Watershed Regressions for Pesticides (WARP)

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Assessment and management of pesticides require far more information than we can afford to directly measure for all the places, times, and pesticides of interest. In addition, many decisions, such as setting monitoring priorities, approving registration of a new pesticide, and determining how much to spend on a management strategy, inherently depend on predicting the potential effects of pesticides on water quality for locations or amounts of use that have never been directly assessed. In these situations, statistical models and other types of models are used for predicting water-quality conditions at unmonitored locations under a range of possible circumstances. The National Water-Quality Assessment (NAWQA) Program  is developing a series of statistical models, based on monitoring data and watershed characteristics, to enable estimation of pesticide concentrations for streams that have not been monitored. The Watershed Regression for Pesticides models are referred to as WARP models.

A complete description of the development and performance of the WARP models is provided in Stone and others (2013). The WARP models for multiple pesticides (WARP-MP) use the atrazine WARP models in conjunction with an adjustment factor for each pesticide modeled. The atrazine WARP models statistically relate atrazine concentrations in streams to watershed characteristics that are determined from data sources with national coverage. The models were developed using standard, widely available statistical techniques.

Frequently Asked Questions About WARP

How was the model developed?

The WARP models for pesticides are developed using linear regression methods to establish quantitative linkages between pesticide concentrations measured at NAWQA and National Stream Quality Accounting Network (NASQAN) sampling sites and a variety of human-related and natural factors that affect pesticides in streams. Such factors include pesticide use, soil characteristics, hydrology, and climate - collectively referred to as explanatory variables. Measured pesticide concentrations, together with the associated values of the explanatory variables for the sampling sites, comprise the model-development data.

The WARP model for estimating atrazine in streams is based on concentrations measured by NAWQA and NASQAN from 1992 to 2007 at 114 stream sites (Figure 1). The atrazine model actually consists of a series of models, each developed for a specific concentration statistic (annual mean and 4-, 21-, 30-, 60-, and 90-day annual maximum moving average).

model development sites

Figure 1. Stream sites included in model development (Stone and others, 2013).

The models are built using the explanatory variables that best correlate with, or explain, the concentration statistics computed from concentrations observed in streams. Although explanatory variables included in the models are significantly correlated with pesticide concentrations, the specific cause-and-effect relations responsible for the observed correlations are not always clear, and inferences regarding causes should be considered as hypotheses.

In developing the models, all potential explanatory variables were required to have values available from existing data sources that include all locations in the conterminous United States, so that national extrapolation would be possible. Many possible variables were considered and these were reduced to 5 explanatory variables that were most significant and yielded optimal model formulations. Each model incorporates an uncertainty analysis, which allows assessment of the reliability of the model predictions and also the expression of model predictions as probabilities that concentrations will exceed a specific value, such as a water-quality benchmark, at a particular location.

Use intensity is the most important factor in the atrazine WARP model - the more intensive the use of atrazine in a watershed, the higher the atrazine concentration in the stream (Stone and others, 2013). The four additional variables are the presence of a soil restrictive layer in the top 25 cm of the soil surface, precipitation during May and June of the sampling year, rainfall erosivity, and the percent of stream flow generated from rainfall on saturated soils (Dunne overland flow). Lerch and Blanchard (2003) found that the presence of a layer impeding the downward movement of surface water to groundwater was associated with higher vulnerability of a watershed for atrazine transport to streams. For most of the model development sites, the months of April through June include the highest atrazine application period. High precipitation during May and June, after atrazine application, increases pesticide runoff to streams. Rainfall erosivity quantifies, respectively, the energy of storms in a specific area (averaged over several years). As this factor increases, atrazine concentrations also increase, indicating that transport of atrazine is highest in areas of high-energy rain storms. Stream water from Dunne overland may originate from lowland and wetland areas that are less likely to be cropped and treated with pesticides. As the percentage of Dunne overland flow to a stream increases, atrazine stream concentrations decrease. Overall, the complete model explains 82 percent of the variance in observed annual mean atrazine concentrations.

The WARP-MP models use the atrazine WARP models in conjunction with an adjustment factor for each pesticide (Stone and others, 2013). The adjustment factor is a multiplicative factor derived from the pesticide's Surface Water Mobility Index (SWMI) and Vapor pressure (Vp). The SWMI characterizes the likelihood that a pesticide would be transported to streams based on the pesticide's soil degradation half-life and organic carbon sorption coefficient (Chen and others, 2002). A pesticide with high Vp has more of a tendency to volatilize to the atmosphere and be less likely to be transported to streams than a pesticide with a low Vp.


What does the model predict?

The WARP models used on this Web site to create maps and graphs are the models for the annual mean and annual maximum moving averages (4-, 21-, 30-, 60-, and 90-day durations), based on Stone and others (2013). For each of these annual concentration statistics, the models can be used to estimate the value for a particular stream, including confidence bounds on the estimate, or the probability that a particular value will be exceeded, such as a water-quality benchmark. Each of these options for applying the model has advantages for specific purposes.

When used to estimate the value of a concentration statistic for a stream, such as the annual mean, the model computes the median estimate of the statistic for all streams with watershed characteristics that are similar to the stream in question. Thus, the computed estimate for a particular stream has an equal chance of being above or below the actual value of the statistic. The confidence that the estimated value is within a certain magnitude of the actual value is indicated by the 95-percent confidence limits, which encompass 95 percent of the actual values associated with the predicted value.

When used to estimate the probability that a particular stream has a pesticide concentration greater than a specific threshold, usually a water-quality benchmark, the model prediction and uncertainty are combined to estimate the probability for the stream.


How are predictions made?

Model estimates can be made for either concentration values or probabilities for most stream reaches included in the U.S. Environmental Protection Agency (EPA) River Reach file (USGS, https://water.usgs.gov/lookup/getspatial?erf1_2), which include more than 600,000 miles of streams and more than 60,000 individual stream reaches with watersheds. The term "stream" refers to all River Reach file segments, regardless of drainage basin area. Model development stations spanned over 5 orders of magnitude in terms of watershed area and model predictions are not biased with respect to watershed area. However, model estimates are not made available for streams with watersheds smaller than 75 square kilometers because of the high potential uncertainty in explanatory variables, such as pesticide use, for small watersheds. In addition, model estimates are not made available for streams with watershed characteristics, including pesticide-use intensity, outside the range of those used to develop the WARP models.

In addition to streams, River Reach file segments may actually represent reservoirs. The WARP models were developed with stream (flowing water) data to predict concentration distributions in streams. The application of these regression models to lakes and reservoirs will provide under predicted concentrations for the annual mean (Larson and others, 2004). Model estimates are not made available for River Reach file segments that represent reservoirs.

Annual agricultural pesticide use intensity was estimated from USGS county-level pesticide use estimates (https://water.usgs.gov/nawqa/pnsp/usage/maps/). The county-level pesticide use estimates for the U.S. were then combined with national land cover data to generate a raster dataset of pesticide use intensity, following the method described in Nakagaki and Wolock (2005).

Estimating pesticide concentrations for the roughly 60,000 stream reaches required that regression predictor variables be calculated for the entire basin draining to the downstream end of each stream reach. For example, the predictor variables for the stream reach at the mouth of the Mississippi River are based on the chemical and physical characteristics of the entire upstream river basin. The process of computing the explanatory variables incorporated several steps. For illustration, the steps below describe the process for calculating atrazine use intensity. The required geographic data include a raster dataset of atrazine use intensity for the conterminous U.S., the River Reach file, and a raster dataset of incremental catchments, which are the local drainage areas of all headwater streams, tributary streams, and stream segments lying between confluences. The processing steps are:

  1. The incremental catchments are intersected with the atrazine use intensity grid to compute atrazine use in each incremental catchment.
  2. The known association between the individual stream reaches and corresponding incremental catchments is used to assign incremental atrazine use values to each stream reach. Similarly, the correspondence between the individual stream reaches and the incremental catchments is used to assign incremental drainage area values to each stream reach.
  3. The topology (spatial connections) of the stream network is used to accumulate, in a downstream direction, all the incremental atrazine use values. This accumulation provides an estimate of total basin atrazine use for each stream reach. Similarly, the incremental drainage areas are accumulated in a downstream direction to estimate the total drainage area for each stream reach.
  4. The total basin atrazine use is divided by the total drainage area to calculate the atrazine use intensity for each stream reach.

How can WARP be used to assess the potential for effects of pesticides on humans or aquatic life?

The potential for pesticide concentrations in stream water to adversely affect human health or aquatic life is evaluated by NAWQA using screening-level assessments (Gilliom and others, 2006) similar in concept to EPA screening-level assessments (EPA, 2004). The NAWQA screening-level assessments compare site-specific estimates of pesticide exposure (concentration statistics or concentrations) with water-quality benchmarks derived from standards and guidelines established by EPA, toxicity values from EPA pesticide risk assessments, and USGS Health-Based Screening Levels (HBSLs). The EPA standards, guidelines, and toxicity values were developed by EPA as part of the Federal process for assessing and regulating pesticides.

Screening-level assessments are not a substitute for either risk assessments, which include many more factors (such as additional avenues of exposure), or site-specific studies of effects. Rather, comparisons of measured or estimated concentrations with water-quality benchmarks provide a perspective on the potential for adverse effects, as well as a framework for prioritizing additional investigations that may be warranted. Concentrations that exceed a benchmark do not necessarily indicate that adverse effects are occurring - they indicate that adverse effects may occur and that sites where benchmarks are exceeded may merit further investigation. The characteristics and limitations of screening-level assessments are summarized below.

Characteristics and limitations of screening-level assessments

Screening-level assessments are a first step toward addressing the question of whether or not pesticides are present at concentrations that may affect human health or aquatic life. They provide a perspective on where effects are most likely to occur and what pesticides may be responsible. Screening-level assessments are primarily intended to identify and prioritize needs for further investigation and have the following characteristics and limitations:

  • Most water-quality benchmarks selected for the screening-level assessment are estimates of no-effect levels, such that concentrations below the benchmarks are expected to have a low likelihood of adverse effects and concentrations above a benchmark have a greater likelihood of adverse effects, which generally increases with concentration.
  • The presence of pesticides in streams at concentrations that exceed benchmarks does not indicate that adverse effects are certain to occur. Conversely, concentrations that are below benchmarks do not guarantee that adverse effects will not occur, but indicate that they are expected to be negligible (subject to limitations of concentration estimates and benchmarks).
  • Most water-quality benchmarks for pesticides are based on toxicity tests of individual chemicals, whereas pesticides usually occur as mixtures. Comparisons to single-compound benchmarks may tend to underestimate the potential for adverse effects.
  • For some benchmarks, there is substantial uncertainty in underlying estimates of no-effect levels, depending on the methods used to derive them and the quantity and types of toxicity information on which they are based.
  • Estimates of pesticide exposure derived from either measured or estimated concentrations are also uncertain, particularly estimates of short-term exposure of aquatic organisms to pesticides in stream water.

Human-health benchmarks for pesticides in water

Benchmarks for assessing the potential for pesticides in water to affect human health are EPA Maximum Contaminant Levels (MCLs) for regulated compounds and USGS Health-Based Screening Levels (HBSLs) for unregulated compounds.

Maximum Contaminant Level (MCL): The maximum permissible concentration of a contaminant in water that is delivered to any user of a public water system. This is an enforceable standard issued by EPA under the Safe Drinking Water Act and established on the basis of health effects and other factors (analytical and treatment technologies, and cost).

Health-Based Screening Level (HBSL): HBSLs are concentrations or ranges in concentration (for carcinogens) that can be used as benchmarks to which contaminant concentrations in water can be compared to evaluate water-quality data in a human-health context. HBSLs were developed collaboratively by the USGS, EPA, New Jersey Department of Environmental Protection, and Oregon Health & Science University. HBSLs are not regulatory standards, are not enforceable, and water systems are not required to monitor for any unregulated compounds for which HBSLs have been developed. HBSL values are developed by using EPA Office of Water methodologies and EPA toxicity values, so they generally are comparable to EPA drinking-water guideline values such as lifetime health advisory levels and risk-specific dose values. Compounds with existing EPA drinking-water guideline values such as lifetime health advisory levels or a risk specific dose are included as HBSLs.

Aquatic-life benchmarks for pesticides in water

Benchmarks for assessing the potential for pesticides in stream water to adversely affect aquatic life were of two general types: (1) ambient water-quality criteria for the protection of aquatic life (AWQC-AL), which were developed by EPA's Office of Water (OW), and (2) benchmarks derived from toxicity values obtained from registration and risk-assessment documents developed by EPA's Office of Pesticide Programs (OPP). Toxicity data from OPP documents were used to supplement OW criteria to expand the coverage of pesticides and to incorporate the most recent toxicity information used by EPA. The following is summarized from Gilliom and others (2006), which contains complete sources, references, and values.

Ambient water-quality criteria for aquatic organisms

EPA's OW derives both acute and chronic criteria, each of which specifies a threshold concentration for unacceptable potential for effects, an averaging period, and an acceptable frequency of exceedances.

Acute AWQC-AL: The highest concentration of a chemical to which an aquatic community can be exposed briefly without resulting in an unacceptable effect. Except where a locally important species is very sensitive, aquatic organisms should not be unacceptably affected if the 1-hour average concentration does not exceed the acute criterion more than once every 3 years, on average. The intent is to protect 95 percent of a diverse group of organisms.

Chronic AWQC-AL: The highest concentration of a chemical to which an aquatic community can be exposed indefinitely without resulting in an unacceptable effect. Except where a locally important species is very sensitive, aquatic organisms should not be unacceptably affected if the 4-day average concentration does not exceed the chronic criterion more than once every 3 years, on average. The intent is to protect 95 percent of a diverse group of organisms.

Toxicity values from risk assessments

Seven types of aquatic toxicity values were compiled from OPP's registration and risk-assessment documents. The OPP toxicity values are for specific types of organisms. Acute and chronic values were compiled for fish and invertebrates, and acute values for vascular and nonvascular plants. A value for aquatic-community effects was available only for atrazine. The types and amounts of toxicity data available for different pesticides were highly variable. EPA estimates the toxicity or hazard of a pesticide by selecting the most sensitive endpoints from multiple acute and chronic laboratory and field studies. For many pesticides, EPA has completed a screening-level ecological risk assessment, which includes acute and chronic assessments for both fish and invertebrates. For some pesticides, acute assessments have also been completed for non-target aquatic plants. NAWQA derived benchmarks from OPP toxicity values, generally following OPP procedures.

In recent years, EPA has developed methods for conducting refined risk assessments, in which probabilistic tools and methods are incorporated to predict the magnitude of the expected impact of pesticide use on non-target organisms, as well as the uncertainty and variability involved in these estimates. The screening-level benchmarks used in NAWQA analysis and summarized below were derived from the toxicity values reported in EPA registration and risk-assessment documents.

In the few cases where refined assessments were available, these were given preference. In deriving a benchmark for a given type of organism (such as fish) and a given exposure duration (acute or chronic), the lowest of the available toxicity values was selected for each benchmark, unless a preferred toxicity value was specified in a refined risk assessment - in which case that preferred toxicity value was used instead. For two of the benchmarks, acute fish and acute invertebrates, the selected toxicity values were multiplied by the EPA level of concern (LOC) of 0.5, so that the benchmark for NAWQA screening corresponds to the acute risk level defined by EPA.

Six benchmarks were based directly on toxicity endpoints used in OPP screening-level assessments:

  • Acute fish: The lowest tested 50-percent lethal concentration (LC50) for acute (typically 96-hour) toxicity tests with freshwater fish, multiplied by the LOC of 0.5.
  • Acute invertebrate: The lowest tested LC50 or 50-percent effect concentration (EC50) for acute (typically 48 or 96-hour) toxicity tests with freshwater invertebrates, multiplied by the LOC of 0.5.
  • Acute vascular plant: The lowest tested EC50 for freshwater vascular plants in acute toxicity tests (typically < 10 days).
  • Acute nonvascular plant: The lowest tested EC50 for freshwater nonvascular plants (algae) in acute toxicity tests (typically < 10 days).
  • Chronic fish: The lowest no-observed-adverse-effects concentration (NOAEC), or the lowest-observed-adverse-effects concentration (LOAEC) if a NOAEC is not available, for freshwater fish in early life stage or full life-cycle tests.
  • Chronic invertebrate: The lowest NOAEC, or LOAEC if a NOAEC is not available, for freshwater invertebrates in life-cycle tests.

One additional benchmark, a benchmark for aquatic-community effects, was derived from the refined risk assessment for atrazine. This endpoint for atrazine incorporates community-level effects on aquatic plants and indirect effects on fish and aquatic invertebrates that could result from disturbance of the plant community.


What are the appropriate uses of the model and this Web site?

Potential users of the model and this Web site include:

  • Federal, state, and local regulatory and management agencies
  • Corporate scientists and environmental consultants
  • Government and academic scientists
  • Stakeholders and interest groups
  • Educators and students

Applications include:

  • Assessment of geographic patterns in stream concentrations of pesticides at scales ranging from national to watershed.
    The WARP model is well suited for characterizing broad geographic patterns in stream concentrations resulting from agricultural applications of pesticides. Broad patterns for regional, state, or multi-county areas are generally reliable for representing the proportions of streams in different concentration categories, but the uncertainty is relatively high in predictions for specific individual streams. For specific streams, it is important for users to evaluate the prediction graph provided for each individual site, which shows all estimated concentration statistics with 95% prediction intervals.
  • Design of monitoring programs and studies.
    One of the most appropriate and useful applications of WARP is to prioritize the needs for monitoring of specific streams, generally targeting those that have high predicted concentrations. By this approach, scarce monitoring resources can be targeted to the streams where the potential for concern is greatest.
  • Identification of streams with the greatest likelihood to have concentrations that exceed a water-quality benchmark.
    Streams with the greatest likelihood of exceeding a human-health benchmark would be those of greatest potential concern if considered as a source of drinking water. Streams with the greatest likelihood of exceeding an aquatic-life benchmark would be the sites where related biological effects are most likely and may merit investigation. The probability estimates by WARP incorporate the influence of predictive uncertainty.
  • Education about the distribution of pesticides in streams and the watershed characteristics that control its concentrations.
    The interactive mapping of model results is designed to be an educational tool that can be used to explore estimated concentrations in different geographic areas in relation to such factors as land use and pesticide use in stream watersheds.

What are the limitations of WARP?

The WARP models have several limitations and constraints that are important to understand when applying the model and its results:

  • The sampling frequencies of the model-development sites were not sufficient to reliably characterize the highest concentrations during a year. Thus, application of the models to predict the annual maximum concentrations is expected to underpredict the actual annual maximums.
  • The WARP regression models were derived for estimation of pesticide concentrations in rivers and streams of the conterminous United States. While the 114 stations used for model development represent a wide variety of environmental settings and a large range of watershed area, some watersheds in the United States have one or more characteristics outside the ranges of the watershed characteristics used to develop the models.
  • The models were developed using data from flowing streams and rivers. Application to lakes or reservoirs would likely result in biased predictions (Larson and others, 2004).
  • The pesticide use data used for the models are estimates for agricultural applications to cropland only. Nonagricultural use of a pesticide in a watershed, if significant, could result in inaccurate (low) predictions of pesticide concentrations in a stream.
  • The WARP models are empirical models based only on nationally available data sets. The models do not include and did not evaluate factors for which there are no national data. Examples are management practices, such as buffer strips and herbicide application methods.

Revision History

Revision 1.1 (September 2016): Added predicted pesticide values for the years 1992, 1997, 2002, and 2007. Revised predicted values for 2012 to use more current Aquatic Life Benchmarks. Added summary plots to assist users with looking at pesticide predictions. Added metadata for predictions and summary plots.

Revision 1.0 (September 2015): Added predicted values for 107 pesticides for 2012 and removed predictions for atrazine for 2011. Revised the legend bins and colors to make more understandable between pesticides.


Chen, W., Hertl, P., Chen, S., and Tierney, D., 2002, A pesticide surface water mobility index and its relationship with concentrations in agricultural drainage watersheds. Environ. Toxicol. Chem. 21:298-308

Gilliom and others, 2006, The Quality of Our Nation's Waters-Pesticides in the Nation's Streams and Ground Water, 1992-2001: U.S. Geological Survey Circular 1291,172 p. https://pubs.usgs.gov/circ/2005/1291/

Larson, S.J., Crawford, C.G., and Gilliom, R.J., 2004, Development and application of Watershed Regressions for Pesticides (WARP) for estimating atrazine concentration distributions in streams: U.S. Geological Survey Water-Resources Investigations Report 03—4047, 68 p. (Also available at https://pubs.usgs.gov/wri/wri034047/.)

Lerch, R.N., and Blanchard, P.E., 2003, Watershed vulnerability to herbicide transport in northern Missouri and southern Iowa streams: Environmental Science & Technology, v. 37, no. 24, p. 5518-5527

Stone, W.W., Crawford, C.G., and Gilliom, R.J., 2013, Watershed Regressions for Pesticides (WARP) models for predicting stream concentrations of multiple pesticides. Journal of Environmental Quality, 42:1838-1851. https://pubs.er.usgs.gov/publication/70055879

EPA (U.S. Environmental Protection Agency), 2004, National recommended water quality criteria: U.S. Environmental Protection Agency, Office of Water and Office of Science and Technology, 23 p. https://www.epa.gov/waterscience/criteria/nrwqc-2004.pdf