CRWR Online Report 96-6
MODELING  AGRICHEMICAL  TRANSPORT
IN  MIDWEST  RIVERS  USING
GEOGRAPHIC INFORMATION SYSTEMS
by
Pawel Jerzy Mizgalewicz, Ph.D.
and
David R. Maidment, Ph.D.
Principal Investigator
December 1996
CENTER FOR RESEARCH IN WATER RESOURCES
Bureau of Engineering Research .The University of Texas at Austin
J. J. Pickle Research Campus. Austin, TX 78712-4497
This document is available online via World Wide Web at
http://civil.ce.utexas.edu/centers/crwr/reports/online.html
iii
MODELING  AGRICHEMICAL  TRANSPORT
IN  MIDWEST  RIVERS  USING
GEOGRAPHIC  INFORMATION  SYSTEMS
Publication No. __________
Pawel  Jerzy  Mizgalewicz,  Ph.D.
The University of Texas at Austin, 1996
Supervisor: David  R.  Maidment
A method is proposed for regionalizing watershed scale water quality
estimates. Elementary watersheds are delineated using digital elevation data and linked
to form a river basin scale watershed network. Elementary watersheds are combined
into stream gauge zones for which the only streamflows into and out of a zone are
those measured at the zone boundary by stream gauges. Time series of monthly
streamflow are obtained by an interpolation procedure in which monthly precipitation
over each elementary watershed is converted to streamflow by a runoff coefficient, and
then adjusted  so that the accumulated streamflow over the gauge zone is equal to the
iv
measured outflow. Concentrations of water quality constituents are found from
regression equations in which the mean annual concentration is estimated as a function
of watershed, chemical application and climatic characteristics, and a ratio of expected
monthly to annual concentration is applied. Parameters of these equations were found
for two constituents: nitrate plus nitrite as nitrogen, and atrazine, using data sampled
by the US Geological Survey at 151 sites in the Missouri, Upper Mississippi and Ohio
River basins. Nitrate plus nitrite concentrations show a fairly uniform seasonal pattern
and some dependence on spatial factors; atrazine concentrations show a strong
seasonal pattern with high values in May and June, and little dependence on spatial
factors. Both constituents appear to increase in concentration with discharge to the 0.3
power approximately. An example application of the method is made to the 32,000
km
2
 Iowa-Cedar River basin using elementary watersheds of average area
approximately 30 km
2
.  In this basin, constituent loading estimates determined using
discharge-dependent concentrations appear to be too large when compared with
independent loading estimates, which suggests that the sampled water quality database
may be somewhat biased towards processes occurring during high runoff rather than
baseflow periods. Loading estimates found from discharge-independent concentrations
are more reasonable.
v
TABLE OF CONTENTS
LIST OF TABLES...........................................................................................................................x
LIST OF FIGURES......................................................................................................................xiii
LIST OF PROCEDURES..............................................................................................................xx
1. INTRODUCTION...............................................................................................1
1.1 MOTIVATION........................................................................................................2
1.2 OBJECTIVES.........................................................................................................3
1.3 SCOPE OF STUDY..................................................................................................4
1.4 PROJECT SUMMARY.............................................................................................5
1.5 CONTRIBUTIONS OF STUDY...................................................................................7
2. LITERATURE REVIEW....................................................................................9
2.1 LINKING GIS WITH WATER QUALITY MODELS......................................................9
2.2 GIS MODELS OF WATER QUALITY......................................................................17
2.3 GIS AS A TOOL FOR SPATIAL DATA EXTRACTION..................................................19
2.4 COMPARISON OF THE PROPOSED METHOD WITH PREVIOUS STUDIES......................22
2.4.1 Time domain...............................................................................................22
2.4.2 Spatial domain............................................................................................22
2.4.3 Model formulation......................................................................................23
3. DATA AND COMPUTER SOFTWARE DESCRIPTION..............................25
3.1 DATA SOURCES..................................................................................................25
3.1.1 Herbicide and nutrient data........................................................................26
vi
3.1.2 Digital Terrain Representation...................................................................31
3.1.3 Reach File 1...............................................................................................32
3.1.4 Atrazine and nitrogen fertilizer use.............................................................34
3.1.5 Hydrologic and climatic data......................................................................36
3.1.6 Maps of mean annual precipitation and temperature..................................37
3.2 COMPUTER SOFTWARE DESCRIPTION...................................................................38
3.2.1 GIS software...............................................................................................39
3.2.2 Statistical software......................................................................................40
4. METHODOLOGY............................................................................................41
4.1 REPRESENTATIVE AGRICULTURAL CHEMICALS....................................................43
4.1.1 Nitrate........................................................................................................44
4.1.2 Atrazine......................................................................................................48
4.2 SELECTION OF ANALYSIS REGION AND MAP COORDINATE SYSTEM........................50
4.3 MATHEMATICAL DESCRIPTION............................................................................54
4.3.1 Overview of transport equations.................................................................54
4.3.2 GIS and cascade modeling..........................................................................58
4.3.3 Regression equation development...............................................................61
4.3.4 Agrichemical runoff from the field..............................................................63
4.3.5 Transport in rivers......................................................................................65
4.3.6 Seasonal variations.....................................................................................67
4.3.7 Extracting values of explanatory variables for the regression analysis........71
4.3.8 Application of the regression models..........................................................73
4.4 GIS MODEL DESCRIPTION...................................................................................74
4.4.1 Subdivision of study region into modeling units..........................................74
4.4.2 Unit watershed flow system.........................................................................78
4.4.3 Ordering system of the modeling units........................................................81
4.4.4 Enhancement of the stream delineation process..........................................82
vii
4.5 REDISTRIBUTION OF THE FLOW RECORD OVER UNGAUGED RIVERS.......................85
4.5.1 GIS database of monthly flow rate and the precipitation depth...................85
4.5.2 Average precipitation depth in modeling units............................................88
4.5.3 Mathematical description...........................................................................90
4.5.4 Example of flow redistribution....................................................................95
4.6 EXPONENTIAL DECAY MODEL.............................................................................98
4.6.1 Exponential decay model overview..............................................................99
4.6.2 Travel time approximation........................................................................101
5. PROCEDURES...............................................................................................108
5.1 CONCENTRATION AND FLOW MEASUREMENTS...................................................109
5.2 PREPARING DATA FOR MODEL PARAMETER ESTIMATION....................................113
5.2.1 Preparing 500 m  (15'') DEM for analysis................................................114
5.2.2 Estimation of watershed parameters.........................................................115
5.2.3 Creating grid of sampling sites.................................................................120
5.2.4 Adjusting location of sampling sites..........................................................121
5.2.5 Extracting parameters of the sampled site watersheds...............................124
5.2.6 Agrichemical application..........................................................................126
5.2.7 Annual temperature and annual precipitation depth.................................128
5.3 PREPARING DATA FOR STATISTICAL ANALYSIS...................................................130
5.4 AGRICHEMICAL CONCENTRATIONS IN THE IOWA-CEDAR RIVER   BASIN.............132
5.4.1 Creating a map of the flow direction.........................................................133
5.4.2 Map of the modeling unit outlets...............................................................139
5.4.3 Watershed connectivity.............................................................................143
5.4.4 Refining modeling units............................................................................144
5.4.5 Database of monthly precipitation depth and monthly flow rate................147
5.4.6 Average precipitation depth in modeling units..........................................148
5.4.7 Spatial distribution of flow........................................................................150
viii
5.4.8 Determining input values for the Iowa-Cedar River model........................154
5.5 ARCVIEW MODEL OF AGRICHEMICAL TRANSPORT.............................................154
5.5.1 Model overview.........................................................................................155
5.5.2 Project ?Model?.......................................................................................158
5.5.3 Project ?Results?.....................................................................................163
5.5.4 Project ?Flwprc?......................................................................................168
5.5.5 Project ?Tools?........................................................................................169
6. RESULTS........................................................................................................170
6.1 SEASONAL VARIATION OF AGRICHEMICALS IN THE MIDWEST STREAMS..............171
6.1.1 Seasonal variation of the atrazine concentration.......................................172
6.1.2 Seasonal variation of the nitrate plus nitrite as nitrogen concentration.....177
6.2 AVERAGE ANNUAL AGRICHEMICAL CONCENTRATION IN THE MIDWEST STREAMS180
6.2.1 Average annual atrazine concentration in the Midwest rivers...................183
6.2.2 Average annual nitrate plus nitrite as nitrogen concentration...................188
6.3 ERROR OF MODEL PREDICTIONS........................................................................192
6.4 COMPARISON OF PREDICTED FLOW WITH OBSERVED ONE...................................197
6.5 AGRICHEMICAL CONCENTRATIONS IN THE CEDAR RIVER BASIN.........................202
7. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS..................213
APPENDICES.....................................................................................................223
APPENDIX A C-CODES............................................................................................223
A1 Program newnx.c--reconstructing the flow connectivity between modeling units
after some of units have been removed...............................................................223
A2 Program fdy4.c--calculating the flow rate in ungauged streams from the
available record................................................................................................226
APPENDIX B  AVENUE SCRIPTS...............................................................................232
ix
B1 Changing ArcView projects from the PushButton Bar..................................235
B2 Scripts from the project ?model?.................................................................237
B3 Scripts from the project ?results?.................................................................263
B4 Scripts from the project ?flwprc?.................................................................264
B5 Scripts from the project ?tools?...................................................................279
APPENDIX C ARC/INFO MACROS--AMLS................................................................292
C1 WSHGS.AML...............................................................................................293
C2 NEXTWSH.AML..........................................................................................297
C3 RAININFO.AML..........................................................................................300
C4 RAINMAP.AML...........................................................................................304
C5 RAINM2.AML..............................................................................................307
C6 SELDATA.AML...........................................................................................309
C7 FD4Y.AML...................................................................................................313
C8 SLOPE3.AML..............................................................................................315
C9 DEMALB.AML............................................................................................318
BIBLIOGRAPHY...............................................................................................319
VITA....................................................................................................................339
x
LIST OF TABLES
Table 3.1 Description of atrazine and nitrate plus nitrite as nitrogen samples published
in USGS Open-File Report 94-396, (Scribner, et al., 1994)............................26
Table 3.2 Temporal distribution of atrazine and nitrate plus nitrite as nitrogen samples
from the Midwestern reconnaissance study; USGS Open-File Report 93-
457, (Scribner, et al., 1993)............................................................................29
Table 4.1 An example of PAT--point attribute table of the USGS gauging station
coverage (e.g., item M199001 contains average flow rate in year 1990,
month 01). Full table contains monthly flow record for 38 stations, for
period from 1940 to 1992 in m
3
/s...................................................................88
Table 4.2. Steps of the recorded flow rate redistribution in gauged zone 5465500 for
June 1990......................................................................................................97
Table 5.1 Summary statistics of the nitrite plus nitrate and atrazine data sets................113
Table 5.2 Selected statistics of watershed parameters determined from DEM. Length
of the flow path used to calculate E
S
 is  in 100 km........................................125
Table 5.3 Summary statistics of annual application of nitrogen fertilizer and atrazine....127
Table 5.4 Description of tables atra7 and nitr7.............................................................130
Table 5.5 Polygon Attribute Table of the cruse coverage..............................................160
Table 5.6 Polygon Attribute Table of the crwsd coverage............................................160
Table 5.7 Fields of the file model2a.dbf (model specification).......................................161
Table 6.1 Selected coefficients of the regression analysis of the atrazine concentration
in the Midwest rivers. Seasonal variation is explained only by the sine-
cosine harmonics. Coefficients related to the dummy variables are not
shown........................................................................................................173
xi
Table 6.2 Selected coefficients of the regression analysis of the atrazine concentration
in the Midwest rivers. Seasonal variation is explained by the sine-cosine
harmonics and by the flow rate. Coefficients related to the dummy variables
are not shown.............................................................................................174
Table 6.3 Seasonal factors of atrazine concentrations in the Midwest rivers estimated
by the regression analysis with and without flow rate record.......................175
Table 6.4 Selected coefficients of the regression analysis of the nitrate concentration in
the Midwest rivers. Seasonal variation is explained only by the sine-cosine
harmonics...................................................................................................177
Table 6.5 Selected coefficients of the regression analysis of the nitrate concentration in
the Midwest rivers. Seasonal variations are explained by the sine-cosine
harmonics as well as the flow record. Coefficients related to the dummy
variables are not shown..............................................................................178
Table 6.6 Seasonal factors of the nitrate plus nitrite as nitrogen concentrations in the
Midwest rivers estimated by the regression analysis with and without flow
rate.............................................................................................................179
Table 6.7 Explanatory variables used to in the analysis of the deseasonalized atrazine
and nitrate plus nitrite as nitrogen concentrations in the Midwest rivers......182
Table 6.8 Results of the stepwise regression analysis of average annual atrazine
concentration in the Midwest rivers (Data = atrazine concentration with
removed seasonal component)....................................................................184
Table 6.9 Results of the regression analysis of average annual atrazine concentrations
in the Midwest rivers (Data = atrazine concentration with removed
component explained by the seasonal factor and the flow rate)....................186
Table 6.10 Quartiles of the explanatory variables selected by the regression analysis of
the deseasonalized agrichemical concentrations...........................................186
xii
Table 6.11 Results of the regression analysis of average annual nitrate plus nitrite as
nitrogen concentrations in the Midwest rivers (Data = nitrate concentration
with removed seasonal component)............................................................188
Table 6.12 Results of the regression analysis of average annual nitrate concentrations
in the Midwest rivers (Data = nitrate plus nitrite as nitrogen concentrations
with removed component explained by the seasonal factor and the flow
rate)...........................................................................................................190
Table 6.13. Mean Standard Errors for the atrazine concentration models (?g/L)..........192
Table 6.14. Mean Standard Errors for the nitrate plus nitrite as nitrogen concentration
models (mg/L)............................................................................................194
Table 6.15 Comparison of predicted and observed flow rate (m
3
/s) for three USGS
gauging stations..........................................................................................197
Table 6.16 Atrazine concentration, load and the flow rate in modeling units that
represent the confluence of the Iowa River with the Cedar River estimated
for June 1990.............................................................................................207
Table 6.17 Relation of the atrazine application to the atrazine load in two Iowa rivers:
the Cedar River at Palisades and the Old Mans Creek at Iowa City (
Chemical application for year 1989, flow data for 1990).............................208
Table 6.18 Relation of the nitrogen fertilizer application to the nitrate plus nitrite as
nitrogen load in two Iowa rivers: the Cedar River at Palisades and the Old
Mans Creek at Iowa City ( Chemical application and flow rate represent
year 1990)..................................................................................................211
xiii
LIST OF FIGURES
Figure 3.1 Location of sampling sites for study of atrazine and nitrate plus nitrite as
nitrogen concentrations in storm runoff; USGS Open-File Report 94-396,
(Scribner, et al., 1994)..................................................................................27
Figure 3.2 Atrazine Concentrations in Old Mans Creek, Iowa (data from USGS Open-
File Report 94-396, Scribner et al., 1994).....................................................28
Figure 3.3 Watersheds sampled during 1989 and 1990 for the USGS reconnaissance
study (Battaglin, 1995).................................................................................30
Figure 3.4 A Digital Elevation Model of the Iowa-Cedar River basin, vertical scale
enlarged 500 times. The white line represents the basin boundaries...............32
Figure 3.5 The Cedar River above Waterloo, IA; rivers selected from Reach File 1........33
Figure 3.6 Atrazine use in the Mississippi-Missouri and Ohio River basins in 1989
(from Battaglin and Goolsby, 1995b)............................................................35
Figure 3.7 Mean annual temperature [?C] in the Mississippi-Missouri and Ohio River
basins by NOAA climate division (USGS, 1991)...........................................37
Figure 3.8 Annual precipitation [mm] in the Mississippi-Missouri and Ohio River
basins by NOAA climate division (USGS, 1991)...........................................38
Figure 4.1 Methodology of the large scale modeling of agrichemical concentrations in
the Midwest rivers......................................................................................42
Figure 4.2 The Mississippi-Missouri and Ohio River Basins...........................................51
Figure 4.3 The Iowa River with tributaries and the USGS gauging stations....................52
Figure 4.4 Reactions and transfers in a natural water system (after O?Connor, et al.,
1983; Thomann and Mueller, 1987; O?Connor, 1988a, b; University of
Mississippi, 1990).......................................................................................57
xiv
Figure 4.5 Example of the cascade modeling within the GIS...........................................60
Figure 4.6 Nitrate plus nitrite as nitrogen concentrations measured in the Sangamon
River at Monticello, Illinois, in May 1990 (Scribner, et al., 1994)................71
Figure 4.7 Example of a grid of spatially distributed values of explanatory variables.......72
Figure 4.8 Example of watershed outlets: (1) beginning of the river, (2) stream
junction, and (3) gauging station.................................................................75
Figure 4.9 Comparison of the frequency of modeling unit area subdivided using
different sets of watershed outlets...............................................................76
Figure 4.10 Division of the Iowa-Cedar River into modeling units using different
threshold drainage areas: 25 km
2
, 400 km
2
, and 2500 km
2
...........................77
Figure 4.11 An example of the flow topology of the unit watersheds; (x,y), x is the unit
ID, y is the ID of downstream to x unit.......................................................78
Figure 4.12 Flow system in the Iowa-Cedar River basin subdivided into modeling units
of different sizes (threshold drainage area: 25 km
2
, 400 km
2
, and 2500
km
2
)............................................................................................................80
Figure 4.13 Comparison of the stream ordering systems: (a) Strahler, (b) Shreve, and
(c) utilized in the agrichemical transport model............................................82
Figure 4.14 The Iowa-Cedar River basin: subwatersheds and selected USGS gauging
stations (numbers represent station ID).......................................................86
Figure 4.15 Weather stations applied to analysis of the hydrologic conditions in the
Iowa-Cedar River watershed.......................................................................87
Figure 4.16 Spatial distribution of monthly precipitation depth [mm/d] in the Iowa-
Cedar River watershed in June 1990............................................................89
Figure 4.17 Cedar River watershed above Charles City, Iowa: An example of gauging
station zones and modeling units.................................................................90
Figure 4.18 Location of the gauged zone 5465500, its subdivision into modeling units,
and the USGS gauging stations...................................................................96
xv
Figure 4.19 Example of time series recorded in gauging stations located along the
Cedar River. The data are for the water year 1990. The logarithmic scale
is used to show all time series in one picture..............................................101
Figure 4.20 Flow path and location of gauging stations which have been used to
illustrate the potential method for time of travel estimation........................102
Figure 4.21 Cross-correlation coefficients: the strength of the linear relationship
between the flow rate in the Cedar River recorded near Conesville, IA,
and the flow rate recorded at indicated locations. All gauging stations are
on one flow path (shown in Figure 4.20)...................................................103
Figure 4.22 Analysis of travel time and flow velocity:  a) cumulative travel time versus
cumulative flow distance;  b) travel time vs. flow distance;  c) velocity vs.
square root of stream slope.......................................................................104
Figure 4.23 Estimation of the ?travel time? for major reaches of the Iowa River and
the Cedar River, IA...................................................................................106
Figure 4.24 Comparison of the velocity from the RF1 database  with the velocity
estimated from a correlation analysis of the flow record in the Iowa River
and tributaries...........................................................................................107
Figure 5.1 Relationship between atrazine ELISA concentration and concentration by
GC/MS estimated from data published in the USGS Open File Report 93-
457...........................................................................................................110
Figure 5.2 Relationship between atrazine ELISA concentration and concentration by
GC/MS estimated by a different authors:  (1) Thurman et al. (1992);
(2) Goolsby et al. (1993) data gathered in 1990;  (3) Goolsby et al. (1993)
data gathered in 1991;   (4) Moody and Goolsby (1993), and  (5) relation
estimated in this study utilizing data from USGS open file report 93-457...112
Figure 5.3 Example of the sampling site (from Battaglin 1995) that is located neither
on the stream from RF1 nor on the stream delineated from the DEM.........121
xvi
Figure 5.4 Sampled watersheds delineated from the 500 m DEM.................................124
Figure 5.5 1? quadrangles of DEM utilized to subdivide the Iowa-Cedar River basin
into modeling units; Map projection: geographic.......................................134
Figure 5.6 Comparison of the stream network delineated from 100 m DEM (a) with
the one delineated from 500 m DEM (b). Both DEMs were adjusted for
RF1 stream network..................................................................................138
Figure 5.7 Selected types of the modeling unit outlets (a) type 1, beginning of the
stream network; (b) type 2, upstream cell of the stream junction; (c) type
3, USGS gauging station...........................................................................139
Figure 5.8 The Iowa-Cedar River basin subdivided into 1032 unit drainage areas of
average area 31.6 km
2
...............................................................................146
Figure 5.9 Runoff (flow in rivers) that occurred in June 1990 in the Iowa-Cedar River
watershed.................................................................................................153
Figure 5.10 An example of the Graphical User Interface: a window for the selection of
the agrichemical application rate in selected counties.................................156
Figure 5.11 Atrazine concentrations along the Cedar River estimated for 1990 (left)
and flow rate along the Cedar River in June 1990 (right)...........................157
Figure 5.12 ?Bar chart? map of the atrazine concentrations estimated for 1990
(preliminary results)-- an example map created within the ArcView project
?Results? (g/m3 = mg/L)...........................................................................164
Figure 5.13 Atrazine concentrations in the Cedar River basin introductory estimated
for May 1990 -- a map created within the ArcView project ?Results?
(g/m3 = mg/L)..........................................................................................165
Figure 5.14 Inconsistency in the assigning IDs to the vectorized grid streams. The
GRID function gridline assigned wrong IDs to the Cedar River
downstream to the junction with the Iowa River........................................166
xvii
Figure 5.15 Flow rate in the Cedar River and tributaries that occurred in June 1990.
The map has been created by linking the polygon attribute table of
interpolated flow measurements by modeling unit with the arc attribute
table of a stream coverage.........................................................................167
Figure 5.16 Monthly flow rate in the lower Cedar River in 1989-1991. Example of
visual tools of ArcView project ?Flwprc? for hydrologic analysis..............168
Figure 6.1 Seasonal factors of atrazine concentrations in the Midwest rivers estimated
by the regression analysis with and without flow rate record......................176
Figure 6.2 Seasonal factors of the nitrate plus nitrite as nitrogen concentrations in the
Midwest rivers estimated by the regression analysis with and without flow
rate included as an explanatory variable.....................................................180
Figure 6.3 Influence of the explanatory variables on the average atrazine concentration
(?g/L). Model without the flow rate (Table 6.7)........................................187
Figure 6.4 Influence of the explanatory variables on the average atrazine concentration
(?g/L). Model with the flow rate (Table 6.8).............................................187
Figure 6.5 Influence of the explanatory variables on the average nitrate plus nitrite as
nitrogen concentration (mg/L). Model without the flow rate (Table 6.11)..191
Figure 6.6 Influence of the explanatory variables on the average atrazine concentration
(mg/L). Model with the flow rate (Table 6.12)..........................................191
Figure 6.7 Difference between measured atrazine concentrations and predicted
concentrations in the Midwest rivers: a) model without the flow rate; b)
model with flow rate included as an explanatory variable...........................193
Figure 6.8 Difference between measured nitrate concentrations and predicted
concentrations in the Midwest rivers: a) model without the flow rate; b)
model with flow rate included as an explanatory variable...........................195
xviii
Figure 6.9 Observed vs. predicted agrichemical concentrations in the Midwest rivers
(model with the flow rate): a) atrazine in ?g/L;   b) nitrate plus nitrite as
nitrogen in mg/L.......................................................................................196
Figure 6.10 Location of the USGS gauging stations to verify method of spatial
redistribution of the observed flow rate.....................................................198
Figure 6.11 Observed and predicted flow rate in selected streams of the Cedar River
basin.........................................................................................................199
Figure 6.12 Spatial distribution of the surface water balance for the modeling units.
Estimated from recorded flow rate, precipitation depth and selected unit
features, the Iowa-Cedar River basin, June 1990.......................................201
Figure 6.13 Comparison of the predicted and observed concentrations of nitrate plus
nitrite as nitrogen in the Cedar River at Palisades, Iowa and the Old Mans
Creek at Iowa City, Iowa, in 1990.............................................................203
Figure 6.14 Comparison of the predicted atrazine concentrations in the Cedar River at
Palisades, Iowa and the Old Mans Creek at Iowa City, Iowa, in 1989 with
the observed concentrations in 1990..........................................................204
Figure 6.15 Profiles of the predicted atrazine concentrations in the Cedar River for
June 1989 and the annual atrazine application (based on the results of the
ArcView model).......................................................................................205
Figure 6.16 Predicted atrazine concentrations (mg/m3 = ?g/L) at the Iowa River and
the Cedar River junction (June 1990)........................................................206
Figure 6.17 Estimated monthly fractions of the annual atrazine load in the Cedar River
at Palisades and the Old Mans Creek near Iowa City, Iowa for year 1990..209
Figure 6.18 Estimated atrazine load in the rivers of the Iowa-Cedar Basin in June
1990.........................................................................................................210
Figure 6.19 Estimated monthly fractions of the annual nitrate load in the Cedar River
at Palisades and the Old Mans Creek near Iowa City, Iowa for year 1990..212
xix
LIST OF PROCEDURES
Listing 5.1 Creating depressionless DEM, calculating drainage area and  delineation of
the stream network...................................................................................115
Listing 5.2 Slope along the flow path...........................................................................116
Listing 5.3 Average slope of the stream network..........................................................117
Listing 5.4 Exponentially decaying flow length.............................................................118
Listing 5.5 Average distance from field to a stream......................................................119
Listing 5.6 Average land slope.....................................................................................119
Listing 5.7 GRID dialog supporting adjustment of sampling sites location....................123
Listing 5.8 Extracting parameters of the sampled site watersheds.................................125
Listing 5.9 Chemical application in sampled watersheds...............................................127
Listing 5.10 Average climatic parameters.....................................................................128
Listing 5.11 Creating a summary Info table of climatic parameters...............................129
Listing 5.12 Selecting type 1 watershed outlets............................................................140
Listing 5.13 Selecting type 2 watershed outlets............................................................141
Listing 5.14 Creating point coverage of gauging stations from latitude-longitude
coordinates...............................................................................................141
Listing 5.15 Fragment of the file latlonfl.cvs containing station IDs and  coordinates....141
Listing 5.16 Projecting the point coverage of USGS gauging stations from Geographic
system into Albers coordinates..................................................................142
Listing 5.17 Identification of the downstream watershed ID.........................................143
Listing 5.18 Eliminating drainage units that are smaller than 1 km
2
...............................144
Listing 5.19 Estimation of the average precipitation depth in modeling units................148
xx
Listing 5.20 Application of the &DO command to repeat action for each month of the
selected time period..................................................................................149
Listing 5.21 Example of the AML that selects precipitation stations that have a
complete record in June, 1996 and creates the grid of precipitation depth
(adopted from RAINMAP.AML)..............................................................150
Listing 5.22 Example of the Arc/Info macro that prepares data and estimates the flow
rate in modeling units (adopted from fd4y.aml, Appendix C7)...................152
Listing 6.1 The S-plus session for estimation of the model of seasonal atrazine
variation. Model does not contain the flow rate component........................172
Listing 6.2 The S-plus session for estimation of the model of seasonal atrazine
variation. Model contains the flow rate component.....................................173
Listing 6.3 The S-plus session for estimation of the model of seasonal nitrate variation.
Model does not contain the flow rate component........................................177
Listing 6.4 The S-plus specification of the seasonal nitrate model. The model contains
the flow rate component.............................................................................178
1. INTRODUCTION
This research is focused on the transport of nutrients and herbicides in surface
waters of the Midwestern United States and it examines the extent to which
Geographic Information System (GIS) technology can be used to automate and
improve the computation of spatio-temporal distribution of selected agricultural
chemicals. Up to now, there have been elaborate flow models and pollutant transport
models in use at the watershed scale. The application of the most widely used
deterministic models such as ANSWERS or SWRRB is limited to agricultural basins
of about 200 km
2
 and 800 km
2
 respectively. An extended version of SWRRB, SWAT
model, has been applied to study the hydrology and crop conditions for the
conterminous U.S. Deterministic models focus mainly on the detailed description of
small-scale physical phenomena and they require huge computer and data resources if
implemented on the scale considered here. In the light of the existing projects, the aim
of this project is to develop a procedure of estimating the distribution of agricultural
chemicals over a region which size is limited only by data availability.
This work proposes a statistical-GIS methodology of determining the amount
of selected agrichemicals (nitrate plus nitrite as nitrogen and atrazine) in the rivers of
the Upper Mississippi-Missouri River and the Ohio River basins, which have a total
drainage area about 2.4*10
6
 km
2
 (data used for model parameter calculations were
collected in sites scattered over this region). Since the agrichemical transport model
requires spatially distributed flow, a technique of spatial redistribution of the discharge
recorded in USGS gauging stations, as well as the application of an agrichemical
transport model is presented here for the Iowa -Cedar River watershed, Iowa and
Minnesota, which has an area of about 32,000 km
2
.
2
1.1 Motivation
It is commonly known that agricultural activity endangers the quality of surface
waters. Farmers apply chemical nutrients to increase soil fertility and use pesticides to
control unwanted plants and destructive insects. About 60 percent of pesticides
(Gianessi and Puffer, 1990) and nitrogen fertilizers (Kolpin, et al., 1991; US
Environmental Protection Agency, 1990) used in the USA are applied to cropland in
twelve Midcontinental States (Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota,
Missouri, Nebraska, North Dakota, Ohio, South Dakota, Wisconsin). Four major
herbicides: alachlor, atrazine, cyanazine, and metolachlor, account for about 73
percent of the pesticides applied (Gianessi and Puffer, 1990).
Numerous studies have been performed on a small watershed scale. But until
recently, few studies have been conducted to evaluate the contamination of rivers in
the Upper Mississippi-Missouri and Ohio River basins.
In 1990, the United States Department of Agriculture (USDA) initiated a
Management System Evaluation Areas (MSEA) program. The major purpose of this
program is to determine the influence of agricultural practices on water quality in the
Midwest and to identify management systems that protect water quality. Ten study
areas were established to gather data for a better understanding of the factors and
processes that control the fate and transport of agricultural chemicals (Hatfield, et al.,
1993). Also, the United States Geological Survey (USGS) conducts observational
studies to determine the distribution, transport and persistence of selected herbicides,
insecticides, and inorganic nutrients in the Mississippi River and its tributaries
(Battaglin, et al., 1993).
3
The Geographic Information System (GIS) offers a unique technology to
formulate more objective and consistent methods to synthesize collected data and to
assess water quality over large areas (Maidment, 1996). This work explores the
applicability of GIS technology to regionalize to large basins the results of small
watershed scale water quality studies, and to evaluate the temporal and spatial
distribution of the loads and concentrations of selected agricultural chemicals in the
surface waters of the Upper Mississippi-Missouri and Ohio River basins.
1.2 Objectives
The general objective of this research is regionalization of watershed scale
measurements. This general objective can be divided into the following goals:
1) To formulate statistical models capable of representing the spatio-temporal
variability of agricultural chemicals in surface waters;
2) To evaluate the applicability of the GIS technology for deriving stream and
watershed characteristics that influence chemical transport processes;
3) To develop a methodology for calculating time series of monthly average
flow rate in ungauged streams;
4) To build a model for predicting concentrations and loads under different
hydrologic conditions and for different agricultural chemical application
rates than those historically observed.
4
1.3 Scope of Study
The following restrictions define the scope of this research:
1) The analysis is limited to two selected agrichemicals - the nutrient, nitrate plus
nitrite as nitrogen, and the herbicide, atrazine. These two chemicals were
chosen because they are representative of nutrients and herbicides,
respectively, and because they are present in measurable quantities in many
Midwest streams and rivers. Although the research is performed for only two
agrichemicals, a similar procedure could be used for other herbicides and
nutrients.
2) Since the model is constructed using GIS technology, and since the available
data are limited, the concentrations and loads of agricultural chemicals in
surface waters are described by regression equations, which have limited
application for making predictions.
3) Observed loads and concentrations as well as chemical application rates are
derived from data published in USGS reports.  Watershed and stream
parameters are derived from a Digital Elevation Model that is available on
Internet. Flow rate and the precipitation data are extracted from CD-ROMs
(Compact Disk Read Only Memory) published by Hydrosphere Inc.
4) Although the regression equations are estimated from data gathered at 151
sampling sites located in eleven Midcontinental States (Illinois, Indiana, Iowa,
Kansas, Michigan, Minnesota, Missouri, Nebraska, Ohio, South Dakota,
Wisconsin), the complete GIS model is developed only for the Iowa-Cedar
River basin, Iowa.
5
5) Model formulation and model parameter estimation are constrained by the
available computer resources (SUN Sparc Station IPX and Sun Ultra).
1.4 Project Summary
This research can be divided into the following steps:
1) Preparation of measurement data for statistical analysis. This step involves data
entry from printed USGS reports, filling in missing values and data correction,
and conversion of data into common units.
2) Development of the general forms of equations that can explain spatial and
temporal variation of the chemical concentration and load in the Upper
Mississippi - Missouri River, the Ohio River and their tributaries.
3) For each watershed associated with a measurement point, determining the
drainage-basin morphometry, climatic characteristics, and chemical application
rate.  A 15-second (500 m resolution) digital elevation model is utilized in the
following steps:
-  delineation of the stream network from the digital elevation model (DEM);
-  location of stations in which the water samples were collected on the
    delineated river network;
-  estimation of the drainage area associated to each measurement point;
-  calculating parameters that characterize this drainage area;
-  evaluating the watershed average annual precipitation as well as the
    average annual temperature; and
-  calculating watershed-averaged chemical application rate.
6
4) Preliminary analysis of the spatio-temporal distribution of the constituent
concentrations in the Mississippi-Missouri and Ohio River basins. This step
includes development of the regression equations that relate measured
agricultural chemical concentrations at a given point to such explanatory
variables as the annual agricultural chemical application and the flow rate.
5) Formulation and application of the methodology for estimation of monthly
flow rate in ungauged streams. This methodology is utilized for a selected
watershed, i.e., the Iowa-Cedar River basin. The 3 arc-second (100 m
resolution) DEM is chosen as a base map for determining the flow direction
and for subdivision of the Iowa-Cedar watershed into small drainage units
(mostly 20 - 50 km
2
). This step is based on the following:
-  constructing a spatio-temporal database of monthly average flow rate and
    monthly average precipitation rate for period from 1960 to 1992;
-  dividing the Iowa-Cedar River into small drainage units, converting resulting
    map from raster into vector format, and building ?flow? topology among the
    drainage units;
-  interpolating or extrapolating recorded flow rate over ungauged drainage
    units using precipitation, estimated flow rate, an average runoff
    coefficient, and drainage area as input to an estimating equation.
6) Estimation of the spatio-temporal distribution of the agricultural chemical
concentration and load. In this step the flow rate identified in step 5 is applied
in the regression equation developed in step 4.
7
1.5 Contributions of Study
This research has the following contributions to the knowledge:
1) The development of a method for application of the GIS technology to
determine factors that influence the process of mobilization and transport of
agricultural chemicals over a very large region;
2) The estimation of the general temporal (monthly) pattern of the average
atrazine and nitrate concentrations in the Upper Mississippi-Missouri and Ohio
River basins;
3) The application of the GIS technology to store time series of recorded monthly
flow rate and precipitation depth (creation of a spatio-temporal database);
4) The development of a spatial analysis routine for estimating monthly time
series of expected flow rate in ungauged streams;
5) The formulation of a GIS spatial model from which concentrations as well as
loads of nitrate plus nitrite and atrazine in streams can be calculated for
different hydrologic scenarios.
In addition to the contributions listed above, during this research a set of new
GIS tools supporting hydrologic modeling has been developed. The following
procedures have been constructed:
1) Automated watershed division into hydrologic sub-units;
2) Improvement of the major flow paths delineated from a digital elevation model
(DEM), and therefore enhancement of the delineated stream network and
8
watershed boundaries by burning in a mapped stream network to the digital
elevation model.
3) Calculation of a new stream order system to describe the topologic
characteristics of a stream network similar to the Shreve or Strahler ordering
methods, that makes flow and transport calculations very efficient; and
4) Building in ArcView hydrologic modeling tools that do not exist in ArcView
for flowaccumulation--accumulating an entity when traveling downstream,
determining drainage area upstream of a given location, and identification of
transport paths.
9
2. LITERATURE REVIEW
This chapter emphasizes research that is focused on GIS applications for
agricultural non-point source pollution modeling. Models that include nutrients or
pesticides are presented. Soil erosion and sediment transport applications are also
mentioned here for completeness of the discussion.
The application of the GIS in modeling non-point source pollution can be
grouped into three categories:
1)  Existing pollution models that are linked with GIS software;
2)  Pollutant transport is modeled entirely within the GIS;
3)  GIS is utilized to extract spatial data required for analysis of non-point source
pollution;
2.1 Linking GIS with Water Quality Models
Water quality models linked with GIS programs are the dominant approach in
modeling non-point source pollution. The GIS provides the data required for the
model, then the model is executed. After calculations, the GIS is used for visual
analysis of results. The most popular pollution model that is linked with GIS software
is AGNPS (Agricultural Non-Point-Source) developed by Agricultural Research
Service (ARS). The model source code is available through the WEB site:
http://www.infolink.morris.mn.us/ars/download.html.
10
AGNPS
AGNPS is an event-based distributed parameter model, that is, it computes
flow and pollutant loadings for a single rainfall event. It calculates runoff from
agricultural watershed and transport processes of sediment, nitrogen, phosphorous,
and COD (Chemical Oxygen Demand). The watershed is represented by square cells
of 0.4 - 16 ha (1 - 40 acres). Each cell is characterized by twenty-two parameters that
include: SCS curve number, terrain description, channel parameters, soil-loss equation
data, fertilization level, soil texture, channel and point source indicators, and an
oxygen demand factor. Sediment runoff is estimated from the modified version of
USLE (Universal Soil Loss Equation) and its routing is performed for five particle size
classes. Calculations of nutrient transport are divided into soluble and sediment-
absorbed phases. Due to the large amount of input data required, the application of
AGNPS is limited to watersheds not larger than 200 km
2
 (Young, et al., 1989;
DeVries and Hromadka, 1993; Engel, et al., 1993). However, it has been applied to
larger basins, by representing the study area by a grid of cells larger than 16 ha. For
example, Morse, et al., (1994) applied AGNPS with 100 ha cells to estimate
concentrations in a 1645 km
2
 watershed.
At least three interfaces between AGNPS and GRASS (Geographical
Resources Analysis Support System) have been constructed: (1) at Michigan State
University (He, et al., 1993), (2) by Srinivasan and Engel (Engel, et al., 1993a; Engel,
et al., 1993b; Engel 1996; Mitchell, et al., 1993a; Mitchell, et al., 1993b),  and (3) by
the Soil Conservation Service as a watershed planning tool in the Hydrologic Unit
Water Quality Project (HUWQ) (Cronshey, et al., 1993; Geter, et al., 1995; Drungil,
et al., 1995).
11
GRASS is the major public domain GIS that supports a raster data structure
with data conversion from vector  data. It performs the basic GIS functions of data
input, storage, manipulation, analysis, and display (Drungil, et al., 1995). Access to the
source code of GRASS provides the flexibility to modify existing GRASS procedures
or to add new ones. GRASS has a considerable ability to support hydrologic analysis.
AGNPS has also been linked with Arc/Info GIS. Jankowski and Haddock
(1993) coupled AGNPS with PC-Arc/Info, a vector based GIS. The interface was
constructed using Arc/Info macro language (SML), Pascal language, and batch
programming. Vieux and Needham (1993) studied the AGNPS model sensitivity to
grid-cell size. They used Arc/Info to generate AGNPS input files and to display model
output.  They demonstrated that the variation of channel erosion, sediment yield, and
delivery ratio due to the cell size selection may introduce unacceptable errors or
erroneous conclusions when analyzing nonpoint pollution using AGNPS.
Morse, et al., (1994) integrated AGNPS, Arc/Info and Oracle, a database
system to estimate the nitrogen, phosphorus and COD concentrations for different
management scenarios in the Bedford-Ouse catchment, UK. They represented the
1645 km
2
 watershed by square cells of 100 ha (1 km * 1 km). Another AGNPS-
Arc/Info integrated system was constructed by Tim and Jolly (1994) to evaluate
effectiveness of several alternative management strategies in reducing sediment
pollution in a 417 ha watershed located in southern Iowa.
AGNPS has also been linked to other GIS programs, such as: ERDAS (Earth
Resources Data Analysis System), a grid cell-based system (Evans and Miller, 1988),
Geo/SQL, a vector-based GIS (Yoon, et al., 1993), and IDRISI, a raster based GIS
(Klaghofer, et al., 1993). This last interface has been used to evaluate erosion and
sediment yields in a lower alpine drainage basin of area of 65 ha (located in Austria).
The interface contained EPIC (Erosion/Productivity Impact Calculator, Williams, et
al., 1990) a field scale comprehensive model developed to predict the long-term
12
relationship between erosion and productivity. EPIC?s components include weather
simulation, hydrology, erosion-sedimentation, nutrient cycling, plant growth, tillage,
soil temperature, economics, and plant environment control.
SWRRB
Cronshey, et al., (1993) describe an interface that combines GRASS and a
watershed scale water quality model SWRRB (Simulator for Water Resources in Rural
Basins). SWRRB (Arnold, et al., 1990) uses a daily time step for calculations of
sediment yield, flow routing, as well as pesticide and nutrient fate and transport
studies. Basins are subdivided to account for differences in soils, land use, crops,
topography, and weather. The soil profile can be divided vertically into ten layers.
Basins of several hundred square miles can be studied, but the number of sub-basins is
limited to 10. The hydrology component is based on a daily water balance equation
that includes rainfall, runoff, evapotranspiration, percolation, and return flow. Rainfall
intensity hyetographs are calculated by using a modified rational method. The Soil
Conservation Service curve number technique is used to estimate runoff volume. The
evapotranspiration component requires such data as daily solar radiation, mean air
temperature, crop cover and snow cover. Daily precipitation as well as air
temperatures and solar radiation can be supplied as model input or they can be
simulated by a SWRRB weather generator. Sediment yield is computed for each sub-
basin by using the Modified Universal Soil Loss Equation. SWRRB is physically based
and is intended to be used for situations in which calibration data are not available
(DeVries and Hromadka, 1993; Donigian and Huber, 1991).
13
SWAT-QUAL2E
SWAT (Soil and Water Assessment Tool) is an extended version of the
SWWRB model ( Arnold, et al., 1993). It has been linked with GRASS (Srinivasan
and Arnold, 1994; Engel, et al., 1993) and with Arc/Info (Bian, et al., 1996).
The major components of SWAT are similar to SWWRB modules, which
include weather, hydrology, erosion, soil temperature, crop growth, nutrients,
pesticides, subsurface flow, and agricultural management. The model operates on a
daily time step and is capable of simulating 100 or more years. The restriction of only
being able to simulate 10 subbasins, in the case of SWRRB, has been removed in
SWAT. The watershed can be divided into a practically unlimited number of cells
and/or subwatersheds. In addition, each subbasin can be discretized into virtual areas
that have a unique soil and land use combination. The hydrologic response is
generated in each virtual area. The output of the subbasin is calculated as a weighted
average of the virtual area hydrologic responses. The new features of SWAT include:
routing of the flow through the basin streams and reservoirs, simulating lateral flow,
groundwater flow, stream routing transmission losses, and modeling sediment and
chemical transport through ponds, reservoirs, and streams (Mamillapalli, 1996).
The SWAT-GRASS model has been applied for small scale modeling as well
as for continental scale hydrologic modeling. For example, Jacobson, et al., (1995)
evaluated the water quality impacts of the diverse crops and management practices in a
4.6 km
2
 subwatershed of the Herrings Marsh Run Watershed in the North Carolina
Coastal Plains. On the other scale extreme, Srinivasan, et al., (1995) applied the
SWAT-GRASS interface and such data as a map of soils (STATSGO), map of land
use (USGS LULC) and a DEM to estimate the following features for the entire U.S.:
- average annual rainfall;
14
- average annual total water yield;
- average annual actual evapotranspiration (plant ET was calculated as a function
of leaf area, root depth, and irrigation);
- average annual Penman-Montieth potential evapotranspiration; and
- annual grain yield and biomass production.
The U.S. was divided into 78,863 STATSGO polygons for this analysis.
In 1996 the QUAL2E (Enhanced Stream Water Quality Model) water quality
component was incorporated into SWAT to simulate instream dynamics. The first-
order decay relationships for algae, dissolved oxygen, carbonaceous biochemical
oxygen demand, organic nitrogen, ammonium nitrogen, nitrate nitrogen, nitrite
nitrogen, organic phosphorus, and soluble phosphorus used in QUALE2E were
adopted in SWAT with various adjustments (Ramanarayanan, et al., 1996).
QUAL2E model uses a finite-difference solution of the advective-dispersive
mass transport, reaction, and sink/source equation. The stream network is divided into
headwaters, reaches, and junctions. The changes in flow conditions are represented as
a series of steady- flow water profiles. Such parameters as velocity, cross-sectional
area, and water depth that are required for the mass transport calculations are
computed from the flow rate. For each river reach, QUAL2E requires specification of
as many as 26 physical, chemical, and biological parameters. (DeVries and Hromadka,
1993; Camara and Randal, 1984; Schoellhamer, 1988). Compiling such data at a
regional scale would take a very great investment of time and resources.
15
ANSWERS
Rewerts and Engel (1991; Engel, 1993; Engel, 1996) integrated the GRASS
GIS with ANSWERS (Aerial Nonpoint Source Watershed Environment Response
Simulation). ANSWERS (Beasley, et al., 1982) calculates runoff, erosion,
sedimentation and phosphorus movement from watersheds. The watershed is divided
into a grid of square cells. For each cell the following parameters are defined: slope,
aspect, soil porosity, moisture content, field capacity, infiltration capacity, USLE
erodibility factor, crop and management factors. A channel is described by width and
roughness. Runoff, erosion, sedimentation, and water quality related to sediment
associated chemicals (for example, dissolved and sediment-bound ammonium,
sediment bound total Kjeldahl nitrogen, and dissolved and sediment-bound
phosphorus) are computed for each cell and routed (Beasley and Huggins, 1991;
Donigian and Huber, 1991).
Typical cell sizes range from 0.4 to 4 ha with smaller cells providing more
accurate simulations. During rainfall events the time step is 60 seconds. If there is no
precipitation, the model uses a daily time step (Wolfe, et al., 1995).
De Roo (1993) applied the ANSWERS-GENAMAP GIS-PC-RASTER
interface to calculate surface runoff and soil erosion in the Yendacott catchment, UK
(147 ha), the Etzenrade catchment (225 ha) and Catsop catchment (46 ha) in The
Netherlands. Engel, et al., (1993b) compared the results of GRASS-ANSWERS
model, with two other NPS models that were integrated with GIS: AGNPS and
SWAT. The simulated results matched observed values reasonably well. Wolfe, et al.,
(1995) created a user interface that links Arc/Info GIS with ANSWERS. The system
has been designed for evaluating the overall effectiveness of selected best management
practices at the farm scale.
16
HSPF
Al-Abed and Whiteley (1995) linked PC-Arc/Info GIS with the Hydrologic
Simulation Program-Fortran (HSPF) to simulate the effects of changes in land use and
in resource management strategies on the irrigation water quality in the Grand River,
Ontario, with a drainage area of 6,965 km
2
.
HSPF simulates both watershed hydrology and water quality (Johanson, et al.,
1980). The rainfall is distributed into interception loss, surface runoff, interflow, and
flow into the lower soil zone or groundwater storage. Soil is divided into three
moisture zones: an upper soil zone, that influences the rapid runoff, a lower soil zone,
and a groundwater storage zone. Some of the water from the groundwater storage
becomes stream base flow (DeVries and Hromadka, 1993).
The water quality component simulates silt, clay, and sand sediment transport,
including resuspension and settling processes. It can also calculate nutrient and
pesticide concentrations. The nutrient processes include DO (dissolved oxygen), BOD
(biological oxygen demand), nitrogen, phosphorus, pH, phytoplankton, zooplankton,
and benthic algae. HSPF simulates such transfer and reaction processes as hydrolysis,
oxidation, biodegradation, volatilization, sorption, and chemical exchange between
benthic deposits and the water column. The program user must supply parameters for
each of the modeled processes (Donigian and Huber, 1991; DeVries and Hromadka,
1993).
The watershed is divided into segments--parcels of land that are exposed to
weather conditions described by one set of meteorological time series. Hydraulic
routing requires division of the major streams into modeling segments (Al-Abed and
Whiteley, 1995).
17
2.2 GIS models of Water Quality
Some GIS programs are equipped with a macro language that allows the user
to write models within the application. For example, Arc/Info has very powerful macro
language, AML (Arc/Info Macro Language). In addition, external procedures written
in such programming languages as C/C++ or FORTRAN can be executed by macro,
thus the modeling process can be very efficient. This section discuss models of water
pollution built using GIS tools.
White and Hofschen (1993) developed a spatial model for assessing nutrient
loads in New Jersey rivers using Arc/Info. They used 3 arc-sec digital elevation models
(DEM) to partition the study area (15,385 km
2
) into 2,893 drainage basins (polygons)
with a network of 10,916 stream segments (arcs). The time of travel was assumed as
the basis for calculating predictors of water quality. A simple formula v = 0.38 * Q
0.24
,
which was estimated for New Jersey, was used to estimate the flow velocity in each
reach. A first-order decay reaction was assumed to calculate the non-conservative
downstream transport.  White and Hofschen attempted to improve the model by
representing the decay constant as a function of stream slope, and the nonpoint source
yields as a function of subbasin gradient, but the model performance showed no
improvement with these refinements. White and Hofschen found that the time of
travel, which was calculated from the exponential velocity formula, underestimated by
a factor of 0.57 the time of travel of dye-tracer, that is, the dye took approximately
twice as long to traverse the stream as the formula suggested. This travel time
underestimation was accommodated by assignment of higher values of pollutant decay
than those reported in the literature.
18
Smith, et al., (1993) constructed a GIS model of total phosphorus
concentrations in New Jersey streams. The core of this model is a regression equation
that relates transformed (natural logarithm) total phosphorus concentration measured
at a given point to transformed concentrations resulting from exponentially decayed
phosphorous loads in the upstream watershed. In this study, the classical approach of
modeling first-order reaction was modified. Instead of using the time of travel and time
decay coefficient, the travel distance and a distance decay coefficient for phosphorus
were applied in the model respectively. The data from 104 long term sampling
stations, collected in the period from 1982 to 1987 were utilized to estimate regression
coefficients. The area of the studied region was 15,401 km
2
. The sources of
phosphorous were represented by such variables as area of agricultural land, total
human population, and total municipal effluent flow.
Zollweg, et al. (1995) constructed a GRASS model of the phosphorus
transport for the 25.7 ha Brown Watershed, an upland agricultural watershed in
Pennsylvania. The GRASS script language was used to describe the physical processes
that originally were modeled by the Soil Moisture-based Runoff Model (SMoRMod).
SMoRMod is a distributed spatially variable model. Such parameters as climatic
variables, topography, land use, and soils distribution constitute the input. The
watershed is divided into rectangular cells. For each cell, the infiltration, soil moisture,
groundwater flow, and surface runoff are estimated. The surface runoff is translated
through the channel system to the watershed outlet where the storm runoff hydrograph
is calculated. The phosphorous module determines the P content of the storm runoff
generated over the landscape and transport of this P to the watershed outlet (Zollweg,
et al., 1995).
Hession and Shanholtz (1988) incorporated the Universal Soil Loss Equation
(USLE) with delivery ratio into the Virginia Geographic Information System
19
(VirGIS). The model was used to estimate the potential sediment loading in Virginia?s
Chesapeake Bay drainage area.
2.3 GIS as a tool for spatial data extraction
The most basic application of the GIS is spatial data manipulation, data
extraction for further analysis, and presentation of results in map form. This section
discusses work in which the GIS tools have been utilized to support statistical analysis
of surface water pollution.
Cressie and Majure (1994) used Arc/Info to determine explanatory variables
for a statistical model of the variation in pollutant concentration from dairies in
streams of the Upper North Bosque watershed located principally in Erath County,
Texas. The Arc/Info GRID and Digital Elevation Models (DEM) were used to
determine drainage basins and the lengths along flow paths. Cressie and Majure
assumed a spatially constant flow velocity (0.5 m/s), and using simple map algebra,
they determined a 3-day flow-time area of influence for each stream measurement site.
Seventeen explanatory variables including a number of dairies per acre, a number of
animals per acre, lagoons per acre, waste application method, soil hydrologic code,
average slope, distance to basin outlet, and precipitation were considered. All
variables, except one (seasonal variation), were determined using the GIS. The authors
concluded that the GIS was an important tool in observational studies due to its ability
to construct explanatory variables at the appropriate scale.
Mueller, et al., (1993) applied logistic regression to relate discrete categories
of nitrate concentrations to such explanatory variables as land use in the drainage
basins upstream from the sampling sites, percentile of daily streamflow at the time of
20
sampling, acreage of the basin in corn, acreage in soybeans, density of cattle, and
population density.
Logistic regression is used when the independent variable is discrete or
categorical rather than continuous. It has the following form: log[p/(1-p)] = a + b
k
X,
where p is the probability of data value being in one of the possible categories, a is the
intercept, b
k
 are k regression coefficients, and X is the vector of explanatory variables.
The percentiles (P
j
) are computed using equation P
j
 = A
(n+1)*j
, where: A is a data set
ordered from smallest to largest (A
i
, i = 1, ... n), n is the sample size of A, and j is the
fraction of data less than or equal to the percentile value, e.g. for 25th percentile
j = 0.25 (Helsel and Hirsh, 1995).
Mueller, et al., (1993) extracted data from GIS databases stored in
1:2,000,000- scale maps of the conterminous United States. The GIS software was
used only to areally weight the extracted data and sum it by basin; their model did not
include stream transport. Better classification of nitrate concentration was achieved by
a model that included the flow percentile, the areal extent of corn and soybean
production, the density of cattle, and the density of population, as compared to the
model that contained percentile of flow, nitrogen fertilizer application, and population
density. In addition, Mueller, et al., found that as the percentile of flow increased, the
probability of nitrate concentration being in a higher category also increased. The
logistic regression analysis results led these researchers to a conclusion that the level
of nitrate contamination in midwestern streams is most strongly related to streamflow
and to several characteristics of the upstream basin, including the areal extent of corn
and soybean production, the density of cattle, and the population density.
From the observations made on the Mississippi River and four tributaries
during a one - year period (from April 1, 1991 to March 31, 1992), Battaglin et al.
(1993) estimated a single relationship between the annual use of nitrogen and nitrate
transport: N
transport
 = -0.2 + 0.1547 N
use
 and a linear relationship between annual
21
atrazine use and the atrazine transport: A
transport
 = -12 * + 0.0156 * A
use
, (in metric
tons). They used a GIS to estimate the nitrogen and atrazine use within gauged
watershed from the county level sales of nitrogen fertilizer and atrazine herbicide. In
addition, Battaglin et al. estimated that 321 Mg (ton) of atrazine and 33.7 Mg (ton) of
alachlor were discharged from the Mississippi River basin to the Gulf of Mexico in
streamflow (from April 1, 1991 to March 31, 1992), while the amounts of these
herbicides applied in the basin were approximately equal. This suggests that atrazine is
much more persistent agrichemical than is alachlor.
Moody and Goolsby (1993) report the results of a large scale USGS study of
herbicide transport in the Lower Mississippi River. Although they did not use a GIS,
this work is mentioned here since it is one of the few large scale sampling studies
available on the Mississippi River. During May 26-29, 1990, water samples for triazine
herbicide analysis were collected every 16 km from Baton Rouge in Louisiana, upriver
to the Mississippi-Ohio River confluence (distance of 1900 km). The measurements
showed the background level of ~2.7 ?g/L of triazine herbicides and an upriver
concentration gradient of 0.2 ?g/L per 100 km (concentration decreased going
downstream). The authors suggest that the longitudinal spatial variability in
concentration is a result of cross-channel gradients and the addition of 'slugs' of water
from various upriver tributaries. A routing scheme was used to predict the location of
water masses. This routing method was tested by using the measurements of the
specific conductance. The average flow velocity was v = 6 km/h that gives about 13-
day residence time of water in the Mississippi River over the distance sampled in this
study. It is interesting that the measurements show about 50% decrease in the load
whereas the reported atrazine half-life in water is about 140 days (Thurman, et al.,
1992).
22
2.4 Comparison of the proposed method with previous
studies
2.4.1 Time domain
The model presented in this dissertation is designed to represent average
monthly values of flow rate, agrichemical concentration, and chemical load in streams
of the Midwest. Introduction of a seasonal component to the model fills a gap in
existing GIS models of pollutant transport. Most of the hybrid models that have been
introduced in Section 2.1, are capable of performing continuous-time simulations
(SWAT-GIS), event - related calculations (AGNPS), or daily computations
(SWRRB-, ANSWERS-GIS). The models of surface water pollution that are
constructed within GIS (discussed in Section 2.2) estimate annual average chemical
concentrations for a study period. Even the USGS studies do not evaluate changes in
chemical concentration in Midwest surface waters on a monthly basis. Seasonal
variations are represented by usually three terms of the year: pre-planting, post-
planting, and Fall low flow (Goolsby, et al., 1993a; Goolsby and Battaglin, 1993;
Scribner, et al., 1993). The USGS model of agricultural chemical transport in the
Midwest rivers relates the annual chemical load with annual agrichemical use
(Battaglin, et al., 1993). The statistical model presented here explains seasonal
variations of concentration on a monthly basis.
2.4.2 Spatial domain
The model is designed to predict the loads and concentrations in such large
basins as the Upper Mississippi River basin ( drainage area 490,000 km
2
), the Ohio
23
River basin (526,000 km
2
), or the Upper Missouri-Mississippi-Ohio River basin (above
Ohio-Mississippi River junction, about 2,400,000 km
2
 of drainage area). A more
detailed version of the model has been applied for evaluation of nitrate and atrazine
concentrations in the Iowa-Cedar River basin, Iowa of 32,000 km
2
 - an area larger
than the reported limits of application of hybrid models discussed in Section 2.1 and
models constructed within GIS, presented in Section 2.2.
Krysanova, et al., (1996), specifies limitations of selected pollution models: for
example, AGNPS and ANSWERS are limited to watersheds of about 200 km
2
,
SWRRB was developed for agricultural basins as large as 600-800 km
2
, and SWAT is
intended to be applied in watersheds up to 25,000 km
2
. Besides the present study the
only models known to the author that can be applied for a such large area as the
Midwest region are the annual agrichemical load functions presented in Section 2.3,
which were estimated by Battaglin (1993).
2.4.3 Model formulation
The proposed model can be classified in the second category discussed
previously in Section 2.2, namely models constructed within GIS. Because
concentrations and loads estimated by the model are spatially and temporally
distributed, the model can be characterized as a distributed system. On the other hand,
the agrichemical concentration or load is calculated at a given location by applying
average values that characterize the total upstream drainage area in a regression
equation. Thus the model can also be considered as a lumped system.
The major differences between existing GIS models and the one presented here
result from the spatial extent for which the model has been developed--the Upper
Missouri-Mississippi River and the Ohio River basins. It utilizes data available for the
24
whole US, i.e., digital elevation data and the agrichemical application rates, thus the
model contains a limited number of parameters, not including either time-decay nor
length-decay coefficients.
25
3. DATA AND COMPUTER SOFTWARE
DESCRIPTION
3.1 Data sources
The data used in this study are divided into five groups:
1) Measurements of atrazine and nitrate concentrations in surface waters of
the Midwest as well as the location of the sampling sites and the stream
flow rate at the time chemical measurements were made. The atrazine and
nitrate data are described in Section 3.1.1.
2) Digital elevation models (DEM) and digital stream maps (Reach File 1 or
RF1). They are used to determine ?flow paths? of travel of the chemical
from the point of application to the basin outlet. The DEMs are introduced
in Section 3.1.2 and the RF1 is discussed in Section 3.1.3.
3) Data that define the source of chemicals in the system, i.e., maps of annual
application of agricultural chemicals. The maps of fertilizer and herbicide
application are presented in Section 3.1.4.
4) Hydrologic and climatic record. The hydrologic and climatic data serve
mainly for the development of the flow model, which spatially and
temporally distributes recorded flow rate. The hydrologic data are
discussed in Section 3.1.5.
26
5) Maps of average annual temperature and precipitation. These maps are
utilized to characterize the climatic regions in which the sampled
watersheds are located. They are introduced in Section 3.1.6.
3.1.1 Herbicide and nutrient data
The data utilized in this study has been extracted from two USGS publications:
 1) Open-File Report 94-396, ?Concentrations of Selected Herbicides, Two
Triazine Metabolites, and Nutrients in Storm Runoff from Nine Stream
Basins in the Midwestern United States, 1990-92? (Scribner, et al., 1994);
2) Open-File Report 93-457, ?Reconnaissance Data for Selected Herbicides,
Two Atrazine Metabolites, and Nitrate in Surface Water of the Midwestern
United States? (Scribner, et al., 1993).
Table 3.1 Description of atrazine and nitrate plus nitrite as nitrogen samples
published in USGS Open-File Report 94-396, (Scribner, et al., 1994).
Drainage
Number of samples No of sampled days
Name Station ID Area Sampled Period
Atrazine NO
2
+NO
3
Atrazine NO
2
+NO
3
km
2
(GCMS) as Nitrogen (GCMS) as Nitrogen
West Fork Big 6880800 3,123 4/03/90-7/27/90 37 176 28 57
        Blue R., NE 3/26/91-3/09/92 106 96 64 63
Sangamon R., IL 5572000 1,425 4/04/90-8/23/90 53 255 43 101
4/12/91-3/25/92 198 168 93 93
Huron R., OH 4199000 961 3/30/90-8/20/90 59 208 53 142
Delaware R., KS 6890100 995 4/04/90-6/29/90 32 154 25 45
Roberts Cr., IA 5412100 267 4/03/90-7/21/90 22 133 20 43
Old Man's Cr. IA 5455100 521 4/16/90-7/02/90 49 171 30 46
Cedar R., IA 5431200 12,261
(1)
4/15/90-6/29/90 41 187 33 60
Silver Cr., IL. 5594800 1,202 4/13/90-8/17/90 34 120 29 59
Iroquois R., IL 5526000 5,416 4/04/90-8/18/90 49 177 46 71
Total: 680 1845 464 780
(1) for analysis a drainage area estimated from DEM has been used (17,409 km
2
)
27
USGS study of agrichemicals in storm runoff. USGS Open-File Report 94-
396 contains data that were collected from nine streams in five Midwestern States
during late spring-early summer of 1990. Two of the nine streams (the Sangamon
River and the West Fork Big Blue River) were sampled from April 1991 to March
1992. Table 3.1 contains detailed information about number of samples and the time
interval during which samples were collected. Figure 3.1 shows the location of
sampling sites, watersheds that were delineated from the 500 m DEM (Digital
Elevation Model), and selected rivers from RF1 (digital map of rivers).
Platte R.
Missouri R.
Mississippi R.
Ohio R.
Kansas R.
Illinois R.
Iroquois R.
Sangamon R.
Silver Cr.
Cedar R.
Old Mans Cr.
Roberts Cr.
Delaware R.
WestForkBigBlueR.
Huron R.
250 0 250 500 Kilometers
Figure 3.1 Location of sampling sites for study of atrazine and nitrate plus
nitrite as nitrogen concentrations in storm runoff; USGS Open-File
Report 94-396, (Scribner, et al., 1994).
28
Concentrations of eleven herbicides, two triazine metabolites, nutrients,
streamflow, specific conductance, and pH were measured. The location of each
sampling site is described by latitude and longitude. Such estimates as cropland
percentage, atrazine use, and nitrogen use are also presented in Open-File Report 94-
396. Figure 3.2 presents an example of measured atrazine concentrations in Old Mans
Creek in Iowa.
0
5
10
15
20
25
30
35
40
45
50
100 110 120 130 140 150 160 170 180
Day of 1990
Concentration 
[mg/m
3
]
APR MAY JUN
Figure 3.2 Atrazine Concentrations in Old Mans Creek, Iowa (data from USGS
Open-File Report 94-396, Scribner et al., 1994).
Reconnaissance study of 147 streams. In Open-File Report 93-457 Scribner,
et al., (1993) present data for selected herbicides, two atrazine metabolites, and nitrate
29
plus nitrite as nitrogen in surface water of the Midwestern United States, 1989-90.
One hundred and forty seven Midwestern streams were studied. Two to three samples
per site were taken annually--before application of herbicides (March or April), during
the first major runoff after application of herbicides (May, June, or July), and in the
Fall during a low-flow period when most of the streamflow was derived from the
ground water (August - November). Table 3.2 presents the distribution of samples
within studied period and Figure 3.3 shows the reconnaissance study drainage areas.
Table 3.2 Temporal distribution of atrazine and nitrate plus nitrite as nitrogen
samples from the Midwestern reconnaissance study; USGS Open-
File Report 93-457, (Scribner, et al., 1993).
Number of samples
Month Atrazine (GC/MS) Nitrate + Nirite as Nitrogen
1989 1990 1989 1990
MAR 64 38 95 38
APR 25 10 48 10
MAY 69 36 72 37
JUN 51 13 51 13
JUL 11 5 12 5
AUG 1 - 1 -
SEP 1 - 1 -
OCT 114 - 114 -
NOV 30 - 32 -
Total: 366 102 426 103
Atrazine concentrations are reported as two different (but related )
components: ELISA atrazine and GC/MS atrazine, since this chemical is usually
measured by two methods: ELISA ( Enzyme-Linked Immunosorbent Assay) and
GC/MS (gas chromatography/mass spectrometry). The ELISA test is easier to
perform but is less precise than the GC/MS method. It is affected to varying degrees
by the existence of propazine, prometon, simazine, deethylatrazine, cyazine, and
deisopropylatrazine (Thurman, et al., 1990).
30
ELISA and GC/MS results can be related by regression so that results
determined by ELISA can be converted to an estimate of what a GC/MS measurement
of the same sample would have yielded (Thurman, et al., 1992; Moody and Goolsby,
1993; Goolsby, et al., 1993; Gruessner, et al., 1995). In this study, the atrazine
concentrations measured by the GC/MS method are utilized.
500 0 500 1000 Kilometers
Figure 3.3 Watersheds sampled during 1989 and 1990 for the USGS
reconnaissance study (Battaglin, 1995).
31
3.1.2 Digital Terrain Representation
Elevation data form the spatial framework for modeling basic hydrologic
processes. In this research, a Digital Elevation Model is used not only to determine the
paths of travel of agricultural chemicals, but also to divide the study region into small
watersheds or modeling units, to determine the ?flow? topology between the modeling
units, to delineate the stream network, and to determine the characteristics of the
drainage area. Two versions of DEM are utilized: 100 m ( derived from 3-second)
DEM is applied for the Iowa-Cedar River watershed and 500 m (15 second) DEM is
used for the Upper Mississippi-Missouri and Ohio River basin.
The Digital Elevation Model (DEM) consists of a 2-D array of ground
positions at regularly spaced intervals. One-Degree DEM files (3x3 arc-second data
spacing) are available throughout the US and therefore they have been used in this
research. The majority of 1-Degree DEMs were produced by the Defense Mapping
Agency (DMA) either from cartographic (maps 1:24,000 scale through 1:250,000
scale) or from photographic sources. Some of these DEMs were created by regriding
7.5-minute and 30-minute DEMs. The compressed (and uncompressed) DEM files are
available via the Internet at   ftp://edcftp.cr.usgs.gov/pub/data/DEM/250/. The maps
needed can also be selected from the map of the USA that is displayed on the screen:
http://edcwww.cr.usgs.gov/glis/hyper/guide/1_dgr_demfig/index1m.html
The 500m DEM was created by resampling 1-Degree DEM files. It has been
released by the USGS on a CD-ROM ( Rea and Cederstrand, 1995). In this research,
the 500 km DEM has been applied to create a map of the drainage area of each
sampling site from which measurements have been utilized for model development.
Although for some regions the quality of determined flow direction was poor and
some editing had to be done, the 500 m DEM appeared to have an optimal resolution.
At the cost of precision, the Mississippi-Missouri-Ohio River basin of area about
32
2.4*10
6
 km
2
 could be treated as a one processing unit using 500m or 15? data, which
was impossible for a 3? DEM. Since the size of this basin grid is about 90 Mb (500 m
DEM, integer values), the complexities of the analysis are restricted by the available
computer power and memory.
Figure 3.4 A Digital Elevation Model of the Iowa-Cedar River basin, vertical
scale enlarged 500 times. The white line represents the basin
boundaries.
3.1.3 Reach File 1
Reach File 1 (RF1) is a representation of streams in the conterminous United
States at a scale of approximately 1:500,000.  The original file was prepared by the US
Environmental Protection Agency (USEPA). In 1994 it was translated from a
33
mainframe computer into an Arc/INFO coverage. RF1 in Arc/Info export format is
available via Internet:   http://nsdi.usgs.gov/nsdi/wais/water/rf1.HTML.
Iowa
Minnesota
Cedar R. at Charles City, IA
Cedar R. at Janesville, IA
Cedar R. at Waterloo, IA
Cedar R. near Austin, MN
Figure 3.5 The Cedar River above Waterloo, IA; rivers selected from Reach
File 1.
Because of the size of the entire RF1 data set (its Arc/INFO Export file
occupies 57 MB), it also is available in 18 separate files, each covering a 2-digital
hydrologic unit code (Water Resources Region).
34
In this research, RF1 is applied to adjust the DEM in order to ensure that the
streams delineated from the DEM are compatible with the streams from RF1. Figure
3.5 shows an example of RF1 for the Cedar River above Waterloo, Iowa.
3.1.4 Atrazine and nitrogen fertilizer use
In 1995, the USGS published maps of herbicide and nitrogen-fertilizer use
(Battaglin and Goolsby, 1995a, b). Five coverages summarizing the use of 96
herbicides were constructed from tabular estimates of herbicide use by county and by
crop published in Gianessi and Puffer (1991). Atrazine use in the Mississippi-Missouri
and Ohio River basins in 1989 extracted from the USGS coverage is presented in
Figure 3.6.
Although the crop acreages used in the assessment were from 1987, the
herbicide use estimates generally reflect the 1989 usage amount. Data from such
sources as surveys of weed scientists, surveys of farmers, and crop acreage, were
utilized to make these estimates. Estimates of the number of pounds of atrazine used
per square mile in 1989 are contained the Arc/Info coverage HERBICIDE1 (attribute
H1980.USE), obtained from National Spatial Data Infrastructure (NSDI), National
Geospatial Data Clearinghouse:
http://nsdi.usgs.gov/nsdi/wais/water/herbicide1.HTML.
Battaglin and Goolsby (1995a) constructed seven coverages summarizing
annual nitrogen sales in U. S. counties, for the fertilizer years 1985-1991. The fertilizer
year starts July 1 of the previous year and ends June 30, e. g. fertilizer year 1990 starts
07/01/89 and ends 06/30/90). The maps were prepared from estimates reported by the
U. S. Environmental Agency (years 1985-89) and from Jerald Fletcher in cooperation
with the National Fertilizer and Environmental Research center, Tennessee Valley
35
Authority (years 1990 and 1991). The sales of fertilizer do not account for the use of
manure.
Coverages of nitrogen fertilizer use estimates are available in Arc/Info export
format from National Spatial Data Infrastructure (NSDI), National Geospatial Data
Clearinghouse:  http://nsdi.usgs.gov/nsdi/wais/water/nit89.HTML, .../nit90.HTML,
and .../nit91.HTML). Total nitrogen-fertilizer use in tons per square mile from July,
1989 to June, 1990 is stored in attribute NTOT90 of coverage NIT90; nitrogen-
fertilizer use from July, 1990 to June, 1991 is in attribute NTOT91 of coverage
NIT91.
Atrazine application in 
2
g/km /yr
0-0.01
0.01-3000
3000-10000
10000-20000
20000-56414
200 0 200 400 600 Kilom eters
Figure 3.6 Atrazine use in the Mississippi-Missouri and Ohio River basins in
1989 (from Battaglin and Goolsby, 1995b)
36
3.1.5 Hydrologic and climatic data
The gauging station locations, drainage areas, and the daily flow data for
31,000 USGS gauging stations are available from the CD-ROM set published by
Hydrosphere Data Products, INC. (Hydrosphere, 1993a). These data originate from
the USGS WATSTORE system (Daily and Peak Values Files For Stream Flows).
Additional data such as daily rainfall, snowfall, maximum temperature and
minimum temperature, which were observed at 17,000 NCDC Stations, are also
available on the CD-ROM set published by Hydrosphere Data Products, Inc.
(Hydrosphere, 1993b).
For the purpose of this research the following data have been exported from
Hydrosphere CD-ROMS in ASCII (text) format:
- Monthly flow rate measured in all USGS gauging stations in the Iowa Cedar
River basin, for the years up to 1992;
- Monthly precipitation depth measured in all NCDC gauging stations in the
Iowa Cedar River basin and within a 50 km buffer outside the basin for the
years up to 1992; and
- Description of the gauging sites (to extract such information as drainage area
and station location-- latitude and longitude).
37
3.1.6 Maps of mean annual precipitation and temperature
Arc/Info coverages of the mean annual precipitation and temperature in U.S.
have been published by the USGS in 1991 (USGS, 1991). The mean values as well as
the standard deviations were calculated for the period from 1951 to 1980 and stored in
the attribute table of the map of National Oceanic and Atmospheric Administration
(NOAA) Climate Divisions (each state is divided into nine climate zones). The map
originator is National Climatic Data Center. The Arc/Info coverage is available via
Internet at  http://nsdi.usgs.gov/nsdi/wais/water/climate_div.HTML. Figure 3.7  and
Figure 3.8 present the mean annual temperature and the mean annual precipitation in
the Upper Mississippi-Missouri and Ohio River basins, respectively.
Figure 3.7 Mean annual temperature [?C] in the Mississippi-Missouri and
Ohio River basins by NOAA climate division (USGS, 1991).
38
Figure 3.8 Annual precipitation [mm] in the Mississippi-Missouri and Ohio
River basins by NOAA climate division (USGS, 1991).
3.2 Computer software description
Section 3.2.1 presents the Geographic Information System software used in
this research. Section 3.2.2 introduces statistical program, S-Plus, used to develop a
regression model. The research was performed on SUN SPARC station IPX, SUN
ULTRA (operation system UNIX) and 486DX2-66 (operation system DOS).
39
3.2.1 GIS software
Arc/Info and ArcView constitute the GIS software used in this research.
(Arc/Info and ArcView are registered trademarks of the Environmental Systems
Research Institute, Inc., Redlands, California). Arc/Info is a spatial analysis system
which represents spatial data in separate layers and it provides operators for
manipulating these data. It contains three basic spatial primitives for vector data:
Points, Lines, and Polygons. This software supports also three derived data structures:
Grids (a rectangular mesh of points), Triangulated Irregular Networks (a TIN is a set
of points connected by triangles), and Networks (a set of connected arcs with assigned
flow properties). Each spatial primitive can have an associated record in a database, an
Info file. The fields of this record contain user specified descriptive attributes, such as
area, length, category, name, etc. The one to one correspondence between the spatial
features (point, arc or polygon) and data records (Info) is the basis of the hybrid
Arc/Info data model.
Besides the Arc/Info core system, two Arc/Info processors are extensively
used in this research: GRID and TABLES. GRID manipulates maps in raster format or
grids. TABLES is used to handle the data stored in the following attribute tables:
   - point attribute table (PAT) associated with a point coverage;
   - arc attribute table (AAT), an Info table of an arc coverage;
   - polygon attribute table (PAT), an Info table of a polygon coverage; and,
   - value attribute table (VAT), an Info table attached to a grid.
The Arc/Info macro language (AML) enables the automation of complex or repeated
tasks.
ArcView is a GIS software completely operated from a graphical user
interface. Although it can perform only simple spatial operations on the maps in vector
40
format, it has very powerful and convenient tools to manage attribute tables. Avenue,
an object oriented script language within ArcView, allows the user to build complex
GIS applications. ArcView is available for workstations and  for personal computers.
ArcView version 2.1 was used in this research (ESRI, 1995).
3.2.2 Statistical software
The data analysis and model parameter estimation were performed by the
application of two computer programs: Microsoft Excel spreadsheet version 5.0a
(Microsoft and Excel are registered trademarks of Microsoft Corporation) and the
statistical software, S-Plus version 3.2 (S-PLUS is a registered trademark of
MathSoft, Inc.)  MS Excel was used mainly as a preprocessor for data editing, simple
calculations such as unit conversion, and data verification. All the statistical analysis
which is presented in this project was performed using S-Plus.
S-Plus is an interpreted language that evaluates expressions. The results of the
expression is an object. All input data must be one of the S-Plus objects. Two types of
objects have been utilized in this research:
- vector, a set of elements in a special order, and
- data frame, that represents data in a two dimensional table.
There are two more S-Plus objects that are designed to store tables, array and matrix,
but the data frame, unlike the matrix, can have values of different modes in different
columns (MathSoft, 1993; Venables and Ripley, 1994). A detailed description of the
application of S-Plus in this study is presented in Section 6.
41
4. METHODOLOGY
In this section a detailed description of the methodology developed for
modeling agrichemical transport is presented. Two agrichemicals are selected: a
nutrient, nitrate plus nitrite as nitrogen, and a herbicide, atrazine. These chemicals are
introduced in Section 4.1. Section 4.2 describes two geographic analysis regions: one
region used for developing a statistical model, and another smaller region used for GIS
model development and its verification. The regression equations that relate chemical
concentrations to the chemical application on the field, selected watershed descriptors,
climatic variables, and the month of a year, are developed utilizing the USGS data
collected in more than 150 watersheds scattered over the Mississippi - Missouri Basin
above Thebes, Illinois, and the Ohio Basin above Grand Chain, Illinois. A GIS
application of these equations is developed and verified for the Iowa-Cedar River
watershed located in Iowa and Minnesota.
A detailed mathematical description of the statistical model is presented in
Section 4.3.  It provides an overview of the transport equations, introduces the
explanatory variables which explain the spatial and seasonal (monthly) variations of the
nitrate and atrazine concentrations in surface waters, and explains the concept of
spatio-temporal ?cascade? modeling within GIS. The watershed parameters of the
statistical model are estimated from the 500 m DEM.
The GIS model of agrichemical transport in the Iowa-Cedar River basin is
presented in Sections 4.4 - 4.6. Section 4.4 describes the methodology of discretizing
the watershed, i.e., subdividing the basin into small (about 30 km
2
) hydrologic units
and determining the flow connectivity between these units utilizing the 3 arc-sec DEM.
42
Since the GIS model is designated to estimate the concentrations and loads in all
streams, a methodology of redistributing the observed flow rate over ungauged rivers
has been developed. Section 4.5 presents details of the monthly flow redistribution
technique as well as the application of the GIS capabilities to store and manipulate
flow and precipitation time series.
The following flow chart summarizes the methodology developed for the large
scale agrichemical transport in the Midwest rivers:
Selection of Representative
Agrichemicals
Selection of the Analysis Region
and Map Coordinate System
Mississippi - Missouri Basin
andOhioRiverBasin
Iowa-Cedar River
Basin
Regression Model Development
data:
- agrichemical concentrations &
flow rate from USGS Reports
- watershed morphometry
estimated from 500 m DEM
Delineation of modeling units
and their "flow" topology
from 100 m DEM
Building GIS database (maps
and attributes) of the recorded
flow rate and precipitation
depth time series
Redistribution of the flow
record over ungauged rivers
data: precipitation, flow rate
and drainage area
Estimation of watershed
morphometry for each
modeling unit
Model verification:
reconstruction of agrichemical
concentrations in the Cedar
River in 1990.
- temperature and precipitation
by NOAA climate divisions
Figure 4.1 Methodology of the large scale modeling of agrichemical
concentrations in the Midwest rivers.
43
An alternative and less successful approach to modeling agrichemical transport
to the main one developed in this research is briefly introduced in Section 4.6. This
model is based on a first order reaction as well as a method of travel time estimation
which is presented there.
In this section and in the following sections, the words river, stream, and
stream/river reach are used interchangeably. Similarly, drainage area, watershed and
basin are considered here as equivalent terms. Sometimes one word nitrate is used to
represent nitrate plus nitrite as nitrogen. Unit watershed, elementary watershed, and
modeling unit refer to the smallest drainage area or partial drainage area into which
the region under investigation is divided. Each modeling unit is considered as lumped
system. Names of maps, computer files, database fields, as well as computer
commands are printed in a Courier font.
4.1 Representative agricultural chemicals
Two constituents are selected for the study of the transport of agricultural
chemicals in surface waters: nitrate plus nitrite as nitrogen, and atrazine. The following
factors influenced this selection:
- nitrogen and atrazine are representative of nutrients and herbicides,
respectively,
- nitrate plus nitrite as nitrogen and atrazine are present in measurable quantities
in many Midwest streams, and
44
- nitrate plus nitrite as nitrogen was the only nutrient measured during both
studies performed by the USGS: the reconnaissance study (Scribner, et al.,
1993) and the analysis of agrichemical concentrations in storm runoff
(Scribner, et al., 1994).
It is assumed that the nitrate plus nitrite concentrations in Midwest streams are mainly
derived from chemical fertilizers.
4.1.1 Nitrate
Nitrogen (N) in soils natural waters occurs as organic or inorganic N. The
inorganic forms, include ammonium (NH
4
+
), nitrite (NO
2
-
), nitrate (NO
3
-
), nitrous
oxide (N
2
O), nitric oxide (NO), and elemental N (N
2
). The three most important
forms, NH
4
+
, NO
2
-
,and NO
3
-
, usually represent 2 to 5% of the total soil N. The source
of NH
4
+
 is from mineralization of organic N and from fertilizers. During nitrification,
NH
4
+
 is converted to NO
2
-
, (which is toxic to plant roots) by bacteria Nitrosomonas
(2NH
4
+
 + 3O
2
 = 2NO
2
-
 + 2H
2
O + 4H
+
), and then oxidized to NO
3
-
 by Nitrobacter
(2NO
2
-
 + O
2
 = 2NO
3
-
). The NO
3
-
 anion is very mobile and subject to leaching losses
(Tisdale, et al., 1993).
Nitrate in streams is derived from many anthropogenic and natural resources
including chemical fertilizers, animal wastes, domestic sewage, legumes, mineralization
of vegetation, soil organic matter, and from the atmosphere through electrical,
combustion and industrial processes. NO
3
-
 is a very soluble and mobile anion. It can be
transported from agricultural fields in both overland flow and subsurface flow, and by
volatilization into the atmosphere. Ammonium is adsorbed by the soil colloids and
moves very little until converted to NO
3
-
. The following are typical concentrations in
45
streams stated in mg/L as nitrogen, where 1 mg N/L = 1.2159 mg NH
3
/L = 3.2845 mg
NO
2
/L = 4.4268 mg NO
3
/L): total nitrogen 0.1-10 mg/L, organic nitrogen 0.1-9 mg/L,
ammonia 0.01-10 mg/L, nitrite 0.01-0.5 mg/L, nitrate 0.23 mg/L, and nitrogen gas 0-
18.4 mL/L (McCutcheon, et al., 1993).
Standard measurements of nitrogen in surface waters include Kjeldahl nitrogen
(ammonia plus organic nitrogen), nitrite plus nitrate, nitrite, and nitrogen in plants. The
USGS reports utilized in this research (Scribner, et al, 1993, Scribner, et al., 1994) do
not contain data about organic nitrogen in surface waters. Only nitrite plus nitrate
concentrations were measured during the USGS reconnaissance study of agrichemicals
in Midwest rivers (Scribner, et al., 1993). Nitrate, nitrite, and ammonia were measured
in two rivers, the West Fork Big Blue River near Dorchester, Nebraska, and the
Sangamon River at Monticello, Illinois, during the analysis of agrichemicals in storm
runoff from April, 1991 to March 1990 (Scribner, et al., 1994). In most samples of the
Sangamon River the concentrations of ammonia were less than 0.1 mg/L, while the
nitrate concentrations were 7 - 14 mg/L during the months from November to June
and 0.4-3 mg/L during the months from July to October. The concentrations of nitrate
in the West Fork River were smaller than the concentrations in the Sangamon River,
rarely exceeding 3 mg/L . The September-October concentrations were below the
reporting limit. The ammonia levels varied from about 0.1 to 0.4 mg/L except the
summer months in which the ammonia concentrations in most samples were less than
0.05 mg/L.
The proportions of the different forms of the nitrogen in Midwest rivers may
be illustrated by the samples collected in five sites (Floyd, Carville, Northwood, Cedar
Falls, Gilbertville, and Bertram) along the Cedar River, Iowa, from May 1984 to
September 1985 (Squillace and Engberg, 1988). The following median concentrations
were reported:
46
- dissolved nitrite plus nitrate as nitrogen 3.5 - 5.1 mg/L
- dissolved ammonia as nitrogen 0.03 - 0.1 mg/L
- dissolved organic nitrogen 0.25 - 0.85 mg/L
Thus it can be seen that most nitrogen in streams of the Midwest is present as nitrate
plus nitrite.
In contrast to overland transport, in which nitrate takes minutes or hours to get
to a stream, downward vertical leaching and subsequent underground travel is a long
process which takes months or years. The soil system has a strong memory with
respect to nitrate production and leaching. Jones and Burt (1993) presented a study in
which 64% of annual nitrate concentration in streams was explained by a stepwise
regression involving the year of measurement, and each of the previous two years. It
may take nitrate years or even decades to appear in rivers as a base flow pollutant.
There are some losses of nitrate due to erosion, but for humid temperate
climates, erosion is generally an insignificant process compared with leaching and
runoff (OECD, 1986). Other authors indicate that the adsorption has no marked
influence on the rate of NO
3
-
 movement (Keeney, 1983; Bailey and Swank 1983). The
predominant losses of nitrate in an agricultural field are due to assimilation by row
crops and by other terrestrial and aquatic plants.
Although the best time of fertilizer application is at the time of peak N demand
of the crop, it is seldom feasible to apply the chemical then. In north central United
States most of the N application occurs late summer and fall. It is influenced by the
following factors (Tisdale, et al., 1993):
- Temporal and spatial distribution of the rainfall. Because of N mobility in soils,
the greater the surplus rainfall, the greater the possibility of loss of N through
leaching.
47
- Temporal and spatial distribution of temperature. Since higher temperatures
enhance nitrification, ammonia N applied before planting is more subject to
nitrification and leaching.
- Technical factors. In late winter the ground may be to wet for machinery to be
operated and spring application is usually too late for small grains to respond in
yield to the nitrogen fertilizer applied.
Fall application of nitrogen fertilizers as well as the decrease in temperature
during late fall, winter, and early spring, causes high nitrate plus nitrite concentrations
in surface waters at those times. These concentrations decrease in late spring and
summer when the plant demands for nutrients are high (Goolsby and Battaglin, 1983;
Davis and Keller, 1983). In addition, a significant decrease in nitrate concentration in
surface water may result from assimilation of nitrate by algae and by instream riparian
macrophytes (Heathwaite, 1993; Moore, 1991) as well as nitrate may be converted by
the denitrification bacteria and various chemical processes into free nitrogen and
nitrogen oxides which escape into the atmosphere. Since these processes are
stimulated by high temperatures and low flow rates, the highest loss of nitrate in lakes
and rivers occurs during the summer. Lakes and reservoirs act as a "buffer," thus they
are less responsive to seasonal changes than are rivers (OECD, 1986).
Denitrification and other processes of biochemical degradation of nitrate can be
modeled as a first order reaction with an "overall" decay rate dependent on
temperature and carbon content. Some losses may result from infiltration (river water
seepage into groundwater).
48
4.1.2 Atrazine
Atrazine is a herbicide that controls broadleaf weeds in fields of corn and
sorghum. It is one of the most widely used herbicides in the United states (Comfort
and Roeth, 1996). The EPA has set the drinking water health limit (MCL, Maximum
Contamination Level) for atrazine at 3 ?g/L (ppb). Conventional water treatment does
not remove this herbicide. Recent studies conducted in 29 communities throughout the
Midwest, Louisiana, and the Chesapeake Bay detected high concentrations of atrazine
in tap water during months from May through July, some of them exceeding EPA
MCL of 3 ?g/L (EWG, 1996)
Numerous laboratory tests as well as field studies have been performed to
determine the behavior of this herbicide in different chemical and physical
environments for almost half of the century. Some of the published parameters are as
follows: Atrazine (2-chloro-4-ethylamino-6-isopropylamino-s-triazine) is a low
solubility herbicide; its water solubility in typical temperature and pH varies from 30 to
35 ppm (mg/L). The volatility of this chemical is very low ( vapor pressure = 0.3*10
-6
mm Hg = 0.00004 Pa). Published values of the octanol extrability coefficient (soil
sorption coefficient) K
oc
 are from 130 to 172. The octanol-water partition coefficient
K
ow
 equals 251 (e.g., Weber, 1972; Hamaker, 1975; Wauchope, 1978; Rao, et al.,
1983; Weber, 1988; Plimmer, 1988).
There are two parameters that characterize chemical decay in soil: half-life and
chemical persistence. The half-life is the length of time it takes for a sample to reduce
to half of its original weight or mass. The chemical persistence is the time for 90%
disappearance of chemical from soil. Kruger, et al. (1993) reported half-life of atrazine
in soil under unsaturated conditions ranged from 41 d to 231 d, whereas in saturated
soil at the 90-120 cm depth, the half-life was 87 d. Similar values were cited by
49
Goring, et al. (1975). Wauchope (1978) determined that atrazine persistence in soil is
12 months and may vary from 6 to 18 months, which corresponds to a half-life from
55 d to 165 d, depending on climate and soil.
Atrazine decays into many degradation products which can be more persistent
and mobile than their parent compound. During a USGS 1991 Mid-continent survey of
near-surface aquifers, deethylatrazine, an atrazine metabolite, was the most frequently
detected compound followed by atrazine, and then deisopropylatrazine, another
atrazine metabolite (Kolpin et al., 1983). The half life of the deisopropylatrazine is
much longer in surface water than in soil (Goolsby et al., 1993 pp. 51-62, Comfort and
Roeth, 1996). However, Kruger et. al. (1993) found that deisopropylatrazine may be
even less persistent under saturated conditions then in saturated soil. Their estimate of
the deisopropylatrazine half-life ranged from 32 d to 173 d in the top 30 cm of
unsaturated soil, and from 58 d to 173 d in saturated soil at 90 to 120 cm depth.
Weber (1988) presented results of research, which he conducted with J. A.
Best, on the effect of pH on the dissipation of atrazine applied to soil. No parent
component volatilization was detected; 0.1%-0.2% was found in leachate, plants used
two to four percent. Ninety percent of atrazine was retained in the soil layer.
The adsorption and movement of s-triazines in soil depends upon such factors
as soil organic matter, clay minerals, pH, temperature, soil moisture, concentration and
species of other ions in the system (Weber, 1972; Weber, 1988; Goring, et al., 1975).
In the CREAMS model, pesticide in runoff is partitioned between the solution phase
and the sediment phase (Knisel, et al., 1983).
Study by the USGS of the occurrence of herbicides in precipitation in the
Midwest and Northeastern United States showed that significant amounts of atrazine
were lost through volatilization and subsequently returned to the land through
precipitation washout. The amount of atrazine in precipitation washout was
50
approximately equal to one half the loading found in the Mississippi River flowing into
the Gulf of Mexico (Goolsby, et al., 1993, pp. 75-86). Plimmer (1988) discussed
reports which described the identification of atrazine in fog. These findings were
apparently in contradiction to the findings about negligible volatilization published by
Weber (1977, 1988). As was pointed out by Kenaga (1975), volatility of  a pesticide is
applied to heterogeneous surfaces such as natural water, soil, foliage, wood, or glass,
is variable because sorption varies. There is a possibility that atrazine enters the
atmosphere adsorbed on particulate matter through dust blowing from the land
surface.  The process of atrazine volatility is not well understood.
4.2 Selection of analysis region and map coordinate system
The Mississippi - Missouri River basin above Thebes, Illinois (drainage area
1.85*10
6
 km
2
 ) together with the Ohio River basin above Grand Chain, Illinois
(drainage area 0.53*10
6
 km
2
) constitute the primary region that is used for estimation
of statistical model parameters. Its extent is determined by the USGS reconnaissance
study of selected herbicides and nitrate in Midwestern United States (Scribner, et al.,
1993). This region is one of the most extensive agricultural areas in the country,
producing over 80% of all US corn and soybeans (Oberle and Burkart, 1994).
51
Figure 4.2 The Mississippi-Missouri and Ohio River Basins.
Since processing data for an area that covers almost three million square
kilometers requires a computer with adequate operational and storage memory, the
final model is built, and verified on a selected subregion, i.e., the Iowa-Cedar River
watershed in Iowa (area = 32,000 km
2
). There are two sites in the Iowa-Cedar Basin
for which measurement of agricultural chemicals are available: Old Man?s Creek near
Iowa City and Cedar River at Palisades, Iowa. Flow rate is recorded in about 30
USGS gauging stations in the Iowa-Cedar Basin. A diversity of such geographic
features as lakes, reservoirs, wetlands, hills, plains, and a wide range of stream sizes
makes the Iowa-Cedar Basin a very good representation of the Midwest. Figure 4.3
shows the Iowa and Cedar Rivers, and the location of gauging stations.
52
Iowa
Minnesota
MO
WI
IL
NE
SD
Figure 4.3 The Iowa River with tributaries and the USGS gauging stations.
53
All maps utilized in this research are represented in Albers Conical Equal Area
Projection, generally accepted for large maps of the USA. This projection has the
valuable property of equal area representation, combined with a scale error that is
practically the minimum attainable in any system covering such a large area in a single
sheet.
The following parameters are applied (standard for USA): units = meters, first
standard parallel = 29?30'00'', second standard parallel = 45?30'00'', latitude of
projection's origin = 23?00'00'', false easting = 0.000 m, false northing = 0.000 m,
longitude of central meridian = -96?00'00''.  Using one common projection for the
whole Midwest eliminates the problems associated with merging separately modeling
regions into one unit.
The Albers projection is of the conical type, in which the meridians are straight
lines meeting in common point beyond the limits of the map, and the parallels are
concentric circles, the center of which is at the point of intersection of the meridians.
The meridians and the parallels intersect at right angles and the arcs of longitude along
any given parallel are of equal length. The spheroid is intersected by a cone at two
parallels known as the standard parallels for the area to be represented. On the two
standard parallels, arcs of longitude are represented by their true lengths, or at an
exact scale. Between the standard parallels, the scale along the meridians is too large
and beyond them too small (Deetz and Adams, 1969).
The Albers projection is constructed in such a way that the area of the earth?s
surface between any pair of parallels and meridians is correctly preserved in the flat
map representation.
54
4.3 Mathematical description
4.3.1 Overview of transport equations
There are two basic mechanisms that are responsible for the transport of
dissolved and suspended solutes in surface waters: advection and diffusion/dispersion.
These two processes are described by the advection-dispersion equation which is the
fundamental equation for majority of the pollutant transport models. Equation (4.1)
describes one-dimensional advection-dispersion in a reach with a uniform cross-
sectional area.
?
?
?
?
?
?
?
?
+
==
??
c
t
 = -
vc
x
 + 
x
E
c
x
 S
 + 
K
c
x i
i
n
j
j
m
11
(4.1)
where:
c = concentration of pollutant [g/m
3
]
t = time [s]
x = distance along the river [m]
-E
x
?c/?x = mass flux due to the longitudinal dispersion [g/m
2
s]
E
x
= longitudinal dispersion coefficient [m
2
/s]
-vc = mass flux due to advection [g/m
2
s]
S
i
= i-th source/sink of the constituent [g/m
3
s]
i = 1...n, n = number of sources/sinks
K
j
= decay rate due to the j-th process [1/s]
v = flow velocity [m/s]
55
The source/sink term, S
i
 and reaction term, K
j
c represent a wide range of
features such as lateral flux, transient storage, biotic and abiotic retention, benthic flux,
periphyton retention, sediment retention, reaeration, photosynthesis, and nitrification
(U. of Mississippi, 1990, James and Elliot, 1993).
Dynamic models solving (Eq. 4.1) have been used mainly for pollution
incidents such as spills and runoff discharges. Their applicability for large scale
modeling of nitrate/atrazine transport at the scale attempted in this research is limited,
mainly because:
- Numerical solution of the advection-dispersion equation requires subdivision of
the time domain into relatively short intervals (minutes, hours), but this is less
useful when calculating monthly means of chemical transport in extensive
stream networks over large areas;
- It is difficult to write a procedure which solves the dispersion-advection
equation using a GIS script language, so such a model has to be solved
externally to the GIS.
Lagrangian type transport models, such as a Moving Segment Model (MSM),
can be efficiently incorporated into GIS. In MSM (James and Elliot, 1993) the stream
is subdivided into series of segments. Within each segment the variations of chemical
concentration are calculated by summing, for example, hourly changes due to all the
processes involved. The process within the block is described by the following
equation:
?
?
?
==
??
c
t
 = S + 
K
c
i
i
n
j
j
m
11
(4.2)
where: S
i
 is the i-th source/sink and K
j
 is the j-th reaction coefficient.
56
The segments (blocks) move downstream with travel time ? which may be a
function of such parameters as flow rate, cross-sectional area, friction coefficient,
slope, and stream curvature. For a detailed representation of the constituent transport
in surface water at least the following processes should be represented (O'Connor, et
al., 1983; Thomann and Mueller, 1987; O'Connor, 1988a,b; University of Mississippi,
1990):
- Sorption and desorption between dissolved and particulate components in the
sediment and water column;
- Settling and resuspension of particles;
- Diffusive exchange between the sediment and water column;
- Loss and gain of the chemical due to the chemical and biochemical reactions
such as biodegradation, volatilization, and photolysis;
- Advective and diffusive transport of the chemical in water and as a bed
transport;
- Net deposition and loss of chemical to deep sediments.
Figure 4.4 shows these major reaction mechanisms and transfer routes of
chemicals and solids in both river water and the river bed.
57
Dissolved
component
c
d
Component on
suspended particles
c
p
Suspended
particles
m
Adsorption
K
1
Desorption
K
2
Sedimentation
(settling)
K
s
Resuspension
(scour)
K
u
Diffusive
Exchange
K
f
Decay
K
c
Decay
K
p
Volatilization
K
v
Particulate
component
c
bp
Bed
solids
m
b
Dissolved
component
c
bd
Complexation
Ionization
Assimilation to
food chain
Photolysis
Rainfall
Surface runoff
Litterfall
Waste discharges
Bank and floodplain
erosion
Transport
Water-bed inteface
Air - water interface
Air
Water
Bed
Adsorption
Desorption
Figure 4.4 Reactions and transfers in a natural water system (after O?Connor,
et al, 1983; Thomann and Mueller, 1987; O?Connor, 1988a, b;
University of Mississippi, 1990).
The processes in surface waters can be described by the mass balance
equations for the dissolved and particulate components (Eq. 4.3 and Eq 4.4). For a
specific chemical, e.g. nitrate or atrazine, some processes must be included in the
transport model whereas some processes may not significant and therefore can be
neglected.
s
1s 2p vs f bs s cs p p q s p
dc
dt
 = -
Kc
+
Kc
-
Kc
+
K
(
c
-
c
)-
Kc
+
Kc
-
K
(
c
+
c
) (4.3)
58
p
1s 2 p s p u bp p cbs pbp
dc
dt
 = 
Kc Kc
-
Kc
+
K
(
c
-
c
)-
Kc
+
Kc
? (4.4)
where:
K
v
, K
f
, K
s
, K
u
= the bulk transfer coefficients of volatilization, dissolved
    exchange, settling and scour respectively;
c
s
, c
p
= dissolved and particulate concentrations in water, respectively;
c
b
, c
bp
= dissolved and particulate concentrations in bed;
K
c
, K
p
= decay coefficients of dissolved and particulate form;
K
1
= K
0
r
c
m; K
0
 = adsorption coefficient, r
c
 = adsorptive capacity,
     m = concentration of solids;
K
2
= desorption coefficient;
K
q
= coefficient of dilution due to the groundwater inflow.
4.3.2 GIS and cascade modeling
GIS technology gives the opportunity to construct versatile ?cascade? models.
The idea of cascade modeling incorporated here into GIS has been extracted from the
methodology used in forecasting the municipal water use (Maidment and Parzen,
1984; Mizgalewicz, 1991).
The GIS cascade structure is two dimensional. It can be applied both in space
and time. In the time domain, a general model describes spatial distribution of annual
average amounts of agricultural chemicals in rivers. The annual values are then broken
into seasonal or monthly values. For example, the annual average concentrations c
y
 for
the Midwest can be estimated by the general function:
59
cf
y
=()? (4.5)
where: X is a vector of explanatory variables such as annual agrichemical application
and watershed morphometry (area, land slope, stream slope, stream length,
overland flow length) which do not change with time.
The Equation (4.5) can be further extended by adding a seasonal component,
as monthly fractions S(m), to break down the annual predictions of concentration c
y
into monthly values c(m):
cm cSm f Sm
y
() () ()()==? (4.6)
Cascade modeling enables further extending of the Eq. (4.6) by adding such elements
as year to year trend and an irregular random component.
Cascade modeling in the spatial domain implies that the modeling process is
subdivided into several levels of resolution, i.e., the Upper Mississippi-Missouri and
Ohio River can be subdivided into three basins: the Missouri River Basin above
junction with the Mississippi River, the Upper Mississippi River Basin, and the Ohio
River Basin. The transport of agricultural pollutants in the Upper Mississippi River is
estimated by utilizing results of sub-models that describe transport in individual
component basins such as the Des-Moines River, the Skunk River, the Iowa-Cedar
River, and Wisconsin River Basins.
Additional spatial subdivision of the Midwest can be performed by introduction
of climate zones. Each zone is defined, for instance, by a specific range of
temperatures and precipitation depths. Thus, the Eq. (4.6) could have the following
form:
cmg f Smg(,) ()()(,,)=? ??? (4.7)
60
where: c(m,g) is the monthly (m) agrichemical concentration in rivers modified for the
climate zones (g) ; g(T,P,Z) is a function of T - zonal temperature, P - zonal
precipitation depth, and Z - zone location.
The diagram shown in Figure 4.5 illustrates the example of spatio-temporal cascade
modeling within GIS.
Annual average
concentration
c(y) = f(X)
Annual average
concentration
by climate zone
c(y,g) = c(y)g(T,P,Z)
Monthly average
concentration
c(m) = c(y)S(m)
Monthly concentr.
by climate zone
c(m,g) = c(y,g)S(m)
c(m,g) = c(m)g(T,P,Z)
Climate zone
adjustment factor
g(T, P, Z)
Monthly fractions
(seasonal index)
S(m)
Spatial Domain
T
e
m
p
o
r
a
l
D
o
m
a
i
n
Figure 4.5 Example of the cascade modeling within the GIS.
Parameters of the mathematical description of the chemical application-runoff
process and chemical losses in streams are stored in a GIS attribute table. Moreover,
the equations are stored as objects in a database table. Storing equations as a database
objects not only permits one to fully implement the cascade modeling technique into
the GIS but also it simplifies the structure of the model, allows one to test and
compare an unlimited number of equations, and permits changes to the mathematical
61
description by simple record editing operations. The model prototype is constructed
within ArcView, a GIS application (ESRI, 1995).
4.3.3 Regression equation development
There is no complete and consistent data base of parameters required for
comprehensive modeling the agrichemical runoff from the field and its transport in
surface waters of the Midwest.  The runoff and transport parameters have to be
estimated from such data as:
(1) The observed flow rate and the measured agrichemical concentrations in the
variety of watersheds scattered over the upper Mississippi-Missouri and Ohio
River basins;
(2) The DEM from which a watershed morphometry can be calculated; and
(3) Parameters that describe the climatic conditions of the sampled watershed.
Thus, a model based on statistical analysis of observed concentration data is used in
this research.
Watershed morphometry, annual agrichemical rate, normal annual temperature,
and normal precipitation depth do not depend on the month of the year. These
parameters are used here to explain the average annual agrichemical concentration c
y
in Midwest rivers. The following linear relationship is tested by the regression analysis
(A detailed discussion of the set of explanatory variables that have potential
application in the large scale model of agrichemical runoff from the field and transport
in the river network is presented in Section 4.3.4 and Section 4.3.5):
62
c ASLAESQ
T T P P error
ypLL SS
avg avg
=++++++++
++ + + +
????????
?? ? ?
012345 67
8 9 10 11
(4.8)
where:
c
y
 = average annual constituent concentration (concentration with removed
seasonal component) [mg/L nitrate, ?g/L atrazine];
A
p
 = annual chemical application rate [kg/km
2
/yr];
S
L
 = average slope of the land [dimensionless];
L
L
 = average length of the constituent travel path, from the point of application to 
the stream network within a given watershed to the sampling point [km];
A = drainage area [km
2
];
E
S
 = average of the exponent of negative flow distance in streams
= 
1
1
n
L
s
ik
i
n
s
exp( )?
=
?
;
n
s
 = number of cells that constitute the stream network within a sampled 
watershed;
L
ik
 = length of the flow path from the i-th stream cell to the watershed
outlet k  [10
2
 km] (since the Missouri River is a very long river, units
10
2
 km are applied to enhance the Arc/Info-GRID calculations);
S
S
 = average slope of the stream network [dimensionless];
Q = flow rate at a given stream location [m
3
/s];
T = normal annual temperature at sampling site [?C]
T
avg
= normal annual temperature, average over sampled watershed [?C]
P = normal annual precipitation depth at sampling site [mm]
P
avg
= normal annual precipitation depth, average over sampled watershed [mm]
?
0
, ?
1
, ?
2
 ...  =  regression coefficients.
63
The right hand side of Eq. (4.8) represents two major components of the
transport process: runoff from the field and losses in the stream, as well as the climatic
conditions that affect the transport processes:
1) ?
1
A
p
+?
2
S
L
+ ?
3
L
L
+ ?
4
A  describe changes in mass applied U
R
 on a field as it
travels from the point of application to a stream;
2) ?
5
E
S
+?
6
S
S
+ ?
7
Q reflect the losses of agrichemical in rivers; and
3) ?
8
T+?
9
T
avg
+ ?
10
P+ ?
11
Pavg, incorporates into the model the effects of the
climate zone on the agrichemical transport.
More details on each of the model variables are now presented.
4.3.4 Agrichemical runoff from the field
Agrichemical application rate A
p
. Since it is a common practice to put more chemical
on the field than the amount that can be completely utilized by the vegetation and the
chemical - microbiological processes, some of the nutrients and herbicides are
transported in runoff from the field. Many studies show that the more chemical is
applied on fields, the higher are chemical loads carried by rivers (e.g., Battaglin, et al.,
1993).
Land slope S
L
. The higher the slope of the land S
L
, the chemicals are more susceptible
to washout, therefore greater losses of the chemical from the field can be expected.
This complex process is influenced by gravitational forces. Since vegetation has a
smaller chance to uptake nutrient or herbicide when the land slope is higher (due to the
shorter residence time), a greater portion of the mass applied on the field should reach
64
the stream network. Models of erosion and sediment transport include a slope
parameter.
Distance to a stream L
L
. The influence of the average distance L
L
 between the point
of herbicide or nutrient application and the location of the stream network on the
amount of mass that enters the stream is not as obvious as watershed slope. (Here, the
L
L
 is an average distance measured along the flow path between all cells that do not
represent a stream network and the cells that constitute the streams, within a given
watershed). Intuitively it may be expected that since the longer the average travel path
is, the larger the chemical losses are and thus the coefficient ?
3
, from Eq. (4.8),
estimated by the regression analysis should be negative. But, since the predictor
variable L
L
 represents complex watershed features, the coefficient ?
3
 does not
necessarily have to be negative.  The average length of the land-flow path depends on
the stream density, i.e., on the length of the streams per unit area of watershed. The
more streams there are within a given watershed, the shorter the length of the overland
flow. The density of the stream network influences the amount of chemical that enters
a unit length of the stream. Therefore, for watersheds characterized by a higher value
of L
L
 , the amount of chemical that enters a stream (mass per unit length) is higher
than the amount reaching the stream network which is located in a watershed with
smaller L
L
.
Climate. Both precipitation (P, P
avg
) and temperature (T, T
avg
) have an impact on
vegetation growth. Moreover, the greater the water surplus (precipitation minus
potential evaporation), the greater the possibility of loss of agrichemical through
leaching if the crop is not growing vigorously or through washout if the land is not
protected by a plant cover. Denitrification depends on the amount of water in soil,
whereas nitrification rate is highly correlated with the temperature (Tisdale, et al.,
1993).
65
The influence of climate on the concentrations in surface waters can be
illustrated by comparison of studies performed in different climatic regions. For
example, the largest number of atrazine detections in Swedish stream waters was in
July, August and September (Kreuger and Brink, 1993), whereas in the Midwestern
United States the major atrazine runoff occurs in May and June (Scribner, et al.,
1994). The Swedish vegetation period is short (6-8 months) and cold (3?-17? C)
Since the region under scrutiny extends from about 37? N to 50? N (latitude)
and from 79? W to 114? W (longitude) the spatial distribution of the average
temperature and the average precipitation influences not only the spatial distribution of
the chemical runoff from the field but it also causes spatially different agrichemical
application times. The difference in climate conditions within the studied region could
be represented by a spatially distributed adjustment coefficient as well as a time shift
introduced into periodic functions that describe seasonal variation of agrichemical
concentration in the surface water. The time-shifting of periodic functions is not
studied in this research.
4.3.5 Transport in rivers
Exponent of negative stream-flow distance E
S
. The explanatory variable E
S
 has been
introduced to represent agrichemical losses in streams. It is defined by the following
formula (excerpted from Eq. 4.8):
E
n
L
S
s
ik
i
n
s
=?
=
?
1
1
exp( ) (4.9)
66
where:
 n
s
 = number of cells that constitute the stream network within a sampled
 watershed;
L
ik
 = length of the flow path from the i-th stream cell to the watershed
outlet k  [10
2
 km]
Equation (4.9) is a simplified version of the discrete model of exponential losses of
chemical as it travels downstream. The following paragraph explains the development
of the explanatory variable E
S
.
The losses of agrichemical in streams can be described by an exponential
function of the travel time (the traditional approach) or by an exponential function of
the travel distance (Smith. et al., 1993). Although it is possible to estimate the travel
time from the observed flow time series, in this research the agrichemical decay has
been related to the travel distance, i.e., the amount of chemical that enters the stream
in point i (cell i in raster representation of river) decays as it travels downstream
according to the following equation:
RRkL
ki Sik
i
n
=?
=
?
exp( )
1
(4.10)
where:
R
k
 = total agrichemical mass in a runoff from k-th watershed [kg/m
3
];
k.. = index of sampled watershed outlet (cell k);
R
i
 = chemical load that enters the stream in point i (cell i) [kg/m
3
];
n = number of all cells that constitute the stream network located within k-th 
watershed;
k
S
= overall distance decay coefficient [1/10
2
 km];
L
ik
 = length of the flow path from stream cell i in which the chemical runoff from a
67
field enters the stream network to the watershed outlet located in cell k  
[10
2
 km].
Since application of the Eq. (4.10) is very computationally intensive, the following
assumptions have been made to construct it?s simplified form, i.e., equation (4.9):
- a unit mass of chemical enters the stream network (?R
i
 = 1 within sampled
    watershed);
- the chemical that enters surface water is uniformly distributed over all stream 
    cells, i.e., the amount of chemical that enters the stream at each cell of the
    stream network within sampled watershed equals 1/n
s
;
- the overall distance decay coefficient is equal one, k
S
 = 1 (the chemical losses
    depend only on the chemical travel distance L)
Stream slope S
s
. The stream slope parameter is introduced into the agrichemical
transport equation to represent two physical features: flow velocity that is directly
related to the chemical travel time, and stream power that affects sedimentation and
resuspension of deposits as well as their transport.
4.3.6 Seasonal variations
The seasonal variations of the nitrate concentration as well as the atrazine
concentration in surface waters are modeled by two sets of 12 values, calculated by
the following formula:
68
()
Sm
akm bkm
aki bki
kk
k
kk
ki
()
exp( sin( / ) sin( / )
exp( sin( / ) sin( / )
=
+
+
=
==
?
??
212 212
212 212
1
5
1
5
1
12
pipi
pipi
(4.11)
where:
S(m) = the seasonal factor of month m (average S(m) = 1)
sin(2kpim/12), and cos(2kpim/12)  =  components of the Fourier series (the cycle 
corresponding to k = 1 has a 12-month period, k = 2, 3, 4, and 5 are 
harmonics of period 12/m months;
m  = month of a year (1 for January);
 i = index of the month (i = 1, 2, ... 12);
k = index of the harmonics;
a
k
 and b
k
 = regression coefficients.
The exponent of the periodic function in Eq. (4.11) is a result of the
agrichemical transport model specification in which a linear function that describes the
average concentration in a stream is multiplied by a seasonal factor. To estimate the
coefficients a
k
 and b
k
 from the concentration data the logarithmic transformation of
concentration data is necessary. Two models have been selected to determine the
variation of the constituent concentration in sampled rivers. The first one explains
monthly changes by selected harmonics of the Fourier series (Eq. 4.12), whereas the
other model, in addition to the sine-cosine components, embodies the flow rate to
isolate the flow effect from the systematic seasonal the variations (Eq. 4.13):
[] ()
ln ( , ) sin( / ) sin( / )cjd w a km b km
jk k
k
=+ +
=
?
212 212
1
5
pipi(4.12)
69
and
       
[] [ ]()
ln ( , ) ln ( , ) sin( / ) sin( / )cjd w a Qjd a km b km
jk
k
=+ + +
=
?0
1
5
212 212pipi(4.13)
where:
ln[...] = natural logarithm;
c(j,d) = concentration measured at site j on day d (?g/L or mg/L);
Q(j,d) = flow rate measured at site j on day d (m
3
/s);
w
j
 = an intersect specific for the j-th sampled watershed, determined by the
 regression analysis;
a
0
, a
k
 and b
k
 = regression coefficients;
j = index of the sampling site;
d = day of sample collection;
k = harmonics number;
m = month of the year.
By combining (Eq. 4.11) with (Eq. 4.12) and (Eq. 4.11) with (Eq. 4.13) the relation
between the average annual concentration in a sampled stream can be given by the
following equations:
()cj w a ki b ki
yj k k
ki
( ) exp( ) exp( sin( / ) sin( / )=+
==
?
212 212
1
5
1
12
pipi(4.14)
and the model including the flow rate is specified by:
()cj wQ a ki b ki
yQ j
a
kk
ki
( ) exp( ) exp( sin( / ) sin( / )=+
=
0
212 212
1
5
1
12
pipi(4.15)
70
The flow rate is introduced into analysis to examine the effects of the flow rate
on the concentration level. However, the data utilized in this research may be biased by
extreme flow conditions. At least one third of the reconnaissance data (Scribner, et.
al., 1993) contain measurements made during the first major runoff after application of
herbicides (33% of atrazine samples collected in 1989, and 50% of atrazine samples
taken in 1990). Twenty five percent of nitrate plus nitrite as N measurements were
collected in May and June of 1989 and 50% of nitrate samples represent
concentrations in major runoff events after fertilizer application in 1990. Also, the
gathering of samples in nine rivers of Midwest (Scribner, et. al., 1994) was designed to
study the concentrations of selected herbicides and nutrients in storm runoff rather
than to investigate the seasonal changes of agrichemicals in the Midwest rivers.
The general relation between flow rate and the chemical concentration is as
follows: When flow increases, concentration increases. This is a result of the ?washout
effect?. If the flow increases above a level at which the chemical washout is in balance
with the chemical dilution, the concentration does not increase. Further increase in
flow may produce further chemical dilution and therefore decrease in concentration.
Figure 4.6 shows an example of such a nitrate concentration pattern observed in the
Sangamon River at Monticello, Illinois, in May 1990 (Scribner, et al., 1994). As flow
increases up to about 40 m
3
/s, the nitrate concentration level rises. A further increase
of the flow, up to 80 m
3
/s, does not produce a change of the concentration level. For
flows larger than 80 m
3
/s the dilution effect becomes significant and the nitrate
concentration decreases when the flow rate increases.
71
Flow [m3/s]
0
5
10
15
20
0 50 100 150 200 250 300 350
NO3+NO2 as N
concentration [mg/L]
Figure 4.6 Nitrate plus nitrite as nitrogen concentrations measured in the
Sangamon River at Monticello, Illinois, in May 1990 (Scribner, et
al., 1994).
Research performed by Walling and Webb (1984, work cited by Jones and
Burt, 1993) shows that in most streams the annual nitrate variations do not have a
perfectly symmetrical sinusoidal form; the annual minimum and maximum occur 4-6
weeks later and 2-3 weeks earlier then the timing suggested by a single harmonic.
Furthermore, no clear seasonal variations of nitrate concentration exist in catchments
where groundwater with a consistently high nitrate concentration mixes with quick
flow of varying origin and concentration (Jones and Burt, 1993).
4.3.7 Extracting values of explanatory variables for the regression analysis
The estimation of values of explanatory variables such as agrichemical
application rate, total application, average stream slope, average land slope, exponent
72
of the negative flow length, and average distance from the field to the closest stream is
performed in two steps: (1) Grids of spatially distributed parameters are constructed
for the Upper Mississippi - Missouri River and the Ohio River basins, and (2) for each
cell that represents a sampled watershed outlet the value of the explanatory variable is
extracted.
Here, the grid of spatially distributed parameters means a grid which each cell
contains average or sum calculated for the total drainage area upstream to the given
cell. Figure 4.7 shows selected cells that contain a value that characterize the upstream
watershed. This concept is supported by Arc/Info-Grid commands such as
flowaccumulation and flowlength.
a cell
selected cells that determine
the drainage areas
major flow paths
Figure 4.7 Example of a grid of spatially distributed values of explanatory
variables.
73
4.3.8 Application of the regression models
Once their parameters have been determined, the agrichemical transport
models (Eq. 4.6) can be used in the following way:
- Estimation of average monthly and average annual concentrations in rivers of the
Upper Mississippi-Missouri basin, including the Ohio River basin. The
calculations are made using grid-map algebra. The calculations are estimated in
all cells (9.6 *10
6
 cells of size 500 m ) that constitute the basin. The equations
that describe chemical concentration in rivers require only a map of distribution
of the total agricultural chemical use, the parameters of watersheds that can be
easily determined from digital elevation model, and the maps of annual
temperature and precipitation depth. Only models that do not utilize the flow
rate can be applied. Since the calculation of the concentrations over such a
large area is very computationally and computer disk space intensive, it is not
presented in this dissertation.
- Calculation of average monthly agrochemical concentrations in the Iowa-Cedar
River basin. The map of flow rate is required for obtaining a spatial picture of
atrazine and nitrate concentrations in surface waters.  The estimation is
performed for the watershed subdivided into 1032 subwatersheds of average
area 31.6 km
2
 utilizing maps in a vector format. The regression equations are
applied to each subwatershed utilizing the data from an attribute table that
characterizes the upstream drainage area. A GIS approach to model the
concentrations in rivers is discussed in the following Section 4.4. The
procedure of the spatial distribution of the historical flow record is presented in
Section 4.5.
74
4.4 GIS model description
4.4.1 Subdivision of study region into modeling units
Elementary watersheds, i.e., modeling units that are considered lumped
systems, constitute the smallest units into which a region is subdivided. Each unit is
characterized by set of parameters such as area, agricultural chemical application,
slope, depth of precipitation, water runoff, average elevation, and an equation that
relates the mass of chemical applied and the mass of chemical runoff.
Since the GIS offers very convenient tools for data storage and manipulation,
all attributes can be stored and extracted by models that operate on different spatial
scales. The order of processing the individual watersheds is the researcher?s choice.
Moreover, each watershed does not need to be divided into modeling units of the same
size. To make the modeling process efficient, such features as density of spatial
information and diversity of terrain should influence the assumed size of the
elementary unit.
A watershed is explicitly defined by its outlet point. This hydrologic property is
utilized here to subdivide the region under investigation into elementary drainage
areas. Three types of watershed outlet locations are considered:
1) Points in which the drainage area exceeds a threshold value. Streams originate
at these points. In this research a threshold value of 25 km
2
 drainage area has
been assumed;
2) Points located immediately upstream of a stream junction; and
75
3) Gauging station sites.
Figure 4.8 shows example of selected watershed outlets and corresponding modeling
units:
(1)
(1)
(2)
(2) (3)
(2)
Figure 4.8 Example of watershed outlets: (1) beginning of the river, (2) stream
junction, and (3) gauging station.
The watershed structure, developed by Maidment (1993) for hydrologic
modeling utilizes type (2) and (3) watershed outlets which are positioned at the stream
junctions and at the gauging station locations. In this study, this set of watershed
outlets has been extended by adding the points in which the stream network,
delineated from DEM, begins (type 1 outlet). A test has been performed to determine
the influence of additional unit watersheds on the uniformity of region subdivision and
the control on the unit area. The Iowa-Cedar River basin has been subdivided using
two sets of outlets. Full set: Median unit watershed area = 25.8 km
2
 and mean = 31.6
km
2
, reduced set (type 1 outlets not included): median = 37.9 km
2
 and mean = 46.7
km
2
. By including the outlets of type 1, the median of unit watershed drainage areas is
very close to the threshold drainage area (25 km
2
). Figure 4.9 compares the
frequencies of modeling unit area.
76
0
50
100
150
200
250
300
350
400
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 >1500
Area km
2
Frequency
Watershed outlets at
beginning of stream
network, junctions,
and gauging stations
Watershed outlets at
stream junctions and
gauging stations
Figure 4.9 Comparison of the frequency of modeling unit area subdivided
using different sets of watershed outlets.
The following list summarizes the advantages of the addition of type(1) outlets:
- The watershed is subdivided into more uniform (similar area) modeling units
and one has more control on the area of units;
- It makes possible the determination of the flow and the constituent load in all
nodes of the stream network. Each node has a defined contributing area; and
- The representation of all streams can be standardized. Each reach has input
(inflow or load that enters the reach at the upstream end), lateral loss or gain,
and output (outflow or load that leaves the reach at its end).
77
The threshold area of 25 km
2
 was selected after many tests with different
threshold areas were performed. A smaller threshold area results in very dense stream
network and thus large number of areas of size of 1-2 cells. After Arc/Info conversion
of these small units from raster format (grid) into vector format many of them
disappeared. In addition, smaller than 25 km
2
 threshold areas are not justified by the
data used in the research. For example, the agrichemical application rate is published
with a county-size spatial resolution. The stream network delineated from a 3'' DEM
using 25 km
2
 areas, is slightly more dense that the one represented by the RF1
(1:500,000 digital map of rivers).
A larger threshold value than 25 km
2
 resulted in very coarse subdivision of
studied region and a low density stream network. Figure 4.10 presents the Iowa-Cedar
River watershed divided into modeling units of different sizes.
Figure 4.10 Division of the Iowa-Cedar River into modeling units using different
threshold drainage areas: 25 km
2
, 400 km
2
, and 2500 km
2
.
78
4.4.2 Unit watershed flow system
The network flow system is common function in vector GIS (Maidment,
1993). Here the flow system has been extended: instead of arcs, unit watersheds
(polygons) compose the flow system. The flow topology is described by two numbers:
the modeling unit ID and the ID of the downstream unit, i.e., the next unit on the flow
path. The ID = 0 of the next unit indicates that there are no more downstream units.
Figure 4.11 shows an example of the description of the flow topology of the modeling
units.
(1,3)
(2,5)
(5,6)
(6,0)
(3,5)
(4,2)
Figure 4.11 An example of the flow topology of the unit watersheds; (x,y), x is
the unit ID, y is the ID of downstream to x unit.
The flow direction indicator is the basic concept in the raster-based hydrologic
modeling. For example, Arc/Info Grid denotes the next cell in the flow path by one of
eight numbers: 1 represent flow into E (East) neighbor cell, 2 in SE cell, 4 in S cell,
79
8 in SW cell, 16 in W cell, 32 in NW cell, 64 in N cell, and 128 in NE cell. These
numbers are called ?flow direction?. Since modeling units are not regular spatial
shapes, as the cells are, it is not possible to create an uniform numbering system of the
flow direction. The method proposed here describes the flow connectivity by
specifying the ID of the next unit on the flow path.
Addition of an item that describes the flow direction into the unit watershed
attribute table makes it possible to utilize most of the concepts of hydrologic
modeling, so far used in raster GIS, in the vector environment. Such functions as flow
accumulation, basin delineation, and flow length can be applied for any shapes and
thus for unit drainage areas. The flow system described here may be adopted for all
models in which the conditions in a modeling unit do not influence the conditions in an
upstream unit such as kinematic wave routing and constituent decay as a pollutant
flows downstream.
In this study, the flow connectivity of the unit watersheds is used to calculate
cumulative or average parameters of drainage area upstream of a given point. These
values are applied to the regression equation to estimate agricultural chemical
concentration in the runoff. The following list presents selected examples of
application of the unit watershed flow system that have been programmed in the
Arc/View script language:
- weighted average of a feature (for example agrichemical application ) for the
total drainage area upstream of each (or selected) modeling unit (like the Grid
function zonalaverage);
- accumulated value over total upstream drainage area going along the flow path
(vector version of the Grid flowaccumulation function); and
80
- difference between the inputs and the output for each modeling unit, flow
difference or ?flow-decumulation?.
The unit watershed approach of modeling agrichemical transport can be
considered as a semantic data model:
... semantic data modeling --- creating abstractions of geographic
data layers which map one to one with their geographic representation
but which are simplified in a functional description to the level needed
for hydrologic modelling. (Maidment, 1993)
Figure 4.12 shows examples of the conceptual stream network. The links have been
developed by connecting the cells immediately below each modeling unit outlet. Thus,
although the system is conceptual, each node is located on the river represented in
Grid format.
Figure 4.12 Flow system in the Iowa-Cedar River basin subdivided into
modeling units of different sizes (threshold drainage area: 25 km
2
,
400 km
2
, and 2500 km
2
).
81
In this system, the outflow from the source watershed (first order watershed) is
a point inflow into the stream. The outflow from an intermediate watershed can be
represented as a lateral inflow applied on the stream length or can contribute directly
to the outflow from the reach, as applied in this research. Thus the conceptual stream
network attribute table contains three items that describe the water or agrichemical
mass flow conditions:
- Inflow (sum of inflows from upstream units);
- Lateral inflow; and
- Outflow.
In addition, the arc attribute table can contain wide range of items that describe the
links (length, slope, RF1-ID, agrichemical decay coefficient, travel time) as well as the
parameters of the beginning node and the ending node (elevation, coordinates, and
length from the watershed outlet). In this research only the conceptual stream network
represented by unit watersheds is utilized. Since the unified system of hydrologic unit
IDs is developed in this research, the attributes of unit watersheds and the attributes of
stream reaches can be linked, i.e., stream parameters such as actual flow length or
stream slope can be attributed to modeling units.
4.4.3 Ordering system of the modeling units
To enhance the calculations performed by the GIS model, the following system
of ordering modeling units has been utilized: The most upstream units are assigned an
order one. An interior unit has the order equal to the maximum order of the upstream
units increased by one. Figure 4.13 compares this ordering method with the Strahler
82
and the Shreve ordering systems (ESRI, 1992). The proposed ordering system allows
one to perform calculations in consecutive manner: initially all the first order units are
processed, then the order is increased by one and all units of order two are evaluated.
The routing is performed until the unit of the highest order is calculated.
1
1
1
1
2
2
2
1
3
1
3
1
1
1
1
2
2
3
1
5
1
6
1
1
1
1
2
2
3
1
4
1
5
(a) (b) (c)
Figure 4.13 Comparison of the stream ordering systems: (a) Strahler, (b)
Shreve, and (c) utilized in the agrichemical transport model.
4.4.4 Enhancement of the stream delineation process
The grid that describes the cell-to-cell flow (flowdirection) is crucial for all
hydrologic analysis that is performed in a rasterized environment. Procedures such as
stream and watershed boundary delineation, dividing a basin into modeling units,
stream slope calculation, length of the flow path estimation, and connection of
hydrologic units, are examples of operations that cannot be performed without the
map of flow direction. Moreover, the accuracy of all derived information depends on
the precision of the flow direction grid. Therefore, an effort has been made to develop
a method to improve the map that represents the flow paths. The RF1-digital
1:500,000 map of the US rivers has been selected as a basis for the spatial framework
83
of the entire flow system. The following explanations support the application of a map
of existing rivers to correct the flow system determined from a DEM:
- Since the location of a stream that is delineated from elevation data depends on
the cell size, the stream networks determined from the DEMs of different
resolutions are not compatible. Thus, the gauging stations linked to one grided
river system will not be in agreement with other grided river systems derived
from DEM grids of different cell sizes.
- The stream system constitutes the best framework for the spatial flow. It took
hundreds of thousands of years for a river bed to develop to its current form.
Since the river location practically does not change, other information such as
position of gauging stations may be related to the location of the stream reach.
- In flat regions, the streams delineated from the DEM tend to be straight lines,
whereas, in reality the rivers have a tendency to meander. This causes an
overestimation of the stream slope and an underestimation of the river length in
purely DEM-derived streams.
- RF1 represents the true river system, whereas, the stream network delineated
from the DEM just approximates the same system.
The process of the DEM adjustment is based on the converting the RF1 into
grid form and then increasing the elevation of all DEM cells, that do not represent
gridded RF1, by an arbitrary value (e.g., 10,000 m). This operation forces the Grid
GIS to create a map of flow direction that is compatible with the flow system
represented by the vector map of rivers (RF1). The method of enhancing the flow
system development has the following disadvantages:
84
- Since the elevations of the DEM are changed, the modified DEM can not be
used for other tasks than the flow direction estimation.
- The stream network has to be represented by a single line. A double line
description of rivers can be utilized if the distance between the lines is smaller
than the cell size.
- All existing loops in the river network have to be removed or opened to
eliminate the ambiguous flow paths.
- All lakes have to be converted into line representations or to polygons.
- The cell width applied for the adjustment process should be smaller than half of
the distance between any streams in RF1, to avoid connections of stream
networks from different basins that may be created when converting from
vector format into raster format.
If the river network does not fulfill the above mentioned requirements, some editing
after converting into grid format is necessary.
Incorporating the RF1 into a grid has an additional advantage. By assigning the
reach ID from RF1 to the raster river representation, the attribute table of RF1 can be
linked with the attribute table of derived grids. Thus, such information as the average
flow velocity, average flow rate or stream names that are in the RF1 attribute table can
be used for grid models and vice versa, the parameters estimated in grid such as reach
slope, drainage area and flow length can be assigned to the streams in vector RF1. The
RF1 - Grid link extends the grid-network procedure for hydrologic modeling
developed by Maidment (1992).
85
4.5 Redistribution of the flow record over ungauged rivers
The flow rate is essential to estimate the agrichemical concentration and load in
all rivers of the area under investigation. In this study, the historical flow record is
utilized instead of synthetic values. The high or low flow conditions are modeled by
selecting a year from the past that had the high or low flow rate recorded. The flow
measurements are available only in locations in which the USGS gauging stations are
located. Therefore, a procedure that calculates the flow rate in ungauged stations has
been developed. This section describes this procedure.
4.5.1 GIS database of monthly flow rate and the precipitation depth
To make the model of transport of agrichemicals capable of reconstructing
historical conditions, a database of the recorded average monthly flow rate and a
database of the observed average monthly precipitation depth must be constructed.
Since the model is developed within the GIS, the data structure of the flow and
precipitation time series must be incorporated into the geographic system. The
advantages of this approach are as follows:
- Compactness of the system. Spatial and temporal data are stored in one format
that is specified by the GIS;
- Efficiency of the system. The spatio-temporal features can be viewed, queried,
and processed directly by the procedures built into such GIS software as
Arc/Info or ArcView;
- Easy to maintain. Data can be organized by spatial units (e.g., political or
hydrologic units) and/or by temporal unit (e.g., year, month or decade);
86
- Simple to understand. Data are stored in attribute tables, records represent the
spatial domain whereas the columns (items) represent the time domain.
The GIS database of monthly flow rate and the database of the average
monthly precipitation depth is developed in two steps: first a map of monitoring
stations is created and then, for each map, the attribute table with the measurements is
built.
5457000
5459500
5457700
5458000
5449000
5449500
5462000
5458500
5458900
5463000
5464000
5463500
5451500
5451700
5464500
5452000
5451900
5452200
5453100
5453000
5454000
5454300
5454500
5455100
5455500
5455700
5465000
5465500
Figure 4.14 The Iowa-Cedar River basin: subwatersheds and selected USGS
gauging stations (numbers represent station ID).
The gauging station maps are created utilizing the latitude and longitude of
gauging sites published by Hydrosphere (1993 a, b; 1994). Although there are 38
87
USGS stations in the Iowa-Cedar River basin only the 28 stations with complete flow
record for period from 1960 to 1992 have been used for analysis. Figure 4.14 shows
the map of the USGS gauging stations selected for modeling the spatial distribution of
recorded flow rate.
The map of National Weather Service Climate stations contains 86 stations
that are located within the Iowa-Cedar River basin and within the 50-km buffer zone
outside the basin. Figure 4.15 shows the map of the climate stations. All climate
stations are utilized to create precipitation maps.
Figure 4.15 Weather stations applied to analysis of the hydrologic conditions in
the Iowa-Cedar River watershed.
88
A fragment of the point attribute table that contains average monthly flow rates is
presented in Table 4.1.
Table 4.1 An example of PAT--point attribute table of the USGS gauging
station coverage (e.g., item M199001 contains average flow rate in
year 1990, month 01). Full table contains monthly flow record for 38
stations, for period from 1940 to 1992 in m
3
/s.
GSFLOW_ GSFLOW_ID STATION_ID M199001 M199002 M199003 M199004 M199005
1 1 5457000 1.339 1.419 13.111 15.036 18.519
2 3 5459500 0.292 0.357 3.228 2.274 6.513
3 4 5457700 2.444 3.596 22.201 23.390 31.630
4 5 5458000 0.165 0.294 5.239 3.143 4.955
5 6 5449000 0.004 0.020 0.697 0.413 0.445
6 9 5449500 0.154 0.204 1.481 1.141 2.917
7 10 5462000 1.444 1.855 15.150 12.601 26.618
4.5.2 Average precipitation depth in modeling units
The process of spatial redistribution of the measured monthly average flow
requires the average precipitation depth for each modeling unit. GIS water quality
models such as SWAT-GRASS utilize the rainfall depth observed in the closest
weather station to the subbasin (Ramanarayan, et al., 1996, Krysanova, et al., 1996).
The methods commonly used in hydrology for spatial estimation of rainfall from rain
gauges are the Thiessen polygon method (Chow, et al., 1988) and the inverse distance-
squared method (Smith, 1993). There are two other functions available in Arc/Info
GIS: kriging and trend (fitting a polynomial regression surface). In this research the
Arc/Info IDW function (inverse distance-squared method) has been applied. It creates
a grid of spatially distributed values extracted from the attribute table of point
89
coverage. The calculations are very fast, thus it was feasible to create maps of spatial
distribution of monthly average precipitation depth for the Iowa-Cedar River basin for
the period from 1950 to 1992. Figure 4.16 presents the map of precipitation depth
estimated for June 1990.
June 1990 [mm/d]
0.0 - 5.0
5.0 - 7.0
7.0 - 8.0
8.0 - 9.0
9 .0- 11.0
Precipitation depth
Figure 4.16 Spatial distribution of monthly precipitation depth [mm/d] in the
Iowa-Cedar River watershed in June 1990.
90
4.5.3 Mathematical description
There are about 38 USGS gauging stations in the Iowa-Cedar River basin
(some of them are not in service). One or more gauging stations determine a drainage
area (or partial drainage area), referred to as a gauging station zone or zone. The
gauging station constitutes a point through which a known amount of water flows
from one zone to an other zone. The runoff from each modeling unit depends on two
factors: 1) the water balance calculated for the unit?s respective zone and 2) the
distribution of the precipitation depth over the gauging zone. Figure 4.17 illustrates an
example of a gauging zone and modeling units.
G43G68G61G72G6cG65G73 G43G69G74G79G2c G49G41
G41G75G73G74G69G6eG2c G4dG4e
Gauging Stations Gauging Station Zones
Modeling Units
within the Zones
Figure 4.17 Cedar River watershed above Charles City, Iowa: An example of
gauging station zones and modeling units.
91
The process of spatial redistribution of the measured monthly average flow is
performed in four steps. Each step is performed separately for a given month. Since
the method only redistributes observed values using drainage area and precipitation as
a weight, the effect of the snow accumulation and the evaporation on the spatial
distribution of the flow is included in the flow record for the gauging zones. Within
each zone neither the snow accumulation nor evaporation or groundwater transfer are
explicitly taken into consideration but they are considered implicitly by using varying
runoff coefficient in each month of each year. The precision of data used for the
agrichemical transport such as county level chemical application do not justify
construction of a very detailed flow model that would require information about
spatially distributed temperature, snow depth, land use, aspect, solar radiation etc. The
steps of the flow rate interpolation are as follows:
1) Estimation of an average runoff coefficient relating monthly precipitation to
discharge;
2) Approximation of the flow in streams;
3) Evaluation of error between estimated flow and gauged flow;
4) Correction of estimated flow rate at the gauge and over all modeling units
within gauged zone.
Estimation of average runoff coefficient.  Using recorded outflow from the first
order zones, i.e. watersheds determined by the most upstream gauging stations, an
average runoff coefficient C
f
  is calculated according to the following equation:
Cm
Qm
aAmPm
f
j
j
jj
j
()
()
()* ()
=
?
?
(4.16)
92
where:
C
f
(m) = average runoff coefficient for the m-th month [dimensionless]
Q
j
 (m) = average flow recorded  in j-th gauging station during m-th month [m
3
/s]
P
j
 (m) = average monthly precipitation depth [mm/d]
A
j
 (m) = j-th watershed area [km
2
]
m = month
j = index of the first order watersheds
a = units conversion factor.
First approximation of the flow in streams.  The runoff from the modeling units is
summed along the flow path, moving downstream from a first order stream toward the
outlet of the basin. The mass balance for the i-th unit is described by the following
formula:
?= ?+
?
Qm Q m aC mPmAm
i k fii
k
() () ()()() (4.18)
where:
Q'
i
(m) = estimated cumulative flow at the outlet point of the i-th unit [m
3
/s]
Q'
k
(m) = estimated cumulative flow at the outlet point of the k-th unit [m
3
/s]
k = index of units in the immediate upstream vicinity of the i-th unit
 C
f
(m), P
i
 (m), A
i
 (m), = average runoff coefficient, average monthly precipitation 
   depth in unit i, and i-th unit area, respectively
To make calculations more efficient, when the flow path crosses the border of
the gauging station zone, i.e. at a gauging station, the calculated cumulative flow
?Q'
k
(m) is substituted by the measured value Q
j
(m). This substitution of values ensures
93
that the observed inflow is used to calculate accumulated flow in each zone, and the
resulting error at the zone outlet is due only to inaccuracy of water balance estimated
within the zone (errors do not propagate from zone to zone). Thus, the water balance
in unit downstream to the gauging station is:
?= +Qm Qm aC mPmAm
ij fii
() () ()() () (4.18)
where:
Q'
i
(m), C
f
(m), P
i
 (m), A
i
 (m),  = same as for (Eq. 4.17)
Q
j
(m) = observed inflow into modeling unit i, from zone j. This value equals to
the outflow from zone j [m
3
/s]
Error evaluation. In this step, the difference between estimated and observed flow,
?Q
j
(m), is calculated for each zone j:
?Qm Qm Qm
jji
() () ()=?? (4.19)
where:
Q
j
(m) = observed outflow from zone j
Q'
i
(m) = estimated cumulative flow at the outlet point of the i-th unit that
    is also the outlet point of the j-th gauging station zone.
Correction of the cumulative flow.  The correction of the estimated
cumulative flow is the crucial process of the flow distribution method. Two weighting
coefficients k
1
 and k
2
 are applied. The coefficient k
2
 redistributes error according to the
cumulative runoff calculated for each zone separately - the flow in rivers is created
only by the estimated runoff C
f
P(m)A(m). There are no inflows from the upstream
zones. Thus the coefficient k
2
 redistributes error according to the drainage area and the
94
precipitation depth within each zone separately. It is calculated for each modeling unit
as a proportion of the runoff Q
x
i
(m) from the drainage area upstream of the given, i-th
unit outlet (within the zone j) to the total runoff Q
x
j
(m) from the zone j (at the
beginning of the flow path it is very small, at the zone outlet it equals one):
k
Qm
Qm
i
i
x
j
x2
=
()
()
(4.20)
To put more burden of the error correction on the major rivers rather than
small streams, the coefficient k
1
 has been introduced. There is a higher probability that
the estimated error is due to the losses/gains of the river between the two gauging
stations than to the losses/gains in small streams located far from measurement points.
In another words, the further from the gauged reach a stream is located, the higher is
the uncertainty of the flow is and therefore, the more appropriate it is to apply the
average basin runoff coefficient  to estimate the stream flow rate.
The coefficient k
1
 is calculated using total cumulative flow, i.e., the
approximated flow in the streams of the whole basin as a proportion of the estimated
cumulative flow Q'
i
(m) at the outlet point of the i-th modeling unit to the cumulative
flow Q'
j
(m) at the outlet of zone j in which the i-th unit is located:
k
Qm
Qm
i
i
j
1
=
?
?
()
()
(4.21)
The adjustment of estimated flow (Eq. 4.18 and Eq. 4.19) can be represented
by the following formula:
?? = ? +Qm Qm kk Qm
iiij
() () ()
12
? (4.22)
where:
Q''
i
(m) = corrected cumulative flow at the outlet point of the i-th modeling unit;
95
Q'
i
(m) = estimated cumulative flow at the outlet point of the i-th modeling unit;
?Q
j
(m) = error, difference between observed and estimated cumulative flow at the 
outlet of zone j;
k
1
,k
2
=  weighting coefficients.
4.5.4 Example of flow redistribution
This section shows an example of the redistribution of the recorded flow rate in
the gauged zone 6565500 in which the Iowa River joins the Cedar River for June
1990. The location of this zone is shown in Figure 4.18.
The average runoff coefficient for the June 1990 is calculated using recorded
outflow and redistributed measured precipitation depth in the first order gauged zones
of the Iowa-Cedar basin from Eq. (4.17):
Cmf()
.4
.
.==
345
891 6
0 387
where m indicates June 1990, 345.4 m
3
/s is the cumulative discharge from the first
order basins, and 891.6 m
3
/s is the product of monthly precipitation and drainage area
over all first order basins.
The outflow from the zone, station 5465500 (the Iowa River at Wapello),
equals to 827.621 m
3
/s. The measured inflows at stations 5455700 (the Iowa River
near Lone Tree) and 5465000 the Cedar River near Conesville) are 285.039 m
3
/s and
491.895 m
3
/s respectively.
96
Station 5455700
IowaRivernearLoneTree
Q = 285.039 m3/s
Station 5465500
Iowa River at Wapello
Q = 827.621 m3/s
Station 5465000
Cedar River near Conesville
Q = 491.895 m3/s
Figure 4.18 Location of the gauged zone 5465500, its subdivision into modeling
units, and the USGS gauging stations.
The estimated outflow from the zone is equal to the sum of inflows from
upstream zones plus the runoff from zone due to the precipitation (40.034 m
3
/s):
? =++
=++=
QmQmQmaCmPmAm
ms
f5465500 5455700 5465000 5465500 5465500
3
285 039 491895 40 034 816 968
() () () () () ()
... ./
The error of estimated flow is calculated according to the equation (4.19):
97
?Qm ms
5465500
3
827 621 816 968 10 653() . . . /=?=
The correction coefficients k
1i
 and k
2i
 are calculated according to the equations (4.20)
and (4.21) respectively. k
1i
 is calculated by dividing column Q
i
'(m) by Q
j
'(m) = 816.968
m
3
/s and k
2i
 is calculated by dividing column Q
i
x
 (m) by Q
j
x
 (m) = 40.03 m
3
/s.
Table 4.2. Steps of the recorded flow rate redistribution in gauged zone
5465500 for June 1990.
Unit Next Order Area P C
f
P
i
A
i Q
i
x
 (m) Q
i
' (m)
k
2i
k
1i Q
i
" (m)
ID unit ID km
2
mm/d m
3
/s m
3
/s m
3
/s - - m
3
/s
100644 644 1 29.29 9.1 1.198 1.198 1.198 0.0299 0.0015 1.198
644 675 2 69.53 8.9 2.773 3.970 3.970 0.0992 0.0049 3.975
100666 666 1 25.96 8.8 1.027 1.027 1.027 0.0256 0.0013 1.027
663 671 58 28.22 8.5 1.076 1.076 286.115 0.0269 0.3502 286.216
657 665 74 11.59 9.1 0.475 0.475 492.370 0.0119 0.6027 492.446
665 680 75 64.89 8.5 2.469 4.066 495.961 0.1016 0.6071 496.618
100664 664 1 25.03 9.5 1.065 1.065 1.065 0.0266 0.0013 1.065
100668 668 1 30.68 8.3 1.139 1.139 1.139 0.0285 0.0014 1.139
668 667 2 19.56 8.3 0.727 1.866 1.866 0.0466 0.0023 1.867
666 671 2 10.85 8.4 0.409 1.436 1.436 0.0359 0.0018 1.437
667 671 3 36.08 8.2 1.333 4.192 4.192 0.1047 0.0051 4.197
664 665 2 1.39 9.2 0.057 1.122 1.122 0.0280 0.0014 1.123
100673 673 1 25.08 8.3 0.933 0.933 0.933 0.0233 0.0011 0.933
100676 676 1 26.31 8.3 0.977 0.977 0.977 0.0244 0.0012 0.978
671 675 59 20.17 8.2 0.738 7.442 292.481 0.1859 0.3580 293.190
670 667 2 1.41 8.2 0.052 0.993 0.993 0.0248 0.0012 0.993
673 681 2 64.83 8.2 2.379 3.312 3.312 0.0827 0.0041 3.315
100672 672 1 25.09 9.0 1.008 1.008 1.008 0.0252 0.0012 1.008
100670 670 1 25.66 8.2 0.941 0.941 0.941 0.0235 0.0012 0.941
100678 679 1 29.79 8.1 1.087 1.087 1.087 0.0271 0.0013 1.087
100674 674 1 30.8 8.0 1.110 1.110 1.110 0.0277 0.0014 1.110
675 677 60 6.4 7.9 0.227 11.639 296.679 0.2907 0.3631 297.803
674 677 2 42.37 7.8 1.478 2.587 2.587 0.0646 0.0032 2.590
672 679 2 47.07 8.4 1.764 2.772 2.772 0.0692 0.0034 2.775
676 681 2 59.99 8.2 2.216 3.194 3.194 0.0798 0.0039 3.197
681 685 3 73.53 7.8 2.565 9.071 9.071 0.2266 0.0111 9.097
677 680 61 1.37 7.7 0.047 14.274 299.313 0.3566 0.3664 300.705
680 682 76 27.33 7.7 0.949 19.289 796.223 0.4818 0.9746 801.225
5465500 684 78 62.05 7.8 2.173 40.034 816.968 1.0000 1.0000 827.621
100683 683 1 25.13 8.0 0.904 0.904 0.904 0.0226 0.0011 0.904
679 5465500 3 11.98 7.9 0.427 4.285 4.285 0.1070 0.0052 4.291
685 682 4 57.49 7.8 2.001 14.168 14.168 0.3539 0.0173 14.234
682 5465500 77 3.36 7.9 0.118 33.576 810.510 0.8387 0.9921 819.373
683 685 2 63.18 7.7 2.193 3.096 3.096 0.0773 0.0038 3.100
98
For example, consider modeling unit number 663 which is located on the Iowa
River just downstream of the Lone Tree gauge (station 5455700). The January 1990
precipitation on this model unit was 8.5 mm/d on average, thus with a drainage area of
28.22 km
2
 and a runoff coefficient C
f
 of 0.3874, the runoff from this modeling unit is
28.22 * 8.5 * 0.3874 = 92.926 km
2
mm/d = 92.926/86.400 m
3
/s= 1.076 m
3
/s.
The outflow from unit 663 is a sum of inflow and estimated outflow:
Q
i
'(m) = 285.039 + 1.076 =286.115 m
3
/s.
The correction coefficients are:
k
1
 = 286.115/816.968 = 0.3502,   and   k
2
 = 1.076/40.034 = 0.0269,
thus, the adjusted flow in the Iowa River at the outlet point of the unit 663 is:
Q
i
''(m) = 286.115 + 0.3502*0.0269*10.653 = 286.216 m
3
/s.
4.6 Exponential decay model
This section discusses a model which estimates loads in rivers assuming the
chemical losses in rivers are governed by a first order reaction, i.e., the agrichemical
mass exponentially decays as it travels from one modeling unit to the next downstream
unit. The preliminary model has been developed to calculate the concentrations in
rivers utilizing the results of a CEEPS (Comprehensive Environmental Economic
Policy Evaluations System) metamodel developed by the Iowa State University?s
Center for Agricultural and Rural Development (Bouzaher and Monale, 1993).
99
The CEEPS applies two models of chemical runoff from the field: PRZM
(Mullins, et al., 1993) for pesticides and EPIC for nutrients. These results specify the
proportion of agrichemical mass applied that leaves the field as runoff. Unfortunately,
the author of this dissertation was unable to obtain the spatial distribution of these
chemical application-loss relations over the Iowa-Cedar river to estimate the rate of
agrichemical losses in rivers necessary to develop and test the complete GIS model
with CEEPS data as input. Since it is not in the scope of the research to develop such
a CEEPS model, only its outline for the completeness of discussion, is included below.
4.6.1 Exponential decay model overview
The spatial model frame is based on the watershed divided into modeling units
described in previous sections. The mass that enters the stream in a unit watershed is
calculated using export factors:
MUZ
iii
= (4.23)
where:
M
i
 = agrichemical mass that enters surface water in the i-th modeling unit;
U
i
 = total agrichemical application in the i-th unit; and
Z
i
 = export factor that depends, e.g., on agricultural management practices.
This factor also includes all chemical losses in i-th unit.
As the agrichemical mass load travels along the flow path it decays. The decay
process can be related to travel time or to travel distance. It is assumed here that the
time decay coefficient or distance decay coefficient represent such processes as decay,
100
sorption, desorption, volatilization, exchange between sediment and water column,
settling, scour, and dilution. The equations (4.24 and 4.25) describe this process
utilizing a travel time and a time decay coefficient:
MM
in i out j
j
,,
=
?
(4.24)
and
MM ktM
out i in i T i i i,, ,
exp( )=?+ (4.25)
where:
M
in,i
 = agrichemical mass that enters i-th modeling unit;
M
out,j
 = output mass from the j-th unit;
j = indicator of units that are immediate upstream of the unit i;
M
out,i
 = agrichemical mass that leaves i-th modeling unit;
M
i
 = agrichemical mass in runoff from i-th unit;
k
T,i
 = time loss coefficient, applied to the mass that enters i-th unit;
t
i
 = time that takes the constituent to travel through i-th unit.
To describe the agrichemical losses by an exponential function of river reach
length the k
T,i
 t
i
 component of the equation (4.25) must be substituted by a distance
loss coefficient k
L,i
 and a travel distance L
i
 (Eq. 4.26).
MM kLM
out i in k L i i i,, ,
exp( )=?+ (4.26)
where:
k
L,i
 = distance loss coefficient, applied to the mass that enters i-th unit;
L
i
 = travel distance through i-th unit.
101
Since the database of the average monthly precipitation depth, the monthly
water runoff from the field as well as the average monthly flow rate in river for all
modeling units it is feasible to apply concentrations (traditional approach: cc
kt
T
10
=
?
)
instead of loads.
4.6.2 Travel time approximation
Since no information about the river cross sections is available as yet, a special
procedure has been developed to determine the distribution of time of travel and flow
velocity.  The visual analysis of daily flow record along the flow path has revealed that
there is a time shift between flow time series. Figure 4.19 presents an example of the
flow rate time series along the flow path from the gauging station "Winnebago River
at Mason City, Iowa" to the gauging station "Iowa River at Wapello, Iowa".
Figure 4.19 Example of time series recorded in gauging stations located along
the Cedar River. The data are for the water year 1990. The
logarithmic scale is used to show all time series in one picture.
102
Lagged cross-correlation coefficients can be applied to test the linear
relationship between flow time series recorded in the gauging stations located on the
same flow path. Six gauging stations along the Cedar River shown in Figure 4.20 have
been selected for preliminary analysis.
Cedar R. near Austin, MN
Cedar R. at Charles City, IA
Cedar R. at Janesville, IA
Cedar R. at Waterloo, IA
Cedar R. at Cedar Rapids, IA
Cedar R. near Conesville, IA
Iowa R. at Wapello, IA
Figure 4.20 Flow path and location of gauging stations which have been used to
illustrate the potential method for time of travel estimation.
The cross-correlation coefficients between the time series recorded at the
gauging station "Cedar River near Conesville, IA" and the time series recorded in
remaining gauging stations have been calculated. Figure 4.21 shows the estimated
103
coefficients. For example, the cross-correlation between the flow recorded in gauging
station "Cedar River near Conesville" and the flow recorded in gauging station "Cedar
River at Cedar Rapids" has the maximum value for a two-day lag. This suggests that it
takes about two days for the water to flow from Cedar Rapids to Conesville.
0.4
0.5
0.6
0.7
0.8
0.9
1
CEDAR R. NEAR AUSTIN, MN
CEDAR R. AT CHARLES CITY, IA
CEDARR.ATJANESVILLE,IA
CEDAR R. AT WATERLOO, IA
IOWA R. AT WAPELLO, IA
CEDAR R. AT CEDAR RAPIDS, IA
CEDAR R. NEAR CONESVILLE, IA
0-2-4-6-8-10-12-14 2
4 6 8
10
12
14
Lag (days)
Correlation
coefficient
Figure 4.21 Cross-correlation coefficients: the strength of the linear relationship
between the flow rate in the Cedar River recorded near Conesville,
IA, and the flow rate recorded at indicated locations. All gauging
stations are on one flow path (shown in Figure 4.20).
The projection of the travel time over the ungauged regions is much more
difficult than the projection of the flow velocity, except the case when a simple relation
between the travel time and the travel distance is applied. Figures 4.22a and 4.22b
show such a relationship which indicates that the travel time can be substituted by the
104
travel distance. Figure 4.22c presents the flow velocity as a function of the square root
of the stream slope.
0.2
0.4
0.6
0.8
1
0 0.01 0.02 0.03
0
1
2
3
4
5
6
7
8
0 100 200 300 400 500
Travel Time [d]
Travel Time [d]
Velocity [m/s]
Travel Distance [km]
Travel Distance [km]
sqrt ( slope )]
a)
b)
c)
G76 G3d G30G2eG32G33 G2b G32G32G2eG33G32 G53G6fG30G2eG35
Figure 4.22 Analysis of travel time and flow velocity:
a) cumulative travel time versus cumulative flow distance;
b) travel time vs. flow distance;
c) velocity vs. square root of stream slope.
105
The travel time shown in Figure 4.22 represents the lag time for which the
cross-correlation coefficient has the maximum value. The slope for each stream reach
has been calculated from the digital elevation model (DEM). The flow length has been
calculated by the Arc/Info function flowlength.
The same exercise has been repeated for the Iowa River. Two river sections
have been excluded from the analysis: one between Rowan and Marshalltown
(maximum correlation between no-lagged series) and other between Marengo and
Iowa City (the Lake Coralville causes that the maximum correlation coefficient to be
estimated for nine-day lagged series). The following relationship between ?travel
time?, the stream slope, and the stream length has been estimated for both the Iowa
River and the Cedar River:
t
L
So
=
+0 3 20 0
05
..
.
(4.27)
where:
t = travel time [d]
So = stream slope
L = stream length [km]
The Equation (4.27) gives a good approximation of the ?travel time? in the Iowa River
and the Cedar River. Figure 4.23 shows that the error of prediction for all stream
reaches is below 0.5 day (the precision of determining a lag time of the maximum
correlation is 0.5 day.)
106
Klemee - Rowan
Marshalltown - Marengo
Iowa City - Lone Tree
Austin - Charles City
Charles City - Janesville
Janesville - Waterloo
Waterloo - Cedar Rapids
Cedar Rapids - Conesville
Conesville - Wapello
Travel Time [days]
0 0.5 1.0 1.5 2.0 2.5
Lag time of the maximum correlation
t=L/v=L/(0.3+20*So )
G30G2eG35
Figure 4.23 Estimation of the ?travel time? for major reaches of the Iowa River
and the Cedar River, IA.
Figure 4.24 compares the flow velocity extracted from the RF1 database with
the flow velocity estimated by the correlation analysis. There is no visible relation
between these two data sets. The flow velocity estimated from the correlation of flow
record is about three times higher then the one published with RF1. According to the
RF1 velocities, it takes constituent almost a month to travel from Austin, MN to
Wapello, IA. Further analysis is needed to clarify the reasons for this discrepancy.
107
0
0.2
0.4
0.6
0.8
00.5 11.52
Velocity from the correlation
analysis [m/s]
Velocity from the RF1
database [m/s]
Figure 4.24 Comparison of the velocity from the RF1 database with the velocity
estimated from a correlation analysis of the flow record in the Iowa
River and tributaries
108
5. PROCEDURES
This Section describes the procedures utilized to construct the model of
agrichemical transport in the Midwest rivers. Section 5.1 shows the steps of preparing
published concentrations and flow rate for statistical analysis. Section 5.2 presents
Arc/Info procedures that have been prepared to estimate parameters that characterize
watersheds within the Upper Mississippi-Missouri River and the Ohio River basins,
These parameters include average slope of the rivers, average land slope, distance
from the field to the stream along the flow path, exponentially decayed stream length,
agrichemical application, average annual temperature, and average annual precipitation
depth. Section 5.3 explains the process of converting the database of observations and
the sampled watershed characteristic into Splus data objects for further statistical
analysis. To make the presentation clearer and more consistent, the detailed
description of the statistical analysis is discussed together with presentation of the
results in Chapter 6.
Sections 5.4 and 5.5 explain the models of the agrichemical transport in the
rivers of the Iowa-Cedar River basin.  These models apply results of the statistical
analysis of the data that describe the atrazine and nitrate concentrations in the Midwest
rivers, the flow rate, watershed morphometry and the climatic parameters. Section 5.4
discusses the method of subdividing the Iowa-Cedar River basin into hydrologic units
utilizing a digital elevation model and a digital map of rivers. This section describes
also the GIS database of the flow rate and the precipitation depth and the process of
the spatial redistribution of the recorded flow rate. The prototype of the agrichemical
transport model programmed within the ArcView GIS is presented in Section 5.5.
109
5.1 Concentration and flow measurements
The data printed in the USGS Open File Report 94-396 (Scribner, et al., 1994)
have been manually entered into a computer. The following items have been extracted
from the USGS Report:  sampling-site name, date of collection (month/day/year),
collection time (24-hour), stream-flow (ft
3
/s), nitrate plus nitrite as nitrogen (mg/L),
atrazine ELISA (?g/L), and atrazine GC/MS (?g/L). If more than one sample was
taken during one day, the average daily flow-weighted concentration has been
calculated as ccQQ
ii
i
i
i
=
??
 where: c = concentration, Q = flow rate.
The following values have been entered into a computer from the USGS
reconnaissance study (USGS Open File Report 93-457, Scribner, et al., 1993): State,
site name, date of collection (month/day/year), stream-flow (ft
3
/s), nitrate plus nitrite
as nitrogen (mg/L), atrazine ELISA analyzed in Iowa laboratory (?g/L), atrazine
ELISA analyzed in Kansas laboratory (?g/L), and atrazine GC/MS (?g/L). About 43
missing values of GC/MS atrazine concentration have been determined from ELISA
tests using following regression equation that relates ELISA atrazine and GC/MS
atrazine (the equation has been estimated utilizing data published in USGS Open File
Report 93-457):
atrazine =  -0.0101 + 0.82547 ELISA + 0.09316 ELISA
2
 (5.1)
R
2
 = 0.92, 175 observations, Standard Error 0.74 ?g/L.
Figure 5.1 shows observed GC/MS atrazine vs. predicted atrazine (Eq. 5.1).
110
Atrazine by ELISA g/L
?
Atrazine by GC-MC g/L?
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0.00 2.00 4.00 6.00 8.00 10.00
Atrazine by GC/MS - measured
Atrazine by GC/MS - estimated
Figure 5.1 Relationship between atrazine ELISA concentration and
concentration by GC/MS estimated from data published in the
USGS Open File Report 93-457.
The estimation of the CG/MS atrazine concentrations from the ELISA tests is
commonly used in practice. Figure 5.2 compares the estimated in this research
relationship with the functions developed by different authors.
Thurman et al. (1992) estimated the following quadratic function (Fig. 5.1, line 1):
atrazine =  0.21 + 2 ELISA - 0.73 ELISA
2
 +0.15 ELISA
3
(5.2)
R
2
 = 0.93, n = 127. It is evident from Figure 5.2 that there is an error in the published
equation.
111
Goolsby et al. (1993) fitted two regression equations for GC/MS values
(Fig. 5.2, line 2 and line 3, respectively), as a function of ELISA values, for samples
taken in 1990:
 atrazine = -0.01 + 0.70 ELISA (5.3)
R
2
 = 0.94; st. error of estimate = 0.09 ?g/L, and for samples taken in 1991:
 atrazine =  0.80 ELISA (5.4)
R
2
 = 0.78; st. error of estimate = 0.10 ?g/L
In another study, Moody and Goolsby (1993) estimated the following relationship
(R
2
 = 0.94, Fig. 5.2, line 4):
atrazine =  0.13 + 0.51 ELISA (5.5)
Gruessner et al. (1995) described the relation between ELISA atrazine and GC/MS
atrazine by the equation (5.6):
 ELISA = 0.029 + 1.16 atrazine (5.6)
sample size = 217, r = 0.96.
This survey of equations shows that slightly different relationships between
CG/MS atrazine and ELISA atrazine are estimated from different data sets.
112
Atrazine by ELISA g/L
?
Atrazine by GC-MC g/L?
1
2
3
4
5
0
1
2
3
4
5
6
7
8
012345
Figure 5.2 Relationship between atrazine ELISA concentration and
concentration by GC/MS estimated by a different authors:
(1) Thurman et al. (1992);
(2) Goolsby et al. (1993) data gathered in 1990;
(3) Goolsby et al. (1993) data gathered in 1991;
(4) Moody and Goolsby (1993), and
(5) relation estimated in this study utilizing data from USGS open 
        file report 93-457.
The streamflow record has been converted from cubic feet per second (ft
3
/s)
into cubic meters per second (m
3
/s). The two chemical data sets, one from the USGS
Open File Report 94-396, and the other from USGS Open File Report 93-457, have
been merged and the column containing the site identification number (USGS Station
ID) has been added. A simple substitution method (Helsel and Hirsh, 1995) has been
applied to values below the reporting limit. For atrazine, 0.025 ?g/L replaced a less-
then 0.05 ?g/L value and for nitrite-nitrate as nitrogen, 0.05mg/L was substituted for a
less than 0.1 mg/L value. The summary statistics of the atrazine, nitrite/nitrate-nitrogen
concentrations and loads, and the corresponding flow rates are presented in Table 5.1.
113
Table 5.1 Summary statistics of the nitrite plus nitrate and atrazine data sets.
Nitrite/Nitrate data set Atrazine data set
Statistics Flow Load Concentr. Flow Load Concentr.
m
3
/s g/s mg/L m
3
/s mg/s ?g/L
Mean 82.22 249.8907 5.22 101.15 296.62 5.35
Standard Error 19.20 16.95 0.14 26.82 39.04 0.37
Median 8.85 28.92 2.91 9.72 11.77 1.00
Standard Dev. 694.55 613.18 5.21 819.46 1192.48 11.33
Skewness 22.43 5.43 1.23 19.09 14.06 4.92
Minimum 0.0028 0.0002 0.05 0.0028 0.0011 0.03
Maximum 20416.56 7603.12 26.00 20416.56 27124.85 116.00
5.2 Preparing data for model parameter estimation
To estimate sampled watershed characteristics, a system of distributed
watershed parameters has been developed. This system is composed of a set of grids
that describe spatial distribution of such parameters as average agrichemical
application rate, average river slope, drainage area, land slope, distance from a field to
the river, average annual temperature, and average annual precipitation depth for the
Upper Mississippi-Missouri and the Ohio Basins. Each grid cell contains a value that
describes a feature of the drainage area upstream of that cell. The 500 m resolution
grid, based on the 15 second DEM, is used to accomplish this task. The following
factors justify this approach:
1) Watershed parameters, that explain the measured loads and concentrations
of selected agrichemicals in Midwest rivers, are used to estimate loads and
concentrations in unsampled streams;
2) Estimating parameters for a region that has area almost 3*10
6
 km
2
, and
which is represented by a grid of about 3800 rows and 5800 columns is a
114
very computer intensive process, so a 100 m cell size would be too
intensive;
3) A grid-based distributed system of parameters does not require a prior
subdivision of region into watersheds nor specification of a watershed
outlet.
5.2.1 Preparing 500 m  (15'') DEM for analysis
The 500 m DEM released by Rea and Cederstrand (1995) has been used in this
study. Since it was published using the Albers Equal Area coordinate system with
standard projection parameters, no projection was needed.
To ensure that the whole region contributes to the outflow, the DEM
depressions must be removed. This is performed by the GRID procedure fill
(Listing 5.1, line 1) which produces a ?filled? DEM, mwfil, and a grid that contains
the flow direction, mwfdr. GRID determines one of the eight directions of the flow
from the steepest descent: value 1 represents flow in E (east) direction, 2 in SE
direction, 4 - S, 8-SW 16 - W, 32 - NW, 64 - N, and 128 in NE direction. No
adjustment of the elevations, i.e.,  ?burning in? RF1 streams has been applied to the
500 m DEM due to the size of the files.
The drainage area upstream of each cell is calculated by summing the number
of contributing cells and is calculated by the procedure
flowaccumulation(mwfdr), and multiplying by the area of single cell that is
equal to a certain value(in this case, 500 m * 500 m = 0.25 km
2
: Listing 5.1, line 2).
The stream network is delineated by assuming that a stream is created from the
outflow from area at least of 50 km
2 
 , threshold number of cells (line 3 of Listing 5.1).
115
The grid function con ( condition , true, false ) is a conditional
statement. The expression condition is evaluated for each cell in the analysis
window. If it is TRUE, the expression true identifies the value to be used to
calculate the output cell values. If condition is FALSE the output cell is evaluated
according to the expression false, or, if this expression is not stated, the output cell
value is set to NODATA.
Listing 5.1 Creating depressionless DEM, calculating drainage area and 
delineation of the stream network.
1: fill mwdem mwfil sink # mwfdr
2: mwarea = 0.25 * flowaccumulation ( mwfdr )
3: mwstr = con ( mwarea > 50, 1 )
Before further calculations are made, the stream network delineated from the
DEM is compared with the RF1 map to visually verify the flow system. One major
inaccuracy was found: the Wisconsin River, a Mississippi River tributary, flowed
North to the Great Lakes. To correct this error the elevation of some cells of the DEM
were changed to force the flow in proper direction. Correction of the flow system can
also be made by making changes directly to the flow direction grid. The process shown
in Listing 5.1 was repeated until satisfactory map of the flow system was constructed.
5.2.2 Estimation of watershed parameters
This section presents procedures for estimating the grids which each cell
contains the following parameters of the upstream drainage area: average slope of the
stream network, average exponent of the stream network length, average distance
from field to river, and average slope of the watershed.
116
Slope along the flow path. To estimate the average land slope and the average stream
slope, a grid that contains values of the cell slope, measured along the flow path, has
to be constructed. Listing 5.2 shows an example of the AML that calculates the slope
according to the relation (H
i+1
 -H
i
)/?
L
, where H
i+1
 is the elevation stored in the cell,
e.g.,  mwfil(1,0) pointed by the flow direction grid mwfdr, Hi is the elevation of
the processed cell (mwfil), and ?
L
 is the distance; cell width (variable %grd$dx%)
or cell diagonal ( variable %diag%), depending on the flow direction value. The full
listing of the procedure that calculates the slope along the flow path, is presented in
Appendix C8.
Listing 5.2 Slope along the flow path.
1: &describe mwfil
2: &sv diag = 1.414213562 * %grd$dx%
3: DOCELL
4:   if (mwfdr == 1)
5:     slope3 = ( mwfil - mwfil(1,0) ) / %grd$dx%
6:   else
7:   if (mwfdr == 2)
8:     slope3 = ( mwfil - mwfil(1,1) ) / %diag%
9:   else
10: 
11: 
12:  . . .
13: 
14:   if (mwfdr == 128)
15:     slope3 = ( mwfil - mwfil(1,-1) ) / %diag%
16:   else
17:     slope3 = 0
18: END
Average slope of the stream network. First, the cells that compose the stream
network are selected from the grid which contains a description of the direction of
flow, mwfdr, - the grid strfdr is created. The number of cells in the upstream
stream network is then calculated, using the grid command flowaccumulation.
117
The same command is used to calculate the sum of the slopes.  A grid of average river
slope upstream of each cell is obtained by dividing the grid of sum of slopes,
slpfacfac, by the grid with the number of cells in the upstream network, strfac.
To save disk space, the resulting grid, strslp, is multiplied by 1,000,000 and its
values are converted into integer representation. Listing 5.3 shows the GRID dialog
which performs this procedure.
Listing 5.3 Average slope of the stream network.
1: strfdr = con ( mwstr > 0 , mwfdr )
2: strfac = flowaccumulation ( strdir )
3: slpsfac = flowaccumulation ( strdir, slope3 )
4: strslp = slpsfac / strfac
5: slps6i = int ( strslp * 1000000 )
Average exponent of the negative stream network length. According to the
information presented in Section 4.3.5 the methodology has been simplified by
assuming that the mass that enters the surface waters upstream of each cell is equal to
one and is uniformly distributed along the river. The reduced formula describing
variable E
S
  (Eq. 4.9) has the following form:
E
n
L
Sk
k
ik
i
n
=?
=
?
1
1
exp( ) (5.7)
where:
E
Sk
 = weighted average of the exponent of negative flow distance in rivers 
upstream to the k-th cell (decay),
n
k
 = number of cells that constitute the upstream network (strfac),
L
ik
 = length of the flow path from the i-th stream cell to the k-th cell [10
2
 km].
Listing 5.4 shows the GRID dialog for computing parameter E
Sk
. The command
flowlength, that determines the downslope distance along the flow path, from
118
each cell to the outlet on the edge of the grid, is used to create the grid, mwflg. The
exponent of the negative flow distance, expressed in 100 km, is then calculated. The
cells that comprise the stream network are selected and the cumulative value of the
exponent of the negative flow distance is determined.
Since function flowlength calculates the distance from each cell to the
outlet on the edge of the grid, not to the watershed outlet, the grid, strexfac, must
be divided by the grid, mwexpflg, according to relation:
exp( )
exp( )
exp( )
?=
?
?
=
=
?
?
L
L
L
ik
i
n
io
i
n
ko1
1
(5.8)
where:
L
ik
 = length of the flow path from the i-th stream cell to the k-th cell,
L
io
 = length of the flow path from the i-th stream cell to the outlet on the edge of 
the grid (cell o),
 L
ko
 = length of the flow path from the watershed outlet (cell k) to the outlet on the 
edge of the grid (cell o).
The division by strfac in line 5, Listing 5.4, is introduced to account for the
assumption of a unit mass entering river network. The purpose of the operation stated
in the last line of Listing 5.4 is to reduce the size of the computer file; integer grids
occupy considerably less disk space than the real-number grids (30%-90% less).
Listing 5.4 Exponentially decaying flow length.
1: mwflg = flowlength ( mwfdr )
2: mwexpflg = exp ( -0.00001 * mwflg )
3: mwexpstr = con ( mwstr > 0 , mwexpflg )
4: strexfac = flowaccumulation ( mwfdr , mwexpstr )
5: decay = ( strexfac / mwexpflg ) / strfac
6: decs6i = int ( decay * 1000000 )
119
Average length of the flow path from field to the stream. To exclude the cells that
represent a stream network from calculations, a grid containing one in the cells that do
not belong to the river network, and zero for the stream cells is created in line 1,
Listing 5.5. The downslope distance, along the flow path, from each cell that does not
represent a stream to all cells that stand for river is calculated in line 2, Listing 5.5.
The average value is determined by summation of all distances upstream (line 3,
Listing 5.5) and by dividing the resulting grid, lndflfac, by the total number of
cells within the given drainage area that are not streams, lndfac (line 5, Listing 5.5).
Listing 5.5 Average distance from field to a stream.
1: lnd1str0 = con ( isnull(mwstr) , 1 , 0 )
2: lndflg = flowlength ( mwfdr , lnd1str0 )
3: lndflfac = flowaccumulation ( mwfdr , lndflg )
4: lndfac = flowaccumulation ( mwfdr , lnd1str0 )
5: alndflg = lndflfac / lndfac
6: alndflgi = int ( alndflg )
Average land slope. Listing 5.6, line 1 shows the command used to create a grid ,
xlndslp, containing the value of the slope in the cells that do not belong to the
stream network, and zero for the stream cells. The average slope, lndslp, is
calculated by first, summing all of the upstream values of slope, (line 2, Listing 5.6)
and by dividing this cumulative slope grid, slplfac, by the total number of cells
within the given drainage area that do not represent streams, lndfac, (line 3,
Listing 5.6). The last operation converts the slope grid into an integer format.
Listing 5.6 Average land slope.
1: xlndslp = con ( isnull ( mwstr ) , slope3 , 0 )
2: slplfac flowaccumulation ( mwfdr , xlndslp )
3: lndslp = slplfac / lndfac
4: slpl6i = int ( lndslp * 1000000 )
120
5.2.3 Creating grid of sampling sites
A grid that represents the USGS sampling sites (watershed outlets) is
necessary to extract the parameters of the reconnaissance watersheds from the grids of
distributed parameters. This section describes the process used to create such a grid
from available data.
The Arc/Info map sta_recon obtained from Battaglin (1995) of 147
sampling sites that are described in USGS Open File Report 93-457 (Scribner, et al.,
1993) was converted into raster format by the following GRID operation:
sites1 = pointgrid ( sta_recon, station, #, #, 500 )
Unfortunately, four of the nine stations from USGS Open-File report 94-396
(Scribner, et al., 1994) are not represented in the sta_recon coverage. Therefore, a
coverage of these four sampling sites was constructed from published latitude-
longitude coordinates (generate). The attribute table was created (build) and the
coordinates of the resulting coverage were changed from geographic projection into
Albers projection (project). Finally, this coverage was converted into grid sites2
and merged with grid sites1:
site_all = con ( isnull(sites1) , sites2, sites1)
The site identification numbers, given in attribute table of the sta_recon
coverage (Battaglin, 1995) of the three sites, have been changed to site identifiers that
are published in USGS Open-File Report 93-457 (Scribner, et al., 1993), as follows:
The Mississippi River at Winfield,  ID = 1 has been changed to ID = 05587450
(the Mississippi River at Grafton);
The Ohio River near Olmstad, ID = 2 has been assigned ID = 03612500
(the Ohio River near Grand Chain);
121
The Wabash River near Griffin ID = 3 has been replaced by ID = 03378500
(the Wabash River near New Harmony).
The drainage area of the original station and the one which replaced it is identical for
all three sites.
5.2.4 Adjusting location of sampling sites
The location of most of the sampling sites is not completely consistent with the
stream network delineated from the 500 m DEM. Figure 5.3 presents an example of a
sampling site (Sta-recon map from Battaglin, 1995) that is located neither on the
RF1 stream, nor on the stream network that has been delineated from the DEM.
Mississippi River
Dardenne Cr.
Peruque Cr.
Cuivre R.
Mississippi R. delineated
from 500 m DEM
Streams from FR1
Mississippi R. at Winfield
Figure 5.3 Example of the sampling site (from Battaglin 1995) that is located
neither on the stream from RF1 nor on the stream delineated from
the DEM.
122
The cells that represent both the sampling site and the watershed outlet must
be located on the proper flow path. The following procedure has been developed to
adjust the position of gauging stations:
 - constructing a grid of sampling sites that contains published values of drainage
area (areap). This step has been performed within ArcView. The new item ,
dareakm2, has been added to the value attribute table (VAT) of the grid
site_all. This VAT is linked to the point attribute table(PAT) of the coverage
sta_recon that contains in item darea (the USGS estimates of drainage area
in mi
2
). The values of dareakm2 have been calculated in ArcView using the
following formula in ?field calculate? entry box: [dareakm2] = [darea] * 2.59,
where 2.5900 is the square mile-to-square kilometer conversion factor.
The grid, areap, is created from the grid, site_all, by a simple GRID
assignment statement (line 1, Listing 5.7);
   - assigning the drainage area value to each cell in the circular neighborhood of cells
in grid areap. A five cell radius is assumed (line 2, Listing 5.7);
   - calculating the absolute value of the relative difference between the published
drainage area and the distributed values that have been estimated from the DEM in
each sampling site cell within its neighborhood (line 3, Listing 5.7);
   - creating grid of zones (zone5) by assigning a unique number to every continuous
area with the same value (line 4, Listing 5.7);
   - within each zone, finding a cell that has the smallest difference between the
drainage area determined from DEM and the area given by USGS (smallest value
in each zone of grid, error5) (line 5, Listing 5.7);
123
- assigning the site identification number to the cells that have minimum error (lines
6 and 7 of Listing 5.7);
- selecting cells with a relative error of drainage area smaller than 20% (line 8,
Listing 5.7)
Listing 5.7 GRID dialog supporting adjustment of sampling sites location.
1: areap = site_all.dareakm2
2: usgsarea = focalmax (areap, CIRCLE, 5 )
3: error5 = int ( abs ( ( 100000 * (usgsarea - mwarea) ) /
usgsarea ) )
4: zones5 = regiongroup ( usgsarea, #, FOUR)
5: er_min5 = zonalmin (zones5 , error5 )
6: id_zone = focalmax ( site_all, CIRCLE, 4)
7: siteid5 = con (( er_min5 == error5 ) , id_zone )
8: siteer20 = con ( er_min5 < 20000 , siteid5 )
Wherever possible, the locations of watershed outlets that have a difference in
drainage area larger then 20% have been adjusted manually using the grid editor
included in ArcTools processor. The results have been stored as mwout grid. About
13% of stations had an error in drainage area larger than 20%. The discrepancies are
due to the relatively low resolution of the DEM used in this analysis and, therefore,
small precision of the watershed boundaries. These discrepancies are also due to errors
in the estimation of drainage area by the USGS. For example, Kalkhoff and Kuzniar
(1991) state that the drainage area of sample site 05412100, the Roberts Creek above
St. Olaf, Iowa, is equal to 70 mi
2
, whereas Scribner et al. (1993) published a number
that is 47% larger (103 mi
2
). The grid mwout has been used to delineate watersheds
from the 500 DEM:
mwwsh = watershed ( mwfdr, mwout )
Figure 5.4 shows the sampled watersheds delineated from the 500 m DEM.
124
500 0 500 1000 Kilometers
Figure 5.4 Sampled watersheds delineated from the 500 m DEM.
5.2.5 Extracting parameters of the sampled site watersheds
Listing 5.8 shows the process of extracting watershed parameters from the
grids of distributed values and associating them with the site identification number. As
a result a VAT is created that contains the following items: mwout (site ID),
slps6i2 (stream slope), decs6i2 (decayed flow length), flgl0i2 (flow length
from field to stream), and slpl6i2 (land slope).
125
Listing 5.8 Extracting parameters of the sampled site watersheds.
   In GRID:
1: slps6i2 = con ( mwout > 0 , slps6i )
2: decs6i2 = con ( mwout > 0 , decs6i )
3: flgl0i2 = con ( mwout > 0 , alndflgi )
4: slpl6i2 = con ( mwout > 0 , slpl6i )
5: comslps =  combine ( mwout , slps6i2 )
6: comdecs =  combine ( mwout , decs6i2 )
7: comflgl =  combine ( mwout , flgl0i2 )
8: comslpl =  combine ( mwout , slpl6i2 )
   In Arc/Info:
1: copy comslpl comtot
2: joinitem comtot.vat comflgl.vat comtot.vat mwout mwout
3: joinitem comtot.vat comslps.vat comtot.vat mwout mwout
4: joinitem comtot.vat comdecs.vat comtot.vat mwout mwout
Since the parameters were multiplied by 100000 to convert them to integers, a
new Info table that contains the recalculated floating point values has been constructed
using Arc/Info and ArcView tools. The items and their units in the new table are as
follows: station_id, area (km
2
), decstr (e
100km
), slpstr (dimensionless),
slplnd (dimensionless), and alflgkm (km). The summary of statistics for a
selected parameters of sampled watersheds are presented in Table 5.2. The average
land surface slope is approximately one percent while the average stream slope is
about six times flatter, or 0.17%.
Table 5.2 Selected statistics of watershed parameters determined from DEM.
Length of the flow path used to calculate E
S
 is  in 100 km.
Statistics Area
Decayed
stream length
Stream
Slope
Land
Slope
Land
length
km
2
E
S
S
S
S
L
L
L
 [km]
Mean 36493 0.59124 0.00168 0.01091 3.34
Standard Error 18360 0.01877 0.00007 0.00057 0.04
Median 1685 0.63221 0.00146 0.00871 3.23
Standard Deviation 224117 0.22912 0.00091 0.00700 0.50
Minimum 173 0.00353 0.00039 0.00130 2.45
Maximum 2335354 0.91928 0.00702 0.04486 5.51
126
5.2.6 Agrichemical application
The mass of agricultural chemical that was applied within each watershed in
which the concentrations and flow rate were measured, has been calculated using
Arc/Info-GRID. This procedure is presented in Listing 5.9. A detailed description of
the process is given below:
- In the first four lines of Listing 5.9 the polygon coverages NIT89, NIT90,
NIT91, and HERBICIDE1, are converted into grid maps that have cell size
equal to 500 m, and grid values equal to the values from items NTOT89.USE,
NTOT90.USE, NTOT91.USE, and H1080.USE, respectively. Lines 5-8
transform the application units into grams per square kilometer (g/km
2
) and
modify the format of numbers from double precision to integer to reduce the
size of the files. The total application of the nitrogen-fertilizer in all cells
upstream of a given cell is calculated in line 9, 10, and 11 for 1989, 1990, and
1991, respectively. The total application of atrazine is determined in line 12.
- The cells that contain the amount of chemical application in the watersheds
under investigation are selected in line 13 and they are converted into integer
format in line 14 in order to construct a VAT (line 15). The total chemical
application map is combined with the grid that contains the site ID number to
create a table (VAT) that contains two important items: mwout--the
watershed ID and nit89g--the value of chemical use. Lines 13-16 process
nitrogen-fertilizer use in 1989. By a similar procedure, the use of the remaining
agrichemicals is estimated for each sampled watershed.
127
Listing 5.9 Chemical application in sampled watersheds.
1: xn89 = polygrid(nit89 , ntot89.use, #, #, 500 )
2: xn90 = polygrid(nit90 , ntot90.use, #, #, 500 )
3: xn91 = polygrid(nit91 , ntot91.use, #, #, 500 )
4: xa89 = polygrid(herbicide1 , h1980.use, #, #, 500 )
5: n89gkm2 = int ( xn89 *350262.198 )
6: n90gkm2 = int ( xn90 *350262.198 )
7: n91gkm2 = int ( xn91 *350262.198 )
8: a89gkm2 = int ( xa89 *175.1312741 )
9: n89g = flowaccumulation ( mwfdr, n89gkm2 * 0.25)
10: n90g = flowaccumulation ( mwfdr, n90gkm2 * 0.25)
11: n91g = flowaccumulation ( mwfdr, n91gkm2 * 0.25)
12: a89g = flowaccumulation ( mwfdr, a89gkm2 * 0.25)
13: na89g = con (mwout > 0, n89g )
14: ni89g = int ( na89g )
15: buildvat ni89g
16: comn89 = combine (mwout, ni89g)
Table 5.3 shows a summary of the statistics of estimated agricultural chemical use in
the sampled watersheds. The application rate has been determined by dividing the total
agrichemical application by the drainage area.
Table 5.3 Summary statistics of annual application of nitrogen fertilizer and
atrazine.
Nitrogen fertilizer Atrazine
Statistics Application Appl. rate Application Appl. rate
kg/yr kg/km
2
/yr kg/yr kg/km
2
/yr
Mean 43705590 5878.1 219644 26.66
Standard Error 7170678 51.7 40274 0.42
Median 10298910 6034.0 48695 25.32
Standard Deviation 259336782 1871.2 1230168 12.74
Minimum 245134 481.6 466 1.00
Maximum 4.79E+09 9481.1 19294461 50.55
128
5.2.7 Annual temperature and annual precipitation depth
Listing 5.10 shows the procedure of creating grids of annual precipitation
depth. In line 1 grid prinyr (annual precipitation depth in inches) is created from
Arc/Info coverage clim_div, utilizing data stored in its polygon attribute table item
pre.mean. Line 2 converts vector map of average temperature (item tmp.mean)
into grid representation tmf. In lines 2 and 3 the units are changed from inches to
millimeters for precipitation, and from degrees Fahrenheit to degrees Celsius for
temperature. Since the Missouri Basin extends behind the US borders, and the
clim_div coverage contains data only for the US, temperature of 5 ?C (line 4) and
precipitation depth of 333 mm (line 3) has been assumed for the Canadian part of the
Missouri Basin. A grid of annual precipitation depth in watershed upstream of each
cell (prmmavg) is calculated by summing all precipitation-cells over drainage area
(line 7, grid mwprfac) and then by dividing the result by the number of cells that
constitute upstream drainage area (line 8). The distributed system of the watershed-
average temperature tmcavg is calculated in lines 9 and 10.
Listing 5.10 Average climatic parameters.
1: prinyr = polygrid (clim_div, pre.mean)
2: tmf = polygrid (clim_div, tmp.mean )
3: prmm0 = 25.4 * prinyr
4: tmc0 = 5 * (tmf - 32 ) / 9
5: prmm = con (isnull (prmm0), 333 , prmm0 )
6: tmc = con (isnull (tmc0 ), 5 , tmc0 )
7: mwprfac = flowaccumulation(mwfdr , prmm)
8: prmmavg = mwprfac / mwfac
9: mwtcfac = flowaccumulation(mwfdr , tmc)
10: tmcavg = mwtcfac / mwfac
The process of extracting temperature and precipitation data for the sampling
sites is presented in Listing 5.11. In lines 1-4 the climate grids are converted into
129
integer format. Before conversion, all grids are multiplied by 1000 to preserve the
decimal component (three decimal digits). Lines 5-8 shows constructing grids that
contain values only in cells that represent sampled watershed outlets. The VATs that
relate sampling site ID stored in grid mwout, and the estimated parameter (command
combine) are created in lines 9-12. The summary Info table clim.dat is
constructed in lines 13-15. This table contains the following items:
  - mwout = sampled watershed ID;
  - tca103s = average temperature over sampled watershed;
  - tc103s = annual temperature at sampling site;
  - pmma103s = annual precipitation depth, average for sampled watershed;
  - pmm103s = annual precipitation depth at sampling site.
The temperature stored in the clim.dat is in 10
-3
 ?C and the precipitation depth is
in 10
-3
 mm.
Listing 5.11 Creating a summary Info table of climatic parameters.
1: pmm1000 = int ( prmm * 1000 )
2: pmma1000 = int ( prmmavg * 1000 )
3: tc1000 = int ( tmc * 1000 )
4: tca1000 = int ( tmcavg * 1000 )
5: pmm103s = con ( mwout > 0 , pmm1000 )
6: pmma103s = con ( mwout > 0 , pmma1000 )
7: tc103s = con ( mwout > 0 , tc1000 )
8: tca103s = con ( mwout > 0 , tca1000 )
9: com1 = combine (mwout , pmm103s)
10: com2 = combine (mwout , pmma103s)
11: com3 = combine (mwout , tc103s)
12: com4 = combine (mwout , tca103s)
13: arc joinitem com1.vat com2.vat clim.dat mwout mwout
14: arc joinitem clim.dat com3.vat clim.dat mwout mwout
15: arc joinitem clim.dat com4.vat clim.dat mwout mwout
130
5.3 Preparing data for statistical analysis
The Info tables that contain selected watershed features and annual atrazine
and nitrogen-fertilizer application have been merged with the table that contains
measured flow and concentration in 153 sampling sites on the Midwest rivers. Two
tables have been created: atra7 and nitr7. The table, atra7, contains the
following data:
Table 5.4 Description of tables atra7 and nitr7.
atra7 nitr7
state state name abbreviation
name name of the sampling site;
id station id;
area drainage area in km
2
;
use total mass of atrazine use in kg/yr;
appl atrazine application rate in
kg/km
2
/yr;
date month/day/year of sample collection;
day day in which sample was collected,
1...365;
month month in which sample was
collected, 1-12;
flowm3s flow rate in m
3
/s;
loadmgs atrazine load in g/s;
loadgd atrazine load in g/d;
concmgm3 concentration in ?g/L (mg/m
3)
;
decstr exponent of negative flow length;
declnd exponent of negative distance from
field to stream network;
slpstr slope of the streams;
slplnd average slope of the land;
alflgkm average length from field to stream
network in km;
prmm precipitation at sampling site mm/yr
prmmavg precipitation depth in sampled
watershed mm/yr
tmc annual temperate at sampling site ?C
tmcavg average temperature in sampled
watershed ?C
state state name abbreviation
name name of the sampling site;
id station id;
area drainage area in km
2
;
use total mass of N-fertilizer use in kg/yr;
appl nitrogen-fertilizer application rate in
kg/km
2
/yr;
date month/day/year of sample collection;
day day in which sample was collected,
1...365;
month month in which sample was
collected, 1-12;
flowm3s flow rate in m
3
/s;
loadgs nitrate load in g/s;
loadkgd nitrate load in kg/d;
concgm3 concentration in mg/L (g/m
3)
;
decstr exponent of negative flow length;
declnd exponent of negative distance from
field to stream network;
slpstr slope of the streams;
slplnd average slope of the land;
alflgkm average length from field to stream
network in km;
prmm precipitation at sampling site mm/yr
prmmavg precipitation depth in sampled
watershed mm/yr
tmc annual temperate at sampling site ?C
tmcavg average temperature in sampled
watershed ?C
131
The statistical program Splus operates only on objects. All data and results of
statistical analysis are stored as objects. A table can be stored as an array object or as
a frame object. The atra7 and nitr7 data sets have been imported into Splus data
object frames:
atra7 _ read.table("atra7" , header=T)
nitr7 _ read.table("nitr7" , header=T)
Stepwise regression has been used to estimate model parameters.  The following
commands show an Splus session for selecting significant components of the model by
the stepwise regression:
alnc.lm _ lm(log(concmgm3) ~ 1, data = atra7)
ac1a _ step(alnc.lm, ~ log(appl) + log(flowm3s)
+           + log(decstr) + slpstr
+           + log(alflgkm) + log(slplnd)
+           + month + sin(pi*month/12) + cos(pi*month/12)
+           + sin(2*pi*month/12) + cos(2*pi*month/12)
+           + sin(4*pi*month/12) + cos(4*pi*month/12)
+           + sin(6*pi*month/12) + cos(6*pi*month/12)
+           + sin(8*pi*month/12) + cos(8*pi*month/12)
+           + sin(10*pi*month/12) + cos(10*pi*month/12)
+           + sin(12*pi*month/12) + cos(12*pi*month/12) )
The results of regression analysis are displayed by the Splus command summary()
summary (ac1a)
Different models have been tested by adding or removing model components. The
following line shows removing variable log(appl) from the model ac1a:
ac1a2 _ update(ac1a, . ~ . - log(appl) )
Two diagnostic plots have been used to visually validate the assumption that the
residuals are normally distributed:
1) plot of residuals versus fitted values
plot(fitted(ac1a), studres(ac1a) )
132
2) a normal quantile plot of residuals
qqnorm(resid(ac1a))
qqline(resid(ac1a))
The data can be transformed within the specification of the regression model, as well
as  the new columns in the data frames can be derived from the original data set.
Below are two examples of creating new values from existing ones:
nitr7[,"srslpstr"] _ sqrt ( nitr4[,"slpstr"] )
nitr7[,"etstr"] _ nitr6[,"decstr"] ^ ( 1 / nitr7[,"srslpstr"] )
The results of the statistical analysis of data and the agrichemical transport models
selection are discussed in Chapter 6.
5.4 Agrichemical concentrations in the Iowa-Cedar River
basin
The procedure of modeling of agricultural chemical concentration and load in
the Iowa River and its tributaries includes:
- The Iowa-Cedar River basin is subdivided into modeling units, using the 100 m
DEM. This step includes such operations as downloading 1? DEMs via
Internet, converting the RF1 river map from vector format to raster format,
determining a map of the flow direction, creating a map of the USGS gauging
stations, constructing a map of modeling unit outlets, and determining
modeling unit boundaries;
- The map of modeling units is converted from grid into vector format;
133
- The parameters of the total drainage area that is defined by the outlet point of
the modeling unit, such as average distance from the field to the stream, and
watershed slope, are estimated from the 100 m DEM, and inserted into
modeling unit polygon attribute table;
- The mean monthly runoff at each outlet of the modeling unit is calculated,
utilizing the measured runoff in 28 USGS gauging stations and observed
precipitation depth from 86 NCDC stations;
- The link between map of counties that contain data about the agrichemical
application and the map of unit watersheds is established;
- The equation that describes the concentration of agrichemicals in streams is
incorporated into the GIS database;
- For each spatial unit and each month of the year, a regression equation is
applied to calculate chemical concentration at the elementary watershed outlet;
- The spatial distribution of chemical loads is estimated by multiplying the
concentration by the mean monthly flow rate at each outlet.
5.4.1 Creating a map of the flow direction
Downloading DEM via Internet. Nine, one-degree quadrangles (mason city-w.gz,
mason city-e.gz, waterloo-w.gz, waterloo-e.gz, dubuque-w.gz, des moines-w.gz,
des moines-e.gz, davenport-w.gz, and davenport-e.gz) of DEMs that contain digital
elevation data for the region enclosed by meridians: 90? and 94? West (longitude) and
by parallels 41? and 44? North (latitude), have been downloaded from the USGS
National Geospatial Data Clearinghouse via Internet
134
(http://edcwww.cr.usgs.gov/glis/hyper/guide/1_dgr_dem). Figure 5.5 shows the
location and the names of the downloaded quadrangles.
44?
43?
42?
41?
40?
-94? -93? -92? -91? -90?
Des Moines
Davenport
Waterloo Dubuque
Mason City
W
W
W
W
W
E
EE
E
Figure 5.5 1? quadrangles of DEM utilized to subdivide the Iowa-Cedar River
basin into modeling units; Map projection: geographic.
The files have been uncompressed (UNIX command gunzip), and modified
as explained below. The DEM files do not contain record delimiters, thus they should
be added by the following UNIX command:
dd if=inputfilename of=outputfilename ibs=4096 cbs=1024 conv=unblock
No direct conversion of the USGS DEM's into Arc/Info GRID format is
supported. The Arc command demlattice has been used to convert a DEM in
USGS or TAME format into a lattice. The following example shows the conversion of
the DEM waterloo_e.dem into Arc lattice us4292lat:
135
Arc: demlattice waterloo_e.dem us4292lat USGS
After all nine DEMs were converted into lattices, they were merged to construct a
single map. For example, the following grid command has been used to merge four
lattices:
Grid: crlat1 = merge(us4394lat, us4393lat, us4294lat, us4293lat)
In Arc/Info, the concepts of lattice and grid are similar, with one important
exception. A lattice is a regularly-spaced sample of points representing a surface. Elevation
values in a lattice correspond to discrete points. In a grid, the values apply to the entire cell.
Although both lattice and grid apply the same data structure, the fact that a lattice
represents data at points (has no area) and grid cell has an area, causes differences in how
various operators interpret the data contained in a lattice and within a grid. The further
analysis described here, in which the lattices were treated as grids, was not affected by
these differences.
Since imported maps are in geographic coordinate system (latitude/longitude) they
have been projected into Albers system (project), assuming the cell size of output grid
equal to 100 m. Appendix C9 contains a macro that converts a grid into Albers Equal Area
coordinates. The following parameters have been used:
Units         METERS
Datum         NAD83
Spheroid      GRS1980
1st standard parallel =  29 30  0.000
2nd standard parallel =  45 30  0.000
central meridian      = -96  0  0.000
latitude of projection's origin = 23  0  0.000
Converting river map from vector format into grid representation. The following
GRID commands have been applied to specify the cell size and the map extent of the
rasterized RF1:
136
setcell crdem
setwindow crdem
The portion of the RF1 map that represents rivers in the Iowa-Cedar River basin has
been converted into grid format by applying the linegrid command:
crrf1 = linegrid ( rf1, rf1_id )
The item, rf1-id, from the AAT (arc attribute table) has been used to assign values
to the cells that represent rivers. This item has been selected since it allows one to
relate the grid VAT table with the RF1.FLOW Info table, through one of the following
identification fields: CUSEG (hydrologic cataloging unit code and reach segment
number) or RR (Reach File ID --an unique identifier for each river reach). The table,
RF1.FLOW, contains useful information for hydrologic modeling. For example, it
comprises such items as: LFVEL--low flow velocity, MFVEL--mean flow velocity,
MNFLO--USGS mean annual flow, and SVTEN--USGS 7-10 Year Flow (Lanfear,
1994).
The raster version of RF1 was edited using Arc/Info interactive editing
environment, arctools. The lakes were replaced by a single line or, if the region of
lake was enclosed, by the series of cells that fill up the enclosed region. The resulting
data set was saved under the original grid name, crrf1.
Creating a map of the flow direction and delineation of the stream network.
To ensure that the flow paths delineated from the DEM are in line with the RF1 river
network, the terrain map has been adjusted. Elevations of all cells that do not represent
the real stream network have been raised by 10000 m:
crdem2 = con ( isnull ( crrf1 ), crdem + 10000 , crdem )
137
The value 10,000 was selected arbitrarily. During this research it was found that this
increment should be larger than the maximum elevation of the DEM within the analysis
region for two reasons:
1) To ensure that the cells that constitute the stream network are lower than the
cells that do not represent the stream. For example, increasing the elevation of
all cells that do not represent the stream network by 5 m in the DEM which
values vary from 0 to 50 m does not ensure the stream-cells to be below the
neighboring land-cells (except for smoothed DEMs). Thus an uncertainty
about the compatibility between RF1 rivers and the delineated rivers is
introduced;
2) To easily select all cells that have been adjusted. Selection can be made by a
single conditional grid expression, for example, all adjusted cells in grid
crdem2 can be set to 1 by the following grid assignment:
 output = con ( crdem2 > 9000 , 1 ).
The depressions have been removed to ensure that the whole region
contributes to the runoff, and the flow direction grid crfdr has been built:
fill crdem2 crfill2 crfdr
Rivers have been delineated under the assumption that the runoff from a drainage area
of 25 km
2
 produces a stream. To all cells that have an accumulated number of cells
greater than 2500 (= 25 km
2
 with 100 m DEM cells) ?flowing? into them, the value
one has been assigned:
crfac = flowaccumulation ( crfdr)
crstr25 = con ( crfac > 2500 , 1, 0)
Conversion of the RF1 file into a 500 m by 500 m raster format revealed that
the cell size of 500 m is too large to represent 1:500,000 river network, without
138
ambiguity. Some of RF1 reaches are closer to each other than one kilometer, and if
converted into 500 m grid they are artificially connected. When applied in the
procedure described above, i.e., if the RF1 streams are burned into the 500 m DEM,
these connected rivers cause the GRID command flowdirection to determine a
false direction of flow (due to the difference in elevation of watersheds). As a result,
the water flows from one watershed into another through connected streams that
belong to different basins. Figure 5.6 shows the low precision of the streams
delineated from 500 m DEM adjusted for RF1 streams. The same streams but
delineated from a 100 m DEM adjusted for RF1 almost perfectly represent the RF1
rivers--this justifies the application of the 100 m DEM in this study.
Long Creek, North Fork, IA
Long Creek, South Fork, IA
G28G61G29
G28G62G29
Figure 5.6 Comparison of the stream network delineated from 100 m DEM (a)
with the one delineated from 500 m DEM (b). Both DEMs were
adjusted for RF1 stream network.
139
5.4.2 Map of the modeling unit outlets
A watershed is explicitly defined by its outlet point. Therefore, to subdivide the
basin into elementary watersheds, a set of points -- elementary watershed outlets--
must be specified. Three types of watershed outlets are utilized to subdivide the Iowa-
Cedar River basin into units:
- The most upstream cell of the first order stream;
- The most downstream cell of each reach; and
- The cells that represent the USGS stations.
Figure 5.7 shows examples of watershed outlets
stream network
selected watershed outlets
(a) (b)
(c)
Figure 5.7 Selected types of the modeling unit outlets
(a) type 1, beginning of the stream network;
(b) type 2, upstream cell of the stream junction;
(c) type 3, USGS gauging station
140
Beginnings of the delineated stream network (type 1 outlets). As was mentioned in
Section 4, the type 1 outlets have been introduced to have more control on the
average area of the modeling unit and to determine the flow (and chemical load)
conditions at the beginning of the river system. Listing 5.12 shows the Grid dialog that
selects appropriate cells. In line 1, the raster stream network crstr25 is divided into
?grid zones? crlsl. In Arc/Info GIS a grid zone is developed from the cells that have
the same value. Command streamlink assigns an unique value to each stream
reach. In line 2, zonalmin function finds the minimum value in flowaccumulation
grid crfac delineated by the zones of crlsl and assigns it to all cells of the reach.
Function streamorder (line 3) assigns to each reach a numeric order (Strahler or
Schreve). In line 4, the most upstream cell in the first order stream is found by
selecting the cell that has the same value in both grids, crlmn and crfac. The value
of the selected cells is equal to the value from the grid crlsl increased by 100,000,
to indicate the type 1 outlet and thus the type of watershed (source watershed). This
number also indicates (after subtracting 100,000) the ID of the downstream unit
(intermediate watershed) making the numbering system of the hydrologic structure
consistent and efficient.
Listing 5.12 Selecting type 1 watershed outlets.
1: crlsl = streamlink ( crstr25 , crfdr )
2: crlmn = zonalmin (crlsl , crfac )
3: crlso = streamorder ( crstr25 , crfdr )
4: crlpu = con(crlso == 1 AND crlmn == crfac, crlsl + 100000)
River junctions (type 2 outlets). The type 2 outlets are determined by selecting the
most downstream cell in each stream reach. The selection is made by finding in each
?grid zone,? defined by grid crsls, a cell that has the maximum value in
141
flowaccumulation grid crfac (Listing 5.13). The last operation shown in Listing 5.13
merges the grid of type 1 outlets with the grid of type 2 outlets.
Listing 5.13 Selecting type 2 watershed outlets.
1: crlmx = zonalmax (crlsl , crfac )
2: crlpd = con(crlmx == crfac, crlsl)
3: crlud = con ( isnull( crlpu), crlpd, crlpd)
USGS gauging stations (type 3 outlets) The description of the USGS gauging
stations published by Hydrosphere (Hydrosphere, 1994) contains latitude and
longitude. These coordinates have been used to produce a point coverage of the
USGS stations (Listing 5.14). Listing 5.15 shows a part of the file,
latlonfl.csv, that contains point coordinates.
Listing 5.14 Creating point coverage of gauging stations from latitude-longitude
coordinates.
Arc: generate xgsflow
Generate: input latlonfl.csv
Generate: points
Generate: q
Arc: build xgsflow point
Listing 5.15 Fragment of the file latlonfl.cvs containing station IDs and 
coordinates.
5448500,-337370,154670
5449000,-337051,154831
5449500,-337056,153936
5451700,-334285,151225
. . .
To make the point coverage compatible with other maps used in this study, it has been
projected into Albers system of coordinates as follows (Listing 5.16):
142
Listing 5.16 Projecting the point coverage of USGS gauging stations from
Geographic system into Albers coordinates.
Arc: project cover xgsflow gsflow
Input
Projection geographic
units ds
Parameters
output
Projection    ALBERS
Zunits        NO
Units         METERS
Spheroid      GRS1980
Xshift        0.0000000000
Yshift        0.0000000000
Parameters
 29 30  0.000 /* 1st standard parallel
 45 30  0.000 /* 2nd standard parallel
-96  0  0.000 /* central meridian
 23  0  0.000 /* latitude of projection's origin
0.00000 /* false easting (meters)
0.00000 /* false northing (meters)
end
The grid representation of the USGS stations that is compatible with the
delineated stream network has been developed using Arc/Info grid editor tools
(arctools). The following line combines the grid with the USGS stations crgs
with the grid of watershed outlets crlud:
crout = con ( isnull( crlud), crgs, crlud)
Since the gauging station cells may overlap with other cells representing
watershed outlets units the following statement can be used to establish the priority of
which cell needs to be selected in the final map of the modeling units (grids priority
from the highest to the lowest: crlpu, crgs, crlpd):
crout = con( isnull(crlpu) , con( isnull(crgs), crlpd, crgs), crlpu)
The map of modeling units is created by the following Grid statement:
crwsh = watershed (crfdr , crout)
143
An Arc/Info script has been developed to create the following grids: stream
network, watersheds, and watershed outlets. The complete listing of this program,
wshgs.aml, is presented in Appendix C1. A first order watershed, and its outlet cell,
have an ID number in the range 100000 < ID < 200000. This number is the ID of the
first order stream increased by 100000. A watershed that drains through the point at
which the gauging station is located assumes the USGS gauging station identification
number, 5448500 for example.
5.4.3 Watershed connectivity
To determine the average value of the model parameters for the drainage area
upstream of a given point, the sum of values for all upstream modeling units must be
calculated. All these units can be identified if the position of each unit on the flow path
is known. The Arc/Info script nextwsh.aml creates an Info file with two items that
store the modeling unit ID number and the ID number of the next unit on the flow path
(downstream unit). The listing of the macro nextwsh.aml is shown in Appendix
C2. The major part of this AML assigns to the cell that corresponds to the watershed
outlet crout a value from the cell, located in watershed grid crwsh, that is pointed
by the flow direction crfdr. In line 1, Listing 5.17, a value zero is assigned to all
cells that have NODATA (xcrwsh). This step is necessary to ensure that the next
watershed to the last unit on the flow path is indicated by the ID equal zero (no
downstream units). Lines 2-9 create a grid crnxt similar to the grid of watershed
outlets crout but with ID of the downstream unit.
Listing 5.17 Identification of the downstream watershed ID.
1: xcrwsh = con ( isnull ( crwsh ), 0, crwsh )
2: crnxt = con (crout > 0, con (crfdr == 1, xcrwsh(1,0), ~
3:         con (crfdr == 2, xcrwsh(1,1), ~
144
4:         con (crfdr == 4, xcrwsh(0,1), ~
5:         con (crfdr == 8, xcrwsh(-1,1), ~
6:         con (crfdr == 16, xcrwsh(-1,0), ~
7:         con (crfdr == 32, xcrwsh(-1,-1), ~
8:         con (crfdr == 64, xcrwsh(0,-1), ~
9:         con (crfdr == 128, xcrwsh(1,-1), -1)))))))))
5.4.4 Refining modeling units
Two problems occurred when the grid of modeling units was converted into
vector format:
1) Small zones were not converted into visible polygons, although the records in
polygon attribute tables were created. This makes it impossible to select
records in the PAT by pointing to polygons on the screen;
2) A simple grid zone had more than one component area and the components
were connected by the cell corner. It was converted into more than one
polygon, i.e., one modeling unit was described by two records in the PAT. For
this unit, the value that represents an area in the VAT, after conversion into a
polygon coverage, was listed in the PAT twice. Thus, the modeling unit had
two times larger area in vector map than the same unit represented in the grid.
To solve the problems mentioned above, all zones of smaller area than one km
2
(1 km
2
 = 100 cells 100 m * 100 m ) were incorporated into neighboring units. The
GRID nibble command replaces areas in a grid corresponding to a mask with the
values of the nearest neighbors (Listing 5.18):
Listing 5.18 Eliminating drainage units that are smaller than 1 km
2
aaa = crwsh.count
aaa2 = con (aaa > 100 , 1 )
crwsh2 = nibble(crwsh, aaa2, DATAONLY )
145
The nibble command has also been used to remove the upstream portion of
the unit composed of two parts connected only by the cell corner.
The removal of small drainage areas introduced discontinuity of the flow
system. A program was written in C language to determine the new relation between
modeling units. The C code of the program newnx.c is listed in Appendix A1. This
procedure requires two text (ASCII) files. In the first file, each line contains two
numbers separated by a comma: unit_id and the downstream unit_id, for the original
set of modeling units. The second file contains only the list of unit_id --identification
numbers of units that remained from the original set after some of them have been
removed. Program newnx creates an ASCII file in which it stores updated
information about system connectivity. In each line, the following numbers are written,
separated by a comma: unit_id, downstream unit_id, and numeric order of the unit in
the flow system.
By assigning a numeric order to each unit, the further calculations are more
efficient. The method of stream numbering is as follows: all exterior units, i.e., the
most upstream units are assigned an order 1. The order of each interior unit is
calculated as the maximum order of the upstream units increased by one.
The advantage of the program written in C over the procedure written in
Arc/Info macro language or in ArcView script language Avenue, is that the
C program, after minor changes, can be used by both Arc/Info and ArcView, whereas
program written in AML can be executed only from Arc/Info, and a script written in
Avenue language can only be run from ArcView. The additional advantage of writing
more complex procedures in such languages as FORTRAN or C is that the time of
execution is very fast. The time gain is on the order 1000, i.e., the computational
hours can be reduced to seconds.
146
The following assignment creates the final map of the modeling units in vector
format (weed tolerance = 180 m):
crwsd = gridpoly ( crwsh3 , 180 )
The map of subdivision of the Iowa -Cedar River basin into 1032 modeling
units is presented in Figure 5.8.
Figure 5.8 The Iowa-Cedar River basin subdivided into 1032 unit drainage
areas of average area 31.6 km
2
.
147
5.4.5 Database of monthly precipitation depth and monthly flow rate
The time series of the average monthly flow rate and the average precipitation
depth for 38 USGS gauging stations and 86 climate stations, for the time period from
January 1940 to September of 1992, have been extracted from the Hydrosphere CD-
ROMs (Hydrosphere 1993 a, b) and stored in a worksheet format.
The units of measurements have been changed:
  - cubic feet per second (cfs) into  cubic meter per second (m
3
/s) (flow) and
  -  inch per day into centimeter per day (cm/d) (precipitation).
For each parameter, two sets of ASCII comma delimited files have been
created. One set contains identification numbers of observation stations and respective
longitude and latitude, expressed in decimal seconds. The other set of files comprise
the station ID number and the time series of flow or precipitation.
The point coverage of 86 precipitation stations has been created from the
ASCII files and projected into Albers Equal Area system of coordinates. This
procedure is identical to the one described in a previous section for generation of point
coverage of USGS stations.
The ASCII files that contain flow and precipitation measurements have been
converted into Arc/Info INFO files and linked with the appropriate maps.
148
5.4.6 Average precipitation depth in modeling units
The method of spatial redistribution of measured flow rate utilizes the
precipitation depth as a weighting factor. Therefore, the monthly average precipitation
depth must be calculated for each modeling unit. The example of the GRID dialog
which calculates a raster map of the average precipitation depth, in modeling each
modeling unit for May 1990 is shown in Listing 5.19.
The grid of distributed precipitation depth has been created directly from the
climate station map. The inverse distance weighting procedure iwd has been applied.
To make the calculations shorter and to save the disk space, 100 times larger cells
(width = 1000 m, area =1 km
2
) than those used for the stream and modeling unit
delineation have been assumed (setcell 1000). The average values for each
modeling unit have been determined by the zonalmean function.  To create an
attribute table, the cell values must be represented as integers. In line 7 of listing 5.19,
the grid, xxx1, that contains zonally averaged precipitation depth is first multiplied
by 10000 to preserve the decimal part and then converted into integer format. The
command combine has been used to create a table in which the modeling unit
identification number (stored in grid crwsd) is related to the estimated average
precipitation depth (stored in grid xxx2).
Listing 5.19 Estimation of the average precipitation depth in modeling units.
1: setcell 1000
2: setwindow MAXOF
3: xxx = idw ( gsrain , m199005 )
4: setcell crwsd
5: setwindow crwsd
6: xxx1 = zonalmean ( crwsd , xxx )
7: xxx2 = int ( 10000 * xxx1 )
8: xxxcom = combine (crwsd, xxx2)
149
Since the procedure described above must be executed for each month, it has
been included into AML?s DO feature that repeats calculations for each month of the
specified time period,. i.e., from month %fm% of the year %fy% to month %tm% of the
year %ty%. An example of the &DO block is presented in Listing 5.20
Listing 5.20 Application of the &DO command to repeat action for each month of
the selected time period.
1: &DO yr = %ty% &to %fy% &by -1
2:   &DO mt = 12 &to 1 &by -1
3:     &s ab = [calc %yr% = %fy%] AND [calc %mt% lt %fm%]
4:     &s bb = [calc %yr% = %ty%] AND [calc %mt% gt %tm%]
5:     &s cc = %ab% OR %bb%
6:     &IF NOT %cc%  &THEN
7:       &do
8:          . . .  /* here, block to be repeated
9:       &end
10:    &end
11: &end
Appendix C3 contains the code of the Arc/Info macro RAININFO.AML. This
program calculates average values for specified zones and then writes them into an
INFO file. The user must specify the period for which the estimates have to be made,
the point coverage that holds the time series, and the grid that divides the region into
zones. The output of the macro is the Arc/Info INFO file that contains for each zone
the ID number and the series of computed zonal averages.
In the approach presented above, only stations that have complete time series,
i.e., stations that have no missing values, have been applied. The macro
SELDATA.AML that is included in Appendix C6 selects stations that have a complete
record in the specified time interval.
To include all available measurements of precipitation depth, another approach
has been tested. The stations that have data for the processing month have been used,
unlike the method discussed above in which only the stations that have data for all
150
months of the specified time period have been utilized. For each month, station
selection is performed (Arc/Info command reselect) and then the grids of spatial
distribution of the precipitation depth are calculated (IDW procedure). This task is
performed by the macro RAINMAP.AML (attached in Appendix C4). The results
were slightly different, but since the zonal averages were calculated later, the
differences were insignificant. Listing 5.21 shows an example procedure that selects all
stations from the database (coverage prcmap) that have a complete record in June,
1966 (point coverage xxx), and then it creates the grid of precipitation (pm196606)
by the inverse distance-squared method:
Listing 5.21 Example of the AML that selects precipitation stations that have a
complete record in June, 1996 and creates the grid of precipitation
depth (adopted from RAINMAP.AML).
1: arc reselect precmap xxx point
2: res m196606 ge 0
3: ~
4: n
5: n
6: arc build xxx point
7: pm196606 = int ( 1000 * idw ( xxx, m196606 ) )
8: kill xxx all
5.4.7 Spatial distribution of flow
Three approaches have been made to incorporate the procedure described in
Section 4.5 into GIS. Coding has been made in:
1) Avenue, the script language of ArcView;
2) Arc/Info macro language, AML;
3) C programming language.
151
For the first two approaches, the calculations of the flow rate for a single
month took hours, whereas the program written in C language redistributed the flow
record in a few seconds. Therefore a method that uses the Arc/Info Tables to prepare
the data and then utilizes the C program to calculate the flow rate in modeling units
has been developed. It is explained here for a single month: March 1990. The full
Arc/Info macro--fd4y.aml--is presented in Appendix C7. The C program--
fd4y.c--is listed in Appendix A2.  The fd4y program requires two input files and it
stores the results in one output file. In lines 2 and 3 of Listing 5.22, the Arc/Info
processor, Tables, creates the first input file xxxgsin in which the following items of
the point attribute table gsfl28.pat are stored:
- station_id = ID number of the USGS gauging station;
- station_nx = ID number of the downstream USGS station;
- m199003 = item that contains flow record for March 1990
The second input table, xxxunin, is prepared in lines 4 and 5. The following items
are unloaded from the polygon attribute table unprec.pat:
- unit_id = modeling unit ID number;
- unit_nx = ID number of the downstream unit
- gswsh = ID of the USGS gauging station that is located downstream from the
given unit;
- area_km2 = area of the unit;
- order = modeling unit order in the flow system; and
- pm199003 = item that contains average precipitation depth.
The program fd4y is executed in line 6. Since UNIX is a multitasking system,
the AML must wait until fd4y finishes calculations. Lines 7 to 10 contain the loop in
which AML checks if fd4y program created output file xxxunout. In lines 11 to
14, the temporary INFO file m199003.dat  is created in which the results of the
152
fd4y calculations are stored (line 15). Then, the estimated flow rate is attached to the
Arc/Info database file unflow.pat (line 17) and the temporary file m199003.dat
is deleted (line 18). In the complete version of this procedure (fd4y.aml), the
process described here is repeated for all months of the specified time period. Figure
5.9 presents an example of estimated runoff that occurred in June 1990.
Listing 5.22 Example of the Arc/Info macro that prepares data and estimates the
flow rate in modeling units (adopted from fd4y.aml,
Appendix C7)
1: tables
2: select gsfl28.pat
3: unload xxxgsin station_id station_nx m199003 DELIMITED INIT
4: select unprec.pat
5: unload xxxunin unit_id unit_nx gswsh area_km2 order pm199003
DELIMITED INIT
6: &sys fdy4 xxxgsin xxxunin xxxunout
7: &s i = 0
8: &do &until [exists xxxunout -file]
9:   &s i = %i% + 1
10: &end
11: define m199003.dat
12: unit_id,4,8,B
13: qm199003,4,12,F,4
14: ~
15: add from xxxunout
16: select m199003.dat
17: &sys arc joinitem unflow.pat m199003.dat unflow.pat unit_id
order
18: kill m199003.dat
153
Flow, June 1990 [m3/s]
0.4 - 1.0
1.0 - 1.5
1.5 - 3.0
3.0 - 13.0
13.0- 843.898
Figure 5.9 Runoff (flow in rivers) that occurred in June 1990 in the Iowa-
Cedar River watershed.
154
5.4.8 Determining input values for the Iowa-Cedar River model
The flow rate at the outlet of each modeling unit has been estimated by the
procedure described in Section 5.4.7.
The distributed system of watershed parameters and normal weather parameters have
been created for the Iowa-Cedar River using 100 m grid according to the methodology
discussed in Section 5.2.2. The concentration models determined by the regression
analysis relate agrichemical concentration to parameters of the upstream drainage area.
Thus it is important to get parameters for the entire upstream area at each unit
watershed outlet rather than data just for the modeling unit belonging to that point.
The characteristics of the drainage area that is upstream of each modeling unit outlet,
have been extracted from the distributed system of watershed parameters according to
the methodology discussed in Section 5.2.5.
5.5 ArcView model of agrichemical transport
The computer version of the agrichemical transport model is completely
constructed within the GIS software ArcView. A modular structure has been utilized.
Such a structure not only makes the model simple and easy to understand, but also it
allows improvement of the model or addition of new blocks without changing the
model?s core components. The program execution is supported by a customized
155
graphical user interface (GUI). Tools that enhance the graphical representation of the
results are developed. The ArcView model contains procedures for representing
hydrologic processes.
5.5.1 Model overview
The ArcView application is divided into four projects (a project is a collection
of associated documents: views, tables, layouts, charts, and scripts). Each project is
designed to perform a different task. Four buttons that allow user to switch between
projects have been placed in the PushButton Bar (the avenue scripts assigned to each
button are listed in Appendix B1). These buttons have the following functions:
Runs the ?model? project. This project is designed to prepare entry data for the
agrichemical transport model as well as to calculate concentrations and loads.
Runs the ?results? project which is designed to display the results as maps of
agrichemical concentration and load.
Executes project ?flwprc? which provides visualization of the flow record for a
selected modeling unit.
Project ?tools? contains the fundamental tools for hydrologic modeling.
The project ?model? is the main component of the ArcView application.
Projects ?results?, ?flwprc?, and ?tools? are supporting modules. The scripts
associated with the project ?model? are listed in Appendix B2. The scripts used by the
156
projects ?results?, ?flwprc?, and ?tools? are presented in Appendices B3, B4, and B5,
respectively.
The agrichemical transport model is navigated through a set of buttons that,
when pressed, execute particular model components. The data entry and the data
selection is maintained by a set of windows. Figure 5.10 presents an example of a
window that supports selection of the agrichemical application rate to be used for
concentration estimation. This window contains three input fields. In the first field, the
user can enter the name of agrichemical application database that will be utilized for
predicting the chemical concentrations and loads in the Iowa-Cedar River basin. The
second field allows user to multiply the application rate in the counties which are
selected by ArcView tools. This feature is introduced to study the response of the
concentration in rivers after the application rate has been increased or decreased by a
specified percentage. The last entry field permits one to specify an application rate for
a selected county or all counties without the necessity of editing the attribute tables
directly. This field is deactivated if a negative value is entered.
Figure 5.10 An example of the Graphical User Interface: a window for the
selection of the agrichemical application rate in selected counties.
157
 The presentation tools support drawing bar charts at the center of selected
units. They are developed to enhance the presentation of the data and the model
results on a map. Figure 5.11 shows examples of the application of the presentation
tools.
0.0000000
2.5000000
5.0000000
7.5000000
10.0000000
Conc. mg/m3
0.0000
250.0000
500.0000
750.0000
1000.0000
Flow (6/90) m3/s
Figure 5.11 Atrazine concentrations along the Cedar River estimated for 1990
(left) and flow rate along the Cedar River in June 1990 (right).
The hydrologic modeling is supported by scripts that perform the following tasks:
- Selection of the units downstream of a selected point;
- Selection of all units upstream of a selected unit;
- Estimation of the watershed weighted average of an entity such as chemical
application rate;
- Accumulation of values when moving downstream (flow accumulation);
158
- Calculation of the unit mass balance (reverse operation to flow accumulation);
and
- Determination of the order of the unit (all exterior units/streams are assigned
an order of one, an interior unit has the order equal to the maximum order of
the upstream units increased by one).
5.5.2 Project ?Model?
When opened, the project ?Model? displays the following maps:
1) Agrichemical application rate by county (window: Application Rate, theme:
Use);
2) The Iowa-Cedar River basin divided into modeling units (window: Modeling
Units, theme: Units).
Five buttons are designed to select different activities:
Edit Application. This button displays dialog boxes that allow the user to
specify the agrichemical application rate. If the view-window ?Application
Rate? is active, the application in either all, or selected counties can be
specified. Additionally, the application rate of nitrogen fertilizers estimated for
1989, 1990, and 1991, and application rate of atrazine estimated for 1989 can
be selected. A multiplier that increases/decreases application rate by a given
percentage also can be used to simulate the different policy scenarios. If the
view-window ?Modeling units? is active, the application rate in each modeling
unit can be modified.
Edit Cumulative Flow Rate. This button shows dialog boxes for selecting the
flow record (by selecting a year) that will be used for calculations and for
159
adjusting the selected values. For example, all data can be multiplied by a
factor that represents extreme conditions. The adjustment may be performed
for all months of the specified year or for each individual month.
Select Year. This button allows the user to specify a year for a model that has a
trend component. There is no trend in the current model.
Select Month. The dialog box displayed by this button specifies if the
calculations will be performed for all months or only for selected months of a
year.
Run. Executes the script that performs the calculations.
First Order Reaction. Calculates concentrations and loads assuming
exponential decrease of the agricultural constituent along the flow path. The
current model does not contain a map of spatially distributed decay rates that
allows one to estimate concentrations by this method.
The following coverages and data files constitute the core database of the model:
1) Coverage cruse--a map of 47 counties that are within the Iowa-Cedar River
basin. Table 5.5 presents the items of cruse?s PAT.
160
Table 5.5 Polygon Attribute Table of the cruse coverage.
Field (Item) Description
Fips county FIPS code
St state
Cntyname county name
N89kgkm2, N90kgkm2,
N91kgkm2
estimated average nitrogen fertilizer application rate for the years
1989, 1990, and 1991, respectively [kg/km
2
]
A89kgkm2 estimated average atrazine application rate for 1989 [kg/km
2
]
Temp field reserved for storage of results of partial calculations
Use application rate selected for the estimation of concentrations and
loads
2) Coverage crwsd--map of 1032 modeling units. Table 5.6 lists the items of the
attribute table.
Table 5.6 Polygon Attribute Table of the crwsd coverage.
Field (Item) Description
Unit_id ID of the modeling unit
Gswsh ID of the USGS gauging station downstream of the modeling unit
Unit_nx ID of the next unit on the flow path (downstream unit ID)
Order a number that specifies location of the unit on the flow path
Areakm2 area of the unit [km
2
]
Careakm2 drainage area upstream of the unit outlet [km
2
]
Alndslp average land slope of unit drainage area
Alndlgkm average length on the flow path from the land to the stream network [km]
Chemuse Agrichemical application rate in the unit [kg/yr/km
2
]
Cchemuse average agrichemical application rate over the unit drainage area
[kg/yr/km
2
]
Travtime Agrichemical travel time across the unit [d] (no data available)
Losscoef Overall loss coefficient in the unit [1/d] (no data available)
Expofact Export factor, fraction of the applied agricultural chemical in the unit
that enters the surface water (no data available)
Tcavg Annual average temperature for upstream drainage area [?C]
Pmmavg Annual precipitation depth, average over upstream drainage area [mm]
Flow01...Flow12 monthly flow rate that flows through the unit outlet [m
3
/s]
Conc01...Conc12 concentration at the unit outlet (atrazine [mg/m
3
], nitrate plus nitrite as
nitrogen [g/m
3
])
Load01...Load12 chemical load (flow * concentration, atrazine [mg/s], nitrate plus nitrite
as nitrogen [g/s])
161
3) File Model2a.dbf -- model specification. Table 5.7 shows the fields of this file.
Table 5.7 Fields of the file model2a.dbf (model specification).
Field Description
Year a year that is used to estimate the trend coefficient;
Ftrend mathematical description of the trend. Current version of the model assumes no
trend, i.e. the trend is described by the following equation: 1.00+(0.0000*Year)
Trendcf trend coefficient which is calculated according to the information stored in
items Year and Ftrend
Si01...Si12 seasonal index, 12 values that represent the monthly variations of the
agrichemical concentration around the annual average.
Model model name, e.g. Nitrate01, Atrazine01, Atrazine02
Sel contains 1 if the model is selected for calculations, 0 otherwise
Equation equation for estimation of agrichemical concentrations. Four models are
available,
1) atrazine model without the flow rate [?g/L]:
(-1.5575+(0.026*U)+(0.7998*LL)+(0.4559*TA)-(0.0048*PA))*TR*SI
2) atrazine model with the flow rate [?g/L]:
(-0.8142+(0.0133*U)+(0.3346*LL)+(38.8804*LS)+(0.2732*TA)-
(0.0029*PA))*(Q^0.2899)*TR*SI
4) nitrate plus nitrite as nitrogen model without the flow rate [mg/L]:
(-7.424541+(0.001062*U)-(1.033063*TA)+(0.019339*PA))*TR*SI
5) nitrate plus nitrite as nitrogen model with the flow rate [mg/L]:
(-7.57848+(0.00064886*U)+(0.776683*LL)+(173.6409*LS)-
(0.520245*TA)+(0.0088545*PA))*(Q^0.3432)*TR*SI
Three multiplicative models are included only for testing purposes:
x1) nitrate plus nitrite as nitrogen [g/m
3
]:
0.000143208*(U^1.3814)*(A^(-0.5556))*(Q^0.4240)*(LL^0.9522)*TR*SI
x2) for atrazine [g/m
3
]:
0.0001265546*(U^0.8323)*(SL^0.3591)*(Q^0.0940)*(LL^0.9208)*TR*SI
x3) for atrazine, same as (x2) but different output units [mg/m
3
]
0.1265546*(U^0.8323)*(SL^0.3591)*(Q^0.0940)*(LL^0.9208)*TR*SI
where: U = application rate, A = drainage area, Q = flow rate, LL = average
overland flow length, SL = land slope, TA = average temperature, PA =
average precipitation, TR = trend coefficient, and SI = seasonal index.
Comments comments and model description
162
4) File Linkuse.dbf--description of the link between counties and modeling units
(1517 records). Three items describe the link: Fips (county FIPS code), Unit_id
(ID number of the modeling unit or part of the modeling unit that is located in the
county described by the FIPS code), and Area_km2 (area of the unit or part of the
unit that is located in the county specified by the FIPS code [km
2
]).
5) Coverage Unflow -- map of 1032 modeling units. The PAT file contains item
Unit_id, and items Qm196001...Qm199209, that store the cumulative flow rate
estimated for the period from January 1960 to September 1992.
6) Coverage Unprec -- map of 1033 modeling units. The PAT file contains item
Unit_id, and items Pm195001...Pm199306, that store the average precipitation
depth estimated for the period from January 1950 to June 1993.
The ArcView script equat6 (Appendix B2) calculates concentrations and
loads. This script first selects the record that contains the value of item [Sel] equal
to 1. Then equat6 extracts the value from the item [Year], retrieves the equation
that describes the trend from the item [Ftrend], calculates the trend coefficient, and
stores it in the item [Trendcf].
In the next step, the script extracts the equation from the item [Equation] and
replaces the symbolic names U, A, LS, LL, and Q with the corresponding item names
[Cchemuse], [Careakm2], [Alndslp], [Alndlgkm], and one of the item
[Qm01]...[Qm12]. The symbolic name TR is replaced by the value stored in the item
[Trendcf] and the name SI is replaced by the value from one of the items
[Si01]...[Si12]. The concentrations are calculated for each month of the year by the
Avenue request calculate and the results are stored in the items
163
[Conc01]..[Conc12]. The loads are estimated by multiplication of the flows and
concentrations. The products are stored in the items [Load01]...[Load12].
Calculations of the agrichemical concentration in surface waters, according to
the first order process, are performed by the script decay1. This Avenue program
has been written for future extentions of the agrichemical transport model, for
example, to utilize the results of the CEEPES (Comprehensive Environmental
Economic Policy Evaluation System) modeling program developed by Iowa State
University?s Center for Agricultural and Rural Development, CARD (Bouzaher and
Monale, 1993).
5.5.3 Project ?Results?
This project reserves the space for preparing the maps of estimated
agrichemical concentration and load in surface water. Three scripts, executed from the
button bar, , , and , draw the bar charts of the monthly average chemical
concentration, chemical load and flow rate, respectively. Figure 5.13 presents the
preliminary agrichemical model results of the estimation atrazine concentrations in
1990 in the form of bar charts located along the Iowa River and the Cedar River.
164
0.0000000
0.0015000
0.0030000
0.0045000
0.0060000
At90 g/m3
Figure 5.12 ?Bar chart? map of the atrazine concentrations estimated for 1990
(preliminary results)-- an example map created within the ArcView
project ?Results? (g/m3 = mg/L).
The results of the calculations can be presented on the map of modeling units. Figure
5.13 shows an example of atrazine concentrations in streams for May 1990.
165
Atrazine May 90 g/m3
0.001 - 0.002
0.002 - 0.003
0.003 - 0.003
0.003 - 0.004
0.004 - 0.006
Figure 5.13 Atrazine concentrations in the Cedar River basin introductory
estimated for May 1990 -- a map created within the ArcView project
?Results? (g/m3 = mg/L).
The ArcView model of the agrichemical transport represents the flow system
as a network of connected modeling units. Since the Arc/Info-Grid procedures that
166
convert grid of rivers into vector format do not preserve proper numbering of the
stream reaches, i.e., some reaches are split and they are identified by two or more IDs
(Fig. 5.14), the modeling unit approach has been used to simplify the model.
665
665
677
677
680
Cedar River
Iowa River
Flow
Direction
Figure 5.14 Inconsistency in the assigning IDs to the vectorized grid streams.
The GRID function gridline assigned wrong IDs to the Cedar
River downstream to the junction with the Iowa River.
The vector representation of the stream network created by both,
streamline and gridline commands can not be used for the modeling without
extensive editing of the stream coverage. However, such a map of rivers can be used
for data presentation purposes. Figure 5.15 shows flow rate in the streams of the
Iowa-Cedar Basin created by linking the polygon attribute table of modeling unit
coverage with the arc attribute table of the streams map.
167
Flow in m3/s, June 1990
0.512 - 5
5- 30
30 - 200
200 - 800
800 - 843.898
Figure 5.15 Flow rate in the Cedar River and tributaries that occurred in June
1990. The map has been created by linking the polygon attribute
table of interpolated flow measurements by modeling unit with the
arc attribute table of a stream coverage.
168
5.5.4 Project ?Flwprc?
The bar charts that represent the monthly flow rate and the average
precipitation depth for a selected time period can be drawn at the center of selected
modeling units (  draws charts of the flow rate and  draws charts of the
precipitation depth). The script associated with the button  displays all recorded
flow rate (monthly values from January 1960 to December 1992) for a specified
modeling unit. Since charts of monthly flow rate for multiple year periods can be
drawn, the wet or dry years can be easily identified. Figure 5.16 presents the monthly
flow for years from 1989 to 1991.
0.0000
200.0000
400.0000
600.0000
800.0000
Flow m3/s
Figure 5.16 Monthly flow rate in the lower Cedar River in 1989-1991. Example
of visual tools of ArcView project ?Flwprc? for hydrologic analysis.
169
5.5.5 Project ?Tools?
The following tools have been created to support the model of agrichemicals in surface
waters (Avenue scripts are included in Appendix B5):
 - Determines the unit/stream order in the flow system (Avenue script order6);
 - Calculates weighted average for each modeling unit total drainage area (script
upavg2);
 - Accumulates values going along the flow path (script cumul2); and
 - Calculates the difference between the unit inputs and the unit output (script
decom2).
170
6. RESULTS
According to the methodology described in Section 4 and the procedures
discussed in Section 5, the models of the agrichemical concentrations in the Midwest
rivers are developed in two steps. First, the seasonal components are estimated, one
for the nitrate plus nitrite as nitrogen concentration and the other for the atrazine
concentration. The seasonal changes of the concentrations are discussed in
Section 6.1. The second step of the model development estimates a regression
equation that explains the average annual concentration in the sampled rivers. The
process of representing the deseasonalized agrichemical concentration by such
explanatory variables as chemical application, watershed morphometry, and
climatologic parameters is presented in Section 6.2. Section 6.3 discusses the
differences between the modeled concentrations and the measured ones. The statistical
models of agrichemical concentrations have been developed utilizing data that
characterize the Upper Mississippi-Missouri and the Ohio River basins.
The precision of the spatial redistribution of the monthly flow record is tested
in Section 6.4. The flow measured in the USGS stations distributed over the Iowa-
Cedar River watersheds is utilized in that portion of the study. Section 6.5 describes
the application of the statistical models that are incorporated into the GIS - ArcView
to predict atrazine and nitrate plus nitrite concentrations as well as the chemical loads
in the Iowa River, the Cedar River and in their tributaries.
For the clarity of presentation, some information from Section 4 and Section 5
is repeated here.
171
6.1 Seasonal variation of agrichemicals in the Midwest
streams
All seasonal models assume each station to have an annual average
concentration represented by a constant around which the amount of agrichemical
oscillates seasonally. By utilizing dummy variables, created by the S-plus function
factor(), the regression equation describes the mean annual concentration by
constants that are different for each site and by a set of sine-cosine functions
describing monthly variation that are common for all sampling sites. Equation 6.1
(presented in Section 4.3.6 as Eq. 4.12) represents the regression model utilized to
estimate the seasonal variations of the atrazine concentration as well as the nitrate plus
nitrite as nitrogen concentration. The model that includes the flow rate as an
explanatory variable is described by the Equation 6.2 (Eq. 4.13).
[] ()
ln ( , ) sin( / ) sin( / )cjd w a km b km
jk k
k
=+ +
=
?
212 212
1
5
pipi(6.1)
and
      
[] [ ]()
ln ( , ) ln ( , ) sin( / ) sin( / )cjd w a Qjd a km b km
jk
k
=+ + +
=
?0
1
5
212 212pipi(6.2)
where:
ln[...] = natural logarithm;
c(j,d) = concentration measured at site j on day d (?g/l or mg/l);
Q(j,d) = flow rate measured at site j on day d (m
3
/s);
w
j
 = intersect specific for the j-th sampled watershed;
a
0,
 a
k
 and b
k
 = coefficients;
j = index of the sampling site;
d = day of sample collection;
172
k = harmonics number;
m = month of the year.
6.1.1 Seasonal variation of the atrazine concentration
The following listing shows an example of the S-plus regression model
specification for seasonal variation of the atrazine concentrations in surface waters of
the Mississippi-Missouri River and the Ohio River basins.
Listing 6.1 The S-plus session for estimation of the model of seasonal atrazine
variation. Model does not contain the flow rate component.
1: a4si _ lm ( log(Concmgm3) ~ factor(Id)
2: +   + sin(2*pi*Month/12) + cos(2*pi*Month/12)
3: +   + sin(4*pi*Month/12) + cos(4*pi*Month/12)
4: +   + sin(6*pi*Month/12) + cos(6*pi*Month/12)
5: +   + sin(8*pi*Month/12) + cos(8*pi*Month/12)
6: +   + sin(10*pi*Month/12) + cos(10*pi*Month/12) , data = atra7)
In Listing 6.1 the results of the least square calculations are stored in an S-plus
object that is named by the user a4si. The natural logarithm of the atrazine
concentration Concmgm3 is the dependent variable. Column Concmgm3 in the data
frame atra7 contains concentrations in ?g/L. The independent variables are
trigonometric functions and the factorized variable Id. Id is the name of a column in
the data frame atra7 that contains sampling site identification numbers. Function
factor tells the least square procedure lm to treat the variable as a factor that has
p = 151 levels (the number of distinct Id values). The p-1 columns are added to the
173
model matrix, and then the procedure lm estimates a value (intercept) for each Id
category.
Table 6.1 shows selected results of the regression analysis of the atrazine
concentration in the Midwest rivers. Since only the seasonal component is important in
the analysis, Table 6.1 does not contain the 151 intercept terms.
Table 6.1 Selected coefficients of the regression analysis of the atrazine
concentration in the Midwest rivers. Seasonal variation is explained
only by the sine-cosine harmonics. Coefficients related to the
dummy variables are not shown.
Explanatory variable        Value Std. Error  t value Pr(>|t|)
sin((2 * pi * Month)/12)  -0.1174   0.0975    -1.2040   0.2289
cos((2 * pi * Month)/12)  -1.5085   0.1256   -12.0105   0.0000
sin((4 * pi * Month)/12)  -0.1655   0.1085    -1.5261   0.1274
cos((4 * pi * Month)/12)   0.7244   0.1191     6.0829   0.0000
sin((6 * pi * Month)/12)   0.0397   0.1018     0.3903   0.6964
cos((6 * pi * Month)/12)  -0.2813   0.1128    -2.4933   0.0129
sin((8 * pi * Month)/12)  -0.3014   0.0871    -3.4594   0.0006
cos((8 * pi * Month)/12)  -0.0256   0.1153    -0.2218   0.8245
sin((10 * pi * Month)/12)  0.1521   0.1003     1.5167   0.1297
cos((10 * pi * Month)/12)  0.0700   0.0795     0.8809   0.3787
Residual standard error: 1.021 on 772 degrees of freedom
Multiple R-Squared: 0.7555
F-statistic: 14.91 on 160 and 772 degrees of freedom
Table 6.2 presents the regression coefficients of the seasonal model that
contains the flow rate. A similar S-plus dialog has been used to the one presented in
Listing 6.1, except the independent variable log(Flowm3s)-- the natural logarithm
of the flow rate in m
3
/s -- has been added to the model specification. Listing 6.2 shows
this dialog.
Listing 6.2 The S-plus session for estimation of the model of seasonal atrazine
variation. Model contains the flow rate component.
1: a4siq _ lm ( log(Concmgm3) ~ factor(Id) + log(Flowm3s)
2: +   + sin(2*pi*Month/12) + cos(2*pi*Month/12)
174
3: +   + sin(4*pi*Month/12) + cos(4*pi*Month/12)
4: +   + sin(6*pi*Month/12) + cos(6*pi*Month/12)
5: +   + sin(8*pi*Month/12) + cos(8*pi*Month/12)
6: +   + sin(10*pi*Month/12) + cos(10*pi*Month/12) , data = atra7)
Table 6.2 Selected coefficients of the regression analysis of the atrazine
concentration in the Midwest rivers. Seasonal variation is explained
by the sine-cosine harmonics and by the flow rate. Coefficients
related to the dummy variables are not shown.
Explanatory variable        Value Std. Error  t value Pr(>|t|)
            log(Flowm3s)   0.2899   0.0297     9.7696   0.0000
sin((2 * pi * Month)/12)  -0.4237   0.0972    -4.3589   0.0000
cos((2 * pi * Month)/12)  -1.3266   0.1200   -11.0542   0.0000
sin((4 * pi * Month)/12)  -0.1536   0.1024    -1.5002   0.1340
cos((4 * pi * Month)/12)   0.5409   0.1140     4.7457   0.0000
sin((6 * pi * Month)/12)   0.0401   0.0960     0.4174   0.6765
cos((6 * pi * Month)/12)  -0.2170   0.1067    -2.0337   0.0423
sin((8 * pi * Month)/12)  -0.3110   0.0823    -3.7814   0.0002
cos((8 * pi * Month)/12)   0.0200   0.1089     0.1832   0.8547
sin((10 * pi * Month)/12)  0.1359   0.0947     1.4352   0.1516
cos((10 * pi * Month)/12)  0.0970   0.0751     1.2920   0.1967
Residual standard error: 0.9638 on 771 degrees of freedom
Multiple R-Squared: 0.7825
F-statistic: 17.23 on 161 and 771 degrees of freedom
Regardless of the statistical significance, all harmonics have been utilized to
determine the monthly seasonal factors of atrazine concentration. The seasonal factors
S(m) have been calculated by the following formula (Eq. 4.11) that ensures that the
average of 12 seasonal factors equals one:
()
Sm
akm bkm
aki bki
kk
k
kk
ki
()
exp( sin( / ) sin( / )
exp( sin( / ) sin( / )
=
+
+
=
==
?
??
212 212
212 212
1
5
1
5
1
12
pipi
pipi
(6.3)
where:
S(m) = the seasonal factor of month m;
175
i = index of the month (i = 1, 2, ... 12);
k = index of the harmonics;
a
k
 and b
k
 = regression coefficients from Table 6.1 or Table 6.2.
Table 6.3 shows non-normalized seasonal factors (described by the numerator
of right hand side of Equation 6.3) as well as the normalized seasonal factors S(m) in
the way that the average value over a year is equal to one (Eq. 6.3).
Table 6.3 Seasonal factors of atrazine concentrations in the Midwest rivers
estimated by the regression analysis with and without flow rate
record.
Month Not-normalized Normalized
without flow with flow without flow with flow
1 0.26 0.23 0.11 0.12
2 0.41 0.36 0.17 0.19
3 0.47 0.43 0.19 0.22
4 0.77 0.60 0.32 0.31
5 9.06 6.00 3.72 3.13
6 11.23 7.44 4.61 3.88
7 3.60 3.30 1.48 1.72
8 1.55 2.09 0.64 1.09
9 0.47 0.82 0.20 0.43
10 0.51 0.72 0.21 0.37
11 0.52 0.63 0.22 0.33
12 0.36 0.41 0.15 0.21
Average 2.43 1.92 1.00 1.00
Seasonal factors of the atrazine concentration are also presented in Figure 6.1.
Some trace amount of atrazine exists in the rivers throughout the year. The major
transport occurs after chemical application on the field, in May and in June. The
average monthly concentration in late Spring and early Summer is about 20 times
higher then the average concentration in the months from September to April.
176
0.00
1.00
2.00
3.00
4.00
5.00
12345678910112
Without flow
With flow
Seasonal Factor
Month
Figure 6.1 Seasonal factors of atrazine concentrations in the Midwest rivers
estimated by the regression analysis with and without flow rate
record.
The seasonal factors estimated without utilizing the flow rate have slightly
higher amplitude than the ones that have been calculated by the regression model with
the flow rate. This indicates, that the seasonally varying flow rate is correlated with the
atrazine concentration. The flow coefficient listed in Table 6.2 describes a positive
relationship between the atrazine concentration and the flow rate: c =  ... Q
0.2899
. It
represents not only the relationship between flow and concentration at an individual
site, but also reflects the ?spatial? relationship of concentrations in rivers of different
sizes.
177
6.1.2 Seasonal variation of the nitrate plus nitrite as nitrogen concentration
Listing 6.3 presents the S-plus dialog which has been applied to estimate the
seasonal variations of the nitrate plus nitrite as nitrogen. The nitrate concentrations
(mg/L) are stored in the in the column Concgm3 of the S-plus data frame nitr7.
The results of the least square procedure lm are written to the S-plus object n4si.
Listing 6.3 The S-plus session for estimation of the model of seasonal nitrate
variation. Model does not contain the flow rate component.
1: n4si _ lm ( log(Concgm3) ~ factor(Id)
2: +   + sin(2*pi*Month/12) + cos(2*pi*Month/12)
3: +   + sin(4*pi*Month/12) + cos(4*pi*Month/12)
4: +   + sin(6*pi*Month/12) + cos(6*pi*Month/12)
5: +   + sin(8*pi*Month/12) + cos(8*pi*Month/12)
6: +   + sin(10*pi*Month/12) + cos(10*pi*Month/12) , data = nitr7)
Table 6.4 shows selected results of the regression analysis of seasonal nitrate
concentration changes in the Midwest rivers. The coefficients related to the
factor(Id) (150 coefficients plus one intercept) are not shown.
Table 6.4 Selected coefficients of the regression analysis of the nitrate
concentration in the Midwest rivers. Seasonal variation is explained
only by the sine-cosine harmonics.
Explanatory variable        Value Std. Error  t value Pr(>|t|)
sin((2 * pi * Month)/12)   0.8789   0.0871    10.0874   0.0000
cos((2 * pi * Month)/12)   0.0892   0.1095     0.8147   0.4154
sin((4 * pi * Month)/12)   0.1397   0.0964     1.4495   0.1475
cos((4 * pi * Month)/12)   0.6929   0.1040     6.6653   0.0000
sin((6 * pi * Month)/12)  -0.3028   0.0873    -3.4706   0.0005
cos((6 * pi * Month)/12)  -0.0526   0.0974    -0.5407   0.5889
sin((8 * pi * Month)/12)  -0.0318   0.0755    -0.4215   0.6735
cos((8 * pi * Month)/12)  -0.2373   0.1010    -2.3494   0.0190
sin((10* pi * Month)/12)   0.2794   0.0888     3.1445   0.0017
cos((10* pi * Month)/12)  -0.0878   0.0628    -1.3986   0.1622
Residual standard error: 0.948 on 1147 degrees of freedom
Multiple R-Squared: 0.6803
F-statistic: 15.26 on 160 and 1147 degrees of freedom
178
Nitrate plus nitrite as nitrogen model specification is displayed in Listing 6.4.
The natural logarithm of the flow rate log(Flowm3s), has been added to the model
determined in Listing 6.3. The results are stored in the object n4siq. Estimated
model parameters, excluding coefficients related to the factor(Id), are displayed
in Table 6.5.
Listing 6.4 The S-plus specification of the seasonal nitrate model. The model
contains the flow rate component.
1: n4siq _ lm ( log(Concgm3) ~ factor(Id) + log(Flowm3s)
2: +   + sin(2*pi*Month/12) + cos(2*pi*Month/12)
3: +   + sin(4*pi*Month/12) + cos(4*pi*Month/12)
4: +   + sin(6*pi*Month/12) + cos(6*pi*Month/12)
5: +   + sin(8*pi*Month/12) + cos(8*pi*Month/12)
6: +   + sin(10*pi*Month/12) + cos(10*pi*Month/12) , data = nitr7)
Table 6.5 Selected coefficients of the regression analysis of the nitrate
concentration in the Midwest rivers. Seasonal variations are
explained by the sine-cosine harmonics as well as the flow record.
Coefficients related to the dummy variables are not shown.
Explanatory variable        Value Std. Error  t value Pr(>|t|)
            log(Flowm3s)   0.3432   0.0213    16.1054   0.0000
sin((2 * pi * Month)/12)   0.5789   0.0809     7.1570   0.0000
cos((2 * pi * Month)/12)   0.3487   0.1003     3.4776   0.0005
sin((4 * pi * Month)/12)   0.1035   0.0871     1.1882   0.2350
cos((4 * pi * Month)/12)   0.5066   0.0946     5.3546   0.0000
sin((6 * pi * Month)/12)  -0.2964   0.0788    -3.7596   0.0002
cos((6 * pi * Month)/12)  -0.0136   0.0880    -0.1550   0.8769
sin((8 * pi * Month)/12)  -0.0290   0.0682    -0.4255   0.6706
cos((8 * pi * Month)/12)  -0.1488   0.0914    -1.6275   0.1039
sin((10* pi * Month)/12)   0.2397   0.0803     2.9851   0.0029
cos((10* pi * Month)/12)  -0.0326   0.0568    -0.5733   0.5666
Residual standard error: 0.8565 on 1146 degrees of freedom
Multiple R-Squared: 0.7393
F-statistic: 20.19 on 161 and 1146 degrees of freedom
All sine-cosine terms have been used to calculate the seasonal factors. Likewise
for the atrazine model (Eq. 6.1), the exponent of the sum of harmonics, non-
normalized seasonal factors, has been normalized to make the average of the seasonal
179
factors equal one. Table 6.6 compares the seasonal factors for two models, one
without flow rate and the other with the flow rate.
Table 6.6 Seasonal factors of the nitrate plus nitrite as nitrogen concentrations
in the Midwest rivers estimated by the regression analysis with and
without flow rate.
Month Not-normalized Normalized
without flow with flow without flow with flow
1 2.69 2.31 2.10 1.94
2 1.64 1.49 1.28 1.26
3 1.70 1.58 1.33 1.33
4 1.09 0.84 0.85 0.71
5 1.64 1.05 1.28 0.88
6 1.66 1.06 1.30 0.89
7 1.14 0.95 0.89 0.80
8 0.52 0.59 0.41 0.50
9 0.09 0.17 0.07 0.14
10 0.43 0.66 0.34 0.56
11 1.28 1.62 1.00 1.36
12 1.50 1.94 1.17 1.63
Average 1.28 1.19 1.00 1.00
The seasonal variations of the nitrate plus nitrite as nitrogen in the Midwest
rivers are also visualized in Figure 6.2. The variations of nitrate exhibit a different
pattern than do the variations of atrazine. The amplitude of nitrate oscillations is much
smaller than the one for atrazine. For the nitrate, the range of seasonal factors varies
between 0.1 and 2.1, whereas the range of atrazine factors is from 0.1 to 4.6.
For the months from February to June, nitrate concentrations fluctuate very
little around the annual average value. From June the concentration level decreases
reaching the minimum in September (about 10% of the annual average). Then nitrate
concentration increases to a maximum value, 200% of annual average, in January. The
180
variations of the nitrate plus nitrite concentration evaluated from the reduced model
generally agree with the published patterns (for example, for Great Britain: Jones and
Burt, 1993, for Slovakia: Mendel and Repa, 1994), except for April, when the
concentrations are lower then the ones estimated for May, June and July. The high
May - July concentrations can be explained by the late Spring (May) application of
fertilizers.
0.00
1.00
2.00
3.00
4.00
5.00
12345678910112
Without flow
With flow
Seasonal Factor
Month
Figure 6.2 Seasonal factors of the nitrate plus nitrite as nitrogen concentrations
in the Midwest rivers estimated by the regression analysis with and
without flow rate included as an explanatory variable.
6.2 Average annual agrichemical concentration in the
Midwest streams
One hundred fifty one average concentration levels, each for one sampling site,
have been assumed to calculate seasonal changes of the agrichemicals. This section
181
presents the results of the regression analysis of deseasonalized concentration data.
The seasonal component has been removed from the concentration measurements
c(j,d) by dividing the concentrations by the respective seasonal factor S(m):
cjd
cjd
Sm
ns
(, )
(, )
()
= (6.4)
where:
c
ns
(j,d) = deseasonalized agrichemical concentration;
c(j,d) = observed concentration at site j on day d;
j = sample site indicator;
m = month of the year when the sample was collected;
S(m) = seasonal factor;
A second set of the deseasonalized concentration measurements has been
calculated by removing from the data a component that is explained by both the flow
rate Q and the seasonal factor S
q
(m). The process of preparing agrichemical
concentration observations for further analysis is described by the Eq. 6.5.
cjd
cjd
SmQjd
nsq
q
a
(, )
(, )
()(,)
= (6.5)
where:
c
nsq
(j,d) = concentration with removed seasonal and flow components;
Q(j,d) = observed flow rate at j-th site, on day d;
S
q
(m) = seasonal factor estimated from a model that includes flow rate;
a = a coefficient estimated by the regression during seasonal changes of
 concentration analysis;
d, m, j, c(j,d) = same as in Eq (6.4)
182
The deseasonalized observations have been utilized to determine the model
that relates the average annual concentration level at a given location to the annual
agrichemical application rate, parameters that describe the watershed upstream to that
location, and to selected climatologic variables. A linear form was assumed to model
the average annual atrazine and nitrate concentrations (Eq. 6.6):
cjd abXj
ns
(, ) ()=+ (6.6)
where:
c
ns
(j,d) = observed, deseasonalized concentration at site j on day d (for the
   seasonal model with the flow rate this dependent variable is c
nsq
(j,d) );
a = intercept;
b = vector of regression coefficients;
X(j) = vector of explanatory variables.
Table 6.7 Explanatory variables used to in the analysis of the deseasonalized
atrazine and nitrate plus nitrite as nitrogen concentrations in the
Midwest rivers.
Variable description Symbol S-plus var. Units
Agrichemical total application U
Use
kg/yr
Agrichemical application rate A
p
Appl
kg/km
2
/yr
?Decayed? stream network length E
S
Decstr
e
(-100km)
Average slope of the streams S
S
Slpstr
-
Average travel distance from the field to the closest stream L
L
Alflgkm
km
Land slope L
S
Slplnd
-
Drainage area A
Area
km
2
Average annual temperature at sampled site T
Tc
?C
Average annual temperature over sampled watershed T
avg
Tcavg
?C
Annual precipitation depth at sampled site P
Pmm
mm
Annual precipitation depth over sampled watershed P
avg
Pmmavg
mm
183
Table 6.7 shows the explanatory variables used to develop these models. The
notation of the predictor variables shown in column ?Symbol? is compatible with the
notation that has been introduced in Section 4, whereas the column ?S-plus var.?
contains names of variables used in S-plus sessions.
The following Section 6.2.1 discusses selected models of the deseasonalized
(average annual) atrazine concentrations whereas Section 6.2.2 presents models of the
deseasonalized nitrate concentrations.
6.2.1 Average annual atrazine concentration in the Midwest rivers
The following S-plus stepwise variable selection procedure has been used to
determine the variables and their coefficients to explain the average annual atrazine
concentration in rivers studied:
stepcs1 _ step ( csnq.lm, ~ Area + Appl + Flowm3s + Decstr + Slpstr
+               + Slplnd + Alflgkm + Tc + Tcavg + Pmm + Pmmavg )
where: stepcs1 is the object in which the results are stored and step is the S-plus
stepwise regression procedure. The object csnq.lm contains results of the least
squares analysis of the simplest model (the simplest model is composed only of an
intercept). It is created by the following command:
csnq.lm _ lm ( csnq ~ 1, data = atra8)
184
Selected explanatory variables, the regression coefficients as well as their significance
are presented in Table 6.8.
Table 6.8 Results of the stepwise regression analysis of average annual
atrazine concentration in the Midwest rivers (Data = atrazine
concentration with removed seasonal component).
  Variable      Value Std. Error   t value   Pr(>|t|)
(Intercept)   -1.5575    1.2660    -1.2303     0.2189
       Appl    0.0260    0.0120     2.1785     0.0296
    Alflgkm    0.7998    0.2651     3.0171     0.0026
      Tcavg    0.4559    0.1166     3.9093     0.0001
     Pmmavg   -0.0048    0.0014    -3.3401     0.0009
Residual standard error: 4.002 on 928 deg. of freedom
Multiple R-Squared: 0.04599
F-statistic: 11.18 on 4 and 928 degrees of freedom
The model has a very low R
2
 which raises questions about the application of
the regression equation to explain the average concentration. The low R
2
 is partially a
result of applying daily deseasonalized concentrations to estimate the annual average
concentration. Even after the seasonal component was removed, the deseasonalized
daily concentration varies significantly, for example, the deseasonalized concentrations
in the Sangamon River at Monticello, Illinois, vary from 0.2 ?g/L to 19 ?g/L (mean
=1.8, standard deviation = 2.7), or those in the West Fork Big Blue River near
Dorchester, Nebraska, vary from 0.08 ?g/L to 8.7 ?g/L (mean =3.2 , st. dev. = 2.0),
The other reason for the low variance explained is that only 5 stations have
data available for period longer than 3 months. The majority of Midwest rivers (94%)
were sampled on average three times per year, a number too small to construct a
statistically sound spatial model of the average annual concentration. It must be noted,
that although the reconnaissance samples were collected by depth integrating
techniques at three to five locations across each stream (Thurman, et al., 1992, work
cited by Scribner, et al., 1993) they represent the conditions of the stream only at the
time the sample was taken. The herbicide concentration in a river after application
185
during runoff can change significantly in a short period of time. For example, the
atrazine concentration in the Old Mans Creek, Iowa, increased during one day
05/16/1996, from 0.57 ?g/L (Q = 256 cfs, time = 00:15) to 6.2 ?g/L (Q = 307 cfs,
time = 6:15), and then to 47 ?g/L (Q = 304 cfs, time =22:15) (Scribner, et al., 1993).
Thus, characterizing the average annual river conditions by three samples can not be
supported by a good summary statistics.
Despite the low R
2
 the model is further analyzed. The coefficients have
expected signs. Increase in atrazine application causes an increase of the atrazine
concentration in rivers. The longer the average distance of the overland flow, the less
dense river network is, and the higher are the concentrations in rivers. This is a result
of atrazine accumulation when it travels from a field to the surface water.
The positive coefficient for temperature indicates that in ?warmer? regions,
where more agricultural activity is performed, the rivers are more polluted. Thus, in
such regions higher river pollution may be expected than in colder watersheds.
The negative relationship between atrazine concentration and the annual
precipitation depth suggests, that considering average annual conditions, the rainfall
?dilutes? polluted water. Regions that have smaller annual precipitation tend to have
higher atrazine concentrations. On the other hand, if a single event is considered, the
rainfalls that occur in a short time after atrazine application cause a positive
relationship between the river flow rate and the atrazine concentrations, which is
indicated by the regression analysis of seasonal variations discussed in Section 6.1.1.
A similar analysis to the one presented above has been performed for the
atrazine concentrations with the seasonal cycle removed as well as the flow related
components. The atrazine application rate, despite its statistical insignificance, was
forced into the equation selected by the stepwise regression analysis. The coefficients
of the final model are listed in Table 6.9.
186
Table 6.9 Results of the regression analysis of average annual atrazine
concentrations in the Midwest rivers (Data = atrazine concentration
with removed component explained by the seasonal factor and the
flow rate).
  Variable      Value Std. Error   t value   Pr(>|t|)
(Intercept)   -0.8142   0.9148     -0.8901     0.3737
       Appl    0.0133   0.0087      1.5353     0.1251
     Slplnd   38.8804  16.8116      2.3127     0.0210
    Alflgkm    0.3346   0.1751      1.9109     0.0563
      Tcavg    0.2732   0.0736      3.7131     0.0002
     Pmmavg   -0.0029   0.0009     -3.1999     0.0014
Residual standard error: 2.516 on 927 deg. of freedom
Multiple R-Squared: 0.03118
F-statistic: 5.966 on 5 and 927 degrees of freedom
The regression included the average slope of the watershed into the model.
This suggests, that the watershed slope has influence on the concentration. Indeed, it is
easier to mobilize and transport agrichemical in steep slope-watersheds than in flat-
watersheds.
Table 6.10 Quartiles of the explanatory variables selected by the regression
analysis of the deseasonalized agrichemical concentrations.
Statistics
Area Appl Appl Slplnd Alflgkm Tcavg Pmmavg
Statistics
atrazine nitrogen
km
2
kg/km
2
/yr kg/km
2
/yr - km ?C mm
Minimum 173 1.00 482 0.001 2.4 5.0 487
First quartile 961 18.08 4544 0.005 3.1 9.4 759
Median 1425 25.32 6034 0.006 3.3 10.4 886
Third quartile 3521 34.18 7372 0.011 3.5 10.7 921
Maximum 2335354 50.55 9481 0.045 5.5 13.5 1148
Average 19109 26.66 5878 0.009 3.4 10.0 848
Figure 6.3 and Figure 6.4 show the influence of the selected explanatory
variables on the average concentration represented by the model described in Table 6.7
and Table 6.8, respectively. The change in concentration is related to the change in
each variable assuming the minimum, first quartile (25th percentile), median (50th
187
percentile), third quartile (75th percentile), and maximum value. The values of the
quartiles are listed in Table 6.10.
Atrazine application rate
[kg/km2/yr]
Travel distance from the
fieldtothestream [km]
Average annual temperature
over sampled watershed [C]
Annual precipitation depth
over sampled watershed [mm]
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Min 1st Qt Med 2nd Qt Max
Concentration change g/L
?
Figure 6.3 Influence of the explanatory variables on the average atrazine
concentration (?g/L). Model without the flow rate (Table 6.7).
0
1
2
3
4
5
6
7
8
Min 1st Qt Med 2nd Qt Max
12345
Atrazine application rate
[kg/km2/yr]
Travel distance from the
field to the stream [km]
Average annual temperature
over sampled watershed [C]
Annual precipitation depth
over sampled watershed [mm]
Land slope
Concentration change g/L
?
Figure 6.4 Influence of the explanatory variables on the average atrazine
concentration (?g/L). Model with the flow rate (Table 6.8).
188
6.2.2 Average annual nitrate plus nitrite as nitrogen concentration
Parallel to the analysis of the atrazine concentrations, an analysis of the
deseasonalized nitrate plus nitrite as nitrogen concentration has been conducted. The
investigation was initiated by the model selected by the following S-plus stepwise
regression procedure:
stepcs1 _ step ( csnq.lm, ~ Area + Appl + Flowm3s + Decstr + Slpstr
+           + Slplnd + Alflgkm + Tc + Tcavg + Pmm + Pmmavg )
where scnq.lm is an object that contains results of the simplest regression model 
csnq.lm _ lm(ncsnq ~ 1 , data = n8v1).
The final model atcs1 of the average annual nitrate concentration is
presented in Table 6.11.
Table 6.11 Results of the regression analysis of average annual nitrate plus
nitrite as nitrogen concentrations in the Midwest rivers (Data =
nitrate concentration with removed seasonal component).
Variable         Value  Std. Error    t value   Pr(>|t|)
(Intercept)  -7.424541    0.8887      -8.3541     0.0000
       Appl   0.001062    0.0001      17.7787     0.0000
      Tcavg  -1.033063    0.0855     -12.0820     0.0000
     Pmmavg   0.019339    0.0012      16.3178     0.0000
Residual standard error: 3.862 on 1304 deg. of freedom
Multiple R-Squared: 0.3025
F-statistic: 188.5 on 3 and 1304 degrees of freedom
The nitrate model has much better statistics than the analogous atrazine model.
The coefficients for the climate variables have opposite signs to the respective
coefficients in the atrazine equation. This proves that nitrate transport proceeds quite
differently than atrazine transport does. The estimated inverse relationship between
189
nitrate concentration and the temperature shows that higher temperature enhances
microbial activity and the vegetation uptake, which affects the nitrate concentration
not only seasonally but also spatially (due to the climatic differences).
Tisdale, et al., (1993) pointed out that because of nitrogen mobility in soils, the
greater the surplus rainfall, the greater the possibility of loss of nitrogen through
leaching. This association is supported here by the estimated positive relationship
between annual precipitation and the deseasonalized nitrate plus nitrite as nitrogen
concentration in the Midwest rivers.
Regions with higher rainfall have greater surface runoff and greater leaching
through the soil. Both, the surface flow and the groundwater transport atrazine and
nitrate. Since atrazine decays, and since the groundwater transport takes months or
years, the atrazine concentration in the surface waters is mainly related to surface
runoff events that occur after atrazine application on the field in late spring and early
summer. Thus  for a single event that occurs after atrazine application, the expected
relationship between precipitation and concentration is positive (except for extremely
large rainfalls). But for the long period of time this relationship becomes an opposite
one, since a large fraction of the river flow is from groundwater (e.g., groundwater
constitutes 80% of the flow in the Cedar River, Iowa) and a high portion of the annual
precipitation occurs before atrazine use. Thus, for regions with higher annual
precipitation depth the lower average annual atrazine concentration can be expected if
other explanatory variables are constant.
Nitrate is very a persistent chemical. It enters the river not only with the
surface runoff but also it is transported by the subsurface flows that supply the river
with nitrate all year around. The long-term average of the annual precipitation depth is
an indicator of the magnitude of agrichemical transport by the leaching and
groundwater flow.
190
Table 6.12 shows selected variables and coefficients estimated for the model of
the nitrite and nitrate as nitrogen concentration without the seasonal part and without
the component explained by the measured flow rate.
Table 6.12 Results of the regression analysis of average annual nitrate
concentrations in the Midwest rivers (Data = nitrate plus nitrite as
nitrogen concentrations with removed component explained by the
seasonal factor and the flow rate).
Variable        Value   Std. Error    t value    Pr(>|t|)
(Intercept)    -7.57848    1.0244     -7.3977      0.0000
       Appl  0.00064886    0.0001     11.5591      0.0000
      Tcavg   -0.520245    0.0643     -8.0874      0.0000
     Pmmavg   0.0088545    0.0009      9.7573      0.0000
     Slplnd    173.6409   18.3246      9.4758      0.0000
    Alflgkm    0.776683    0.1674      4.6390      0.0000
Residual standard error: 2.879 on 1302 degrees of freedom
Multiple R-Squared: 0.1636
F-statistic: 50.95 on 5 and 1302 degrees of freedom
Figure 6.5 and Figure 6.6 show the range of the influence of the selected
explanatory variables on the average concentration represented by the model described
in Table 6.11 and Table 6.12, respectively. The change in concentration is related to
the change in each variable assuming the minimum, first quartile (25th percentile),
median (50th percentile), third quartile (75th percentile), and maximum value. The
values of the quartiles are listed in Table 6.10 (Section 6.2.1). The slope of lines
between first and third quartiles (Fig. 6.11 and Fig.6.12) indicates that the nitrate
fertilizer application rate has relatively high influence on the nitrate concentration in
the Midwest rivers.
191
Concentration change (mg/L)
0
2
4
6
8
10
12
14
16
18
20
Min 1st Qt Med 2nd Qt Max
Nitrogen fertilizer application
rate [kg/km2/yr]
Average annual temperature
over sampled watershed [C]
Annual precipitation depth
over sampled watershed [mm]
Figure 6.5 Influence of the explanatory variables on the average nitrate plus
nitrite as nitrogen concentration (mg/L). Model without the flow
rate (Table 6.11).
Concentration change (mg/L)
0
2
4
6
8
10
12
14
16
18
20
Min 1st Qt Med 2nd Qt Max
Nitrogen fertilizer application
rate [kg/km2/yr]
Travel distance from the
field to the stream [km]
Average annual temperature
over sampled watershed [C]
Annual precipitation depth
over sampled watershed [mm]
Land slope
Figure 6.6 Influence of the explanatory variables on the average atrazine
concentration (mg/L). Model with the flow rate (Table 6.12).
192
6.3 Error of model predictions
The mean squared error (MSE) of the estimate for the agrichemical
concentrations about the model is calculated from the following equation:
MSE
cc
n
=
?
?
( G24)
2
(6.7)
where:
c = measured agrichemical concentration;
G24c = modeled concentration;
 n = sample size.
Figure 6.7 shows the difference between measured atrazine concentrations and
the predicted ones by two models: one developed without utilizing flow rate as an
independent variable, and the other one calculated utilizing recorded flow rate. Since
the atrazine concentrations are high in May and the June, the prediction errors are also
much higher in these month than the errors in the other months of the year. Thus two
standard errors have been calculated for each model. One MSE for May and June and
the other for July - April. Table 6.13 summarizes the results:
Table 6.13. Mean Standard Errors for the atrazine concentration models (?g/L).
Model Mean Squared Error
May, June July-April
Model 1(no flow) 14.23 1.34
Model 2 (with flow) 16.55 1.92
Sample size 442 491
193
The relatively high error for the period from late summer to early spring is due
to the high variability of measured concentrations in June (10% of sample) that often
are larger than 3 ?g/L, and some as large as 16 ?g/L observations in March. For
example, the concentration measured in the Auglaize River near Fort Jennings, Ohio
on 03/14/89 was 15 ?g/L and on 03/21/90 was 16 ?g/L. (Scribner, et al., 1993).
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 30 60 90 120 150 180 210 240 270 300 330 360 390
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 30 60 90 120 150 180 210 240 270 300 330 360 390
Day
Day
Error
Error
(model without the flow rate)
(model with the flow rate)
(a)
(b)
Figure 6.7 Difference between measured atrazine concentrations and predicted
concentrations in the Midwest rivers:
a) model without the flow rate;
b) model with flow rate included as an explanatory variable.
194
Figure 6.8 presents the difference between measured nitrate concentrations and
the predicted ones. The differences do not exhibit clear seasonal variations as was the
case for the atrazine models. Therefore, just one mean squared error has been
calculated for each model. The errors are listed in Table 6.14.
Table 6.14. Mean Standard Errors for the nitrate plus nitrite as nitrogen
concentration models (mg/L).
Model Mean Squared
Error
Model 1(no flow) 4.04
Model 2 (with flow) 13.43
Sample size 1308
Both Figure 6.8 and Table 6.14 indicate that the model that uses the flow rate
for predictions overestimates the concentrations for high discharges. It is clearly visible
for rivers with the extremely high flow events. For example, the flow of 20,500 m
3
/s
(721,000 cfs) was recorded in the Ohio River near Grand Chain. Illinois, on 3/16/1989
and almost 9,000 m
3
/s (309,000 cfs) on 6/11/89. The model predicted an unrealistic
concentration of 310 mg/L and 200 mg/L respectively, whereas the observed levels
were less than the reporting limit of 0.1 mg/L.
It must be noted that the standard errors are estimated using daily observations
and daily predictions. The models are not intended to calculate the agrichemical in the
surface waters on a daily basis but they are designed to estimate average monthly
conditions. Thus such a very high flow rates as the one recorded for the Ohio River
near Grand Chain on 3/16/1989 can not be used as a representation of the mean
monthly flow. The errors discussed in this section serve only as a rough model
verification and as an indicator of how the daily concentrations scatter around the
mean monthly prediction.
195
Day
Day
Error
Error
(model without the flow rate)
(model with the flow rate)
-20
-10
0
10
20
0 30 60 90 120 150 180 210 240 270 300 330 360 390
-400.00
-300.00
-200.00
-100.00
0.00
100.00
0 30 60 90 120 150 180 210 240 270 300 330 360 390
(a)
(b)
Figure 6.8 Difference between measured nitrate concentrations and predicted
concentrations in the Midwest rivers:
a) model without the flow rate;
b) model with flow rate included as an explanatory variable.
The observed atrazine concentrations and the observed nitrate
concentrations are compared to the predicted values by the model with the flow rate in
Figure 6.9a and Figure 6.9b respectively. The plot of observed values vs. predicted
concentrations by the model without the flow rate exhibits a similar pattern to the one
shown in Figure 6.9.
196
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100 1000
Observed
Predicted
a) (atrazine)
Observed
Predicted
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100
b) (nitrate)
Figure 6.9 Observed vs. predicted agrichemical concentrations in the Midwest
rivers (model with the flow rate): a) atrazine in ?g/L;   b) nitrate
plus nitrite as nitrogen in mg/L.
197
6.4 Comparison of predicted flow with observed one
Verification of the method of spatial redistribution of the recorded flow rate is
performed within the Iowa-Cedar River basin.  Three USGS gauging stations:
(a) Shell Rock R. near Northwood, IA (5459000) (b) Fourmile Cr. near Traer, IA
(5464137); and (c) Prairie Cr. at Fairfax, IA (5464640) has not been utilized in
redistribution process. Figure 6.10 shows location of these gauging stations as well as
the location of selected USGS stations whose record have been used in the flow rate
estimations. Table 6.15 compares the predicted flow with the observed values.
Table 6.15 Comparison of predicted and observed flow rate (m
3
/s) for three
USGS gauging stations.
Sample 1 Sample 2 Sample 3
USGS station ID 5459000 5464137 5464640
Modeling unit ID 71 388 486
Time period 1960/01-1986/09 1962/10-1980/12 1966/10-1982/9
Sample size 321.00 209.00 192.00
Mean predicted 5.37 0.48 3.66
Mean measured 5.33 0.33 3.78
Std. dev. of predicted 5.23 0.54 3.86
Std. dev. of measured 6.24 0.42 4.45
Mean difference -0.05 -0.15 0.12
Std. dev. of difference 3.48 0.29 1.88
Although, the normality of the error has not been verified, the following
normal deviates of difference between observed and estimated flow have been
estimated (as an approximation of the valid statistical indicator), Sample1: z
1
 = 0.24,
Sample2: z
2
 = -7.5, and Sample 3: z
3
 = 0.89. The error is significant for Sample2.
This comparison shows that the inaccuracy in predicted flow is larger for units located
198
farther from gauging stations that the error for units that are closer to a measurement
point.
Selected stations used to calculate the monthly flow rate
in ungaged streams
Stations used to verify the method of spatial redistribution
of the observed flow rate
Q = average flow rate calculated from available daily
measurements for a period from 1940 to 1992
Shell Rock R. near Northwood, IA (5459000)
Q = 4.57 m3/s
Cedar R. at Waterloo, IA (5464000)
Q=87m3/s
Fourmile Cr. near Traer, IA
(5464137) Q = 0.25 m3/s
Prairie Cr. at Fairfax, IA (5464640)
Q=3.78m3/s
Cedar R. near Conesville, IA (5465000)
Q=136m3/s
Winnebago R. at Mason City (5459500)
Q = 7.90 m3/s
Shell Rock R. at Shell Rock (5462000)
Q = 27.8 m3/s
Cedar R. at Cedar Rapids, IA (5464500)
Q = 111 m3/s
Figure 6.10 Location of the USGS gauging stations to verify method of spatial
redistribution of the observed flow rate.
Figure 6.11 presents the time series of the observed and predicted flow rate in
three selected streams of the Cedar River basin. Although the flow redistribution
199
method is a very simple one, estimated monthly flow rates in ungauged streams are
very close to the true values.
USGS Station 5459000
USGS Station 5464137
USGS Station 5464640
estimated measured
Flow [m3/s]
Flow [m3/s]
Flow [m3/s]
missisng data 1974/10-1975/9
40
30
20
10
0
1960 1965 1970
1975
197019651963 1975 1980
4.0
3.0
2.0
1.0
0.0
1967 1970 1975 1980
30
25
20
15
10
5
0
Year
Year
Figure 6.11 Observed and predicted flow rate in selected streams of the Cedar
River basin.
200
The method of spatial redistribution of the measured flow has a potential
application in estimation of water losses and identification of modeling units that do
not contribute to the flow in rivers.  In addition, the information about the difference
between outflow and inflow for each individual modeling watershed can be used to
model the transport of agrichemicals between a field and the stream network. Negative
balance, i.e. inflow into an unit is greater than the outflow from the unit, means water
losses, occurs mainly in regions where lakes exist. It also may indicate groundwater
recharge zones. Since the unit with a negative surface water balance do not contribute
to the flow in the river, it is unlikely that such a unit significantly contributes to the
river pollution.
On the other hand, the high positive surface water balance indicates a big
contribution of the unit surface and subsurface flow to the river flow, and thus a large
agrichemical contribution may be expected.
Figure 6.12 shows the estimated surface water balance for each modeling unit
of the Iowa-Cedar River basin in June 1990. The ArcView script decom2 has been
applied to calculate the difference between the cumulative flow at the unit outlet and
the sum of the cumulative inflows which enter the unit. The spatially distributed flow
in rivers in the Iowa - Cedar River, in June 1990 (Figure 5.7), has been utilized.
201
-14.85 - 0
0 - 1
1 - 2
2 - 3
3 - 9.95
Surface water balance by
modeling unit, June 1990 [m3/s]
Figure 6.12 Spatial distribution of the surface water balance for the modeling
units. Estimated from recorded flow rate, precipitation depth and
selected unit features, the Iowa-Cedar River basin, June 1990.
202
6.5 Agrichemical concentrations in the Cedar River basin
This section presents the application of the methodology developed in this
dissertation to estimate the agrichemical concentrations in the Iowa-Cedar River basin.
The regression equations that describe the atrazine and nitrate concentration in the
midwest rivers have been derived from the data gathered in more that 150 sampling
points scattered over the Upper Mississippi-Missouri River and the Ohio River basins.
Therefore the models reflect the regional average conditions in the rivers, and for a
specific watershed, the model results may be considerably different from the available
measurements.
The monthly flow rate for the year 1990, as well as the annual nitrogen
fertilizer use in 1990 have been extracted from the GIS database for the Iowa-Cedar
Basins. After the Arc/View model performed calculations, the results for two units
that represent Old Mans Creek at Iowa City (unit_ID = 5455100) and the Cedar River
at Palisades (unit_ID = 475) have been extracted for further analysis. Figure 6.13
compares calculated concentrations of nitrate plus nitrite as nitrogen in the selected
locations with the values published by the USGS (Scribner, et al., 1994). The
predictions are much lower than the observations, except for the Cedar River in April
and the Old Mans Creek in June, when the estimated nitrate concentrations are close
to the measured ones. The plot of the measurements shows a significant increase of
agrichemical at the end of April-beginning of May: from about 2 mg/L (April) to as
high as 13 mg/L (May) in the Cedar River at Palisades, and from about 10 mg/L
(April) to as high as 25 mg/L (May) in the Old Mans Creek near Iowa City. Most
likely the jump in the concentration level was caused by the late Spring application of
nitrogen fertilizers..
203
Modeling nitrogen in the surface waters is a very difficult task. Even such
advanced model as GRASS-SWAT-QUAL2E has difficulties to make predictions that
agree with the measurements. ?Researchers agree that modeling nitrogen is one of the
most challenging tasks even at field scale.? (Ramanarayanan, et al., 1996)
observed ( instataneous or daily average)
predicted, model without the flow rate
Cedar River at Palisades
Jan Mar May Jul Sep Nov
Concentration [mg/L]
Old Mans Creek near Iowa City
Jan Mar May Jul Sep Nov
Concentration [mg/L]
predicted, model with the flow rate
Figure 6.13 Comparison of the predicted and observed concentrations of nitrate
plus nitrite as nitrogen in the Cedar River at Palisades, Iowa and
the Old Mans Creek at Iowa City, Iowa, in 1990.
An exercise similar to the one for nitrate plus nitrogen has been performed for
the atrazine. Since no herbicide usage has been available for 1990, the values estimated
for the 1989 have been applied in the calculations. Figure 6.14 shows the predicted
values of the atrazine concentration in the Cedar River at Palisades and in Old Mans
Creek near Iowa City. The estimated values are compared with the measured
concentrations in 1990 (Scribner, et al., 1994). Unlike the nitrate, the predictions of
the atrazine are within the range of the observed values.
204
Old Mans Creek near Iowa City
Jan Mar May Jul Sep Nov
Cedar River at Palisades
Jan Mar May Jul Sep Nov
Concentration [ g/L]
Concentration [ g/L]
observed ( instataneous or daily average)
predicted, model without the flow rate
predicted, model with the flow rate
? ?
?
Figure 6.14 Comparison of the predicted atrazine concentrations in the Cedar
River at Palisades, Iowa and the Old Mans Creek at Iowa City,
Iowa, in 1989 with the observed concentrations in 1990.
The ArcView model of the agrichemical transport in surface waters has very
versatile tools to create profiles along a selected flow path. Figure 6.15 presents such
profiles of the atrazine application and the atrazine concentration in the Cedar River
estimated for June 1989. For selected unit watersheds that represent the Cedar River,
three items have been extracted from the attribute table:
- calculated concentration for June 1989;
- annual atrazine application; and
- length of the flow path.
Moving downstream, the average increase of the herbicide mass applied to the field is
about 1.25 t/km of the Cedar River (if major tributaries such as the Iowa River and the
Rock Shell River are excluded from calculations, the increase of atrazine application is
205
400 kg/km). The concentration in the upper portion of the river under study increases
going downstream, with the rate of 1.0 ?g/L/100 km. In the downstream portion of
the river, the rate decreases to 0.3 ?g/L/100 km.
Concentration
g/L
Application
kg/yr
Junction with
the Mississippi R.
Stream length
Junction with the Iowa River
0
5
10
15
20
25
30
35
0 100 200 300 400 500 km
0
100000
200000
300000
400000
500000
600000
700000
Concentration, model with the flow rate
Concentration, model without the flow rate
Atrazine application
?
Figure 6.15 Profiles of the predicted atrazine concentrations in the Cedar River
for June 1989 and the annual atrazine application (based on the
results of the ArcView model).
206
The model estimates the concentrations based on the agrichemical application
in the upstream drainage area, and the selected parameters of the watershed. To check
if the mass balance at river junctions is reasonable, i.e., if the amount of the atrazine in
the Iowa River is high enough to create in the Cedar River an increase in concentration
of about 0.8 ?g/L (Figure 6.15), the bar charts of the concentration for units close to
the junction have been drawn utilizing the model tools (Figure 6.16). Indeed, the
concentration in the Iowa River exceeds 8 ?g/L, a value that is high enough to
produce concentration of 6.8 ?g/L after water from Iowa River mixes with the Cedar
River.
Cedar River
Iowa River
7.5
5.0
2.5
0.0
10.0
Concentration
g/L (mg/m3)?
Figure 6.16 Predicted atrazine concentrations (mg/m3 = ?g/L) at the Iowa River
and the Cedar River junction (June 1990).
207
Table 6.16 shows estimated values of atrazine concentration, load and the flow
rate in the modeling units that represent the confluence of the Iowa River with the
Cedar River.
Table 6.16 Atrazine concentration, load and the flow rate in modeling units
that represent the confluence of the Iowa River with the Cedar
River estimated for June 1990.
Parameter Units Unit 677
(Iowa River)
Unit 665
(Cedar River)
Unit 680
(Iowa R + Cedar R)
Concentration ?g/L 8.2 6.0 6.8
Flow rate m
3
/s 301 496 800
Load kg/month 6,375 7,764 14,143
Drainage Area km
2
11,500 20,146 31,637
Application t/yr 222.4 379.0 601.4
Applic. rate kg/km
2
/yr 19.335 18.812 19.000
Further analysis has been performed to verify if  the models (with and without
flow rate)  can be used for making predictions of total annual chemical transport in the
midwest rivers. The annual load has been calculated for two Iowa rivers, the Cedar
river at Palisades and the Old Mans Creek at Iowa City. The atrazine application rate
in 1989 was extracted from the USGS maps (Battaglin and Goolsby, 1995 a, b). The
1990 monthly flow rate was used to predict concentrations and loads. The calculations
have been performed by the ArcView agrichemical transport model. The selected
results have been extracted from the polygon attribute table of the map of modeling
units and they are presented in Table 6.17.
208
Table 6.17 Relation of the atrazine application to the atrazine load in two Iowa
rivers: the Cedar River at Palisades and the Old Mans Creek at
Iowa City ( Chemical application for year 1989, flow data for 1990).
Sampling Application Model with Estimated Load as a fraction
site kg/yr flow rate load kg/yr of application %
Cedar River at 325416 no 9639 3.0
      Palisades yes 31456 9.7
Old Mans Creek at 9440 no 845 8.9
      Iowa City yes 1660 17.6
The model that applies flow rate to evaluate atrazine concentration, predicts
high atrazine loads: the predicted annual load for the Old Mans Creek is as high as
18% of total atrazine application and in the Cedar River it is about 10 % of herbicide
use.
The model that does not utilize flow rate to calculate chemical concentrations
gives smaller load estimates, 3% and 9% for the Old Mans Creek and the Cedar River
respectively. These results are very close to the published agrichemical runoff from the
field: Squillace and Engberg (1988) estimated that 1.5% - 4% of atrazine applied,
depending on the assumed rate of chemical application, was transported by the Cedar
River, Iowa in 1985. Two - three percent applied atrazine was carried by the Wye
River, Maryland when substantial runoff occurred within two weeks of application
(Wu, et al., 1983, cited by Squillace and Engberg, 1988). Based on the extensive
review of literature on pesticides losses in runoff waters Wauchope (1978) stated that
losses as high as 5 % can be expected for pesticides formulated as wettable powders
(atrazine is such a pesticide), and, in addition, losses may be three times higher if a
large runoff occurs about 2 weeks of application. The estimated transport of atrazine
in the Mississippi River and its four tributaries (from 04/1991 to 03/1992) varied from
0.58% of use for Platte River at Louisville, Nebraska, to 1.83% in Illinois River at
Valley City, Illinois (Battaglin, et al., 1993).
209
Figure 6.17 shows the monthly distribution of the loads, represented as a
fraction of the annual load, in the sites under investigation. These bar charts indicate
that the seasonal variation of atrazine loads is very realistic, about 70% of total
atrazine load in the Cedar River at Palisades and about 80% of total load in the Old
Mans Creek have occurred in May and June (average for 1990).
Squillace and Engberg (1988) estimated that 70% of the annual chemical load
in the Cedar River, calculated for period from May 1984 through November 1885,
occurred in June 1984. Thus, the models give realistic temporal distribution of the
atrazine loads in the rivers of the Iowa-Cedar Basin.
Concentration model does not utilize flow rate
Concentration model utilizes flow rate
123456789101112
70
60
50
40
30
20
10
0
123456789101112
70
60
50
40
30
20
10
0
Cedar River at Palisades Old Mans Creek near Iowa City
Month
Month
Fraction %
Fraction %
Figure 6.17 Estimated monthly fractions of the annual atrazine load in the
Cedar River at Palisades and the Old Mans Creek near Iowa City,
Iowa for year 1990.
The spatially distributed atrazine loads in the rivers of the Iowa-Cedar Basin in
June 1990 are presented in Figure 6.18. The concentration were evaluated by the
?without-flow? model.
210
Figure 6.18 Estimated atrazine load in the rivers of the Iowa-Cedar Basin in
June 1990.
211
The nitrate plus nitrite as nitrogen loads were calculated for the same
rivers as were the atrazine loads. The 1990 nitrogen fertilizer application has been
extracted from the USGS maps of the annual nitrogen fertilizers sales in US counties
(Battaglin and Golsby, 1995a). Table 6.18 presents selected results of the calculations
made by the ArcView agrichemical transport models.
Table 6.18 Relation of the nitrogen fertilizer application to the nitrate plus
nitrite as nitrogen load in two Iowa rivers: the Cedar River at
Palisades and the Old Mans Creek at Iowa City ( Chemical
application and flow rate represent year 1990).
Sampling Application Model with Estimated Load as a fraction
site t/yr flow rate load t/yr of N application %
Cedar River at 123651 no 28234 22.8
      Palisades yes 95221 77.0
Old Mans Creek at 3165 no 1267 40.0
      Iowa City yes 2589 81.8
The nitrogen loads constitute large portion of the nitrogen fertilizers
application. The model that utilizes the flow rate to estimate the concentrations
forecasts relatively large loads. However, as shown in Figure 6.13, the model ?without
flow rate? predicts concentrations that are in agreement with the observed values
(Cedar River at Palisades) or are lower than the observed ones (Old Mans Creek near
Iowa City). Thus the estimated fractions of total chemical use are realistic. For
comparison, the average transport of nitrate in the Mississippi River and its four
tributaries (from 04/1991 to 03/1992) was about 15.5% of use (Battaglin, et al.,
1993). It must be noted that the nitrate plus nitrite as nitrogen in Midwest rivers is not
only a result of the nitrogen fertilizer application but it is also related to other sources
of the nitrogen such as discharge from municipal treatment plants and manure nitrogen
212
inputs. For example, Coote, et al., 1978 explained 92% of the nitrate variability in the
Canadian Great Lakes Basin rivers by row crops and manure nitrogen inputs.
The monthly fractions of the annual nitrate loads are shown in Figure 6.19
Concentration model does not utilize flow rate
Concentration model utilizes flow rate
123456789101112
50
40
30
20
10
0
123456789101112
50
40
30
20
10
0
Cedar River at Palisades Old Mans Creek near Iowa City
Month
Month
Fraction %
Fraction %
Figure 6.19 Estimated monthly fractions of the annual nitrate load in the Cedar
River at Palisades and the Old Mans Creek near Iowa City, Iowa for
year 1990.
Although the seasonal pattern of the nitrate plus nitrite as nitrogen
concentration in the midwest rivers differs from the atrazine concentration variations,
the seasonal pattern of the nitrate load shown in Figure 6.19 is similar to the atrazine
one. The high transport in Summer months is due to high flow rate that is recorded in
the Iowa-Cedar Rivers, especially in June, July, and August.
213
7. SUMMARY, CONCLUSIONS, AND
RECOMMENDATIONS
The primary result of this work is the development of a GIS (Geographical
Information System) methodology for the large scale modeling of agricultural chemical
concentrations in surface waters. Two chemicals were selected for model
development: a nutrient, nitrate plus nitrite as nitrogen, and a herbicide, atrazine.
Statistical models which allow one to estimate concentrations in a region as large as
the upper Mississippi River, the Ohio River, and their tributaries have been
constructed. Two sets of models are presented in this dissertation: one for nitrate plus
nitrite concentration predictions and another one for calculation of the atrazine
concentrations. Each set contains a function which utilizes the flow rate, among other
explanatory variables, to estimate chemical concentrations and another function which
allows one to calculate concentrations without using the flow rate.  All models are of a
cascade type in which mean annual concentrations are derived from local watershed
characteristics and the result is multiplied by a monthly factor to account for seasonal
variations. Spatial variability within the region under investigation is represented
indirectly by climatological parameters: mean annual temperature and mean annual
precipitation depth.
The methodology developed in this research can be applied using raster GIS as
well as vector GIS, however, since raster GIS requires huge computer resources to do
calculations cell by cell, the final agrichemical model has been built using ArcView, a
vector GIS where the cells are grouped into modeling zones.
214
The raster GIS, Arc/Info GRID, proved to be very convenient environment to
determine a wide range of watershed characteristics using digital elevation models, and
maps of agrichemical application, normal temperature and precipitation.  This research
revealed that it is possible to create a grid of a 2.4*10
6
 km
2
 basin, in which each cell
(here 500 m by 500 m) contains a characteristic of the drainage area upstream of this
cell, such as:
- watershed morphometry (watershed area, longest stream length, average
exponent of the negative stream length, average stream slope, average distance
of overland flow, average land slope);
- average agrichemical application rate; and
- normal temperature and normal precipitation depth.
The resulting stack of grids of distributed watershed parameters can be used for data
extraction from cells that represent sampling sites, and it can also be used after the
relationship between constituent concentration and the watershed parameters has been
established, to calculate agrichemical concentration in each cell for which the
relationship is applicable.
GIS tools can be applied to a digital elevation model (DEM) to divide the
region under investigation into hydrologic units whose size depends on such features
as the diversity of terrain, density of spatial information, size of the basin, and
computer resources. A method was developed in this research to divide a large basin
into hydrologic modeling units and to create a system of flow connectivity between
these units which allows one to build efficient hydrologic models using a concept of a
set of modeling units within a stream gauge zone. This method was extensively tested
for the Iowa-Cedar River watershed, Iowa, using 100 m grid resolution. It includes the
following five steps:
215
- correction of the DEM to make both the delineated stream network and the
delineated watershed boundaries compatible with the digital map of the rivers
RF1 (River Reach File 1).
- stream network delineation using threshold value of 25 km
2
 drainage area;
- development of a map of the modeling unit outlets (points in which the drainage
area exceeds a threshold value, points located immediately upstream of a
stream junction, and gauging station sites);
- delineating modeling units and converting them from grid representation into
vector form;
- determining the flow topology between the units.
The method of adjusting the 100 m DEM by ?burning in? streams improves the
stream and watershed delineation. The major streams delineated from the adjusted
DEM are compatible with the RF1 (River Reach File) stream reach network. This
feature allows one to exchange stream attributes between RF1 and the DEM-derived
watershed characteristics. ?Burning in? streams was found to be the simplest, and
quickest method of making a realistic digital stream network. Moreover, this method
makes less changes to the original DEM compared to other methods (e.g. smoothing,
spline surface fitting), which may be important for such tasks as calculation of the
flood volume. A shortcoming of this method is that it can produce parallel streams,
although in the Iowa River basin only two, insignificant parallel streams were noticed.
Since some of the RF1 streams are close enough to be connected after they are
converted into a 500 m grid, the maximum cell size for adjusting DEM using RF1
should be smaller than 500 m.
216
Three types of modeling unit outlets have been utilized here: cells that
represent the beginning points of the stream network, cells immediately upstream of
the stream junctions, and cells that represent USGS (United States Geological Survey)
gauging stations. Including stream starting points in the set of modeling unit outlets
makes possible the determination of the drainage area, discharge and constituent load
in each node of the stream network. It also gives one more control over the average
area of unit watershed. For example, in the Iowa-Cedar River basin, the average area
of the modeling units determined utilizing all types of watershed outlets was 31.6 km
2
(threshold area for stream delineation = 25 km
2
) whereas excluding stream starting
points from the set of watershed outlets points produced units of average area 46.7
km
2
.
The threshold area of 25 km
2
 or 2500 cells for stream delineation was found to
be an optimal area for dividing the Iowa-Cedar River basin into modeling units. A
smaller threshold area resulted in very dense stream network and a large number of
very small unit watersheds (represented by 1-2 cells) and was not justified by the
spatial resolution of data used in this research. A larger threshold value than 25 km
2
resulted in very coarse subdivision of the region studied and a low density stream
network. The stream network delineated from a 100 m DEM using 25 km
2
 limit, was
slightly more dense than the one represented by the 1:500,000 digital map of rivers,
Reach File 1.
The flow topology of irregular spatial shapes such as unit watersheds can be
efficiently described by assigning to each modeling unit the identification number of
the downstream unit.
The GIS can be used to store and manipulate spatially distributed time series.
In this research, a point coverage of the 86 National Climatic Data Center weather
stations that are located within the Iowa-River basin and within the 50-km buffer zone
217
outside the basin was created. The attribute table of this coverage stored the monthly
values of the precipitation depth for years from 1960 to 1992. These data were used to
calculate the average monthly precipitation depth in 1032 modeling units by the
inverse squared distance weighting procedure. A similar GIS database of the monthly
flow rate was created for the 38 USGS gauging stations located in the drainage area.
The attribute table of the stations point coverage contains flow time series from 1960
to 1992 (384 columns or items).
A methodology that redistributes the observed flow record over all modeling
units according to the spatial distribution of precipitation and the drainage area was
developed. A coverage of modeling units with an attribute table containing 32 years of
monthly flow rate was created. Tests performed for three stream gauges not included
in the flow redistribution process showed that the method of observed discharge
interpolation/extrapolation gives very good estimates of the monthly flow in ungauged
rivers. Although this method was developed for a vector representation of the
watershed, it could also be applied to redistribute the flow rate using a grid
representation of the study region. The procedure of the discharge calculations in
ungauged rivers was programmed in both the ArcView script language Avenue and in
the C language.
The approach of storing of the equations that describe the agrichemical
concentration as well as the seasonal factors in a database file, instead of including
them in the Avenue code, is a very efficient way of model specification. The equations
can be easily updated or changed without the necessity of making changes in the
computer program. The ArcView script extracts both the equations and their
parameters from the database files and then calculates agrichemical concentrations and
loads in the Iowa-Cedar River basin.
218
The credibility of the statistical model predictions is influenced by the data used
for parameter estimation. The estimates of agrichemical monthly variability may be
influenced by the fact that 90% of the atrazine samples were taken in the months
March-July, and October. Similarly, the winter months are not well represented in the
nitrate plus nitrite as nitrogen data. Only 1.2% of all nitrate samples were taken in the
months from December to February. Since the majority of data represent the
conditions of rivers during major runoff events after herbicide and nitrogen
application, the predictions of the average monthly concentration level may be
overestimated.
The regional model of the seasonal atrazine variations in Midwest rivers shows
that the major transport occurs after chemical application on the field, in May and
June. The average monthly concentrations estimated without considering the influence
of flow rate on concentration level for months May, June and July are 3.7, 4.6 and 1.5
times higher than the annual average respectively. The atrazine concentrations in most
of the remaining months of the year are less than 30% of annual average
concentration.
If flow rate is included in the study of monthly concentration variation, the
seasonal factors for the May, June, July, and August are respectively 3.1, 3.8, 1.7, and
1.1 times higher than the annual average. The monthly fractions for months from
September to April vary between 0.2 and 0.4, except January in which the
concentration is the smallest (10% of annual average).
Nitrate plus nitrite as nitrogen exhibits a different seasonal pattern compared to
that for atrazine. The highest concentrations can be expected in January (twice the
average annual level), and the lowest concentrations in months from August to
November: 10%-50% of average. The monthly factors estimated utilizing the flow rate
are slightly higher than the factors estimated without the flow rate in months from
219
April to July, and they are lower than the ?no-flow? factors from August to December.
Both atrazine and nitrate plus nitrite as nitrogen appear to increase in concentration
with discharge to the 0.3 power approximately.
The average annual atrazine concentration in the Midwest rivers is described
by linear functions of chemical application rate, average overland flow length, normal
temperature and normal precipitation depth. In addition, the model that was developed
utilizing the flow rate contains the average land slope. The spatial regression models
for atrazine have very low R
2
 (less than 0.05, F statistic > 6). There are two major
reasons for the low variance explained by the linear models:
1) Highly variable daily concentration values were used to estimate the regression
equations;
2) Ninety four percent of the Midwest rivers whose data were used, were sampled
on average three times a year, a number too small to construct a statistically
sound spatial model of the average annual concentrations.
It is possible that better statistics could be obtained if instead of daily, the monthly
average atrazine concentrations for all months of a year were used for the regression
analysis.
The average annual nitrate plus nitrite concentration in the Midwest rivers is
explained by the nitrogen fertilizer application rate, normal temperature, and normal
precipitation (for the model without the flow rate, R
2
 = 0.30, F = 188), and by
fertilizer application rate, land slope, average overland flow length, normal
temperature, and normal precipitation (for the model with the flow rate, R
2
 = 0.16,
 F = 51).
The atrazine model that uses the flow rate in its calculation of atrazine
concentrations overestimates the loads. For example, for the flow conditions of 1990,
220
the atrazine model predicted annual load in Old Mans Creek, Iowa as 18% of the
herbicide application, and for the Cedar River at Palisades, Iowa as 10 % of the
application. The analogous nitrate model overestimated the concentrations measured
in 1990 in the Cedar River at Palisades but it predicted reasonably well the
concentrations in Old Mans Creek.
The atrazine model that does not utilize the flow rate to calculate the
concentration predicted atrazine transport as 3% and 9% of the application for the
Cedar River at Palisades and Old Mans Creek respectively. These numbers are similar
to the values published in literature. The concentrations predicted by the nitrate model
that does not utilize the flow rate, were close to the observations made in the Cedar
River in May and June 1990, but they were in the lower range of the measurements in
Old Mans Creek near Iowa City.
Since the coefficients of the agrichemical transport models have been
determined from the data collected in streams scattered over the Midwest, the
reasonable extent of the region for concentration predictions is the Upper Missouri -
Mississippi - Ohio River basin (above the Ohio-Mississippi River junction).
The major foundings of this research can be grouped into four categories listed
below:
? Modeling on different spatial scales
The GIS technology was successfully applied to perform analysis on following
spatial scales:
data region (area 2,400,000 km
2
);
simulation region (area 32,000 km
2
);
gauged zone (average area 1,100 km
2
); and
modeling unit (average area 30 km
2
).
221
? Terrain - based modeling
-  ?burning in? streams in DEM method significantly improves the stream network
and the watershed boundaries delineated from a digital elevation model;
-  automatic division of the simulation region into consistent system of hydrologic
modeling units grouped into stream gauge zones is a useful tool supporting
hydrologic modeling process;
-  a distributed system of drainage area parameters allows evaluation of any
watershed morphometry descriptor in all points of the region under
investigation with the resolution of the DEM (here 500 m for data region, and
100 m for simulation region).
? Spatial interpolation of streamflow
The method used for calculating monthly discharge in ungauged streams predicted
accurately the discharges in ungauged streams as shown by predicted and observed
flow comparisons at three test gauges.
? Regional modeling of agrichemicals in surface waters
-  Spatio-temporal cascade modeling can be applied within GIS to construct
models agrichemical transport;
-  Atrazine showed a strong seasonal pattern with high values in May and June;
-  Nitrate plus nitrite as nitrogen exhibited a weak seasonal pattern gradually
changing from lowest value in September to the highest value in January.
-  Both constituents appeared to increase in concentration with discharge to the
0.3 power approximately;
222
-  Regression equations of average annual atrazine concentrations had a very low
explanatory power (R
2
 < 0.05), whereas equations that describe average annual
nitrate concentrations were satisfactory (R
2
 > 0.16);
-  The negative relationship between atrazine concentration and the normal
precipitation depth and the positive relationship between nitrate concentration
and the precipitation suggests that the atrazine transport occurs mainly with an
overland flow whereas nitrate can be also transported by infiltration and
ground water flow.
-  Constituent loading estimates determined using discharge-dependent
concentrations appeared to be too large when compared with independent
loading estimates;
-  Water quality data used in this research may be biased towards processes
occurring during high runoff rather than baseflow periods.
The recommendations for extending and modifying the work
-  expand the analysis for baseflow periods. This requires an additional set of
concentration measurements which together with the data used in this research
will represent average monthly conditions rather than runoff events.
-  instead of using daily measurements, use average monthly concentrations and
discharges to determine concentration regression equations. The average
monthly concentration values need to be estimated before the spatio-temporal
atrazine and nitrate pattern is estimated by regression.
-  introduce an intervention function. Such a function will incorporate into the
model the time of agrichemical application on the field.
-  since the mean annual concentration models were unsatisfactory, additional
analysis of average annual concentration is required perhaps provided by
deterministic simulation models.
223
Appendices
Appendix A C-codes
This Appendix contains the following programs written in C language:
1)  newnx.c - reconstructs the flow connectivity between modeling units after
some of units have been removed;
2) fdy4.c--estimates discharge in ungauged streams.
A1 Program newnx.c--reconstructing the flow connectivity between
modeling units after some of units have been removed
/* newnx.c
* from new1.c, 9/21/95
* Pawel Mizgalewicz, CRWR UT at Austin  */
/****************************************************************
*  newnx.c -- reconstructs the flow connectivity between units
*  after some of them have been removed. Requires two ASCII, comma
*  delimited files:
*    file 1) full set of units. Each line should contain:
*            unit_id, next unit_id
*    file 2) reduced set of units. Each line should contain the
*            unit_id number
*  Output file: unit_id, id of downstream unit, unit order
*
* USAGE: newnx infile1 infile2 outfile
****************************************************************/
#include <stdio.h>
main (argc, argv)
  int argc;
  char *argv[];
  /* arg 1) input_file (oid, onx => old ID, old NEXT)
224
   2) input_file (nid => new ID)
   3) output_file (nid, nnx, nor => ID, new NEXT, order) */
 {
  char loop, found;
  int i, j, k, onn, nnn, nni, nor[1200], nix[1200];
  long id, nx, ix,
       oid[1200], onx[1200], nid[1200], nnx[1200];
  FILE *fgsin, *funin, *ftable2;
  if (argc < 3 )
   {
    printf ("wrong number of arguments = %d \n", argc);
    exit(1);
   }
  fgsin = fopen (argv[1], "r");
  i = 0;
  while (fscanf(fgsin, "%li,%li", &id,&nx) != EOF)
   {
    oid[i] = id;
    onx[i] = nx;
    ++i;
   }
  onn = i-1;
  fclose(fgsin);
  funin = fopen (argv[2], "r");
  i = 0;
  while (fscanf(funin, "%li", &id) != EOF)
   {
    nid[i] = id;
    nnx[i] = 0;
    ++i;
   }
  nnn = i-1;
  nni = i;
  fclose(funin);
  /* To each new unit assign old_next    */
  for (i = 0; i <= nnn; ++i)
    for (k = 0; k <= onn; ++k )
      if ( nid[i] ==  oid[k] )
       {
nnx[i] = onx[k];
break;
       }
  /* check if all next are valid (have new_id specified)*/
  for (i = 0; i <= nnn; ++i)
   {
    found = 0;
    ix = 0;
    while (!found)
     {
      ++ix;
      for (j = 0; j <= nnn; ++j)
if ( ( nnx[i] == nid[j] ) || ( nnx[i] == 0 ) )
 {
  found = 1;
  break;
225
 }
      if (found) continue;
      /* if not found, go to old table and read next_id  */
      for (j = 0; j <= onn; ++j)
if ( nnx[i] == oid[j] )
 {
  nnx[i] = onx[j];
  break;
 }
      if(ix > 1000000) printf("error %i\n", ix);
     }
   }
 /*  ===============  WATERSHED ORDER ================= */
 /* Set initial value of order array */
  for (i = 0; i <= nnn; ++i)
   {
    nor[i] = 1;
    nix[i] = nni;
   }
  /* Select first order items */
  for (i = 0; i <= nnn; ++i)
   {
   j = 0; loop = 1;
   while ( loop )
    {
     if (nnx[i] == nid[j])
      {
       nor[j] = 0;
       nix[i] = j;
       loop = 0;
      }
     ++j;
     if (j == nni) loop = 0;
    }
   }
  /* order of the remaining streams */
  for (i=0; i<=nnn; ++i)
    if(nor[i] == 1)
     {
      j = nix[i];
      k = 2;
      while ((nor[j] < k) && (j != nni))
       {
nor[j] = k;
j = nix[j];
k = k + 1;
       }
     }
  /* Write results to output file */
  ftable2 = fopen (argv[3], "w");
  for (j = 0; j <= nnn; ++j )
    fprintf(ftable2, "%li,%li,%i\n", nid[j], nnx[j], nor[j] );
  fclose(ftable2);
  return 0;
 }
226
A2 Program fdy4.c--calculating the flow rate in ungauged streams
from the available record
/************************************************************/
/* fdy4.c  -- calculates flow rate in all modeling units from
*             the available record. The average precipitation
*             depth is used as a weight.
*  arguments:
*            1) file name that contains USGS flow record
*            2) file name that contains modeling unit data
*            3) name of the output file.
*  input: two ASCII files, each record contains the following
*         values, coma delimited:
*         file one specified by the first argument:
*            gsid = USGS station identification number,
*            gsnx = ID number of the downstream USGS station,
*            gsqo = flow rate;
*         file two specified by the second argument:
*            unid = modeling unit identification number,
*            unnx = ID number of the downstream modeling unit,
*            ungsid = ID number of the USGS station that
*                     determines the zone in which the unit
*                     is located (ID of the gauging station that
*                     is downstream of the modeling unit),
*            unar = area of the modeling unit,
*            unor = modeling unit order in the flow system,
*            unpr = average precipitation depth;
*  output:   ASCII file specified by the third argument:
*            unid = modeling unit identification number,
*            unqc = flow rate estimated in modeling unit
*                   (this flow is cumulative, i.e., it
*                   is a runoff from the drainage area
*                   determined by the modeling unit outlet. */
/************************************************************/
#include <stdio.h>
#define size 512
main (argc, argv)
  int argc;
  char *argv[];
  /* arg 1) input_file (gs) must have: id, next, and flow.
 2) input (modeling units--un)
    must have: id, next, gsid, area, order, precip.
 3) output_file: unid, qc (cumulative)
      used in ArcView version:
 4) name_id (copied from first column)
 5) name_out */
227
 {
  char loop, notfound;
  int i, j, k, l, n, unormx, d;
  int unor[2000], unixx[2000], ungsix[2000], gsused[100], or,
      gsni, gsnn, unni, unnn, unormxi;
  long gsid[100], gsnx[100], id, nx, idgs,
       unid[1200], unnx[1200], ungsid[1200];
  float gsqo[100], gsqi[100], gsvl[100], gscf[100],
unar[1200], unqo[1200], unpr[1200], unqc[1200], unqct[1200],
ar, qo, pr, rncf, sum1, sum2, xxx, x2;
  /* gsor[100], gsar[100], gspr[100] deleted, gsvl[100] created */
  char buf[size];
  FILE *fgsin, *funin, *ftable2;
  if (argc < 3 )
   {
    printf ("wrong number of arguments = %d \n", argc);
    exit(1);
   }
  fgsin = fopen (argv[1], "r");
/*  fgets(buf, size, fgsin);  */
  i = 0;
  while (fscanf(fgsin, "%li,%li,%f", &id,&nx,&qo) != EOF)
   {
    gsid[i] = id;
    gsnx[i] = nx;
    gsqo[i] = qo;
    ++i;
   }
  gsnn = i-1;
  gsni = i;
  fclose(fgsin);
/* look for records that has Q = 0. All records that has Q=0 will
   have instead of next-id, the id they should have as a new unit.
*/
    for ( i = 0; i <= gsnn; ++i )
   {
    if ( gsqo[i] > 0.0 ) continue;
    for ( j = 0; j <= gsnn; ++j )
      if ( gsid[i] == gsnx[j]) gsnx[j] = gsnx[i];
   }
/*  =========================================================*/
  funin = fopen (argv[2], "r");
 fgets(buf, size, funin); /* tables unload first, dummy record */
  i = 0;                  /* that have negative area !!!!      */
  while (fscanf(funin, "%li,%li,%li,%f,%i,%f",
 &id,&nx,&idgs,&ar,&or,&pr) != EOF)
   {
    unid[i] = id;
    unnx[i] = nx;
    ungsid[i] = idgs;
    unar[i] = ar;
    unor[i] = or;
    unpr[i] = pr;
228
    ++i;
   }
  unnn = i-1;
  unni = i;
  fclose(funin);
  /* update ungsid[i] */
  for ( i = 0; i <= gsnn; ++i )
   {
    if ( gsqo[i] > 0.0 ) continue;
    for ( j = 0; j <= unnn; ++j )
      if ( gsid[i] == ungsid[j]) ungsid[j] = gsnx[i];
   }
 /* rebuild GS arrays, i.e. remove records GSQO <= 0  */
    i = 0;
  for ( j = 0; j <= gsnn; ++j )
   {
    if ( gsqo[j] <= 0.0 ) continue;
    gsid[i] = gsid[j];
    gsnx[i] = gsnx[j];
    gsqo[i] = gsqo[j];
    gsvl[i] = 0.0;
    gsqi[i] = 0.0;       /* initialization of the inflow table */
    gsused[i] = 0;
    ++i;
   }
  gsnn = i-1;
  gsni = i;
  /* Set UNGSIX index, i.e. index that relates UNID with the GSID
  = record in UN table with the record in GS table,
    if ungsid[] = 0, i.e.,. no gauging station assigned to this
record
     index = gsnn + 1 = gsnx    */
  for (i = 0; i <= unnn; ++i)
   {
    if ( ungsid[i] == 0 )
     {
      ungsix[i] = gsni;
      continue;
     }
    for (k = 0; k <= gsnn; ++k )
     {
      if ( ungsid[i] ==  gsid[k] )
ungsix[i] = k;
     }
   }
  for (i = 0; i <= gsnn; ++i )
    {
      for (j = 0; j <= unnn; ++j )
       if ( ungsid[j] == gsid[i] )
       {
  gsvl[i] = gsvl[i] + ( unpr[j] * unar[j] );
      }
    }
229
  /* Calculate runoff coefficient, use first order GS watersheds only
*/
  sum1 = 0.0;
  sum2 = 0.0;
  xxx = 1.0 / 8640.0 ;  /*  area in km2, prec in 0.001 cm/d, -> m3/s
*/
  notfound = 1;
  for (i = 0; i <= gsnn; ++i)
   {
    notfound = 1;
    for (j = 0; j <= gsnn; ++j )
     {
      if (gsnx[j] == gsid[i] )
{
  notfound = 0;
  break;
}
     }
    if ( notfound == 1 )
     {
     ++n;
     sum1 = sum1 + gsqo[i];
     sum2 = sum2 + ( gsvl[i] * xxx);
     }
   }
/*   printf("s1  s2  %f,%f\n",sum1,sum2);  */
   rncf = sum1 / sum2;
  /* 1) Calculate runoff from all UN watersheds */
  /* 2) assign initial values to both, unqc[] and unqct[]  */
  /* 3) fill array unixx[], index of the next/downstream unit */
  /*    is set in "find maximum order" module */
  for (i = 0; i <= unnn; ++i)
   {
    unqo[i] = rncf * unpr[i] * unar[i] * xxx ;
    unqc[i] = unqo[i];
    unqct[i] = unqo[i];
    for ( j = 0; j <= unnn; ++j)
     {
      if (unid[j] == unnx[i])
{
 unixx[i] = j;
 break;
}
     }
   }
  /* Find maximum UN order */
  unormx = 0;
  for (i = 0; i <= unnn; ++i)
   {
    if ( unormx < unor[i] )
     {
      unormx = unor[i];
230
      unormxi = i;
     }
   }
   unixx[unormxi] = unni;
  /* Calculate zonal cumulative UN flow (zonal = within GS zone) */
  for (k = 1; k < unormx; ++k)
   {
    for (i = 0; i <= unnn; ++i)
     {
      if ( unor[i] != k )
continue;
      j = unixx[i];
      if ( ungsid[j] != ungsid[i] )
continue;
      unqc[j] = unqc[j] + unqc[i];
     }
   }
  for (i = 0; i <= unnn; ++i)
   {
    unqct[i] = unqc[i];
   }
  /* Calculate sum of GS inflow  (inflows ?  */
  for (i = 0; i <= gsnn; ++i)
   {
    for (j = 0; j <= gsnn; ++j)
     {
      if ( gsnx[i] == gsid[j] )
{
gsqi[j] = gsqi[j] + gsqo[i];
}
     }
   }
  /* 1) Estimate correction factors GSCF */
  /* 2) Assign correction factor for the UN watersheds which are
  /* outside GS zones, i.e., most downstream UN watersheds
  /* (next wsh for the last unit has GSID = 0) */
  for (i = 0; i <= gsnn; ++i)
   {
    x2 = rncf * gsvl[i] * xxx;
    gscf[i] = ( gsqo[i] / ( gsqi[i] + x2 ) - 1.0 ) /x2 ;
    if (gsnx[i] == 0 )
     {
      gscf[gsni] = gscf[i];
      gsid[gsni] = 0;
     }
   }
  /* Calculate cumulative flow (total= observed inflow + calculated
     cumulative flow */
  for (i = 0; i <= unnn; ++i )
   {
    k = i;
    j = unixx[k];
    l = ungsix[k];
231
    if ( ungsid[k] == ungsid[j] )  continue;
    if ( gsused[l] == 1 ) continue;
    xxx = gsqo[l];
    gsused[l] = 1;
    while (j < unni )
     {
      unqct[j] = unqct[j] + xxx;
      k = j;
      j = unixx[k];
      if ( ungsid[j] != ungsid[k] ) break;
     }
   }
  /* Final distribution of flow */
  for ( i = 0; i <= unnn; ++i)
   {
    j = ungsix[i];
    unqc[i] = unqct[i] * (1. + ( gscf[j] *unqc[i] ) );
   }
  /* Write results to output file */
  ftable2 = fopen (argv[3], "w");
  /* arc view version:
  fprintf ( ftable2, "\"%s\",\"%s\"\n", argv[4], argv[5]);
  */
  for (j = 0; j <= unnn; ++j )
    fprintf(ftable2, "%li,%f\n", unid[j], unqc[j] );
  fclose(ftable2);
  return 0;
 }
232
Appendix B  Avenue scripts
This Appendix contains the following ArcView-Avenue scripts
1) Scripts that allow user to switch between different modules of the
agrichemical transport model;
gotoapr Opens a project that is specified in the first parameter
gtflwprc Opens the project "flwprc.apr", (maps of the flow rate and precipitation depth),
property: Click
gtflwu  Opens the project "flwprc.apr", property: Update
gtmodel Opens the project ?model.apr? (data preparation and model execution), property:
Click
gtmodu Opens the project ?model.apr?, property: Update
gtresult Opens the project ?results.apr? (results of last model execution), property: Click
gtresu Opens the project ?results.apr?, property: Update
gttools Opens the project ?tools.apr? (selected tools for hydrologic maps preparation),
property: Click
gttoou Opens the project ?tools.apr?, property: Update
2) Scripts from the project ?model?;
edflow3 Displays the dialog box to select and modify the cumulative flow rate. Changes are
made for the selected (or all) polygons active on the "Modeling Units" view. Assigned
to the button EQc, property: Click.
edflow3u Assigned to the button EQc (flow rate selection and modification), property: Update.
233
eduse2 Runs scripts "eduse2a" and "eduse2a" that support editing the agrichemical
application rate. Assigned to button EAP. Property: Click.
eduse2a Displays the dialog box to edit agrichemical application rate. Changes will be made to
selected (or all) county polygons displayed on an active view (executed from the script
"eduse2")
eduse2m Displays the dialog box to edit agrichemical application rate. Changes will be made to
selected (or all) modeling unit polygons displayed on active view (executed from the
script "eduse2")
eduse2u Assigned to button EAP (edit application rate). Property: update.
equat6 Calculates concentrations and loads for all or selected months of the year. Assigned to
the button RUN, property: Click.
Selmodel Displays the dialog box to select a model: equation: c = f(Flow, Area, Time, Use, X).
Assigned to the button SMo, property: Click.
Stime1 Displays the dialog box to select a year ( time variable for a model). Assigned to the
button SYr, property: Click.
upwavq1 Calculates weighted average for upstream units. Incorporated into scripts eduse.
selup2 Selects upstream units (active theme must have the following fields: unit_id, unit_nx,
and order). Assigned to a button in category: Tools, property: Apply.
Seldown2 Selects downstream units (active theme must have the following fields: unit_id,
unit_nx, and order). Assigned to a button in category: Tools, property: Apply.
Selup2u Update event for buttons that select upstream and downstream units ("selup2",
"seldown2"). Assigned to a button in category: Tools, property: Update.
decay1 Calculates the concentrations and loads of a chemical that exponentially ?decays? as it
is carried by water. Assigned to the button FOR, property: Click.
3) Scripts from the project ?model?;
Cchart1 Draw charts of the concentration (12 months) at the center of selected features,
property Click (runs script "schart1").
Lchart  Draw charts of the load (12 months) at the center of selected features, property Click
(runs script "schart1").
234
Qchar1 Draw charts of the flow rate (12 months) at the center of selected features, property
Click (runs script "schart1").
4) Scripts from the project ?flwprc?;
pmchar1 Draws charts of the precipitation depth at the center of selected features, for selected
months, property: Click, (executes script "schart1")
pmchar1u Draws charts of the precipitation depth, property: Update
qmchar1 Draws charts of the flow rate at the center of selected features, for selected months,
property: Click, (runs script "schart1").
qmchar1u Draws charts of the flow rate, property: Update.
schart1 Draws charts, is executed from such scripts as pmchar1 and qmchar1 (Adopted from
ESRII examples supplied with Avenue).
movie2 Displays charts in a sentence, category: tools, property: apply (script qmchar1u is used
in the property: Update).
aliaset  Sets the alias names for fields, that describe a chart axis.
5) Scripts from the project ?tools?;
order6 Determines the order of a stream/watershed in a flow system
upavg2 calculates weighted average over upstream units
cumul2 Accumulates values, going downstream (flow accumulation)
decom2 calculates the difference between the inflows and the outflow, the reverse process to
the flow accumulation
235
B1 Changing ArcView projects from the PushButton Bar.
gotoapr Opens a project that is specified in the first parameter
'gotoapr.ave
gotoname = self.get(0)
theProject = av.GetProject
prname = theproject.getname
if (nil <> theProject) then
  if (theProject.IsModified) then
    res = MsgBox.SaveChanges("Do you want to save changes to " +
theProject.GetName + "?", "ArcView", true)
    if (nil = res) then exit end
    if (res) then
      av.Run("Project.Save", nil)
      if (theProject.IsModified) then exit end
    end
  end
end
xxx = theproject.getfilename.asstring.substitute(prname,gotoname)
theFName = xxx.asfilename
if (nil <> theProject) then
  theProject.Close
end
av.ClearGlobals
av.PurgeObjects
Project.Open(theFName)
gtflwprc Opens the project "flwprc.apr", (maps of the flow rate and
precipitation depth), property: Click
xxx = av.run("gotoapr",{"flwprc.apr"})
gtflwu  Opens the project "flwprc.apr", property: Update
prname = av.GetProject.getname
if(prname = "flwprc.apr") then
  self.setenabled(false)
else
  self.setenabled(true)
end
236
gtmodel Opens the project ?model.apr? (data preparation and model
execution), property: Click
xxx = av.run("gotoapr",{"model.apr"})
gtmodu Opens the project ?model.apr?, property: Update
prname = av.GetProject.getname
if(prname = "model.apr") then
  self.setenabled(false)
else
  self.setenabled(true)
end
gtresult Opens the project ?results.apr? (results of last model execution),
property: Click
xxx = av.run("gotoapr",{"results.apr"})
gtresu Opens the project ?results.apr?, property: Update
prname = av.GetProject.getname
if(prname = "results.apr") then
  self.setenabled(false)
else
  self.setenabled(true)
end
gttools Opens the project ?tools.apr? (selected tools for hydrologic maps
preparation), property: Click
xxx = av.run("gotoapr",{"tools.apr"})
gttoou Opens the project ?tools.apr?, property: Update
prname = av.GetProject.getname
if(prname = "tools.apr") then
  self.setenabled(false)
else
  self.setenabled(true)
end
237
B2 Scripts from the project ?model?
edflow3 Displays the dialog box to select and modify the cumulative flow
rate. Changes are made for the selected (or all) polygons active on
the "Modeling Units" view. Assigned to the button EQc, property:
Click.
'edflow3.ave
'====================================================
'data table name:   Cumulative flow
'         fields:   "Unit_id", m199001 ...
'model table name:  feature table of "units" ("Crwsd")
'          fields:  "Unit_id", "Qm01 .. Qm12"
'====================================================
theView = av.getproject.finddoc("Modeling Units")
FTmodl = theview.findtheme("Units").Getftab
FTflow = av.getproject.finddoc("Cumulative flow").getVtab
'FTflow = fldoc.findtheme("unflow").getftab
if ((FTmodl = nil) or (FTflow=nil)) then
  msgbox.error("Can't get ftab of units or cumulative flow",
         " Units or flow unaccessible")
  exit
end
'check if all fields can be found:
'current version of edflow1 and v2 assumes that all fields exist
sp = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
ln1 = "Assume flow conditions of:"
ln3 = "( to apply factor to current values enter: NO )"
ln4 = "Multiply flow rate for all months by:"
ln5 = "      Apply multiplication factor to each month:"
ln6 = "Multiply flow rate for January by......."
ln7 = "Multiply flow rate for February by....."
ln8 = "Multiply flow rate for March by.........."
ln9 = "Multiply flow rate for April by............"
ln10 = "Multiply flow rate for May by............."
ln11 = "Multiply flow rate for June  by..........."
ln12 = "Multiply flow rate for July  by............"
ln13 = "Multiply flow rate for August by........"
ln14 = "Multiply flow rate for September by."
ln15 = "Multiply flow rate for October by......"
ln16 = "Multiply flow rate for November by.."
ln17 = "Multiply flow rate for December by.."
labls = {ln1,ln3,ln4,sp,ln5,ln6,ln7,ln8,ln9,ln10,ln11,ln12,
         ln13,ln14,ln15,ln16,ln17}
defts = {"1990"," ","1.00"," ","
","1.00","1.00","1.00","1.00","1.00",
         "1.00","1.00","1.00","1.00","1.00","1.00","1.00"}
238
tytul = "    Select flow rate"
while (true)
  xlist = msgBox.Multiinput(tytul,
    "Monthly average flow rate m3/s", labls, defts )
  if (xlist.count = 0) then
    exit
  end
  for each i in 0..16
    if ((i=0) or (i=1) or (i=3) or (i=4))then
      continue
    end
    if (xlist.get(i).isnumber.not) then
      msgbox.error(xlist.get(i)++"is not a number",
      "Error in line "++i.asstring)
      continue
    end
  end
  if (xlist.get(0) = "no" )then
    break
  end
  yr = xlist.get(0).asnumber
  if ((yr < 1960) or (yr>1991)) then
    msgbox.error(xlist.get(0)++"out of range (1960-1991)",
      "Error in year field ")
      continue
  end
  break
end
if (xlist.get(0) = "no" ) then
  if(Ftmodl.iseditable.not) then
    Ftmodl.seteditable(true)
  end
  for each m in 1..12
    av.setstatus (m * 100 /12)
    av.showmsg("Processing month "++m.asstring++" ... ")
    if (m <10) then
      nameto = "Flow"+"0"+m.asstring
    else
      nameto = "Flow"+m.asstring
    end
    im = m + 4
    expr = "["+nameto+"] *"+xlist.get(2)+"*"+xlist.get(im)
    Ftmodl.calculate(expr,Ftmodl.findfield(nameto))
  end
  if(Ftmodl.iseditable) then
    Ftmodl.seteditable(false)
  end
  exit
end
' Find the table and join fields for the tables
field1 = Ftmodl.FindField("Unit_id")
field2 = Ftflow.FindField("Unit_id")
' Now perform the join....
Ftmodl.Join( field1, Ftflow, field2)
if(Ftmodl.iseditable.not) then
239
  Ftmodl.seteditable(true)
end
for each m in 1..12
  if (m <10) then
     namefrom = "Qm"+xlist.get(0)+"0"+m.asstring
     nameto = "Flow"+"0"+m.asstring
  else
     namefrom = "Qm"+xlist.get(0)+m.asstring
     nameto = "Flow"+m.asstring
  end
  im = m + 4
  expr = "["+namefrom+"] *"+xlist.get(2)+"*"+xlist.get(im)
  Ftmodl.calculate(expr,Ftmodl.findfield(nameto))
end
if(Ftmodl.iseditable) then
  Ftmodl.seteditable(false)
end
FTmodl.unjoinall
edflow3u Assigned to the button EQc (flow rate selection and modification),
property: Update.
' edflow3u.ave : update event for "edit/select flow rate"
' Is enabled when  "Modeling Units" view is active.
' =======================
theView = av.GetActiveDoc
if (theView.GetEditableTheme <> NIL) then
  SELF.SetEnabled(FALSE)
  exit
end
t = theView.GetName
if (  t = "Modeling Units" ) then
   SELF.SetEnabled(TRUE)
   exit
end
SELF.SetEnabled(FALSE)
eduse2 Runs scripts "eduse2a" and "eduse2a" that support editing the
agrichemical application rate. Assigned to button EAP. Property:
Click.
'eduse2.ave
'================
t = av.GetActiveDoc.GetName
if ( t = "Modeling Units") then
  av.run("eduse2m","")
  exit
end
if (t = "Application Rate") then
240
  av.run("eduse2a","")
  exit
end
msgbox.Info("Modeling Units or Application Rate must be active",
            "Raquired View is not Active")
eduse2a Displays the dialog box to edit agrichemical application rate.
Changes will be made to selected (or all) county polygons displayed
on an active view (executed from the script "eduse2")
'eduse2a.ave (updated eduse1b.ave)
'edtuse.update script checked the existence of themes.
'====================================================
'link table name:   "County link unit file" extracted from
'                   feature table of "Useunit"
'         fields:   "Fips", "Unit_id", "area_km2"
'model table name:  feature table of Units (alias of "Crwsd")
'          fields:  "Unit_id", "Chemuse"
'county table name: feature table of Use feature from
'                   "Application Rate" view, (alias of "cruse")
'           fields: "Fips", "use"
'====================================================
theView = av.getproject.finddoc("Modeling Units")
FTmodl = theview.findtheme("Units").Getftab
FTlink = av.getproject.finddoc("linkuse.dbf").getvtab
FTcnty = av.getproject.finddoc("Application
Rate").findtheme("use").GetFtab
if ( Ftlink.haserror ) then
  msgbox.error ( " Can't find link table",
               "theme "++FTmodl.asstring)
  exit
end
'check if all fields can be found:
FDumdl = FTmodl.findfield("Unit_id")
if ( FDumdl = nil ) then
  msgbox.error ( " Can't find Unit_id field",
               "theme "++FTmodl.asstring)
  exit
end
FDfcty = FTcnty.findfield("Fips")
  if ( FDfcty = nil ) then
    msgbox.error ( " Can't find Fips field",
               "theme "++FTcnty.asstring)
    exit
  end
FDucty = FTcnty.findfield("use")
  if ( FDucty = nil ) then
    msgbox.error ( " Can't find Use field",
               "theme "++FTcnty.asstring)
    exit
  end
241
FDtcty = FTcnty.findfield("temp")
  if ( FDucty = nil ) then
    msgbox.error ( " Can't find Temp field",
               "theme "++FTcnty.asstring)
    exit
  end
FDclnk = FTlink.findfield("Fips")
  if ( FDclnk = nil ) then
    msgbox.error ( " Can't find Fips field",
               "theme "++FTlink.asstring)
    exit
  end
FDulnk = FTlink.findfield("Unit_id")
  if ( FDulnk = nil ) then
    msgbox.error ( " Can't find Unit_id field",
                 "theme "++FTlink.asstring)
    exit
  end
FDalnk = FTlink.findfield("area_km2")
  if ( FDalnk = nil ) then
    msgbox.error ( " Can't find Area_km2 field",
               "theme "++FTlink.asstring)
    exit
  end
'FDumdl = FTmodl.findfield("Unit_id")
FDrmdl = FTmodl.findfield("ChemUse")
  if ( FDrmdl = nil ) then
    msgbox.error ( " Can't find ChemUse field",
                 "theme "++FTmodl.asstring)
    exit
  end
'=========================================================
'This part is added for upstream weighetd average procedure
theFTab = FTmodl
FDunit = FDumdl
FDnext = theFtab.FindField("unit_nx")
if ( FDnext = nil ) then
   msgbox.error ( " Can't find unit_nx field",
             "theme "++FTmodl.asstring)
   exit
end
FDorder = theFtab.FindField("order")
if ( FDorder = nil ) then
   msgbox.error ( " Can't find order field",
             "theme "++FTmodl.asstring)
   exit
end
FDitem = FDrmdl
FDadd = theFtab.FindField("Cchemuse")
if ( FDadd = nil ) then
   msgbox.error ( " Can't find Cchemuse field",
             "theme "++FTmodl.asstring)
   exit
end
FDarea = theFtab.FindField("areakm2")
242
if ( FDarea = nil ) then
   msgbox.error ( " Can't find areakm2 field",
             "theme "++FTmodl.asstring)
   exit
end
parlst = {theFTab, FDunit, FDnext, FDorder, FDadd, FDitem, FDarea}
' av.run("upwavg1",parlst)
sp = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
ln1 = "Take values from the database:"
ln2 = "(n89kgkm2, n90kgkm2,n91kgkm2,a89kgkm2)"
ln3 = "( to apply factor to current values enter: NO )"
ln4 = "Multiply data by factor:"
ln5 = "Apply specified value:"
ln6 = "( negative value deactivates this input field )"
ln7 = "( units:  nitrogen [kg/km2], atrazine [kg/km2])"
labls = {sp, ln1, ln2, ln3,sp ,ln4,sp,ln5,ln6,ln7}
multf = 1.000
userv = -1.0
defts = {" ","n89kgkm2"," "," "," ", multf.asstring," ",
userv.asstring," "," "}
tytul = "    Specify Application Rate"
while (true)
  xlist = msgBox.Multiinput(tytul,
    "Annual agrichemical application by county", labls, defts )
  if (xlist.count = 0) then
    exit
  end
  if (xlist.get(7).isnumber.not) then
    msgbox.error(xlist.get(7)++"is not a number", "Error in field
#3")
    continue
  end
  aaa = xlist.get(7).asnumber
  if (aaa >= 0) then
    'edit "application by county" (table in LTpar list) and exit
    'set cruse table editable
    if(FTcnty.iseditable.not) then
      FTcnty.seteditable(true)
    end
    FTcnty.calculate(xlist.get(7),FDucty)
    if(FTcnty.iseditable) then
      FTcnty.seteditable(false)
    end
    'exit
    break
  end
  'check multiplication factor
  if (xlist.get(5).isnumber.not) then
   msgbox.error(xlist.get(5)++"is not a number", "Error in field #2")
   continue
  end
  ' now check the historical record field (AV is not case sensitiwe !
  '  NO = no:
  if(xlist.get(1)="no") then
243
    'set cruse table editable
    if(FTcnty.iseditable.not) then
      FTcnty.seteditable(true)
    end
    expres = xlist.get(5)+"*[use]"
    FTcnty.calculate(expres,FDtcty)
    FTcnty.calculate("[temp]",FDucty)
    if(FTcnty.iseditable) then
      FTcnty.seteditable(false)
    end
    'exit
    break
  end
  'last possibility that user wants historical record !
  hrecord = FTcnty.findfield(xlist.get(1))
  if (hrecord = nil) then
    msgbox.error(xlist.get(1)++"  is neither NO nor field name"++ln2,
     "Error in field #1")
    continue
  end
  'set cruse table editable
  if(FTcnty.iseditable.not) then
    FTcnty.seteditable(true)
  end
  expres = xlist.get(5)+"*["+xlist.get(1)+"]"
  FTcnty.calculate(expres,FDucty)
  if(FTcnty.iseditable) then
    FTcnty.seteditable(false)
  end
  'exit
  break
end  'of while error = false
'make dictionaries:
dlink = dictionary.make(FTlink.getnumrecords)
'dc (dict.) relates fips and edited use (field "use")
dc = dictionary.make(FTcnty.getnumrecords)
'dm (dict.) relates unit_id and cumulative (use * area)
dm = dictionary.make(FTmodl.getnumrecords)
'da (dict.) relates unit id and cumulative area
da = dictionary.make(FTmodl.getnumrecords)
'assign initial values to cumulative (use * area) and (area)
' the average use over modelling unit = cum(use*area)/cum(area)
for each rec in FTmodl
 dm.add(FTmodl.returnvalue(FDumdl,rec),0)
 da.add(FTmodl.returnvalue(FDumdl,rec),0)
end
'fill up the dc dictionary:  Fips ==> use (cruse counties coverage)
for each rec in FTcnty
dc.add(FTcnty.returnvalue(FDfcty,rec),FTcnty.returnvalue(FDucty,rec))
end
'calculate cumulative values
for each rec in FTlink
  unitid = FTlink.returnvalue(FDulnk,rec)
  fips = FTlink.returnvalue(FDclnk,rec)
  area = FTlink.returnvalue(FDalnk,rec)
244
  applic = dc.get(fips)
  oldarea = da.get(unitid)
  oldappl = dm.get(unitid)
  da.set(unitid, oldarea + area )
  dm.set(unitid, oldappl + (area * applic))
end
'Write results into table "crwsd", item "Chemuse"
'set crwsd (model parameters) table editable
if(FTmodl.iseditable.not) then
  FTmodl.seteditable(true)
end
'Write results to "crwsd" table
for each rec in FTmodl
  unitid = FTmodl.returnvalue(FDumdl,rec)
  use = dm.get(unitid)/da.get(unitid)
  av.ShowMsg("Writing to chemuse: "++rec.asString++use.asstring)
  FTmodl.SetValue(FDrmdl, rec, use)
end
av.run("upwavg1",parlst)
'stop edit session (and refresh) "crwsd" table
if(FTmodl.iseditable) then
  FTmodl.seteditable(false)
end
eduse2m Displays the dialog box to edit agrichemical application rate.
Changes will be made to selected (or all) modeling unit polygons
displayed on active view (executed from the script "eduse2")
'eduse2m.ave (old eduse1c.ave)
'edtuse.update script checked the existence of themes.
'====================================================
'model table name:  feature table of "Units"
'          fields:  "Unit_id", "Chemuse"
'====================================================
theView = av.getproject.finddoc("Modeling Units")
FTmodl = theview.findtheme("Units").Getftab
if(theview.findtheme("Units").isactive.not) then
  msgbox.warning("Theme >Units< is not active", "")
end
'check if all fields can be found:
FDrmdl = FTmodl.findfield("ChemUse")
if ( FDrmdl = nil ) then
   msgbox.error ( " Can't find ChemUse field",
             "theme "++FTmodl.asstring)
   exit
end
'=========================================================
'This part is added for upstream weighetd average procedure
theFTab = FTmodl
FDunit = theFtab.FindField("unit_id")
if ( FDunit = nil ) then
   msgbox.error ( " Can't find unit_id field",
245
             "theme "++FTmodl.asstring)
   exit
end
FDnext = theFtab.FindField("unit_nx")
if ( FDnext = nil ) then
   msgbox.error ( " Can't find unit_nx field",
             "theme "++FTmodl.asstring)
   exit
end
FDorder = theFtab.FindField("order")
if ( FDorder = nil ) then
   msgbox.error ( " Can't find order field",
             "theme "++FTmodl.asstring)
   exit
end
FDitem = FDrmdl
FDadd = theFtab.FindField("Cchemuse")
if ( FDadd = nil ) then
   msgbox.error ( " Can't find Cchemuse field",
             "theme "++FTmodl.asstring)
   exit
end
FDarea = theFtab.FindField("areakm2")
if ( FDarea = nil ) then
   msgbox.error ( " Can't find areakm2 field",
             "theme "++FTmodl.asstring)
   exit
end
parlst = {theFTab, FDunit, FDnext, FDorder, FDadd, FDitem, FDarea}
' av.run("upwavg1",parlst)
'=======================================================
sp = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
ln4 = "Multiply data by factor:"
ln5 = "Apply specified value:"
ln6 = "( negative value deactivates this input field )"
ln7 = "( units:  nitrogen [kg/km2], atrazine [kg/km2])"
labls = {sp, ln4,sp,ln5,ln6,ln7}
multf = 1.000
userv = -1.0
defts = {" ", multf.asstring," ", userv.asstring," "," "}
tytul = "    Specify Application Rate"
while (true)
  xlist = msgBox.Multiinput(tytul,
    "Annual agrichemical application by modeling unit",
      labls, defts )
  if (xlist.count = 0) then
    exit
  end
  if (xlist.get(3).isnumber.not) then
    msgbox.error(xlist.get(3)++"is not a number", "Error in field
#1")
    continue
  end
  aaa = xlist.get(3).asnumber
  if (aaa >= 0) then
246
    'put the user value into "ChemUse" field (selected or all recds)
    'set crwsd table editable
    if(FTmodl.iseditable.not) then
      FTmodl.seteditable(true)
    end
    FTmodl.calculate(xlist.get(3),FDrmdl)
    av.run("upwavg1",parlst)
    if(FTmodl.iseditable) then
      FTmodl.seteditable(false)
    end
    break
  end
  'check multiplication factor
  if (xlist.get(1).isnumber.not) then
    msgbox.error(xlist.get(1)++"is not a number", "Error in field
#1")
    continue
  end
  'set crwsd table editable
  if(FTmodl.iseditable.not) then
      FTmodl.seteditable(true)
  end
  expres = xlist.get(1)+"*[ChemUse]"
  FTmodl.calculate(expres,FDrmdl)
  av.run("upwavg1",parlst)
  if(FTmodl.iseditable) then
    FTmodl.seteditable(false)
  end
  break
end
eduse2u Assigned to button EAP (edit application rate). Property: update.
' eduse2u.ave : update event for "edit application"
' Is enabled when either "Application Rate" view or "Modeling Units"
' view is active.
' =======================
theView = av.GetActiveDoc
if (theView.GetEditableTheme <> NIL) then
  SELF.SetEnabled(FALSE)
  exit
end
t = theView.GetName
if ( ( t = "Modeling Units") or (t = "Application Rate") ) then
   SELF.SetEnabled(TRUE)
   exit
end
SELF.SetEnabled(FALSE)
247
equat6 Calculates concentrations and loads for all or selected months of the
year. Assigned to the button RUN, property: Click.
'equat6 modified equat5, time component changed
'    into seasonal index, separate trend,
'    equation includes land-length and land-slope
'    model stored in model2.dbf
'equat4 calculates concentration and load in
'feature attibute table of "crwsd"
'model equations and parameters are stored in model1.dbf
'same as equat3 plus recalculation for selected months
'==================================================
theView = av.getproject.finddoc("Modeling Units")
FTmodl = theview.findtheme("Units").Getftab
if (FTmodl = nil) then
  msgbox.error("Can't find feature table", "Units unaccessible")
  exit
end
tab1 = av.getproject.finddoc("model2.dbf")
vtab1 = tab1.getvtab
if (vtab1 = nil) then
  msgbox.error("Can't find model2.dbf", "model2.dbf unaccessible")
  exit
end
i = -1
fsel = vtab1.findfield("sel")
for each rec in vtab1
  i = i + 1
  if (vtab1.returnvalue(fsel,rec) = 1 ) then
    idmod = i
    break
  end
end
fmodel = vtab1.findfield("Model")
xtxt = "Model:
"+vtab1.returnvalue(vtab1.findfield("Model"),idmod)++"?"
if(msgbox.miniYesNo(xtxt, True).not) then
      exit
end
'========= months selection ================================
yyy = "all OR selected months 0=NO, 1=YES"
mylist = {"1","0","0","0","0","0","0","0","0","0","0","0","0"}
lbs = {"All months . . . . . . . . . . . . . . . . . . . . . . ",
    "January . . . . . . . . . . . . . . . . . . . . . . . . ",
    "February . . . . . . . . . . . . . . . . . . . . . . . ",
    "March  . . . . . . . . . . . . . . . . . . . . . . . . . ",
    "April   . . . . . . . . . . . . . . . . . . . . . . . . . . ",
    "May  . . . . . . . . . . . . . . . . . . . . . . . . . . . ",
    "June   . . . . . . . . . . . . . . . . . . . . . . . . . . ",
    "July  . . . . . . . . . . . . . . . . . . . . . . . . . . .  ",
    "August . . . . . . . . . . . . . . . . . . . . . . . . . ",
    "September  . . . . . . . . . . . . . . . . . . . . .  ",
    "October . . . . . . . . . . . . . . . . . . . . . . . .",
    "November . . . . . . . . . . . . . . . . . . . . . .  ",
248
    "December . . . . . . . . . . . . . . . . . . . . . . "}
xloop = true
while(xloop)
newlist = msgbox.multiinput(yyy, "Recalculate",lbs, mylist)
if(newlist.count = 0) then
  msgbox.info("Operation Canceled", "Process: RUN")
  exit
end
xloop = false
ind = 0
for each x in newlist
  ind = ind + 1
  if(x.isnumber.not) then
    msgbox.error("error in line"++ind.asstring+":"++x,"")
'    msgbox.info(x.asstring, "xxx")
    xloop = true
    mylist = newlist
    break
  end
end
end
if(newlist.get(0).asnumber > 0) then
  for each ind in 1..12
    newlist.set(ind, 1)
  end
else
  for each ind in 1..12
    newlist.set(ind, newlist.get(ind).asnumber)
  end
end
'========= end of months selection =========================
feq = vtab1.findfield("equation")
exp101 = vtab1.returnvalue(feq,idmod)
exp102 = exp101.substitute("U", "[Cchemuse]")
exp103 = exp102.substitute("A", "[Careakm2]")
exp104 = exp103.substitute("LS", "[Alndslp]")
exp105 = exp104.substitute("LL", "[Alndlgkm]")
' calculate trend coefficient
fyear = vtab1.findfield("year")
yr = vtab1.returnvalue(fyear,idmod)
xyr = yr.asstring
trfunc = vtab1.findfield("Ftrend")
trcoeff = vtab1.findfield("Trendcf")
exp400 = vtab1.returnvalue(trfunc,idmod)
exp401 = exp400.substitute("Year", xyr)
if(Ftmodl.iseditable.not) then
  Ftmodl.seteditable(true)
end
if(vtab1.iseditable.not) then
   vtab1.seteditable(true)
end
xxx0 = vtab1.calculate(exp401,trcoeff)
xtr = vtab1.returnvalue(trcoeff,idmod).asstring
exp110 = exp105.substitute("TR", xtr)
' clear fields:
249
'   xxx0 = vtab1.calculate("0",trcoeff)
av.showstopbutton
for each mt in 1..12
  xstop = av.setstatus (mt * 100 /12)
  av.showmsg("Processing month "++mt.asstring++" ... ")
  if(newlist.get(mt) = 0) then
    continue
  end
  if(xstop.not) then
     xyes =msgbox.Miniyesno("Do you want to stop ?", False)
     if(xyes) then
        if(Ftmodl.iseditable) then
           Ftmodl.seteditable(false)
        end
        if(vtab1.iseditable) then
           vtab1.seteditable(false)
        end
        av.clearstatus
        exit
     else
       av.ClearStatus
       av.showstopbutton
     end
  end
  xmt = mt.asstring
  if (mt <10) then
    Qname = "[Flow"+"0"+xmt+"]"
    Cname = "Conc"+"0"+xmt
    Lname = "Load"+"0"+xmt
    Sname = "Si"+"0"+xmt
  else
    Qname = "[Flow"+xmt+"]"
    Cname = "Conc"+xmt
    Lname = "Load"+xmt
    Sname = "Si"+xmt
  end
  'clear fields,
'  xxx0 = Ftmodl.calculate("0",Ftmodl.findfield(Cname))
'  xxx0 = Ftmodl.calculate("0",Ftmodl.findfield(Lname))
  xsi = vtab1.returnvalue(vtab1.findfield(Sname),idmod).asstring
  exp111 = exp110.substitute("SI", xsi)
  exp112 = exp111.substitute("Q", Qname)
  xxx3 = Ftmodl.calculate(exp112,Ftmodl.findfield(Cname))
  exp200 = "["+Cname+"] *"+Qname
  xxx4 = Ftmodl.calculate(exp200,Ftmodl.findfield(Lname))
end
if(Ftmodl.iseditable) then
  Ftmodl.seteditable(false)
end
if(vtab1.iseditable) then
   vtab1.seteditable(false)
end
av.clearstatus
av.clearmsg
250
Selmodel Displays the dialog box to select a model: equation: c = f(Flow, Area,
Time, Use, X). Assigned to the button SMo, property: Click.
' selmodel (puts 1 into field "sel" of "model1.dbf"
' if selected, 0 otherwise.
'===========================================================
tab1 = av.getproject.finddoc("model1.dbf")
vtab1 = tab1.getvtab
if (vtab1 = nil) then
  msgbox.error("Can't find model1.dbf", "model1.dbf unaccessible")
  exit
end
fsel = vtab1.findfield("sel")
fmodel = vtab1.findfield("Model")
modlist = list.make
for each rec in vtab1
  modlist.add(vtab1.returnvalue(fmodel,rec))
end
xselect = msgbox.choiceasstring(modlist,"Select model:",
    "Model selection")
if(xselect <> nil) then
  if(vtab1.iseditable.not) then
    vtab1.seteditable(true)
  end
  for each rec in vtab1
    if(xselect = vtab1.returnvalue(fmodel,rec)) then
       vtab1.setvaluenumber(fsel,rec,1)
    else
       vtab1.setvaluenumber(fsel,rec,0)
    end
  end
   if(vtab1.iseditable) then
     vtab1.seteditable(false)
  end
else
  msgbox.info("No selection made", "Nothing changed !")
end
Stime1 Displays the dialog box to select a year ( time variable for a model).
Assigned to the button SYr, property: Click.
'stime1
' writes year into the field "year" of "model1.dbf"
'====================================================
tab1 = av.getproject.finddoc("model1.dbf")
vtab1 = tab1.getvtab
if (vtab1 = nil) then
  msgbox.error("Can't find model1.dbf", "model1.dbf unaccessible")
251
  exit
end
fyear = vtab1.findfield("Year")
if (fyear = nil) then
  msgbox.error("Can't find field: Year",
         "Field does not exist ?")
  exit
end
yrdef = vtab1.returnvalue(fyear,0).asstring
'prompt for year:
while(true)
  tx = "Specify a value for model's time variable (enter a year)"
  year = msgbox.input(tx,"Setting Model's Time Variable", yrdef)
  if(year = nil) then
    exit
  end
  if (year.isnumber.not) then
    msgbox.error(year++"is not a number",
      "Wrong entry ")
    continue
  end
  yr = year.asnumber
  if ((yr < 1900) or (yr>2999)) then
    msgbox.error(year++"out of range (1900-2999)",
      "Error in year field ")
      continue
  end
  break
end
if(vtab1.iseditable.not) then
  vtab1.seteditable(true)
end
vtab1.calculate(year,fyear)
if(vtab1.iseditable) then
  vtab1.seteditable(false)
end
upwavq1 Calculates weighted average for upstream units. Incorporated into
scripts eduse.
' upwavg1.ave calculates weighted average for upstream units
' This is run from eduse... script
theFTab = self.get(0)
FDunit = self.get(1)
FDnext = self.get(2)
FDorder = self.get(3)
FDadd = self.get(4)
FDitem = self.get(5)
FDarea = self.get(6)
ltunit = list.make
ltnext = list.make
ltorder = list.make
252
ltitem = list.make
ltadd = list.make
unnx = theFTab.GetNumRecords
unnn = unnx - 1
dcarea = dictionary.make(unnx)
dcmass = dictionary.make(unnx)
for each rec in theFTab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  ltunit.Add(Nunit)
  ltnext.Add(theFTab.ReturnValueNumber(FDnext, rec))
  ltorder.Add(theFTab.ReturnValueNumber(FDorder, rec))
  Narea = theFTab.ReturnValueNumber(FDarea, rec)
  Nmass = theFTab.ReturnValueNumber(FDitem, rec) * Narea
  dcarea.add(Nunit, Narea )
  dcmass.add(Nunit, Nmass )
end
' find maximum order
unmaxord = 1
for each i in 0..unnn
  av.ShowMsg("Finding maximum order ..."++i.asString)
  istatus = i * 100 / unnn
  av.SetStatus(istatus)
  if (ltorder.get(i) > unmaxord ) then
        unmaxord = ltorder.get(i)
  end
end
'calculate cumulative values
unmaxord1 = unmaxord - 1
for each k in 1..unmaxord1
  av.ShowMsg("Calculating cumulative values ..."++k.asString)
  istatus = k * 100 / unmaxord
  av.SetStatus(istatus)
  for each i in 0..unnn
    if ( ltorder.get(i) <> k ) then
      continue
    end
    Nunit = ltunit.get(i)
    Nnext = ltnext.get(i)
    Nxmass = dcmass.get(Nunit) + dcmass.get(Nnext)
    Nxarea = dcarea.get(Nunit) + dcarea.get(Nnext)
    dcmass.set(Nnext, Nxmass)
    dcarea.set(Nnext, Nxarea)
  end
end
av.clearMsg
'write results to Ftab
for each rec in theFtab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  Xavg = dcmass.get(Nunit) / dcarea.get(Nunit)
  TheFtab.SetValue( FDadd, rec, Xavg )
end
theFtab.Refresh
if(TheFtab.isEditable) then
    theFtab.SetEditable(false)
end
253
selup2 Selects upstream units (active theme must have the following fields:
unit_id, unit_nx, and order). Assigned to a button in category:
Tools, property: Apply.
'three fields are required:
nm_id = "unit_id"
nm_nx = "unit_nx"
nm_or = "order"
theView = av.GetActiveDoc
theThemes = theView.GetActiveThemes
p = theView.GetDisplay.ReturnUserPoint
shiftk = System.IsShiftKeyDown
if (ShiftK) then
  op = #VTAB_SELTYPE_XOR
else
  op = #VTAB_SELTYPE_NEW
end
t = thethemes.get(0)
if (t.CanSelect.not) then
  exit
end
t.SelectByPoint(p, op)
recs = t.FindByPoint(p)
if(recs.count = 0) then
  exit
end
rec = recs.get(0)
v = t.getFTab
fid = v.findfield(nm_id)
fnx = v.findfield(nm_nx)
ford = v.findfield(nm_or)
if ((fid=nil)or(fnx=nil)or(ford=nil)) then
  msgbox.error ( " Can't find necessary fields",
               " Upstream selection ")
  exit
end
xid = v.returnvalue(fid, rec)
xnx = v.returnvalue(fnx, rec)
rno = rec
rord = v.returnvalue(ford,rno)
if(rord = 1) then
  exit
end
bmap = v.getselection
stk = stack.make
av.showmsg("Selecting upstream elements ...")
while (true)
  for each rcd in v
    'don't look for upstream if first order
    if(rord = 1 ) then
      break
254
    end
    xnx = v.returnvalue(fnx,rcd)
    if(xid = xnx) then
      stk.push(rcd.asstring)
    end
  end
  rno = stk.pop.asnumber
  if(shiftk) then
    if(bmap.get(rno)) then
       bmap.clear(rno)
    else
       bmap.set(rno)
    end
  else
    bmap.set(rno)
  end
  t.blinkrecord(rno)
  rord = v.returnvalue(ford,rno)
  xid = v.returnvalue(fid,rno)
  if((stk.depth = 0 )and (rord = 1)) then
    break
  end
end
av.Clearmsg
Seldown2 Selects downstream units (active theme must have the following
fields: unit_id, unit_nx, and order). Assigned to a button in
category: Tools, property: Apply.
'seldown2
'three fields are required:
nm_id = "unit_id"
nm_nx = "unit_nx"
nm_or = "order"
theView = av.GetActiveDoc
theThemes = theView.GetActiveThemes
p = theView.GetDisplay.ReturnUserPoint
shiftk = System.IsShiftKeyDown
if (ShiftK) then
  op = #VTAB_SELTYPE_XOR
else
  op = #VTAB_SELTYPE_NEW
end
t = thethemes.get(0)
if (t.CanSelect.not) then
  exit
end
t.SelectByPoint(p, op)
recs = t.FindByPoint(p)
if(recs.count = 0) then
  exit
end
255
rec = recs.get(0)
v = t.getFTab
fid = v.findfield(nm_id)
fnx = v.findfield(nm_nx)
ford = v.findfield(nm_or)
if ((fid=nil)or(fnx=nil)or(ford=nil)) then
  msgbox.error ( " Can't find necessary fields",
               " Downstream selection ")
  exit
end
xid = v.returnvalue(fid, rec)
xnx = v.returnvalue(fnx, rec)
rno = rec
rord = v.returnvalue(ford,rno)
if(xnx = 0) then
  exit
end
bmap = v.getselection
av.showmsg("Selecting downstream elements ...")
while (true)
  for each rcd in v
    xid = v.returnvalue(fid,rcd)
    if(xid = xnx) then
      bmap.set(rcd)
      if(shiftk) then
        if(bmap.get(rcd)) then
          bmap.clear(rcd)
        else
          bmap.set(rcd)
        end
      else
        bmap.set(rcd)
      end
      xnx = v.returnvalue(fnx,rcd)
      if (xnx = 0) then
        exit
      end
    end
  end
end
msgbox.error("I cann't find the most downstream reach",
              "Last reach not found")
Selup2u Update event for buttons that select upstream and downstream
units ("selup2", "seldown2"). Assigned to a button in category:
Tools, property: Update.
'selup2.update
' Is enabled when prpoer fields are found in active
'three fields are required:
nm_id = "unit_id"
nm_nx = "unit_nx"
256
nm_or = "order"
theView = av.GetActiveDoc
if (theView.GetEditableTheme <> NIL) then
  SELF.SetEnabled(FALSE)
  exit
end
for each t in theView.GetThemes
  if (t.IsVisible.not) then
    continue
  end
  if (t.IsActive.not) then
    continue
  end
  fid = t.getftab.findfield(nm_id)
  fnx = t.getftab.findfield(nm_nx)
  ford = t.getftab.findfield(nm_or)
  if ((fid<>nil)and(fnx<>nil)and(ford<>nil)) then
     SELF.SetEnabled(TRUE)
     exit
  end
  break
end
SELF.SetEnabled(FALSE)
decay1 Calculates the concentrations and loads of a chemical that
exponentially ?decays? as it is carried by water. Assigned to the
button FOR, property: Click.
' decay1.ave Calculates loads and concentrations
'            in surface waters. Chemical losses
'            are governed by the first order reaction.
'unit conversion factor
' Assumptions:
' application rate is in kg/km2/yr
' area is in km2
' then, the mass runoff is in kg/year
' to make load units g/s
' the conversion factor equal to 0.00003170979
' 1000 (g/kg) / ( 365 days * 86400 seconds )
' must be applied:
conversf = 0.00003170979
' flow is in m3/s, thus concentration is in g/m3
' or mg/L
' The usercoef represents seasonal index, confidence
' limits, extreme conditions, application timing etc.
' It is a multiplier of mass runoff from the field.
usercoef = 1
' This part is for an Attribute table !!!)
' note: dbf table contains a dummy (first) record
' that may influence calculations (unlikely)
' but will produce avenue errors (dividing by 0)
257
theView = av.getproject.finddoc("Modeling Units")
theFtab = theview.findtheme("Units").Getftab
TBunit = theFtab
' Ask user for needed fields:
TXunit = "unit_id"
TXnext = "unit_nx"
TXorder = "order"
TXarea = "Areakm2"
TXuse = "Chemuse"
TXtrat = "Travtime"
TXloss = "Losscoef"
TXexpt = "Expofac"
TXflow = "Flow"
FDunit = theFtab.FindField(TXunit)
FDnext = theFtab.FindField(TXnext)
FDorder = theFtab.FindField(TXorder)
FDarea = theFtab.FindField(TXarea)
FDuse = theFtab.FindField(TXuse)
FDtrat = theFtab.FindField(TXtrat)
FDloss = theFtab.FindField(TXloss)
FDexpt = theFtab.FindField(TXexpt)
FDflow = theFtab.FindField(TXflow)
' Make a list of VTunit fields
LSFDunit = theFtab.GetFields
' If the default fields can not be found, ask user for
' the required fields:
if(FDunit=nil) then
  ' Select current_unit id field (from entity)
  FDunit = MsgBox.List(LSFDunit, "Select a field that contains"
      ++NL++"the watershed/stream ID", "Unit ID")
end
' If not selected, quit
IF (FDunit = nil) then
  exit
end
if(FDnext=nil) then
  ' Select downstream_unit id field
  FDnext = MsgBox.List(LSFDunit, "Select a field that contains"
       ++NL++" the downstream unit ID", "Downstream unit ID")
end
' If not selected, quit
IF ( FDnext = nil) then
  exit
end
if(FDorder=nil) then
  ' Select order field
  FDorder = MsgBox.List(LSFDunit, "Select field that contains"
     ++NL++" the watershed/stream order","Order")
end
' If not selected, quit
IF ( FDorder = nil) then
  xxx = msgbox.info("Create a field of stream order",
       "Missing fields")
  exit
end
258
if(FDarea=nil) then
  ' Select field that contains area of the modeling unit
  FDarea = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"modeling unit area (km2)", "Area")
end
' If not selected, quit
IF ( FDarea = nil) then
  exit
end
if(FDuse=nil) then
  ' Select field that contains the application rate within unit
  FDuse = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"application rate (kg/km2/yr)", "Application Rate")
end
' If not selected, quit
IF ( FDuse = nil) then
  exit
end
if(FDexpt=nil) then
  ' Select field that contains the export factors
  FDexpt = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"the export factors", "Export factor")
end
' If not selected, quit
IF ( FDexpt = nil) then
  exit
end
if(FDtrat=nil) then
  ' Select field that contains travel time through modeling unit
  FDtrat = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"unit travel time (day)", "Travel Time")
end
' If not selected, quit
IF ( FDtrat = nil) then
  exit
end
if(FDloss=nil) then
  ' Select field that contains the loss coefficient
  FDloss = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"the loss coefficient (1/d)", "Loss coefficient")
end
' If not selected, quit
IF ( FDloss = nil) then
  exit
end
if(FDflow=nil) then
  ' Select field that contains the accumulated flow rate
  FDflow = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"the total flow rate", "Flow rate")
end
' If not selected, quit
IF ( FDflow = nil) then
  exit
end
' Prompt for a name (name of the field, that will be created)
259
TXconc = msgbox.input("Enter the name of concentration field ",
"Concentration", "conc_gm3")
FDconc = theFtab.FindField(TXconc)
xx = false
if (FDconc = nil) then
  xx = msgbox.YesNo( TXconc++"field is not in the table "
  ++TBunit.asString+nl+"Do you want to create this field ?",
   "Field not Found !", true)
  if (xx.not) then
    exit
  end
  fenum = FDflow.gettype
  fprec = 6
  fwidth = 12
  xxx = msgbox.input("Please specify a width of the conc. field",
   "Width of the new field" , fwidth.asstring)
  fwidth = xxx.asnumber
  IF ( fwidth = nil) then
    exit
  end
  xxx2 = msgbox.input("Please specify number of decimal places:",
   "Precision of the new field" , fprec.asstring)
  fprec = xxx2.asnumber
  IF ( fprec = nil) then
    exit
  end
  'check if the theFtab can be edited if not, set it editable
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
  ' Create a new field
  if(theFtab.CanAddFields) then
    FDconc = field.Make(TXconc,fenum,fwidth,fprec)
    theFtab.AddFields({FDconc})
  else
   msgBox.warning("Can not add a field to"++theFtab.asString,
                   "Can not edit table")
    exit
  end
else
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
end
' Prompt for a name (name of the field, that will be created)
TXload = msgbox.input("Enter the name of load field ",
"Load", "load_gm3")
FDload = theFtab.FindField(TXload)
xx = false
if (FDload = nil) then
  xx = msgbox.YesNo( TXload++"field is not in the table "
  ++TBunit.asString+nl+"Do you want to create this field ?",
   "Field not Found !", true)
  if (xx.not) then
    exit
260
  end
  fenum = FDflow.gettype
  fprec1 = 6
  fwidth1 = 16
  xxx3 = msgbox.input("Please specify a width of the load field",
   "Width of the new field" , fwidth1.asstring)
    fwidth1 = xxx3.asnumber
  IF ( fwidth1 = nil) then
    exit
  end
  xxx4 = msgbox.input("Please specify number of decimal places:",
   "Precision of the new field" , fprec1.asstring)
    fprec1 = xxx4.asnumber
  IF ( fprec1 = nil) then
    exit
  end
  'check if the theFtab can be edited if not, set it editable
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
  ' Create a new field
  if(theFtab.CanAddFields) then
    FDload = field.Make(TXload,fenum,fwidth1,fprec1)
    theFtab.AddFields({FDload})
  else
   msgBox.warning("Can not add a field to"++theFtab.asString,
                   "Can not edit table")
    exit
  end
else
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
end
'the conversion factor and a multiplier
while(true)
  TXcf = msgbox.input("Enter a conversion factor"++NL++
            "(kg/yr -> g/s)", "Conversion Factor",
            conversf.asstring)
  if(TXcf = nil) then
    exit
  end
  if(TXcf.isnumber.not) then
    msgbox.error(TXcf++"is not a number","Wrong entry")
    continue
  end
  conversf = TXcf.asnumber
break
end
while(true)
  TXum = msgbox.input("Enter a multiplier of the"++NL++
            "chemical runoff from the field",
            "Runoff Multiplier", usercoef.asstring)
  if(TXum = nil) then
    exit
261
  end
  if(TXum.isnumber.not) then
    msgbox.error(TXum++"is not a number","Wrong entry")
    continue
  end
  usercoef = TXum.asnumber
break
end
'create lists
ltunit = list.make
ltnext = list.make
ltorder = list.make
'ltadd = list.make
'ltexnkt = list.make
'ltroff = list.make
unnx = theFTab.GetNumRecords
unnn = unnx - 1
dcload = dictionary.make(unnx)
dcexnkt = dictionary.make(unnx)
for each rec in theFTab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  ltunit.Add(Nunit)
  ltnext.Add(theFTab.ReturnValueNumber(FDnext, rec))
  ltorder.Add(theFTab.ReturnValueNumber(FDorder, rec))
  xk = theFTab.ReturnValueNumber(FDloss, rec)
  xt = theFTab.ReturnValueNumber(FDtrat, rec)
  exnkt = number.geteuler^( -1 * xk * xt )
  dcexnkt.add(Nunit, exnkt )
  xa = theFTab.ReturnValueNumber(FDarea, rec)
  xu = theFTab.ReturnValueNumber(FDuse, rec)
  xe = theFTab.ReturnValueNumber(FDexpt, rec)
  xroff = xa * xu * xe * usercoef * conversf
  dcload.add(Nunit, xroff )
end
' find maximum order
unmaxord = 1
for each i in 0..unnn
  av.ShowMsg("Finding maximum order ..."++i.asString)
  istatus = i * 100 / unnn
  av.SetStatus(istatus)
  if (ltorder.get(i) > unmaxord ) then
        unmaxord = ltorder.get(i)
  end
end
'calculate values of load
unmaxord1 = unmaxord - 1
for each k in 1..unmaxord1
  av.ShowMsg("Decaying and decaying ..."++k.asString)
  istatus = k * 100 / unmaxord
  av.SetStatus(istatus)
  for each i in 0..unnn
    if ( ltorder.get(i) <> k ) then
      continue
    end
    Nunit = ltunit.get(i)
262
    Nnext = ltnext.get(i)
Nxvalue = dcload.get(Nunit) * dcexnkt.get(Nnext) + dcload.get(Nnext)
    dcload.set(Nnext, Nxvalue)
  end
end
av.clearMsg
av.clearStatus
'write results to Ftab
for each rec in theFtab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  Nload = dcload.get(Nunit)
  TheFtab.SetValue( FDload, rec, Nload )
  Nflow = theFTab.ReturnValueNumber(FDflow, rec)
  if (Nflow = 0 ) then
    Nconc = 0
  else
    Nconc = Nload / Nflow
  end
  TheFtab.SetValue( FDconc, rec, Nconc )
end
theFtab.Refresh
if(TheFtab.isEditable) then
    theFtab.SetEditable(false)
end
263
B3 Scripts from the project ?results?
Cchart1 Draw charts of the concentration (12 months) at the center of
selected features, property Click ( runs script "schart1")
' Cchart1, One year of Concentrations from crwsd
chtitle = msgbox.input("Enter a legend's title",
        "Concentration Charts", "Conc. (m)g/m3")
if (chtitle <> nil ) then
  LTpar = {chtitle,"Conc",true,1978,1979, 1, 12}
  av.run("schart1",LTpar)
end
Lchart  Draw charts of the load (12 months) at the center of selected
features, property Click ( runs script "schart1").
' Lchart1, One year of load from crwsd
chtitle = msgbox.input("Enter a legend's title",
        "Load Charts", "Load (m)g/s")
if (chtitle <> nil ) then
  LTpar = {chtitle, "Load", true, 1978, 1979, 1, 12}
  av.run("schart1",LTpar)
end
Qchar1 Draw charts of the flow rate (12 months) at the center of selected
features, property Click ( runs script "schart1").
' Qchart1, One year of flow from crwsd
chtitle = msgbox.input("Enter a legend's title",
        "Flow Charts", "Flow m3/s")
if (chtitle <> nil ) then
  LTpar = {chtitle, "Flow", true, 1978, 1979, 1, 12}
  av.run("schart1",LTpar)
end
264
B4 Scripts from the project ?flwprc?
pmchar1 Draws charts of the precipitation depth at the center of selected
features, for selected months, property: Click, ( executes script
"schart1")
' PMchar1,  displays multiple years of precipitation
'                  depth from gsprec or unprec
'====================================================
'' title, prefix, one_year, fy, ty, fm, tm,
'====================================================
sp = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
ln1 = "Legend title:"
ln3 = "From year (min 1960):"
ln4 = "From month:"
ln5 = "To year (max 1991)"
ln6 = "To month"
labls = {ln1,ln3,ln4,ln5,ln6}
defts = {"Precip. cm/d", "1990","1","1990","12"}
tytul = "  Specify title and time interval"
while (true)
  xlist = msgBox.Multiinput(tytul,
    "Draw charts of monthly average precipitation", labls, defts )
  if (xlist.count = 0) then
    exit
  end
  for each i in 0..4
    if (i=0)then
      continue
    end
    if (xlist.get(i).isnumber.not) then
      msgbox.error(xlist.get(i)++"is not a number",
      "Error in line "++i.asstring)
      continue
    end
  end
  fy = xlist.get(1).asnumber
  ty = xlist.get(3).asnumber
  fm = xlist.get(2).asnumber
  tm = xlist.get(4).asnumber
  if (fy < 1960) then
    msgbox.error(xlist.get(1)++" - year out of range ( < 1960 )",
      "Error in year field ")
      continue
  end
  if (ty > 1991) then
    msgbox.error(xlist.get(3)++" - year out of range ( 1991 < )",
      "Error in year field ")
265
      continue
  end
  if ((fm < 1) or (fm>12)) then
    msgbox.error(xlist.get(3)++" - month out of range (1-12)",
      "Error in year field ")
      continue
  end
   if ((tm < 1) or (tm>12)) then
    msgbox.error(xlist.get(4)++" - month out of range (1-12)",
      "Error in year field ")
      continue
  end
  break
end
  LTpar = {xlist.get(0), "PM", false, fy, ty, fm, tm}
  av.run("schart1",LTpar)
pmchar1u Draws charts of the precipitation depth, property: Update
'Pmchar1u.ave
'multiple years data
'update event for "draw charts of precipitation"
' Is enabled when a theme is active and first
theView = av.GetActiveDoc
if (theView.GetEditableTheme <> NIL) then
  SELF.SetEnabled(FALSE)
  exit
end
xx = theView.GetActiveThemes
if(xx.count <> 0) then
  visnm = xx.get(0).getname
  if (( visnm = "unprec") or (visnm = "gsprec")) then
     SELF.SetEnabled(TRUE)
     exit
  end
end
SELF.SetEnabled(FALSE)
qmchar1 Draws charts of the flow rate at the center of selected features, for
selected months, property: Click, (runs script "schart1",)
' QMchar1,  multiple years of flow from gsflow or unflow
'====================================================
'' title, prefix, one_year, fy, ty, fm, tm,
'====================================================
sp = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
ln1 = "Legend title:"
ln3 = "From year (min 1960):"
ln4 = "From month:"
ln5 = "To year (max 1991)"
266
ln6 = "To month"
labls = {ln1,ln3,ln4,ln5,ln6}
defts = {"Flow m3/s", "1990","1","1990","12"}
tytul = "  Specify title and time interval"
while (true)
  xlist = msgBox.Multiinput(tytul,
    "Draw charts of monthly average flow rate", labls, defts )
  if (xlist.count = 0) then
    exit
  end
  for each i in 0..4
    if (i=0)then
      continue
    end
    if (xlist.get(i).isnumber.not) then
      msgbox.error(xlist.get(i)++"is not a number",
      "Error in line "++i.asstring)
      continue
    end
  end
  fy = xlist.get(1).asnumber
  ty = xlist.get(3).asnumber
  fm = xlist.get(2).asnumber
  tm = xlist.get(4).asnumber
  if (fy < 1960) then
    msgbox.error(xlist.get(1)++" - year out of range ( < 1960 )",
      "Error in year field ")
      continue
  end
  if (ty > 1991) then
    msgbox.error(xlist.get(3)++" - year out of range ( 1991 < )",
      "Error in year field ")
      continue
  end
  if ((fm < 1) or (fm>12)) then
    msgbox.error(xlist.get(3)++" - month out of range (1-12)",
      "Error in year field ")
      continue
  end
   if ((tm < 1) or (tm>12)) then
    msgbox.error(xlist.get(4)++" - month out of range (1-12)",
      "Error in year field ")
      continue
  end
  break
end
theView = av.GetActiveDoc
lstact = theView.GetActiveThemes
for each t in lstact
  if ( t.getname = "unflow") then
    LTpar = {xlist.get(0), "Qm", false, fy, ty, fm, tm}
    av.run("schart1",LTpar)
    exit
  end
  if ( t.getname = "gsflow") then
267
    LTpar = {xlist.get(0), "M", false, fy, ty, fm, tm}
    av.run("schart1",LTpar)
    exit
  end
end
qmchar1u Draws charts of the flow rate, property: Update
'Qmchar1u.ave
'multiple years data
'update event for "draw charts of flow"
' Is enabled when the theme is active and first
theView = av.GetActiveDoc
if (theView.GetEditableTheme <> NIL) then
  SELF.SetEnabled(FALSE)
  exit
end
xx = theView.GetActiveThemes
if(xx.count <> 0) then
  visnm = xx.get(0).getname
  if (( visnm = "unflow") or (visnm = "gsflow")) then
     SELF.SetEnabled(TRUE)
     exit
  end
end
SELF.SetEnabled(FALSE)
schart1 Draws charts, is executed from such scripts as pmchar1 and
qmchar1 (Adopted from ESRII examples supplied with Avenue)
' MakeBarChartSpotSymbols
' title, prefix, one_year, fy, ty, fm, tm,
ltitle = self.get(0)
prefix = self.get(1)
one_year = self.get(2)
fy = self.get(3)
ty = self.get(4)
fm = self.get(5)
tm = self.get(6)
' title for legend
'ltitle = "Flow m3/s"
' prefix (field name = prefix + 01..12  or prefix + yr + mt)
'prefix = "M"
' one year will be displayed ???
'one_year = false
'fy = 1988
'fm = 1
'ty = 1990
'tm = 12
' optional legend color
if(one_year) then
268
  fy = 1989
  ty = 1989
  fm = 1
  tm = 12
end
'Script.The.SetNumberFormat("d.ddddd")
'The max. bar height and width are calculated as perc. of height of
'displayed area. The largest bar is drawn at this height and the rest
'are scaled accordingly. A value of 0.1 means the largest bar will be
'0.1 of the height of the current display. Four sizes (small, medium,
'large and x-large) are programmed as examples.
bar_size = MsgBox.ListAsString ({"Small","Medium","Large","X-
Large"},"Select bar size:","Bar Symbols")
if (bar_size = "Small") then
  max_bar_height = 0.1
  bar_width = 0.01
  legend_gridlines = 2
elseif (bar_size = "Medium") then
  max_bar_height = 0.2
  bar_width = 0.02
  legend_gridlines = 3
elseif (bar_size = "Large") then
  max_bar_height = 0.3
  bar_width = 0.03
  legend_gridlines = 4
elseif (bar_size = "X-Large") then
  max_bar_height = 0.4
  bar_width = 0.04
  legend_gridlines = 5
else
  exit  'Cancel selected'
end
'Number of gridlines on legend bar. Uncomment the following line
'to override above settings.
legend_gridlines = 4
legend_color = Color.GetCyan
'draw_gridlines = MsgBox.YesNo("Draw gridlines on the bars?","Bar
Symbols",False)
draw_gridlines = true
'Point size of text used in legend
leg_text_size = 8
'To ignore specific data values (eg., those that mean "nodata") put
'the values in this list and they will not be charted. This list
'should always contain 0, to prevent drawing zero size bars.
ignore_values = {0}
'List of colors
'Make your own custom colors here and make sure to add to both
'the color_list and also color_names...
pink = Color.Make
pink.SetRGBList({255,105,180})
olive = Color.Make
olive.SetRGBList({188,238,104})
orange = Color.Make
orange.SetRGBList({255,69,0})
gold = Color.Make
269
gold.SetRGBList({255,215,0})
maroon = Color.Make
maroon.SetRGBList({255,52,179})
color_list = {Color.GetBlue, Color.GetCyan, gold,
              Color.GetGray, Color.GetGreen, Color.GetMagenta,
maroon,
              olive, orange, pink, Color.GetRed, Color.GetYellow }
color_names = {"Blue", "Cyan", "Gold", "Gray", "Green", "Magenta",
               "Maroon", "Olive", "Orange", "Pink",
               "Red", "Yellow"}
'Number of colors
num_colors = 12
theView = av.GetActiveDoc
theProjection = theView.GetProjection
project_flag = theProjection.IsNil.Not  'true if projected
theTheme = theView.GetActiveThemes.Get(0)  'Get first active theme
theFTab = theTheme.GetFTab
shpfield = theFtab.FindField("Shape")
gra_list = theView.GetGraphics
'This section prompts the user for the fields in the
'FTab to generate the bar symbols from.
f= " "
max_field_prec = 0      'Field precision of selected fields
selected_fields = {}    'Fields selected by user
numeric_fields = {}     'Numeric fields in the FTab
field_aliases = {}      'List of field aliases
all_fields = theFtab.GetFields
'Build list of numeric fields from all fields.
'Also list of field aliases to display to user.
for each f in all_fields
  if (f.IsTypeNumber) then
    numeric_fields.Add(f)
    field_aliases.Add(f.GetAlias)
  end
end  'for
'Select fields for bar symbols
user_colors = {}
done = FALSE
field_count = 0
for each yr in fy..ty
  for each mt in 1..12
    if (( yr = fy) and ( mt < fm)) then
      continue
    end
    if (( yr = ty) and ( mt > tm)) then
      continue
    end
    if (mt < 10 ) then
      txt = "0"+mt.AsString
    else
      txt = mt.AsString
    end
    if(one_year) then
      fname = prefix+txt
270
    else
      fname = prefix+yr.AsString+txt
    end
  if (fname <> nil) then
    field_count = field_count + 1
    f = theFTab.findfield(fname)
    selected_fields.Add(f)
    user_colors.Add(color_list.Get(field_count - 1 mod num_colors))
    'Store max field precision of selected fields for later use.
    max_field_prec = (max_field_prec Max f.GetPrecision)
  else
    'Cancel selected.
    done = TRUE
  end 'if
end   'month
end   'year
field_count = selected_fields.Count
if (field_count = 0) then
  'User did not select any fields to symbolize
  exit
end
'Set bar height and width in page display units
view_extent = theView.GetDisplay.ReturnVisExtent
max_bar_height = view_extent.GetHeight * max_bar_height
bar_width = view_extent.GetHeight * bar_width
'Iterate thru selection bitmap or all records in FTab if no
selection.
iter = theFtab.GetSelection
num_records = iter.Count
'If no selected set, set iteration to all records in FTab.
if (num_records = 0) then
  iter = theFTab
  num_records = theFTab.GetNumRecords
end
min_height = 0
max_height = 0
for each rec in iter
  for each f in selected_fields
    cur_height = theFTab.ReturnValueNumber(f,rec)
    if (ignore_values.FindByValue(cur_height) > -1) then
      'Ignore values user wants to ingore
      continue
    end
    min_height = (min_height Min cur_height)
    max_height = (max_height Max cur_height)
  end  'for
end   'for
'Since the max height of a bar could be negative, find abs value of
'both min and max values to determine a scale factor. When building
the
'actual bar for a field, divide field value by this scale factor.
That
'way the maximum bar height (max_bar_height) will = the max field
value,
271
'whether positive or negative; all other field values are scaled
accordingly.
ht_scale_factor = (min_height.Abs) Max (max_height.Abs)
'Figure out break points for legend to allow adding gridlines to
legend
'and (optionally) actual bars on map. This set of code figures out a
'round number larger than the maximum field value, then divides that
'number by the number of legend classes desired. Then it rounds the
break
'point to a "nice" round number. E.g., given a max field value of
123,
'and 3 classes, this set of code will create a legend with break
points
'at 45, and a top value of 135.
if (ht_scale_factor < 1) then
  theLog = ht_scale_factor.Log(10).Floor
else
  theLog = ht_scale_factor.Log(10).Truncate
end  'if
x = ht_scale_factor / (10^(theLog))
y = (10 * x + 0.5).round * 10.^(theLog) / 10
x = y / legend_gridlines
if (x < 1) then
  theLog = x.Log(10).Floor
else
  theLog = x.Log(10).Truncate
end  'if
x2 = x / (10^(theLog))
legend_break_val = (2 * x2 + 0.5).round * 10.^(theLog) / 2
'Map value to display page units
legend_break_height = legend_break_val / ht_scale_factor *
max_bar_height
'Start drawing bar symbols
gra_list.UnselectAll
av.ShowStopButton
av.ShowMsg("Creating bar symbols...")
counter = 0
gra_group = GraphicGroup.Make
'For each selected record make the bars
for each rec in iter
  acolor = -1  'initialize color index
  'find the center of the feature to place bar symbol at
  ctr = theFtab.ReturnValue(shpfield,rec).ReturnCenter
  if (project_flag) then
    'Project the centroid if the view has a projection
    ctr = ctr.ReturnProjected(theProjection)
  end
  xcen = ctr.GetX
  ycen = ctr.GetY
  'Add line signaling zero in bar chart
  line_start_pt = (xcen - ((field_count * bar_width) / 2))@ycen
  line_end_pt = line_start_pt + ((bar_width * field_count)@0)
  aline = Line.Make(line_start_pt,line_end_pt)
  gr = GraphicShape.Make(aline)
  gra_group.Add(gr)
272
  'set starting point for drawing bars
  bar_start_pt = line_start_pt
  bar_count = 0  'number of bars drawn
  for each f in selected_fields
    bar_count = bar_count + 1
    acolor = acolor + 1
    'Convert field value to bar height;divide by height scale factor.
    thevalue = theFTab.ReturnValueNumber(f,rec)
    aheight = (thevalue / ht_scale_factor) * max_bar_height
    if (ignore_values.FindByValue(thevalue) > -1) then
      'Don't draw values user wants to ingore
      bar_start_pt = bar_start_pt + (bar_width@0)
      continue
    end  'if
    'draw the bar for the field
    abox = rect.Make(bar_start_pt,bar_width@aheight)
    gr = GraphicShape.Make(abox)
    'the symbol of a poly is a rasterfill, thus SetStyle request
works.
    gr.GetSymbol.SetStyle(#RASTERFILL_STYLE_SOLID)
    gr.GetSymbol.SetColor(user_colors.Get(acolor))
    gra_group.Add(gr)
    'Draw reference lines on bar to indicate value
    if (draw_gridlines) then
      num_tics = (aheight.Abs / legend_break_height).Floor
      c = 0
      while (c <> num_tics)
        c = c + 1
        if (aheight < 0) then
          tic_start_pt = bar_start_pt - (0@(c * legend_break_height))
        else
          tic_start_pt = bar_start_pt + (0@(c * legend_break_height))
        end  'if
        tic_end_pt = tic_start_pt + (bar_width@0)
        aline = Line.Make (tic_start_pt,tic_end_pt)
        gr = GraphicShape.Make(aline)
        gra_group.Add(gr)
      end  'while
    end  'if
    bar_start_pt = bar_start_pt + (bar_width@0)
  end  'for each f in selected_fields
  'Clone bar chart and add it to the graphic list. Then reuse graphic
group.
  'AddBatch used so that once ALL bar symbols for ALL records are
created
  'they are drawn to the screen. Using Add request is much slower.
  gg = gra_group.Clone
  gra_list.AddBatch(gg)
  'Add bar chart to the Theme's graphic list so that when the
  'theme is not drawn, the bar symbols won't draw either.
  theTheme.GetGraphics.Add(gg)
  gra_group.Empty
  counter = counter + 1
  progress = (counter / num_records) * 100
  more = av.SetStatus(progress)
273
  if (Not more) then
    'Break if user presses Stop button.
    break
  end
end  ' for each rec in iter
gra_list.UnselectAll
if (not ((num_records = 1) and (aheight = 0))) then
  'Special case where only 1 record selected, and the total of the
fields
  'of the record is zero; essentially no bars are drawn, so endbatch
  'should not be executed.
  gra_list.EndBatch
end
'Start building the legend.
'Set text size for legend
text_sym = av.GetSymbolWin.ReturnCurrentSymbol(#SYMBOL_TEXT).clone
text_sym.SetSize (leg_text_size)
'Add dummy text to get an idea for spacing of graphic elements
'Spacing of objects in legend = current point size of text.
gr = GraphicText.Make("ABC",0@0)
gr.SetSymbol (text_sym)
gr.SetSelected(TRUE)
gra_list.Add(gr)
spacing = gra_list.ReturnSelectedExtent.GetHeight
gra_list.RemoveGraphic(gr)
'Set number of decimal places for legend text equal to max field
precision
'This code builds a string like "d.ddd"
numformat = "d."
if (max_field_prec <> 0) then
  for each i in 1..max_field_prec
    numformat = numformat+"d"
  end
end  'if
'Draw legend at (0,0) then move it to the correct location
pnt = 0@0
abox = Rect.Make (pnt,bar_width@(legend_gridlines *
legend_break_height))
gr = GraphicShape.Make(abox)
gr.GetSymbol.SetStyle(#RASTERFILL_STYLE_SOLID)
gr.GetSymbol.SetColor(legend_color)
gra_group.Add(gr)
'Add "0" text in legend
gr = GraphicText.Make(0.SetFormat(numformat).AsString,
  (pnt + ((bar_width + spacing)@(-spacing / 2))))
gr.SetSymbol (text_sym)
gra_group.Add(gr)
'Draw a reference lines on bar.
for each i in 1..legend_gridlines
  line_start_pt = 0@(i * legend_break_height)
  line_end_pt = line_start_pt + (bar_width@0)
  aline = Line.Make (line_start_pt,line_end_pt)
  gr = GraphicShape.Make(aline)
  gra_group.Add(gr)
  'Add text indicating value represented by square
274
  atext = (legend_break_val * i).SetFormat(numformat).AsString
  'Add text string to right of line
  gr = GraphicText.Make(atext,(line_end_pt + (spacing@(-spacing /
2))))
  gr.SetSymbol (text_sym)
  gra_group.Add(gr)
  'gra_group.SetSelected (TRUE)
  'Clone graphic group;otherwise it would get deleted on Empty
  'gra_list.Add(gra_group.clone)
  'gra_group.Empty
end  'for
gra_group.SetSelected (TRUE)
'Clone graphic group;otherwise it would get deleted on Empty
gra_list.Add(gra_group.clone)
gra_group.Empty
gra_list.UngroupSelected   'Workaround
gra_list.GroupSelected
extent = gra_list.ReturnSelectedExtent
x = extent.ReturnOrigin.GetX
y = extent.GetTop + spacing
gr = GraphicText.Make(ltitle,(0@y))
'gr = GraphicText.Make("Flow Rate",(x@y + (x@0)))
'gr = GraphicText.Make("TEXT EXAMPLE",(x@y + ((spacing * 2)@0)))
gr.SetSymbol (text_sym)
gra_group.Add(gr)
'  acolor = acolor + 1   'Get next color
'  y = y + (spacing * 2) 'Move y up for next box
'end  'for
gra_group.SetSelected(TRUE)
gra_list.Add(gra_group)
gra_list.UngroupSelected  'Workaround
gra_list.GroupSelected
'Draw white box to place legend in
extent = gra_list.ReturnSelectedExtent
origin = extent.ReturnOrigin - (spacing@spacing)
size = extent.ReturnSize + ((2*spacing)@(2*spacing))
arect = Rect.Make(origin,size)
gr = GraphicShape.Make(arect)
gr.GetSymbol.SetStyle(#RASTERFILL_STYLE_SOLID)
gr.GetSymbol.SetColor(Color.GetWhite)
gra_list.Add(gr)
gra_list.MoveSelectedToFront
gr.SetSelected(TRUE)
gra_list.GroupSelected
'Move legend to lower-left corner of View
alegend = gra_list.GetSelected.Get(0)
alegend.Invalidate
alegend.SetOrigin(theView.GetDisplay.ReturnVisExtent.ReturnOrigin)
alegend.Invalidate
'Merge the graphic legend into the theme's graphic list
theTheme.GetGraphics.Merge(theView.GetGraphics.GetSelected)
gra_list.UnselectAll
av.ClearMsg
av.ClearStatus
275
movie2 Displays charts in a sentence, category: tools, property: apply (script
qmchar1u is used in the property: Update)
'movie2.ave
theView = av.GetActiveDoc
theThemes = theView.GetActiveThemes
p = theView.GetDisplay.ReturnUserPoint
t = thethemes.get(0)
if (t.CanSelect.not) then
  exit
end
t.SelectByPoint(p,#VTAB_SELTYPE_NEW )
recs = t.FindByPoint(p)
if(recs.count = 0) then
  exit
end
vv = t.getftab.updateselection
selchart = {"Horizontal", "Vertical"}
c = msgbox.choiceasstring(selchart, "Make a selection",
    "Chart type selection")
if (c = nil) then
  exit
end
theView = av.GetActiveDoc
visnm = theView.GetVisibleThemes.get(0).getname
if ( visnm = "Gsflow") then
     prefix = "M"
     xnote = "Available: 1940 - 1991"
     if(c = "Horizontal") then
       TheChart = av.getproject.FindDoc("MovieMh")
     end
     if(c = "Vertical") then
       TheChart = av.getproject.FindDoc("MovieMv")
    end
end
if ( visnm = "unflow") then
     prefix = "Qm"
     xnote = "Available: 1960 - 1991"
     if(c = "Horizontal") then
       TheChart = av.getproject.FindDoc("MovieQmh")
     end
     if(c = "Vertical") then
       TheChart = av.getproject.FindDoc("MovieQmv")
    end
end
CHtable = TheChart.GetVtab
sp = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"
ln4 = "First year:"
ln5 = "Last year:"
labls = {sp, ln4,ln5}
fy = 1960
276
ty = 1991
fm = 1
tm = 12
defts = {" ", fy.asstring, ty.asstring}
while (true)
  xlist = msgBox.Multiinput(xnote,"Movie2", labls, defts )
  if (xlist.count = 0) then
    exit
  end
  if ((xlist.get(1).isnumber.not) or (xlist.get(1) < 1940)) then
    msgbox.error(xlist.get(1)++"is not a correct year", "Error in
field #1")
    continue
  end
  if ((xlist.get(2).isnumber.not) or (xlist.get(2) > 1991)) then
    msgbox.error(xlist.get(2)++"is not a correct year", "Error in
field #2")
    continue
  end
  break
end
av.showmsg(" Looking for the maximum value to set Y scale . . .")
fy = xlist.get(1).asnumber
ty = xlist.get(2).asnumber
bmap = Chtable.getselection
rec = -1
rec = bmap.getnextset(rec)
step = -1
lablst = list.make
'for each i in 0..11
'  lablst.add("x")
'end
'======== find maximum value  to set Y(or X) scale ========
xxmax = 0
for each yr in fy..ty
 for each mt in 1..12
  if (( yr = fy) and ( mt < fm)) then
    continue
  end
  if (( yr = ty) and ( mt > tm)) then
    continue
  end
  step = step + 1
  'if ( step < 12 ) then
  '  continue
  'end
  if (mt < 10 ) then
    txt = "0" + mt.AsString
  else
    txt = mt.AsString
  end
  name = prefix + yr.AsString + txt
  XFld=Chtable.FindField(name)
  xx22 = Chtable.returnvalueNumber(xfld,rec)
  if ( xx22 > xxmax ) then
277
    xxmax = xx22
  end
 end
end
nomonths = step
msgbox.info("Maximum value is"++xxmax.asstring,"Maximum")
av.clearmsg
av.showstopbutton
if(thechart.getwin.isopen.not) then
  thechart.getwin.open
  thechart.getwin.minimize
end
TheList=TheChart.GetFields
TheFList = TheChart.getVtab.GetFields
if(c = "Horizontal") then
  thechart.getYaxis.setboundsmax(xxmax)
end
if(c = "Vertical") then
  thechart.getXaxis.setboundsmax(xxmax)
end
step = -1
for each yr in fy..ty
av.showmsg(" YEAR: "++yr.asstring)
 for each mt in 1..12
  if (( yr = fy) and ( mt < fm)) then
    continue
  end
  if (( yr = ty) and ( mt > tm)) then
    continue
  end
  step = step + 1
  if ( step = 12 ) then
    if(msgbox.miniYesNo("Start ?", True).not) then
      exit
    end
    thechart.getwin.restore
    if(thechart.getwin.isopen.not) then
      thechart.getwin.activate
    end
  end
  if (mt < 10 ) then
    txt = "0" + mt.AsString
  else
    txt = mt.AsString
  end
  xstatus = av.setstatus(100 * step / nomonths)
  if(xstatus.not) then
     rlt = msgbox.yesno("Do you really want to stop?","Stop movie",
true)
     if(rlt) then
       rlt2 = msgbox.yesno("Do you want to minimize the chart
window?",
           "Close Window ?", true)
       if(rlt2) then
         thechart.getwin.minimize
278
       end
       exit
     else
       av.ClearStatus
       av.showstopbutton
     end
  end
  name = prefix + yr.AsString + txt
  NewTitle = txt + " / " + yr.asstring
  NewFld=TheChart.getVtab.FindField(name)
  TheList.Remove(0)
  Thelist.add(newfld)
  TheChart.GetTitle.SetName(NewTitle)
  theChart.SetSeriesFromRecords(true)
  theChart.Getwin.Open
 end
end
av.ClearStatus
rlt2 = msgbox.yesno("Do you want to minimize the chart?",
           "Close Window ?", true)
       if(rlt2) then
         thechart.getwin.minimize
       end
aliaset  Sets the alias names for fields, that describe a chart axis.
'aliaset.ave
xFtable = av.GetActiveDoc.getvtab
prefix = "QM"
fy = 1960
ty = 1992
fm = 1
tm = 9
for each yr in fy..ty
 for each mt in 1..12
  if (( yr = fy) and ( mt < fm)) then
    continue
  end
  if (( yr = ty) and ( mt > tm)) then
    continue
  end
  if (mt < 10 ) then
    txt = "0" + mt.AsString
  else
    txt = mt.AsString
  end
  name = prefix + yr.AsString + txt
  XFld=xFtable.FindField(name)
txalias = mt.asstring+"/"+yr.asstring
xxx = XFld.setalias(txalias)
 end
end
279
B5 Scripts from the project ?tools?
order6 Determines the order of a stream/watershed in a flow system
'order6.ave  Adds a field that contains a numbering
'            system to specify the stream order
'            in a flow system.
TBunit = av.GetActiveDoc
xxx = TBunit.getGUI
if ( xxx <> "Table") then
  xxx2 = TBunit.asstring++"is active"
  msgbox.warning("A Table must be active", xxx2)
  exit
end
VTunit = TBunit.getVtab
'assume the default fields in UNIT table:
TXunit = "Unit"
TXnext = "Downstream"
FDunit = VTunit.FindField(TXunit)
FDnext = VTunit.FindField(TXnext)
'create list of fields that are in VTunit
LSFDunit = VTunit.GetFields
'if the default fields can not be found, ask user for required
fields:
if(FDunit=nil) then
  'Select current_unit id field
  FDunit = MsgBox.List(LSFDunit, "Select a field that contains"
           ++NL++" the watershed/stream ID",
            "Unit_id Selection")
end
'if not selected, quit
IF ( FDunit = nil) then
  exit
end
if(FDnext=nil) then
  'Select downstream_unit id field
  FDnext = MsgBox.List(LSFDunit, "Select a field that contains"++NL++
             "the downstream unit ID", "Next_id Selection")
end
IF ( FDnext = nil) then
  exit
end
TXorderField = msgbox.input("Enter the name of order field ",
"Order Field Selection", "Order")
FDorder = vtunit.FindField(TXorderField)
xx = false
if (FDorder = nil) then
  xx = msgbox.YesNo( TXorderField++"field is not in the table "
  ++TBunit.asString+nl+"Do you want to create this field ?",
   "Field not Found !", true)
'end
  if (xx.not) then
280
    exit
  end
 'check if the VTunit can be edited if not, set it editable
 if(VTunit.isEditable.not) then
  VTunit.SetEditable(true)
 end
 if(VTunit.CanAddFields) then
   f1  =  Field.Make( TXorderfield,#FIELD_SHORT, 5, 0 )
   'Add fields
   VTunit.AddFields({f1})
 else
  msgBox.warning("Can not add a field to"++VTunit.asString,
                   "Can not edit table")
  exit
 end
else
 f1 = FDorder
 if(VTunit.isEditable.not) then
  VTunit.SetEditable(true)
 end
end
LSunit = list.make
LSnext = list.make
LSord = list.make
LSrecnxt = list.make
nx = VTunit.GetNumRecords
nn = nx - 1
nst = 100/nx   'variable used in status displaying
av.ShowMsg("Creating lists ...")
for each rec in VTunit
  av.ShowMsg("Creating lists ..."++rec.AsString)
  av.SetStatus(rec * nst)
  LSnext.Add(VTunit.ReturnValueNumber(FDnext, rec))
  LSunit.Add(VTunit.ReturnValueNumber(FDunit, rec))
  LSord.Add(1)
  LSrecnxt.Add(nx)
end
LSrecnxt.Add(nx)
'search for first order streams/watersheds and create list of the
'record numbers pointed by the "next/downstream unit" field
for each i in 0..nn
  av.ShowMsg("Searching for first order streams/watersheds
..."++i.asString)
  av.SetStatus(i * nst)
  for each j in 0..nn
    if ( LSnext.get(i) = LSunit.get(j) ) then
      LSord.set(j , 0 )
      LSrecnxt.set(i , j)
      Break
    end
  end
end
'write downstream record pointers into field f2
'for each rec in VTunit
'  VTunit.SetValue( f2, rec, LSrecnxt.Get( rec ))
281
'end
'determine order of the rest of streams
for each i in 0..nn
  av.ShowMsg("Calculating order ..."++i.asString)
  av.SetStatus(i * nst)
  if ( LSord.get(i) <> 1 ) then
    continue
  end
  j = LSrecnxt.get(i)
  k = 2
  while (j <> nx)
    if ( LSord.get(j) >= k ) then
      break
    end
    LSord.set(j , k )
    j = LSrecnxt.get(j)
    k = k + 1
  end 'while
end 'i
'write stream/watershed order into Table
for each rec in VTunit
  VTunit.SetValue( f1, rec, LSord.Get( rec ))
end
'refresh table and set it "not editable"
VTunit.Refresh
if(VTunit.isEditable) then
    VTunit.SetEditable(false)
end
upavg2 calculates weighted average over upstream units
' upavg2.ave calculates weighted average
'    for upstream units:
'    output = upstr_sum(input*wght)/upstr_sum(wght)
'==================================================
' note: dbf table contains a dummy (first) record
' that can influence calculations !!!
TBunit = av.GetActiveDoc
xxx = TBunit.getGUI
if ( xxx <> "Table") then
xxx2 = TBunit.asstring++"is active"
msgbox.warning("A Table must be active", xxx2)
exit
end
TheFtab = TBunit.getVtab
' Ask user for required fields:
TXunit = "unit_id"
TXnext = "unit_nx"
TXorder = "order"
TXitem = "input"
TXadd = "output"
TXwgt = "weight"
FDunit = theFtab.FindField(TXunit)
282
FDnext = theFtab.FindField(TXnext)
FDorder = theFtab.FindField(TXorder)
FDadd = theFtab.FindField(TXadd)
FDitem = theFtab.FindField(TXitem)
FDarea = theFtab.FindField(TXwgt)
' Make a list of VTunit fields
LSFDunit = theFtab.GetFields
' If the default fields can not be found, ask user
' for the required fields:
if(FDunit=nil) then
  ' Select current_unit id field (from entity)
  FDunit = MsgBox.List(LSFDunit, "Select a field that contains"
      ++NL++"the watershed/stream ID", "From-unit Selection")
end
' If not selected, quit
IF (FDunit = nil) then
  exit
end
if(FDnext=nil) then
  ' Select downstream_unit id field
  FDnext = MsgBox.List(LSFDunit, "Select a field that contains"
       ++NL++" the downstream unit ID", "To-unit Selection")
end
' If not selected, quit
IF ( FDnext = nil) then
  exit
end
if(FDorder=nil) then
  ' Select order field
  FDorder = MsgBox.List(LSFDunit, "Select field that contains"
     ++NL++" the watershed/stream order","Order field Selection")
end
' If not selected, quit
IF ( FDorder = nil) then
  xxx = msgbox.info("Create a field of stream order",
       "Missing fields")
  exit
end
if(FDitem=nil) then
  ' Select field that contains values to be averaged
  FDitem = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"values to be averaged", "Feature Selection")
end
' If not selected, quit
IF ( FDitem = nil) then
  exit
end
if(FDarea=nil) then
  ' Select field that contains weight
  FDarea = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"weight", "Weight Selection")
end
' If not selected, quit
IF ( FDarea = nil) then
  exit
283
end
' Prompt for a name (name of the field, that will be created)
TXadd = msgbox.input("Enter the name of output field ",
"Output Field Selection", "output")
if (TXadd = nil) then
  exit
end
FDadd = theFtab.FindField(TXadd)
xx = false
if (FDadd = nil) then
  xx = msgbox.YesNo( TXadd++"field is not in the table "
  ++TBunit.asString+nl+"Do you want to create this field ?",
   "Field not Found !", true)
'end
  if (xx.not) then
    exit
  end
  'check the setting of "input" field
  fenum = FDitem.gettype
  fprec = FDitem.getprecision
  fwidth = FDitem.getwidth
  xxx1 = msgbox.input("Please specify precision"++
    "(decimal part) of the output field",
    "Width of the new field" , fprec.asstring)
   fprec = xxx1.asnumber
  IF ( fprec = nil) then
    exit
  end
 xxx2 = msgbox.input("Please specify total width of the output
field",
   "Width of the new field" , fwidth.asstring)
   fwidth = xxx2.asnumber
  IF ( fwidth = nil) then
    exit
  end
  'check if the theFtab can be edited if not, set it editable
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
  ' Create a new field
  if(theFtab.CanAddFields) then
    FDadd = field.Make(TXadd,fenum,fwidth,fprec)
    theFtab.AddFields({FDadd})
  else
    msgBox.warning("Can not add a field to"++theFtab.asString,
                   "Can not edit table")
    theFtab.SetEditable(false)
    exit
  end
else
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
end
'create lists
284
ltunit = list.make
ltnext = list.make
ltorder = list.make
ltitem = list.make
ltadd = list.make
unnx = theFTab.GetNumRecords
unnn = unnx - 1
dcarea = dictionary.make(unnx)
dcmass = dictionary.make(unnx)
for each rec in theFTab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  ltunit.Add(Nunit)
  ltnext.Add(theFTab.ReturnValueNumber(FDnext, rec))
  ltorder.Add(theFTab.ReturnValueNumber(FDorder, rec))
  Narea = theFTab.ReturnValueNumber(FDarea, rec)
  if (Narea = 0 ) then
    msgbox.error("The weight can not be zero !"++
     NL++"record:"++rec.asstring++"field:"++
     FDarea.asstring, "Division by zero" )
     theFtab.SetEditable(false)
     exit
  end
  Nmass = theFTab.ReturnValueNumber(FDitem, rec) * Narea
  dcarea.add(Nunit, Narea )
  dcmass.add(Nunit, Nmass )
end
' find maximum order
unmaxord = 1
for each i in 0..unnn
  av.ShowMsg("Finding maximum order ..."++i.asString)
  istatus = i * 100 / unnn
  av.SetStatus(istatus)
  if (ltorder.get(i) > unmaxord ) then
        unmaxord = ltorder.get(i)
  end
end
'calculate cumulative values
unmaxord1 = unmaxord - 1
for each k in 1..unmaxord1
  av.ShowMsg("Calculating cumulative values ..."++k.asString)
  istatus = k * 100 / unmaxord
  av.SetStatus(istatus)
  for each i in 0..unnn
    if ( ltorder.get(i) <> k ) then
      continue
    end
    Nunit = ltunit.get(i)
    Nnext = ltnext.get(i)
    Nxmass = dcmass.get(Nunit) + dcmass.get(Nnext)
    Nxarea = dcarea.get(Nunit) + dcarea.get(Nnext)
    dcmass.set(Nnext, Nxmass)
    dcarea.set(Nnext, Nxarea)
  end
end
av.clearMsg
285
av.clearstatus
'write results to Ftab
for each rec in theFtab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  Xavg = dcmass.get(Nunit) / dcarea.get(Nunit)
  TheFtab.SetValue( FDadd, rec, Xavg )
end
theFtab.Refresh
if(TheFtab.isEditable) then
    theFtab.SetEditable(false)
end
cumul2 Accumulates values, going downstream (flow accumulation)
' cumul2.ave Adds a field or writes to the existing
'            field the accumulated values. Summation
'            is performed downstream, along the flow
'            path.
' note: dbf table contains a dummy (first) record
' that can influence calculations !!!
TBunit = av.GetActiveDoc
xxx = TBunit.getGUI
if ( xxx <> "Table") then
xxx2 = TBunit.asstring++"is active"
msgbox.warning("A Table must be active", xxx2)
exit
end
TheFtab = TBunit.getVtab
' Ask user for needed fields:
TXunit = "unit_id"
TXnext = "unit_nx"
TXorder = "order"
TXitem = "item_x"
FDunit = theFtab.FindField(TXunit)
FDnext = theFtab.FindField(TXnext)
FDorder = theFtab.FindField(TXorder)
'FDadd = theFtab.FindField(TXadd)
FDitem = theFtab.FindField(TXitem)
' Make a list of VTunit fields
LSFDunit = theFtab.GetFields
' If the default fields can not be found, ask user for
' the required fields:
if(FDunit=nil) then
  ' Select current_unit id field (from entity)
  FDunit = MsgBox.List(LSFDunit, "Select a field that contains"
      ++NL++"the watershed/stream ID", "From-unit Selection")
end
' If not selected, quit
IF (FDunit = nil) then
  exit
end
if(FDnext=nil) then
  ' Select downstream_unit id field
  FDnext = MsgBox.List(LSFDunit, "Select a field that contains"
286
       ++NL++" the downstream unit ID", "To-unit Selection")
end
' If not selected, quit
IF ( FDnext = nil) then
  exit
end
if(FDorder=nil) then
  ' Select order field
  FDorder = MsgBox.List(LSFDunit, "Select field that contains"
     ++NL++" the watershed/stream order","Order field Selection")
end
' If not selected, quit
IF ( FDorder = nil) then
  xxx = msgbox.info("Create a field of stream order",
       "Missing fields")
  exit
end
if(FDitem=nil) then
  ' Select field that contains values to be accumulated
  FDitem = MsgBox.List(LSFDunit, "Select a field that contains"
  ++NL++"values to be summed", "Feature Selection")
end
' If not selected, quit
IF ( FDitem = nil) then
  exit
end
' Prompt for a name (name of the field, that will be created)
TXadd = msgbox.input("Enter the name of output field ",
"Output Field Selection", "Accumulated")
FDadd = theFtab.FindField(TXadd)
xx = false
if (FDadd = nil) then
  xx = msgbox.YesNo( TXadd++"field is not in the table "
  ++TBunit.asString+nl+"Do you want to create this field ?",
   "Field not Found !", true)
'end
  if (xx.not) then
    exit
  end
  'check the setting of "item" field
  'ESRI gives no information how wide a field can be!
  fenum = FDitem.gettype
  fprec = FDitem.getprecision
  fwidth = FDitem.getwidth
  if(fwidth < 13) then
      fwidth = fwidth + 3
  elseif (fwidth = 13) then
    fwidth = 15
  elseif (fwidth > 13) then
  xxx = msgbox.input("Please specify a width of output field",
   "Width of the new field" , fwidth.asstring)
    fwidth = xxx.asnumber
  end
  IF ( fwidth = nil) then
    exit
287
  end
  'check if the theFtab can be edited if not, set it editable
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
  ' Create a new field
  if(theFtab.CanAddFields) then
    FDadd = field.Make(TXadd,fenum,fwidth,fprec)
    theFtab.AddFields({FDadd})
  else
   msgBox.warning("Can not add a field to"++theFtab.asString,
                   "Can not edit table")
    exit
  end
else
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
end
'create lists
ltunit = list.make
ltnext = list.make
ltorder = list.make
ltitem = list.make
ltadd = list.make
unnx = theFTab.GetNumRecords
unnn = unnx - 1
dcadd = dictionary.make(unnx)
for each rec in theFTab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  ltunit.Add(Nunit)
  ltnext.Add(theFTab.ReturnValueNumber(FDnext, rec))
  ltorder.Add(theFTab.ReturnValueNumber(FDorder, rec))
  Nitem = theFTab.ReturnValueNumber(FDitem, rec)
'  ltitem.Add(Nitem)
  dcadd.add(Nunit, Nitem )
end
' find maximum order
unmaxord = 1
for each i in 0..unnn
  av.ShowMsg("Finding maximum order ..."++i.asString)
  istatus = i * 100 / unnn
  av.SetStatus(istatus)
  if (ltorder.get(i) > unmaxord ) then
        unmaxord = ltorder.get(i)
  end
end
'calculate cumulative values
unmaxord1 = unmaxord - 1
for each k in 1..unmaxord1
  av.ShowMsg("Calculating cumulative values ..."++k.asString)
  istatus = k * 100 / unmaxord
  av.SetStatus(istatus)
  for each i in 0..unnn
    if ( ltorder.get(i) <> k ) then
288
      continue
    end
    Nunit = ltunit.get(i)
    Nnext = ltnext.get(i)
    Nxvalue = dcadd.get(Nunit) + dcadd.get(Nnext)
    dcadd.set(Nnext, Nxvalue)
  end
end
av.clearMsg
av.clearStatus
'write results to Ftab
for each rec in theFtab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  TheFtab.SetValue( FDadd, rec, dcadd.get(Nunit) )
end
theFtab.Refresh
if(TheFtab.isEditable) then
    theFtab.SetEditable(false)
end
decom2 calculates the difference between the inflows and the outflow, the
reverse process to the flow accumulation
' decom2.ave for all modeling units calculates
' the difference between sum of inputs and the
' output ( deaccumulate values)
' note: dbf table contains a dummy (first) record
' that can influence the calculations !!!
TBunit = av.GetActiveDoc
xxx = TBunit.getGUI
if ( xxx <> "Table") then
xxx2 = TBunit.asstring++"is active"
msgbox.warning("A Table must be active", xxx2)
exit
end
TheFtab = TBunit.getVtab
' Ask user for requireded fields
TXunit = "unit_id"
TXnext = "unit_nx"
TXorder = "order"
TXitem = "input"
'TXadd = "decom_fd"
FDunit = theFtab.FindField(TXunit)
FDnext = theFtab.FindField(TXnext)
FDorder = theFtab.FindField(TXorder)
'FDadd = theFtab.FindField(TXadd)
FDitem = theFtab.FindField(TXitem)
' Make a list of VTunit fields
LSFDunit = theFtab.GetFields
' If the default fields can not be found, ask user for
' the required fields:
if(FDunit=nil) then
  ' Select current_unit id field (from entity)
289
  FDunit = MsgBox.List(LSFDunit, "Select a field that contains"
      ++NL++"the watershed/stream ID", "From-unit Selection")
end
' If not selected, quit
IF (FDunit = nil) then
  exit
end
if(FDnext=nil) then
  ' Select downstream_unit id field
  FDnext = MsgBox.List(LSFDunit, "Select a field that contains"
       ++NL++" the downstream unit ID", "To-unit Selection")
end
' If not selected, quit
IF ( FDnext = nil) then
  exit
end
if(FDorder=nil) then
  ' Select order field
  FDorder = MsgBox.List(LSFDunit, "Select field that contains"
     ++NL++" the watershed/stream order","Order field Selection")
end
' If not selected, quit
IF ( FDorder = nil) then
  xxx = msgbox.info("Create a field of stream order",
       "Missing fields")
  exit
end
if(FDitem=nil) then
  ' Select a field that contains values to be decomposed
  FDitem = MsgBox.List(LSFDunit,
          "Select a field that contains"++NL++
          "the values to be decomposed",
          "Input Field Selection")
end
' If not selected, quit
IF ( FDitem = nil) then
  exit
end
' Prompt for a name (name of the field, that will be created)
TXadd = msgbox.input("Enter the name of the output field ",
"Output Field Selection", "Decomposed")
FDadd = theFtab.FindField(TXadd)
xx = false
if (FDadd = nil) then
  xx = msgbox.YesNo( TXadd++"field is not in the table "
  ++TBunit.asString+nl+"Do you want to create this field ?",
   "Field not Found !", true)
'end
  if (xx.not) then
    exit
  end
  'check the setting of "item" field
  'width and the precision of the input field are assumed
  fenum = FDitem.gettype
  fprec = FDitem.getprecision
290
  fwidth = FDitem.getwidth
  ' Create a new field
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
  if(theFtab.CanAddFields) then
    FDadd = field.Make(TXadd,fenum,fwidth,fprec )
    theFtab.AddFields({FDadd})
  else
  msgBox.warning("Can not add a field to"
      ++theFtab.asString, "Can not edit table")
  exit
  end
else
  if(theFtab.isEditable.not) then
    theFtab.SetEditable(true)
  end
end
'create lists
ltunit = list.make
ltnext = list.make
ltorder = list.make
ltitem = list.make
ltadd = list.make
unnx = theFTab.GetNumRecords
unnn = unnx - 1
dcadd = dictionary.make(unnx)
dcdec = dictionary.make(unnx)
for each rec in theFTab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  ltunit.Add(Nunit)
  ltnext.Add(theFTab.ReturnValueNumber(FDnext, rec))
  ltorder.Add(theFTab.ReturnValueNumber(FDorder, rec))
  Nitem = theFTab.ReturnValueNumber(FDitem, rec)
  dcadd.add(Nunit, Nitem )
  dcdec.add(Nunit, Nitem )
end
' find maximum order
unmaxord = 1
for each i in 0..unnn
  av.ShowMsg("Finding maximum order ..."++i.asString)
  istatus = i * 100 / unnn
  av.SetStatus(istatus)
  if (ltorder.get(i) > unmaxord ) then
        unmaxord = ltorder.get(i)
  end
end
'calculate decomposed values
unmaxord1 = unmaxord - 1
for each k in 1..unmaxord1
  av.ShowMsg("Decumulating values ..."++k.asString)
  istatus = k * 100 / unmaxord
  av.SetStatus(istatus)
  for each i in 0..unnn
    if ( ltorder.get(i) <> k ) then
291
      continue
    end
    Nunit = ltunit.get(i)
    Nnext = ltnext.get(i)
    Nxvalue = dcdec.get(Nnext) - dcadd.get(Nunit)
    dcdec.set(Nnext, Nxvalue)
  end
end
av.clearMsg
av.clearstatus
'write results to Ftab
for each rec in theFtab
  Nunit = theFTab.ReturnValueNumber(FDunit, rec)
  TheFtab.SetValue( FDadd, rec, dcdec.get(Nunit) )
end
theFtab.Refresh
if(TheFtab.isEditable) then
    theFtab.SetEditable(false)
end
292
Appendix C Arc/Info macros--AMLs
This Appendix contains the following Arc/Info procedures written in Arc/Info
Macro Language (AML):
1) WSHGS.AML - Creates the following grids: stream network, watersheds,
and watershed outlets;
2) NEXTWSH.AML - Creates an info file that contains two items: ID and the
downstream watershed ID. Also creates a grid of watershed outlets that
contains the ID of downstream watershed;
3) RAININFO.AML- Based on the time series stored in the attribute table of
the point coverage, and the grid that specify the spatial division into zones,
this AML calculates zonal averages and stores them in Arc/Info INFO
table;
4) RAINMAP.AML - Creates grids of average monthly precipitation;
5) RAINM2.AML - Creates an INFO table from the grids of average monthly
precipitation;
6) SELDATA.AML - Creates point coverage of stations with complete
record of flow rate/precipitation depth in selected months;
7) FD4Y.AML - Supports the process of redistribution of the flow rate
recorded in theUSGS stations;
8) SLOPE3.AML - Calculates the slope along a flow path;
9) DEMALB - Converts a grid into Albers Equal Area coordinate system;
293
 C1 WSHGS.AML
/* -----------------------------------------------------------------
/*   Program: WSHGS.AML
/*   Purpose: Creates the following grids: stream network,
/*            watersheds, and watershed outlets.
/*            The watershed outlet grid contains:
/*            the most upstream cell of the first order stream,
/*            the most downstream cell of each reach, and the cells
/*            created from a point coverage of USGS stations.
/*            Runs only in GRID
/* -----------------------------------------------------------------
/*     Usage: &r WSHINFO <fdir> <facc> <fbas> <trsh> <fout> <item>
/*                   <fwsh> <flpp> <fstr>
/* Arguments: (input)
/*            fdir = (grid) flow direction
/*            facc = (grid) flow accumulation
/*            fbas = (grid) area under investigation (basin, mask)
/*            trsh = (value) threshold for stream delineation
/*                   ( if grids are in meters, then trsh is in km2 )
/*            fout = (point) selected flow gauging stations
/*               (additional pour points for watersheds delineation)
/*            item = (text) name of the item from <fout> which will
/*                   be used in "pointgrid" conversion.
/*
/*            (output, grids that will be created)
/*            fstr = (grid) stream network
/*            fwsh = (grid) drainage areas
/*            flpp = (grid) outlets
/*
/* Temporary: lso, lsl, lmx, lpd, lmn, lpu, lgs, lpx, (grids)
/*   Globals: none (see Temporary)
/*   Locals:  tresh (variable)
/* -----------------------------------------------------------------
/*     Notes: The first order watersheds (and the respective outlets)
/*            have ID number in the range 100000 < ID < 200000.
/*            Cellsize and Window of <fdir> are assumed.
/*            This AML checks neither for the existence and
/*            correctness of the input files nor for the existence
/*            of files that have the same names as the temporary
/*             files and the files to be created.
/*    If an error occurs then all grids and all info files that
/*    have the same name as output grids and temporary grids are
/     erased !!!
/* ----------------------------------------------------------------
/*   History: Author Pawel Mizgalewicz  11/21/93
/*            updated for point coverage  05/15/95
/*            working name net4.aml ( tested for the Cedar River
/*            - Iowa River basin, grid = 3000^2 cells, basin =
/*            3.2*10e6 cells of size 100m*100m).
/*            edited 6/13/95, 6/21/95, 2/19/96
/*=================================================================
294
&args fdir facc fbas trsh fout item fwsh flpp fstr
&severity &error &routine bailout
&if [SHOW PROGRAM] <> GRID &then ; &return This only runs in GRID.
&if [null %fstr%] &then
 &do
  &call usage
  &return
 &end
&messages &off
/* GRID settings:
&s xxcell = [show setcell]
&s xxwindow = [show setwindow]
setwindow %fdir%
setcell %fdir%
/* -----------------------------------------------------------------
/* Creating a stream network
/* -----------------------------------------------------------------
/* calculate threshold in number of cells
&sv trsh = %trsh% * 1000000    /* conversion into meters (map units)
&sv tresh = %trsh% / ( $$cellsize * $$cellsize )
&type stream delineation ... [date -vfull]
%fstr% = con ( %facc% >= %tresh% AND %fbas% > 0 , 1 )
/* -----------------------------------------------------------------
/* Finding the most downstream cell in each reach (watershed outlet)
/* -----------------------------------------------------------------
&type streamorder [date -vfull]
lso = streamorder ( %fstr% , %fdir% )
&type streamlink [date -vfull]
lsl = streamlink ( %fstr% , %fdir% )
&type zonalmax [date -vfull]
lmx = zonalmax (lsl , %facc% )
&type lpd condition [date -vfull]
lpd = con ( lmx == %facc% , lsl, 0 )
kill lmx all
/* lpd contains cells that have been selected by finding cell with
/* the largest value of the flowaccumulation within each partial
/*  drainage area.
/* lpd cells have value equal to the stream_ID and the watershed-ID.
/* -----------------------------------------------------------------
/* Finding the most upstream cell in each first order reach (wshed
outlet)
/* -----------------------------------------------------------------
&type zonalmin [date -vfull]
lmn = zonalmin (lsl , %facc% )
&type lpu condition [date -vfull]
lpu = con ( lso == 1 AND lmn == %facc%, lsl + 100000 , 0 )
&type lfs focalsum for first order wshds [date -vfull]
kill lso all ; kill lsl all ; kill lmn all
/* lpu contains cells that have been selected by finding cell with
/* the smallest value of the flowaccumulation within first order
/* partial watersheds.
295
/* lpu cells have value equal to the stream_ID (and the watershed-ID)
/* increased by 100 000. Numbers >100 000 and <200 000 are used to
/* identify first order watersheds
/* (flow gauging station_ids are large numbers, for example 5448500)
/* -----------------------------------------------------------------
/* Converting point coverage into grid.
/* Cell value = value from %item%
/* -----------------------------------------------------------------
lgs = pointgrid ( %fout% , %item%, #, #, #, ZERO )
/* -----------------------------------------------------------------
/* Creating grid with all potential outlets
/* -----------------------------------------------------------------
&type all outlets [date -vfull]
lpx = con ( lpu == 0 , con ( lgs == 0 , lpd, lgs ) , lpu )
kill lpu all    /* upper end of first order reach
kill lgs all    /* usgs gauging stations
kill lpd all    /* down (lowest) end of the reach
&type setnull cells == 0  [date -vfull]
%flpp% = setnull ( lpx < 1, lpx )
&if not [ exists %flpp%.vat -info ] &then ; buildvat %flpp%
kill lpx all
/* all watershed outlets must be located on the stream network.
/* Gauging stations, which are located on the first cell of the first
/* order stream will not affect the value of the cell e.g. node
number
/* will not be changed.
/* -----------------------------------------------------------------
/* Delineating watersheds
/* -----------------------------------------------------------------
&type watershed [date -vfull]
%fwsh% = watershed ( %fdir% , %flpp% )
&if not [exists %fwsh%.vat -info] &then ; buildvat %fwsh%
&type watershed end [date -vfull]
/* restore GRID settings:
setcell %xxcell%
setwindow %xxwindow%
&messages &on
&return
/*-------------
&routine USAGE
/*-------------
&type Usage: &r WSHGS <fdir_grid> <facc_grid> <basin_grid>
<tresh_num>
&type              <fout_point> <item> <watershed> <pour_points>
<streams>
&return &inform
/*-------------
&routine EXIT
/*-------------
/* delete all temporary files:
&if [exists lso -grid ] &then ; kill lso all?
&if [exists lsl -grid ] &then ; kill lsl all
&if [exists lmx -grid ] &then ; kill lmx all
296
&if [exists lpd -grid ] &then ; kill lpd all
&if [exists lmn -grid ] &then ; kill lmn all
&if [exists lpu -grid ] &then ; kill lpu all
&if [exists lgs -grid ] &then ; kill lgs all
&if [exists lpx -grid ] &then ; kill lpx all
/* on error erase grids that exist or that have been created
&if [exists %fwsh% -grid ] &then ; kill %fwsh% all
&if [exists %flpp% -grid ] &then ; kill %flpp% all
&if [exists %fstr% -grid ] &then ; kill %fstr% all
/* restore GRID settings:
setcell %xxcell%
setwindow %xxwindow%
&messages &on
&return
/*--------------
&routine BAILOUT
/*--------------
&severity &error &ignore
&call exit
&return &warning An error has occurred in WSHGS.AML
/* -----------------------------------------------------------------
/*     EXAMPLE OF APPLICATION
/* -----------------------------------------------------------------
/* grid
/*      /* input
/* &s fdir = $HOME/iowa/data/crfdr     /* crfdr =
flowdirection(elev_grid)
/* &s facc = $HOME/iowa/data/crfac     /* crfac = flowaccumulation
(crfdr)
/* &s fbas = $HOME/iowa/data/crbas     /* basin or watershed
/* &s trsh = 25                        /* units in km2
/* &s fout = $home/iowa/test90/stations/gsflow  /* point coverage
/* &s item = station_id                /* item in %fout% coverage
/*      /* output
/* &s fwsh = crwsh                     /* watersheds
/* &s flpp = crlpp                     /* pour points
/* &s fstr = crstr                     /* stream network
/*
/* &r wshgs %fdir% %facc% %fbas% %trsh% %fout% %item% %fwsh% %flpp%
%fstr%
/*
/* q                                   /* quit from GRID
/*
/* &return                             /* return from example AML
/* -----------------------------------------------------------------
297
C2 NEXTWSH.AML
/* -----------------------------------------------------------------
/*   Program: NEXTWSH.AML
/*   Purpose: Creates an info file that contains two items: ID and
/*            the downstream watershed ID. Also creates a grid of
/*            watershed outlets that contains the ID of downstream
/*            watershed.
/*            Runs only in GRID
/* -----------------------------------------------------------------
/* Usage: &r NEXTWSH <fdir> <fwsh> <flpp> <infn> <idin> <nxin> <fnxt>
/* Arguments: (input)
/*            fdir = (grid) flow direction
/*            fwsh = (grid) watersheds (partial drainage areas)
/*                          value in VAT = unit_id number
/*            flpp = (grid) pour points ( watershed outlets)
/*                          value in VAT = unit_id number
/*            (output)
/*            infn = (info file) name of the info file to be created
/*            idin = (item) name of the item in which the unit_id
/*                          number will be stored
/*            nxin = (item) name of the item in which the downstream
/*                          unit_id will be stored
/*            fnxt = (grid) similar to %flpp% (watershed outlets):
/*                     the values in VAT are not equal to the unit_id
/*                     number, they equal to the downstream unit
/*                     ID number.
/* Temporary: xxxtmp, xxxcomnx, (GRIDS)
/*            xxxtmp1 (INFO)
/*   Globals:
/*    Locals: see Temporary
/* ----------------------------------------------------------------
/*     Notes: The ID of the next watershed for the most downstream
/*            watershed equals 0.
/*            If the flowdirection in watershed pour point can't be
/*            determined, the next watershed ID = -1
/*        This AML checks neither for the existence and correctness
/*        of the input files nor for the existence of files that have
/*        the same names as the temporary files and the files to be
/*        created.
/*        If an error occurs then all grids and all info files that
/*        have the same name as output grids/info files and temporary
/*            grids/info are erased !!!
/* ---------------------------   ----------------------------------
/*   History: coded by Pawel Mizgalewicz  12/20/93
/*         and converted into a stand alone procedure
/*         6/10 - 6/21/95, 2/19/96
/*  ================================================================
&args fdir fwsh flpp infn idin nxin fnxt
&severity &error &routine bailout
&if [SHOW PROGRAM] <> GRID &then ; &return This only runs in GRID.
298
&if [null %fnxt%] &then
 &do
  &call usage
  &return
 &end
&messages &off
/* GRID settings:
&s xxcell = [show setcell]
&s xxwindow = [show setwindow]
setcell %fwsh%
setwindow %fwsh%
/* -----------------------------------------------------------------
&type searching for next (downstream) watershed ...   [date -vfull]
/* -----------------------------------------------------------------
&sv wsh = xxxtmp
%wsh% = con ( isnull ( %fwsh%), 0, %fwsh% )
%fnxt% = con (%flpp% > 0, con (%fdir% == 1, %wsh%(1,0), ~
        con (%fdir% == 2, %wsh%(1,1), ~
        con (%fdir% == 4, %wsh%(0,1), ~
        con (%fdir% == 8, %wsh%(-1,1), ~
        con (%fdir% == 16, %wsh%(-1,0), ~
        con (%fdir% == 32, %wsh%(-1,-1), ~
        con (%fdir% == 64, %wsh%(0,-1), ~
        con (%fdir% == 128, %wsh%(1,-1), -1)))))))))
kill xxxtmp all
&if not [exists %fnxt%.vat -info] &then ; buildvat %fnxt%
xxxcomnx = combine ( %flpp% , %fnxt% )
/* the %fnxt% grid is similar to the %flpp%, watershed outlets grid.
/* The cell value is equal to the next watershed ID number
/* -----------------------------------------------------------------
&type Creating the info file  ...  [date -vfull]
/* -----------------------------------------------------------------
arc additem xxxcomnx.vat xxxtmp1 %idin% 4 8 B
arc additem xxxtmp1 xxxtmp1 %nxin% 4 8 B
cursor xxnext declare xxxtmp1 info rw
cursor xxnext open
&do &while %:xxnext.aml$next%
  &s :xxnext.%idin% = [value :xxnext.%flpp%]
  &s :xxnext.%nxin% = [value :xxnext.%fnxt%]
  cursor xxnext next
&end
cursor xxnext close
cursor xxnext remove
arc pullitems xxxtmp1 %infn%
%idin%
%nxin%
end
kill xxxcomnx all
&s x = [delete xxxtmp1 -info]
/* restore GRID settings:
setcell %xxcell%
setwindow %xxwindow%
&messages &on
&return
299
/*-------------
&routine USAGE
/*-------------
&type Usage: &r NEXTWSH <fdir_grid> <wsh_grid> <pourpt_grid>
<newINF_name>
&type               <id_item_name> <next_id_item_name> <nextwsh_grid>
&return &inform
/*-------------
&routine EXIT
/*-------------
/* delete all temporary files:
&if [exists xxxtmp1 -info ] &then ; &s x = [delete xxxtmp1 -info]
&if [exists xxxtmp -GRID] &then ; kill xxxtmp all
&if [exists xxxcomnx -GRID] &then ; kill xxxcomnx all
&if [exists %fnxt% -GRID] &then ; kill %fnxt% all
/* restore GRID settings:
setcell %xxcell%
setwindow %xxwindow%
&messages &on
&return
/*--------------
&routine BAILOUT
/*--------------
&severity &error &ignore
&call exit
&return &warning An error has occurred in NEXTWSH.AML
/* -----------------------------------------------------------------
/*     EXAMPLE OF APPLICATION
/* -----------------------------------------------------------------
/* grid
/*      /* input
/* &s fdir = $HOME/iowa/data/crfdr/* crfdr = flowdirection(elev_grid)
/* &s fwsh = crwsh                /* watersheds
/* &s flpp = crlpp                /* pour points
/*     /* output
/* &s fnxt = crnxt                /* outflow,value=downstream wshd ID
/* &s infn = %fnxt%.dat           /* new info file
/* &s idin = unit_id              /* item (unit ID)
/* &s nxin = next_id              /* item ( downstream unit ID)
/*
/* &run nextwsh %fdir% %fwsh% %flpp% %infn% %idin% %nxin% %fnxt%
/*
/* q                              /* quit from GRID
/*
/* &return                        /* return from example AML
/* -----------------------------------------------------------------
300
C3 RAININFO.AML
/* -----------------------------------------------------------------
/*   Program: RAININFO.AML
/*   Purpose: Based on the time series stored in the attribute table
/*            of the point coverage, and the grid that specify the
/*            spatial division into zones, this AML calculates
/*            zonal averages and stores them in Arc/Info INFO table
/*   Method:  For a given month of the selected period this AML
/*            creates a grid of spatially distributed feature
/*            such as rainfall, temperature, or evaporation.
/*            The Inverse Distance Weighting IDW procedure is
/*            applied. To use different method only one line
/*            need to be changed. In the next step this AML
/*            calculates average values for all zones, specified by
/*            and stores them in INFO file. The procedure is
/*            repeated for all months from the specified time
/*            Runs only in GRID
/* -----------------------------------------------------------------
/*     Usage: &r RAININFO <fy> <fm> <ty> <tm> <p_data> <zone>
/*                       <outinf> {id_itm} {prc} {kcell} {prx}
/* Arguments: (input)
/*            fy, fm = from year, from month
/*            ty, tm = to year, to month
/*            p_data = (coverage) point coverage that contains time
/*                     series
/*            zone   = (grid) defines zones and their IDs
/*            outinf = (info) output info file to be created
/*            id_itm = (item) name of the item in which the zone ID
/*                     will be stored, default {id_itm} = zone_id
/*            prc    = (number) the values must be converted
/*                     into integer numbers to create VAT.
/*                     Before conversion they are multiplied by
/*                     <prc> to preserve decimal part of value.
/*                     default {prc} = 1000 (three decimal places)
/*            kcell  = (number) cell size multiplier.
/*                     The grid that is created from point coverage
/*                     will assume the size of the cell from
/*                     <zone> grid multiplied by {kcell}
/*                     default {kcell} = 1
/*            prx    = (prefix) Items that are created
/*                     in <outinf> info file will named as follows:
/*                     <prx> + item name from input coverage <p_data>
/*                     default {prx} = "p".
/* Temporary: xxx, xxx2, xxxcom (grid), xxxtmp1 (info)
/*    Locals: ab, bb, cc, nitem, prfnitem, yr,mt  (variables)
/* -----------------------------------------------------------------
/*     Notes: The following convention is used for naming the items
/*            in PAT (table that stores original time series)
/*            myyyymm,     where:  m indicates monthly values,
/*            yyyy = year, mm = month, for example item m197603
/*            carries data for March 1976.
301
/* -----------------------------------------------------------------
/*    History: Coded by Pawel Mizgalewicz  05/05/95
/*             Modified 06/18/1995 - 6/21/95,
/*             02,20,96 - defaults added for id_itm prc kcell.
/* -----------------------------------------------------------------
&args fy fm ty tm p_data zone outinf id_itm prc kcell prx
&severity &error &routine bailout
&if [SHOW PROGRAM] <> GRID &then ; &return This only runs in GRID.
&if [null %outinf%] &then
 &do
  &call usage
  &return
 &end
&if [null %prx%] &then ; &s prx = p
&if [null %kcell%] &then ; &s kcell = 1
&if [null %prc%] &then ; &s prc = 1000
&if [null %id_itm%] &then ; &s id_itm = zone_id
&messages &off
/* GRID settings:
&s xxcell = [show setcell]
&s xxwindow = [show setwindow]
&describe %zone%
&sv size = [calc %grd$dx% * %kcell%]
&type cell size = %size%
/* -----------------------------------------------------------------
/*       Make a copy of %zone%.VAT file and add item %zone%
/* -----------------------------------------------------------------
arc additem %zone%.vat xxxtmp1 %zone% 4 5 B
cursor xxcur1 declare xxxtmp1 info rw
cursor xxcur1 open
&do &while %:xxcur1.aml$next%
  &s :xxcur1.%zone% = %:xxcur1.VALUE%
  cursor xxcur1 next
&end
cursor xxcur1 close
cursor xxcur1 remove
/* -----------------------------------------------------------------
/*       Do it for all selected years and months
/* -----------------------------------------------------------------
&DO yr = %ty% &to %fy% &by -1
  &DO mt = 12 &to 1 &by -1
    &s ab = [calc %yr% = %fy%] AND [calc %mt% lt %fm%]
    &s bb = [calc %yr% = %ty%] AND [calc %mt% gt %tm%]
    &s cc = %ab% OR %bb%
    &IF NOT %cc%  &THEN
      &do
        &s templ = mxxxx0y
        &s nitem = [subst %templ% xxxx %yr% ]
        &if %mt% lt 10 &then
            &sv nitem = [subst %nitem% y %mt% ]
          &else
302
            &sv nitem = [subst %nitem% 0y %mt% ]
        &type  processing item %nitem% ... [date -vfull]
        setcell %size%
        setwindow MAXOF
        xxx = idw ( %p_data% , %nitem%  )
        setcell %zone%
        setwindow %zone%
        xxx2 = int ( %prc% * zonalmean ( %zone% , xxx  ))
        kill xxx all
        xxxcom = combine (%zone%, xxx2)
        kill xxx2 all
        &s prfnitem = %prx%%nitem%
        arc additem xxxcom.vat xxxcom.vat %prfnitem% 4 12 F 4 xxx2
        cursor xxcur1 declare xxxcom.vat info rw
        cursor xxcur1 open
        &do &while %:xxcur1.aml$next%
           &s :xxcur1.%prfnitem% = [calc %:xxcur1.xxx2% / %prc%]
           cursor xxcur1 next
        &end
        cursor xxcur1 close
        cursor xxcur1 remove
        arc joinitem xxxtmp1 xxxcom.vat xxxtmp1 %zone% %zone%
        arc dropitem xxxtmp1 xxxtmp1 xxx2
        kill xxxcom all
      &end
 &end
&end
/* -----------------------------------------------------------------
&type Adding ID item ... [date -vfull]
/* -----------------------------------------------------------------
arc additem xxxtmp1 xxxtmp1 %id_itm% 4 8 B # %zone%
cursor xxcur2 declare xxxtmp1 info rw
cursor xxcur2 open
&do &while %:xxcur2.aml$next%
           &s :xxcur2.%id_itm% = [value :xxcur2.%zone%]
           cursor xxcur2 next
&end
cursor xxcur2 close
cursor xxcur2 remove
/* -----------------------------------------------------------------
&type Cleaning INFO table (dropping redundant items) .. [date -vfull]
/* -----------------------------------------------------------------
arc dropitem xxxtmp1 xxxtmp1 value
arc dropitem xxxtmp1 xxxtmp1 count
arc dropitem xxxtmp1 %outinf% %zone%
&s x = [delete xxxtmp1 -info]
/* restore GRID settings:
setcell %xxcell%
setwindow %xxwindow%
&messages &on
&return
/*-------------
&routine USAGE
/*-------------
&type Usage: &r RAININFO <fy> <fm> <ty> <tm> <pnt_data> <zone>
303
&type                   <out_inf> <ID_item> <prc> <kcell> {prefix}
&return &inform
/*-------------
/* &routine CHECK
/*-------------
/* IF temporary file exists, inform and exit
/* If file to be build exists , inform and exit
/* If input file is not correct or does not exist, inform and exit
/* return
/*-------------
&routine EXIT
/*-------------
/* delete all temporary files:
&if [exists xxxtmp1 -info ] &then;   &s x = [delete xxxtmp1 -info]
&if [exists xxx -GRID] &then ; kill xxx all
&if [exists xxx2 -GRID] &then ; kill xxx2 all
&if [exists xxxcom -GRID] &then ; kill xxxcom all
/* restore GRID settings:
setcell %xxcell%
setwindow %xxwindow%
&messages &on
&return
/*--------------
&routine BAILOUT
/*--------------
&severity &error &ignore
&call exit
&return &warning An error has occurred in RAININFO.AML
/* -----------------------------------------------------------------
/*     EXAMPLE OF APPLICATION
/* -----------------------------------------------------------------
/* grid
/* &s fy = 1990
/* &s fm = 1
/* &s ty = 1990
/* &s tm = 12
/* &s pdat = ../stations/gsrain
/* &s zone = crwsh
/* &s id unit_id
/*
/* &r raininfo %fy% %fm% %ty% %tm% %pdat% %zone% prcinf2 %id% 10000
10 r
/*
/* q
/* &return
/* -----------------------------------------------------------------
304
C4 RAINMAP.AML
/* -----------------------------------------------------------------
/*   Program: RAINMAP.AML
/*   Purpose: Creates GRIDS of average monthly precipitation
/*            (10e-3 cm/d -- value from PAT is multiplied by 1000,
/*             assumed cell size = 1000)
/*            Stations that have complete record of precipitation for
/*            a given month (from specified time period) are used.
/*            rainm2.aml uses output to put values into an INFO file
/*            Runs only in GRID
/* -----------------------------------------------------------------
/*     Usage: &r RAINMAP <fy> <fm> <ty> <tm> <xxxdat> {YES|NO}
/* Arguments: (input)
/*            fy, fm = from year, from month
/*            ty, tm = to year, to month
/*            xxxdat = info file that contains precipitation depth
/*            yes|no = yes - include records with values = 0
/*                     no - exclude records and stations that have 0
/*                          (default = no)
/* Temporary: xxxxx1
/*    Locals: templ, nitem, nit, yr,mt, selec (variables)
/* -----------------------------------------------------------------
/*     Notes: Data are stored in PAT (point). Each record is related
/*            to gauging station. The following naming convention is
/*            used for items: myyyymm, where:
/*            m = indicates monthly values,
/*            yyyy = year, mm = month, for example, item m197603
/*            contains records for March 1976
/*            Info file is created by rainm2.aml
/* -----------------------------------------------------------------
/*    History: Coded by Pawel Mizgalewicz  08/08/95
/*             edited 02/20/96
/* -----------------------------------------------------------------
&args fy fm ty tm xxxdat zero
&severity &error &routine bailout
&if [SHOW PROGRAM] <> GRID &then ; &return This only runs in GRID.
&if [null %xxxdat%] &then
 &do
  &call usage
  &return
 &end
&if [null %zero%] &then ; &s zero = YES
&s xx = [translate %zero%]
&select %xx%
  &when NO
    &s klm = gt
  &when YES
    &s klm = ge
  &otherwise
305
    &do
      &call usage
      &return
    &end
&end /* select
&messages &off
setwindow maxoff
setcell 1000
&DO yr = %fy% &to %ty%
  &DO mt = 1 &to 12
    &s ab = [calc %yr% = %fy%] AND [calc %mt% lt %fm%]
    &s bb = [calc %yr% = %ty%] AND [calc %mt% gt %tm%]
    &s cc = %ab% OR %bb%
    &IF NOT %cc%  &THEN
      &do
        /* &s nit = %nit% + 1
        &s templ = mxxxx0y
        &s nitem = [subst %templ% xxxx %yr% ]
        &if %mt% lt 10 &then
             &sv nitem = [subst %nitem% y %mt% ]
           &else
             &sv nitem = [subst %nitem% 0y %mt% ]
       &type %nitem%
       /* &s namit%nit% = %nitem%
       &sv selec = res %nitem% %klm% 0
       &type selecting complete records %selec%
arc reselect %xxxdat% xxxxx1 point
%selec%
~
n
n
      &end
    arc build xxxxx1 point
    p%nitem% = int ( 1000 * idw ( xxxxx1, %nitem% ) )
    kill xxxxx1 all
  &end
&end
&messages &on
&return
/*-------------
&routine USAGE
/*-------------
&type Usage: &r RAINMAP <from_yr> <from_mt> <to_yr> <to_mt>
<data_point>
&type               {YES|NO}
&return &inform
/*-------------
&routine EXIT
306
/*-------------
/* delete all temporary files:
&if [exists xxxxx1 -COVER] &then ; kill xxxxx1 all
&messages &on
&return
/*--------------
&routine BAILOUT
/*--------------
&severity &error &ignore
&call exit
&return &warning An error has occurred in RAINMAP.AML
/* -----------------------------------------------------------------
/*     EXAMPLE OF APPLICATION
/* -----------------------------------------------------------------
/*      /* input
/* &s data = $HOME/iowa/data/gsprec    /* point coverage and data
/* grid
/* &run rainmap 1940 1 1993 6 %data% YES
/* q
/* &return                             /* return to Arc/Info prompt
/* -----------------------------------------------------------------
307
C5 RAINM2.AML
/* -----------------------------------------------------------------
/*   Program: RAINM2.AML
/*   Purpose: Creates an INFO table from the grids of average
/*            monthly precipitation (needs grid of zones)
/*            (10e-3 cm/d -- value from PAT was multiplied by 1000,
/*             in original rainmap.aml assumed cell size = 1000 )
/*            (rainmap.aml creates grids of precipitation)
/*            Runs only in GRID, output: integer values !!!
/* -----------------------------------------------------------------
/*     Usage: &r RAINM2 <fy> <fm> <ty> <tm> <ppath> <zones> <idname>
/*                      <frominfo> <toinfo>
/* Arguments: (input)
/*            fy, fm = from year, from month
/*            ty, tm = to year, to month
/*            ppath = path to directory that contains grids of
/*                    precipitation
/*            zones = zones for calculatuing average prec. depth
/*            idname = same as zones, contains identification
/*                      number for zones (unit_id, modeling units)
/*            frominfo = info file that contains station id numbers
/*            toinfo = output info file
/*                     copy of frominfo + precipitation items
/* Temporary: xxxcom
/*    Locals: templ, nitem, nit, yr,mt,(variables)
/* -----------------------------------------------------------------
/*     Notes: Post processor for RAINMAP.AML
/*            RAINMAP.aml changes units, here means are converted to
/*            integer values !!!
/*            The following naming convention is
/*            used for items: myyyymm, where:
/*            m = indicates monthly values,
/*            yyyy = year, mm = month, for example, item m197603
/*            contains records for March 1976
/*            Info file is created by rainm2.aml
/* -----------------------------------------------------------------
/*    History: Coded by Pawel Mizgalewicz  95
/*             edited 02/20/96
/* -----------------------------------------------------------------
&args fy fm ty tm ppath zones idname frominfo toinfo
/* &s ppath = ../rain25/
/* &s zones = crwsh
/* &s idname = unit_id
/* &s frominfo = crwshc.dat
/* &s toinfo = crwshc.datp
/* &sv fy = 1990
/* &sv fm = 1
/* &sv ty = 1990
/* &sv tm = 12
308
copyinfo %frominfo% %toinfo%
&type ...aml, start  [date -vfull]
grid
&messages &off
setwindow %zones%
setcell %zones%
/* %idname% = %zones%
/* repeat in reverse order
&DO yr = %ty% &to %fy% &by -1
  &DO mt = 12 &to 1 &by -1
    &IF %mt% ge %fm% and %mt% le %tm% &THEN
      &do
        &s templ = mxxxx0y
        &s nitem = [subst %templ% xxxx %yr% ]
        &if %mt% lt 10 &then
             &sv nitem = [subst %nitem% y %mt% ]
           &else
             &sv nitem = [subst %nitem% 0y %mt% ]
&type p%nitem% processing ... [date -vfull]
p%nitem% = zonalmean ( %zones% , %ppath%p%nitem%
xxxcom = combine ( %idname% , p%nitem% )
kill p%nitem% all
&sys arc joinitem %toinfo% xxxcom.vat %toinfo% %idname% %idname%
kill xxxcom all
     &end
  &end
&end
&type rain series - point cover created, exiting ... [date -vfull]
&return
309
C6 SELDATA.AML
/* -----------------------------------------------------------------
/*   Program: SELDATA.AML
/*   Purpose: Selects the items that contain data for specified
/*            time period. Then, selects gauging stations that
/*            have complete record (no missing data).
/*            Creates point coverage of selected stations with data
/*            for specified months
/*            Runs only in ARC
/* -----------------------------------------------------------------
/*     Usage: &r SELDATA <xxxdat> <xxxhed> <joinit> <xxxout> {YES|NO}
/* Arguments: (input)
/*            fy, fm = from year, from month
/*            ty, tm = to year, to month
/*            xxxdat = info file that contains flow database
/*            xxxhed = point coverage that represents location of
/*                     observation stations. xxxdat and xxxhed must
/*                     contain common item to relate these tables
/*                    (for example item station_id)
/*            joinit = name of the common item for both tables
/*            (output)
/*            xxxout = point coverage which contains selected flow
/*                     records or precipitation measurements,
/*                     as well as selected gauging stations.
/*            yes|no = yes - include records with values = 0
/*                     no - exclude records and stations that have 0
/*                          (default = no)
/* Temporary: %xxxout%tmp (cover), xxxxx1 (info)
/*    Locals: temp1, nitem, nit, yr,mt, selec (variables)
/* -----------------------------------------------------------------
/*     Notes: Data file is an INFO file. Each record is related to
/*            gauging station. The following naming convention is
/*            used for items:
/*            myyyymm, where m indicates monthly values,
/*            yyyy = year, mm = month, for example item m197603
/*            contains records for March 1976
/*            Due to the Arc/Info restrictions only about 65-month
/*            period can be selected in single run of this AML
/* -----------------------------------------------------------------
/*    History: Coded by Pawel Mizgalewicz  05/05/95
/*             Modified 06/15/1995, edited 2/20/96
/* -----------------------------------------------------------------
&args fy fm ty tm xxxdat xxxhed joinit xxxout zero
&severity &error &routine bailout
&if [SHOW PROGRAM] <> ARC &then ; &return This only runs in ARC.
&if [null %xxxout%] &then
 &do
  &call usage
  &return
310
 &end
&if [null %zero%] &then ; &s zero = no
&s xx = [translate %zero%]
&select %xx%
  &when NO
    &s klm = gt
  &when YES
    &s klm = ge
  &otherwise
    &do
      &call usage
      &return
    &end
&end /* select
/* -----------------------------------------------------------------
/*       Make a copy of point coverage
/* -----------------------------------------------------------------
copy %xxxhed% %xxxout%tmp   /* create temporary file
&sv pultmp = xxxxx1         /* temporary info file
/* -----------------------------------------------------------------
&type Selecting years and months  ...          [date -vfull]
/* -----------------------------------------------------------------
PULLITEMS %xxxdat% %pultmp%
%joinit%
&DO yr = %fy% &to %ty%
  &DO mt = 1 &to 12
    &s ab = [calc %yr% = %fy%] AND [calc %mt% lt %fm%]?
    &s bb = [calc %yr% = %ty%] AND [calc %mt% gt %tm%]
    &s cc = %ab% OR %bb%
    &IF NOT %cc%  &THEN
      &do
        &s templ = mxxxx0y
        &s nitem = [subst %templ% xxxx %yr% ]
        &if %mt% lt 10 &then
            &sv nitem = [subst %nitem% y %mt% ]
          &else
            &sv nitem = [subst %nitem% 0y %mt% ]
        &type  selecting item %nitem%
%nitem%
      &end
 &end
&end
end
/* join selected items with header file (point coverage)
joinitem %xxxout%tmp.pat xxxxx1 %xxxout%tmp.pat %joinit% %joinit%
&sv st = [delete xxxxx1 -info]
/* -----------------------------------------------------------------
&type Selecting gauging stations that have full record  ...  [date -
vfull]
/* -----------------------------------------------------------------
reselect %xxxout%tmp %xxxout% point
&DO yr = %fy% &to %ty%
311
  &DO mt = 1 &to 12
    &s ab = [calc %yr% = %fy%] AND [calc %mt% lt %fm%]
    &s bb = [calc %yr% = %ty%] AND [calc %mt% gt %tm%]
    &s cc = %ab% OR %bb%
    &IF NOT %cc%  &THEN
      &do
        /* &s nit = %nit% + 1
        &s templ = mxxxx0y
        &s nitem = [subst %templ% xxxx %yr% ]
        &if %mt% lt 10 &then
             &sv nitem = [subst %nitem% y %mt% ]
           &else
             &sv nitem = [subst %nitem% 0y %mt% ]
       &type %nitem%
       /* &s namit%nit% = %nitem%
       &sv selec = res %nitem% %klm% 0
       &type selecting complete records %selec%
%selec%
~
n
y
      &end
  &end
&end
&type end
%selec%
~
n
n
build %xxxout% point
kill %xxxout%tmp all
&return
/*-------------
&routine USAGE
/*-------------
&type Usage: &r SELDATA <from_yr> <from_mt> <to_yr> <to_mt>
<data_info>
&type              <station_cover> <join_item> <out_cover> {YES|NO}
&return &inform
/*-------------
&routine EXIT
/*-------------
/* delete all temporary files:
&if [exists %pultmp% -info ] &then ; &s x = [delete %pultmp% -info]
&if [exists %xxxout%tmp -COVER] &then ; kill %xxxout%tmp all
&messages &on
&return
/*--------------
&routine BAILOUT
/*--------------
&severity &error &ignore
&call exit
&return &warning An error has occurred in SELDATA.AML
312
/* -----------------------------------------------------------------
/*     EXAMPLE OF APPLICATION
/*------------------------------------------------------------------
/*      /* input
/* &s data = $HOME/iowa/data/gsflow.pat /* Info file of monthly flows
/* &s head = $HOME/iowa/data/crfhd    /* coverage of gauging stations
/* &s cname  = station_id             /* common item
/*     /* output
/* &s fout = mflow91                  /* output coverage
/*
/* &run seldata 1991 1 1991 12 %data% %head% %cname% %fout% NO
/*
/* &return                           /* return to Arc/Info prompt
/* -----------------------------------------------------------------
313
C7 FD4Y.AML
/* -----------------------------------------------------------------
/* fd4y.aml
/*          1) Creates ASCII files that contain data required
/*             for C program fd4y. ( fd4y calculates flow rate in
/*             all modeling units based on the flow recorded in
/*             USGS gauging stations).
/*          2) Stores the results obtained from fd4y program in
/*             PAT--polygon attribute table
&s prc = unprec.pat
&s flw = gsfl28.pat
&s out = unflow.pat
&s fy = 1960
&s fm = 1
&s ty = 1992
&s tm = 9
/*  input1 xxxgsin, ASCII file
/*  input2 xxxunin, ASCII file
/*  output xxxunout, ASCII file
tables
&DO yr = %ty% &to %fy% &by -1
  &DO mt = 12 &to 1 &by -1
    &s ab = [calc %yr% = %fy%] AND [calc %mt% lt %fm%]
    &s bb = [calc %yr% = %ty%] AND [calc %mt% gt %tm%]
    &s cc = %ab% OR %bb%
    &IF NOT %cc%  &THEN
      &do
        &s templ = mxxxx0y
        &s nitem = [subst %templ% xxxx %yr% ]
        &if %mt% lt 10 &then
            &sv nitem = [subst %nitem% y %mt% ]
          &else
            &sv nitem = [subst %nitem% 0y %mt% ]
        &type  processing item %nitem% ... [date -vfull]
/* =====================================================
select %flw%
unload xxxgsin station_id station_nx %nitem% DELIMITED INIT
select %prc%
unload xxxunin unit_id unit_nx gswsh area_km2 order p%nitem%
DELIMITED INIT
&sys fdy4 xxxgsin xxxunin xxxunout
&s i = 0
&do &until [exists xxxunout -file]
  &s i = %i% + 1
314
&end
define %nitem%.dat
unit_id,4,8,B
q%nitem%,4,12,F,4
~
add from xxxunout
select %nitem%.dat
&s x = [delete xxxunout -file]
&if %x% eq 0 &then
   &type file xxxunout has been deleted
&else
   &type ERROR: could not delete file xxxunout
&s x = [delete xxxgsin -file]
&if %x% eq 0 &then
   &type file xxxgsin has been deleted
&else
   &type ERROR: could not delete file xxxgsin
&s x = [delete xxxunin -file]
&if %x% eq 0 &then
   &type file xxxunin has been deleted
&else
   &type ERROR: could not delete file xxxunin
&sys arc joinitem %out% %nitem%.dat %out% unit_id order
kill %nitem%.dat
      &end
 &end
&end
q
q
&return
315
C8 SLOPE3.AML
/* -----------------------------------------------------------------
/*   Program: FSLOPE.AML
/*   Purpose: Calculates slope along the flow path. Calculates the
/*            difference between the elevation of the current cell
/*            and the elevation of the next cell on the flow pathand
/*            divides the result by the distance between these cells
/*            Runs only in GRID
/* -----------------------------------------------------------------
/*     Usage: &r FSLOPE <fdir> <dem> <fslp>
/* Arguments: (input)
/*            fdir = (grid) flow direction
/*            dem  = (grid) elevation
/*            (output)
/*            fslp = (grid) slope grid
/* Temporary: none
/* -----------------------------------------------------------------
/*     Notes: If flow direction is
/*            different than 1, 2, 4, 8, 16, 32, 64, and 128,
/*            the slope  0 is assumed.
/*            Vertical and horizontal units shuld be the same
/* -----------------------------------------------------------------
/*   History: Coded by Pawel Mizgalewicz  10/02/94 (slope3.aml)
/*            edited 16/06/95, 21/06/95, 02/24/96
/*            ( version with DOCELL -> slope3.aml)
/*            ( version with CONdition -> slope2.aml )
/*  =================================================================
&args fdir dem fslp
&severity &error &routine bailout
&if [SHOW PROGRAM] <> GRID &then ; &return This only runs in GRID.
&if [null %fslp%] &then
 &do
  &call usage
  &return
 &end
&messages &off
/* GRID settings:
&s xxcell = [show setcell]
&s xxwindow = [show setwindow]
setcell minof
setwindow maxof
/* -----------------------------------------------------------------
&type calculating slope ... [date -vfull]
/* -----------------------------------------------------------------
&describe %dem%
&sv diag = 1.414213562 * %grd$dx%
DOCELL
  if (%fdir% == 1)
316
    %fslp% = ( %dem% - %dem%(1,0) ) / %grd$dx%
  else
    if (%fdir% == 2)
      %fslp% = ( %dem% - %dem%(1,1) ) / %diag%
    else
      if (%fdir% == 4)
        %fslp% = ( %dem% - %dem%(0,1) ) / %grd$dx%
      else
        if (%fdir% == 8)
            %fslp% = ( %dem% - %dem%(-1,1) ) /  %diag%
        else
          if (%fdir% == 16)
              %fslp% = ( %dem% - %dem%(-1,0) ) / %grd$dx%
          else
            if (%fdir% == 32)
               %fslp% = ( %dem% - %dem%(-1,-1) ) / %diag%
            else
              if (%fdir% == 64)
                 %fslp% = ( %dem% - %dem%(0,-1) ) / %grd$dx%
              else
                if (%fdir% == 128)
                   %fslp% = ( %dem% - %dem%(1,-1) ) / %diag%
                else
                   %fslp% = 0
END
&type end of fslope [date -vfull]
/* restore GRID settings:
setcell %xxcell%
setwindow %xxwindow%
&messages &on
&return
/*-------------
&routine USAGE
/*-------------
&type Usage: &r FSLOPE <fdir_grid> <elevation_grid> <slope_grid>
&return &inform
/*-------------
&routine EXIT
/*-------------
/* on error delete slope grid:
&if [exists %fslp% -GRID] &then ; kill %fslp% all
/* restore GRID settings:
setcell %xxcell%
setwindow %xxwindow%
&return
/*--------------
&routine BAILOUT
/*--------------
&severity &error &ignore
&call exit
&return &warning An error has occurred in FSLOPE.AML
/* -----------------------------------------------------------------
/*     EXAMPLE OF APPLICATION slope of stream reaches
/* -----------------------------------------------------------------
/* grid                                /* start GRID
317
/*      /* input
/* &s fdir = $HOME/iowa/data/crfdr
/*                             /* crfdr = flowdirection(elev_grid)
/* &s dem  = $HOME/iowa/data/crdem     /* elevation grid
/* &s fstr = crstr
/*     /* output
/* &s fslp = crslp                     /* slope grid
/* &s strs = strslp                    /* stream slope
/*
/* /* create slope grid
/* &run fslope %fdir% %dem% %fslp%
/*
/* /* assign unique number to each reach
/* xxxlsl = streamlink(%fstr%)
/*
/* /* calculate average slope
/* %strs% = zonalmean ( xxxlsl , %fslp% )
/*
/* kill xxxlsl all                     /* delete temporary grid
/* kill %fslp% all                     /* delete slope grid
/* q                                   /* quit from GRID
/*
/* &return                             /* return from example AML
/* -----------------------------------------------------------------
318
C9 DEMALB.AML
/* DEMALB.AML - converts a grid into Albers Equal Area coordinates
&args input output csize
%output% = project (%input% , #, NEAREST, %csize% )
OUTPUT
Projection    ALBERS
Zunits        NO
Units         METERS
Datum         NAD83
Spheroid      GRS1980
Xshift        0.0000000000
Yshift        0.0000000000
Parameters
 29 30  0.000 /* 1st standard parallel
 45 30  0.000 /* 2nd standard parallel
-96  0  0.000 /* central meridian
 23  0  0.000 /* latitude of projection's origin
0.00000 /* false easting (meters)
0.00000 /* false northing (meters)
END
&return
319
BIBLIOGRAPHY
Al-Abed, N. and H. R. Whiteley, 1995. Modeling Water Quality and Quantity in the
Lower Portion of the Grand River Watershed, Ontario. Proc. of the
International Symposium on Water Quality Modeling, April 2-5, 1995,
Orlando FL., ASAE (American Society of Agricultural Engineers), St. Joseph,
MI. pp. 213-222.
Arnold, J. G., J. R. Williams, A. D. Nicks, and N. B. Sammons, 1990. SWRRB A
Basin Scale Simulation Model for Soil Water Resources Management, Texas
A&M University Press, College Station.
Arnold, J. G., B. A. Engel, and R. Srinivasan, 1993. Continuous time grid cell
watershed model. In Heatwole, C. D. (ed.),  Application of Advanced
Information Technologies : Effective Management of Natural Resources.
Information and Electrical Technologies Division of American Society of
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VITA
Pawel Jerzy Mizgalewicz was born in Krakow, Poland, on January 4, 1956,
the son of Czeslawa Mizgalewicz and Jerzy Mizgalewicz. After completing his work at
XIV Grammar School, Krakow, Poland, in 1975, he entered the University of
Technology at Krakow. He received the degree of Master of Science from the
University of Technology in June, 1980. During the following years he was employed
as a research-scientist (1980-1984) and a graduate teacher (1984-1993) at the
University of Technology, Krakow. Most of his research and publications are related
to the urban water distribution systems, sewage networks, and drainage systems.
He received the Polish Ministry Award for research in 1986.
In September, 1988, he entered The Graduate School of The University of
Texas at Austin. He received the degree of Master of Public Affairs and the degree of
Master of Science from the University of Texas in December 1991. From 1989 to
present he is employed as a graduate research assistant at the Center for Research in
Water Resources, University of Texas at Austin.
Permanent address: ul. Jaremy 14B/43, 31-318 Krakow, Poland
This dissertation was typed by Pawel J. Mizgalewicz.