit under the zero scenario is reduced to 74% of that under the baseline scenario in the first year, and continually reduced to 33% in the last year. The magnitude of the reduction increases with years. 320 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Pro f it (b illio n US$ ) baseline scenario zero scenario Figure 7. 41. Total agricultural profits under the baseline and the zero scenario Among the demand sites, the midstream and downstream demand sites have a larger reduction in irrigation profit than upstream demand sites. Figure 7.42 presents the ratio of irrigation profit under the zero scenario to that under the baseline scenario, for selected demand sites. The figure also shows that irrigation profit under the zero scenario decreases more in later years due to higher water demands without simultaneous improvement in water supply and application capacities. The inflow to the Aral Sea is also reduced in some years under the zero scenario, as shown in Figure 7.43. This implies that river water withdrawal under the zero scenario is even larger than that under the baseline scenario because of low water distribution and use efficiency. 321 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years zero scen/baseline scen Fergana Mid_syd Low_syd Figure 7. 42. Ratios of agricultural profit under the zero scenario to that under the baseline scenario. 0 2 4 6 8 10 12 14 16 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years In flo w (km 3 ) baseline scen: total 259.3 zero scen: total 239.5 target: total 288.0 Figure 7. 43. Inflow to the Aral Sea (km 3 ) under the baseline and the zero scenario. 322 With low water distribution efficiency, more of the diverted water does not reach the crop field, but is lost to evaporation and groundwater recharge. Moreover, lower drainage efficiency allows more drainage to percolate into the groundwater. Figure 7.44 shows less salt discharge to the river under the zero scenario than under the baseline scenario. Because of less salt discharge, reservoir salinity does not increase over the years under the zero scenario. As discussed in Chapter 4, Section 4.3.2.2, a low field application efficiency means more water for salt leaching in the crop root zone. Results from the zero scenario shows that if the current status continues, there will be a slight salinity increase (up to 0.6 g/l at demand site Low_syd) in the soil even at the downstream demand sites. The groundwater salinity under the zero scenario shows an increasing tendency in all demand sites due to low drainage efficiency. At demand sites Low_syd and Fergana, groundwater salinity, up to 2.0 and 1.6 g/l respectively, has similar changes with that under the baseline scenario. 0 5 10 15 20 25 30 35 40 45 50 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Excess salt discharge (million tons) baseline zero scen. Figure 7. 44. Salt discharge to the river under the baseline and the zero scenario. 323 As a summary, the results from the zero scenario reflect a tradeoff between irrigation water supply and environmental objectives. Maintaining the current status of water supply, water use and water demand over a period of 30 years will lead to a large decline in irrigation profits although severe environment problems may be avoided. 7.5.2 What if the irrigated area decreases or increases by various rates? In the baseline scenario, it is assumed that the total irrigated area increases by about 5% in the next 30 years. The baseline scenario is taken as one of the irrigation scenarios. The other irrigation scenarios assume the total irrigated area decreases by about 10%, or increases by 10% and 58% in the next 30 years, respectively. In the following, the results from these irrigation scenarios are presented. The agricultural profits under the irrigation scenarios are plotted over 30 years in Figure 7.28. Irrigation profit is higher for the scenarios with higher increasing rates of the irrigated area. However, in the very dry years and the last one of consecutive dry years (year 24), the profit does not increase significantly with the irrigated area. Actually, the result shows that in these years, the area for some crops is not planted due to water shortage and excess soil salinity. Especially in the final 10 years, the soil salinity has reached up to the crop salinity tolerance in some crop fields, and part of the crop area is left unplanted. Taking the scenario with the highest increasing rate (58%) as an example, in the downstream demand site Low_syd, in year 22, the irrigated area for wheat-maize is reduced from 207.0 to 59.2 (1,000 ha), as in that year, soil salinity in the field of wheat-maize is up to 4.5 dS/m. Since most of the crop field is left unplanted, rainfall in the field is mainly used for salt leaching. In the following year, the soil 324 salinity of this field is thus reduced to 3.0 dS/m, and the crop area then increases to 127.0 (1,000 ha). 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Irrigation profit( IP , 10 9 US$) irri. area incr. by 58% irri. area incr. by 10% irri. area incr. by 5% irri. area decr. By -10% Figure 7. 45 Agricultural profits under the baseline and the irrigation scenario Due to the increased water withdrawal for irrigation, the inflow to the Aral Sea is tremendously reduced in some years under the irrigation scenarios with higher irrigated area increasing rate, as shown in Figure 7.29. The total inflow in 30 years under the highest irrigation area is reduced to 60% of that under the baseline scenario. 325 0 2 4 6 8 10 12 14 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Infl ow (km 3 ) Irri. area incr. by 58%, total 173 km3 irri. area incr. by 10% total 266.2 km3 irri. area incr. by 5%, total 259.3 km3 irri. area decr. by -10%, total 301.5 km3 Figure 7. 46. Inflow to the Aral Sea under the baseline and the irrigation scenario Environmental problems are expected to get worsen with increase of the irrigated area in the river basin, due to the increased irrigation water withdrawal and increased salinity discharge. The total amount of excess salt discharge under the irrigation scenario with the highest increasing rate is 1.3 times the amount of that under the scenario with a 10% decreasing rate. Figures 7.30 ? 32 present the excess salt discharge, salt concentration in the groundwater, and salinity in the soil. 326 As can be seen, when the increasing rate of irrigated area is high, agricultural production is increased while substantial risk is imposed on soil and water quality, as well as on the environment. On the other hand, as mentioned before, during the later years, the water and soil salinity is so high that some irrigated area is left unplanted in the downstream demand sites. Therefore, it may be concluded that a larger increase in the irrigated area will further deteriorate the sustainability of the water resources system in the basin. 0.9 10.9 20.9 30.9 40.9 50.9 60.9 70.9 80.9 90.9 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Sal t mass (10 6 ton) irri. area incr. by 58%, total 1309 million tons irri. area incr. by 10% , total 1031 million tons irri. area incr. by 5%, total 975 million tons irri. area decr. By -10%, total 947 million tons Figure 7. 47. Excessive salt discharge to the river system 327 0.5 1 1.5 2 2.5 3 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Salt concentration (g/l) irri. area incr. by 58% irri. area incr. by 10% irri. area incr. by 5% irri. area decr. By -10% Figure 7. 48. Salinity in the groundwater at demand site Low_syd under the baseline and the irrigation scenarios 0 0.5 1 1.5 2 2.5 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Soil salinity (dS/m) irri. area incr. by 58% irri. area incr. by 10% irri. area incr. by 5% irri. area decr. By -10% Figure 7. 49. Salinity in the soil (demand site: Low_syd, and crop field cotton-forage) under the baseline and the irrigation scenario. 328 7.5.3 What if the I&M water demand increases rapidly? Due to the anticipated rapid socio-economic development in the basin, more water may be needed for industrial and municipal purposes. In the baseline scenario, I&M water demand is assumed to increase by 1% per year, and in the I&M scenario, the increasing rate is up to about 3% per year. In year 30, the I&M water demand is 2 times of the demand in year 1. Since we assume that the I&M water demand must be satisfied as a model constraint, more I&M water demand will affect both irrigation water supply and ecological water use. This is discussed in the following based on the results from the M&I scenario. Figure 7.50 presents two ratios comparing the I&M scenario and the baseline scenario over years. One is the ratio of total irrigation profit, and the other is the ratio of inflow to the Aral Sea under the I&M scenario to the inflow in the baseline. The minimum ratio of agricultural profit is about 86%, while the minimum ratio of inflow to the Aral Sea is about 31%, and both minimum ratios take place year 24. In very wet years, the effect is less severe, while in very dry years or years after consecutive dry years, the effect is considerable. Water and soil quality is slightly better in this scenario compared to the baseline, due to less water withdrawal for irrigation. The groundwater salinity in downstream demand site Low_syd increases to 1.9 g/l in year 30, which is lower than 2.1 g/l under the baseline scenario. The highest water salinity occurs in the Kayakum Reservoir at 1.4 g/l. This is slightly lower than the 1.5 g/l under the baseline scenario. Soil salinity in the cotton-forage field at Low_syd in year 30 is also slightly lower (1.2 g/l vs. 1.3 g/l). 329 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Ra tios Ratios of flow releaset Ratios of agri. profit Figure 7. 50. Comparison of total agricultural profit and Aral Sea inflow: ratios of the I&M scenario to the baseline scenario. 7.5.4 What if both the irrigated area and the I&M water demand increase rapidly? The high demand scenario combines the water demand assumptions in both the irrigation scenario (the highest irrigated area expansion) and the I&M scenario, assuming that the irrigated area increases by 2% per year, and that the non-irrigation water demand increases by 3% per year. Figure 7.51 shows the ratios of agricultural production, and each of them shows comparisons of the irrigation and high demand scenario with respect to the baseline scenario, respectively. Ratios under the high demand scenario are lower than those of the irrigation scenario, because under the former, more water is used for non-irrigation purposes. Particularly in dry and very dry years, irrigation profit does not increase although the irrigated area increases. Part of the irrigated 330 area is actually left unplanted due to water shortage or/and high soil salinity. This condition is more apparent in the high demand scenario due to the high demand for both the irrigation and non-irrigation water. 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Ratios of agri. profit high demand to baseline irrigation to baseline Figure 7. 51. Comparison of total agricultural profit under the irrigation scenario and the high demand scenarios: ratios relative to the baseline scenario. The results show that the inflows to the Aral Sea are much reduced due to the high demand for both irrigation and non-irrigation water under the high demand scenario, as shown in Figure 7.52. The total amount of inflow in 30 years is 258, 173, and 143 km 3 under the baseline, irrigation and high demand scenarios, respectively. The inflow is about one half of the inflow target (288 km 3 ) under the high demand scenario. Thus, rapid increases in irrigation and I&M water demands will continually reduce the inflows to the Aral Sea. Changes in water and soil quality are shown in Figures 7.53-7.56. Basically, the impacts under the high demand scenario are higher than in the 331 baseline scenario but lower than in the irrigation scenario. We notice that the sequence of irrigation water supply from high to low is: irrigation, high demand, and then baseline scenario, and water and soil salinity from high to low follows the same sequence. Here, again we see that irrigation water withdrawal is critical for the conditions of water and soil salinity. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Ratio (to inflow target) baseline scen: total 259.3 High demand. scen: total 143 irri. scen: total 173.5 Figure 7. 52. Comparison of inflow to the Aral Sea under the baseline, the irrigation, and the high demand scenario: ratios relative to the inflow target. 332 0 20 40 60 80 100 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years excess salt discharge (million tons) baseline scen: total 975 high demand total 1118 irrig. scen: total 1310 Figure 7. 53. Comparison of water and soil quality under the baseline, the irrigation, and the high demand scenarios ? excess salt discharge 0 0.5 1 1.5 2 2.5 3 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years salt concentr ation (g/l) baseline irrigation high demand Figure 7. 54. Comparison of water and soil quality under the baseline, the irrigation, and the high demand scenarios ? groundwater salinity at demand site Low_syd. 333 0 0.5 1 1.5 2 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years salt concentration (g/l) baseline scen. irri. Scen. high demand Figure 7. 55. Comparison of water and soil quality under the baseline, the irrigation, and the high demand scenarios ? surface water salinity of the Kayakum Reservoir 0 0.5 1 1.5 2 2.5 3 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Soil salinity (dS/m) baseline irrigation high demand Figure 7. 56. Comparison of water and soil quality under the baseline, the irrigation, and the high demand scenarios ? soil salinity in field cotton-forage at demand site Low_syd. 334 7.5.5 What if the target of release to the Aral Sea is fully satisfied? Under this scenario, we assume that the target inflow to the Aral Sea is satisfied in all years. It is found that even under this constraint, the irrigated area is still not affected much. However, the agricultural profit is considerably reduced due to lower crop yields. Figure 7.57 shows the total agricultural profit under this scenario and the baseline scenario. The profit is more affected in wet years, because the flow target in wet years is high. The total value of irrigation profit in all years under the flow scenario is about 90% of that under the baseline scenario. The excessive salt discharge in 30 years under the flow scenario is 948 million tons, slightly less than the 975 million tons under the baseline scenario. Impacts on salinity in the surface and groundwater water and on the soil salinity under this scenario are close to those under the baseline scenario. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Pr ofit (billion U S $ ) baseline scenario flow scenario Figure 7. 57. Total agricultural profit under the baseline and the flow release scenario 335 7.5.6 What if the first priority is put on hydropower generation? Hydropower generation is considered in the long-term modeling by including net hydropower profit in the total benefit of water uses in the basin. Because the magnitude of the hydropower profit is far less than the irrigation profit in the whole river basin, hydropower generation will have less priority than irrigation in the modeling, if no additional constraint is included in the model. However, as mentioned before, in the real world, the upstream country Kyrgyzstan, who depends on hydropower for most of its power supply, especially in winter period, attempts to hold more water coming in vegetation period in the Toktogul Reservoir for hydropower generation in winter period. This arises a major negotiation between Kyrgyzstan and downstream countries who need more water for irrigation in the vegetation period. One alternative is to have Kyrgyzstan not hold water in vegetation period, while the downstream countries help Kyrgyzstan to get some reimbursement in power generation, for example, trading coal to Kyrgyzstan at a cheap price. All other scenarios defined above assume this policy is feasible, and then hydropower generation resulting from the modeling under those scenarios is much lower than that in the current reality. The hydropower scenario assumes Kyrgyzstan holds enough water in the Toktogul Reservoir so that hydropower generation in winter months will meet the demand as much as possible. This scenario is implemented by putting a penalty item in the objective function of the yearly model (YM). If hydropower generation in winter months is less than the demand, the objective (the total benefit of water uses) will be penalized. A large weight is assigned to the hydropower penalty item so that hydropower generation gets higher priority than other water uses including irrigation and environmental and water uses. In the following the result from the hydropower scenario is compared to that from the 336 baseline scenario, which shows the effect from the upstream hydropower generation to the downstream irrigation is then studied. Figure 7.58 shows the agricultural profit resulting from the baseline scenario and the hydropower scenario, respectively. The values of agricultural profit under the hydropower scenario are lower than those under the baseline scenario in all years. The hydropower generated in non-vegetation months (October ? March) resulting from the two scenarios is presented in Figure 7.59. The values of hydropower are higher under the hydropower scenario than those under the baseline scenario in all the years. For both the irrigation profit and the hydropower, the differences between the two scenarios are relative small in wet years, and large in dry years, which reflects the effects of water scarcity to water uses in the river basin. 0.6 0.8 1 1.2 1.4 1.6 1.8 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Agricultural profit (billion US$) Baseline scen. Hydropower scen. Figure 7. 58 Irrigation profit (IP) under the hydropower scenario and the baseline scenario. 337 0.6 1000.6 2000.6 3000.6 4000.6 5000.6 6000.6 7000.6 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic levels Hydropwer (million KWH) Baseline scen. Hydropower scen. Figure 7. 59. Hydropower in non-vegetation months (Oct.-Mar.) under the hydropower scenario and the baseline scenario Under the hydropower scenario, the performance of the major reservoirs is quite different from that under the baseline scenario. Figures 7.60-62 compare the reservoir utilization coefficients for the three reservoirs along the main river, including Toktogul, Kayrakum and Chardara Reservoir. As discussed in Section 7.4.1.1, these reservoirs, especially Toktogul and Kayrakum Reservoir, are not very active in the inter-year flow control. However, under the hydropower scenario, we see the significant increase of the reservoir utilization coefficients, especially in normal and wet years. Therefore, we may conclude that the upstream hydropower generation has a critical role in the decision of the operation rules of the major reservoirs. 338 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic years Reservoir utilization coefficient Baseline scen. Hydropower scen Figure 7. 60. The Toktogul Reservoir utilization coefficient under under the hydropower scenario and the baseline scenario. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic years Reservoir utilization coefficient Baseline scen. Hydropower scen Figure 7. 61. The Kayrakum Reservoir utilization coefficient under the hydropower scenario and the baseline scenario. 339 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years with hydrologic years Reservoir utilization coefficient Baseline scen. Hydropower scen Figure 7. 62. The Chardara Reservoir utilization coefficient under the hydropower scenario and the baseline scenario. 7.6 SUSTAINABILITY ANALYSIS Based on the results from the scenarios presented above, in this section the sustainability criteria defined in Section 6.2 are analyzed. The inter-relationships between the prescribed sustainability criteria are discussed, as well as different aspects of these criteria. Throughout the analysis in this section, the in-depth sustainability status of the water resources system in the study area is described. 7.6.1 Water supply reliability Water supply reliability is defined in terms of reliability, reversibility, and vulnerability with respect to irrigated area and environmental water use. The irrigated area refers to the total irrigated area in the basin, and the environmental water use is defined as the annual release to the Aral Sea from the Syrdarya River. Figure 7.63 shows two ratios under the baseline scenario. One is the ratio of the computed irrigated area to the planned irrigated area, and the other is the ratio of computed flow to the Aral Sea to the prescribed flow target, over all study years. The irrigated area is sustained over the years while the flow to the Aral Sea 340 fluctuates with the hydrologic levels in the study years. However it should be noted that crop yields fluctuate with hydrologic levels, too. Referring to Section 6.4.1, the irrigated area can be sustained under an assumption that the water-yield coefficient (eq. 3-4) is larger than an empirical value (0.5, suggested by FAO, 1979). The water-yield coefficient is a function of soil water moisture and soil salinity. Therefore, under the baseline scenario, the water and salinity condition will not cause much reduction in irrigated area. However, as discussed before, at the downstream demand site, Low_syd, the irrigated area is considerably reduced in some dry years. 0 0.5 1 1.5 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Rati os irrigated area / planned irrigated area flow release / target Figure 7. 63. Ratios of computed irrigated area to the planned irrigated area, and ratios of computed flow to the Aral Sea to the flow target, under the baseline scenario. 341 Figure 7.64 presents the numbers of consecutive failure years in each year for both irrigated area and flow release to the Aral Sea. A failure year with regard to irrigated area is defined as a year with the ratio of computed irrigated area to the planned area less than 0.85. The same critical value is specified regarding to the flow to the Aral Sea. The distribution of these numbers over the years reflects the resilience (reversibility) of the water supply system. No failure year occurs to irrigated area, but the ratio of flow to the Aral Sea to the flow target is less than 0.85 in three consecutive years (year 23, 24, and 25). 0 1 2 3 4 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years C onsecutive failur e year s irrigated area flow release Figure 7. 64. Numbers of consecutive failure years for both irrigated area and flow release to the Aral Sea. The vulnerability of water supply is represented by the maximum risk, i.e., the minimum RIA (ratio of actual irrigated area to the target of the irrigated area) and REW (actual ecological release to the target). Under the baseline scenario, the maximum risk for irrigated area is 2%, while for the flow to the Aral Sea, it is 72%. 342 Table 7.17 shows the items related to the criterion of water supply reliability under the various scenarios defined above. The mathematical definitions of these items are given in table 6.1. Under the zero scenario, 97% of irrigated area will be sustained over the study period, no failure year for irrigated area occurs, and the maximum risk is 11%. Recalling the discussion in Section 7.5.1, the crop yield may decrease dramatically even if irrigated area is not reduced much. For the flow into the Aral Sea, the zero scenario presents an unacceptable solution: only 44% of the flow target can be satisfied, 17 consecutive failure years may occur, and in some years, there is almost no inflow to the sea (i.e. the risk is up to 99%). The conditions are similarly negative for the high demand scenario. The zero scenario shows that poor technologies in water distribution, irrigation, and drainage impose negative impacts on water supply reliability, while the high demand scenario shows that excessive increase in water demand can also reduce the water supply reliability. Comparing the values under the irrigation scenario and the I&M scenario, we find that the excessive increase in irrigation water demand has a stronger effect on water supply reliability, as well as on other aspects of sustainability in the water resource system of the study area, as discussed later. Table 7. 17. Indices of water supply reliability under various scenarios Scenarios REL ia Rel fl Rev ia Rev fl Vul ia Vul fl Baseline 1.00 0.85 0 3 0.02 0.56 Zero scenario 0.97 0.44 0 17 0.11 0.99 Irrigation scenario(highest) 0.96 0.59 0 8 0.09 0.97 I&M scenario 1.00 0.74 0 5 0.02 0.68 High demand Scenario 0.96 0.49 0 10 0.11 0.97 Flow scenario 0.94 1.00 1 0 0.15 0.00 343 In the flow scenario, we assume that the prescribed flow target to the Aral Sea is satisfied in all years. Even under this condition, the irrigated area is not much affected since 94% of irrigated area will be sustained. The maximum irrigated area reduction is 15% of the projected area in 30 years. In summary, in various cases, irrigated area in the study area can be sustained, but the crop yield may decline dramatically under some cases. The flow into the Aral Sea is sensitive to technological and water demand conditions. Excessive increase in water demands, especially irrigation water demand, and poor conditions in the water distribution and application system, will most probably reduce the reliability of water supply in the study area. 7.6.2 Equity As described in Section 6.2.3, equity is considered in both spatial and temporal terms with respect to water use benefits over all years in the time horizon and over the spatial domain. Figures 7.65 (1)-(5) show the changing rate of water use benefits from year to year (eq. 6-5) at each demand site. Figure 7.66 presents the changing rate of the total water use benefit in the basin over all years. The spatial equity is expressed as the standard deviation of the average changing rate over all demand sites (eq. 6-9), and the temporal equity is expressed as the standard deviation of the changing rate of the total water use benefit in the basin over all years (eq. 6-6). Therefore a larger value for these items shows a more intensive fluctuation. Some statistics relating to changes in the water use benefits under various scenarios are displayed in Table 7.18. 344 -0.6 -0.4 -0.2 0 0.2 0.4 nnwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Chan g e rate NARYN -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 nwvwvddnnnnnwnwdnwnnvdndddwnnndd Years C hange rate LOW_SYD Figure 7. 65 (1)-(2) Changing rates of water use benefit at each demand site. -0.3 -0.2 -0.1 0 0.1 0.2 0.3 nwvwvddnnnnnwnwdnwnnvdndddwnnndd Years C hanging rate ARTUR 345 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 nwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Changing rate FERGANA Figure 7. 65 (3)-(4) Changing rate of water use benefit at each demand site. -0.6 -0.4 -0.2 0 0.2 0.4 nwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Changing rate MID_SYD Figure 7. 65 (5) Changing rate of water use benefit at each demand site. -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 nwvwvddnnnnnwnwdnwnnvdndddwnnndd Years Chan g in g rate Average Figure 7. 66. Changing rate of water use benefit, average value over all demand sites. 346 Table 7. 18. Indices of equity: statistics of increasing rate of water use benefit under various scenarios Annual increasing rate in the whole basin Long-term average increasing rate Scenarios Min. Max. Mean Variation Min. Max. Mean Variation Baseline -0.266 0.181 0.006 0.11 -0.015 0.008 0.001 0.01 Zero scenario -0.758 0.24 -0.039 0.195 -0.062 -0.02 -0.04 0.01 Irri. scenario -0.387 0.421 -0.03 0.24 -0.024 0.0124 0 0.02 I&M scenario -0.465 0.234 -0.01 0.13 -0.027 0.001 -0.001 0.01 High dmd. scenario -0.296 0.405 0.016 0.18 -0.054 0.005 -0.02 0.03 Flow scenario -0.246 0.301 0.007 0.12 -0.085 0.006 -0.026 0.03 347 Actually the advanced water storage and delivery infrastructure in the basin provides substantial facilities for mitigating the effect of uneven distribution of water sources in the basin. Based on these facilities, appropriate policies can be implemented to make water evenly available to different demand sites in the basin. When comparing the values of the spatial equity index under various scenarios, it can be seen that excessive water demand for irrigation, industrial and municipal, or environmental water uses may cause uneven development among the demand sites. These conditions have less effect on upstream demand sites, and more on downstream demand sites, since 70% of the water sources in the river basin stem from the upstream areas of the basin. The temporal equity issue seems to be more significant than the spatial equity issue in the river basin. For example, under the baseline scenario, the changing rate of the total water use benefit in the basin over all years ranges from ?0.40 to 0.12, the average value is 0.0, and the standard deviation is 0.11. The temporal equity is affected by changes in water demand over the years, as well as hydrologic fluctuations. The standard deviation is larger under the scenarios with higher water demands including the high demand scenario and the zero scenario, as can be seen in Table 7.18. The zero scenario has relatively low water distribution and water use efficiency, which indirectly increases water demand. 348 7.6.3 Environmental integrity The criterion of environmental integrity is implemented in the long-term modeling by minimizing the highest salt concentration in surface water (reservoir) and groundwater, as well as soil salinity in the crop field over all years. Since soil salinity is embedded in the crop yield function (eq. 3-21), the control of soil salinity is also indirectly involved in maximizing crop production. The environmental impacts have been discussed in Section 7.5. An excessive increase in irrigation water withdrawals will impose significant negative impacts on water and soil quality in the study area. Table 7.19 presents the maximum salt concentration in surface water and groundwater. Table 7.20 presents the crop area weighted average soil salinity at each demand site in the first year and in the last year. The conclusions based on these two tables are similar to the ones already stated in Section 7.5: (1) excessive increase in irrigation water will significantly increase water and soil salinity in midstream and downstream areas of the basin; and (2) the downstream demand site will be most seriously affected in surface water, groundwater, and soil salinity. Table 7. 19. Indices of environmental integrity: maximum salt concentration in surface and ground water. Groundwater salinity Surface water salinity Scenarios Low_syd Mid_syd Fergana Chardara Kayrakum Toktogul Baseline 2.08 1.72 1.59 1.06 1.47 0.4 Zero scen. 2.04 1.54 1.56 0.97 1.16 0.4 Irri. scen. 2.69 2.30 1.88 1.15 1.83 0.4 I&M scen 1.93 1.84 1.60 1.03 1.46 0.4 High dm. Scen. 2.39 2.23 2.00 0.96 1.71 0.4 Flow scen. 2.02 1.68 1.58 1.13 1.46 0.4 349 Table 7. 20. Indices of environment integrity: crop area weighted average soil salinity at each demand site in the first year and in the last year. Scenarios Years NARYN LOW_SYD ARTUR CHAKIR MID_SYD FERGANA Year 1 0.209 0.567 0.267 0.400 0.300 0.400Zero scen Year 30 0.209 0.457 0.265 0.407 0.312 0.404 Year 1 0.258 0.700 0.317 0.400 0.347 0.451Baseline Year 30 0.304 0.852 0.697 0.604 0.553 0.737 Year 1 0.261 0.630 0.300 0.400 0.385 0.415Irrigation scenario Year 30 0.455 2.990 0.757 0.661 1.362 1.323 Year 1 0.300 0.700 0.300 0.400 0.338 0.446I&M scenario Year 30 0.331 1.092 0.638 0.551 0.552 0.859 Year 1 0.282 0.600 0.256 0.400 0.356 0.400High dmd. scenario Year 30 0.392 3.132 1.099 0.643 1.119 1.416 Year 1 0.258 0.700 0.317 0.400 0.347 0.451Flow scenario Year 30 0.352 0.889 0.714 0.624 0.553 0.737 7.6.4 Socio?economic acceptability Under the criterion of socio-economic acceptability, we evaluate investments for water development facilities, with respect to the corresponding water use benefits. The benefits include profit from irrigation, profit from hydropower generation, and benefit from environmental water use. Investments include those for improving water distribution, irrigation and drainage, drainage reuse, and disposal/treatment facilities. Table 7.21 presents the sum of the benefits and investments over all study years under various scenarios. Under the zero scenario, no investment takes place, but compared to other scenarios, a big decline in profits occurs. This shows that some improvements of water development facilities will be necessary for sustaining the economy that heavily depends on irrigated agriculture in the area. However, as shown before, compared to other scenarios, water and soil salinity problems are less serious under this scenario. This environment benefit is not directly included in the total benefit shown in Table 7.21. 350 Table 7. 21. Indices of socio-economic acceptability: benefits and investments Scenarios Total Water use Benefit (TWB) in 30 years (billion US$) Total Investment (INV) in 30 years (billion US$) Baseline 46.85 0.21 Zero scen. 26.27 0 Irri. scen. 43.75 0.36 I&M scen. 45.77 0.25 High dmd. scen 41.09 0.37 Flow scen. 44.08 0.2 Comparing the baseline scenario and the high irrigation scenario, we see that the baseline scenario has larger benefit with smaller investment. Thus, the socio-economic acceptability of the baseline scenario is better than the irrigation scenario with high irrigation water demand. Under this scenario, excessive irrigation water use not only reduces instream water uses, but also creates water and soil salinity problems that eventually lead to substantial decline in crop yields. If we compare the I&M scenario to the baseline scenario, we see that the former has less total benefit but larger investment. However, it should be noted that the benefit from M&I water uses is not counted in the benefit presented here. Therefore, the I&M scenario with high demand of industrial and municipal water may not necessarily be inferior to the baseline scenario with respect to socio- economic acceptability. 351 Obviously, there is a tradeoff between irrigation water diversion and water release to the Aral Sea. The scenario with full satisfaction of the Aral Sea inflow target has almost the same water development investment as the baseline scenario, but the former has less benefit. As defined before, the inflow scenario is equal to the baseline scenario in all aspects except that the full inflow target to the Aral Sea is pre-decided for the scenario. The comparison here implies that under the prescribed economic measurement of the irrigated agriculture profit and the measurement of the benefit from environmental and ecological water use, full satisfaction of the Aral Sea inflow target may not be economically efficient under the specific conditions. However, these economic measurements are counted with uncertainties. Further research will be necessary to come to more robust conclusions. 7.6.5 Tradeoff between multiple criteria Above, the individual performance of the four criteria has been discussed. The inter-relationships between these criteria are addressed in the following. Tradeoff relations exist between these criteria, particularly between water supply reliability and environmental integrity, between equity and economic efficiency (socio-economic acceptability). In this sense, The GA-LP approach can provide a number of alternatives consisting of different combinations of these criteria. As mentioned before, the GA-LP searches better solutions by examining candidate solutions through ?generations?, a group of solutions that are assumed to evolve gradually, and to reach a fixed level finally. In later generations, most of the candidate solutions are similar regarding to their fitness. However, these candidates may still represent different solutions to the problem, and each of these candidates may be recognized as an alternative, as presented in Table 7.22. The first three alternatives are all based on the baseline scenario. They yield a very close total objective value, and they have the same or very close 352 values for indices of reversibility and environmental integrity. Alternative 3 is different from the other two in the economic index and the equity indices (temporal and spatial equity), as well as the reliability index. Note that all indices are minimization-induced, i.e., the smaller, the better. Compared to the other two, Alternative 3 has a better economic efficiency, but equity is worse both in time and in space. Moreover the risk in water supply is higher. Alternative 1 is preferred to alternative 2 in economic efficiency, but it is worse with regard to spatial equity. Alternatives 4 and 5 are based on the high water demand scenario; their objective values are very close. Alternative 4 is preferred to alternative 5 in environmental integrity, but has a worse performance in water supply reliability and economic efficiency. A systematic tradeoff analysis can be carried out by running a number of scenarios in which the different criteria are given different weights, and then summarizing the performance of these criteria under various runs. Table 7. 22. Comparison of alternatives for tradeoff analysis Alternatives Risk 1 Rev 2 Vul 3 Teq 4 Seq 5 Econ 6 Envi 7 Objective 8 Alternative 1 0.072 0.05 0.285 0.106 0.005 0.3387 0.124 0.615 Alternative 2 0.072 0.05 0.284 0.109 0.003 0.3414 0.124 0.617 Alternative 3 0.076 0.05 0.286 0.118 0.009 0.3274 0.124 0.615 Alternative 4 0.07 0.05 0.306 0.119 0.005 0.3520 0.134 0.682 Alternative 5 0.06 0.05 0.281 0.116 0.004 0.3610 0.143 0.685 1 Risk of water supply, 2 Reversibility of water supply, 3 Vulnerability of water supply, 4 Temporal equity, 5 Spatial equity, 6 Socio-economic acceptability, 7 Environmental preservation, 8 Total objective. 353 7.7 SUMMARY This chapter presents the prototype long-term dynamic modeling as a useful tool for sustainability analysis in water resources management in an irrigation-dominated river basin. Water resources planning and management over a period of 30 years in the Syrdarya River basin is studied as an example of the application of the long-term dynamic modeling framework. Data requirement and availability for both water demand and water supply aspects have been described. The effectiveness and limitations of the GA-LP modeling approach developed in Chapter 5 are discussed based on a detailed modeling result analysis. It can be concluded that this approach is effective in identifying good solutions for a large- scale, long-term model like the one developed in this research. In order to analyze the relationships between water uses and long-term economic and environmental consequences, a baseline scenario and a number of other scenarios have been defined and run. Under each scenario, the long-term consequences associated with specific water uses are simulated, displayed, and compared with those under the baseline scenario. Analysis is addressed with respect to each aspect of the pre-defined sustainability criteria and the inter- relationships between the criteria. Due to incomplete data, the findings for the study area from the modeling result analyses may need further verification. The major findings include: (1) The current irrigated area may be sustained in the study years, and at the same time, 90% of the target of flow release to the Aral Sea can be satisfied, with modest water and soil salinity increase, under appropriate crop pattern changes and water distribution and application facility improvements. However, in very dry years (frequency of 6.7%) and consecutive dry years, crop yields and flow release flow to the Aral Sea will both considerably decline. Full satisfaction of the 354 flow release target will reduce irrigation profit by 10%. High demand of industrial and municipal water will reduce both crop yield and the flow release, but the irrigated area can still be sustained; (2) Improvements of current water supply and use facilities are necessary to sustain the agricultural production system in the basin. If the infrastructure remains the current level, the irrigation profit (IP) will continually decrease, by 26% in the first year, and 67% in the last year. (3) Excessive increase in irrigated area will significantly degrade the water and soil environment, and finally, even the crop production system; (4) The upstream demand site (Naryn) seems to be free of water and soil salinity problems, and the two demand sites (Chakir and Artur) which mainly depend on tributaries for their water supply are less affected in water and soil salinity. Fergana, which is the largest irrigation water demand site, may suffer substantial groundwater salinisation. The midstream demand site, Mid_syd, is found to have potential waterlogging problems, and the downstream demand site, Low_syd, suffers from the most severe water and soil salinity problems. (5) Cotton fields will likely decline, without dominating irrigated area at all demand sites. Cotton-forage fields and wheat-maize fields will rotate over some years. (6) Satisfying the power demand in winter months at the upstream demand sites will reduce the irrigation profit (IP). In some dry years IP decreases by 28% compared to the baseline scenario. In this case study, we assume that the period up to 2020 follows one series of hydrologic fluctuations. Although this series may reflect some hydrologic changes in the study years, it is very limited to capture hydrologic uncertainties, which is 355 required for sustainability analysis in water resources management. More supporting data and innovative methodology are needed to incorporate comprehensive hydrologic uncertainties into the modeling framework developed in this research. 356 Chapter 8 Summary and Conclusion This research develops a modeling framework for quantitative analysis of sustainable water resources management at the river basin scale. Sustainable development has been recognized as a sound philosophy for today?s world. In light of this philosophy, broad guidelines and principles have been identified for sustainable water resources management that are critical to regional development, particularly in arid and semi-arid areas of the world. In order to apply these guidelines and principles to the designing, operating and maintaining of water resources systems in specific regions, we need to translate them into operational concepts, and translate the qualitative descriptions into quantitative analysis. In this work, we specify the problem as one of long-term water resources management in river basins with arid and semi-arid climate, where irrigation is the major water user, and the main pollution to the environment is salinity resulting from poor irrigation practices. Sustainable water management is defined to ensure a stable and flexible water supply capacity for crop water demands, and at the same time to keep a stable relationship between irrigation practices and the associated environment. An innovative systems approach has been developed to model and analyze sustainability issues related to water resources management. The modeling framework of this research is distinguished from those in previous literature first in its integrated hydrologic-agronomic-economic- institutional approach to modeling at the river basin scale. Modeling sustainability presupposes essential relations between water uses and the associated long-term consequences at an appropriate spatial scope. In this research, a river basin is defined as a natural spatial unit for sustainability analysis in water resources 357 management, and essential hydrologic, agronomic, economic and institutional relationships are integrated into a coherent analytical framework at the river basin scale to reflect the interdisciplinary nature of water resources problems. The hydrologic component includes flow and salinity balance and distribution from crop field to river network. Both in-stream and off-stream water uses are considered. Emphasis is put on irrigation, in which on-farm water application and salinity transport are simulated. Deep percolation to groundwater, return flow to river system, and their salinity are calculated in both short- and long-term time frames, in order to evaluate the environmental impacts associated with short- and long-term irrigation practices, such as waterlogging, soil salinisation, and surface and groundwater water quality reduction. A crop production function that includes water and salinity variables is the critical connection between the multiple components in the integrated model. Based on an empirical yield-water relationship (FAO, 1977) and an empirical yield-salinity relationship (Mass and Hoffman, 1979), a nonlinear crop production function is derived and applied in the model. In this crop production function, crop yield is a function of both soil moisture and soil salinity, which are resulted from soil water and salinity balance directly, and are further related to water and salinity balance in the entire river basin network. That is to say, through the crop production function, crop yield is related to the performance of the entire hydrologic system. Furthermore, crop production, which is equal to crop yield multiplied by crop area, determines the irrigation profit involved in the economic relationships of the model. Therefore, the newly developed crop production function connects the hydrologic, agronomic and economic components together into an endogenous system. Economic relationships determine water use benefits from irrigation, hydropower generation, and environment water use, subsidy for infrastructure 358 investments, and penalty tax on excessive salt discharge. Profit from irrigation is calculated as crop revenue minus cropping cost and water supply cost; profit from hydropower generation is equal to revenue from power sale minus hydropower generation cost; and benefit from environment water use is formulated based on an empirical assessment of the value of water flow release for environmental purposes. The total investment for infrastructure improvements in the basin is assumed to equal to the government input plus the tax revenue on excessive salt discharge. The subsidy allocation among different demand sites, different crop fields, and different facilities (water delivery system, irrigation and drainage system, drainage reuse and disposal system etc.), is determined from the model by maximizing total water use benefit in the whole basin, as well as by the prescribed sustainability criteria in the long-term modeling. Penalty tax, as an economic incentive, is imposed on excessive salt discharge with the return flow from crop fields to rivers. Values of this item are determined for years with different hydrologic conditions in the long-term modeling. Institutional directives are considered in the model too. It is assumed that there is such a central authority in the river basin who can make decisions, standing on the overall socio-economic benefits and environmental impacts in the region of the river basin. With this assumption, instead of fix-quantity proposals for water use rights, empirical water demand functions based on the crop production function for individual demand sites are specified, so that optimal inter-demand site and inter-crop water allocations can be identified from the modeling. In particular, externalities that are resulted from excessive water diversion and salt discharge by upstream demand sites, and produce negative effects to downstream demand sites, are controlled in the model through the river basin network by the prescribed equity criteria. 359 Essential hydrologic, agronomic, economic and institutional relationships are integrated in an endogenous modeling framework implemented at the river basin scale. Outputs from the modeling framework are examined in terms of economic efficiency, equity, environmental impact, and risk from hydrologic uncertainties, which shows the modeling framework can provide policy instruments designed to make more rational economic use of water resources. Another aspect of this modeling framework different from others is incorporating prescribed sustainability criteria into the long-term modeling so as to control short-term decisions. In the context of this research, sustainability criteria are proposed in terms of water supply reliability, environmental system integrity, equity in water allocation, and socio-economic acceptability. Water supply reliability considers the frequency of system failures (risk), the system resilience (reversibility), and the magnitude or the severity of a system failure (vulnerability). Environmental system integrity ensures no irreversible, cumulative impacts on water and soil salinity, as well as the ecological system. Equity assumes even distribution of water accessibility for irrigation development among different demand sites (spatial equity) and from current to future (temporal equity). Socio-economic acceptability considers the economic efficiency of infrastructure investments. Criteria in these aspects are expressed in mathematical forms based on the items resulting from the modeling. These expressions are specifically defined for the case study area of this research, and they are subject to changes if applied to other study areas. The indices of the multiple criteria then are normalized into the objective function of the long-term modeling, with a weight or a scaling factor for each index (eq. 6-19). The third innovative development of this modeling framework is a combined inter-year optimal decision model (the yearly model, YM) and an inter- year control program (IYCP). The integrated hydrologic-agronomic-economic- 360 institutional model at the river basin scale, which is applied to a one-year time horizon with 12 periods, is defined as a short-term model. The objective function of the short-term model is to maximize the total water use benefit within one year. The major state variables include reservoir storage, groundwater table, soil moisture, and soil salinity. The major decision variables include water withdrawals, reservoir releases, groundwater pumping, drainage disposal and reuse, water allocation and source blending for crops, efficiencies in water delivery, irrigation, and drainage, irrigated area for different crop fields, and tax rate on excessive salt discharge. For the long-term modeling framework, the time horizon is extended to 30 years. The long-term modeling framework is composed of a series of yearly models (YM) and an inter-year control program (IYCP). The yearly model includes the same relationships as the short-term model. However, for computing efficiency, it is formulated as a linear model by approximation and decomposition, and it is solved by an integrated simulation and optimization procedure. All yearly models have the same structure, but different initial conditions and inputs. Transmissions between the yearly models are maintained by setting the ending condition from the YM in year y as the initial condition of the YM in year y+1. The IYCP has two functions. One is to provide ?proposals? to the yearly models by generating the inter-year control variables, including water sustained at the end of individual years, efficiencies in water delivery, drainage, and irrigation, crop acreage, and tax for excessive salt discharge. The other is to evaluate the outputs from all yearly models, according to the prescribed sustainability criteria, and calculate the fitness of each proposal based on the long- term objective function discussed above. In the long-term modeling, the long-term consequences resulting from short- term ?wait-and-see? actions (decisions in the yearly models), with predicted 361 changes and uncertainties on both water demand and supply in the future, is traced and controlled. Therefore, in the combined short-term and long-term modeling framework, short-term decisions are directed by both short-term desires and long-term adjustments. The long-term decision making attempts to reach a long-term optimality: satisfying the immediate demands and desires without compromising those of future years. The Syr Darya River basin in Central Asia is the case study area of this research, where a great need exists for water policy analysis tools of the type developed in this research. The basin network includes 11 river reaches, 11 reservoirs, 6 aquifers, 5 hydropower stations, and 6 water demand sites located from upstream to downstream of the basin. Within each demand site, three soil plots, sandy clay (scl), loam (l), and sandy loam (sl) are identified (only for the short-term model, and a lumped soil type is used for the long-term model). For each soil plot, five crops are considered, including cotton, forage, wheat, maize, and alfalfa (perennial forage), and these crops are grouped into four types of crop combinations according to the historic crop patterns in the area. The study area chosen in this research has one of the most complicated human water development systems in the world, with one of the most well-known unsustainable water management cases too. In the Syr Darya River basin, the expansion of irrigation in the last 30 years has produced serious environmental and ecological consequences, including the increase of salinity in surface and groundwater water, waterlogging, soil salinity accumulation, as well as the depletion of inflow to the Aral Sea. The question answered through the case study is: can such a high level of irrigated agriculture be sustained while preventing or minimizing adverse environmental and ecological impacts? For this research, what we are more interested in is whether we can use the modeling framework developed in this research to provide 362 useful information for decision making in solving the problems of the case study area. Both a short- and long-term model are applied to the case study. Data heavily depend on several previous research projects for the river basin. A complete model calibration and verification are beyond the effort of this research. For the short-term model, comparisons show the results from the model are close to those in the published papers or reports (e.g., EC, 1995; Raskin et al., 1992). The short-term model was also judged by some local professionals. Detailed short-term and long-term analyses based on the modeling outputs are demonstrated for the study area. The short-term analytical issues include operation of water storage facilities (reservoirs and aquifers), irrigation and drainage management, agronomic analysis, economic analysis, and uncertainty analysis. It is shown that hydrologic system operations are derived by both agricultural production and in-stream water use (for hydropower generation and ecological use). Irrigation and drainage management, including the determination of the appropriate infrastructures, has important contributions to the outcomes of water uses. Economic analysis explores the economic values of water uses under various scenarios of hydrologic conditions and infrastructure status. Economic incentives, including water supply prices, crop prices and taxes on excess salt discharge, are shown to have profound influences on the decisions in hydrologic and agronomic components. Output from the short-term model shows some in- depth interactions among multiple components in the integrated model. However, the short-term decisions result in some unsustainable statuses of the river basin system, including large increase of soil and water salinity. The long-term model is used for an in-depth analysis of sustainability in water resources management of the case study area. The effects of the inter-year controls on reservoir operation, salt discharge control, crop pattern change and 363 infrastructure improvement are demonstrated, which shows the short-term decisions are adjusted by the inter-year controls, as well as optimized within individuals years. The long-term consequences of water and soil salinity, water flow depletion from ecological uses, as well as irrigated area reduction and crop yield reduction, are simulated. In order to search a robust relation between water uses and the associated environment in a long-term time frame, a baseline scenario based on the ?best? estimated data, and a number of other scenarios have been defined and run for various water demand and supply cases. Finally, analysis is addressed with respect to each pre-defined sustainability criteria, as well as the tradeoffs between the criteria. The output from the long-term modeling is compared to that from the short-term modeling in terms of some intra-year decisions and results, such as reservoir operation, infrastructure improvement, crop acreage, irrigation profit, and water and soil salinity. For reservoir operation, the short-term modeling shows the reservoirs on the main river take the main role in intra-year flow regulation; the long-term modeling finds the reservoirs on the main tributaries (Andijan Reservoir and Charkir reservoir) are active in inter-year flow regulation, even more than the reservoirs on the main river. Differences are also shown in infrastructure improvements. From the short-term modeling, the irrigation efficiency (field application efficiency) increases to the upper bound (about 0.85), the drainage improvement is not economically attractive, and drainage reuse is attractive even in a normal year. All of these may be beneficial to the intra-year irrigation profit, however they may lead to unsustainable states with regard to high salinity in water and soil. From the long-term modeling, the irrigation efficiency gradually increases up to a moderate level in 30 years, especially in downstream demand sites (Low_syd and Artur), the drainage improvement is attractive, and drainage reuse is only preferable in dry years, except for the 364 upstream demand site (Naryn), where salinity is low in field drainage. The short- term and long-term modeling result in different irrigated area for various crops. From the short-term modeling, the cotton-forage field dominates the irrigated area. The irrigated area at the downstream demand site (Low_syd) is significantly reduced due to water shortage and high salinity even in a normal year. The long- term modeling shows a significant increase of irrigated area for wheat-maize, and a rotation between cotton-forage and wheat-maize over the study years. No significant reduction of irrigated area occurs at the downstream demand site except in dry years. As expected, the short-term modeling results in a higher irrigation profit (up to 2.75 billion dollars in a normal year) than the long-term modeling (up to 1.68 billion dollars in a normal year). As a sacrifice, the short- term modeling ends with a high increase of salinity in surface water (by 1.5 times), and soil salinity over crop salinity tolerances in most of the demand sites. Based on these comparisons, we can see that the long-term modeling reflects the prescribed sustainability criteria. It shows consideration of reliability and equity in water supply, and also shows a balance between irrigation profits and their associated environmental consequences through appropriate crop pattern changes and infrastructure improvements. Various scenario analyses of the long-term modeling show the states of the irrigation system and the associated environment, with consideration of sustainability. If the current conditions, including crop patterns and infrastructures continue in the future 30 years, agricultural profit will continually decrease with years, and the decreasing magnitude increases with years. Compared to the baseline scenario, the agriculture profit in the first year decreases by 26%, and in the last year (the 30 th year) by 67%. For an agricultural economy depending on irrigation in the Syr Darya River basin, the continuation of the current condition will not maintain sustainability in the area, even no further environmental impacts 365 are found under this case. Improvements of current water supply and use facilities, as well as the adjustment of current crop patterns, are necessary to sustain the agricultural production system in the Syrdarya River basin. Excessive increase in irrigated area will significantly degrade the water and soil environment, and finally, even the crop production system. A number of scenarios with different increase of the irrigated area are analyzed. It is found that although the irrigation profit increases with the irrigated area, flow release to the Aral Sea decreases. Even a small increase of irrigated area will put the environment on risk, and high irrigation expansion will most probably destroy the environment, as well as the irrigation system itself. The baseline scenario, with 25% increase of the non-irrigation water demand and 10% increase of the irrigated area in the next 30 years, is recommended to decision-makers for further consideration. Under this scenario, an increasing tendency is shown for the irrigation profit, except in some dry years; 90% of the target of flow release to the Aral Sea can be satisfied, with modest water and soil salinity increase. However, in very dry years (frequency of 6.7%) and consecutive dry years, crop yield and flow release flow to the Aral Sea will both considerably decline, which shows that some extra measures such as delivering water from other basins and increasing drainage treatment, may be necessary to deal with the drought. The conflict between irrigation withdrawal and flow release to the Aral Sea is one the most important concerns in the study area. Compared to the baseline scenario, the flow scenario shows full satisfaction of the flow release target will reduce irrigation profit by only 10% within the next 30 years. Therefore we may conclude that the conflict between irrigation withdrawal and flow release to the Aral Sea may be mitigated by appropriate policies and 366 infrastructure improvements as demonstrated in the baseline and the flow scenarios. Negotiation between hydropower demand at the upstream country and irrigation demand at downstream countries remains another important issue of decision making in the study area. The hydropower scenario, assuming that hydropower demand in winter months will be satisfied as much as possible, shows satisfaction of the hydropower demand will reduce irrigation profit in all types of hydrologic years. In very dry years, the irrigation profit is reduced by up to 28%, compared to that under the baseline scenario. The hydropower scenario results in higher reservoir storage utilization for the reservoirs on the main river than other scenarios, in which we assume that Kyrgyzstan does not hold water in the vegetation period, while the downstream countries help Kyrgyzstan to get some reimbursement in power generation in winter months. Analysis is addressed for each aspect of the prescribed sustainability criteria, as well as the inter-relations of those criteria. For water supply reliability, we find with the assumptions on farmers? decision (crop yield can not be lower than half of the maximum crop yield), irrigated area may be sustained under various water supply conditions, even crop yield may decline dramatically with dry years. Flow to the Aral Sea is sensitive to technological and water demand conditions. Excessive increase in irrigation water demands and poor technological conditions will most probably destroy the sustainability of both irrigation-dependent agricultural economy and the environment in the river basin. Considering environmental integrity, analysis is made for individual demand sites, as well as the entire river basin. The upstream demand site (Naryn) seems to be free of water and soil salinity problems, and the two demand sites (Chakir and Artur) which mainly depend on tributaries for their water supply are less affected in water and soil salinity. Fergana, which is the largest irrigation 367 water demand site, may suffer substantial groundwater salinisation. The midstream demand site, Mid_syd, is found to have potential waterlogging problems, and the downstream demand site, Low_syd, suffers the most severe water and soil salinity problems. Equity analysis shows that the uneven spatial distribution of water sources in the basin can be mitigated by substantial facilities and appropriate policies, and then all demand sites have almost equal opportunity for their irrigation development. The total water use benefit is affected by changes in water demand, as well as hydrologic fluctuations over the years. The inter-year equity problem is more significant than the inter-site equity in the basin, especially with high water demand for both irrigation and non-irrigation purposes. Economic efficiency analysis shows that large increase in irrigated area is not economically efficient, i.e., larger investment results in less profit. As mentioned before, continuation of current technology status (zero investment) will result in large loss of water use benefit. For the inter-relations of all prescribed criteria, analysis shows that tradeoff relations exist between these criteria, particularly between water supply reliability and environmental integrity, and between equity and economic efficiency. Due to the incomplete data availability and limited efforts in this research, findings from the modeling conducted in this research may not be thought as the real solutions to the problems in the basin, before they are verified by further work. However, the modeling framework clearly demonstrates the powerful capacity of analyzing water resources management problems in the study area, and shows implications for long-term reservoir operations, water supply and use facility improvements, irrigated area develop and crop patterns in the basin for 368 sustaining the agricultural production system and the environment of the study area. Solving large-scale nonlinear water resources management models has been identified as one of the difficulties in water resources systems analysis. The models developed in this research can not be solved directly using currently available algorithms. Three approaches are presented in this research for solving these large, nonlinear and nonconvex models. The general bender?s decomposition (GBD) based approach can be used to search for approximate globally optimal solutions of large nonconvex nonlinear models. An example including a large number of bilinear equations (flow * constituent concentration) shows that the GBD-based approach solves the model faster than some popular nonlinear algorithms such as MINOS and CONOPT2. The combined genetic algorithm and linear programming (GA-LP) can be used to find approximate global solutions or feasible solutions for large models with high nonlinearity and nonconvexity. It is robust in finding approximate global or feasible solutions to complex NLP models. The approach is used to solve the long-term model. It is also used to solve a typical multiple-reservoir operation model. With the increase of the model size, the convergence time increases approximately linearly (i.e., there is no indication of a ?curve of dimensionality?). The ?piece-by-piece? approach is applied to solve the short-term model that is large and nonlinear, and includes multiple compartments. The special structure required by this approach is similar to a simulation modeling structure that is common in engineering, and the advantage of this approach is providing a method based on the currently available solvers to solve problems formulated as holistic optimization models. 369 Although all these approaches require some special model structures, they can be used to solve a large range of water resources management models, and models in other related fields too. A great wish of this research is to bring the philosophy of sustainability into traditional water resources management modeling. From conceptual specification to model development, and from data preparation and model test, to result demonstration, the modeling framework developed in this research is strongly recommended as a useful analytical tool for sustainability analysis in water resources management in river basins with substantial irrigation water demand. Within this modeling framework, essential hydrologic, agronomic, economic, and institutional relationships are integrated into an endogenous system at the river basin scale, and thus the integrity of water resources systems and inter- relationships between water application, economic welfare and environmental impact can be reflected and analyzed. This provides a way for quantitative analysis of the relationships of decisions-benefits-consequences, which is required in sustainable water resources management. Sustainability analysis also requires methods for tracing and controlling long-term consequences which are resulted from short-term decisions, as well as long-term changes and uncertainties in both water demand and supply. It also requires methods for handling the tradeoffs between current and future so that the spirit of sustainability can be reflected: satisfying the immediate demands and desires without compromising those of future years. The modeling framework provides such methods through combined short-term optimal decisions and long-term controls based on the prescribed sustainability criteria. Overall, the most important output of this research may be developing, solving and analyzing mathematical models for sustainability analysis in water resources management. This research may be added as another successful story of applying systems approach for water resources management. 370 However, in formulating, solving and analyzing the modeling framework developed in this research, a number of limitations become apparent. The modeling framework includes multiple components, and assumptions are made for each of these components. In this research, no rigorous study has been conducted to show how these assumptions within the different components affect each other and how they affect the modeling output if they are combined together in an endogenous system. Further research is needed to verify the inter- relationships between the hydrologic, agronomic, environmental, and institutional components integrated in the model. Uncertainties with data of these components may be cross-dependent, and if put together but not well handled, they may distort the model output. A systematic approach to treat uncertainties within multiple components of an endogenous system is necessary to make this system robust in realistic analysis. Also apparent is the limitation of data availability. Although data from several previous projects are used in this research, a lot of required data, especially the forecast data about system future status are still not available, and they could only be estimated or guessed. Obviously, this kind of modeling framework, which requires data from multiple components and data from both current and future periods, will not make any sense if not enough data are available. Additionally, multidisciplinary data and mixed types of data (i.e. experiment data, statistical data, and empirically estimated data) require attention with respect to their temporal and spatial resolution when they are used in an endogenous system. Although the long-term dynamic model is solved effectively by the GA- LP approach, the computing time is long and the application of the model to real world problems may be limited. Fortunately, the structure of the long-term modeling framework shows great potential for using parallel computing 371 algorithms, which will tremendously save computing time. As discussed in Section 7.3, within one generation, the yearly model will be run for each individual. Actually there is no requirement for the sequencing of the runs. That is to say, all individuals can be run simultaneously. Parallel algorithms are recognized to conduct this kind of work very efficiently. Besides these limitations discussed above, some weak points exist with the components included in the modeling framework, which will be most subject to change in the future. First, the modeling framework heavily depends on how the sustainability criteria are expressed mathematically. Obviously it will be very difficult, if not impossible, to define general forms of those criteria, even for a single case study. The mathematical expressions of sustainability criteria in this research are closely related to our understanding of the specific problems in the study area. Furthermore, those multiple criteria are simply normalized in the objective function by weights or scaling factors that reflects the relative importance of each criterion. If this modeling framework is applied to another river basin, then the definitions and mathematical expressions of the sustainability criteria will be changed based on the specific conditions in the basin. The modeling framework heavily depends on some empirical relationships in hydrologic, agronomic, and economic components. Although these relationships are claimed to be suitable universally, the parameters should be calibrated to the study area, and the assumptions with these relationships should be checked carefully according the specific conditions in the study area. Particularly, in the economic relationships, prices (crop prices and hydropower prices) and costs (water supply costs, hydropower generation costs and cropping costs) are assumed to be constant over all study years in the long-term model. However, these items will change in the future. For practical use of the long-term modeling, either we need to provide better estimations to these parameters, or we 372 need to include more economic relationships in the model so that some of these items such as crop prices can be determined within the model (Rosegrant et. al. 1995). As a summary, with all these limitations and weaknesses, to bring this work from research to practice, the following work is needed in the future: (1) checking all assumptions involved in different components of the model according to the conditions in the real world; (2) checking and changing the mathematical forms of the sustainability criteria until they can effectively reflect sustainability in water resources management in the basin; (3) updating and verifying data, especially those parameters that are included in some important empirical hydrologic, agronomic and economic relationships, like the crop production functions. For those parameters that are highly uncertain, sensitivity analysis should be conducted for them; (4) verifying model output; (5) analyzing uncertainties with the data. An innovative methodology is needed to incorporate comprehensive hydrologic uncertainties into the long-term modeling framework, and to handle uncertainties in multiple components systematically; and (6) defining and running more scenarios to search robust and comprehensive policies for the study area. It may be worth reflecting on the value of this research as a Ph.D. dissertation in water resources engineering, i.e. developing such as a tool for policy analysis in water resources management. Researchers in various fields, such as civil and agricultural engineering, agronomy, economics and public affairs, all develop and apply their own models for water resources management problems. This research attempted to bring their work together. At a first glance, nobody should doubt this is a great idea. The progress of operation research and computer software and hardware, as well as substantial research in each of these fields, already or very likely provides the necessary conditions for people to build 373 an integrated model for water resources management in the real world. However, this work seems to be ambitious for a single dissertation, and the author was worried about being trapped into what was beyond his ability and about being diverted from what he should focus on. Fortunately, based on all previous work cited in this dissertation, the study here reaches a viable modeling framework for sustainable water resources management. In short, although this work has its limits in theory and application in water resources management, it shows the feasibility, effectiveness, and range of possible analysis of advanced mathematical modeling in analysis of sustainability, a concept of utmost importance that will strongly influence the future water resources management. 401 Bibliography Abdel_buyem, M. S., and R. W. Skaggs (1993). ?Extension of DRAINMOD for simulation water management in arid regions?, Transc. Am. Soc. Agri. Engr. ASAE, 36(1): 210-220. Ahlfeld, D. P., Mulvey, J. M., Pinder, G. F., and Wood. E. F. (1988). ?Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory, 1., model development?, Water Resour. Res., 24(3): 431-441. Alaerts, G. J., Blair, T. L., and F. J. A. Hartvelt (eds.) (1991). A Strategy for Water Sector Capacity Building, IHE Report Series 24, IHE, Delft, NL 1991 pp. Alley, W. M. (1986). ?Regression approximations for transport model constraint sets in combined aquifer simulation-optimization studies?, Water Resour. Res., 22(4): 581-586. ASCE and working group, UNESCO/IHP, IV Project M-4.3 (1998). Sustainability criteria for water resources systems, task Committee on Sustainability Criteria, Water Resources Planning and Management Division, American Society of Civil Engineers. Augustine, O.E. (eds.) (1989). Dynamic programming for optimal water resources systems analysis, Englewood Cliffs, N.J.: Prentice Hall. Baumol, W. J. and Oates, W. E. (1988). The theory of environmental policy / William J. Baumol, Wallace E. Oates. 2nd ed. Cambridge (Cambridgeshire) ; New York : Cambridge University Press. Bear, J. (1977). Hydraulics of groundwater, New York : McGraw-Hill International Book Co. Becker, L., and Yeh, W. W-G. (1972) "Identification of parameter in unsteady open channel flows?, Wat. Resour. Res., 18(4): 956-965. Ben-Asher, J. and P.R. Berliner (1994). ?Runoff irrigation? in Management of water use in agriculture, eds. K.K. Tanji and B. Yaron. New York: Springer-Verlag. 402 Benders, J. F. (1962). ?Partitioning procedures for solving mixed variables programming problems?, Numerische Mathematik, 4, 238-252. Berck, P. and G. Helfand (1990). ?Reconciling the von Liebig and differentiable crop production functions?, American Journal of Agricultural Economics, 72: 985-996. Biswas, A. K. (1994). "Sustainable water resources development: some personal thoughts?, Wat. Resour. Development, 10(2): 109-116. Biswas, A. K. (1996). ?Capacity building for water management: some personal thoughts?, Wat. Resour. Development, 12(4): 399-405. Bonnis G. and R. Steenblik (1998). ?Overview of the main issues and policies?, the Athens Workshop, Sustainable Management of Water in Agriculture: Issues and Policies, Organization for Economic Co-operation and Development (OECD). Booker, J. E., and R. A. Young (1994). "Modeling intrastate and interstate markets for Colorado River water resources" J. Environ. Econ. and Management, 26(1):66-87. Braat, L. C., and W. F. J. Lierop (1987). "Integrated economic - ecological modeling?, in Integrated Economic Ecological Modeling, ed. by L. C. Braat and W. F. J. Lierop, pp49-67, North-Holland. Bras, R. L. and D. Seo (1987). ?Irrigation control in the presence of salinity: extended linear quadratic approach? Water Resour. Res., 23(7):1153- 1161. Bresler E., and D. Yaron (1972). "Soil water regime in economic evaluation of salinity in irrigation", Water Resour. Res., 8:791-800. Bresler, E., D. Yaron, and A. Segev (1983). "Evaluation of irrigation water quality for a spatially variable field", Water Resour. Res., 19(6): 1613- 1621. Brooke, A., Kendrick, D., and Meeraus, A. (1988,1998) GAMS: a User?s Guide, Scientific Press. 403 Brown, L., B. McDonald, J. Tysseling, and C. Dumars (1982). ?Water reallocation, market efficiency, and conflicting social values? in Water and agri.in the Western U.S.: Conservation, Reallocation, and Markets, ed. By G. D. Weatherford, Westview Press, Boulder, Colo. Bruce, M., and D. Shrubsole (1994). Canadian Water Management visions for sustainability, Cambridge. Cai, X., D. C. McKinney, L. S. Lasdon, and D. Watkins (1998). ?Search global optimum solutions for large scale nonconvex NLP problems in water resources management modeling?, submitted. Carley, M., and C. Ian (1992). Managing Sustainable Development, London, Earthsacn. Cieniawski, S. E., W. Eheart, and S. Ranjithan (1995) ?Using genetic algorithms to solve a multiobjective groundwater monitoring problem?, Water Resour. Res., 31(2); 399-409. Chow, V. T., D. R. Maidment and L. W. Mays (1987). Applied Hydrology, McGraw-Hill, N. Y. Clemmens A. J. and A. R. Dedrick (1994). ?Irrigation techniques and evaluations, Management of Water Use in Agriculture?, Tanji, K. K. And B. Yaron, eds. Daly, H.E., and J. B. Cobb (1989). For the common good: redirecting the economy toward community, the environment, and a sustainable future Boston, Beacon Press. Dandy, G. and P. Crawley (1992). ?Optimum operation of a multiple reservoir system including salinity effects?, Water Resources Research 28(4): 979- 990. Dariane A. B. and T. C. Hughes (1991). ?Application of crop yield functions in reservoir operation?, water Resources Bulletin, Vol. 27 No. 4, pp649-656. Daza, O. H., and R. C. Peralta (1993) ?A framework for integrating NPS pollution preventing and optimal perennial groundwater yield planning? in Mgmt. Irrig. Drain. Systems: Integrated perspectives, ed. By K. G. Allen, Park City, Utah. pp. 297-304. 404 De Wit, C. T. (1958). Transpiration and crop yields. Institute of Biological and Chemical Research on Field Crops and herbage. Wageningen. The Netherlands, Vers-Landbouwk, onder Z. No. 64-6-S Gravevage. Dinar, A., and J. Letey (1991). ?agricultural water marketing, allocative efficiency, and drainage reduction", J. Enriron. Econ. Mgmt. 20: 210-223. Dinar, A., and J. Letey (1996). Modeling Economic Management and Policy Issues of Water in Irrigated Agriculture, Praeger Publishers. Doorenbos, J., and W. O. Pruitt (1977). Guidelines for predicting crop water requirements, FAO irrigation and Drainage Paper, no. 24. Doorenbos, J., and W. O. Pruitt (1979). Crop yield vs. Water, FAO irrigation and Drainage Paper, no. 33. Drud, A. S. (1994). ?CONOPT - A Large Scale GRG Code?, ORSA J. on Computing 6, 207-216. Eagleson, P. S. (1978). ?Climate soil and vegetation, 5, a derived distribution of storm surface runoff?, Water Resour. Res., 14(5): 740-748. Easter, J. (1997). ?Water markets? in Water Resources: Environmental Plng., Mgmt. Development., ed. by A. K. Biswas, Mcgraw-Hill, N. Y. European Commission (1995). Water Resources Management & Agricultural Production in the Central Asian Republics, WARMAP Project Report, Vol. 1-6. Faisal, I. M., R. A. Young and J. W. Warner (1997). "Integrated economic- hydrologic modeling for groundwater basin management?, Water Resour. Development 13(1): 21-34. Falkenmark, M. (1977) "Reduced water demand - results of Swedish antio- pollution program?, Ambio. FAO (1977). Crop water requirements, FAO Irrigation and drainage paper 24, Rome, Italy. FAO (1979). Yield response to water, FAO Irrigation and drainage paper 33, Rome, Italy. 405 FAO (1996). Food Production: the Critical Role of Water, World Food Summit, Rome, Italy. Fedra, K., and D.G. Jamieson (1996). "The 'WaterWare' decision-support system for river-basin planning. 2. planning capacity", J. Hydrology, 177:177- 198. Feinerman, E., and D. Yaron (1983). "Economics of irrigation water mixing within a farm framework", Water Resour. Res. 19(2):337-345. Fiering, M. B. (1982). "Alternative indices of resilience?, Water Resour. Res., 18:33-39. Floudas C. A., Aggarwal A. and Ciric A. R. (1989). ?Global optimum search for nonconvex NLP and MINLP problems?, Computers chem. Engng., 13(10): 1117-1132. Floudas, C. A. (1995). Nonlinear and Mixed-Integer Optimization. Oxford Univ. Press, New York. Gardner, R., E. Ostrom, and J.M. Walker (1990). ?The nature of common pool resources? Rationality and Society, 2:335-358. Gardner, R. L., and R. A. Young (1988). "Assessing strategies for control of irrigation-induced salinity in the Upper Colorado River basin, Amer. J. Agr. Econ. 70:37-49. GEMS (1988). Assessment of freshwater quality (UNEP/WHO). Geoffrion A. M. (1972). ?Generalized Benders decomposition?, J. Optimization Theory Applic.10: 237-248. Gidroproekt (1976). ?Concepts of Water Use Rules for the Naryn-Syr Darya Cascade of Reservoirs: Book 2 Water Calculations?, All-Union Design Prospecting and Research Institute, Central Asian Division, Tashkent (translated to English by USAID EPT Project April, 1998). Gini, M. (1984). Simulation of water allocation and salt movement in the root zone, Master?s thesis, Dep. Of Civ. Eng., Mass. Inst. Technol., Cambridge, Mass. 406 Glascoe L. G., Y. Eren, and J. W. Bulkley (1997). "A predictive model of salinity and crop-production in the Jezreel Valley of Israel?, in the proceedings of ASCE Water Resour. Plng. Mgmt. Div. Annual conference, Houston. Gleick, P. H. (1989). "Climate change, hydrology, and water resources?, Reviews of Geophysics, 7(3): 329-344. Gleick, P.H. (1986). "Regional hydrologic consequence of increases in atmospheric CO2 and other trace gases?, Climate change, 10:137-161. Goodchild, M.F. (1993). ?Data models and data quality: problems and prospects? in Environmental modeling with GIS, eds. M.F. Goodchild, B.O. Parks, and L.T. Steyaert. New York: Oxford University Press, pp. 8-15. Gorelick, S. M. (1983). "A review of distributed parameter groundwater management modeling methods?, Water Resour. Res., 19(2): 305-319. Goldberg, D. E. (1989). Genetic Algorithms, Addison-Wesley, Reading, Mass. Golubev, G. N. (1993). "Sustainable water development: implications for the future?,, Wat. Resour. Development, 9(2): 127-153. Griffin, R. C. and D. W. Bromley (1982) "Agricultural runoff as a nonpoint externality: a theoretical development?, Am. J. Agr. Econ., 64(3):547-552. Grigg, N. S. (1996). Water Resources Management, McGraw-Hill. Haan, C. T. (1977). Statistical methods in hydrology, Ames : Iowa State University Press, Hanks, R. J., ?Crop coefficients for transpiration?, Advances in evapotranspiration, ASAE, 430-438. Haimes, Y. Y. (1977). Hierarchical analyses of water resources systems: modeling and optimization of large-scale systems, McGraw-Hill, New York. Halhal, D., G. A. Walters, D. Ouazar, and D. A. Savic (1997). ?Water network rehabilitation with structured messy genetic algorithm?, J. Wat. Resour. Plng. Mgmt., ASCE, 123(3):137-145. Hanks, R. J., and J. C. Andersen (1979). ?Physical and economic evaluation of irrigation return flow and salinity on a farm?, in Salinity in Irrigation and water Resources, ed. By D. Yaron and M. Dekker, N.Y. 407 Hanks, R.J. (1983). Yield and water use relationships: An overview. In Limitations to efficient water use in crop production, eds. H.M. Taylor, W.R. Jordan and T.R. Sinclair. Madison, Wisc.: American Society of Agronomy. Hanks, R. J. (1974). ?Model for predicting plant growth as influenced by evapotranspiration and soil water?. Agronomy Journal 66:660-665. Hanks, R. J. (1985). ?Crop coefficients for transpiration?. Advances in Evapotranspiration, Am. Society of Agri. Engr. (ASAE), 430-438. Hanks, R.J. and R.W. Hill. (1980). Modeling crop response to irrigation in relation to soils, climate and salinity. Oxford: Pergamon. Hashimoto, T., D. P. Loucks, and J. R. Stedinger (1982). "Robustness of water resources systems?, Water Resour. Res., 18(1): 21-26. Hashimoto, T., J. R. Stedinger, and D. P. Loucks (1982). "reliability, resiliency, and vulnerability criteria for water resources system performance evaluation?, Water Resour. Res., 18(1): 14-20. Harza (1995), Hydropower generation study in Central Asia. Harza Engr. and Sci. Company, Chicago. Hill, R. W., R.J. Hanks, and J.L. Wright (1982). Crop yield models adapted to irrigation scheduling programme. Research Report 99, Uath Agric. Experimental Station, Uath State Univ., Logan, Uath. Holland, J. H. (1975). Adaptation in natural and artificial systems. MIT Press, Cambridge, Mass. Howe, C. W., Schurmeier, D. R., and Shaw, W. D. Jr. (1986). "Innovative approaches to water allocation: the potential for water markets?, Water Resour. Res., 22(4): 439-445. Howe, C. W., and D. V. Orr (1974). ?Effects of agricultural acreage reallocation on water availability and salinity in the upper Colorado River?, Water Resour. Res., 10(5): 893-897. 408 Huang C., A. S. Mayer (1997). ?Pump-and-treat optimization using well locations and pumping rates as decision variables?, Water Resour. Res. Vol. 33 , No. 5 , p. 1001-1012. Jensen, M. E. (1968). ?Water consumption by agricultural plants? in Water deficit and plant growth, Vol 11, T. T. Kozlowski (Editor). Academic Press, New York, pp 1-22. Jensen, M. E., Wright, J.L. and Pratt, B.L. (1971). ?Estimating soil mositure depletion from climatic, crop and soil data. Trans. ASAE, 14(5):954-959. Kacmarek, Z., N. W. Arnell, and E. Z. Stakhiv (1996). "Water resources management?, in Intergovernmental Panel on Climate Change Second Assessment Report, Chap. 10, Cambridge University Press. Kirshen, P. H., and N. M. Fennessey (1993). Potential impacts of climate change upon the water supply of the Boston metropolitan area, U.S. Environmental Protection Agency. Kumar C. N., N. Indrasenan, and K. Elango (1998), ?Nonlinear programming model for extensive irrigation? , J. of Irri. and Drain. Engr., Vol. 124, No. 2, pp. 123-126. Kundzewicz, Z. W., and J. Kindler (1995). "Multiple criteria for evaluation of reliability aspects of water resource systems?, Proceedings of a Boulder Symposium, IAHS publ. no. 231. Labadie, J. W., D. G. Fontane, and T. Dai (1994). "Integration of water quantity and quality in river basin network flow modeling?, ASCE Water Resource Planning and Management Annual Conference. Lam, D. C., and Swayne, D. A. (1991). ?Integrated database, spreadsheet, graphics, GIS, statistics, simulation models, and expert systems: experience with the RAISON system on microcomputers? In NATO, ASI Series, Vol. 26, edited by D. P. Loucks and J. R. de Costa, 429-59, Germany. Lasdon L. (1970). Optimization Theory for large systems, Macmillan Publ. Co. INC., New York. 409 Latif, M. and James L. D. (1991 ). ?Conjuctive water use to control waterlogging and salinization?, J. of Wat. Resour. Plng. and Mgmt., 117(6): 104-114. Lee, D.J. and R.E. Howitt (1996). ?Modeling regional agricultural production and salinity control alternatives for water quality policy analysis?, American Journal of Agricultural Economics 78(1): 41-53. Lefkoff, L. J., and S. M. Gorelick (1990a). "Simulating physical processes and economic behavior in saline, irrigated agriculture: model development?, Water Resour. Res., 26(7): 1359-1369. Lefkoff, L. J., and S. M. Gorelick (1990b). "Benefits of an irrigation water rental market in a saline stream-aquifer system?, Water Resour. Res., 26(7): 1371-1381. Lettenmaier, D. P., G. Mccabe, and E. Z. Stakhiv (1996). ?Global climate change: effect on hydrologic cycle?, chapter 29 in Water Resources Handbook, ed. by L. Mays, McGraw-Hill, N.Y. Loucks, D. P. (1987). ?Water quality - economic modeling?, in Economic- Ecological Modeling, ed. By L. C. Braat, and W. F. J. Lierop, Elsevier Sci. Publ., North-Halland. Loucks, D. P. (1996). ?Surface water systems,? in Water Resources Handbook, ed. by L. Mays, McGraw-Hill, N.Y., Chap. 15, 1996. Loucks, D. P., French, P. N., and Taylor, M. R. (1996). ?Development and use of map-based simulation shells for creating shared-vision models?, HydroGIS?96, IAHS publ. no 235, pp695-702. Loucks, D. P., M. R. Taylor, and P. N. French (1994). Interactive Mas-Balance Simulator of River-Aquifer Systems: IRAS Program Description and Operating Manual. School of Civil Engr. And Envirn. Engr., Cornell Univ., Ithaca, New York. Louie, P. W. F., W. G. Yeh, and N. Hsu (1984). "Multiobjective water resources management planning?,, J. Wat. Resour. Plan. Managt., 110(1)39-56. Mass, E. V., and G. J. Hoffman (1977). "Crop salt tolerance-current assessment, J. Irrig. Drain. Div. Am. Soc. Civ. Eng., 1039IR2):115-134. 410 Matanga, B. G., and M. A. Marino (1979). "Irrigation planning, 2, water allocation for leaching and irrigation purposes?, Water Resour. Res., 1593): 679-683. Mays, L. W., and Y. Tung (1992). Hydrosystems Engineering and Management, McGraw-Hill, New York. Mckinney, D. C., and Cai, X. (1996). ?Multiobjective optimization model for water allocation in the Aral Sea Basin?, the 2nd American Institute of Hydrology (AIH) and Tashkent Institute of Engineers for Irrigation (IHE) conjunct conf. on the Aral Sea basin water resources problems, Tashkent, Uzbekistan, July. Mckinney, D.C., Karimov A, and Cai, X. (1997). ?Aral Sea regional water allocation model for the Amudarya River?, Environmental Policy and Technology Project, U.S. Agency for International Development. Mckinney D. C., and X. Cai (1997). Multiobjective water resources allocation model for the Naryn-Syrdarya Cascade, Working paper for Envirn. Policy and Technology Project. McKinney C. D. X. Cai, M. Rosegrant, C. Claudia, C. A. Scott (1999). Integrated Basin-Scale Water Resources Management Modeling: Review and Future Directions, Research paper in International Water Management Institute Colombo, Sri Lanka, in press. McKinney D. C., and M. D. Lin (1994). Genetic Algorithm Solution of Groundwater Management Models. Water Resources Res. 30, 1897-1906. Michalewicz, Z. (1992). Genetic algorithms + Data structure = Evolution programs, Springer-Verlag, New York, N. Y. Micklin, P. P. (1993). ?The shrinking Aral Sea?, Geotimes, 38(4): 14-18. Miller, J. R., and G. C. Russell (1992). "The impacts of global warming on river runoff?,, Journal of Geophysical Research, 97:2757-2764. Moore, M.R., N.R. Gollehon and D.H. Negri (1997). ?Alternative forms for production functions of irrigated crops?, The Journal of Agricultural Economics Research, 44: 16-32. 411 Moy, W., and J. L. Cohon, and C. S. Revelle (1986). "A programming model for analysis of the reliability, resilience, and vulnerability of a water supply reservoir?, Water Resour. Res., 22(4): 489-498. Musharrafieh G. R., R. C. Peralta, L. M. Dudley, and R. J. Hanks (1995). "Optimization irrigation management for pollution control and sustainable crop yield?, Water Resour. Res., 31(4):1077-1086. Murtagh, B. A. and M. A. Saunders (1982). ?A Projected Lagrangian Algorithm and its Implementation for Sparse Nonlinear Constraints?, Mathematical Programming Study 16, 84-117. Nash, L. L., and P. H. Gleick (1991). "Sensitivity of streamflow in the Colorado basin to climate changes?, Journal of Hydrology, 125:221-241. Nemec, J., and J. C. Schaake (1982). "Sensitivity of water resource systems to climate change?, J. Of Hydrol. Sci., 27:327-343. Noel, J. E., and R. E. Howitt (1982). "Conjunctive multibasin management: an optimal control approach?, Water Resour. Res., 18(4): 753-763. OECD (1998). the Athens Workshop, Sustainable Management of Water in Agriculture: Issues and Policies, Organization for Economic Co-operation and Development (OECD). Oliveira, R., and D. P. Loucks (1997). ?Operating rules for multireservoir systems?, Water Resour. Res., 33(4):839-852. Paris, Q and K.K. Knapp (1989). Estimation of von Liebig response functions. American Journal of Agricultural Economics 71: 178-186. Parsons, J. E., R. W. Skaggs, and C. W. Doty (1991). ?Development and testing of a water management model (WATERCOM) :development?, Trans. Of Am. Society Agr. Engr.,34(1):120-128. Perry C. J. and A. Narayanamurthy (1998). Irrigation indicators, research report, International Water Management Institute, Colombo, Sri Lanka. Peralta, R. C., K. Kowalski, and R. R. A. Cantiller (1988). ?Maximizing reliable crop production in a dynamic stream/aquifer system?, Tansc. of Am. Soc. Agr. Engr., 31(6): 1729-1742. 412 Peralta, R. C., A. Gharbi, L. S. Willardson, and a. Peralta (1990). ?Optimal conjunctive use of ground and surface waters?, in Mgmt. Of on farm irrig. Systems, ed. By G. Hoffman, T. Howell, and K. Soloman, pp. 426- 458, Am. Soc. Agr. Engr., St. Joseph, Mich. Postel, S. (1995). Conserving water: the untapped alternative, (Worldwatch Institute). Prajamwong, S., G. P. Merkley, and R. G. Allen (1997). "Decision support model for irrigation water management?, J. of Irrig. Drain. Div., 123(2): 106- 115. Prendergast, J. (1993). "Engineering sustainable development?, Civil Engineering, p 39 -44, Oct. Raskin, P., E. Hansen, Z. Zhu, and D. Stavisky (1992). ?Simulation of water supply and demand in the Aral Sea Region?, Water International, 17: 55- 67. Reitsma, R. (1996). ?Structure and support of water-resources management and decision-making?, J. Of Hydrg. 177: 253-268. Reitsma, R., P. Ostrowski, and S. Wehrend. 1994. Geographically distributed decision support: the TVA TERRA System. In Water policy and management. Solving the problems, eds. D.G. Fontaine and H.N. Tuvel. New York: American Society of Civil Engineers. Revelle, R. R. and Waggoner, P.E. (1983). ?Effects of a carbon dioxide-induced climatic change on water supplies in the western United States?, in Changing Climate, National Academy of Seciences. National Academy Press, Washington D.C. Rosegrant, M. W, McKinney, D.C. et al. (1999). Intersectoral water allocation in the river basin: the Maipo basin in Chile. Research Report, International Food Policy Research Institute (IFPRI), Washington D.C. in press. Rosegrant, M. W., and Binswanger, H. P. (1994). "Markets in tradable water rights: potential for efficiency gains in developing-country water resources allocation?, World Development, 20: 1613-1625. Rosegrant, M.W. and R.S. Meinzen-Dick (1996). Multi-country research program: Water resource allocation: Productivity and environmental 413 impacts (MP-10). Program statement and methodology. Washington, D.C.: International Food Policy Research Institute. Savic, D. A., and Walters, G. A. (1997). "Genetic algorithms for least-cost design of water distribution networks?, J. Water Resour. Plng. and Mgmt., ASCE, 123(1); 61-77. Scherer, C. R. (1977). "Water allocation and pricing for control of irrigation- related salinity in a river basin?, Water Resour. Res. 13(4): 225-238. Sergageldin, I. (1995). "Water resources management: a new policy for a sustainable future?, Wat. Resour. Development, 11(3): 221-231. Sharply and Williams (1990). ?EPIC-erosion/productivity impact calculator 1: model documentation?, Tech, bull., No. 1768, U.S. Department of Agriculture, Washington, D. C. Simonovic, S. P. (1997). ?Risk in sustainable water resources management? in Sustainability of Water Resources under Increasing Uncertainties, IAHS, Publ. No. 240. Simonovic, S. P. (1996a). "Decision support systems for sustainable management of water resources: 1. General principles?, Water International, 21(4): 223-232. Simonovic, S. P. (1996b). "Decisoin support systems for sustainable management of water resources: 2. Case studies?, Water International, 21(4): 233-244. Skaggs, R. W. (1980). A water management model for drained soils, Tech. Bull. No. 207, North Carolina Agri. Service. Skaggs R. W., and C. Murugaboopathi (1994). ?Drainage and subsurface water management?, in Management of Water Use in Agriculture, Tanji, K. K. And B. Yaron, eds. Skogerboe, G., V., and W. R. Walker (1973). ?Salt pickup from agriculture lands in the Grand valley of Colorado?,, J. Environ. Qual., 2(3): 377-382. Smedema, L. K., and Rycroft, O. W. (1990). Land drainage, Batsford, London, U.K. 414 Spulber, N., and A. Sabbaghi (1994). Economics of Water Resources: From Regulation to privatization, Kluwer Academic Publishers, Norwell, Mass. Takayama, T., and G. G. Judge (1996). "Spatial equilibrium and quadratic programming?, J. Farm Econ. 46(1): 67 -93. Turgeon, A. (1981). ?A decomposition method for the long-term scheduling of reservoirs in series?, Water Resour. Res., 17(6): 1565-1570. United Nations (1976). Long-term Planning of water Management, New York. United Nations Conference on Environment and Development (UNCED) (1992). " Report of the United Nations conference on environment and development, Chap. 5 and 18, Rio de Janeiro, June. U. S. Department of Agriculture, Soil Conservation Service (SCS) (1967). Irrigation Water Requirement, Technical Release No. 21, Engineering Div., SCS 83 p. Vaux, H. J., and R. E. Howitt (1984). "Managing water scarcity: an evaluation of interregional transfers?, Water Resour. Res. 20:785-792. Vaux, H.J. and W.O. Pruitt (1983). ?Crop-water production functions? in Advances in irrigation, ed. D Hillel. New York: Academic Press. Watkins, D. W. and D. C. McKinney (1997). Decomposition Methods for Water Resources Optimization Models with Fixed Costs. Advances in Water Res. Watkins, D.W. Jr., and D.C. McKinney (1997). "Finding Robust Solutions to Water Resources Problems?, J. Water Resour. Plan. and Mgmt., ASCE, 123(1): 49-58. WCED (World Commission on Environmental and development) (1987). Our Common Future. (?The Brundtland Report?), Oxford University Press, 338 pp. White G. F. (1969). Strategies of American water management, Ann Arbor, University of Michigan Press. World Bank (1992). World development report 1992: development and the environment, Washington D. C. 415 Yaron, D., E. Danfoss, and Y. Vaadia (1969). Irrigation in arid zones, The Volcani Inst., Bet-dagan, Israel. Yaron, D, and A.. Olian (1973). "Application of dynamic programming in Markov chains in the evaluation of water quality in irrigation?, Amer. J. Agr. Econ., 55:467-471. Yaron, D., E. Bresler, H. Bielorai, and B. Haprinist (1980). "A model for optimal irrigation scheduling with saline water?, Water Resour. Res. 16(2): 257- 262. Yaron, B, and H. Frenkel (1994). ?Water suitability for Agriculture?, in Management of Water Use in Agriculture, Tanji, K. K. And B. Yaron, eds. Yeh, W., W-G (1985). Reservoir management and operation models: a state-of- the-art review, Water Resour. Res, 21(12), pp1797-1818. Young, R. A. (1996). "Water Economics?, in Water Resources Handbook, ed. by L. Mays, McGraw-Hill, N.Y., Chap. 3. Zilberman, D. (1998). ?The impact of agriculture on water quality?, in the Athens Workshop, Sustainable Management of Water in Agriculture: Issues and Policies, Organization for Economic Co-operation and Development (OECD). Vita Ximing Cai, was born in Hubei Province, the People?s Republic of China, on August 25, 1966, the son of Ronghua Ma and Yadong Cai. He graduated from Huanggang High School in Huangzhou, Hubei Province, in 1985 and entered Tsinghua University in Beijing. In 1990, Mr. Cai received the degree of Bachelor of Engineering. From 1990 to 1992, he worked in Tsinghua University as an assistant lecturer. From 1992 to 1994, he continued his graduate study in Tsinghua University, and received his Master of Engineering in 1994. From 1994 to 1995, he studied at Clemson University in South Carolina, U.S.A, and then he transferred to The University of Texas at Austin. In 1993, Mr. Cai married Ms. Tong Zhang. Permanent address: No. 12, Apt# 9, Tsinghua University Bejing, P.R. China, 100084 This dissertation was word processed by the author. 374 Appendix A Deterministic form of a Chance-Constrained Model with Nonlinear Constraints Mays and Tung (1992) gave the deterministic form for a linear chance- constrained model with random parameters on the right-hand-site of the equations, like abx cx ?? ) ~ ( .. min APts (A-a1) where the right hand side coefficient ~ b is random, and a is a vector of specified reliability of compliance (or confidence). Here we show a general model, linear or nonlinear, with random parameters on the right-hand-site of the equations has the same deterministic form as the linear model. The model can be written as: abxg x ?? ) ~ )(( .. )( min Pts f (A-a2) where f(x)is the objective function, and g(x) is a vector of constraint equations. Both f(x) and g(x) can be linear or nonlinear. Assuming the random RHS coefficient b ~ , has a cumulative density function (CDF) b F~ , with mean b ? ~ and standard deviation b ?~ . Equation (A-b2) is equivalent to: ag(x)b ??? 1) ~ (P (A-a3) 375 which is expressed in terms of the CDF of the random RHS coefficient, b ~ , as, a(g(x))F b ??1~ (A-a4) Using the standardized variate of the random RHS coefficient, that is, bbb )/??b(Z ~~~ ~ ?= , Equation (A-a4) can be expressed as: a1) ? ?g(x) (F b b Z b ?? ? ~ ~ ~ (A-a5) The deterministic equivalent of the stochastic model in (A-a2) is the inverse of equation (A-a5): ) 1 ~ ~ ~ a(1F ? ?g(x) b Z b b ?? ? ? (A-a6) which can be written as ba,1bb ?Z?g(x) ~~~ ?+? ? (A-a7) 376 Appendix B Notes on the Genetic Algorithm Program The genetic algorithm appied in the GA-LP approach is based on a Fortran program, UTBGA (Unievrsity of Texas Binary-Code Genetic Algorithm), developed by Dr. Min-der Lin and Dr. Daene McKinney in Center for Research in Water Resources (CRWR), the University of Texas at Austin. It was modified in this research so that it could be used in the GA-LP approach, described in Chapter 5 and further in Chapter 6. Basically the primary program was split into four parts as described in Table A.b1. 377 Table A.b 1 Components of the genetic algorithm applied in the GA-LP approach Sub- programs Function Input Output INIT Create the first generation randomly. Parameters required by the genetic algorithm, including bounds of the decision variables. ? Values for the inter-year control variables, put in four files, area.in, eff.in, wsf.in, and tax.in, described in Appendix I. ? The first generation saved in an output file. GEN Create offspring generations based on the fitness of the pervious generation. ? Parameters required by the genetic algorithm, including bounds of the decision variables; ? Previous generation saved in an output file; and ? Fitness values of the individuals in the previous generation. ? Values for the inter-year control variables, put in four files, area.in, eff.in, wsf.in, and tax.in, described in Appendix I. ? The generation saved in an output file. GROUP Group similar individuals Individuals created from INIT or GEN Grouped individuals FIT Calculate fitness of individuals. This program can also be coded in the GAMS model. External modeling result for individual, from the GAMS model in this research. Fitness for individuals, saved in an output file. 378 The combined GAMS model and the genetic algorithm are run through a batch file. The batch file used in a UNIX machine is shown in Figure A.b1. #!/bin/ksh (operation system specification) echo GA-LP approach echo echo generate initial generation init (create the first generation) echo echo cp emp res_gen.dat (renew a result file) echo echo interactive process between GA and GAMS echo set the number of generations echo ngen=300 while [ ngen -ne 0 ] do ngen=`expr $ngen - 1` echo generation $ngen gams longm lo=0 (run the GAMS model) echo entering GA fit (calculatw fitness) cat res.out>>res_gen.dat gen (create a new generation) gp (group similar individuals) echo entering GAMS done Figure A.b1. A List of the job file for running the long-term model in the UNIX system 379 Appendix C Generic Analysis of the Network-Based Water Allocation System We first derive some generic relationships of yield-water, and yield ? salinity within an irrigation demand site, and then extend the relationships to include the effect from upstream diversion and drainage load. For simplicity, we use a diagram shown in Figure A.c1, including an upstream demand site and a downstream demand site. What is presented within a demand site is shown in Figure 3.6. The following derivation should be referred to these two figures. The symbols used in this section are defined as below: y = crop yield, s = soil salinity, m = soil moisture, w = water available to the crop field, s w = salt concentration in water applied to the crop field, d = diversion to a downstream demand site, s d = salt concentration in diverted water (d), q = downstream river flow, s q = salt concentration with q, d = diversion to a upstream demand site, ds = salt concentration with d , q = downstream river flow, s q = salt concentration with q , r = return flow from the upstream demand site, rs = salt concentration with r , 380 i = inflow to the river reach between two demand sites, i s = salt concentration with i, Upstream demand site q d r q i d Downstream demand site Figure A.c1 A simple diagram of the river basin network for water allocation With the definitions of the items above, generic equations describing relationships among these items can be written as: ),( smfy y = (A-c1) r 381 ),0( pemwfm m = (A-c2) ),0,0,( pessmswfs ws = (A-c3) ),,,,( wacdrlweiredsdfw w = (A-c4) ),,,,,,,( wacsdrslweiredssdfs drlwdsw w = (A-c5) ),,( wppcpoqfd d = (A-c6) qd ss = (A-c7) irdqq ++?= (A-c8) [ ] qsisrsdqs i rq q /)( ?+?+??= (A-c9) ),0,0,,,,,,,,( taxmsslwdredpedneiredssdfr lw dr = (A-c10) ),0,0,,,,,,,,( taxmsslwdredpedneiredssdfs lw d s r r = (A-c11) The items showing the conditions for the above equations are specified as: dr = drainage reuse, s dr = salt concentration in drainage reuse (dr), po = policy controls, 382 pc = physical capacity, wac = water allocation among crops, wp = water supply price, tax = tax on excessive salt discharge, lw = local water source, s lw = salt concentration in local source, pe = precipitation infiltrated into the root zone, s0 = initial soil salinity (previous soil salinity accumulation), m0 = initial soil moisture, and eds, eir, edn, and edp are defined as before. It should be noted that some of these items, such as drainage reuse (dr), water allocation among crops (wac) and irrigation and drainage infrastructure levels (eds, eir, edn, and edp), are decision variables in the equation (A-c4) and (A-c5). Since we want to focus on the analysis of the effect from upstream demand site, those internal decisions within a demand site are treated as given conditions in equation (A-c1)-(A-c11). The partial differential equations of crop yield (y) with other items are derived based on the relationships (eq. A-c1 ? A-c11), and we discuss these derivations in the rest of this section. In the beginning, we define: s f f yy s ? ? = (A-c12) m f f yy m ? ? = (A-c13) When soil salinity is over the crop tolerance, 0< y s f , otherwise 0= y s f . For a specific growth stage, there is a point of soil moisture that is best for crop 383 growth (Vaux and Pruitt, 1983). Below this point, 0> y m f , and above this point, 0< y m f . For proper irrigation purpose, we should have 0> m y f . In equation (A-c2), soil moisture (m) is a function of w, the water applied to the crop field, with conditions of initial soil moisture (m0) and precipitation (pe); soil salinity (s) is a function of both water (w) and salt concentration in the water (s w ), with the same conditions as soil moisture, plus initial soil salinity (s0). We have: m w y m y w ff w m m y f ?= ? ? ? ? ? = (A-c14) s s y s w y s ww ff s s s y f ?= ? ? ? ? ? = (A-c15) where, 0> m w f before soil moisture reaches the field capacity, and 0> s s w f . Since 0> y m f and 0< y s f , we have 0> y w f and 0< y s w f . The value of m w f depends on initial soil moisture (m0) and precipitation (pe), we have 0)0(/ 0, since 0 , , > d w w m m y fff . The value of w d f depends on all the conditions associated with equation (A-c4). Better canal lining (high delivery and distribution efficiency), and better irrigation system (high irrigation efficiency) will make the value of d w f larger. Since d w f is with a specific crop field, larger fraction of diversion distributed to the crop field will increase the value of d w f . The decision on water allocation among crops depends on the economic value of water applied to the crop, as well as some policy requirements. Since ,0< y s f the effect from salinity in the water withdrawal to the value of y d f depends on the value of w w s d s s w d s w ffff + , in which 0, , ? s s w d w ff and the value of s w f and w s d f depends on more conditions. From equation (A-c15), water applied to crop field is blended with multiple sources. Generally salt concentration in drainage and groundwater is high, water with low salinity is used to dilute the water with high salinity. In this way, water withdrawal dilutes the water applied to crop field, i.e, 0< s w f . However, when the salinity in water withdrawal is higher even than the local sources, then 0> w s f , and it will make 385 0< w d s w y s fff , which means salinity in water withdrawal produce negative impact to water withdrawal for irrigation purpose. The similar explanation can be made to the value of w s d f . The partial differential relation between crop yield (y) and salinity in water withdrawal (s d ) is: w wd s d s s y s d w wd y s fff s s s s s y s y f = ? ? ? ? ? ? = ? ? = (A-c17) where, 0, , > w dw s s s s ff given ,0< s y f we have 0< y s d f We can further relate crop yield (y) to river flow (q), and salinity in river water (s q ). Based on equation (A-c5) and equation (A-c16), we have d q y d y q ff q d d y q y f = ? ? ? ? = ? ? = (A-c18) where y d f has been discussed above. Considering the downstream flow requirement and diversion capacity, the larger river flow allows larger diversion, which generally leads d q f >0, and thus y q f >0. However, the value of d q f also depends on the water price, which presents an economic incentive for water withdrawal. The increase of water price causes the decrease of water value of the demand site, and when the water value of the demand site is reduced to zero d q f =0, i.e., water withdrawal will not be related to river flow. From equation (A-c7), s q and s d are identical, therefore, y s q f is identical to y s d f , and 0< y s d f . 386 By now we have discussed the partial differential relationships of crop yield with water available to the crop, water withdrawal to the demand site, river flow, and the salinity associated with these items. Decisions specified with these relationships include water withdrawal, water allocation among crops, source blending for irrigation and infrastructure improvements on water delivery and on- field use. In the following we discuss the extended relationships which relate the crop yield at one demand site to water withdrawal, return flow, and salinity in return flow at the upstream demand site. Equations (A-c19) ? (A-c20) present these relationships respectively. q q s d y s r d y q q q y d ffff d s s y d r q y f +?= ? ? ? ? +? ? ? ? ? = )1()1( (A-c19) and ()( ) ( )( )[ ] () 2 1 ? ++? ???+?+??????++?= irdq fsisrsdsqssfirdqf r d i rqqqr r d s d q (A-c20) in which r d f is a critical factor. If r d f =1, then, y d f is simplified as ( ) irdq ssf f qr y s y d q ++? ? = (A-c21) Given 0< y s q f , equation A-c17, and 0>=++? qirdq , if 0>? qr ss (which is the normal case in reality), then 0< y d f , which implies even upstream 387 diversion does not affect river flow to downstream ( r d f = 1), the increase of salinity in return flow due to the diversion will still make negative contribution to downstream crop yield. In reality, if soil salinity is high at upstream irrigated fields, then upstream withdrawal will both reduce downstream flow, and increase salinity in downstream flow. As shown in equation (A-c19), if r d f < 1 (i.e., the magnitude of return flow change is less than that of the diversion change, which is generally true in areas with (semi) arid weather.), the negative effect from flow reduction is apparent, and the effect from salinity is also negative, except ()( ) ( )( ) 01 ? qr ss then 0< y r f . Normally we have 1)( 1 >= ? r d d r ff , and then the flow effecting item to y r f , )1( d r y q ff ? <0, which implies the return flow from the upstream demand site does not simply increase the flow to the downstream, because 1)( 1 >= ? r d d r ff means large return flow corresponds even larger diversion, and finally the flow to downstream is reduced. Only if 1)( 1 <= ? r d d r ff , that is to say, only if a smaller diversion produces larger return flow, does the return flow make positive contribution to the downstream flow. That is hardly true in the real world. Finally the relation between crop yield (y) and salt concentration in return flow from the upstream demand site is shown as: 389 q r w qw r s s s s s s y s r q q w w r y s ffff s s s s s s s y s y f = ? ? ? ? ? ? ? ? = ? ? = (A-c27) q r f q r s s = (A-c28) and further, by equation (A-c17), y s r f is written as: y s y s q r f q r f ?= (A-c29) As discussed above, y s q f <0, and then y s r f <0. y d f , y r f and y s r f show the effect of upstream water withdrawal and drainage to the crop production of a downstream demand site, and they provide an analytical form for the externality involved in water allocation in a river basin. r d f (= dr ?? / ) is critical to the effect from upstream withdrawal, as well as return flow. The increase of r d f will reduce the flow effect, but will increase the salinity effect. As discussed above, water price (wp) can be taken as an economic policy to control the water withdrawal by a demand site. A high water price will reduce the marginal value of water withdrawal and then force the demand site to withdraw less water. Therefore a higher water price set up for an upstream demand may discount the negative effect to the downstream demand site, at some loss of avenue of the upstream demand site due to the less water supply. Tax on excessive salt discharge may force a demand site to reduce the amount of drainage or the salt concentration in drainage, or the both. The amount 390 of drainage can be reduced through on-field drainage disposal. However, as shown in equation (A-c19), the reduction of drainage amount may make the ?flow effect? more serious. Drainage treatment for river discharge will reduce the ?salinity effect? while keeping the ?flow effect? unaffected. A tradeoff relationship exists between the cost of drainage disposal or treatment, and the economic damage of the downstream demand site due to the ?flow effect? and ?salinity effect? from the upstream demand site. In this research, instead of a complete, more detailed analytical form of all hydrologic-agronomic-economic relationships, a mathematical programming model is developed to include these relationships at a whole river-basin scale with an extension to crop field. Quantitative analysis will be conducted based on output from the model. 391 Appendix D Glossary ia ? percentage which specifies a safety threshold for irrigated area ? change rate of TWB between year y and y-1 ? average of ? d ? change rate of benefit for each demand site ? price elasticity of demand ? intercept calibrated to "normal" production in the crop price function ? market share of the commodity in the crop price function a i , ? i constant coefficients in reservoir topological equations ?(IP) change of irrigation profit ?(R) change of ratio of assumed to primary efficiency ?(TWB) change of total water use benefit ?? elasticity of demand of water ? Lagrangian multipliers ? 0 soil osmotic potential due to the presence of solved salts ? m soil matric potential, resulting exclusively from the soil matrix ?s saturated soil matric potential ?t time duration of one period ? ratio of groundwater discharge to rivers to groundwater table 392 ? v standard deviation ? computing time discounting coefficient o vector, intermediate variables that are only related to flow and storage variables q vectors of flow and storage (volume) variables s vectors of slack variables u vector of Lagrange multipliers for the constrain a, b, c vectors of parameters g 1 , g 2 , g 3 vectors, sets of equations x, y, z vectors of variables x 0 , y 0 , z 0 initial values of vectors x, y, and z, respectively ~ b stochastic variable/parameter, right-hand side ~ A stochastic variable/parameter, technological coefficients (n, n2) all links from n to n2. (n1, n) all links from n1 to n, A reservoir surface area, and AEW actual ecological and environmental water use AIA actual irrigated area AIA actual irrigated area (AIA) AINV_DN annual investment for improving drainage collection systems AINV_DN annual investment for improving drainage collection systems AINV_DP annual investment for improving drainage disposal/treatment systems AINV_DP annual investment for improving drainage disposal/treatment systems AINV_DS annual investment for improving water delivery & distribution systems AINV_DS annual investment for improving water delivery & distribution systems AINV_IR annual investment for improving irrigation system AINV_IR annual investment for improving irrigation systems applications AR artificial recharge to aquifers 393 ASF crop field area in which soil salinity is over crop salinity tolerance B the slope of the yield-salinity curve at salinity values in the range S e > S? BT binary string of a number of bits c soil?s pore connectivity index C salt concentration with flow cdn cost per unit of drainage collection (not including fixed investments) cdr cost for per unit drainage collection (not including fix investment) cdt cost per unit of drainage disposal (not including fixed investments) cdt cost for per unit drainage disposal (not including fix investment) CETA cumulative actual evapotranspiration CETM cumulative maximum evapotranspiration cg groundwater pumping cost cmp consumptive use rate of the non-irrigation water supply cp crop patterns cpw power generation cost cr cost for per unit drainage reuse d(K s ) change of K s , and D_REV delivery from reservoirs to a farm [L 3 ] D_REV delivery from reservoirs to a demand site [L 3 ] D_RIV diversion from rivers to a demand site [L 3 ] D_RIV diversion from rivers to a farm [L 3 ] dm demand sites DN drainage from a crop field, including surface drainage and subsurface drainage DP deep percolation drn natural drainage to reservoirs, constant parameter in the model DS discharge from the aquifer associated with the demand site dy change of crop yield 394 dz change of the soil moisture EB ecological water use value ECe soil saturated extraction in dS/m ECg salinity in groundwater extraction ECp salinity in the percolation, expressed as electric conductivity [dS/m] ECr salinity in tailwater expressed as electric conductivity ECw salinity in water application, expressed as electric conductivity [dS/m] ECw salinity in the water application, expressed as electric conductivity [dS/m] ECw salinity of irrigation water in dS/m EDN drainage efficiency, the ratio of drainage from field to total percolation EDS water delivery & distribution efficiency EDT ratio of drainage disposal/treatment to total drainage EIR irrigation efficiency, the ratio of total water infiltrating into crop root zones over total water env index for environment integrity ER effective rainfall [L] ET 0 reference crop evapotranspiration ETA actual evapotranspiration [L] ETA actual evapotranspiration [L] ETM maximum evapotranspiration ev economic benefit from environmental water uses Evap evaporation rate in length, constant parameter fc fixed crop input cost per unit area fd crop fields G number of generations in the genetic algorithm GD depth of water table GE groundwater extract by absorption [L] GINP government investment for infrastructure 395 grechg groundwater recharge gws groundwater salinity, and H reservoir surface elevation hg groundwater level HP profit from power generation I number of individuals in the genetic algorithm IAN area remaining fallow due to water shortage and salinity IM income of demand site dm in year y IND an individual of a generation Inflow stream inflow inflow0 normal annual inflow to the sea by historic records INV annual investment and operating/maintenance cost inv_dn annual investment for increasing one unit of drainage inv_dp annual investment for increasing one unit of drainage disposal in inv_ds annual investment for per unit of water saving from delivery systems inv_ir annual investment per unit of water saving from irrigation systems IR infiltrated precipitation [L] K hydraulic conductivity k ap coefficient of soil water stress effect for soil evaporation k at coefficient of soil water stress effect for transpiration kat the coefficient of soil water stress effect for transpiration kc crop evapotranspiration coefficient kct crop transpiration coefficient ks coefficient of soil salinity effect ky crop yield response factor varying among crop growth stages lbd lower bound in the GBD-based approach LS local surface water source m soil connectivity and tortuosity coefficient 396 MES salt mass in return flow in excess of what was presented in the original diversion mv marginal value of water n water supply or demand nodes in the river basin network n1 a from-node in the river basin network n2 a to-node in the river basin network NG prescribed number of generations in genetics algorithms NI number of individuals in a generation (genetic algorithm) NP natural recharge to aquifer NREV net revenue from irrigation at a demand Obj objective value pcp crop selling price PDEM power demand PM groundwater pumped [L 3 ] PN percolation in crop fields in [L] PN percolation in a crop field, the amount of water leaving root zones to downward soil layers ppw power selling price PW hydropower generation Q in inflow during a time period Q out outflow during a time period RD root zone depth [L] REL reliability RELS flow to downstream reservoir(s) REUSE drainage reuse [L 3 ] REV reversibility rev reservoir rfe evaporation loss rate of the return flow 397 rgp the ratio of government investment to the local investment RIA reduced irrigated area RUE reservoir utilization efficiency (RUE) RUSE drainage reuse s aquifer storativity S? salinity threshold for a crop Sa areas with specific soil types SBD subsidy for improving water use capacities S e average root zone salinity, in saturated soil extract SEA socio-economic acceptability SEQ spatial equity Sgw groundwater salinity sim index of similarity (sim) between these two individual SL surface water leakage SM salt balance sub-model Sp salt in percolation SR surface runoff (tailwater) Sso soil salinity in crop field fd Ssw surface water salinity st crop growth stages, tst ? ST storage at the end of a time period. STR reservoir storage t time periods (months) T number of the time periods tax tax imposed on excessive salt discharge TEQ inter-year equity TEW target of AEW TIA the target irrigated area in each year 398 TIA target of IA) TIA total irrigated area at a demand site T LP time for linear programming Tol tolerance TP cumulative transpiration by the crop TPM Maximum TP TR total rainfall TS total available water storage in a river basin TSBD total available subsidy tt index of the time series tw average tail water level constant parameter in the model TWB total social benefit for the region of the river basin TWB total water use benefit (TWB) TYLD total yield of crop cp from all fields at all demand sites in the river basin ubd upper bound in the GBD-based approach V c economic value of water with a crop V d economic value of water with a demand site veco socio-economic value from per unit of ecological water use under the condition of water scarcity VUN vulnerability WA water available to a crop [L 3 ] WAF total water applied to crop fields WAPF total water applied to crop fields, including diversion, local surface source, and groundwater WD total water diversion from rivers and reservoirs, including local sources WDA diverted water available for use in a demand site WDN drainage from a crop field, including surface drainage and subsurface drainage 399 WDP deep percolation WDR historic water use right WDT amount of drainage disposed in a demand site WECO water for ecological use wenv weights (or scaling factors) assigned to env WEU water effectively used by crops WFLD surface water allocated to crop fields [L 3 ] w gs , w ss , w ws weights assigned to gs, ss, and ws, 0.1=++ wsssgs www WIF water infiltrating into crop root zones, NOT including effective rainfall win inflow to the root zone withdw withdrawal to water demand sites, constant parameter wout outflow from the root zone wpen weight assigned for the penalty item wrev weights (or scaling factors) assigned to rel wrev weights (or scaling factors) assigned to rev wsea weights (or scaling factors) assigned to sea wseq weights (or scaling factors) assigned to seq WSF water shortage (water demand minus water demand) WSMI water supply for municipal and industrial use WSU water sustained at the end of a year wteq weights (or scaling factors) assigned to teq wvun weights (or scaling factors) assigned to vun YA actual crop yield YF gs number of consecutive years in which gs y RGS ?> YF ss number of consecutive years in which ss y RSS ?> YF ws number of consecutive years in which ws y RWS ?> YM maximum yield without either water stress effect or soil salinity effect 400 Z soil moisture content in root zone in percentage Zs moisture content at field capacity Zw moisture content at wilting point