U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2011–1141

National Water-Quality Assessment Program

Watershed Regressions for Pesticides (WARP) 

for Predicting Atrazine Concentration in Corn Belt Streams

Watershed Regressions for Pesticides (WARP) 

for Predicting Atrazine Concentration 

in Corn Belt Streams 

By Wesley W. Stone and Robert J. Gilliom

National Water-Quality Assessment Program

Open-File Report 2011–1141

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

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Suggested citation:

Stone, W.W., and Gilliom, R.J., 2011, Watershed regressions for pesticides (WARP) for predicting atrazine 

concentration in Corn Belt streams: U.S. Geological Survey Open-File Report 2011–1141, 18 p.
iii

Foreword

The U.S. Geological Survey (USGS) is committed to providing the Nation with reliable scientific 

information that helps to enhance and protect the overall quality of life and that facilitates effective 

management of water, biological, energy, and mineral resources (http://www.usgs.gov/). Information on 

the Nation’s water resources is critical to ensuring long-term availability of water that is safe for drinking 

and recreation and is suitable for industry, irrigation, and fish and wildlife. Population growth and 

increasing demands for water make the availability of that water, measured in terms of quantity and 

quality, even more essential to the long-term sustainability of our communities and ecosystems.

The USGS implemented the National Water-Quality Assessment (NAWQA) Program in 1991 to support 

national, regional, State, and local information needs and decisions related to water-quality management and policy (http://water.usgs.gov/nawqa). The NAWQA Program is designed to answer: What is the 

quality of our Nation’s streams and groundwater? How are conditions changing over time? How do natural 

features and human activities affect the quality of streams and groundwater, and where are those effects 

most pronounced? By combining information on water chemistry, physical characteristics, stream habitat, 

and aquatic life, the NAWQA Program aims to provide science-based insights for current and emerging 

water issues and priorities. From 1991 to 2001, the NAWQA Program completed interdisciplinary assessments and established a baseline understanding of water-quality conditions in 51 of the Nation’s river 

basins and aquifers, referred to as Study Units (http://water.usgs.gov/nawqa/studies/study_units.html).

National and regional assessments are ongoing in the second decade (2001–2012) of the NAWQA Program 

as 42 of the 51 Study Units are selectively reassessed. These assessments extend the findings in the Study 

Units by determining water-quality status and trends at sites that have been consistently monitored for 

more than a decade, and filling critical gaps in characterizing the quality of surface water and groundwater. 

For example, increased emphasis has been placed on assessing the quality of source water and finished 

water associated with many of the Nation’s largest community water systems. During the second decade, 

NAWQA is addressing five national priority topics that build an understanding of how natural features and 

human activities affect water quality, and establish links between sources of contaminants, the transport 

of those contaminants through the hydrologic system, and the potential effects of contaminants on humans 

and aquatic ecosystems. Included are studies on the fate of agricultural chemicals, effects of urbanization 

on stream ecosystems, bioaccumulation of mercury in stream ecosystems, effects of nutrient enrichment 

on aquatic ecosystems, and transport of contaminants to public-supply wells. In addition, national syntheses of information on pesticides, volatile organic compounds (VOCs), nutrients, trace elements, and aquatic 

ecology are continuing. 

The USGS aims to disseminate credible, timely, and relevant science information to address practical and 

effective water-resource management and strategies that protect and restore water quality. We hope this 

NAWQA publication will provide you with insights and information to meet your needs and will foster 

increased citizen awareness and involvement in the protection and restoration of our Nation’s waters. 

The USGS recognizes that a national assessment by a single program cannot address all water-resource 

issues of interest. External coordination at all levels is critical for cost-effective management, regulation, 

and conservation of our Nation’s water resources. The NAWQA Program, therefore, depends on advice 

and information from other agencies—Federal, State, regional, interstate, Tribal, and local—as well as 

nongovernmental organizations, industry, academia, and other stakeholder groups. Your assistance and 

suggestions are greatly appreciated.

William H. Werkheiser

USGS Associate Director for Water
iv

Acknowledgments

Syngenta Crop Protection, Inc., and Waterborne Environmental, Inc., provided watershed 

boundaries used in development of the explanatory variable data for the AEEMP and AMP sites. 

The authors thank Naomi Nakagaki, Jeffrey Martin, Gail Thelin, Michael Wieczorek, and 

David Wolock of the USGS for their assistance in preparing the data for analysis.
v

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Methods...........................................................................................................................................................2

Site Selection.........................................................................................................................................2

Calculation of Concentration Statistics ............................................................................................4

Watershed Characteristics 

Used as Explanatory Variables .............................................................................................4

Statistical Analysis ...............................................................................................................................4

Transformations of Response 

and Explanatory Variables ............................................................................................6

Selection of Explanatory Variables...........................................................................................6

Analysis of Model Fit...................................................................................................................7

Estimation of Prediction Intervals.............................................................................................7

Atrazine Models.............................................................................................................................................7

Analysis of Significant Explanatory Variables .................................................................................8

Model Performance..............................................................................................................................9

Model Limitations................................................................................................................................12

Summary and Conclusions.........................................................................................................................14

References Cited..........................................................................................................................................14

Appendixes ...................................................................................................................................................17

Figures

1. Map showing the location of sampling sites used for WARP-CB 

model development and evaluation...........................................................................................3

2. Boxplot explanation for atrazine use intensities for the WARP-CB 

and National WARP model-development sites........................................................................9

3–4. Diagrams showing:

3. Atrazine concentration statistics from concentrations observed 

at model-development and evaluation sites in relation to values 

of the same statistics predicted by the WARP-CB models. ...................................10

4. Prediction intervals for atrazine concentration statistics predicted 

by the WARP-CB models..............................................................................................11

5–6. Boxplots showing:

5. Residual errors for atrazine concentration statistics predicted 

by WARP-CB and National WARP models. ...............................................................13

6. Box plot showing potential prediction errors among concentration 

statistics predicted by use of the atrazine WARP-CB models...............................13
vi

Tables

1. Watershed characteristics considered as explanatory variables 

for WARP-CB models ...................................................................................................................5

2. Summary of statistics and coefficients for the atrazine WARP-CB models.......................7

3. Summary statistics for the WARP-CB explanatory variables ...............................................8

4. Summary of performance of the WARP-CB and National models 

with the 75 WARP-CB model-development site years ...........................................................9

Conversion Factors

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in)

millimeter (mm) 0.03937 inch (in)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2

) 247.1 acre

square kilometer (km2

) 0.3861 square mile (mi2)

Volume

liter (L) 0.2642 gallon (gal)

Mass

gram (g) 0.03527 ounce, avoirdupois (oz)

kilogram (kg) 2.205 pound avoirdupois (lb)

Hydraulic conductivity

micrometer per second (μm/s) 0.1417 inch per hour (in/h) 

Concentrations of atrazine are given in micrograms per liter (μg/l).
vii

Acronyms

AEEMP Atrazine Ecological Effects Monitoring Program

AMP Atrazine Monitoring Program

ARTDRN percentage of the watershed that is artificially drained

CP Mallow’s Cp

MLR multiple linear regression

NAWQA National Water-Quality Assessment Program

NCWQR National Center for Water Quality Research

PERHOR percentage of streamflow due to Hortonian overland flow

PI prediction interval

PMJN total precipitation during May and June of the year of sampling

R2 coefficient of multiple determination

RSE residual standard error

SRL soil restrictive layer

SRL25 percentage of the watershed with a soil restrictive layer within 

top 25 centimeters

SSURGO Soil Survey Geographic database

UI atrazine use intensity, the annual agricultural use in a watershed

USDA U.S. Department of Agriculture

USEPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey

WA watershed area

WARP Watershed Regression for Pesticides

WARP-CB Watershed Regression for Pesticides for the Corn Belt region

Watershed Regressions for Pesticides (WARP) 

for Predicting Atrazine Concentration in Corn Belt Streams

By Wesley W. Stone and Robert J. Gilliom

Abstract

Watershed Regressions for Pesticides (WARP) models, 

previously developed for atrazine at the national scale, can 

be improved for application to the U.S. Corn Belt region by 

developing region-specific models that include important 

watershed characteristics that are influential in predicting 

atrazine concentration statistics within the Corn Belt. WARP 

models for the Corn Belt (WARP-CB) were developed for 

predicting annual maximum moving-average (14-, 21-, 30-, 

60-, and 90-day durations) and annual 95th-percentile atrazine 

concentrations in streams of the Corn Belt region. All streams 

used in development of WARP-CB models drain watersheds 

with atrazine use intensity greater than 17 kilograms per 

square kilometer (kg/km2). The WARP-CB models accounted 

for 53 to 62 percent of the variability in the various concentration statistics among the model-development sites. 

The 95-percent prediction intervals are well within a factor 

of 10 above and below the predicted concentration statistic. 

WARP-CB model predictions were within a factor of 5 of 

the observed concentration statistic for over 90 percent of 

the model-development sites. The WARP-CB residuals and 

uncertainty are lower than those of the National WARP model 

for the same sites. The WARP-CB models provide improved 

predictions of the probability of exceeding a specified criterion 

or benchmark for Corn Belt streams draining watersheds with 

high atrazine use intensities; however, National WARP models 

should be used for Corn Belt streams where atrazine use intensities are less than 17 kg/km2

 of watershed area.

Introduction

The Watershed Regressions for Pesticides (WARP) 

models use watershed characteristics as explanatory variables to predict pesticide concentration statistics in streams 

(Larson and Gilliom, 2001). For watersheds with inadequate direct measurement of pesticide concentrations, 

WARP model predictions can and have been used in the 

selection of vulnerable watersheds for more intensive study 

(U.S. Environmental Protection Agency, 2007). WARP 

models are based on empirical relations between pesticide 

concentrations observed at monitoring sites and selected 

watershed characteristics available nationally. Larson and 

others (2004) and Stone and Gilliom (2009) developed WARP 

models specifically for atrazine at the national scale, and these 

are referred to as “National WARP models” in subsequent 

discussion. The monitoring sites used to develop the National 

WARP models are distributed across the United States and 

cover a wide range of atrazine use intensity and watershed 

characteristics (Stone and Gilliom, 2009). The most influential variable in the National WARP models is use intensity, 

expressed as annual mass applied within a watershed divided 

by watershed area. Atrazine use intensity varies considerably 

across the United States (Gilliom and others, 2006), and the 

National WARP model-development sites reflect this wide 

range in atrazine use intensity. The National WARP models 

are well suited for guiding and planning of more intensive 

assessments of vulnerable watersheds at a national level. For 

some agricultural regions, however, there are opportunities 

for improving predictions by developing regional models that 

make use of region-specific data on stream concentrations and 

watershed characteristics to better represent the conditions in 

the region—in this case the Corn Belt.

The Corn Belt region of the United States includes all 

or parts of Iowa, Illinois, Indiana, Minnesota, South Dakota, 

Nebraska, Kansas, Missouri, Ohio, and Wisconsin (fig. 1). 

These states were the top 10 states in terms of corn-for-grain 

acres harvested and accounted for approximately 79 percent of 

the Nation’s corn-for-grain acreage in the 2007 (U.S. Department of Agriculture, 2007a). Most of the agricultural use of 

atrazine is associated with corn production, and measured 

stream concentrations of atrazine closely match the geographic 

distribution of corn cultivation (Gilliom and others, 2006). 

Use intensity is the most influential variable in the National 

WARP models, and atrazine use intensity within the Corn Belt 

is high and not widely variable (fig. 1). WARP models can be 

improved for application to the Corn Belt region by developing region-specific models that include important watershed 

characteristics that are influential in predicting atrazine concentration statistics within the Corn Belt. These new WARP 

models are called Corn Belt WARP (WARP-CB) and they 

reduce the uncertainty in predicted atrazine concentrations 

for high-use areas within the Corn Belt. The primary objectives of this report are to present WARP-CB models for annual 
2 Watershed Regressions for Pesticides (WARP) for Predicting Atrazine Concentration in Corn Belt States

maximum moving-average concentrations (14-, 21-, 30-, 60-, 

and 90-day durations) and annual 95th-percentile concentrations specific to the high-atrazine-use areas of the Corn 

Belt, evaluate the influence of explanatory variables on the 

predicted concentration statistics, and evaluate the accuracy 

and uncertainty associated with the predicted concentration 

statistics. 

Methods

Methods used in this study included selection of stream 

monitoring sites for the models, calculation of atrazineconcentration statistics, and development and evaluation of 

regression models to predict atrazine-concentration statistics.

Site Selection

This study was limited to stream monitoring sites 

with atrazine concentration data suitable for estimating 

concentration statistics such as annual maximum moving 

averages (14-, 21-, 30-, 60-, and 90-day durations) and the 

annual 95th-percentile concentrations. Ideally, a candidate 

site would have been sampled daily, at least during runoff 

events throughout the high atrazine use period, in order 

to accurately characterize short-term concentrations such 

as the annual maximum 14- and 21-day moving average 

(U.S. Environmental Protection Agency, 2010b). However, 

sites with such high sampling frequencies are few. Sites were 

thus chosen to balance the objective of increasing the accuracy 

of calculated atrazine concentration statistics with the objective of retaining a large number of sites for model development and evaluation. The site selection criteria were based on 

the days between sampling dates during the period of annual 

high atrazine use for the Corn Belt, April 15 through July 30. 

The maximum moving-average and 95th-percentile concentrations are expected to occur during the high-atrazine-use period 

for the Corn Belt (Crawford, 2001; Crawford, 2004). Sites 

where the maximum interval between samples was 10 days 

or less between April 15 and July 30 were selected for use in 

model development. This 10-day maximum interval between 

sample dates ensures that at least two samples will be used 

in the computation of the 21-day moving-average concentrations during the high-use season. Lerch and others (2011) and 

U.S. Environmental Protection Agency (2007) both show that 

maximum moving-average concentrations calculated from 

data collected at regular intervals as short as every 4 days 

were biased low when compared to moving-average concentrations calculated from data collected more frequently and 

targeting runoff events. However, for the purposes of building regression models for the Corn Belt, not enough sites and 

data are available with such high-frequency targeted sampling 

as described in Lerch and others (2011) and, therefore, the 

regression models include sites likely to have low-biased estimates for short duration concentration statistics.

Data from sites sampled by the U.S. Geological Survey 

National Water-Quality Assessment (NAWQA) program, the 

National Center for Water Quality Research (NCWQR) of 

Heidelberg University, Tiffin, Ohio (National Center for Water 

Quality Research, 2009), the and the U.S. Environmental 

Protection Agency Atrazine Ecological Effects Monitoring 

Program (AEEMP) Midwestern Stream Monitoring project 

(U.S. Environmental Protection Agency, 2010a) were evaluated for site selection. In all, 44 sites met the selection criteria 

for 1 or more years of sample collection (fig. 1). Of these 

44 sites, 2 had only 1 year of data meeting the selection criteria, whereas the other 42 sites all had more than 2 years of 

data collection that met the criteria. To expand the number of 

observations available for model development, 2 years of data 

were used for 42 of the 44 sites with sufficient data. Limiting the number of years used to 2 for each site prevents any 

one site from having more influence on model development 

because of having more data in the analysis. When more than 

2 years of data met the selection criteria for a site, the 2 years 

with the highest number of samples were selected for use. 

The total number of site and year combinations available for 

model development was 86, including the 2 sites with only 

1 year of data. Of the 86 site years selected, 73 of the site and 

year combinations also had at least 2 samples used to calculate 

the 14-day moving-average concentrations during the atrazine 

high-use season. WARP-CB models were not developed for 

the annual mean or lower annual percentiles because the sites 

selected for model development did not have sufficient sampling to adequately characterize the atrazine stream concentrations outside of the high-use season. Specifically, because 

the AEEMP site sampling strategy targeted only the high-use 

season, use of measured atrazine concentrations to calculate 

and predict annual means and lower annual percentile concentrations for these sites would produce estimates that may be 

substantially biased high. 

Sites selected for model development include 37 AEEMP 

sites sampled between 2004 and 2007, 5 NCWQR sites 

sampled between 1995 and 1998, and 2 USGS NAWQA sites 

sampled between 1992 and 1998. The AEEMP sampling 

typically occurred during 4-day fixed intervals; however this 

fixed-interval sampling was augmented for some site and years 

with autosamplers that collected stream samples during runoff 

events (U.S. Environmental Protection Agency, 2007). For 

the AEEMP site and year selection, years with autosamplercollected data characterizing runoff events were chosen over 

years with only fixed-interval sampling. 

Data used for model evaluation included 11 site and year 

combinations from the pool of selected AEEMP and NCWQR 

site years and 10 sites from the U.S. Environmental Protection 

Agency Atrazine Monitoring Program (AMP) for Community 

Water Systems (U.S. Environmental Protection Agency, 2011). 

The model-evaluation site and year combinations chosen from 

the pool of selected AEEMP and NCWQR site years represent 

different areas of the Corn Belt and are independent of the 

remaining 75 site and year combinations that were used to 

develop the regression models. The AMP sites represent rivers 
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2007 atrazine use, in 

kilograms per square kilometer

of county agricultural land

< 55 - 10 > 17

>10 - 17

Indiana

Illinois

Missouri

Kansas

Nebraska

South Dakota

Minnesota

Wisconsin

Cor

Model SWhite-filled 

used only f

#* AEEM

") USGS!( NCW$+ AMP

Figure 1. Location of sampling sites used for WARP-CB model development and evaluation. (2007 estimated atrazine use derived from ThAbbreviations: AEEMP, U.S. Environmental Protection Agency Atrazine Ecological Effects Monitoring Program; USGS, U.S. Geological SurvCenter for Water Quality Research; AMP, U.S. Environmental Protection Agency Atrazine Monitoring Program.)
4 Watershed Regressions for Pesticides (WARP) for Predicting Atrazine Concentration in Corn Belt States

and streams that were sampled weekly from April through July 

and biweekly the remainder of the year (U.S. Environmental Protection Agency, 2003). The AMP site data used in the 

model evaluation were collected during 2005 and 2006, and all 

the selected AMP sites had atrazine use intensity greater than 

17 kg/km2 of watershed area.

Calculation of Concentration Statistics

The annual maximum moving-average and 95th-percentile concentrations of atrazine were calculated by means of the 

methods described in Stone and others (2008). As described 

previously, the AEEMP data include results from fixed-interval 

sampling and samples collected by autosamplers during runoff 

events. For the AEEMP sites, both the fixed-interval samples 

and the autosampler data were used in the calculation of 

concentrations statistics. Hourly atrazine concentrations were 

estimated for the entire period of record (multiple years) for 

each site through linear interpolation of actual observations. 

The hourly concentration estimates were averaged to obtain an 

estimated daily concentration. The hourly estimates facilitated 

computations for days with multiple samples but were not 

used for other purposes. The estimated daily concentrations 

were used to estimate the annual 95th-percentile concentrations. Moving-average concentrations for the selected durations (14, 21, 30, 60, and 90 days) were computed for each 

day; for example, the 14-day moving average for a particular 

day includes the average of that day and the 13 previous days. 

The estimated moving-average concentrations then were 

truncated to the 1-year WARP development period for each 

site and year combination, and the maximum moving-average 

concentrations were determined for each of the durations. 

Calculated concentration statistics for the WARP-CB model 

sites are listed in appendix 1. 

Watershed Characteristics 

Used as Explanatory Variables

The many watershed characteristics evaluated as potential explanatory variables in the WARP-CB model development are listed in table 1. Data and detailed descriptions of the 

potential explanatory variables used in model development are 

listed in appendixes 1 and 2. Potential explanatory variables 

representing pesticide use, land use and population, agricultural management practices, soil properties, physical watershed characteristics, weather and climate characteristics, and 

hydrological properties were considered. 

The above-mentioned watershed characteristics are 

largely the same used by Stone and Gilliom (2009) for the 

National WARP models, with the notable exception of an 

additional variable representing the potential presence of 

a soil restrictive layer in the watershed. The presence of a 

shallow clay pan or low-permeability layer in the soils of a 

watershed has been associated with increased vulnerability 

for transport of pesticides to streams (Lerch and Blanchard, 

2003; U.S. Environmental Protection Agency, 2007). Highpotential-runoff soils may have a low-permeability soil layer 

and may also be associated with hydrologic group C and D 

soils (U.S. Department of Agriculture, 2007b). Past development of National WARP models included variables intended 

to characterize high-potential-runoff soils within watersheds, 

such as the K-factor (mean soil erodibility in the watershed) and the mean percentage of watershed soils classified 

as hydrologic soil groups C and D. The availability of Soil 

Survey Geographic (SSURGO) data for the Corn Belt region 

provides the opportunity to better characterize the extent of 

a low-permeability soil layer in the development site watersheds. For the purposes of this study, this soil layer of low 

permeability is called a Soil Restrictive Layer (SRL). The 

SRL variables were developed from SSURGO soil data tables 

(U.S. Department of Agriculture, 2010) and were based on 

three soil depth zones (0–25, 0–50, and 0–100 cm below land 

surface). For the purposes of this study, a saturated hydraulic 

conductivity of less than or equal to 1 μm/s was considered to 

indicate a layer of low permeability. The SSURGO data tables 

were evaluated to generate a data table of the percent presence 

for each soil-depth-zone-specific SRL within the SSURGO 

map units, based on the weighted average of the components 

of each SSURGO map unit. A 30-m-resolution raster image of 

the SSURGO map units for the Corn Belt was produced from 

the original 10-m-resolution raster image of the SSURGO map 

units. The data tables for the percent presence of the depthzone-specific SRLs for the SSURGO map units was combined 

with the 30-m raster image of SSURGO map units to produce 

a 30-m-resolution raster image of SRL values. Watershed 

polygons for the WARP-CB sites were converted to 30-m-resolution raster images and overlain with the 30-m-resolution 

National Land Cover Dataset 2001 to produce a raster image 

of agricultural land within each watershed. The watershed raster image of agricultural land was overlain with the SRL raster 

image to determine the mean percentage of the watershed with 

a depth-zone-specific SRL.

Statistical Analysis

A regression approach was used in the development of 

the WARP-CB models. Statistical methods used to support 

the regression approach include transformations of response 

and explanatory variables, selection of explanatory variables, 

analysis of model fit, and estimation of prediction intervals.

The National WARP models were developed with maximum likelihood regression methods because of the presence 

of censored observations in the national model-development 

data. However, the WARP-CB model-development data do not 

contain censored observations; therefore, standard multiple 

linear regression (MLR) methods were used to develop the 

WARP-CB models. 
Methods 5

Table 1. Watershed characteristics considered as explanatory variables for WARP-CB models.—Continued

[WARP-CB, Watershed Regression for Pesticides for Corn Belt region; USLE, Universal Soil Loss Equation; cm, centimeter; d, day; km, kilometer; km2, square 

kilometer; m, meter; mm, millimeter; yr, year]

Variable Description

Pesticide use

UI Annual atrazine agricultural-use intensity (kg/km2

).

Land use and population

AG Percent of basin with agricultural land use.

FOREST Percent of basin with forest land use.

URBAN Percent of basin with urban land use.

POPDEN Mean 2000 population density in watershed (people/km2

).

Agricultural management practices

ARTDRN Percent of the watershed that is artificially drained.

CONTILL Percent of the watershed with corn crop and conservation tillage.

REGTILL Percent of the watershed with corn crop and regular tillage.

IRRI Percent of the watershed that is irrigated.

TILE Percent of the watershed that is drained by subsurface tiles.

Soil properties

AWC Mean available water capacity (fraction) in watershed.

CLAY Mean percent clay in watershed soils.

HGAB Mean percent of watershed soils classified as hydrologic soil groups A and B.

HGCD Mean percent of watershed soils classified as hydrologic soil groups C, D, and C/D.

K Mean soil erodibility of uppermost soil horizon in watershed (K-factor for USLE).

SRL25 Mean percent of agricultural area watershed soils with a soil restrictive layer (saturated hydraulic conductivity ≤ 1 μm/s) 

within top 25 cm of soil layer. 

SRL50 Mean percent of agricultural area watershed soils with a soil restrictive layer (saturated hydraulic conductivity ≤ 1 μm/s) 

within top 50 cm of soil layer.

SRL100 Mean percent of agricultural area watershed soils with a soil restrictive layer (saturated hydraulic conductivity ≤ 1 μm/s) 

within top 100 cm of soil layer.

ORGM Mean percent organic matter in watershed soils.

PERM Mean soil permeability in the watershed (cm/h). 

SAND Mean percent sand in watershed soils.

SILT Mean percent silt in watershed soils.

Physical watershed characteristics

WA Watershed area (km2

).

ELEV Mean basin elevation (m).

LATC Latitude of basin centroid (decimal degrees).

LONC Longitude of basin centroid (decimal degrees).

SLOPE Mean percent slope in watershed.

Weather/climate characteristics

ADRY Mean annual number of consecutive dry days, 1961–1990.

APPT Mean annual 1961–1990 precipitation (cm/yr).

APPTI Mean annual 1961–1990 precipitation intensity (mm/d).

ATEMP Mean annual 1961–1990 temperature (C).

WET Mean annual number of consecutive wet days, 1961–1990.

R Mean annual 1971–2000 rainfall erosivity (R-factor for USLE).

PYEAR Total precipitation during the year of sampling (mm).

PAPRJUN Total precipitation during April, May, and June of the year of sampling (mm).
6 Watershed Regressions for Pesticides (WARP) for Predicting Atrazine Concentration in Corn Belt States

Table 1. Watershed characteristics considered as explanatory variables for WARP-CB models.—Continued

[WARP-CB, Watershed Regression for Pesticides for Corn Belt region; USLE, Universal Soil Loss Equation; cm, centimeter; d, day; km, kilometer; km2, square 

kilometer; m, meter; mm, millimeter; yr, year]

Variable Description

Weather/climate characteristics (continued))

PAPRSEP Total precipitation during April through September of the year of sampling (mm).

PMAY Total precipitation during May of the year of sampling (mm).

PMJN Total precipitation during May and June of the year of sampling (mm).

PMJL Total precipitation during May, June, and July of the year of sampling (mm).

Hydrologic properties

CONTACT Mean subsurface contact time (days).

PERDUN Percent of watershed streamflow contributed by saturation or Dunne overland flow.

PERHOR Percent of watershed streamflow contributed by infiltration-excess or Horton overland flow.

PET Mean potential evapotranspiration (cm).

ROFF Mean annual 1951–1980 runoff (cm/yr).

Transformations of Response 

and Explanatory Variables

MLR models used for testing hypotheses and estimating 

confidence or prediction intervals require that the variance of 

the residuals be constant and that the residuals be independent 

and normally distributed (Helsel and Hirsch, 2002). Departures from these requirements can result in flawed estimates 

of model coefficients. A means of addressing possible departures from model assumptions is through transformation of 

either the response or the explanatory variables or both (Neter 

and others, 1985). Various transformations were considered 

to minimize departures from the requirements of the MLR 

method. The logarithm of concentration was used as the 

response variable throughout model development. For the 

explanatory variables, logarithmic, square-root, and third-root 

transformations, as well as the untransformed value, were 

considered during development of the regression models.

Because the response variable is a logarithmic transformation, concentrations predicted by the model (after retransformation) are the median concentrations expected for sites 

that have a given set of explanatory values, rather than the 

mean concentrations. Predicted concentration statistics were 

not adjusted for transformation bias because estimates of 

median values of the statistics were considered more appropriate for the purposes of this study.

Selection of Explanatory Variables

A stepwise approach was used for the initial selection 

of explanatory variables to include in the regression models. The StepAIC procedure of Venables and Ripley (1999), 

implemented in S-PLUS, was used for the initial selection 

of explanatory variables to include in the regression models. 

The StepAIC procedure, based on Akaike’s Information Criterion (Akaike, 1974), balances model goodness of fit with the 

number of parameters needed to achieve that fit. The procedure attempts to quantify the concept of model parsimony by 

choosing simpler models over complex ones unless a complex 

model substantially improves the fit of the model.

Variable selection began with all of the potential explanatory variables and their transformations, too many to include 

in the StepAIC procedure at one time. Groups of 12 variables were randomly selected and then evaluated with the 

StepAIC procedure. The random selection and evaluation of 

variables was repeated 2,000 times. Variables selected greater 

than 50 percent of the time by the StepAIC procedure for 

all repetitions were retained in the analysis. When multiple 

transformations of a variable were retained by the StepAIC 

selection process, the transformed or untransformed value 

with the highest frequency of retention was carried forward in 

the analysis. Less than 50 percent of the potential explanatory 

variables were retained through this initial StepAIC process; 

however, this process resulted in the retention of far too many 

variables than practical for the final models. Final model selection used a combination of StepAIC, Mallow’s Cp, multicollinearity evaluation, and scientific judgment. Mallow’s Cp, 

like StepAIC, balances model goodness of fit with the number 

of parameters needed to achieve that fit. Models and their 

explanatory variables with the lowest Cp values were retained 

for further evaluation. Multicollinearity among explanatory 

variables was measured through use of variance inflation factors (Helsel and Hirsch, 2002). When explanatory variables 

had high variance inflation factors, they each were evaluated 

independently in the models. Finally, potential models were 

subjectively evaluated for reasonableness (for example, the 

models predict increasing concentration with increasing runoff) and their overall contribution to explaining the variation 

in atrazine-concentration statistics. 
Atrazine Models 7

Analysis of Model Fit

Diagnostics used to evaluate the regression models 

included leverage, studentized residuals, Cook’s D, and 

DFFITS (Helsel and Hirsch, 2002). Measures of goodness of 

fit, including the residual standard error (RSE) and the coefficient of multiple determination (R-square or R2) were also 

used in evaluation of the regression models. Box and whisker 

plots (Tukey, 1977) were used to qualitatively assess model 

uncertainty and residual errors. 

Comparisons between predicted concentration statistics 

and concentration statistics computed from observations are 

made frequently in the discussion of model performance. 

Terms used for these comparisons are defined here for clarity. 

Concentration statistics generated by the WARP-CB models 

are referred to as “predicted concentration statistics,” and concentration statistics computed from observations are referred 

to as “observed concentration statistics.”

Estimation of Prediction Intervals

Uncertainty in the prediction of a concentration statistic 

can be expressed in terms of a prediction interval (PI) for a 

specified confidence level: the confidence level used in this 

study is 95 percent. Conceptually, each predicted concentration statistic is the median estimate of the particular concentration statistic (for example, percentiles or annual maximum 

moving averages) for all the stream sites that have the same 

combination of values for the explanatory variables. The PI is 

the range of values for a concentration statistic within which 

95 percent of the actual concentration-statistic values are 

expected to occur for all stream sites with the same values of 

explanatory variables. In addition, the PI can be interpreted as 

the range within which the actual concentration statistic for 

an individual site and year is expected to fall 95 percent of the 

time. Prediction intervals were approximated by using normal 

theory and the t-distribution; that is, methods for ordinary least 

squares regression were used (Helsel and Hirsch, 2002). 

Atrazine Models

The models for the 95th-percentile and the annual maximum moving-average atrazine-concentration statistics have

log10(concentration)= (1)

f [SRL25,log (PMJN),(PERHOR)1/2

10 ,log10(WA),ARTDRN,UI]

where

 SRL25 is the percentage of the watershed agricultural 

land with a soil restrictive layer within top 

25 cm of soil surface; 

 PMJN is the total precipitation (mm) during May and 

June of the year of sampling; 

 PERHOR is the estimated percentage of streamflow due 

to Hortonian overland flow; 

 WA is the watershed area (km2

); 

 ARTDRN is the percentage of the watershed that is 

artificially drained; and 

 UI is atrazine-use intensity, the annual 

agricultural use in a watershed (kg) divided 

by watershed area (km2). 

Coefficients and statistics for all models are given in 

table 2, and summary statistics for the explanatory variables 

used in the WARP-CB models are given in table 3. Concentration statistics predicted by these models represent the expected 

median value of the concentration statistic for all sites with the 

same values for the explanatory variables.

Table 2. Summary of statistics and coefficients for the atrazine WARP-CB models.

[WARP-CB, Watershed Regression for Pesticides for Corn Belt region; RSE, residual standard error. Model variables are defined in table 1.]

Model Regression coefficients (p-value) R-square RSE

Intercept SRL25 log PMJN (PERHOR)1/2 log WA 10 10 ARTDRN UI

14-day -3.21

(<0.001)

0.015

(<0.001)

1.01

(<0.001)

0.234

(<0.001)

0.244

(0.002)

0.005

(0.003)

0.0055

(0.158)

0.53 0.38

21-day 3.44

(<0.001)

0.015

(<0.001)

1.06

(<0.001)

0.241

(<0.001)

0.259

(<0.001)

0.005

(0.003)

0.0050

(0.173)

0.56 0.37

30-day -3.45

(<0.001)

0.014

(<0.001)

1.04

(<0.001)

0.244

(<0.001)

0.252

(<0.001)

0.005

(0.001)

0.0045

(0.204)

0.58 0.35

60-day -3.37

(<0.001)

0.014

(<0.001)

0.95

(<0.001)

0.222

(<0.001)

0.269

(<0.001)

0.005

(0.002)

0.0045

(0.156)

0.60 0.32

90-day -3.27

(<0.001)

0.014

(<0.001)

0.87

(<0.001)

0.210

(<0.001)

0.269

(<0.001)

0.004

(0.002)

0.0047

(0.122)

0.61 0.30

95th-percentile

-3.25

(<0.001)

0.015

(<0.001)

0.88

(<0.001)

0.245

(<0.001)

0.261

(<0.001)

0.005

(<0.001)

0.0047

(0.134)

0.62 0.31
8 Watershed Regressions for Pesticides (WARP) for Predicting Atrazine Concentration in Corn Belt States

Table 3. Summary statistics for the WARP-CB explanatory variables.

[WARP-CB, Watershed Regressions for Pesticides for Corn Belt region; mm, milimeters; km2, square kilometers; kg, kilograms; Model variables are defined in 

Table 1.]

Statistic SRL25

(percent)

PMJN

(mm)

PERHOR

(percent)

WA

(km2

)

ARTDRN

(percent)

UI

(kg/km2)

Minimum 0.00 64.5 0.20 23 0.00 17.27

25th percentile 0.00 137.5 6.22 53 5.42 28.69

Median 0.09 191.5 8.00 64 30.93 38.21

Mean 6.37 197.4 8.63 1050 32.86 39.84

75th percentile 7.00 248.0 9.89 112 59.69 49.84

Maximum 92.04 348.7 28.7 29290 81.60 73.66

Analysis of Significant Explanatory Variables

SRL25 was highly significant (p<0.001) and the most 

important explanatory variable in the regression models 

(table 2). Models using only SRL25 as an explanatory variable 

account for 19 to 21 percent of the variability in concentration 

statistics among the development sites. SRL25 is an indication 

of the percentage of the watershed that may have a soil restrictive layer (saturated hydraulic conductivity less than or equal 

to 1 μm/s) within the top 25 cm of the soil column. Lerch and 

Blanchard (2003) found that the presence of a layer impeding 

the downward movement of water to groundwater was associated with higher vulnerability of a watershed for pesticide 

transport to streams. The coefficient for SRL25 is positive in 

all the models (table 2), indicating that watersheds with more 

area underlain by soils with a low-permeability layer have an 

increased potential for transport of atrazine from application 

areas to streams.

PMJN was highly significant (p<0.001) and the second 

most important explanatory variable in the regression models 

(table 2). Models using only PMJN as an explanatory variable 

account for 14 to 17 percent of the variability in concentration statistics among the development sites. PMJN is the total 

precipitation during May and June of the year of sampling 

and a significant explanatory variable in the National WARP 

models. For watersheds within the Corn Belt, the months April 

through June include the highest atrazine application period. 

High precipitation during May and June creates substantial 

surface runoff and increases the potential for recently applied 

atrazine loss to streams, which is consistent with the positive 

coefficient observed for PMJN in all models.

PERHOR was highly significant (p<0.001) and the third 

most important explanatory variable in the regression models 

(table 2). Models using only PERHOR as an explanatory variable account for 12 to 15 percent of the variability in concentration statistics among the development sites. PERHOR is 

the estimated percent Hortonian overland flow contribution 

to the stream. Hortonian overland flow is also called infiltration-excess overland flow and occurs when precipitation 

rates exceed infiltration rates. An area with high precipitation 

intensity and low soil permeability has a higher percentage of 

streamflow from Hortonian overland flow than an area with 

low precipitation intensity and high soil permeability. The 

positive coefficient of this variable in the WARP-CB models 

implies that areas with higher percentage of streamflow from 

Hortonian overland flow also have higher atrazine stream concentrations than those with lower contributions to streamfow 

from Hortonian overland flow.

WA (watershed area) was significant (p<0.01) and positive for all the WARP-CB models (table 2). Watershed area is 

also a significant explanatory variable (positive coefficient) in 

the National WARP models. Larson and Gilliom (2001) listed 

several factors that may contribute to the positive relation 

between watershed area and atrazine concentration in streams. 

For the WARP-CB model-development sites, two of the factors listed by Larson and Gilliom (2001) appear most relevant. 

First, the contribution of water from multiple small streams 

to a large river in a region dominated by agricultural land use 

can result in elevated concentrations that are sustained for a 

longer time than in the individual streams because the timing 

of pesticide application and subsequent runoff can vary among 

the individual streams. Second, in some small streams, the 

highest concentrations may not have been sampled because 

concentrations of pesticides may remain elevated for relatively 

short periods. The computed concentration statistics for these 

small streams may thus be biased low, further strengthening 

the positive relation between watershed area and concentration 

reflected in the coefficients for the watershed-area variable 

in the regression models. Lerch and others (2011) found that 

the moving-average concentration statistics calculated from 

AEEMP monitoring data for Goodwater Creek (MO-02) at 

an interval of every 4 days were biased low in comparison 

to more intensive samples collected during their study at the 

same site. 

ARTDRN was significant (p<0.01) and positive in all 

models (table 2). ARTDRN is the percentage of the watershed 

that has artificial surface and subsurface drainage. ARTDRN, 

as used in the WARP-CB models, is defined by conservation 

practice categories 606, 607, and 608 in the 1992 Natural 

Resources Inventory (U.S. Department of Agriculture, 1995). 

Artificial drainage routes excess water to streams that may 

otherwise slowly percolate to groundwater or pond and eventually evaporate. Artificial drainage used in depressional areas 

or areas of low topographical relief without natural surface 
Atrazine Models 9

 Outside value

(>1.5 times IQR)

Largest value

less than 

1.5 times IQR

75th percentile

25th percentile

Median

Smallest value

less than 

1.5 times IQR

IQR

WARP−CB

 Model Sites

National WARP

 Model Sites

−4

−3

−2

−1

0

1

2

LOGARITHM OF ATRAZINE USE INTENSITY,

IN KILOGRAMS PER SQUARE KILOMETER

Figure 2. Atrazine use intensities for the WARP-CB 

and National WARP model-development sites.

runoff pathways will increase pesticide loss to streams because 

water that may naturally infiltrate to groundwater or evaporate will be transported to streams by the increased surface or 

subsurface drainage (Baker and others, 2007).

UI was not significant in any of the WARP-CB models 

(table 2). UI is the atrazine-use intensity in the watershed. 

Larson and others (2004) and Stone and Gilliom (2009) 

found that atrazine-use intensity in the watershed, as the 

fourth-root transformation, was the most important explanatory variable in the National WARP models. However, this 

is not true for WARP-CB models (table 2). The WARP-CB 

model-development sites represent a much higher and narrower distribution of atrazine-use intensity than the sites 

used in development of the National WARP models (fig. 2). 

Given the small variation in use intensity between the WARPCB model-development sites, atrazine use intensity was not 

expected to be a significant explanatory variable for atrazine 

concentration statistics for the WARP-CB models. However, 

atrazine-use intensity is an important indicator for proper 

application of the WARP-CB and the National WARP models. 

Sites where atrazine use intensities are lower than those used 

in the development of the WARP-CB (atrazine use intensity 

less than 17 kg/km2

 watershed area) should be modeled with 

the National WARP models and not the WARP-CB models.

Table 4. Summary of performance of the WARP-CB and National models with the 75 WARP-CB model-development site years.

WARP-CB models National WARP models

Model Percent of predictions within 

a factor of

Percent of predictions within 

a factor of

10 5 2 10 5 2

14-day 100 93 57 -- -- --

21-day 100 95 60 92 83 45

30-day 100 96 64 -- -- --

60-day 100 97 72 94 88 39

90-day 100 100 75 96 88 43

95th-percentile 100 97 71 96 89 51

Model Performance

The performance of WARP-CB models was evaluated by 

assessment of (1) goodness of fit and model uncertainty, (2) 

performance of the model with the model-development and 

evaluation sites, and (3) comparison to the National WARP 

models applied to WARP-CB development sites. 

Regression-model results for the annual maximum moving-average (14-, 21-, 30-, 60-, 90-day durations) and annual 

95th-percentile concentration WARP-CB models are shown 

in figure 3. Values of R2 ranged from 0.53 for the 14-day 

moving-average model to 0.62 for the 95th-percentile model, 

meaning that the models accounted for 53 to 62 percent 

of the variability in the concentration statistics among the 

75 site and year combinations used for model development. 

All of the predicted concentration statistics are within a factor 

of 10 of the observed concentration statistics at the development and evaluation sites. WARP-CB model predictions for 

development sites were within a factor of 5 of the observed 

concentration statistic for more than 90 percent of the site 

and year combinations (table 4). Regression-model results 

for the evaluation sites in relation to the model-development 

sites also are shown in figure 3. The WARP-CB models do 

not show substantial bias for either the development or the 

evaluation sites.

The PIs for the WARP-CB models are shown in figure 4 

(model-development site years were arranged and numbered 

by order of increasing predicted 95th percentile concentration 

statistic). Concentration statistics are expressed as logarithms, 

resulting in symmetrical intervals for the plotted PIs; the high 

and low bounds of the intervals are the same distance from 

the predicted value. However, expressing the concentration 

statistics as logarithms obscures the fact that the intervals 

are skewed—the upper part of the PI interval covers a wider 

range of values than the lower part. Comparison of the PIs 

among the predicted concentration statistics shows that the PIs 

are largest for the annual maximum 14-day moving-average 

model and smallest for the annual maximum 90-day movingaverage model (fig. 4). The PIs for all models are within a 

factor of 10 of the observed concentration statistics. The PI 

is a function of the fit of the model and the amount of variability explained by the model. The annual maximum 90-day 
10 Watershed Regressions for Pesticides (WARP) for Predicting Atrazine Concentration in Corn Belt States

−2

−1

0

1

2

−2 −1 0 1 2

R−square = 0.53

RSE = 0.38

Annual maximum

14−day moving average

LOGARITHM OF OBSERVED ATRAZINE−CONCENTRATION

STATISTIC, IN MICROGRAMS PER LITER

−2

−1

0

1

2

−2 −1 0 1 2

R−square = 0.56

RSE = 0.37

Annual maximum

21−day moving average

−2

−1

0

1

2

−2 −1 0 1 2

R−square = 0.58

RSE = 0.35

Annual maximum

30−day moving average

−2

−1

0

1

2

−2 −1 0 1 2

R−square = 0.60

RSE = 0.32

Annual maximum

60−day moving average

−2

−1

0

1

2

−2 −1 0 1 2

R−square = 0.61

RSE = 0.30

Annual maximum

90−day moving average

LOGARITHM OF PREDICTED ATRAZINE−CONCENTRATION STATISTIC,

IN MICROGRAMS PER LITER

−2

−1

0

1

2

−2 −1 0 1 2

R−square = 0.62

RSE = 0.31

95th percentile

EXPLANATION

Development sites

Evaluation sites

1:1 line

Within a factor of 10 of 1:1 line

Figure 3. Atrazine concentration statistics from concentrations observed at model-development and 

evaluation sites in relation to values of the same statistics predicted by the WARP-CB models.
Atrazine Models 11

EXPLANATION

Observed concentration Predicted concentration 95% prediction interval

−2

−1

0

1

2

0 1 0 2 0 3 0 40 50 60 7 0

Annual maximum

14−day moving average

LOGARITHM OF ATRAZINE−CONCENTRATION STATISTIC, IN MICROGRAMS PER LITER

−2

−1

0

1

2

0 1 0 2 0 3 0 40 50 60 7 0

Annual maximum

21−day moving average

−2

−1

0

1

2

0 1 0 2 0 3 0 40 50 60 7 0

Annual maximum

30−day moving average

−2

−1

0

1

2

0 1 0 2 0 3 0 40 50 60 7 0

Annual maximum

60−day moving average

−2

−1

0

1

2

0 1 0 2 0 3 0 40 50 60 7 0

Annual maximum

90−day moving average

SITE NUMBER

−2

−1

0

1

2

0 1 0 2 0 3 0 40 50 60 7 0

95th percentile

Figure 4. Prediction intervals for atrazine concentration statistics predicted by the WARP-CB models. (Model-development 

site years were arranged and numbered by order of increasing predicted 95th percentile concentration statistic.)
12 Watershed Regressions for Pesticides (WARP) for Predicting Atrazine Concentration in Corn Belt States

moving-average model has a better model fit and explains 

more variability (RSE = 0.30; R2 = 0.61) than the annual 

maximum 14-day moving-average model does (RSE = 0.38; 

R2 = 0.53).

Residual errors for the WARP-CB development sites 

from application of the WARP-CB and National WARP models are shown in figure 5. The National WARP models have a 

much larger range of residual errors for the WARP-CB modeldevelopment sites in comparison to the WARP-CB models. 

In addition, the National WARP models tend to overestimate 

atrazine concentration statistics for the WARP-CB modeldevelopment sites in comparison to WARP-CB models. Atrazine use intensity is the most important explanatory variable 

in the National WARP models, the tendency of the National 

WARP models to overestimate atrazine concentration statistics for the WARP-CB development sites may be influenced 

by the high use intensities represented by these sites (fig. 2).

Table 4 shows the performance of the WARP-CB and National 

WARP models for the 75 WARP-CB model-development site 

and year combinations. The percentages of model predictions 

within a factor of 10, 5, and 2 of the observed concentration 

statistic are higher for the WARP-CB models than the National 

WARP models.

The levels of uncertainty for the annual maximum 

moving-average (21-, 60-, and 90-day durations) and 95th-percentile WARP-CB and National WARP models are compared 

in figure 6. PI size is represented as the ratio of the upper 

boundary of the interval to the predicted concentration statistic. This is the same as the ratio of the predicted concentration 

statistic to the lower boundary of the interval. The extreme 

values (shown as asterisks) represent sites where one or more 

explanatory variables are relatively extreme in value when 

compared to values for the rest of the sites. The sites with 

relatively extreme values in one or more explanatory variables 

have wider PIs, meaning greater uncertainty in their predicted 

concentration statistic, than sites with explanatory variable 

values that fall closer to the center of the explanatory data. For 

all atrazine concentration statistics, the PIs for National WARP 

models are approximately twice those for the WARP-CB models, indicating that the National WARP models have a higher 

level of uncertainty than the WARP-CB models.

Model Limitations

Application of the regression models for predicting 

atrazine-concentration statistics, and the WARP methodology 

in general, are subject to several important limitations. 

• The WARP-CB models are based on sites with high 

atrazine use intensities (fig. 2). For stream sites where 

atrazine use intensities are lower than the least value 

used in the WARP-CB model development (17 kg/km2 

watershed area), the National WARP models should 

be used, with WARP-CB used only to provide an 

estimated upper limit for comparison to the National 

WARP result. 

• The sampling frequencies of the model-development 

sites may not be sufficient to reliably characterize 

the highest moving-average concentrations during a 

year. Thus, application of the models to predict the 

annual maximum moving-average concentrations for 

relatively short durations such as the 14- and 21-day 

moving average is expected to generally underpredict 

the actual annual maximum moving-average concentrations for these durations. 

• The regression models are designed for prediction of 

atrazine-concentration statistics for streams within the 

Corn Belt region of the United States. Although the 

sites used for model development represent a wide 

variety of environmental settings and a large range 

of watershed areas, it is likely that other watersheds 

within the Corn Belt have one or more characteristics 

outside the ranges of the watershed parameters used to 

develop the models (table 3). Application of the models to streams draining such watersheds would result in 

increased uncertainty in predicted concentrations. 

• The models were developed by using concentration 

data from streams. Application of the models to lakes, 

reservoirs, or streams heavily influenced by reservoirs 

will result in biased predictions because of the influence of water storage on the temporal distribution of 

concentrations. 

• The atrazine-use data used in the models are estimates 

for applications to agricultural land only. Substantial 

nonagricultural use of atrazine in a watershed could 

result in underprediction of atrazine concentrations in a 

stream, if such use cannot be estimated.
Atrazine Models 13

WARP-CB

Model

National

WARP

Model

WARP-CB

Model

National

WARP

Model

WARP-CB

Model

National

WARP

Model

WARP-CB

Model

National

WARP

Model

Annual maximum

21-day moving average

Annual maximum

60-day moving average

Annual maximum

90-day moving average

Annual

95th percentile

-1.0

-1.0

-0.5

0.0

0.5

1.0

1.5

LOGARITHM OF THE OBSERVED CONCENTRATION STATISTIC MINUS

LOGARITHM OF PREDICTED CONCENTRATION STATISTIC

 Outside value

(>1.5 times IQR)

Largest value

less than 

1.5 times IQR

75th percentile

25th percentile

Median

Smallest value

less than 

1.5 times IQR

IQR

models. (Residual error is log10(observed concentration statistic) – log10(predicted concentration statistic).)

Figure 5. Residual errors for atrazine concentration statistics predicted by WARP-CB and National WARP 

WARP-CB

Model

National

WARP

Model

WARP-CB

Model

National

WARP

Model

WARP-CB

Model

National

WARP

Model

WARP-CB

Model

National

WARP

Model

Annual maximum

21-day moving average

Annual maximum

60-day moving average

Annual maximum

90-day moving average

Annual

95th percentile

0

5

10

15

RATIO OF UPPER BOUNDARY OF PREDICTION INTERVAL TO

PREDICTED ATRAZINE CONCENTRATION STATISTIC

 Outside value

(>1.5 times IQR)

Largest value

less than 

1.5 times IQR

75th percentile

25th percentile

Median

Smallest value

less than 

1.5 times IQR

IQR

Figure 6. Potential prediction errors among concentration statistics predicted by use of the atrazine 

WARP-CB models. (Potential prediction error is represented by the ratio of the upper boundary of the 

95-percent prediction interval to the predicted atrazine concentration statistic. Each boxplot shows the 

ratios among the 75 model-development sites and years.)
14 Watershed Regressions for Pesticides (WARP) for Predicting Atrazine Concentration in Corn Belt States

Summary and Conclusions

Regression models (WARP-CB) were developed for 

predicting annual maximum moving-average (14-, 21-, 30-, 

60-, and 90-day durations) and annual 95th-percentile atrazine 

concentrations in streams of the Corn Belt region of the United 

States, using data on watershed characteristics. Predictions of 

atrazine-concentration statistics generated by these models can 

be used to characterize the concentrations of atrazine for comparison to specific water-quality benchmarks for evaluation of 

potential concerns regarding human health and aquatic life.

All sites used in development of the WARP-CB models drain watersheds with high atrazine use intensity. The 

models accounted for 53 to 62 percent of the variability in 

concentration statistics among the 75 sites and years used for 

model development. For all the models, 95-percent prediction intervals are well within a factor of 10 above and below 

the predicted concentration statistic. Over 90-percent of the 

WARP-CB model predictions for the model-development sites 

are within a factor of 5 of the observed concentrations statistic.

The WARP-CB model-development site predictions show 

smaller overall residual error and reduced uncertainty when 

compared to the National WARP model predictions for the 

same sites. Prediction intervals for National WARP models 

are approximately twice those for the WARP-CB models, 

indicating that the National WARP models have a higher level 

of uncertainty than the WARP-CB models. This lower level 

of uncertainty associated with the WARP-CB models will 

improve the predicted probabilities of exceeding a specified 

criterion or benchmark during application of the models. 

However, the WARP-CB models are based on sites with high 

atrazine use intensities. Even within the Corn Belt region, the 

National WARP models should be used instead of the WARPCB models for sites where atrazine use intensities are lower 

than approximately 17 kg/km2

, although WARP-CB can be 

used to provide estimates of upper limits for comparison to the 

National WARP models. 

The National WARP and WARP-CB models are tools for 

predicting atrazine concentrations in unmonitored or inadequately monitored streams. The performance of the models 

for the development and evaluation sites supports the application of the WARP-CB models for predicting annual atrazine 

concentration statistics in streams draining high atrazine use 

areas of the Corn Belt. The WARP-CB models also provide a 

framework to interpret the predictions in terms of uncertainty. 

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Appendixes

Appendixes are separate online documents, accessible at http://pubs.usgs.gov/ofr/2011/1141/.

1. Values of response and explanatory variables used in the WARP-CB model development.

2. Detailed description of the explanatory variables used in the development of the WARP-CB 

models.


Stone and Gilliom—Watershed Regressions for Pesticides (WARP) for Predicting Atrazine Concentrations in Corn Belt Streams—Open-File Report 2011–1141