Parameter Sensitivity in Hydrologic Modeling 
 
 
Implementation by 
David R. Maidment, Ph.D., and 
Tanya Nicole Hoogerwerf 
 
 
Technical Report  
 
 
 
 
The University of Texas at Austin 
May 2002 
 Abstract 
 
Parameter Sensitivity in Hydrologic Modeling 
 
 
David R. Maidment, Ph.D. and Tanya Nicole Hoogerwerf 
The University of Texas at Austin, May 2002 
 
 
 
The computation of discharge from a watershed depends on the lag time 
between rainfall and runoff, while in turn the lag time depends on watershed 
parameters, such as length of the longest flow path, watershed slope, and the SCS 
curve number describing the effects of land use and soils.  This research explores 
the variation in lag time and discharge resulting from traditional and automated 
methods of calculating hydrologic parameters.  Four levels of extracting 
hydrologic parameters are explored:  (1) measurement from paper maps, (2) on-
screen extraction from raster maps, (3) using GIS and two different resolutions of 
grid-based digital elevation models (DEMs), and (4) using a triangulated irregular 
network (TIN).  Results show that variations in watershed area and curve number 
most directly impact the computed discharge, while variations in slope and flow 
path length are relatively insignificant.  
 ii
Table of Contents 
List of Tables..........................................................................................................vi 
List of Figures ......................................................................................................viii 
Chapter 1: Introduction ........................................................................................... 1 
1.1 Background of GIS use in Water Resources Applications ................... 2 
1.2 Project History....................................................................................... 2 
1.3  Objectives.............................................................................................. 3 
1.4 Organization .......................................................................................... 5 
Chapter 2: Literature Review .................................................................................. 6 
2.1 Introduction ........................................................................................... 6 
2.2 Summary of Current Hydrologic Practices of TxDOT ......................... 6 
2.3 Extracting Watershed Parameters from Digital Models........................ 8 
2.3.1 Digital Elevation Models ............................................................. 9 
2.3.2 Triangulated Irregular Networks................................................ 11 
2.4 Lumped Versus Distributed Models ................................................... 14 
2.5 Scale Dependency of Hydrologic Parameters..................................... 15 
2.6 Modeling Urban Areas and Future Conditions ................................... 24 
Chapter 3: Methodology........................................................................................ 26 
3.1 Introduction ......................................................................................... 26 
3.2 Case I:  Traditional Methods............................................................... 27 
3.2.1 The Planimeter ........................................................................... 28 
3.2.2 The Map Wheel.......................................................................... 33 
3.2.3 Parameter Extraction .................................................................. 34 
3.3 Case II:  On-Screen  Digitizing of Raster Graphic Maps.................... 34 
3.3.1 Digitizing in ArcView GIS 3.2 .................................................. 37 
3.3.2 Parameter Extraction.................................................................. 39 
 iii
3.4 Case III:  Automated Methods using a DEM...................................... 40 
3.4.1 Overview of Automated Methods using a DEM........................ 41 
3.4.2 ArcView GIS 3.2........................................................................ 45 
3.4.2.1 CRWR-PrePro............................................................. 46 
3.4.2.2 Parameter Extraction using ArcGIS and CRWR-
PrePro................................................................................ 49 
3.4.3 Watershed Modeling System (WMS) ........................................ 51 
3.4.3.1 TOPAZ ........................................................................ 54 
3.4.3.2 Parameter Extraction................................................... 55 
3.5   Case IV:  Automated Methods using a TIN........................................ 57 
3.5.1 TIN Development and Processing.............................................. 58 
3.5.2 TIN Parameter Extraction .......................................................... 60 
Chapter 4: Application .......................................................................................... 61 
4.1 Site Selection....................................................................................... 61 
4.2 Case I:  Traditional Methods............................................................... 64 
4.3 Case II:  Automated Methods by Digitizing ....................................... 67 
4.4 Case III:  Automated Methods Using a DEM ..................................... 70 
4.4.1 ArcView GIS 3.2 and CRWR-PrePro ........................................ 71 
4.4.1.1 10 Meter DEM ............................................................ 75 
4.4.1.2 30 Meter DEM ............................................................ 76 
4.4.2 Automated Methods Using WMS .............................................. 78 
4.4.2.1 10 Meter DEM ............................................................ 78 
4.4.2.2 30 Meter DEM ............................................................ 81 
4.5 Case IV: Automated Methods Using a TIN........................................ 84 
Chapter 5: Results ................................................................................................. 89 
5.1. Case Study Parameter Results Summary ............................................ 89 
5.2 Elasticity Analysis............................................................................... 95 
5.2.1 Step 1:  Sensitivity of SCS Lag Time to Parameter Variations . 98 
5.2.1.1 Longest Flow Path....................................................... 99 
 iv
5.2.1.2 Slope.......................................................................... 102 
5.2.1.3 Curve Number........................................................... 103 
5.2.1.4  Step 1 Results........................................................... 105 
5.2.2 Step 2:  Sensitivity of Flow to Variations in Lag Time ........... 106 
5.2.2.1 HEC-1 Model ............................................................ 108 
5.2.2.2 Lag Time Variation ................................................... 112 
5.2.2.3 Drainage Area Variation ........................................... 115 
5.2.2.4 Step 2 Results ............................................................ 118 
5.2.3 Results from Elasticity Analysis .............................................. 119 
Chapter 6: Conclusions and Recommendations.................................................. 124 
6.1 Errors Sources Among Parameter Extraction Methods .................... 125 
6.1.1 Parameter Extraction using Paper Maps .................................. 125 
6.1.2 On-Screen Digitizing of Raster Graphic Maps ........................ 126 
6.1.3 Parameter Extraction Using Automated Methods.................... 127 
6.1.4 Parameter Extraction Using TINs ............................................ 128 
6.2 Errors Among Extracted Hydrologic Parameters.............................. 129 
6.2.1 Drainage Area .......................................................................... 129 
6.2.2 Slope......................................................................................... 129 
6.2.3 Longest Flow Path.................................................................... 130 
6.2.4 Perimeter .................................................................................. 130 
6.2.5 Curve Number.......................................................................... 130 
6.3 Significance of Errors........................................................................ 131 
6.4 Additional Sources of Error .............................................................. 134 
6.5 Recommendations ............................................................................. 135 
Appendix A:  Online Internet Resources ............................................................ 137 
Appendix B:  Unmodified HEC-1 Model ........................................................... 138 
Appendix C:  Modified HEC-1 Model in HEC-HMS......................................... 141 
Bibliography........................................................................................................ 150 
 v
List of Tables 
Table 4.1:  Hand Delineation Results.................................................................... 66 
Table 4.2:  On-Screen Digitizing Results.............................................................. 70 
Table 4.3:  10 Meter DEM Watershed Data.......................................................... 75 
Table 4.4:  10 Meter DEM in ArcView Results.................................................... 76 
Table 4.5:  30 Meter DEM Watershed Data.......................................................... 77 
Table 4.6:  30 Meter DEM in ArcView Results.................................................... 78 
Table 4.7:  10 Meter DEM in WMS Results......................................................... 81 
Table 4.8:  30Meter DEM in WMS Results.......................................................... 83 
Table 4.9:  TIN Results ......................................................................................... 88 
Table 5.1:  Area 1 Results ..................................................................................... 90 
Table 5.2:  Area 2 Results ..................................................................................... 91 
Table 5.3:  Area 3 Results ..................................................................................... 91 
Table 5.4:  Curve Number Values......................................................................... 95 
Table 5.5:  Parameter Base Values........................................................................ 99 
Table 5.6:  Longest Flow Path Calculations ....................................................... 100 
Table 5.7:  Slope Calculations............................................................................. 102 
Table 5.8:  Curve Number Measurements .......................................................... 104 
Table 5.9:  Curve Number Calculations.............................................................. 104 
Table 5.10:  Results from Analytical Calculations ............................................. 106 
Table 5.11:  HEC-1 Modifications...................................................................... 110 
Table 5.12:  TxDOT IDF (Intensity-Duration-Frequency) Curves..................... 112 
Table 5.13: HEC-1 Lag Input.............................................................................. 113 
 vi
Table 5.14:  Discharge Variations Due to Lag Variations .................................. 114 
Table 5.15:  Discharge Elasticity Due to Parameter Variation ........................... 115 
Table 5.16:  HEC-1 Area Input ........................................................................... 116 
Table 5.17:  Area Variation................................................................................. 117 
Table 5.18:  Discharge Elasticity due to Area Variations ................................... 118 
Table 5.19:  Parameter Coefficients of Variation (CV) ...................................... 122 
Table 5.20:  Discharge Variations for Area 3 ..................................................... 122 
Table 6.1:  Elasticity Analysis............................................................................. 132 
 vii
List of Figures 
Figure 1.1:  Lag Time Results (Anderson, 2000).................................................... 4 
Figure 2.1:  DEM Grid Cells................................................................................... 9 
Figure 2.2:  30 Meter DEM................................................................................... 10 
Figure 2.3:  TIN Up-Close .................................................................................... 11 
Figure 2.4:  Channel Representation with a TIN .................................................. 12 
Figure 2.5:  Frequency Distribution of Subcatchment Length (Garbrecht et al., 
1999b)............................................................................................... 20 
Figure 2.6:  Frequency Distribution of Subcatchment Slope  (Garbrecht et. al., 
1999b)............................................................................................... 23 
Figure 3.1:  Watershed Parameters ....................................................................... 27 
Figure 3.2:  Planimeter .......................................................................................... 29 
Figure 3.3:  Tracing Arm Movement (Kunkle, 2001)........................................... 30 
Figure 3.4:  Area Calculation (Kunkle, 2001)....................................................... 31 
Figure 3.5:  Final Area Calculation (Kunkle, 2001) ............................................. 33 
Figure 3.6:  Map Wheel......................................................................................... 34 
Figure 3.7:  USGS Digital Raster Graphic (DRG)................................................ 36 
Figure 3.8:  On-Screen Digitizing from a Raster Graphic Map ............................ 37 
Figure 3.9:  New Theme Creation in ArcView ..................................................... 38 
Figure 3.10:  Map-Based Model in ArcView........................................................ 40 
Figure 3.11:  8-Direction Pour Point Model (Anderson, 2000) ............................ 42 
Figure 3.12:  The D-? Model (Tarboton, 1997) ................................................... 43 
Figure 3.13:  30 Meter Delineated DEM............................................................... 45 
 viii
Figure 3.14:  The CRWR-PrePro Menu Bar ......................................................... 47 
Figure 3.15:  WMS Drainage Toolbar .................................................................. 52 
Figure 3.16:  WMS Module .................................................................................. 53 
Figure 3.17:  TOPAZ Grids................................................................................... 55 
Figure 3.18:  Display Options in WMS................................................................. 56 
Figure 3.19:  WMS Calculators............................................................................. 57 
Figure 3.20:  WMS TIN Module........................................................................... 58 
Figure 3.21:  Vertex Options in WMS .................................................................. 59 
Figure 4.1:  Location of Travis County, Texas ..................................................... 62 
Figure 4.2:  Location of Buttermilk and Little Walnut in Travis County ............. 63 
Figure 4.3:  Area 1, Area 2, and Area 3 ................................................................ 64 
Figure 4.4:  Hand Delineation of Area 2............................................................... 65 
Figure 4.5:  Area 1 Digitized................................................................................. 68 
Figure 4.6:  Area 2 Digitized................................................................................. 69 
Figure 4.7:  Area 3 Digitized................................................................................. 69 
Figure 4.8:  Land Use/Land Cover (LULC) Data ................................................. 73 
Figure 4.9:  STATSGO Data................................................................................. 74 
Figure 4.10:  Delineated DEM Study Area ........................................................... 77 
Figure 4.11:  Area 1 Delineated in WMS.............................................................. 79 
Figure 4.12: Area 2 Delineated with WMS........................................................... 80 
Figure 4.13: Area 3 Delineated with WMS........................................................... 80 
Figure 4.14:  Area 1 Delineated with WMS.......................................................... 82 
Figure 4.15:  Area 2 Delineated with WMS.......................................................... 82 
 ix
Figure 4.16:  Area 3 Delineated with WMS.......................................................... 83 
Figure 4.17:  TIN Development in WMS ............................................................. 85 
Figure 4.18:  Points, Breaklines, and Bounding Polygon in WMS....................... 86 
Figure 4.19:  Interpolated TIN for Area 2............................................................. 87 
Figure 4.20:  Area 2 TIN Delineated..................................................................... 88 
Figure 5.1:  Three Study Areas ............................................................................. 89 
Figure 5.2:  Coefficients of Variation ................................................................... 94 
Figure 5.3:  Concept of Elasticity.......................................................................... 96 
Figure 5.4:  Discharge Sensitivity Calculation...................................................... 97 
Figure 5.5:  Step 1 in Calculating the Discharge Sensitivity ................................ 98 
Figure 5.6:  Analytical Calculation of Gradients ................................................ 101 
Figure 5.7:  Slope Gradient Calculation.............................................................. 103 
Figure 5.8:  Curve Number Gradient Calculation............................................... 105 
Figure 5.9:  Step 2 in Calculating the Discharge Sensitivity .............................. 107 
Figure 5.10:  HEC-1 Study Area......................................................................... 108 
Figure 5.11:  Unmodified HEC-1 model (displayed in HEC-HMS)................... 109 
Figure 5.12:  Modified HEC-1 Model (displayed in HEC-HMS)....................... 111 
Figure 5.13:  Discharge Results for Lag Variations............................................ 114 
Figure 5.14:  Discharge Results for Drainage Area Variations........................... 117 
Figure 5.15:  Final Discharge Sensitivity Calculation ........................................ 119 
Figure 5.16:  Elasticity Diagram ......................................................................... 120 
Figure 5.17:  Elasticity Results ........................................................................... 121 
  
 
 x
Chapter 1: Introduction 
Hydrology, as defined by the 2001 Texas Department of Transportation 
(TxDOT) Hydraulic Design Manual, ?deals with estimating flood magnitudes as 
the result of precipitation.?  Estimating the magnitude of an extreme flood event is 
essential in the design of highway drainage facilities such as culverts, bridges, 
storm drain systems, and detention storage facilities.  The time-dependent 
determination of the quantity of water expected to be conveyed by each structure 
is used as a guide when designing the structure so that peak flows associated with 
an extreme flooding event do not cause flooding in areas adjacent to the structure 
and the road.  With proper design of these facilities, damages resulting from an 
extreme flood event are minimized.   
The principal factors affecting flood magnitudes in a watershed include 
runoff (influenced by precipitation and abstractions), watershed area information 
(slope, longest flow path, area), land use, and soil type.  Detention storage 
systems, flow diversions, channelization, and impervious cover from urban 
development also influence the magnitude of an extreme flood event.  Currently, 
TxDOT relies heavily on manual techniques to locate drainage divides and to 
estimate hydrologic parameters such as flow path length, watershed area, slope, 
and abstrations. These parameters are necessary in determining the peak discharge 
at an area outlet, although many runoff estimation techniques assume the size of 
the contributing watershed and the watershed slope as the principal variables. 
 
 1
1.1 BACKGROUND OF GIS USE IN WATER RESOURCES APPLICATIONS 
Recently, the use of automated methods in water resources engineering 
applications has proven to be a viable alternative to more traditional hand 
calculation methods for many engineering agencies.  The Texas Department of 
Transportation (TxDOT) is one of many agencies interested in using automated 
methods to aid in the hydrologic parameter development required for highway 
drainage facility design.   
As a large portion of the cost associated with highway projects is 
attributed to the design and construction of drainage facilities, research has been 
dedicated to exploring a more economical and time efficient means of design.  
Geographic Information Systems (GIS) are a means of simplifying this process in 
that a GIS is capable of computing spatially derived hydrologic parameters such 
as watershed area, SCS curve number (for runoff and lag time computation), 
gridded precipitation, flow length, and slope for each watershed in a relatively 
short time. 
 
1.2 PROJECT HISTORY 
This implementation project follows an investigation conducted by 
Anderson (2000) for the Texas Department of Transportation (TxDOT). Anderson 
implemented GIS-based tools developed by CRWR at two sites in Texas: 
Castleman Creek (McClennan County, TX) and Pecan Bayou (Brown County, 
TX).  The methodology used in Anderson?s investigation utilized tools for 
hydrologic analysis and parameter extraction (CRWR-PrePro), terrain data 
 2
development and floodplain delineation (CRWR-FloodMap and HEC-GeoRAS), 
and lumped parameter hydrologic modeling and steady flow hydraulic analysis 
(HEC-HMS and HEC-RAS).  Anderson?s investigation was a first attempt for 
TxDOT at automating this entire process and for representing the spatial 
variability of the watershed characteristics, integrating hydrologic and hydraulic 
modeling processes with GIS, and displaying an accurate floodplain map of the 
project site.   
 
1.3  OBJECTIVES 
The initial scope of the author?s project was to implement a study in a 
different area of Texas and apply the same methodology as Anderson (2000).  
However, after Anderson?s study was completed TxDOT noted that the watershed 
lag time values calculated using CRWR-PrePro for input into HEC-HMS for the 
Castleman Creek (in McLennan County, Texas) watershed were over four times 
greater than the values calculated previously for a TxDOT hydrologic model of 
the area.  At this point it became evident that some assumptions used in 
Anderson?s automated hydrologic study need to be further investigated.  Figure 
1.1 gives an example of the large differences calculated by Anderson (2000) using 
automated methods and TxDOT using traditional, paper map-based methods. 
 
 3
 
Figure 1.1:  Lag Time Results (Anderson, 2000) 
Discussions with the TxDOT project supervisor, David Stolpa, in March 
2001 pertaining to the use of methods for hydrologic modeling led to other 
uncertainties and doubts about the automated process.  Questions arose regarding 
scale effects of digital elevation models; as well as mechanical processes behind 
calculating slope, area, and longest flow path for a watershed. This uncertainty in 
the parameter values led TxDOT to question how variations in hydrologic 
parameters would ultimately affect watershed lag time values and discharge. 
 Following these conversations, the scope of the research project was 
redefined to explore the variation in lag time and discharge resulting from paper 
map and automated methods of calculating hydrologic parameters.  In order to 
evaluate parameter uncertainty, four levels of extracting hydrologic parameters 
are explored:  (1) measurement from paper maps; (2) on-screen extraction from 
raster maps; (3) using GIS and two different resolutions of grid-based digital 
elevation models (DEMs); and (4) using a triangulated irregular network (TIN).    
This report attempts to quantify the errors associated from parameter 
variation in a two-step process.  The first step is to quantify the error in lag time 
 4
(using the SCS lag equation) based on hydrologic parameter variation. Secondly, 
a HEC-1 model supplied by TxDOT is modified to quantify the error of discharge 
based on lag time and drainage area variations.   
Although the drainage areas under investigation are urbanized, the scope 
of this project does not fully take into account small-scale man-made structures 
such as street gutters, inlets, and drainage ditches and culverts that control surface 
drainage patterns. 
 
1.4 ORGANIZATION 
This implementation project is divided into five principal parts.  Chapter 2 
explores previous work that has been conducted in the issue of scale dependency 
of some hydrologic parameters.  Chapter 3 provides a general overview of the 
steps taken in the four case studies, while Chapter 4 gives a step-by-step account 
of the hydrologic parameter computation process for each of the four case studies.  
Chapter 5 analyzes the results using the concept of elasticity to determine the 
overall effect of parameter variation on the discharge.  The final chapter, Chapter 
6, discusses the findings from this implementation project.  
 
 5
Chapter 2: Literature Review 
2.1 INTRODUCTION 
From 1996 to 1999, the Center for Research in Water Resources (CRWR) 
at the University of Texas at Austin developed hydrologic modeling tools for the 
purpose of floodplain delineation at highway river crossings for TxDOT (Olivera 
et al., 1999). 
From 1999 to 2000, TxDOT funded CRWR to implement these tools and 
to investigate the possibility of combining existing GIS tools, lumped parameter 
hydrologic and one-dimensional hydraulic models, and the visual display 
capabilities of GIS to overcome the historical limitations of floodplain mapping.  
Anderson (2000) implemented these tools at two existing TxDOT drainage 
structures.  Apart from evaluating the feasibility of implementing the tools 
developed at CRWR, Anderson (2000) set out to determine if existing digital data 
are sufficient to produce an accurate representation of the floodplain. 
Since the work of Anderson (2000), many issues have arisen regarding the 
work of GIS in water resources.  This chapter reviews some of these problems 
and work that has been conducted in this area. 
 
2.2 SUMMARY OF CURRENT HYDROLOGIC PRACTICES OF TXDOT 
Currently TxDOT relies heavily on manual methods of watershed 
parameter extraction.  Measurements are taken by hand from paper maps and then 
watershed parameters are entered into a hydrologic model. 
 6
Hydrologic modeling practices used by TxDOT are outlined in the 2001 
TxDOT Hydraulic Design Manual.   Methods used by TxDOT primarily include 
unit hydrographs, the Rational Method, statistical analysis of stream flow data, 
and regional regression equations.  
The NRCS (National Resource Conservation Service) dimensionless unit 
hydrograph along with the NRCS Runoff Curve Number Method (also known as 
the SCS curve number method) is the primary unit hydrograph technique used by 
TxDOT.  The unit hydrograph, a method for estimating storm runoff, was first 
proposed by L. K. Sherman in 1932. The unit hydrograph is defined as the 
watershed response to a unit depth of excess rainfall uniformly distributed over 
the entire watershed and applied at a constant rate for a given period of time 
(Chow et al., 1988). 
Unit hydrograph techniques consider the time distribution of rainfall, the 
initial rainfall losses, and an infiltration rate that decreases during the course of 
the storm.  Variables include the drainage area, time of concentration, curve 
number (if the SCS curve number method is used), rainfall distribution, and total 
design rainfall.  Equations to calculate the time of concentration can also consider 
watershed parameters such as watershed length and slope.  Popular unit 
hydrograph application programs used by TxDOT have included the TR20 (and 
its TR55 variant) and HEC-1.  TxDOT is now moving towards the use of HEC-
HMS.  (Stolpa, 2002) 
The Rational Method is very simple, and is best suited for small urban and 
rural watersheds.  The statistical analysis of stream gauge data method is applied 
 7
when long records (greater than 25 years) are available.  Statistical analysis 
provides peak discharge estimates using annual peak stream flow data. Regional 
regression equations based on the hydrologic parameters area and slope, are 
commonly used for calculating flows at ungauged sites.  These equations were 
developed by the USGS in 1993 to estimate the magnitude and frequency of 
floods at ungauged sites in six separate regions in Texas (Jennings et al., 1993).  
 
2.3 EXTRACTING WATERSHED PARAMETERS FROM DIGITAL MODELS 
Over the last twenty years, digital representations of topographic 
information have become increasingly available in the form of digital terrain 
models (DTMs).  Using computers and extracting watershed data from digital 
terrain models is faster, and provides more reproducible measurements than 
traditional manual techniques using topographic maps (Garbrecht et al., 1999a).   
GIS uses a DTM to describe the spatially distributed attributes of the 
terrain that are classified as topologic and topographic data.  The topography of an 
area describes its elevation and land surface shape, while also important are the 
spatial distribution of terrain attributes other than elevation such as the land cover, 
soil type, and connectivity of the features.  A DTM may be used to represent both 
topographic and/or physiographic features in the format of raster or grid data, 
triangulated irregular network (TIN) data or vector (point, line, and polygon) data  
(Olivera et al., 2000). 
Using automated methods a surface may be analyzed so that drainage 
basin boundaries are defined, stream networks created, and drainage basin data 
 8
computed in a relatively quick time. Once the drainage basin data have been 
computed, geometric modeling parameters can be extracted automatically and 
entered into a hydrologic model  (Nelson et al., 1997).   
 
2.3.1 Digital Elevation Models 
Digital terrain models are commonly found as grids, referred to in this 
document as digital elevation models or DEMs (in other documents DEM data 
includes TIN data).  DEMs are composed of identical square cells arranged in 
rows and columns, each with a unique value to represent the terrain elevation at 
that point, as shown in Figure 2.1. 
 
 
Figure 2.1:  DEM Grid Cells 
 9
DEMs are provided at 1 km grid cell size for the entire world and 30 meter 
cell sizes for the entire United States.  Figure 2.2 shows an example of a 30 meter 
DEM terrain representation in Austin, Texas. 
 
 
Figure 2.2:  30 Meter DEM 
DEMs are used in water resources engineering to identify drainage related 
features such as ridges, valley bottoms, channel networks, and surface drainage 
patterns.  DEMs are also useful in quantifying subcatchment and channel size, 
length, and slope.  The accuracy of this topographic information is a function of 
the quality and resolution of the DEM, in addition to the DEM processing 
algorithms used to extract this information (Garbrecht et al., 1999). 
One solution to reduce the errors associated with DEMs, as described by 
Garbrecht et al. (1999a), is to use a high resolution DEM produced by more 
 10
advanced methods or to customize a DEM.  Another factor affecting accuracy is 
whether the data are integer or floating points. When data are integers, less 
memory is required than when data are floating points; however floating point 
data are more accurate (Olivera et al., 1999).  For this reason quality and 
resolution must be considered when selecting a DEM for hydrologic modeling so 
that both are consistent with the scale of the model and the objectives of the study 
being made (Garbrecht et al., 1999a). 
 
2.3.2 Triangulated Irregular Networks 
Another form of digital data is the triangulated irregular network or TIN.  
TINs, however, are currently not as widely used as grid DEMs, but may be used 
to serve the same purpose.  TINs consist of a set of representative irregularly 
distributed points connected by straight lines to produce triangles, as shown in 
Figure 2.3. 
 
 
Figure 2.3:  TIN Up-Close 
 11
Figure 2.4 shows the ability of a TIN to conform to complex terrain and 
identify channel features. 
 
 
Figure 2.4:  Channel Representation with a TIN 
Delauney triangulation, based on the concept of maximizing the minimum 
angle of all triangles produced by connector lines to their nearest neighbor points,  
is most often used to generate TINs.  Breaklines are used to control the 
smoothness and continuity of the surface such as streamlines or roads by forcing 
triangles to conform to these lines.  For this reason, TINs are generally used for 
surface representation of stream channels in hydraulic modeling since complex 
land surface details may accurately be represented (Lee et al., 1980). 
 12
TINs have the advantage compared to grid-based elevation models in that 
they require less memory than grids. In addition, linear features are more 
accurately represented with TINs than with DEMs. When using grids to model 
channels and other linear features, edges must be always oriented along the 
horizontal, vertical, or diagonal directions.  TINs eliminate this data redundancy 
and are thus better suited for modeling streams and other linear features.  TINs 
can be constructed so that triangle edges conform to features and are not restricted 
to lie in the horizontal, vertical, and diagonal directions.  The TIN data structure is 
also often more efficient because the terrain model can be adapted readily to the 
surface being modeled.  In areas where the terrain is flat, only few a points need 
to be utilized (Nelson et al., 1999). 
Grid-based watershed modeling is advantageous over TIN-based 
watershed delineation in that grids have a simpler data structure than TINS, grid-
based data is very abundant, and grid-based models are reproducible. Other 
disadvantages of TINs result when inserting breaklines.  Inserting breaklines may 
result in small or long thin triangles which, in turn, will cause difficulties in 
numerical round off or tolerance problems.  TINs have the major disadvantage in 
that large TINs are difficult to work with, and editing pits and flat triangles can be 
a very time consuming process, especially when areas are large.  Lastly, 
determining an appropriate resolution for a TIN can be a difficult task (Nelson et 
al., 1999a). 
TIN-based watershed delineation is based on the process of tracing a flow 
across triangle surfaces.  Because each triangle has a flat surface, the mathematics 
 13
behind determining the path of maximum downward gradient is straightforward 
as described by Jones et al. (1990). Watershed boundaries are delineated with 
TINS by identifying outlet locations.  Once outlets have been selected, flow paths 
are traced along the path of steepest descent and by combining together triangles 
whose flow paths pass through a common outlet point.   
 
2.4 LUMPED VERSUS DISTRIBUTED MODELS 
Creating an accurate hydrologic model of an area is a difficult task.  As 
most hydrologic systems are spatially variable, distributed models may be 
required to fully describe the system.  Distributed models require that calculations 
be made on a point-to-point basis within the model, and that flow be calculated as 
a function of time and space throughout the system.  Lumped models on the other 
hand provide a unique representative value for the entire subcatchment.  In a 
lumped model, flow is calculated as a function of time alone  (Nelson et al., 
1997). 
Olivera et al. (1999) discuss how there have been attempts to account for 
spatially distributed terrain attributes based on lumped models, as the boundary 
between lumped models and distributed models is not clearly defined.  For 
example, models such as HEC-1, developed by the US Army Corps of Engineers, 
are neither purely lumped nor purely distributed.  HEC-1 may be used to partition 
the hydrologic system into subsystems and to apply lumped models to each of the 
subsystems.  HEC-1 then routes the responses from each subbasin to the 
watershed outlet.   
 14
Nelson et al. (1997) suggest that although distributed models are the focus 
of current research, lumped models are still more common and preferred because 
regulatory agencies have not accepted distributed models due to the effort 
involved in calibrating and verifying them.   Models known as data reduction 
(DR) models are one way of converting distributed properties of an area, such as 
slope and subcatchment length, into lumped parameters by reducing distributed 
properties into a representative value for each subcatchment (Garbrecht et al., 
1999a).  GIS is a tool that allows the user to jump from strictly lumped models to 
more spatially distributed models, in that a GIS may be used to generate input 
files for lumped models based on a distributed interpretation of the terrain  
(Nelson et al., 1997).   
If the rainfall-runoff response of a watershed is linear, a unit hydrograph 
can be used to relate rainfall to runoff.  Most lumped models are based on either 
synthetic or derived unit hydrographs.  Once a unit hydrograph is determined for a 
watershed, then one can determine the flood hydrograph resulting from any 
measured or design rainfall.  For both traditional and automated processes, the 
unit hydrograph method is commonly used to model rainfall-runoff processes.  
Since the systems are linear, the overall response time can be calculated as the 
sum of the sub-area responses (Nelson et al., 1997).   
 
2.5 SCALE DEPENDENCY OF HYDROLOGIC PARAMETERS 
Although using DEMs provides for quick analysis, there are several 
disadvantages to using DEMs, which include the effect of grid size on some 
 15
certain computed topographic parameters (such as longest flow path), and the 
inability to adjust the grid size to the dimensions of topographic land surface 
features  (Garbrecht et al., 1999). 
 Miller et al. (1999) explored the effects of spatial resolution and accuracy 
of DEMs on hydrologic characterization using GIS.  The study analyzed the area, 
slope, drainage density, and surface variation for watersheds ranging in size from 
0.0016 km
2
 to 146 km
2
, using 2.5, 10. 30, and 40 meter DEMs.  Miller et al. 
(1999) noted an overall reduction in slope with increasing cell size.  In Miller?s 
study, both the mean and standard deviation of watershed slopes are highest for 
IFSAR DEMs (highest resolution DEMs).  A reduction in slope standard 
deviation implies that much of the natural surface has been simplified to a more 
continuous smooth surface (Miller et al., 1999).  
Another observation drawn by Miller et al. (1999) is that the high 
resolution DEMs create more tortuous flow paths, more complex routing, and 
longer drainage networks.  Total drainage lengths were found to be considerably 
different among four DEMs of different cell sizes on smaller watersheds as 
described by the drainage density (length/area).  Mean drainage density is higher 
for watersheds and channels created with high resolution DEMs than for other 
surfaces (0.0104 m for the 2.5 m IFSAR DEM as compared to 0.0085 m for the 
40 m DEM).  
Miller et al. (1999) found that the high resolution IFSAR DEM provided 
significantly different results at small scales when compared to other surfaces, 
while the differences among DEMs at larger scales were reduced.  The final 
 16
conclusion from this study was that the suitability of various digital elevation data 
is primarily a function of the research objectives and scale of application (Miller 
et al., 1999). 
In a study conducted by Garbrecht et al. (1994), the accuracy of drainage 
features extracted from DEMs as a function of DEM resolution is evaluated.  The 
horizontal resolution of a DEM with an original grid spacing of 30 meters is 
decreased by cell aggregation.  Selected drainage features for several hypothetical 
channel network configurations were extracted for a range of DEM resolutions 
using TOPAZ software. 
The study by Garbrecht et al. (1994) concluded that the dependency of 
physical characteristics on grid resolution ?was introduced by the inability of a 
DEM to accurately reproduce drainage features that are at the same scale as the 
spatial resolution of the DEM.?  In other words, the number of channels, the size 
of the drainage area, and the channel network pattern from a low resolution DEM 
may depart considerably from the one obtained by a high resolution DEM.  For 
sinuous channels, the use of a low resolution DEM results in shorter channel 
lengths. For networks with a high drainage density, the use of a low resolution 
DEM leads to channel and drainage area capturing, This being the point at which 
the DEM resolution can no longer resolve the separation between channels or 
drainage boundaries.  If small drainage features are important, then resolution 
must be selected relative to the size of these features (Garbrecht et al., 1994). 
Garbrecht et al. (1999b) discuss the extraction of drainage properties from 
DEMs.  This study compares methods of extracting length and slope values using 
 17
both automated and traditional methods from 177 subcatchments located in the 
USDA-ARS Walnut Gulch Experimental Watershed in Tombstone, Arizona. 
For the manual method in Garbrecht?s study, length is measured 
subjectively as the distance between the upslope subcatchment drainage boundary 
and downslope channel.  Slope is calculated as a lumped parameter by converting 
variable slope into a straight-line profile (Gray?s method) while maintaining the 
horizontal distance and area under the profile.  For the automated methods, DEMs 
were processed using the TOPAZ software, producing 183 subcatchments. Length 
and slope values were extracted using data reduction (DR) models. (Garbrecht et 
al., 1999b) 
Subcatchment length is important in hydrologic modeling applications 
because it is used to estimate runoff travel distance or flow routing distance.  
Garbrecht et al. (1999b) describe two methods for calculating this length using 
data reduction (DR) models.  One method is the average travel distance, and the 
other is the average flow path length, or the distance of overland flow within a 
subcatchment.   
The average travel distance traveled by surface runoff is calculated as the 
average distance from every point in the subcatchment to the first downstream 
channel that the flow reaches at this point, or the arithmetic mean of all travel 
distances within a subcatchment.  For subcatchments that are rectangular in shape 
the average travel distance is about half the subcatchment length, and twice the 
average travel distance corresponds to length from the drainage divide at the 
upstream boundary to the downstream channel, as can be seen in Equation 2.1. 
 18
?
?
=
=
=
s
s
n
i
i
n
i
ii
t
k
kD
L
1
1
       Equation 2.1 
L
t
 is the average travel distance, n
s
 is the total number of cells in the 
subcatchment, D
i
 is the travel distance of cell i to the adjacent channel, and k
i
 is a 
weighting factor with a value of 1 for travel distances originating at subcatchment 
cells, and ? for travel distances originating at channel cells. The weighting factor 
accounts for the fact that channel cells contain a channel and the cell area is 
evenly split between the right and left subcatchments adjacent to the channel.  No 
adjustments are needed for subcatchment cells, so their weighting factor is 1  
(Garbrecht et al., 1999b). 
The second method, the average flow path length, shown in Equation 2.2, 
is different in that not all points in the subcatchment are considered in the length 
calculations.  The flow path in this method is considered as the distance from a 
divide to the first adjacent downstream channel.  Only the cells in the drainage 
divide are considered in this calculation. Drainage divides are not only located at 
the upstream boundary of the subcatchment, but also within the subcatchment as 
defined by local ridges in the topography.  For this reason the flow path length is 
generally shorter than the average travel distance method to the drainage divide. 
(Garbrecht et al., 1999b)  
 
?
=
=
i
n
i
f
i
i
f
l
n
L
1
1
   Equation 2.2 
 19
Under this method L
f
 is the average flow path length, n
i
 is the number of 
flow paths in the subcatchment, i is the flow path counter, and l
f 
the length of 
individual flow paths.  Figure 2.5 shows the results by Garbrecht et al. (1999b) for 
the 177 subcatchments, using manual and automated methods of length 
extraction.   
 
 
Figure 2.5:  Frequency Distribution of Subcatchment Length (Garbrecht et al., 
1999b) 
Figure 2.5 is an example of parameter value variations, in this case 
subcatchment length, that occur using different methods of parameter extraction 
(automated and manual) and different models for data reduction.  The distance to 
divide length is twice the average travel distance for rectangular-shaped 
subcatchments and 1.33 times the average travel distance for triangular-shaped 
subcatchments. The distance to divide and the manual method closely resemble 
each other since they represent the same length from the watershed boundary to 
 20
the downstream channel.  The travel distance consistently gives the smallest 
length value since the this method accounts for all the cells in the watershed       
(Garbrecht et al., 1999b). 
Moglen et al. (2001) show that DEMs at a 30 meter resolution are not 
sufficiently dense for analyzing flat areas; thus a higher resolution grid must be 
used regardless of the quality of the 30 meter grid.  Garbrecht et al. (1999a) note 
the reason that the lower resolution grid will not work is due to the fact that as 
some DEMs (with the exception of NED DEMs, as NED is in floating point 
meters) are reported in meters or feet, the computed slope can only take on a 
limited number of values. For example, a 30 meter DEM in meters could have a 
slope value of zero, or a multiple of 0.033 (for a 1 meter change in elevation). 
These increments may be suitable to model terrain in mountainous terrain with 
large slopes, but insufficient to provide accurate values in flat areas  (Garbrecht et 
al; 1999a). 
Subcatchment slope, similar to subcatchment length, is an important 
variable for runoff calculations.  Garbrecht et al. (1999b) present four DR 
methods of slope calculation.  These are the average terrain slope, the average 
travel distance slope, the average flow path slope, and the global slope. 
Equation 2.3 shows the calculation for average terrain slope is the average 
of the local slope value at every point in the subcatchment.     
 
?
=
=
s
n
i
t
i
s
t
s
n
S
1
1
  Equation 2.3 
 
 21
For the average terrain slope, S
t
 is the average terrain slope, n
s
 is the 
number of subcatchment cells, and s
t
i
 is the terrain slope at cell i  (Garbrecht et al., 
1999b). 
The average travel distance slope, Equation 2.4, is the average of the slope 
from each point in the subcatchment to the next adjacent downstream channel.   
 
?
=
=
s
n
i
c
i
s
c
s
n
S
1
1
  Equation 2.4 
 
S
c
 is the average travel distance slope, n
s
 is the number of cells in the 
subcatchment, and s
c
i 
is the slope of the travel distance that starts at cell i.    The 
travel distance slope of cell i is the mean of all the slopes along the travel distance 
between subcatchment i and the adjacent channel  (Garbrecht et al., 1999b). 
The average flow path slope, Equation 2.5, is the average slope of all the 
flow paths in the subcatchment, as defined as the route followed by the runoff 
starting at the divide and ending at the first adjacent downstream channel   
(Garbrecht et al., 1999b). 
 
?
=
=
f
n
i
f
i
f
f
s
n
S
1
1
 Equation 2.5 
 
S
f
 is the average flow path slope, n
f
 is the number of flow paths in the 
subcatchment, and s
f
i  
is the flow path slope of the flow path starting at cell i.  The 
 22
flow path slope, s
f
i
, is the mean of all slopes along the flow path between divide 
cell i and the adjacent channel (Garbrecht et al., 1999b). 
The global slope, Equation 2.6, is calculated as the average elevation of 
the subcatchment minus the average elevation of the receiving channel divided by 
the average travel distance (Garbrecht et al., 1999b). 
 
t
cs
g
L
EE
S
?
=   Equation 2.6 
S
g
 is the global slope for the subcatchment, E
s
 is the mean elevation of the 
subcatchment, and E
c
 is the mean elevation of the adjacent channel and L
t
 is the 
average travel distance of the subcatchment (Garbrecht et al., 1999b).  Figure 2.6 
shows the results from Garbrecht?s study in terms of slope.   
 
 
Figure 2.6:  Frequency Distribution of Subcatchment Slope  (Garbrecht et. al., 
1999b) 
 23
Figure 2.6 further demonstrates parameter variations among methods of 
parameter extraction.  The average travel distance-based slope method produces 
the smallest slope because it accounts for the flatter slopes in the lower part of the 
subcatchment area, thus emphasizing areas that are more subject to higher 
discharges.  The terrain slope method results in the steepest slope values as this 
method equally emphasizes each maximum local slope value at each cell.  The 
average flow path slope method is steeper than the average travel distance-based 
slope method because there are fewer divides in the lower part of the catchment.   
The global slope and manual methods resemble each other in that the models used 
to calculate these slope values are similar  (Garbrecht et al., 1999b). 
Garbrecht et al. (1999b) conclude that each method is equally valid, and 
the user should select a method that is most appropriate for the user?s application.  
For instance, if the user is most interested in calculating runoff, the average travel 
distance based slope method and the average flow path slope method are better 
suited for this calculation than the terrain slope method (Garbrecht et al., 1999b). 
 
2.6 MODELING URBAN AREAS AND FUTURE CONDITIONS 
Although digital data in the form of DEMs is readily available and easy to 
work with, it does not accurately describe terrain in urban areas.  Barrett (2000) 
suggests in larger areas, where it is not feasible to digitize these drainage systems, 
to delineate the watershed under undeveloped conditions.   The errors associated 
from water entering and leaving the watershed should cancel out, at least with 
larger areas.   
 24
In some cases the digital data in the form of DEMs must be edited to 
reduce the error that occurs from building and road features that are captured in 
the DEM.  Barrett (2000) used a 30 foot grid created from a TIN to help resolve 
the difference in elevation of roads and bridges from the surrounding terrain, as 
these features act as dams when performing flow accumulation. The initial grid 
was also edited manually to improve the stream representation by creating 
openings in the dams, roads and bridges.   
 25
Chapter 3: Methodology 
3.1 INTRODUCTION 
Case studies were conducted as a means to compare traditional methods of 
parameter calculation to automated methods of parameter calculation.  Case 
studies were conducted on each of the four levels of current model development.  
The first case study uses purely traditional methods on paper maps. The second 
level involves using a computer and ArcView GIS 3.2 to digitize the watershed 
boundaries and channels from scanned USGS quadrangle maps.  The third level 
involves using ArcView GIS 3.2 (with CRWR-PrePro) and WMS (Watershed 
Modeling System) to compute hydrologic parameters from two different 
resolution DEMs, a 10 meter DEM and a 30 meter DEM.  The purpose of using 
two different resolution DEMs is to quantify cell scale effects on channel length, 
watershed slope, and watershed area. The final method uses a triangulated 
irregular network (TIN) and the TIN processing capabilities of WMS.   
Figure 3.1 illustrates the watershed parameters that are the focus of this 
investigation. The longest flow path (LFP) is the longest length a drop of water 
will travel in the watershed.  The area of the watershed encompasses all the water 
that will flow to the watershed outlet, and the slope of the watershed is the 
difference in a representative watershed elevation divided by a representative 
watershed length.  Chapter 2 outlines several methods used to calculate slope, 
depending on the application.  The soil type and land use are used to derive a 
 26
curve number, which along with longest flow path and slope, is used to calculate 
the lag time of the watershed. 
 
 
Figure 3.1:  Watershed Parameters 
3.2 CASE I:  TRADITIONAL METHODS 
Traditional hydrologic modeling involves calculating watershed 
parameters based on a paper map.  Two instruments, a planimeter and a map 
wheel, aid in this process.    
Traditional methods of computing terrain-based hydrologic data involve 
delineating the watershed by hand using map contours as guidelines. This is a 
very time consuming process, as drainage divides may be hard to locate.  Pencil 
 27
lines are drawn perpendicular to contour lines to indicate drainage divides.  Once 
the perimeter of the watershed has been established, a planimeter is used to 
measure its area.  Perimeter and length of the longest flow path are measured 
using a map wheel.  Slope is calculated by taking the difference in elevation 
between map contours or from field survey data.   
 
3.2.1 The Planimeter 
A planimeter is an instrument used to trace around the perimeter of an 
object to determine its area.  Planimeters are useful tools in determining surface 
areas from maps and aerial photos. A planimeter mechanically integrates an area, 
and records this area as a tracing point moves along the boundary of the figure to 
be measured.  This number can be converted to an area by multiplying the 
planimeter reading by a constant called the planimeter constant.  This constant 
varies from planimeter to planimeter.   
A planimeter is composed of a graduated drum and disk, vernier, tracing 
arm and point, and anchor arm and point (anchored to table).  An elbow connects 
the tracing arm and anchor arm, and bends and slides freely.  Parallel to the 
elbow, which slides and bends freely, is a wheel with a scale (consisting of a disk, 
drum and vernier) that records how far the wheel has turned.  Figure 3.2 is a 
picture of the planimeter used in this study (Kunkle, 2001). 
 
 
 
 28
 
Figure 3.2:  Planimeter 
Calculating the planimeter constant involves plotting out a square and a 
circle of known areas, placing the anchor base outside of the area to be measured, 
and inserting the anchor arm into the drum assembly.  Once the planimeter 
reading is set to zero (or the initial reading is recorded), the perimeter is traced in 
a clockwise motion and the final readings from the disk, drum, and vernier 
recorded.  The disk reads whole numbers, the drum tenths and hundredths of a 
unit, and the vernier thousandths of a unit.  Three readings of each of the two 
areas should be taken.  Finally, the values derived from areas of the square and 
circle are averaged. 
 The planimeter reading from the average of circle and square value 
calculations is used to solve for the constant C= N/A.  The value N is the 
planimeter reading, A is the known area of the object and C is the planimeter 
constant.  Once the planimeter constant is determined, new areas may be 
 29
measured using the formula A= C*N.  For large areas, individual polygons should 
be solved separately (Knill, 2000). 
Kunkle (2001) describes the basic fundamentals behind this mathematical 
operation.  In Figure 3.3, the blue arm (AB) is the anchor arm. It is anchored to the 
table at Point A, located outside the object to be measured. Point B is the location 
of the measuring wheel (drum, disk and vernier).  The green arm (BC) is the 
tracing arm, and C is the tracing point.  The movement of the anchor arm is 
restricted to a circle.  As the tracing arm moves in a clockwise direction from C to 
C1, the area dw is measured. 
 
 
Figure 3.3:  Tracing Arm Movement (Kunkle, 2001) 
In Figure 3.4, point E divides the area dw into a trapezoid and a triangle to 
separate the components of the sliding and turning motion of the measurement 
wheel.  Area BCE represents the area covered while the tracing arm is pivoting. 
During this pivoting motion d? is the rotation of the arm.  Area EC?B?B is the area 
covered as the tracing arm slides, and dm is the change in the scale reading while 
 30
the arm is sliding.  Both d? and dm are arbitrarily small, and reflect the rotation of 
the scale in a plane perpendicular to the tracing arm. 
 
 
Figure 3.4:  Area Calculation (Kunkle, 2001) 
The area of the pentagon BCEC?B? can be expressed as the sum of area 
BCE and area EC?B?B as shown in Equation 3.1.  The area of BCE is that of a 
triangle, while area EC?B?B is that of a rectangle.  As mentioned earlier, k is the 
length of the tracing arm. 
 
()
kdmdkdw
BBECareaBCEareadw
BBCECareadw
+=
+=
=
?
2
2
1
)''()(
''
  Equation 3.1 
The region traced by the tracing arm is determined by integrating Equation 
3.1.  The formula for W, as shown in Equation 3.2, describes the area of the entire 
region EC?B?B. 
 31
 
??
?
+=
=
dmkdkW
dwW
?
2
2
1
   Equation 3.2 
Since the planimeter begins and ends in the same position, the net change 
in the angle d? is zero.  The net change in the scale reading is due only to the 
change in the scale reading.  Integration of dm over the entire circuit is M, the 
final reading in the scale as also shown in Equation 3.3. 
 
kMW
dmkW
d
=
=?
=
?
?
0?
     Equation 3.3 
 
In Figure 3.5, Kunkle (2001) shows how the final area is determined. 
When the arm is sliding backwards, the area covered is subtracted from the total 
area. The result is only the area crossed by the tracing arm, k.  
 
 
 32
 
Figure 3.5:  Final Area Calculation (Kunkle, 2001) 
3.2.2 The Map Wheel 
The map wheel, shown in Figure 3.6, is a simple device that measures 
length.  A map wheel is comprised of a wheel connected to a scale that measures 
the distance the wheel has traced. This measure is then multiplied by a factor to 
correct for the map scale.   
 
 
 33
 
Figure 3.6:  Map Wheel 
3.2.3 Parameter Extraction 
Using traditional methods, hydrologic parameters are extracted from paper 
maps.  Slope is manually calculated based on the difference in contour line 
elevations from the upper point of the longest flow path and from the outlet.  The 
difference in elevation is divided by the length of the longest flow path. Perimeter 
and longest flow path length are determined by using the map wheel, and area is 
calculated using the planimeter. 
 
3.3 CASE II:  ON-SCREEN  DIGITIZING OF RASTER GRAPHIC MAPS 
The process of on-screen digitizing of raster graphic maps is the next 
closest method to the traditional, paper map based methods of  using a map wheel 
and a planimeter. The methodology is analogous; with the exception that the 
 34
process of digitization involves using a computer-aided mouse to draw drainage 
divides on a scanned map and to trace along lines to determine their length. 
 Geospatial input to watershed models can be described with vector data.  
Points or nodes can be used to represent outlet points, arcs (polylines) can be used 
to represent streams, and enclosed polygons used to represent the watershed. This 
is usually done by digitizing the streams and an approximate boundary for a 
watershed with an image of the site in the background.   In this study a digital 
raster graphic, or DRG, is used as the basis for digitizing as shown in Figure 3.7. 
This is a scanned image of a USGS topographic map produced at a 1:24,000 
scale, obtained by the USGS (Appendix A).  DRGs are frequently used to edit and 
revise other digital data.  Once the USGS map is scanned, the digital image is 
georeferenced to the true ground coordinates and projected into the Universal 
Transverse Mercator (UTM) for projection consistency (USGS, 1999). 
 
 
 35
 
Figure 3.7:  USGS Digital Raster Graphic (DRG) 
Figure 3.8 shows watershed delineation using raster maps.  The arrows 
point in the direction of steepest slope, while the lines divide the drainage 
boundaries.  Arcs may also be used to define canals, railroads, streets, or other 
features that tend to act like streams during a rainfall/runoff event (Nelson et al., 
1997). 
 
 
 
 
 
 
 
 36
 
Figure 3.8:  On-Screen Digitizing from a Raster Graphic Map 
3.3.1 Digitizing in ArcView GIS 3.2 
The first step in digitizing is to create a new theme as selected from the 
ArcView menu, as shown in Figure 3.9. 
 
 
 
 37
 
Figure 3.9:  New Theme Creation in ArcView 
A polyline is used to represent the longest flow path.  Once the polyline is 
drawn (or polygon for area), ArcWorkstation is used to convert the new themes to 
coverages.  After the polylines and polygons are converted to coverages, they are 
processed using the ArcWorkstation commands build and clean.  Following this 
process the coverages are opened once again in ArcView GIS 3.2 and converted 
back to shapefiles.   
 
 38
3.3.2 Parameter Extraction 
Figure 3.10 shows an example of a map-based model along with its length, 
area, and perimeter attributes.  Information provided in the attribute tables for 
each shapefile give the length, area, and perimeter for each shape.  Slope, 
determined using the same method as with paper maps, is calculated by 
subtracting the contour value at the outlet from the contour value at the start of the 
longest flow path.   The difference in elevation is then divided by the length of the 
longest flow path. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 39
 
Figure 3.10:  Map-Based Model in ArcView 
3.4  CASE III:  AUTOMATED METHODS USING A DEM 
In Case III, hydrologic parameters are extracted from a grid-based digital 
elevation model (DEM) using both 10 meter and 30 meter DEM data.  Two 
different processes are used to extract hydrologic parameters from elevation data. 
The first method involves using ArcView GIS 3.2 and CRWR-PrePro, while the 
second method extracts hydrologic parameters using the Watershed Modeling 
System (WMS).  Both methods involve the same fundamental steps.  These 
include 1) a raster-based terrain analysis, 2) raster-based sub-basin and stream 
network delineation, and 3) vectorization of the sub-basins and stream segments.  
 40
3.4.1 Overview of Automated Methods using a DEM 
Topographic, topologic, and hydrologic information from digital spatial 
data can be extracted using a DEM and automated methods.  This section 
describes the fundamental steps that must be taken to process a DEM and 
accurately extract information.  
Errors in DEMs are usually classified as sinks (pits) or peaks.  Removing 
the pits is a standard operation when working with grid-based DEMs.  A peak is 
less detrimental to the calculation of flow direction and is usually ignored.  A 
DEM free of sinks is termed a depressionless DEM, and is the ideal input to 
calculate flow direction for watershed delineation.   
The 8-Direction Pour Point Model as shown below in Figure 3.11 
represents the direction water flows based on the neighboring cell with the lowest 
elevation.  This method is the most widely used raster DEM processing method. 
 
 
 
 
 
 41
 
Figure 3.11:  8-Direction Pour Point Model (Anderson, 2000) 
Most basin delineation techniques for grids are based around the 8-
Direction Pour Point Model concept.  However, the 8-Direction Pour Point Model 
has been criticized because it permits only one flow direction leaving a cell.  
Garbrecht et al. (1999a) note that this is satisfactory if being used for large 
drainage areas with well-defined channels, but the model may be less appropriate 
for overland flow analysis on hill slopes. A second method for determining flow 
direction is the D-? Model developed by Tarboton (1997).   Figure 3.12  below 
depicts this model. 
 42
 
Figure 3.12:  The D-? Model (Tarboton, 1997) 
The D-? Model assigns a flow direction based on steepest slope on a 
triangular facet (Tarboton, 1997).  The automated methods covered in this report 
do not use the D-? approach, and so this method of watershed delineation is not 
further investigated.   
Before computing filling pits and computing flow direction, the user may 
want to ?burn-in? streams.  This process raises the land surface cells off the 
stream cells by an arbitrary elevation so that streams delineated from the DEM 
match those produced in the National Hydrography Dataset (NHD) produced by 
the USGS.  This step is not necessary for high resolution DEMs (Olivera et al., 
1999). 
Once flow direction has been calculated, a flow accumulation grid is 
computed.  This is done by counting the number of contributing cells to each cell 
 43
in the grid.  Based on the flow accumulation grid, a raster-based stream network 
can be developed based on a user-defined cell threshold (Olivera et al., 2000).   
Threshold, a term used to describe the number of cells that drain to a 
point, also defines the number of cells that constitute the beginning of a stream.  
The selected threshold creates a drainage (stream) network based on all the cells 
with a catchment area greater than the threshold.  The choice of threshold is 
complicated. Two methods for determining a threshold are the constant area 
threshold method and the slope-dependent critical support area method.   
The constant threshold area method represents the change in sediment 
transport from sheet flow to concentrated flow, rather than a spatial transition in 
longitudinal slope profiles.  Using the slope-dependent critical support area 
method the drainage density is greater in steeper portions of the catchment, as 
found in natural landscapes (Tarboton et al., 1991).  The constant threshold area 
method is considered more practical in application than the slope-dependent 
critical support area method, and is the only method considered in this report.  In 
this study, both CRWR-PrePro and WMS use the constant threshold area method.  
(Garbrecht et al., 1999)  
Once the DEM has been processed by filling pits, flow direction and flow 
accumulation grids have been computed and a threshold chosen, the user may add 
streams and watershed outlets to the model.  The final step for DEM processing is 
to vectorize the streams and watersheds.  While a grid is convenient for the 
development of hydrologic data, it is inefficient for data storage.  This is because 
with a grid there is a one-to-many relationship for most basin parameters.  A more 
 44
convenient and efficient way to store both stream and basin data is through 
vectors and polygons (Nelson et al., 1997). 
Figure 3.13 below shows an example of a watershed delineated from a 
grid-based digital elevation model (DEM). 
 
 
Figure 3.13:  30 Meter Delineated DEM  
The following paragraphs describe this process using both ArcView GIS 
3.2 (with CRWR-PrePro) and WMS. 
 
3.4.2 ArcView GIS 3.2 
The Environmental Systems Research Institute, Inc. (ESRI) developed 
ArcView GIS 3.2.  This has now been replaced by ESRI?s ArcGIS software 
package. ArcView GIS 3.2 is still very widely used in the professional world, and 
is examined in this study for the reason that the Texas Department of 
 45
Transportation (TxDOT) has this software package, and also that the preprocessor 
under investigation, CRWR-PrePro, operates only with ArcView GIS 3.2.   
 
3.4.2.1 CRWR-PrePro 
CRWR-PrePro was developed by several investigators at CRWR.  It is the 
combination of several pieces of work developed by different researchers over a 
period of time.  The first person to work on CRWR-PrePro was Ferdi Hellwager 
(1997).  That same year, the Watershed Delineator ArcView extension was 
developed by Dean Djokic and Zichuan Ye of ESRI.  This work was followed by 
the Flood Flow Calculator ArcView GIS 3.2 extension in 1997 by CRWR to 
estimate flood peak flows according to regional regression equations using the 
spatial data extraction capabilities of GIS.  Combining these three ArcView 
extensions led to development of a hydrologic modeling tool that prepares an 
input file for the HEC-HMS basin component (Olivera et al., 1999).   CRWR-
PrePro, shown in Figure 3.14, is the predecessor to the more commonly used 
HEC-GeoHMS, as described in the forward of the HEC-HMS User?s Manual 
USACOE-HEC, (2000). 
 
 
 46
 
Figure 3.14:  The CRWR-PrePro Menu Bar 
CRWR-PrePro conducts a raster-based terrain analysis that includes 
burning-in streams, filling sinks, and calculating the flow direction (using the 8-
Direction Point Pour Method as described earlier) and flow accumulation grids. 
Following a raster-based terrain analysis (Fill Sinks, Flow Direction, and 
Flow Accumulation commands), a raster-based sub-basin and reach network 
analysis creates stream definition grids based on threshold (Stream Definition), 
stream segmentation grids (Stream Segmentation), an outlet grid (Outlets from 
Links), and delineated watershed grid (Sub-Watershed Delineation).  Finally sub-
basins and reach segments are vectorized (Vectorize Streams and Watersheds). 
 47
CRWR-PrePro calculates losses using the SCS curve number method or 
the initial plus constant loss method.   To calculate curve number, soils data must 
be obtained.  This may be done easily free of charge by downloading the data 
from the USDA-NRCS website (Appendix A).  Attribute tables that relate to the 
soils data include the mapunit.dbf and comp.dbf tables, which should be added to 
the working directory in ArcView.  The tables are modified and the CRWR-
PrePro function Soil Group Percentages may be executed. This creates a table 
called muidjoin.dbf.  Next Land Use/Land Cover (LULC) data must be obtained.  
Similar to the soils data, these data may be downloaded free of charge from the 
USGS website (Appendix A).  By combining the LULC data and the soils data, a 
curve number grid (CN) may be generated using the Curve Number Grid 
command in CRWR-PrePro.  An additional table that may be obtained off the 
CRWR-PrePro webpage, rcn.txt, is used as a look-up table to link curve number 
values to land use and soils data. Table wshpar.txt is necessary when the initial 
plus constant loss method is used (fields in table include Initial_Loss, 
Const_LossRate, and Wsh_Velocity).  The final CN for each sub-basin is 
calculated as the average of the curve number values within the sub-basin polygon 
(Olivera et al., 1999). 
Once the data are in vector format, hydrologic parameters of sub-basins 
and reaches such as reach length, reach routing method (Muskingum or lag), and 
either number of sub-reaches into which the reach is subdivided (for Muskingum 
routing), or the flow time (for pure lag) are computed.  The other reach 
parameters such as flow velocity and Muskingum X cannot be computed from 
 48
spatial data and must be supplied by the user.  The attributes are generated using 
the CRWR-PrePro command Calculate Attributes (Olivera et al., 1999). 
 
3.4.2.2 Parameter Extraction using ArcGIS and CRWR-PrePro 
CRWR-PrePro uses the SCS unit hydrograph method for sub-basin 
routing, and lag time may be calculated either with the SCS lagtime formula or 
length over velocity.  The SCS equation is most frequently used owing to the fact 
that all the parameters for this equation can easily be extracted using GIS.  The 
SCS Lag Time Equation (1972) is shown below in Equation 3.4.  In Equation 3.4 
TLAG is the lag time in hours, L is the length of the longest flow path in feet, S is 
the slope of the longest flow path, and CN is the average curve number in the sub-
basin.   
 
()[]
5.0
7.08.0
*67.31
9/1000
S
CNL
TLAG
?
=  Equation 3.4 
 
In the case of the length over velocity equation, flow velocities must be 
known for each cell in the subwatershed, and generally this is not readily known.  
As shown in Equation 3.5, TLAG is the lag time in hours, L the length of the 
longest flow path in feet, and v (m/s) is the representative velocity in the longest 
flow path.  As CRWR-PrePro only operates in metric units, all English units are 
converted into metric units. 
 
v
L
TLAG
*60
*3048.0
*6.0=   Equation 3.5 
 49
 
Once the watershed of interest has been clipped, the user is prompted to 
select a time step. The time step is the interval that determines the resolution of 
model 
 rate method, and lag time with only 
the SC
high slope 
of the 
results during a run in HEC-HMS.  Gauge data is linearly interpolated to 
the time interval, which may be chosen to range from 1 minute to 24 hours 
(USACOE-HEC, 2000).  The Muskingum and lag methods are used for flow 
routing in the reaches, depending on the travel time.  If the longest flow path 
(LFP) divided by the reach velocity is less than the time step the pure lag equation 
is used; otherwise Muskingum routing is used.  It is apparent that time step 
selection and velocity have a very large effect on the outcome and should be 
modified accordingly (Olivera et al., 1999). 
In addition to the fact that losses may only be calculated using the SCS 
curve number or the initial plus constant loss
S lagtime formula or length over velocity, another constraint of CRWR-
PrePro is the slope calculation.  CRWR-PrePro calculates slope based on the 
DEM cell elevations at 1% and 99% of the longest flow path divided by their 
distance along the longest flow path, and allows the user no flexibility in 
calculating watershed slope unless the user changes the Avenue code.   
The user may want to calculate the slope at 10% and 85% of the longest 
flow path, not 1% and 99% percent of this flow path.  In this way the 
shallow concentrated flow is not included in the calculations for lag time.  
CRWR-PrePro calculates the longest flow path of a sub-basin in the set of cells 
 50
for which the sum of the downstream flow length to the outlet plus the upstream 
flow length to the drainage divide is maximum (Olivera et al., 1999). 
Preparation of the HMS basin file (an ascii file readable by HEC-HMS) is 
the final step of CRWR-PrePro.  In order to do thi, transfer and parameter tables 
(wshpar.txt and streamp.txt as mentioned above) are needed and are posted on the 
CRWR-PrePro webpage (Appendix A).  All units must be in SI (Syst?me 
International d'unit?s)  (Olivera et al., 1999). In this study only the parameters 
curve number, slope, and longest flow path were extracted from the delineated 
watershed, and thus the HEC-HMS ascii file was not created. 
 
3.4.3 Watershed Modeling System (WMS) 
WMS was developed by the Environmental Modeling Research 
Laboratory (EMRL) at Brigham Young University for use in hydrologic 
computation and modeling.  WMS is a set of modeling codes along with grid and 
mesh generation utilities, and post-processing and visualization tools in both two 
and three dimensions (Nelson et al., 1997).  WMS is different from using 
ArcView GIS 3.2 in conjunction with CRWR-PrePro in that it may be used to run 
different hydrologic modeling programs in addition to computing hydrologic 
parameters.  Similar to a GIS, WMS automates watershed delineation and 
parameter calculation from digital elevation terrain data, importing GIS data, and 
extracting watershed information from the GIS database.   
As shown in Figure 3.15, the WMS drainage menu is similar to the 
CRWR-PrePro menu.  Like CRWR-PrePro, the WMS drainage menu bar contains 
 51
basic DEM processing algorithms to compute flow direction and flow 
accumulation, although in WMS this is done with a program called TOPAZ.  The 
drainage menu in WMS also gives the user the ability to vectorize data       
(Basins->Polygons), and compute the basin data (Compute Basin Data).  
 
 
Figure 3.15:  WMS Drainage Toolbar 
Figure 3.16 shows the editing tools that are included in the DEM module. 
Among these tools are a draw flow path tool, in which a flow path will be traced 
across the DEM from point to point according to the flow direction grid.  
Additional tools include point, vertex, arc and polygon selection and creation 
tools, a measuring tool, and an upstream arc selection tool.   
 
 
 
 52
 
Figure 3.16:  WMS Module 
Additional modules available in WMS include a map module (which 
allows the import of GIS vector-based data to be used in WMS for watershed 
definition and hydrologic attribute mapping), hydrologic modeling with HEC-1, 
NFF (National Flood Frequency), TR-20, TR-55, Rational Method, and HSPF 
(Hydrologic Simulation Program Fortran), and hydrologic/hydraulic calculators. 
Unlike a GIS system, WMS can run hydrologic modeling programs without 
having to export or import data.  
  
 53
3.4.3.1 TOPAZ 
The Watershed Modeling System (WMS) can be used to automatically 
delineate watersheds and sub-basin boundaries from digital elevation models 
(DEMs).  WMS uses TOPAZ to delineate grid elevation data.  However, flow 
directions and accumulations may also be computed by ArcInfo, ArcView, or 
GRASS and imported into WMS in grid ascii format.  In this study, TOPAZ is 
run to determine the flow direction and flow accumulation grids for WMS.   
TOPAZ (Topographic Parameterization) is an automated digital landscape 
analysis tool for topographic evaluation, drainage identification, watershed 
segmentation, and sub-catchment parameterization, and is similar to CRWR-
PrePro, which also uses the 8-Direction Point Pour Model.   
TOPAZ, shown in Figure 3.17, creates three grids:  a new elevation grid 
(relief.dat), a flow direction grid (flovec.dat) and a flow accumulation grid 
(uparea.dat).   
 
 
 
 
 54
 
Figure 3.17:  TOPAZ Grids 
3.4.3.2 Parameter Extraction 
Once a watershed has been delineated in WMS and all its hydrologic data 
has been defined using the Compute Basin Data command, a hydrologic model 
may be run.  Hydrologic parameters were extracted using the Display Options 
tool, shown in Figure 3.18, so that the parameters of interest as calculated by 
WMS are displayed on the map.   
 
 
 
 
 
 55
 
Figure 3.18:  Display Options in WMS 
Because WMS has tools to automatically calculate parameters such as the 
Green-Ampt parameters, time of concentration and other modeling parameters in 
a single application, it can be used to model watersheds more efficiently than 
traditional methods (Nelson et al., 1999a).  Figure 3.19 shows a very handy tool in 
 56
WMS to compute time of travel, using user-defined equations or a variety of 
predefined equations which include the Tulsa District Lag Time Equation, the 
Denver Lag Time Equation, and SCS Lag Time Equation. 
 
Figure 3.19:  WMS Calculators 
3.5   CASE  IV:  AUTOMATED METHODS USING A TIN 
In addition to working with DEM terrain data, WMS also has the 
capability to work with TIN (triangulated irregular network) data.  Similar to grid-
based DEMs, TINs have also been used to characterize watersheds.  TINs may be 
created in many ways, such as from gridded data, raw survey data, and digitizing 
contour data.  Working with TINs is useful in that TINs provide a more precise 
description of the landscape than grids; however TINs are not as widely available 
and used as grids.  TINs consist of a set of vertex points, connected by triangles, 
that represent scattered X, Y, and Z locations. (Nelson et al., 1999b) 
For TINs to be used efficiently for basin delineation and hydrologic 
modeling, they need to be constructed from readily available data such as USGS 
 57
DEMs (Nelson et al., 1999b). According to Nelson et al. (1999b), TINs should be 
constructed around streams, canals, streets, and other linear features so that the 
TIN conforms to these features. 
 
3.5.1 TIN Development and Processing 
Figure 3.20allows the user to create and edit TINs.   
 
 
Figure 3.20:  WMS TIN Module 
 58
The TIN is first created using Vertex Options under the TINs menu bar.  
By selecting an elevation, and a location on the background map (such as a digital 
raster graphic, or DRG), a point is added to the map at the specified elevation as 
shown in Figure 3.21.  Alternatively elevation data can be imported from a 
LIDAR or aerial land survey. 
 
 
Figure 3.21:  Vertex Options in WMS  
Once the user is satisfied with the amount of points, TIN breaklines may 
be added to the model to reflect streams and other terrain features. When 
breaklines are added, the triangles created conform to these lines. So that the TIN 
conforms to the terrain, breaklines must be created where the water drains.  This 
is done by selecting the conceptual (map) model icon and turning off the TIN.   
 59
Using the rough boundary and stream network defined in the conceptual 
model, WMS can create a triangulated irregular network (TIN) using the adaptive 
tessellation algorithm.  The adaptive tessellation algorithm generates a mesh of 
triangular elements.  The mesh lies within the model domain, and honors the 
conceptual model set up of point elevations and channel and watershed 
boundaries.  The boundary defines the TIN extents, and the stream and ridge arcs 
are forced into the TIN as breaklines to ensure that the triangle edges will be 
enforced along all streams and ridges. A stream is created from the triangle edges.  
Following the development of the TIN based on background contour information, 
a DEM may be used as a background elevation source (Nelson et al., 1999b). 
After the TIN has been created, the final step before the TIN can be 
delineated is to condition the TIN.  Conditioning is necessary because there are 
usually flat triangles and pits in the TIN.  WMS comes with tools to condition the 
TIN.  These tools include elevation smoothing, edge swapping, adjusting 
elevations, and adding or deleting vertices (Nelson et al., 1999b). 
 
3.5.2 TIN Parameter Extraction 
Once the basins have been defined, geometric attributes such as stream 
lengths, stream slopes, basin areas, basin slopes, and maximum drainage distance 
within a basin, are automatically computed from the TIN model.  These attributes 
may be combined with runoff curve numbers to generate a runoff model.   
 60
Chapter 4: Application 
This implementation study applies traditional methods in hydrologic 
modeling and compares those traditional processes to those using GIS for three 
differently sized watershed areas.  Four different case studies were performed:  
(1) measurement from paper maps; (2) on-screen extraction from raster maps; (3) 
using GIS and two different resolutions of grid-based digital elevation models 
(DEMs); and (4) using a triangulated irregular network (TIN).    
 
4.1 SITE SELECTION 
The study areas were determined in a meeting Friday, February 9
th
, 2001 
with David Stolpa of TxDOT.  During this meeting Mr. Stolpa mentioned that he 
was interested in comparing analyses for certain area sizes, and these watersheds 
each met this area size criteria.  Buttermilk Creek watershed was chosen initially 
as this is an area in which TxDOT has conducted an analysis for a highway 
project. 
All three study areas are located in Travis County, Texas, as shown in 
Figure 4.1. 
 
 
 
 
 
 61
 
Figure 4.1:  Location of Travis County, Texas 
Within Travis County are two watersheds, Buttermilk and Little Walnut, 
located in northern Austin.  A shapefile of these two watersheds, provided by the 
City of Austin, is shown in Figure 4.2.  Little Walnut is the larger watershed, and 
Buttermilk is the smaller watershed. 
 
 
 
 62
 
Figure 4.2:  Location of Buttermilk and Little Walnut in Travis County 
Area 1, the small area, is a subwatershed of Buttermilk Creek.  This area is 
located at the upper end of Buttermilk.  Area 2 is Buttermilk watershed, and Area 
3 is Little Walnut creek above its confluence with Buttermilk Creek.  The stream 
lines shown are from the National Hydrography Dataset (NHD).  Figure 4.3 gives 
a general idea of the shape and location of the three study areas. 
 
 
 
 63
 
 
Figure 4.3:  Area 1, Area 2,and Area 3 
4.2 CASE I:  TRADITIONAL METHODS 
Two USGS quad maps, Austin East (3097-242) and Pflugerville West 
(3097-243), were required to cover the study area of Buttermilk and Little Walnut 
watersheds.  Measurements were all done by hand for the three differently sized 
areas, Area 1, Area 2, and Area 3. 
The first watershed to be delineated was Area 2 (Buttermilk).  The first 
step to determine Area 2?s boundary was to locate the outlet point from the USGS 
map. This point marks the confluence of Buttermilk with Little Walnut Creek 
watershed.  Using a pencil, the watershed of Buttermilk was traced on the USGS 
maps.  Secondly, the portion of Area 3 (Little Walnut) above its confluence with 
Area 2 was delineated.  The subwatershed of Buttermilk was delineated last (Area 
1). For each area the longest flow path was determined and traced with the pencil.  
Figure 4.4 shows the outlet point for Area 2 and Area 3.   
 
 
 
 64
 
Figure 4.4:  Hand Delineation of Area 2 
 65
The areas were measured by first determining the planimeter constant.  
The constant was determined by measuring a square area of 4 in
2
.  Three readings 
were taken that varied by only 0.002 units.  These three measurements were 
averaged, and a constant of 13.730 calculated.  Following this procedure, a circle 
of area 4 in
2
 was measured three times and the average of these readings 
calculated.  For the circle, an average constant of 13.029 was calculated. The final 
step in determining the overall planimeter constant was by averaging these two 
constants.  In this way, both straight lines and curved lines are taken into account 
in the calculation of area.  The final averaged planimeter constant was 13.380. 
The perimeter and longest flow path length were determined using a map 
wheel.   Similar to measurements taken with the planimeter, each area was 
measured three times, and the average measurement taken.  Lastly, slope was 
calculated by subtracting the elevation of the longest flow path at the outlet of the 
subbasin from the elevation at the start of the longest flow path, divided by the 
length of the longest flow path.  Table 4.1 outlines the results of each calculation 
for area, perimeter, longest flow path, and slope as derived by traditional methods. 
 
Table 4.1:  Hand Delineation Results 
Watershed 
Area 
(mi
2
) 
Perimeter 
(mi) 
Longest Flow Path 
(mi) Slope   (%) 
Area 1 0.55 3.31 1.69 1.27 
Area 2 1.65 6.17 3.14 1.47 
Area 3 8.49 13.83 6.28 0.77 
 
 66
4.3 CASE II:  AUTOMATED METHODS BY DIGITIZING 
In Case II watershed boundaries are digitized using ArcView GIS 3.2 from 
digital raster maps (DRGs) assuming undeveloped conditions.  With the DRG 
placed on the computer screen, new shapefiles are created using the digitizing 
capabilities of ArcView GIS 3.2 and ArcWorkstation.   
A USGS digital raster graphic (DRG) was used as a background in 
ArcView GIS 3.2.  The DRGs used were Austin West (o30097c6.tif and 
o30097d6.tif), produced by the USGS in 1988.   
The first step in digitizing is to create a new theme as selected from the 
ArcView menu.  As discussed in Chapter 3, watersheds are delineated in the same 
fashion as with the paper maps, except with a computer-aided mouse.  For each 
area a polygon was used to represent area, and a polyline to represent the longest 
flow path.  Once the polyline was drawn (or polygon for area), ArcWorkstation 
was used to convert the new themes to coverages using the shapearc command.  
After the polylines and polygons were converted to coverages, they were 
processed using the ArcWorkstation commands build and clean.  Once they were 
built and cleaned, they were opened once again in ArcView and converted back to 
shapefiles.    
During the process of digitization, it became apparent that some areas 
were difficult to digitize because the contour lines could not easily be seen in 
areas with highway overpasses.  In an effort to incorporate parameter variations 
that might be encountered due to highway construction, two delineations were 
 67
made for each study area--one incorporating infrastructure and one disregarding 
the infrastructure. 
Figure 4.5 below shows the digitization results for Area 1, both for 
highways excluded and highways included.  The largest difference occurs at the 
upper end of Area 1, where it is very difficult to distinguish the contour lines. 
 
 
Figure 4.5:  Area 1 Digitized 
The delineation of Area 2 yielded the following, as shown in Figure 4.6.  
As Area 2 lies within Area 1, the digitization of the upper end of Area 2 replicates 
the digitization process for Area 1. 
 
 68
 
Figure 4.6:  Area 2 Digitized 
The delineation of Area 3 is shown in Figure 4.7.  The differences 
between With Highways as opposed to Without Highways are hard to note in this 
figure due to the large area that Area 3 encompasses. 
 
 
Figure 4.7:  Area 3 Digitized 
Watershed parameters are calculated using the GIS (for area, perimeter 
and longest flow path).  From the new shapefile the parameters area and perimeter 
 69
can be calculated automatically.  A longest flow path is also digitized from the 
DRG and its length calculated by the GIS.   
Table 4.2 outlines the results of Area 1, Area 2, and Area 3 from 
digitization. 
 
Table 4.2:  On-Screen Digitizing Results 
Watershed 
No Hwy/ 
Hwy 
Area 
(mi
2
) 
Perimeter 
(mi) 
Longest 
Flow Path 
(mi) Slope   (%) 
No Hwy 0.55 3.42 1.79 1.27 Area 1 
Hwy 0.52 3.24 1.57 1.32 
No Hwy 1.68 6.57 3.28 1.47 Area 2 
Hwy 1.65 6.50 3.09 1.44 
No Hwy 8.85 14.75 6.63 0.77 Area 3 
Hwy 8.87 15.53 6.58 0.78 
 
4.4 CASE III:  AUTOMATED METHODS USING A DEM  
Case III is divided into two parts. The first part describes using ArcView 
GIS 3.2 and CRWR-PrePro to delineate the watersheds and extract watershed 
parameters using two different spatial resolution DEMs.  The second part explores 
using the Watershed Modeling System  (WMS) to also delineate the watersheds 
and extract watershed parameters at the same two spatial resolutions as with 
ArcView GIS 3.2. 
The most widely available grid DEMs in the US are distributed by the 
USGS and are of 7.5 minute resolution (same coverage as a standard USGS 7.5 
minute map series quadrangle), with a grid spacing of 30 x 30 meters.  These 
 70
USGS digital elevation models are produced from models based on aerial 
photographs and satellite remote sensing images.  The USGS 7.5 minute DEM 
data are georeferenced using the Universal Transverse Mercator (UTM) 
coordinate system.   For this study, the DEMs used were developed by the USGS 
and distributed by the Texas Natural Resources Information System (TNRIS).  
The USGS is also producing a 10 meter DEM; however the regional availability 
of these elevation models is less than that of the 30 meter DEMs.   
 
4.4.1 ArcView GIS 3.2 and CRWR-PrePro 
Case III explores using ArcView GIS 3.2 and CRWR-PrePro to delineate 
the watersheds using two different spatial resolutions.   As mentioned previously, 
this part of the study entails using two different resolution grid DEMs: a 10 meter 
DEM and a 30 meter DEM.  All data are projected into the TCMS Albers Equal 
Area georeferencing system.  The Texas Geographic Information Council (TGIC) 
defines a statewide mapping system for use in projected geospatial datasets that 
cover Texas in order to facilitate overlay and integration of datasets.  The Texas 
Centric Mapping System/ Albers Equal Area or TCMS/AEA is defined below: 
 
Mapping System Name: Texas Centric Mapping System/Albers Equal Area 
Mapping System Abbreviation: TCMS/AEA 
Projection: Albers Equal Area Conic 
Longitude of Origin: 100 degrees West (-100) 
Latitude of Origin: 18 degrees North (18) 
 71
Lower Standard Parallel: 27 degrees, 30 minutes (27.5) 
Upper Standard Parallel: 35 degrees (35.0) 
False Easting: 1,500,000 meters 
False Northing: 6,000,000 meters 
Datum: North American Datum of 1983 (NAD83) 
 
The DEMs were clipped by first converting a box theme (as digitized in 
ArcView around the study area) to a coverage using the ArcWorkstation 
command shapearc box boxcov. Then the boxcov coverage was processed using 
the ArcWorkstation build boxcov command.  The cell size was set to that of the 
DEM (setcell grid), and the window to that of the box coverage (setwindow 
boxcov grid).  The coverage was turned into a grid (temp = polygrid [boxcov]), 
set to one (temp2 = temp / temp) and then clipped (clpgrd = temp2 * dem30m).   
Once the DEM was clipped, it was projected into the TCMS Albers 
projection.  This was done in ArcWorkstation.  Each DEM was processed as 
outlined under CRWR-PrePro in Chapter 3. 
The development of a curve number (CN) grid was necessary to estimate 
the spatial variability of runoff from a rainfall event.  After the DEMs were 
clipped, the same was done with the USGS Land Use/Land Cover (LULC) 
coverage and the USDA/NRCS STATSGO soils coverage for the same area.  
Figure 4.8 shows the Land Use/Land Cover data clipped to the area of interest.  
 
 
 72
 
Figure 4.8:  Land Use/Land Cover (LULC) Data 
Figure 4.9 below shows the USDA/NRCS STATSGO soils data clipped to 
the study area.  Similar to the USGS LULC coverage, the STATSGO coverage is 
a 1:250,000-scale map product.  Both coverages are coarse compared to the 
resolutions of the 10 and 30 meter DEMs.  
 
 
 
 
 73
Figure 4.9:  STATSGO Data 
The DEMs were clipped to a small area, and delineated separately for the 
three areas. For each area, a threshold was chosen so that the areas of interest 
would be delineated as separate units.   
 
 74
4.4.1.1 10 Meter DEM 
As each 10 meter DEM covers an area of about 66 mi
2
, the DEMs were 
first merged and clipped so that the study areas were covered completely by the 
DEM.  
For the large watershed an outlet was placed at the confluence with 
Buttermilk.  The steps taken were those described earlier for watershed 
delineation using CRWR-PrePro.  Table 4.3 below outlines these data, and the 
thresholds chosen for each area. 
 
Table 4.3:  10 Meter DEM Watershed Data 
Watershed Threshold Cells in Watershed Area/Cell 
Area 1 4500 13895 100 
Area 2 22500 43504 100 
Area 3 90000 228578 100 
 
In a study conducted by Garbrecht et al. (1999b) on an agricultural 
watershed, digital elevation models were applied to the study areas with cells 
ranging from 5 to 500 meters.  In this study the ratio of average subcatchment 
area to grid cell area was used as an indicator of spatial resolution.  An overall 
catchment-to-grid ratio of 100 was found to be an acceptable threshold of spatial 
resolution for reasonable model result.  For this reason this parameter has been 
incorporated into the analysis.  Table 4.4 below outlines the physical parameters 
determined from this study using a 10 meter DEM.   
 
 75
Table 4.4:  10 Meter DEM in ArcView Results 
Watershed 
Area 
(mi
2
) 
Perimeter 
(mi) 
Longest Flow 
Path (mi) Slope   (%) 
Area 1 0.54 4.08 1.56 1.36 
Area 2 1.68 8.38 3.21 1.43 
Area 3 8.83 20.04 6.96 0.74 
 
4.4.1.2 30 Meter DEM 
The 30 meter DEMs were delineated in a similar fashion to the 10 meter 
DEMs.  The DEMs used for this study are Pflueastm (Pflugerville East), 
Pflugwestm (Pflugerville West), Manorm (Manor), Jollyvillm (Jollyville), 
Austinwestm (Austin West), and Austinestm (Austin East).   
In the same process as done for the 10 meter DEM, LULC and STATSGO 
data were prepared for the 30 meter DEM.  The results for the three areas are 
shown below.  In both cases (10 meter and 30 meter DEM delineations) an outlet 
was added to delineate the large watershed at the confluence with Buttermilk.  
Figure 4.10 shows the three areas delineated separately, and the longest flow path 
for each. 
 
 
 
 
 
 
 76
 
Figure 4.10:  Delineated DEM Study Area 
For the large watershed an outlet was placed at the confluence with 
Buttermilk, as with the 10 meter DEM data.  The steps taken were those described 
earlier for watershed delineation using CRWR-PrePro.  Table 4.5 outlines these 
data, and the thresholds chosen for each area. 
 
Table 4.5:  30 Meter DEM Watershed Data   
Watershed Threshold Cells in Watershed Area/Cell 
Area 1 500 1568 899 
Area 2 2500 4835 900 
Area 3 10000 25427 900 
 
 77
The following table, Table 4.6, outlines the DEM derived parameters from 
this study using a 30 meter DEM.  
 
Table 4.6:  30 Meter DEM in ArcView Results 
Watershed 
Area 
(mi
2
) 
Perimeter 
(mi) 
Longest Flow 
Path (mi) Slope   (%) 
Area 1 0.54 4.06 1.50 1.26 
Area 2 1.68 8.16 3.06 1.39 
Area 3 8.84 19.08 6.78 0.76 
 
4.4.2 Automated Methods Using WMS 
The second part of the DEM-based analysis examines using WMS to 
delineate both the 10 meter and 30 meter DEMs.  Results from the WMS analysis 
are expected to give slightly different results than with ArcView GIS 3.2 and 
CRWR-PrePro, because different algorithms are used to extract the hydrologic 
parameters. 
 
4.4.2.1 10  Meter DEM 
The 10 meter digital elevation data used for the WMS study are the same 
as those used for the CRWR-PrePro study. The same grid that was clipped for the 
CRWR-PrePro study was imported into WMS as a grid ascii file using the import 
data command.  Once this was done the DRG for the area was placed in the 
background to locate the study area. Flow direction and flow accumulation grids 
 78
were computed using TOPAZ.  Figure 4.11 shows the WMS delineating of Area 
1, and its area value as 0.53 mi
2
. 
 
 
Figure 4.11:  Area 1 Delineated in WMS 
Figure 4.12 shows the area of Area 2 to be 1.66 mi
2
.  The white line is the 
longest flow path.  
 
 79
 
Figure 4.12: Area 2 Delineated with WMS 
 
Figure 4.13 shows the area of Area 3 to be 8.76 mi
2
.   
 
 
Figure 4.13: Area 3 Delineated with WMS 
 80
Table 4.7 shows the results from the study using a 10 meter DEM to 
extract watershed parameters in WMS.  
 
Table 4.7:  10 Meter DEM in WMS Results 
Watershed 
Area 
(mi
2
) 
Perimeter 
(mi) 
Longest Flow 
Path (mi) 
Slope   
(%) 
Area 1 0.53 4.09 1.54 1.25 
Area 2 1.66 8.53 3.15 1.41 
Area 3 8.76 19.85 6.81 0.77 
4.4.2.2 30 Meter DEM 
The 30 meter digital elevation data used for the WMS study are also the 
same as those used for the CRWR-PrePro study. The same grid that was clipped 
nto WMS as a grid ascii file, using the 
import 
 TOPAZ computed the flow direction and 
flow accumulation. 
Figure 4.14 shows the area of Area 1 to be 0.53 mi
2
.   
 
for the CRWR-PrePro study was imported i
data command.  Once this was done the DRG for the area was placed in 
the background to locate the study area. 
 81
 
Figure 4.14:  Area 1 Delineated with WMS 
Figure 4.15 shows the area of Area 2 to be 1.67 mi
2
.   
 
 
Figure 4.15:  Area 2 Delineated with WMS 
Figure 4.16 shows the area of Area 3 to be 8.84 mi
2
.   
 
 82
 
Figure 4.16:  Area 3 Delineated with WMS 
Table 4.8 shows the results from the study using a 30-meter DEM to 
extract watershed parameters in WMS.  
 
Table 4.8:  30 Meter DEM in WMS Results
Watershed 
Area 
(mi
2
) Perimeter (mi) 
Longest Flow Path 
(mi) Slope   (%) 
Area 1 0.53 3.76 1.38 1.36 
Area 2 1.67 7.89 2.87 1.46 
Area 3 8.84 18.72 6.66 0.78 
 
 83
4.5 
MS for Area 2, and the watersheds are 
delineated in WMS.  The TIN is made using the conceptual model approach and 
  WMS has the ability to create and 
delineate TINs. Once the TIN has been delin  attributes may 
. 
ptual model appr involve 
digitizing points from a DRG (the same DRG as used in Case II).  This was done 
y opening the TIN module in WMS, and selecting edit vertex points from Vertex 
enu.  Once the Vertex Options box is open, point elevations 
are entered based on contour lines.  Figure 4.17 shows the point elevations 
entered using DRG contour lines as a reference of elevation. 
 
 
CASE IV: AUTOMATED METHODS USING A TIN 
In Case IV a TIN is created in W
interpolating points from a 30 meter DEM.
eated, geometric basin
be computed
The steps to create a TIN using the conce oach 
b
Options in the TIN m
 84
 
Figure 4.17:  TIN Development in WMS 
Points were added until the study area was densely populated with point 
elevations.  Breaklines were added to the model to reflect streams and other 
terrain features as shown on the DRG.  In this way, when the triangles are created 
they are forced to conform to these lines.  To add breaklines, the conceptual 
model icon was selected and the TIN was turned off.   A new coverage of type 
drainage was created with attributes typed as generic to form the bounding 
polygon around Area 2.   Generic arcs were used to cut around the TIN.  Under 
Feature Objects, arcs were converted to polygons.   
To create the streams, stream arcs  (feature type is stream) were generated 
to make the triangle edges conform to the streamlines as shown in Figure 4.18. 
The feature objects were then edited to redistribute spacing of points every 75 
meters (this number was chosen fairly arbitrarily).   
 85
 
Figure 4.18:  Points, Breaklines, and Bounding Polygon in WMS 
Once the triangles were turned on again, the polygon marking the 
boundary around Area 2 was selected, and under feature objects the create TIN 
command was selected.  The TIN options selected for this study are linear 
interpolation from DEM with a size bias of 0.5.   
Once the TIN was conditioned and free of pits and flat triangles, the TIN 
was used to delineate the drainage network.  Figure 4.19 shows the TIN for Area 
2 after it has been interpolated off the 30 meter DEM surface.  Once the TIN is 
ready to be delineated, the user must add an outlet so that the basins may be 
defined. 
 
 
 86
 
Figure 4.19:  Interpolated TIN for Area 2 
Once the TIN is delineated, basin data may also be calculated by WMS for 
input into a hydrologic model as shown in Figure 4.20. 
 
 87
 
Figure 4.20:  Area 2 TIN Delineated 
TINs may be modified very easily, and for this reason are useful data 
sources for urban areas.  This study was not replicated for Area 3, because after 
the time it took to work with Area 2 it was deemed impractical to proceed to the 
larger area.   Table 4.9 shows the results for Area 2. 
 
Table 4.9:  TIN Results 
Watershed 
Area 
(mi
2
) 
Perimeter 
(mi) 
Longest Flow 
Path (mi) Slope   (%) 
Area 2 1.68 7.4 3.14 1.53 
 88
Chapter 5: Results 
5.1. CASE STUDY PARAMETER RESULTS SUMMARY 
The results from the case study are evaluated for the following parameters:  
slope, longest flow path, area, perimeter, and curve number.   Figure 5.1 shows 
the three drainage areas used in this study. 
 
Figure 5.1:  Three Study Areas 
 89
Methods used to extract the watershed parameters (as discussed in detail 
in Chapter 4) include (1) measurement from paper maps; (2) on-screen extraction 
from raster maps; (3) using GIS and two different resolutions of grid-based digital 
elevation models (DEMs); and (4) using a triangulated irregular network (TIN).  
Table 5.1, Table 5.2, and Table 5.3 summarize the results found for Area 1, Area 
2, and Area 3.  It should be noted that perimeter is not a hydrologic parameter.  It 
is evaluated in this study to examine trends in line computation among methods. 
 
Table 5.1:  Area 1 Results 
Area 1 
Area 1 
Case Number 
 Area 
Miles
2
Perimeter 
Miles 
LFP 
Miles
Slope
% 
Hand Case I 0.55 3.31 1.69 1.27 
Digitized-no hwy Case II 0.55 3.42 1.79 1.27 
Digitized-hwy Case II 0.52 3.24 1.57 1.32 
PrePro-30 Case III 0.54 4.06 1.50 1.26 
PrePro-10 Case III 0.54 4.08 1.56 1.36 
WMS-30 Case III 0.53 3.76 1.38 1.36 
WMS-10 Case III 0.53 4.09 1.54 1.25 
Mean  0.54 3.71 1.58 1.30 
Std.Dev.  0.01 0.38 0.13 0.05 
CV(%)  2.07 10.28 8.42 3.65 
 
 
 
 
 
 
 90
Table 5.2:  Area 2 Results 
Area 2 
Area 2 
Case Number 
Area 
Miles
2
Perimeter 
Miles 
LFP 
Miles
Slope
% 
Hand Case I 1.65 6.17 3.14 1.47 
Digitized-no hwy Case II 1.68 6.57 3.28 1.47 
Digitized-hwy Case II 1.65 6.50 3.09 1.44 
PrePro-30 Case III 1.68 8.16 3.06 1.39 
PrePro-10 Case III 1.68 8.38 3.21 1.43 
WMS-30 Case III 1.67 7.89 2.87 1.46 
WMS-10 Case III 1.66 8.53 3.15 1.41 
TIN Case IV 1.68 7.40 3.14 1.53 
Mean  1.67 7.45 3.12 1.45 
StdDev  0.01 0.93 0.12 0.04 
CV(%)   0.81 12.48 3.90 2.97 
 
Table 5.3:  Area 3 Results 
Area 3 
Area 3 
Case Number 
 Area 
Miles
2
Perimeter 
Miles 
LFP 
Miles
Slope
% 
Hand Case I 8.49 13.83 6.28 0.77 
Digitized-no hwy Case II 8.85 14.75 6.63 0.77 
Digitized-hwy Case II 8.87 15.53 6.58 0.78 
PrePro-30 Case III 8.84 19.08 6.78 0.76 
PrePro-10 Case III 8.83 20.04 6.96 0.74 
WMS-30 Case III 8.84 18.72 6.66 0.78 
WMS-10 Case III 8.76 19.85 6.81 0.77 
Mean  8.78 17.40 6.67 0.77 
Std.Dev.  0.13 2.61 0.22 0.01 
CV(%)  1.52 14.99 3.22 1.80 
 
Table 5.1, Table 5.2, and Table 5.3 without further analysis provide 
important information regarding variations of hydrologic parameters as a function 
of area size and method of parameter extraction.  Coefficient of variation (CV), 
 91
the standard deviation of each parameter divided by its mean, is used in addition 
to the standard deviation to evaluate each of the watershed parameters.  Assuming 
that errors are normally distributed, in 68% of the cases the observed variation 
will fall within one standard deviation above or below the mean, or ? CV 
expressed as a percent of the mean. 
The standard deviation for area and slope is small for all three areas.  For 
both Area 1 and Area 2, the drainage area can be determined within 
approximately ? 0.01 square miles (2.07% for Area 1 and 0.81% for Area 2), and 
? 0.13 square miles (1.52%) for Area 3.  For Area 3, using traditional delineation 
techniques on paper maps produces an area smaller than any of the other 
techniques (0.29 square miles below the mean). This is most likely attributed to 
area measurement using the planimeter.   
Similar to area, the standard deviation (as well as the CV) for slope is 
small for all three areas.  The standard deviation for slope is highest for Area 1, at 
a value of 0.05%.   The highest coefficient of variation for slope, as calculated for 
Area 1, is 3.65%. 
Longest flow path and perimeter show different results from area and 
slope, in that there is much more parameter variation among extraction methods.  
Longest flow path was determined within ? 0.13 miles for Area 1, ? 0.12 miles 
for Area 2, and ? 0.22 miles for Area 3.  Precision in determining the longest flow 
path increases as the area becomes larger, with a CV for Area 1 of 8.42% and a 
CV for Area 3 of 3.22%.  This is most likely because the flow path for Area 1 is 
small, and hence there is more error in this measurement.  Secondly, for Area 3 a 
 92
larger portion of the flow path was already marked with a blue line on paper maps 
and on the DRG, whereas for Area 1 the blue line was not drawn on the map. It 
should also be noted that longest flow path using traditional paper map-based 
methods for Area 3 (6.28 miles) is 0.39 miles below the mean of 6.67 miles, well 
below the measurements using other methods of longest flow path extraction. 
Perimeter measurements become less precise as the drainage area 
increases (the CV for Area 1 is 10.28%, while the CV for Area 3 is 14.99%).  In 
addition, the perimeter values found using traditional methods and on-screen 
digitizing of raster graphic maps are smaller than those found using DEMs.  Part 
of the reason for this large variation in perimeter could be due to the subjective 
nature of traditional paper map-based methods and on-screen digitizing of raster 
graphic maps, in addition to the more tortuous path created by digital data.   
Table 5.3 shows that automated methods using CRWR-PrePro, WMS, and 
on-screen digitizing produce more consistent results than using manual hand 
delineation techniques on paper maps to determine area, longest flow path and 
perimeter for large areas. The values for area, longest flow path, and perimeter 
determined using traditional paper map-based methods for Area 3 are much 
smaller than those determined using more automated methods.  Figure 5.2 
outlines the CV results from Table 5.1, Table 5.2, and Table 5.3. 
 
 93
 
Figure 5.2:  Coefficients of Variation 
In Figure 5.2, SCS curve number is shown to give the reader an idea of the 
curve number variation that will be applied to the remainder of the study.   For 
Area 2, a range of curve numbers was evaluated using a curve number selected by 
TxDOT as a low value (85.8), and a curve number derived by STATSGO soils 
data along with Land Use/Land Cover data as a high value (91.7).  TxDOT did 
not provide curve number values for Area 1 and Area 3.  Instead, a range the same 
as used in Area 2 was applied, with the curve number derived by STATSGO soils 
data along with Land Use/Land Cover data as a high value. These values, shown 
in Table 5.4, were used to reflect reasonable variations of curve number that one 
might encounter in hydrologic modeling.   
 
 94
Table 5.4:  Curve Number Values 
 Area 1 Area 2 Area 3
CN- 10m 94.0 91.7 90.7 
CN- 30m 93.9 91.7 90.7 
CN-HEC-1 - 85.82 - 
Range 87-95 85-93 84-92
Mean 91 89 88 
StdDev 2.74 2.74 2.74 
CV (%) 3.01 3.08 3.11 
 
Figure 5.2 shows that for the areas analyzed, there is a general trend for 
both longest flow path (LFP) and slope.  The trend in variations in slope reflects 
the trend in variations in longest flow path, as it is calculated from the longest 
flow path measurement.  Both show higher variations with Area 1 and lower 
variations for Area 3.  Another key point shown by Figure 5.2 is that for the small 
area (Area 1), there is more variation among parameters than for the larger area, 
Area 3, except in the case of perimeter and curve number.   
 
5.2 ELASTICITY ANALYSIS 
In this study ?elasticity? is used as a measure of the influence of one 
variable on another.  While gradient describes the relationship between two 
variables, it is a unit-dependent quantity.  Elasticity, on the other hand, is a 
dimensionless quantity.  In simple terms, elasticity is the percent change in output 
per percent change in input.  If the elasticity is greater than one, the parameter is 
?elastic? in that the dependent variable is more sensitive to the independent 
 95
variable.  If the elasticity is less than one, the parameter is ?inelastic? in that the 
dependent variable is less sensitive to the independent variable.  Figure 5.3 below 
shows the concept of elasticity graphically: 
dx
dy
gradient =
Y* 
dy
input
output
change
change
 
Figure 5.3:  Concept of Elasticity 
The goal of this analysis is to determine the effect of parameter variations 
on the lag time, and subsequently the effect of lag time variations due to 
parameter variations on discharge.  This analysis is conducted only for Area 2. 
The reason for this is that Area 2 is the only study area for which TxDOT has 
created a hydrologic model.  After an analytical calculation of gradients to 
determine lag time elasticity for each parameter, the hydrologic model created by 
TxDOT is used to numerically calculate the elasticity of discharge with lag time 
as shown in Figure 5.4. 
 
X* 
X
dx
Y
dy
elasticity
%
%
*
*
==
dx 
 96
 
Figure 5.4:  Discharge Sensitivity Calculation 
Equation 5.1, Step 1 in calculating the discharge sensitivity, describes the 
calculation of lag time elasticity. The first term in this equation is the gradient.  
The gradient is multiplied by the average parameter value for Area 2, and divided 
by the lag time calculated at the average parameter.  
 
)(
*
)(
)(
avg
avg
parameterlag
parameterlag
parameter
parameter
lag
elasticity
?
?
=
?
 
 Equation 5.1 
 
Equation 5.2, Step 2 in calculating the discharge sensitivity, describes the 
calculation of discharge elasticity based on changes in lag values.  Similar to 
Equation 5.1 the gradient is multiplied by the average lag time value and divided 
by the discharge calculated at the average lag time. 
 
)(
*
)(
)(
avg
avg
lagQ
lagQ
lag
lag
Q
elasticity
?
?
=
?
    
Equation 5.2 
 97
The final step approximates the overall discharge sensitivity as a result of 
variation in parameter values.  Equation 5.3 outlines this calculation.   The results 
from Equation 5.1 describing the lag time elasticity with respect to each 
parameter are multiplied by the discharge elasticity  with respect to lag time as 
calculated by Equation 5.2. 
 
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
)(
*
)(
)(
)(
*
)(
)(
*
)(
*
)(
)(
parameterQ
parameter
parameter
Q
parameterlag
parameter
parameter
lag
lagQ
lag
lag
Q
elasticity
parameterQ
  
Equation 5.3 
 
5.2.1 Step 1:  Sensitivity of SCS Lag Time to Parameter Variations 
Figure 5.5 describes the process analyzed in this section.  Variations in 
parameter values are used to calculate resulting variations in SCS lag times. 
 
 
Figure 5.5:  Step 1 in Calculating the Discharge Sensitivity 
 98
Analytical calculation of the gradient involves plugging in each of the 
parameters derived from each level of parameter extraction into the SCS lag 
equation, shown in Equation 5.4, while holding the other parameters constant.   
 
s
CN
L
t
w
lag
67.31
9
1000
(min)
7.0
8.0
?
?
?
?
?
?
?
=   Equation 5.4 
 
In Equation 5.4, L
w
 is longest flow path in units of feet, and slope is 
expressed as a percentage.  Curve number is symbolized by CN, and t
lag
 is the lag 
time in minutes.   Table 5.5 outlines the base values used for these calculations.  
These numbers are the mean values calculated for Area 2, as shown previously in 
Table 5.2 and Table 5.4. 
 
Table 5.5:  Parameter Base Values 
Parameter Base 
Value 
LFP 3.12 Miles 
Slope 1.45 % 
CN 89 
 
5.2.1.1 Longest Flow Path 
To evaluate changes in SCS lag time that result from changes in the 
longest flow path, the curve number and average slope were held constant while 
 99
longest flow path was allowed to vary.  Table 5.6 gives the lag time values 
calculated for each longest flow path measurement. 
 
Table 5.6:  Longest Flow Path Calculations  
 
LFP 
Miles 
% Slope 
(mean) 
CN 
(mean) 
SCS 
Lag, Min
 1.45 89.00  
Hand 3.14   109.8 
Digitized-no hwy 3.28   113.7 
Digitized-hwy 3.09 108.4 
PrePro-30 3.06   107.5 
PrePro-10 3.21 111.7 
WMS-30 2.87   102.2 
WMS-10 3.15 110.1 
TIN 3.14 109.8 
MEAN 3.12  MEAN 109.0 
?X
max-min
/X
mean
13.2%  ?Y
max-min
/Y
mean
10.6% 
 
Subtracting the highest longest flow path measurement from the lowest 
longest flow path measurement, and then dividing by the mean flow path length 
determines the longest flow path variation.  Figure 5.6 below demonstrates this 
process for the calculation of longest flow path.   
 100
 
Figure 5.6:  Analytical Calculation of Gradients 
As the longest flow path varies by 13.2%, the lag varies by 10.6% when 
evaluated at the base value for longest flow path (3.12 miles).  The elasticity is 
then 10.6 ? 13.2 or 0.80.  As this number is less than one, the relationship 
between longest flow path and lag time is considered inelastic, signifying that lag 
time is not sensitive to changes in longest flow path length.  These results show 
that a 1% increase in longest flow path will cause a 0.8% increase in SCS lag 
time. 
 
 101
5.2.1.2 Slope 
The lag time elasticity with respect to slope was calculated by holding the 
longest flow path and curve number constant and varying the slope.  The results 
from this calculation are shown in Table 5.7. 
 
Table 5.7:  Slope Calculations 
 
% 
Slope 
LFP 
(mean),Miles
CN 
(mean) 
SCS 
Lag, Min.
 3.12 89.00  
Hand 1.47   107.8 
Digitized-no hwy 1.47   107.8 
Digitized-hwy 1.44   108.9 
PrePro-30  1.39   110.9 
PrePro-10 1.43 109.3 
WMS-30  1.46   108.2 
WMS-10 1.41 110.1 
TIN 1.53   105.7 
MEAN 1.45  MEAN 108.6 
?X
max-min
/X
mean
9.7%  ?Y
max-min
/Y
mean
-4.8% 
 
As can be seen from Figure 5.7, there is an inverse relationship between 
lag time and slope.   
 102
 
Figure 5.7:  Slope Gradient Calculation 
The elasticity of lag time with respect to slope is calculated as ?4.8/9.7, or 
?0.50.  In other words, a 1 % increase in slope will cause a 0.5% decrease in SCS 
lag time. 
 
5.2.1.3 Curve Number 
The lag time elasticity with respect to curve number was determined for 
Area 2 by holding slope and longest flow path constant, and varying the curve 
number. Curve numbers for Area 2 are shown in Table 5.8.  These are the same 
values shown earlier in Table 5.4. 
 103
 
Table 5.8:  Curve Number Measurements 
 10m 30m HEC-1
CN range 91.7 91.7 85.8 
 
Table 5.9 outlines the curve number values. As mentioned earlier, this 
range is used to reflect a range of curve numbers that could likely result using 
traditional methods and derived mathematically using digital Land Use/ Land 
Cover and STATSGO soils data. 
 
Table 5.9:  Curve Number Calculations 
 CN 
%Slope
(mean)
LFP 
(mean), Miles
SCS 
Lag, Min. 
 1.45 3.12  
 85   126.4 
86 122.0 
 87   117.6 
88 113.3 
 89   108.9 
90 104.6 
 91   100.4 
92 96.1 
 93   91.9 
MEAN 89 MEAN 109.0 
?X
max-min
/X
mean
9.0%  ?Y
max-min
/Y
mean
-31.7% 
 
This curve is plotted in Figure 5.8.  The graph shows the inverse 
relationship between curve number and lag time. 
 104
 
Figure 5.8:  Curve Number Gradient Calculation 
The elasticity of the lag time to the curve number, -31.7/9.0, is ?3.52.  
These results show that a 1% increase in CN will result in a 3.52% decrease in lag 
time. 
 
5.2.1.4  Step 1 Results  
Table 5.10 summarizes the results from the lag time elasticity study.  
Results show that the only elastic parameter is curve number. Both the longest 
flow path and slope are inelastic parameters. 
 105
 
Table 5.10:  Results from Analytical Calculations 
Variation- 
LFP 
Variation- 
Lag 
Elasticity 
Lag-LFP 
13.2% 10.6% 10.6/13.2=0.80 
Variation-
Slope 
Variation-
Lag 
Elasticity 
Lag-Slope 
9.7% -4.8% -2.8/5.6=-0.50 
Variation-
CN 
Variation-
Lag 
Elasticity 
Lag-CN 
9.0% -31.7% -31.7/9.0=-3.52 
 
5.2.2 Step 2:  Sensitivity of Flow to Variations in Lag Time 
Now that the relationships between physical parameters and SCS lag time 
have been quantified, the next step is to quantify the relationship between SCS lag 
time and discharge.  Figure 5.9 below shows the process analyzed in this section 
in which variations in SCS lag time values are used to calculate resulting 
variations in discharge. 
 106
 
Figure 5.9:  Step 2 in Calculating the Discharge Sensitivity 
In 1992, a contractor for TxDOT developed a HEC-1 model of Buttermilk 
watershed (Area 2) as an undeveloped area.  This pre-developed HEC-1 model 
included areas outside of Buttermilk watershed.  These areas were edited, and the 
new, slightly modified HEC-1 model was imported into HEC-HMS. 
The U.S. Corps of Engineers? Hydrologic Modeling System (HMS) is a 
?next generation? software for the precipitation-runoff simulation that will 
supersede HEC-1.  HEC-HMS contains most of the watershed runoff and routing 
capabilities of HEC-1, in addition to continuous hydrograph simulation over long 
periods of time, and distributed runoff computation using a grid cell depiction of 
the watershed (HEC-HMS User?s Manual, 2000). 
There are two principal parameters that are evaluated in this study with 
respect to discharge:  lag time and drainage area.   After modification of the HEC-
1 model, lag times are varied in each sub-basin.  For each lag time variation, 
 107
discharge is calculated.  Next, the drainage area of each sub-basin is varied, and 
discharge calculated once again for each area variation. 
 
5.2.2.1 HEC-1 Model 
Figure 5.10 shows the area delineated by TxDOT for the HEC-1 model.  
The area in blue is included in the HEC-1 model although it does not pertain to 
Buttermilk (Area 2).  For this analysis, the blue area is deleted from the HEC-1 
model. 
 
 
Figure 5.10:  HEC-1 Study Area 
The corresponding unmodified HEC-HMS diagram (the HEC-1 model 
was imported into HEC-HMS) is shown below in Figure 5.11. 
 
 108
 
Figure 5.11:  Unmodified HEC-1 model (displayed in HEC-HMS) 
As mentioned previously, the HEC-1 model had to be modified for this 
analysis.  Table 5.11 below gives the name of each sub-basin along with its 
drainage area, SCS lag time, and SCS curve number.  In the modification process, 
 109
the area downstream of COMB14 was deleted.  This area includes 183105, LW14 
and 183106 as shown in red italicized print. 
 
Table 5.11:  HEC-1 Modifications 
Sub-basin Area mi
2
SCS Lag (min) SCS Curve 
Number 
Tb711 0.444 15.30 89 
Tb710 0.285 17.88 88 
Tb709 0.052 7.74 80 
Tb708 0.241 15.72 86 
Tb707 0.042 9.36 87 
Tb706 0.121 16.02 84 
Tb1003 0.150 6.66 77 
183101 0.011 - 85 
Tb1001 0.025 11.1 85 
183103 0.004 - 83 
Tb705 0.102 12.3 83 
Tb704 0.046 7.74 87 
Tb702 0.097 9.72 86 
183104 0.004 - 85 
Tb703 0.052 8.22 85 
Tb701 0.088 8.40 86 
183105 0.001 - 86 
Lw14 0.127 7.5 80 
183106 0.006 - 80 
Total Area 1.898   
 
The new area, after modification, is 1.764 mi
2
. The modified model is 
shown in Figure 5.12.  The weighted curve number after modification is 85.82. 
 
 110
 
Figure 5.12:  Modified HEC-1 Model (displayed in HEC-HMS) 
For rainfall-runoff modeling HEC-HMS requires a basin component, a 
precipitation component, and a control component.  The basin and precipitation 
components are heavily dependent on spatial factors.    
The HEC-1 model is imported as the basin component.  For the 
precipitation component, six different return periods are analyzed using the 
 111
TxDOT IDF (Intensity-Duration-Frequency) curves and an alternating block 
cumulative precipitation hyetograph for Travis county and a three-hour design 
storm.  Equation 5.4 and Table 5.12 are used to calculate the cumulative rainfall 
for a three-hour storm in six-minute increments for each sub-basin.  A six-minute 
increment is chosen because this is the value TxDOT used.   
 
()
c
d
bT
a
I
+
=   Equation 5.4 
 
Table 5.12:  TxDOT IDF (Intensity-Duration-Frequency) Curves 
Return 
Period 
2 Years 5 Years 10 Years 25 Years 50 Years 100 Years 
a 56 69 77 87 91 103 
b 8.1 8.6 8.6 8.6 8.6 8.1 
c 0.796 0.780 0.775 0.766 0.751 0.752 
 
5.2.2.2 Lag Time Variation 
The next step was to determine the discharge elasticity from changes in 
lag time.  This was done by proportionally changing the lag time values for each 
of the sub-basins in the HEC-1 model.   Table 5.13 gives the original SCS lag 
value for each sub-basin, followed by 5%, 10%, and 20% increases in lag time, 
then 5%, 10%, and 20% decreases in lag time.   
 
 
 112
Table 5.13: HEC-1 Lag Input 
Subbasin Lag, min Lag +5%
 
Lag +10% Lag +20% Lag -5% Lag -10% Lag -20% 
TB711 15.30 16.07 16.83 18.36 14.54 13.77 12.24 
TB710 17.88 18.77 19.67 21.46 16.99 16.09 14.30 
TB709 7.74 8.13 8.51 9.29 7.35 6.97 6.19 
TB708 15.72 16.51 17.29 18.86 14.93 14.15 12.58 
TB707 9.36 9.83 10.30 11.23 8.89 8.42 7.49 
TB706 16.02 16.82 17.62 19.22 15.22 14.42 12.82 
TB1003 6.66 6.99 7.33 7.99 6.33 5.99 5.33 
TB1001 11.10 11.66 12.21 13.32 10.55 9.99 8.88 
TB705 12.30 12.92 13.53 14.76 11.69 11.07 9.84 
TB704 7.74 8.13 8.51 9.29 7.35 6.97 6.19 
TB702 9.72 10.21 10.69 11.66 9.23 8.75 7.78 
TB703 8.22 8.63 9.04 9.86 7.81 7.40 6.58 
TB701 8.40 8.82 9.24 10.08 7.98 7.56 6.72 
 
Figure 5.13 shows the discharge values in cubic feet per second (cfs) for 
each return period.  The relationship between discharge (Y-axis) and lag time (X-
axis) is given by the linear equations shown in Figure 5.12 for 2, 5, 10, 25, 50, 
and 100-year events. 
 113
 
Figure 5.13:  Discharge Results for Lag Variations 
To determine the percent change in discharge resulting from a percent 
change in lag time (due to parameter variations), the discharge (Q) for each 
corresponding lag variation is calculated using the linear equations relating lag 
time to discharge.  Table  5.14  shows the percent changes in discharge for each 
return period corresponding to each variation in SCS lag time. 
 
Table 5.14:  Discharge Variations Due to Lag Variations 
Lag (From LFP Variations) Q
2
Q
5
Q
10
Q
25
Q
50
Q
100
10.6% -3.04% -2.87% -2.27% -3.14% -3.18% -3.17%
Lag (From Slope Variations) Q
2
Q
5
Q
10
Q
25
Q
50
Q
100
-4.8% 1.38% 1.30% 1.03% 1.42% 1.44% 1.44%
Lag (From CN Variations) Q
2
Q
5
Q
10
Q
25
Q
50
Q
100
-31.7% 9.09% 8.58% 6.79% 9.38% 9.50% 9.48%
 114
For each return period, the elasticity of discharge with respect to SCS lag 
time is calculated by dividing the percent change in discharge by the percent 
change in SCS lag time.  As shown in Table 5.15, there are slight variations in 
discharge elasticity for each return period.  These variations were averaged to 
establish a relationship between SCS lag time and discharge.   The averaged value 
is ?0.28. 
 
Table 5.15:  Discharge Elasticity Due to Parameter Variation 
Elasticity  
Q
2
-Lag 
Elasticity  
Q
5
-Lag 
Elasticity 
Q
10
-Lag 
Elasticity 
Q
25
-Lag 
Elasticity 
Q
50
-Lag 
Elasticity 
Q
100
-Lag 
Elasticity
Q
avg
-Lag
-0.29 -0.27 -0.21 -0.30 -0.30 -0.30 -0.28 
 
Results from this analysis show that a 1% increase in SCS lag time yields 
a -0.28% decrease in discharge. 
 
5.2.2.3 Drainage Area Variation 
The second component involving analysis of the HEC-1 model is to 
evaluate changes in area, and how these changes affect discharge.  Similar to the 
lag time study, the areas of each sub-basin were increased by 5%, 10%, and 20% 
and also decreased by 5%, 10%, and 20%.  Table 5.16 shows these values. 
 
 
 
 
 115
Table 5.16:  HEC-1 Area Input 
Sub-basin 
Area 
Miles
2
Area +5% Area +10% Area +20% Area -5% Area -10% Area -20%
TB711 0.444 0.466 0.488 0.533 0.422 0.400 0.355 
TB710 0.285 0.299 0.314 0.342 0.271 0.257 0.228 
TB709 0.052 0.055 0.057 0.062 0.049 0.047 0.042 
TB708 0.241 0.253 0.265 0.289 0.229 0.217 0.193 
TB707 0.042 0.044 0.046 0.050 0.040 0.038 0.034 
TB706 0.121 0.127 0.133 0.145 0.115 0.109 0.097 
TB1003 0.150 0.158 0.165 0.180 0.143 0.135 0.120 
TB1001 0.025 0.026 0.028 0.030 0.024 0.023 0.020 
183101 0.011 0.012 0.012 0.013 0.010 0.010 0.009 
TB705 0.102 0.107 0.112 0.122 0.097 0.092 0.082 
183103 0.004 0.004 0.004 0.005 0.004 0.004 0.003 
TB704 0.046 0.048 0.051 0.055 0.044 0.041 0.037 
TB702 0.097 0.102 0.107 0.116 0.092 0.087 0.078 
183104 0.004 0.004 0.004 0.005 0.004 0.004 0.003 
TB703 0.052 0.055 0.057 0.062 0.049 0.047 0.042 
TB701 0.088 0.092 0.097 0.106 0.084 0.079 0.070 
 
Figure 5.14 shows the discharge values in cubic feet per second (cfs) for 
each return period.  The relationship between discharge (Y-axis) and area (X-axis) 
is given by the linear equations, also shown in Figure 5.14 below, for 2, 5, 10, 25, 
50, and 100-year events. 
 
 116
 
Figure 5.14:  Discharge Results for Drainage Area Variations 
Table 5.17 gives the variation in area for Area 2 (Buttermilk).  The 
variation in drainage area among methods is 1.80%. 
 
Table 5.17:  Area Variation 
 Area, Miles
2
Hand 1.65 
Digitized-no hwy 1.68 
Digitized-hwy 1.65 
PrePro-30 1.68 
PrePro-10 1.68 
WMS-30  1.67 
WMS-10 1.66 
TIN 1.68 
MEAN 1.67 
?X
max-min
/X
mean
1.8% 
 117
The same steps were taken to determine the effect of drainage area on 
discharge as were taken to determine the effects of lag time on discharge.  For 
each return period, the percent variation in discharge was calculated based on the 
percent variation in drainage area (1.80%).  There were slight variations in 
percent discharge for each return period.  Discharge elasticity for each return 
period was calculated by dividing each discharge variation by 1.80% (the 
variation in drainage area).  There were slight differences in elasticity for each 
return period.  These numbers were averaged to provide an approximate discharge 
elasticity, as shown in Table 5.18.   
 
Table 5.18:  Discharge Elasticity due to Area Variations 
Q
2
Q
5
Q
10
Q
25
Q
50
Q
100
2.05% 1.74% 1.60% 1.96% 2.09% 1.99% 
Elasticity 
Q
avg
-Area
 
Elasticity 
Q
2
-Area 
Elasticity 
Q
5
-Area 
Elasticity 
Q
10
-Area
Elasticity 
Q
25
- Area
Elasticity 
Q
50
- Area
Elasticity 
Q
100
- Area
1.14 0.97 0.89 1.09 1.16 1.11 1.91/1.80=1.06 
 
The resulting elasticity of discharge with respect to area is 1.06.  Hence, a 
1% increase in area yields approximately a 1% increase in discharge, as one 
would expect.  
 
5.2.2.4 Step 2 Results  
Results from the numerical calculations of gradient show that there is a 
constant, inversely proportional, relationship between lag time and discharge.  
 118
This elasticity value, -0.28, shows the relatively inelastic effect of lag time 
changes on discharge, e.g., a 1% increase in lag time results in a 0.28% decrease 
in discharge.  Area, as one would expect, is purely elastic and directly 
proportional to discharge.  In this case a 1% increase in area would result in a 1% 
increase in discharge. 
 
5.2.3 Results from Elasticity Analysis 
The effect of parameter variation on discharge is determined by 
multiplying elasticity results from Step 1 (sensitivity of SCS lag time to parameter 
variations) by Step 2 (sensitivity of flow to variations in discharge).  The overall 
picture is shown once again in Figure 5.15. 
 
 
Figure 5.15:  Final Discharge Sensitivity Calculation 
 
The effect of each parameter (longest flow path, slope, and curve number) 
on discharge was evaluated using the elasticity for both discharge (due to 
 119
variations in lag) and lag (due to variations in each parameter).  These two 
elasticity values are multiplied together.  Figure 5.16 outlines the results from the 
elasticity study.   
 
  
 
 
 
 
 
 
 
 
 
Figure 5.16:  Elasticity Diagram 
 
The following relationships can be drawn from Figure 5.16: 
? A 1% increase in longest flow path length decreases peak 
discharge by 0.22%; 
? A 1% increase in slope increases peak discharge by 0.14%; 
? A 1% increase in curve number increases flow by 1%; 
? A 1% increase in drainage area increases flow by 1%. 
 
LFP 
Slope 
CN 
Area 
Discharge
E=0.80 
E=-0.50 
E=-3.52 
E=-0.28
E=1.06
SCS Lag Time
E=-3.52*-0.28=0.99
E=-0.50*-0.28=0.14
E=0.80*-0.28=-0.22
Parameter
Lag
Change
Change
%
%
Parameter
Q
Change
Change
%
%
Lag
Q
Change
Change
%
%
 120
Both curve number and drainage area have a direct effect on discharge, 
while longest flow path length and slope have minimal influence on discharge.  
Figure 5.17 shows the relative discharge elasticities of longest flow path, slope, 
curve number, and drainage area. 
  
 
Figure 5.17:  Elasticity Results 
An analysis of coefficient of variation (CV) values in Table 5.19, as 
derived for each parameter in Table 5.1, Table 5.2, and Table 5.3, shows that the 
error associated with determining drainage area is small compared to the error 
associated with determining longest flow path, slope, and curve number. 
 
 
 121
Table 5.19:  Parameter Coefficients of Variation (CV) 
Study Area CV (%) Area CV (%) LFP CV (%) Slope CV (%) CN
Area 1 2.07 8.42 3.65 3.01 
Area 2 0.81 3.90 2.97 3.08 
Area 3 1.52 3.22 1.80 3.11 
 
Drainage area CV values are the smallest of the parameter CV values for 
Area 1, Area 2, and Area 3.  Although the relationship between area and 
discharge is elastic, the error associated with determining drainage area is small.  
On the other hand, there is a larger error associated with determining longest flow 
path and slope.  However, since longest flow path and slope are inelastic 
parameters, large errors in determining these values will cause minimal percent 
changes in discharge.   
Table 5.20 shows the percent discharge variations resulting from 
parameter variations for Area 1, Area 2, and Area 3. 
 
Table 5.20:  Discharge Variations for Area 3 
Parameter Discharge CV% 
(Area 1) 
Discharge CV% 
(Area 2) 
Discharge CV% 
(Area 3) 
Area 2.07*1.06=2.19% 0.81*1.06=0.86% 1.52*1.06=1.61% 
LFP 8.42*-0.22=-1.85% 3.90*-0.22=-0.86% 3.22*-0.22=-0.71% 
Slope 3.65*0.14=0.51% 2.97*0.14=0.42% 1.80*0.14=0.25% 
CN 3.01*0.99=3.00% 3.08*0.99=3.05% 3.11*0.99=3.08% 
 
 122
The CV for discharge is calculated by multiplying the CV for each 
parameter by the discharge elasticity with respect to that parameter.  Table 5.20 
shows that curve number will most influence discharge after taking into 
consideration the error that occurs as a result of variations in extracting 
hydrologic parameters. 
 123
Chapter 6: Conclusions and Recommendations 
This implementation project was conducted to provide guidance to 
TxDOT regarding parameter sensitivity in hydrologic modeling.  The principal 
factors affecting flood magnitudes in a watershed include runoff, and watershed 
area information such as slope, flow path length, area, land use, and soil type.  
These parameters are all important in determining the peak discharge at a 
watershed outlet such as a culvert or bridge crossing. Currently TxDOT 
predominantly uses traditional methods of hand delineation to extract hydrologic 
parameters, although TxDOT is moving towards using more automated methods 
for this process. 
The use of GIS in water resources engineering has proved to be aquick 
and relatively simple means of computing hydrologic data.  In 2000, however, 
Anderson (2000) conducted a digital floodplain analysis for TxDOT which led to 
doubts about the automated process.  Anderson?s watershed lag time values were 
significantly greater than values  found in an earlier analysis conducted by 
TxDOT.  In an effort to determine possible causes of this error, four case studies 
were developed to analyze three areas of different size: (1) measurement from 
paper maps; (2) on-screen extraction from raster maps; (3) using GIS and two 
different resolutions of grid-based digital elevation models (DEMs); and (4) using 
a triangulated irregular network (TIN).  This section of the report discusses 
conclusions and recommendations as drawn from the implementation study. 
 
 124
 
6.1    ERROR  SOURCES AMONG PARAMETER EXTRACTION METHODS 
This study examines parameter extraction methods in three drainage areas 
of different size in Austin, Texas.  Area 1, the smallest area, is approximately 0.5 
mi
2
.  Area 2, the medium-sized area, is approximately 1.7 m
2
; and Area 3, the 
largest area, is approximately 8.8 mi
2
.   Errors associated with each of the four 
levels of parameter extraction, in addition to the influence of drainage area size on 
parameter extraction method, are evaluated. 
 
6.1.1 Parameter Extraction using Paper Maps 
Traditional hydrologic modeling involves calculating watershed 
parameters from paper maps.  Calculation of terrain-based hydrologic data 
involves delineating the watershed by hand using map contours as guidelines.  
Once the perimeter of the watershed has been established, a planimeter is used to 
measure its area.  Perimeter and length of the longest flow path are measured 
using a map wheel.  Slope is calculated by taking the difference in elevation 
between map contours. 
Variations in traditional, paper map-based methods were most apparent in 
Area 3.  This drainage area, the largest area under investigation, yielded hand 
measurements for area and longest flow path, 0.29 mi
2
 and 0.39 miles below the 
mean, respectively.  These area and longest flow path values were smaller than 
any of the other area or longest flow path measurements for Area 3.  The length of 
perimeter, although not normally used as a hydrologic parameter, was 3.57 miles 
 125
below the mean using traditional methods of parameter extraction.  For Area 1 
and Area 2 the differences between paper map methods and digital automated 
methods were not as apparent. 
The reason for the large deviation from the mean using traditional 
methods in area, longest flow path, and perimeter measurements is most likely 
due to the error associated with 1) taping two topographic maps together to make 
a map large enough to cover the whole drainage area, 2) difficulty in determining 
flow path and drainage divides from the map contours and 3) the accuracy of 
manual measurement techniques using a map wheel and a planimeter. 
 
6.1.2 On-Screen Digitizing of Raster Graphic Maps 
The process of on-screen digitizing of raster graphic maps closely 
resembles paper map methods.  The methodology is analogous, except that the 
process of on-screen digitizing of raster graphic maps involves using a computer-
aided mouse and a scanned topographic map to draw in watershed boundaries and 
flow paths.  Once the watershed boundaries and flow paths have been determined, 
a GIS (or similar system) computes drainage area, longest flow path length, and 
perimeter.  Slope is calculated by taking the difference in elevation between map 
contours, as done with paper maps. 
On-screen digitizing eliminates the error of taping maps together, and 
interpreting lengths and areas from hand-held instruments. As with paper maps, 
determining flow paths and drainage divides is a very time-consuming and 
subjective process.  On-screen digitizing also has the advantage over paper    
 126
map-based methods in that map features can be ?zoomed-in? or magnified to 
better understand flow paths.  In this study each area was digitized two ways:  by 
attempting to incorporate the effect of urban infrastructure such as major 
highways, and by disregarding this infrastructure.  The on-screen digitizing results 
show that area and longest flow path measurements for Area 3 closely resemble 
results derived from automated processes using DEMs, more so than results 
derived using paper map-based methods.  This result indicates that errors 
associated with physically measuring parameters with a map wheel and 
planimeter largely contribute to the variation in area and longest flow path values 
for Area 3.  For on-screen digitizing of larger areas, the measurement error due to 
the subjective nature of the delineation process is small when compared to the 
error due to hand-held measurement techniques applied to paper maps. 
 
6.1.3 Parameter Extraction Using Automated Methods 
DEM analysis in WMS (Watershed Modeling System) and CRWR-PrePro 
presents errors associated with data resolution and accuracy in describing the 
physical characteristics of a surface.   DEM resolution affects the channel length, 
area, slope, and perimeter measurements.  If the DEM resolution is too low, small 
changes in terrain are not observed and small areas may not accurately be 
described.  If the resolution of the DEM is very high, channel lengths become 
larger due to more tortuous flow paths.  This study showed that flow paths for the 
10 meter DEM were longer than flow paths for the 30 meter DEM for all three 
areas as determined in both WMS and CRWR-PrePro. For Area 1 there was a 4% 
 127
increase in longest flow path using CRWR-PrePro, and a 12% increase using 
WMS.  For the large area, Area 3, there was a 3% increase in longest flow path 
using CRWR-PrePro and a 2% increase using WMS.  Regardless, the longest 
flow path standard deviation for Area 1 is 0.13 miles (with a mean of 1.58 miles), 
and the longest flow path standard deviation for Area 3 is 0.22 miles (with a mean 
of 6.67 miles). Variations are small, and results show that these variations do not 
significantly influence lag time and discharge calculations.  Distributed properties 
such as slope and longest flow path require a method or model to reduce the 
distributed information into a representative value for the entire subcatchment.  
Variations in subcatchment slope and longest flow path values between WMS and 
CRWR-PrePro may be attributed to differences in underlying models used for 
extracting data. 
 
6.1.4 Parameter Extraction Using TINs 
TINs, triangulated irregular networks, consist of a set of vertex points 
connected by triangles, that represent scattered X, Y, and Z locations.  TINs have 
many advantages over DEMs, in that TINs can describe a surface precisely and 
are adaptive to different types of terrain.  The major disadvantage found working 
with TINs in this project is the large amount of time that is required to create, edit, 
and condition the TIN.  For this reason, TIN development was not conducted for 
Area 3.   Parameter values for area, perimeter, and longest flow path did not vary 
significantly for the TIN when compared to the DEM methods and on-screen 
digitizing.  Slope measurement using a TIN, however, produced a greater value 
 128
than any of the other methods implemented.  Probably this is the most accurate 
slope value since the DEM methods tend to smooth out slopes. 
 
6.2       ERRORS AMONG EXTRACTED HYDROLOGIC PARAMETERS 
The parameter variation associated with each of the four levels of 
parameter extraction is evaluated based on a simple statistical analysis using 
standard deviation and coefficient of variation (CV).  The coefficient of variation 
(CV) is defined as the standard deviation divided by the mean for a group of 
measurements. 
 
6.2.1 Drainage Area 
The results for drainage area showed little variation among the different 
methods of parameter extraction.  Results show that drainage area can be 
approximated within ? 0.01 mi
2
 for areas less than approximately 1.6 mi
2
, and 
within ? 0.13 mi
2
 for areas approximately 8.8 mi
2
.  Area measurement, whether 
obtained by using automated or traditional methods, will most likely not result in 
a large error.  This study shows that the maximum coefficient of variation (CV) 
for area, determined by Area 1, is 2.07%.   
 
6.2.2 Slope 
Slope, similar to area, produced fairly consistent measurements for all 
three study areas.  For the largest area, Area 3, slope could be approximated 
within ? 0.01 as percent slope (a CV of 1.80%).  For the small area, Area 1, slope 
 129
could be approximated within ? 0.05 as percent slope (a CV of 3.65%).  The 
mean slope for Area 3 was 0.77%, while the mean slope for Area 1 was 1.30%. 
 
6.2.3 Longest Flow Path 
Longest flow path results produced errors greater than slope or area errors 
for all three study areas.  However, this error decreased from 8.42% to 3.22% as 
the study area size increased from Area 1 to Area 3. For the largest area, longest 
flow path was calculated within ? 0.22 miles, with a mean value of 6.67 miles.  
For the smallest area, longest flow path was calculated within ? 0.13 miles, with a 
mean value of 1.58 miles. 
 
6.2.4 Perimeter 
Watershed perimeter length, although not a hydrologic parameter, was 
examined to evaluate trends in line variation among methods.  Automated 
methods using DEMs produced greater values for perimeter than traditional 
methods for all three study areas.   This resulted in consistently high CV values 
for perimeter.  For Area 1, the CV value was 10.28%, and for Area 3, the CV 
value was 14.99%.  
 
6.2.5 Curve Number 
The SCS runoff curve number obtained by combining land use and soil 
types in GIS for Area 2 was 91.7, while the curve number determined by an 
independent TxDOT study was 85.8.  A range of curve number values, using the 
 130
curve number developed by automated methods as an approximate upper limit, 
and the curve number developed by TxDOT as an approximate lower limit, gave a 
coefficient of variation of 3.08%, and a mean value of 89. This number is used to 
reflect a reasonable error one might encounter in determining SCS curve number. 
 
6.3    SIGNIFICANCE OF ERRORS 
Following hydrologic parameter extraction, ranging from traditional 
methods using paper maps to advanced methods using TINs, a sensitivity analysis 
based on the concept of elasticity was conducted for Area 2.   
Quantifying discharge elasticity with respect to parameter variation is a 
two-step process.  The first step involves determining the variation in SCS lag 
time with slope, longest flow path, and curve number.  Variations in parameter 
values using the four levels of parameter extraction were plotted against resulting 
SCS lag time values.  The range in parameter values, divided by the mean 
parameter value, was used to describe the parameter variation. The range of 
resulting SCS lag times, divided by the mean SCS lag time, was used to quantify 
the lag time variation.  The lag time variation, divided by the parameter variation, 
describes the lag time elasticity with respect to the parameter.  In other words, this 
describes the percent increase that will occur in lag time by a 1% increase in the 
parameter.  If this number is less than 1, then lag time is ?inelastic? with respect 
to the parameter.  If this number is greater than 1, then lag time is ?elastic? with 
respect to the parameter.  An elastic parameter will cause larger variations in lag 
time.   
 131
The second step in quantifying the discharge elasticity with respect to 
parameter variation involves determining the variation in discharge with variation 
in SCS lag time.  This step requires running a HEC-1 model developed by 
TxDOT.  For each return period, the HEC-1 model was run seven times.  The lag 
times were changed in each sub-basin by an equal percentage (5%, 10%, 20%,      
-5%, -10%, and -20%) for each run.  The resulting linear equations were used to 
determine discharge elasticity, or the percent variation in discharge caused by 
fluctuations in SCS lag time.  Dividing the percent variation in discharge by the 
percent variation in SCS lag time gives discharge elasticity with respect to SCS 
lag time for each return period.  This describes the percent change in discharge 
resulting from a 1% change in SCS lag time. 
Table 6.1 shows the overall discharge elasticity with respect to each 
parameter.  Results from the first step (sensitivity of lag time to parameter 
variations) and the second step (sensitivity of discharge with respect to lag time 
variations) are multiplied to produce discharge elasticity with respect to each 
parameter. 
 
Table 6.1:  Elasticity Analysis  
Parameter 
Elasticity 
Lag-Parameter 
Elasticity 
Q
avg
-Lag 
Elasticity 
Q
avg
-Parameter 
LFP 0.80 -0.28 -0.22 
Slope -0.50 -0.28 0.14 
CN -3.52 -0.28 0.99 
Area --- --- 1.06 
 
 132
Results show that although errors associated with parameter extraction 
methods may cause significant changes in lag time values, the errors become less 
significant once entered into a model to calculate discharge.  Table 6.1 shows that 
lag time is inelastic with respect to longest flow path (LFP), as the elasticity of lag 
time with respect to this parameter is 0.8.   Discharge is also inelastic with respect 
to longest flow path, with an elasticity of ?0.22.  This last number, discharge 
elasticity with respect to longest flow path, was determined by multiplying the lag 
time elasticity with respect to longest flow path by the discharge elasticity with 
respect to lag time (-0.28).  The discharge elasticity with respect to slope, 
calculated using the same method as with longest flow path, is also inelastic at a 
value of 0.14. 
Flow path and slope values were originally thought to be large 
contributors to lag time variations.  This analysis shows that this is not necessarily 
the case.   Table 6.1 shows that SCS lag time acts inelastically with respect to 
both slope and longest flow path (-0.50% and 0.80% respectively).  Once entered 
into a hydrologic model, variations in these parameters have minimal effect on 
discharge, with discharge elasticities of 0.14% and ?0.22% respectively.  Thus, a 
1% variation in slope will cause a minimal 0.14% increase in discharge, and a 1% 
variation in longest flow path will cause a 0.22% decrease in discharge. 
Table 6.1 shows that curve number, unlike slope and longest flow path, 
has an elastic effect on lag time.  The lag time elasticity with respect to curve 
number is -3.52. Discharge is also elastic with respect to curve number (at an 
 133
elasticity of 0.99) when lag times, based on curve number variations, are entered 
into a hydrologic model.   
The discharge elasticity with respect to drainage area, calculated to be 
1.06, is also elastic.  Although discharge is more sensitive to drainage area than to 
curve number, errors associated with determining area are small.  For instance, 
Area 3 has a CV for area of 1.52%.  A 1% increase in area will result in a 1.61% 
increase in discharge.  If curve number has a CV of 3%, the resulting discharge 
for a 1% increase in curve number will be 3%.   
 
6.4 ADDITIONAL SOURCES OF ERROR 
This analysis of parameter sensitivity in hydrologic modeling is general 
and meant to serve as a guide for TxDOT engineers.  Several important elements 
were not considered in this report when calculating discharge. 
First of all, the elasticity analysis does not account for curve number 
effects on excess rainfall.  For each change in lag time within the HEC-1 model, 
curve numbers used to calculate excess rainfall were held constant.    
In highly developed areas, parameter extraction methods used in this 
report may not apply. Without a thorough knowledge of the storm sewers and 
other urban structures it is difficult to judge flow paths.  Including buildings and 
structures into the model does not account for the runoff flowing below the 
ground surface or under a bridge.  Storm sewers may enter and leave watersheds, 
and water may flow along roads and enter into one watershed from another area.    
 134
The effects of using traditional methods as opposed to automated methods 
were not fully evaluated for flat areas.  In order to evaluate if the use of automated 
methods still proves viable in areas of low slope, a more thorough investigation 
using several study areas of the same shape and area, but different slopes, would 
have to be implemented. 
 
6.5 RECOMMENDATIONS 
Automated methods, requiring the use of a computer to extract hydrologic 
parameters, produce very consistent results for hydrologic parameters.  Paper 
map-based methods of parameter extraction tend to vary more than do automated 
methods, especially for large areas.   
As with traditional paper map-based methods, on-screen digitization from 
raster graphic maps is a highly subjective process.  However, measurements for 
the large study area closely resemble results derived from automated processes 
using DEMs, more so than results derived using paper maps.  This result implies 
that differences are most likely attributed to errors associated with physically 
measuring parameters with a map wheel and a planimeter, rather than the 
subjective nature of the application.   
As paper map-based methods are more tedious than automated methods 
(with the exception of the TIN), and more time consuming, moving to automated 
methods would accelerate the design process.  Parameters extracted using WMS, 
CRWR-PrePro, different resolution DEMs, and on-screen digitization from raster 
graphic maps do not vary significantly from one another, and any error associated 
 135
with parameter extraction using automated methods will not significantly 
influence discharge calculations.  The recommendation, therefore, is to move 
towards any of the automated methods of hydrologic parameter extraction.  On-
screen digitization of raster graphic maps for small and medium areas eliminates 
the need to work with DEMs.  For large areas, however, DEMs are recommended 
for efficiency and precision. 
The second observation is that discharge is most sensitive to curve 
number, and less sensitive to slope or longest flow path.  Discharge is also 
sensitive to drainage area.  However, this study shows that the error associated in 
calculating drainage area is small compared to the error associated with 
calculating curve number.  Determining an accurate curve number will reduce lag 
time and discharge calculation errors.  The recommendation that results from this 
study is to carefully evaluate soil type, vegetative cover, and land use in a given 
area to obtain as accurate a curve number as possible. 
 
 136
Appendix A:  Online Internet Resources 
 
Data Type Source 
USGS DRG http://mcmcweb.er.usgs.gov/drg/
30 Meter DEM http://edcnts12.cr.usgs.gov/ned/
http://www.tnris.org/DigitalData/DEMs/dem-a.htm.   
STATSGO (USDA-
NRCS) 
http://www.ftw.nrcs.usda.gov/stat_data.html
Land Use/ Land Cover http://edc.usgs.gov/doc/edchome/ndcdb/ndcdb.html
CRWR-PrePro 
webpage 
http://www.ce.utexas.edu/prof/olivera/prepro/prepro.htm  
WMS Webpage http://www.ems-i.com/netpagz/wms.htm
TOPAZ Webpage http://duke.usask.ca/~martzl/topaz/   
 137
Appendix B:  Unmodified HEC-1 Model 
 
ID    LITTLE WALNUT CREEK HEC-1 MODEL; CONVERSION FROM TR-20 
ID    ORIG. DEV'D MURPHEE ENG. 1992; L&M CONVERSION 5/97;  FILE: LW100EX.H1 
ID    THIS FILE IS BASED ON ORIGINAL MTEST4.N INPUT. 
ID    THIS FILE DIFFERS FROM EXIST.IN IN 
ID 
ID    *** EXIST2.IN *** TXDOT MICRO MODEL (3 HR DIMENSIONLESS) 
*DIAGRAM 
*       INITIALIZATION 
IT     2                     300 
IO     5 
*           2 YR    5 YR    10YR    25YR    50YR   100YR  3 HR DEPTHS 
JR  PREC    2.61    3.48    3.98    4.72    5.34    6.03 
*         BEGIN WITH LITTLE WALNUT (LW14) 
KK TB711    * UPPER END OF BASIN 
BA 0.444 
PB  1.00 
IN     6       0       0 
PC0.0000  0.0077  0.0153  0.0230  0.0345  0.0460  0.0613  0.0766  0.0920  0.1111 
PC0.1341  0.1571  0.1916  0.2375  0.3218  0.5824  0.7165  0.7816  0.8238  0.8544 
PC0.8774  0.8966  0.9119  0.9272  0.9425  0.9540  0.9655  0.9770  0.9847  0.9923 
PC1.0000 
UD 0.255 
LS            89 
KKROUT43   * ROUTE TB711 
RS     1    STOR       0 
SV  0.00    0.59    1.19    1.93    2.54    3.31    4.07    4.57    5.59 
SQ     0     180     450     900    1350    2000    2700    3200    4200 
SE 643.0   645.2   646.2   647.2   647.9   648.8   649.6   650.1   650.8 
KK TB710   * ORIGINAL MAP LABEL 
BA 0.285 
UD 0.298 
LS            88 
KKCOMB01   * COMBINE ROUTE43 + TB710 
HC     2 
KKROUT44   * ROUTE COMB01 
RS     1    STOR       0 
SV  0.00    2.93    5.97    9.63   12.70   16.56   20.36   22.87   27.96 
SQ     0     180     450     900    1350    2000    2700    3200    4200 
SE 643.0   645.2   646.2   647.2   647.9   648.8   649.6   650.1   650.8 
KK TB709   * ORIGINAL MAP LABEL 
BA 0.052 
UD 0.129 
LS            80 
KKCOMB02   * COMBINE ROUTE44 + TB709 
HC     2 
KK TB708   * ORIGINAL MAP LABEL 
BA 0.241 
UD 0.262 
LS            86 
KKCOMB03   * COMBINE COMB02 + TB708 
HC     2 
KKROUT45   * ROUTE COMB03 
RS     1    STOR       0 
SV  0.00    2.90    6.51   11.81   16.32   23.25   30.62   35.87   45.79 
SQ     0     180     450     900    1350    2000    2700    3200    4200 
 138
SE 603.0   605.5   606.8   608.1   608.9   609.9   610.8   611.3   612.1 
KK TB707   * ORIGINAL MAP LABEL 
BA 0.042 
UD 0.156 
LS            87 
KKCOMB04   * COMBINE ROUTE45 + TB707 
HC     2 
KK TB706   * ORIGINAL MAP LABEL 
BA 0.121 
UD 0.267 
LS            84 
KKCOMB05   * COMBINE COMB04 + TB706 
HC     2 
KKTB1003   * NORWOOD 
BA 0.150 
UD 0.111 
LS            77 
KK STR80   * FLOW OF TB1003 THROUGH STR80 
KM      CHANNEL STORAGE ROUTING FOR RESERVOIR 80 
RS     1    ELEV   628.5 
SV  0.00    0.50    0.78    2.34    4.81    8.05    9.99   11.92   12.89   14.12 
SV 16.31   21.09   25.86 
SQ     0       0       5      30     110     250     289     325     340     470 
SQ   900    1575    2400 
SE 628.5   629.5   630.0   632.0   634.0   636.0   637.0   638.0   638.4   639.0 
SE 640.0   641.0   642.0 
KKROUT46   * ROUTE STR80 
RS     1    STOR       0 
SV  0.00    0.21    0.43    0.74    0.99    1.57    2.91    3.83    5.50 
SQ     0      35      85     170     240     375     500     600     800 
SE 606.0   606.9   607.3   607.7   607.9   608.4   609.4   610.0   610.9 
KKTB1001   * FIRST MODIFIED AREA - IMPERVIOUS FROM 183 
BA 0.025 
UD 0.185 
LS            85 
KK183I01   * TB1001 AREA CONVERTED TO IMPERVIOUS 
BA 0.011 
UI 213.0       0 
KKCOMB06   * COMBINE ROUTE46 + TB1001 + 183I01 
HC     3 
KKCOMB07   * COMBINE COMB06 + C0MB05 
HC     2 
KKROUT47   *  ROUTE COMB07 
RS     1    STOR       0 
SV  0.00    1.16    2.39    4.15    5.66    8.74   17.13   20.26   28.33 
SQ     0     180     450     900    1350    2000    2700    3200    5100 
SE 587.8   590.8   592.1   593.4   594.4   595.8   598.5   599.3   601.0 
KM 
KK TB705   * ORIGINAL MAP LABEL 
BA 0.102 
UD 0.205 
LS            83 
KM 
KK183I03   * TB705 AREA CONVERTED TO IMPERVIOUS 
BA 0.004 
UI  77.4       0 
KKCOMB10   * COMBINE tb705 + 183i03 
HC     2 
KKCOMB08   * COMBINE ROUT47+ comb10 
HC     2 
KK TB704   * ORIGINAL MAP LABEL 
BA 0.046 
 139
UD 0.129 
LS            87 
KKCOMB11   * COMBINE TB704 + COMB08 
HC     2 
KKROUT48   * ROUT COMB11 
RS     1    STOR       0 
SV  0.00    1.13    2.37    4.06    5.62    7.50    9.34   10.60   13.01   25.00 
SQ     0     180     450     900    1350    2000    2700    3200    4200    8200 
SE 570.0   572.8   574.1   575.4   576.3   577.4   578.3   578.9   580.0   585.0 
KK TB702   * ORIGINAL MAP LABEL 
BA 0.097 
UD 0.162 
LS            86 
KKCOMB12   * COMBINE ROUT48 + tb702 
HC     2 
KK TB703   * ORIGINAL MAP LABEL 
BA 0.052 
UD 0.137 
LS            85 
KK183I04   * TB703 AREA CONVERTED TO IMPERVIOUS COVER 
BA 0.004 
UI  77.4       0 
KKCOMB13   * COMBINE COMB12 + tb703 + 183I04 
HC     3 
KKROUT49   * ROUTE COMB71 
RS     1    STOR       0 
SV  0.00    3.01    5.67    8.99   11.77   15.22   18.50   20.73   25.72   35.00 
SQ     0     180     450     900    1350    2000    2700    3200    4200    7000 
SE 548.0   551.4   552.8   554.2   555.3   556.5   557.6   558.3   559.6   562.6 
KK TB701   * ORIGINAL MAP LABEL 
BA 0.088 
UD 0.140 
LS            86 
KKCOMB14   * COMBINE ROUT49 + TB701 
HC     2 
KK183I05   * TB701 AREA CONVERTED TO IMPERVIOUS COVER 
BA 0.001 
UI  19.4       0 
KKCOMB15   * COMBINE COM14 + 183I05 
HC     2 
KKLW14     * ORIGINAL MAP LABEL 
BA 0.127 
UD 0.125 
LS            80 
KKCOMB16   * COMBINE COMB15 + LW14 
HC     2 
KK183I06   * LW14 AREA CONVERTED TO IMPERVIOUS 
BA 0.006 
UI 116.2       0 
KKCOMB17   * COMBINE 183I06 + COMB16 
HC     2 
ZZ 
 
 
 140
Appendix C:  Modified HEC-1 Model in HEC-HMS 
Basin: Exist2mod.in 
     Description: LITTLE WALNUT CREEK HEC-1 MODEL; CONVERSION FROM TR-20 ORIG. 
DEV'D MURPHEE ENG. 1992; L&M CONVERSION 5/97;  FILE: LW100EX.H1 THIS FILE IS BASED 
ON ORIGINAL MTEST4.N INPUT. THIS FILE DIFFERS FROM EXIST.IN IN  *** EXIST2.IN *** 
TXDOT MICRO MODEL (3 HR DIMENSIONLESS) 
     Last Modified Date: 18 February 2002 
     Last Modified Time: 10:29 
     Version: 2.1.2 
     Default DSS File Name: D:\hmsproj\Exist.in_feb17\Exist.in_feb17.dss 
     Unit System: English 
End: 
 
Subbasin: TB711 
     Canvas X: -386.946 
     Canvas Y: 1940.607 
     Label X: 16 
     Label Y: 0 
     Area: 0.444 
     Downstream: ROUT43 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 89 
 
     Transform: SCS 
     Lag: 15.300 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Reservoir: ROUT43 
     Canvas X: -116.602 
     Canvas Y: 1794.804 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB01 
 
     Route: Modified Puls 
     Routing Curve: Storage-Elevation-Outflow 
     Initial Storage: 0 
     Routing Table in DSS: Yes 
End: 
 
Subbasin: TB710 
     Canvas X: 86.915 
     Canvas Y: 1974.021 
     Label X: 16 
     Label Y: 0 
     Area: 0.285 
     Downstream: COMB01 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 88 
 
     Transform: SCS 
 141
     Lag: 17.880 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Junction: COMB01 
     Canvas X: 32.239 
     Canvas Y: 1752.278 
     Label X: 8 
     Label Y: 5 
     Downstream: ROUT44 
End: 
 
Reservoir: ROUT44 
     Canvas X: 44.389 
     Canvas Y: 1636.850 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB02 
 
     Route: Modified Puls 
     Routing Curve: Storage-Elevation-Outflow 
     Initial Storage: 0 
     Routing Table in DSS: Yes 
End: 
 
Subbasin: TB709 
     Canvas X: 354.221 
     Canvas Y: 1652.038 
     Label X: 16 
     Label Y: 0 
     Area: 0.052 
     Downstream: COMB02 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 80 
 
     Transform: SCS 
     Lag: 7.740 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Junction: COMB02 
     Canvas X: 44.389 
     Canvas Y: 1536.611 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB03 
End: 
 
Subbasin: TB708 
     Canvas X: -356.570 
     Canvas Y: 1527.498 
     Label X: 16 
     Label Y: 0 
     Area: 0.241 
     Downstream: COMB03 
 
 142
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 86 
 
     Transform: SCS 
     Lag: 15.720 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Junction: COMB03 
     Canvas X: 59.577 
     Canvas Y: 1451.559 
     Label X: 16 
     Label Y: 0 
     Downstream: ROUT45 
End: 
 
Reservoir: ROUT45 
     Canvas X: 68.690 
     Canvas Y: 1384.732 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB04 
 
     Route: Modified Puls 
     Routing Curve: Storage-Elevation-Outflow 
     Initial Storage: 0 
     Routing Table in DSS: Yes 
End: 
 
Subbasin: TB707 
     Canvas X: 354.221 
     Canvas Y: 1424.220 
     Label X: 16 
     Label Y: 0 
     Area: 0.042 
     Downstream: COMB04 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 87 
 
     Transform: SCS 
     Lag: 9.360 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Junction: COMB04 
     Canvas X: 71.727 
     Canvas Y: 1302.718 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB05 
End: 
 
Subbasin: TB706 
     Canvas X: -222.917 
     Canvas Y: 1223.741 
 143
     Label X: 16 
     Label Y: 0 
     Area: 0.121 
     Downstream: COMB05 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 84 
 
     Transform: SCS 
     Lag: 16.020 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Junction: COMB05 
     Canvas X: 32.239 
     Canvas Y: 1211.591 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB07 
End: 
 
Subbasin: TB1003 
     Canvas X: 335.996 
     Canvas Y: 1278.417 
     Label X: 16 
     Label Y: 0 
     Area: 0.150 
     Downstream: STR80 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 77 
 
     Transform: SCS 
     Lag: 6.660 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Reservoir: STR80 
     Description: CHANNEL STORAGE ROUTING FOR RESERVOIR 80 
     Canvas X: 348.146 
     Canvas Y: 1090.088 
     Label X: 16 
     Label Y: 0 
     Downstream: ROUT46 
 
     Route: Modified Puls 
     Routing Curve: Storage-Elevation-Outflow 
     Initial Elevation: 628.5 
     Routing Table in DSS: Yes 
End: 
 
Reservoir: ROUT46 
     Canvas X: 384.597 
     Canvas Y: 1014.149 
     Label X: -23 
     Label Y: -21 
 144
     Downstream: COMB06 
 
     Route: Modified Puls 
     Routing Curve: Storage-Elevation-Outflow 
     Initial Storage: 0 
     Routing Table in DSS: Yes 
End: 
 
Subbasin: TB1001 
     Canvas X: 162.854 
     Canvas Y: 935.172 
     Label X: 16 
     Label Y: 0 
     Area: 0.025 
     Downstream: COMB06 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 85 
 
     Transform: SCS 
     Lag: 11.100 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Subbasin: 183I01 
     Canvas X: 238.794 
     Canvas Y: 1187.290 
     Label X: 16 
     Label Y: 0 
     Area: 0.011 
     Downstream: COMB06 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 85 
 
     Transform: User-Specified UH 
     Unit Hydrograph Name: 183I01 
 
     Baseflow: None 
End: 
 
Junction: COMB06 
     Canvas X: 135.516 
     Canvas Y: 1068.825 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB07 
End: 
 
Junction: COMB07 
     Canvas X: 32.239 
     Canvas Y: 1084.013 
     Label X: -66 
     Label Y: -8 
     Downstream: ROUT47 
End: 
 
Reservoir: ROUT47 
 145
     Canvas X: 83.877 
     Canvas Y: 810.631 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB08 
 
     Route: Modified Puls 
     Routing Curve: Storage-Elevation-Outflow 
     Initial Storage: 0 
     Routing Table in DSS: Yes 
End: 
 
Subbasin: TB705 
     Canvas X: -125.715 
     Canvas Y: 841.007 
     Label X: 16 
     Label Y: 0 
     Area: 0.102 
     Downstream: COMB10 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 83 
 
     Transform: SCS 
     Lag: 12.300 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Subbasin: 183I03 
     Canvas X: -92.302 
     Canvas Y: 698.241 
     Label X: 16 
     Label Y: 0 
     Area: 0.004 
     Downstream: COMB10 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 83 
 
     Transform: User-Specified UH 
     Unit Hydrograph Name: 183I03 
 
     Baseflow: None 
End: 
 
Junction: COMB10 
     Canvas X: 190.192 
     Canvas Y: 755.955 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB08 
End: 
 
Junction: COMB08 
     Canvas X: 193.230 
     Canvas Y: 591.926 
     Label X: 21 
     Label Y: -1 
 146
     Downstream: COMB11 
End: 
 
Subbasin: TB704 
     Canvas X: 354.221 
     Canvas Y: 546.363 
     Label X: 16 
     Label Y: 0 
     Area: 0.046 
     Downstream: COMB11 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 87 
 
     Transform: SCS 
     Lag: 7.740 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Junction: COMB11 
     Canvas X: 211.455 
     Canvas Y: 519.025 
     Label X: -10 
     Label Y: 37 
     Downstream: ROUT48 
End: 
 
Reservoir: ROUT48 
     Canvas X: 214.493 
     Canvas Y: 440.048 
     Label X: 15 
     Label Y: 2 
     Downstream: COMB12 
 
     Route: Modified Puls 
     Routing Curve: Storage-Elevation-Outflow 
     Initial Storage: 0 
     Routing Table in DSS: Yes 
End: 
 
Subbasin: TB702 
     Canvas X: -235.067 
     Canvas Y: 637.490 
     Label X: 16 
     Label Y: 0 
     Area: 0.097 
     Downstream: COMB12 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 86 
 
     Transform: SCS 
     Lag: 9.720 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
 147
Junction: COMB12 
     Canvas X: 223.606 
     Canvas Y: 364.109 
     Label X: 23 
     Label Y: -49 
     Downstream: COMB13 
End: 
 
Subbasin: TB703 
     Canvas X: 10.699 
     Canvas Y: 356.652 
     Label X: 16 
     Label Y: 0 
     Area: 0.052 
     Downstream: COMB13 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 85 
 
     Transform: SCS 
     Lag: 8.220 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Subbasin: 183I04 
     Canvas X: 351.184 
     Canvas Y: 382.334 
     Label X: 16 
     Label Y: 0 
     Area: 0.004 
     Downstream: COMB13 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 85 
 
     Transform: User-Specified UH 
     Unit Hydrograph Name: 183I04 
 
     Baseflow: None 
End: 
 
Junction: COMB13 
     Canvas X: 257.019 
     Canvas Y: 248.681 
     Label X: -10 
     Label Y: 29 
     Downstream: ROUT49 
End: 
 
Reservoir: ROUT49 
     Canvas X: 260.056 
     Canvas Y: 166.667 
     Label X: 16 
     Label Y: 0 
     Downstream: COMB14 
 
     Route: Modified Puls 
     Routing Curve: Storage-Elevation-Outflow 
 148
     Initial Storage: 0 
     Routing Table in DSS: Yes 
End: 
 
Subbasin: TB701 
     Canvas X: 123.366 
     Canvas Y: 187.930 
     Label X: 16 
     Label Y: 0 
     Area: 0.088 
     Downstream: COMB14 
 
     LossRate: SCS 
     Percent Impervious Area: 0.0 
     Curve Number: 86 
 
     Transform: SCS 
     Lag: 8.400 
     Show lag in hours: Yes 
 
     Baseflow: None 
End: 
 
Junction: COMB14 
     Canvas X: 275.244 
     Canvas Y: 90.728 
     Label X: 16 
     Label Y: 0 
End: 
 
Default Attributes:  
     Default Basin Unit System: English 
     Default Meteorology Unit System: SI 
     Default Loss Rate: Initial+Constant 
     Default Transform: Modified Clark 
     Default Baseflow: Recession 
     Default Route: Muskingum 
     Enable Flow Ratio: No 
     Enable Evapotranspiration: No 
     Compute Local Flow At Junctions: No 
     Warning On Delete Component: Yes 
     Warning On Change Method: Yes 
End:  
 
 149
Bibliography 
Anderson, David James. 2000. CRWR Online Report 00-11: GIS-Based 
Hydrologic and Hydraulic Modeling for Floodplain Delineation at 
Highway River Crossings. Center for Research in Water Resources, The 
University of Texas at Austin, Austin, Texas. 
Barrett, Michael. 2000. LCRA/Marble Falls Regional Drainage Feasibility Study. 
Center for Research in Water Resources, Bureau of Engineering Research, 
Austin, Texas. 
Chow, V. T., D. R. Maidment, and L. W. Mays. 1988. Applied Hydrology. 
McGraw-Hill, New York, New York. 
Djokic, D., Z. Ye, and A. Miller. 1997. Efficient Watershed Delineation Using 
ArcView and Spatial Analyst. Proceedings, 17
th
 Annual ESRI User?s 
Conference, San Diego, California. 
Garbrecht, J. and L. W. Martz. 1994.  Grid Size Dependency of Parameters 
Extracted from Digital Elevation Models.  Computers and Geosciences, 
20(1): 85-87.  
Garbrecht, J. and L. W. Martz., 1999a. Digital Elevation Model Issues in Water 
Resources Modeling. In Hydrologic and Hydraulic Modeling Support, ed. 
by D. R. Maidment and D. Djokic, Environmental Systems Research 
Institute,  Redlands, California. 1-27. Internet website: 
http://grl/ars/usda.gov/topaz/esri/paperH.htm. 
Garbrecht, J., L. W. Martz, K. H. Syed, and D. Goodrich. 1999b. Determination 
of Representative Catchment Properties from Digital Elevation Models.  
1999 International Water Resources Engineering Conference, American 
Society of Civil Engineers, Session HY-3, Geographic Information 
Systems (GIS) Applications in Hydrologic Engineering, Seattle, 
Washington.  Published on CD-ROM. Internet Website:  
http://grl.ars.usda.gov/topaz/ASCE99/ASCE99.HTM
Hellweger, F. and D. R. Maidment. 1997. HEC-PREPRO: A GIS Preprocessor 
for Lumped Parameter Hydrologic Modeling Programs. CRWR Online 
Report 97-8. Center for Research in Water Resources,  The University of 
Texas at Austin, Austin, Texas. 
 150
Jennings et. al., 1993.  National Summary of U.S. Geological Survey Regional 
Regression Equations for Estimating Magnitude and Frequency of Floods 
for Unguaged Sites.  Water Resources Investigations Report 94-4002. 
Jones, N. L., S.G., Write, and  D.R, Maidment. 1990. Watershed Delineation with 
Triangle-Based Terrain Models.  Journal of Hydrologic Engineering, 
ASCE, 116(10), 1232-1251. 
Knill, Oliver. 2000.  The Planimeter and the Theorem of Green.  Internet 
Website: http://www.math.harvard.edu/~knill/math21a2000/planimeter/
Kunkle, Paul. 2002.  Kunkel?s Mathematics Lessons: The Planimeter.  Internet 
Website: http://www.nas.com/~kunkel/planimeter/planimeter.htm
Lee, D. T., and B. J. Schacter. 1980. Two Algorithms of Constructing a Delauney 
Triangulation. International Journal of Computer and Information 
Sciences, ASCE, 9(3): 219-242. 
Miller, Scott N., D. Phillip Guertin, Kamram H. Syed, and David C. Goodrich., 
1999.  Using High Resolution Synthetic Aperture Radar for Terrain 
Mapping:  Influences on Hydrologic and Geomorphic Investigation.  1999 
Annual Summer Specialty Conference Proceedings, Science Into Policy:  
Water in the Public Realm/ Wildland Hydrology. Internet Website:  
http://www.awra.org/proceedings/Montana99/Miller1/
Moglen, Glen. and Ginger L. Hartman. 2001. Resolution Effects on Hydrologic 
Modeling Parameters and Peak Discharge.  Journal of Hydrologic 
Engineering.  6 (6):     . 
Nelson, James E.and Norman L. Jones. 1996. Utilizing the ArcInfo Data Model to 
Build Conceptual Models for Environmental/Hydraulic/Hydrologic 
Simulations.  ESRI User?s Conference. 
Nelson, James E., Norman L. Jones and Christopher M. Smemoe. 1997.  From a 
Grid or Coverage to a Hydrograph:  Unlocking Your GIS Data for 
Hydrologic Applications. ESRI User?s Conference, July 1997.   
Published on CD ROM. Internet Website: 
http://www.esri.com/library/userconf/proc97/proc97/to200/pap198/p198.h
tm. 
Nelson, James E., Norman L. Jones, and Russell J. Barrett. 1999a.  Adaptive 
Tessellation Method for Creating TINs from GIS Data. ASCE Journal of 
Hydrologic Engineering, 4(1) 
 151
Nelson, James E., Christopher M. Smemoe, and Bing Zhao. 1999b.  A GIS 
Approach to Watershed Modeling in Maricopa County, Arizona, 
American Society of Civil Engineers, Water Resources Planning and 
Management Conference, June 6-10, 1999, Tempe, AZ. Published on CD 
ROM. http://emrl.byu/chris/documents/asceconf.pdf
Olivera, F. and D. R. Maidment. 1999. GIS-Based System of Hydrologic and 
Hydraulic Applications for Highway Engineering.  Research Report 1738-
6. Center for Transportation Research,The University of Texas at Austin, 
Austin, Texas. 
Stolpa, David. 2001-2002. Personal Interviews. 
Tarboton, D. G. 1997. A New Method for the Determination of Flow Directions 
and Upslope Areas in Grid Digital Elevation Models. Water Resources 
Research, 33(2): 309-319. 
Tarboton, D. G., R. L. Bras, and I. Rodriguez-Itube. 1991. On the Extraction of 
Channel Networks from Digital Elevation Data.  Water Resources 
Research, 5(1): 81-100. 
Texas Department of Transportation (TxDOT). 2001 Hydraulic Design Manual. 
USACOE ? HEC. 2000. HEC-HMS Hydrologic Modeling System: User?s 
Manual. Version 2.0.  Hydrologic Engineering Center, Davis, California. 
United States Geological Survey (USGS).  Digital Raster Graphics (DRG). 1999. 
Internet Webpage: http://mcmcweb.er.usgs.gov/drg/
Watershed Modeling System (WMS) Reference Manual, Version 6.0. 1999.  
Environmental Modeling Research Lab., Brigham Young University.  
 152
  
 
 
 
 
 
 
 
 
 
 153