Introduction

In the United States, more than half a billion pounds (more than 226,700,000 kilograms) of pesticides were used annually from 2013 to 2017, including the use of more than 400 different pesticides during any given year, to maintain and improve crop production by controlling weeds, insects, and other pests (Wieben, 2019). Pesticides can enter rivers and streams through transport mechanisms such as shallow groundwater transport and runoff from precipitation and irrigation. Despite the many benefits that pesticides provide, they can potentially harm human and ecological health (Covert and others, 2020; Miller and others, 2020, Norman and others, 2020; Alvarez and others, 2021; Amenyogbe and others, 2021; Bradley and others, 2021; Nowell and others, 2021).

During water years (WY) 2013–18, the U.S. Geological Survey (USGS) National Water-Quality Assessment Project sampled the National Water Quality Network for Rivers and Streams (hereafter, referred to as NWQN) year-round and reported on 221 pesticides at 72 sites across the United States with the goal of better understanding the Nation’s water quality, including the occurrence of pesticides in natural waters (Rowe and others, 2013). A WY begins October 1 of the previous calendar year and ends September 30 of the named water year. There are a few issues that make measuring pesticide concentrations difficult: (1) the seasonality of pesticide concentrations differs from that of most other water-quality constituents; (2) the relation between streamflow and pesticide concentrations is complex; (3) the use of gas chromatography often results in censored data (concentrations that are lower than can be reliably detected by the analytical method used); and (4) pesticide sampling frequencies are often intermittent or low (Vecchia and others, 2008).

To help address these issues, a parametric regression model, SEAWAVE-Q, was specifically developed to analyze trends in chemical concentrations in streams with a seasonal wave (SEAWAVE), an adjustment for streamflow (Q), and other ancillary variables (Vecchia and others, 2008; Ryberg and York, 2020). Because of its robustness in fitting the seasonal patterns of pesticide occurrence in streams across various regions of the United States and its ability to handle large amounts of censored concentration data, SEAWAVE-Q has been used to analyze pesticide trends in several studies (Sullivan and others, 2009; Ryberg and others, 2010; Ryberg and others, 2014; Ryberg and Gilliom, 2015; Oelsner and others, 2017). Still, two issues remain when measuring pesticide concentrations. First, discrete samples are snapshots in time and do not always represent extreme concentrations (Norman and others, 2020). These discrete samples, then, likely underrepresent potential toxicity. NWQN data collection was not intended to characterize the highest concentrations; therefore, NWQN data are likely to be underestimates of actual peak concentrations. Second, other collection methods, such as autosamplers and polar organic chemical integrative samplers, can measure these higher extremes, but the number of discrete samples needed to estimate extreme pesticide concentrations each year would be cost prohibitive for an ambient network (Crawford, 2004).

Pesticide surrogate models have the potential to address these needs by providing near-real-time estimates of pesticide concentrations. For the purposes of this investigation, a surrogate (differing combinations of pH, specific conductance, turbidity, and water temperature) is a continuous in-stream sensor measurement used to compute or estimate the concentration of a water-quality constituent of greater interest (that is, pesticide concentrations; USGS, 2021b). Surrogates also have the potential to be easier and (or) cheaper to measure; for example, turbidity is regularly used as a surrogate for measuring suspended sediment, and specific conductance is used as a surrogate for estimating chloride concentrations (Christensen and others, 2000; Ryberg, 2006; Jastram and others, 2009; Rasmussen and others, 2009; Wood and Teasdale, 2013). The SEAWAVE-Q model already includes variables that represent seasonality and streamflow but also allows for other continuously monitored properties such as pH, specific conductance, turbidity, and water temperature to be used as surrogate variables.

Purpose and Scope

This report documents the development and comparison of three types of regression models using data collected during WY 2013–18 to estimate selected pesticide concentrations at six USGS streamflow-gaging stations. The modeling approaches included (1) a regression that included surrogates and periodic functions (sine-cosine) that are commonly used to model seasonality in concentration data (hereafter referred to as standard surrogate regression); (2) the seasonal wave with flow adjustment (SEAWAVE-Q/RCS-4) model that used restricted cubic splines (RCS) with four knots and included a seasonal component and flow anomalies but excluded surrogates (hereafter referred to as base SEAWAVE-Q); and (3) the seasonal wave with flow adjustment (SEAWAVE-Q/RCS-4) model that used RCS with four knots and included a seasonal component, flow anomalies, and surrogates (hereafter referred to as SEAWAVE-Q [with surrogates]).

Continuously measured streamflow was used in the base SEAWAVE-Q and SEAWAVE-Q (with surrogates) models but not in the standard surrogate regression. Continuously measured water-quality properties (differing combinations of pH, specific conductance, turbidity, and water temperature) were used as surrogates in the standard surrogate regression and SEAWAVE-Q (with surrogates) models. All three types of regression models used discrete water-quality samples analyzed for atrazine, azoxystrobin, bentazon, bromacil, imidacloprid, simazine, or triclopyr (two pesticides per site) and functions of time as additional explanatory variables for seasonality. The purpose of this report was to determine (1) whether the addition of streamflow and seasonality as represented in the base SEAWAVE-Q model produced better fit results than the standard surrogate regression models; and (2) whether the addition of surrogates to the base SEAWAVE-Q model produced better fit results than either standard surrogate regression or base SEAWAVE-Q models.

Study Design and Methods

The NWQN was established in 2013 and consists of sites from a few historical water-quality monitoring networks such as the National Water-Quality Assessment, the National Stream Quality Accounting Network, and the National Monitoring Network with the goal of developing a long-term, consistent network to track the status and trends of the Nation's water quality (Riskin and Lee, 2021). At the time of this investigation, the network comprises about 110 sites (number of sites may vary slightly among years), including 74 river and stream sites with pesticide sampling (Lee and Reutter, 2019; USGS, 2021a).

Selected Sites, Pesticides, and Surrogates Used in Regression Models

Whereas the NWQN analyzed 221 pesticides at 72 sites across the United States, this investigation analyzed 12 site-pesticide combinations (two pesticides for each of six sites) that were chosen on the basis of the availability of pesticide, streamflow, and surrogate data collected from the NWQN river and stream sites (fig. 1; table 1). These six sites were among seven NWQN sites with continuous water-quality monitors. One site, the Ohio River at Olmsted, Illinois, was excluded from this study owing to concerns of how well the data from the water-quality monitor represented values in the channel cross section. Pesticides were analyzed from discrete water-quality samples and included frequently detected pesticides from several classes: atrazine, bentazon, bromacil, simazine, and triclopyr (herbicides); imidacloprid (insecticide); and azoxystrobin (fungicide). Similarly, this study also selected four continuously measured water-quality properties (differing combinations of pH, specific conductance, turbidity, and water temperature including 1-day anomaly values for each) as potential explanatory variables (in other words, surrogates; table 2) in pesticide concentration regression models on the basis of the availability of continuous data at the NWQN pesticide sites. Pesticide concentration, streamflow, and surrogate data (continuously measured field parameters) are available online from the USGS National Water Information System database (USGS, 2020) and the USGS data release associated with this report (Perkins and Bunch, 2022).

Table 1.    

Site information for six sites in the National Water Quality Network during water years 2013–18.

[USGS, U.S. Geological Survey; ID, identification]

Table 1.    Site information for six sites in the National Water Quality Network during water years 2013–18.

USGS station number	Site ID	Site name	Decimal latitude	Decimal longitude	Drainage area (square mile)
14206950	FC	Fanno Creek at Durham, Oregon	45.40345200	−122.75481850	31.5
03374100	HAZ	White River at Hazleton, Indiana	38.48976950	−87. 55002269	11,305
06892350	KR	Kansas River at DeSoto, Kansas	38.98333750	−94.96468930	59,756
07144100	LAR	Little Arkansas River near Sedgwick, Kansas	37.88306739	−97.42448640	1,239
06934500	MR	Missouri River at Hermann, Missouri	38.70980556	−91.43850000	522,500
05082500	RR	Red River of the North at Grand Forks, North Dakota	47.92692340	−97.02924350	30,100

Table 2.    

Combinations of surrogate variables used in the standard surrogate regression and SEAWAVE-Q (with surrogates) models at six National Water Quality Network sites during water years 2013–18.

[mtfa, midterm flow anomalies computed using 30 days of daily streamflow; stfa, short-term flow anomalies computed using 1 day of daily streamflow; TBY, daily median turbidity; SC, daily mean specific conductance; Temp, daily mean water temperature; pH, daily median pH; SC1d, short-term specific conductance anomalies computed using 1 day of daily specific conductance values; pH1d, short-term pH anomalies computed using 1 day of daily pH values; TBY1d, short-term turbidity anomalies computed using 1 day of daily turbidity values]

Table 2.    Combinations of surrogate variables used in the standard surrogate regression and SEAWAVE-Q (with surrogates) models at six National Water Quality Network sites during water years 2013–18.

Surrogate variable group	Model variables
1	mtfa, stfa
2	TBY, mtfa, stfa
3	SC, mtfa, stfa
4	SC, TBY, mtfa, stfa
5	Temp, mtfa, stfa
6	Temp, SC, mtfa, stfa
7	Temp, TBY, mtfa, stfa
8	Temp, TBY, SC mtfa, stfa
9	pH, mtfa, stfa
10	pH, SC, mtfa, stfa
11	pH, Temp, mtfa, stfa
12	pH, TBY, mtfa, stfa
13	pH, SC, Temp, mtfa, stfa
14	pH, SC, TBY, mtfa, stfa
15	pH, Temp, TBY, mtfa, stfa
16	pH, SC, Temp, TBY, mtfa, stfa
17	SC1d, mtfa, stfa
18	pH1d, mtfa, stfa
19	TBY1d, mtfa, stfa

Results

Models were evaluated and compared using the generalized coefficient of determination (generalized R²), Akaike’s Information Criteria, and scale. First, the results from the standard regression models were compared to the base SEAWAVE-Q modeling results. Then, the base SEAWAVE-Q results were compared to the SEAWAVE-Q (with surrogates) results and presented by pesticide analyte.

Comparison of Base SEAWAVE-Q to SEAWAVE-Q (With Surrogates)

The addition of surrogate variables to the base SEAWAVE-Q model also increased generalized R² values but explained a median of only 3 percent more of the variation in the data. The SEAWAVE-Q (with surrogates) model resulted generally in modest improvements to model-performance values and thus, to pesticide concentration estimates (indicated by the lightest blue-shaded cells and the § symbol in table 4).

The following results are presented by pesticide analyte. Each site-pesticide-surrogate instance in table 4 has a different number of observations because of incomplete datasets where continuously measured surrogate data were missing. This makes site-to-site and surrogate-to-surrogate comparisons difficult to assess. The only direct comparisons that can be made are among the results of the three regression model types for each individual site-pesticide-surrogate instance (table 4).

Atrazine

Adding surrogates to the base SEAWAVE-Q model moderately improved estimates of atrazine concentrations. Generalized R² values explained a median of 6 percent more variation in the data for 14 of 15 site-pesticide-surrogate instances. Likewise, AIC and scale values decreased for 14 of 15 site-pesticide-surrogate instances (table 4). One site-pesticide-surrogate instance for atrazine (no. 18 surrogate variable group at HAZ in table 4) resulted in an AIC value that increased, though not by more than 2 AIC units, indicating there is little evidence that one model performs better than the other. For this same site-pesticide-surrogate instance, the generalized R² value and the scale value stayed the same, again indicating that the addition of the surrogate had neither a positive nor a negative effect on the model.

As an example of the estimated daily pesticide concentrations, figures 2A and 2B show model results for atrazine with and without a surrogate (1-day anomaly in pH) and in comparison to observed concentrations at two sites: White River at Hazleton, Indiana, and Kansas River at DeSoto, Kansas, respectively. The base SEAWAVE-Q estimates of pesticide concentrations using only flow anomalies (red line in figs. 2A and 2B) were able to capture some of the seasonal variability in atrazine concentrations. The addition of the 1-day anomaly in pH as a surrogate (green line) did not improve the estimated atrazine concentrations at the White River at Hazleton site (fig. 2A), as the estimated concentrations with and without the surrogate are nearly identical. Gaps in the availability of the surrogate data are represented by the red line (base SEAWAVE-Q model) in figure 2A; however, at Kansas River at DeSoto, Kansas, the addition of the surrogate did result in modest improvements to estimated atrazine concentrations, better capturing the overall observed pattern of concentrations as well as individual high and low concentrations (fig. 2B).

Azoxystrobin

Adding surrogates to the azoxystrobin base SEAWAVE-Q model had mixed effects on the model's performance. Four generalized R² values (out of six site-pesticide-surrogate instances) for azoxystrobin remained the same, whereas the other two instances improved slightly by explaining only 1 and 4 percent more of the variation in the data, respectively (table 4). Likewise, AIC values increased for five of six site-pesticide-surrogate instances, indicating a decline in model performance for those instances when surrogates were added (table 4). Three of the six scale values increased or remained unchanged.

Bentazon

Adding surrogates to the base SEAWAVE-Q model moderately improved estimates of bentazon concentrations. All four generalized R² values improved but only explained 3 percent more of the variation in the data. The AIC values for three of four site-pesticide-surrogate instances decreased somewhat, indicating a small improvement in these instances of the model’s performance. The fourth AIC value increased but not by more than 2 AIC units, indicating there is little evidence that one model performs better than the other. All four scale values for bentazon decreased slightly (table 4).

Bromacil

All three generalized R² values for bromacil remained unchanged with the addition of surrogates to the base SEAWAVE-Q models. AIC and scale values, however, decreased at all three site-pesticide-surrogate instances, indicating some improvement (table 4).

Imidacloprid

Adding surrogates to imidacloprid base SEAWAVE-Q models had mixed results on the model's performance. Three generalized R² values (out of four) increased, explaining a median of only 2 percent more of the variation in the data. Likewise, AIC values increased for three of four site-pesticide-surrogate instances, indicating a decline in those instances of the model’s performance when surrogates were added (table 4). The scale values remained unchanged or decreased only slightly.

Simazine

For simazine, the addition of surrogates to the base SEAWAVE-Q model resulted in little improvement on the model's performance. The generalized R² values remained unchanged for two out of three site-pesticide-surrogate instances (table 4). The third generalized R² value increased, explaining only 2 percent more of the variation in the data. AIC values increased for two of three site-pesticide-surrogate instances, indicating a decline in those instances of the model’s performance (table 4). Likewise, two of the three scale values increased or remained unchanged.

Triclopyr

Adding surrogates to the base SEAWAVE-Q model moderately improved all three model criteria for triclopyr. All four generalized R² values increased, explaining a median of 4 percent of the variation in the data. Likewise, AIC and scale values decreased for all four site-pesticide-surrogate instances (table 4).

Summary and Conclusions

During water years 2013–18, the U.S. Geological Survey National Water-Quality Assessment Project sampled the National Water Quality Network for Rivers and Streams year-round and reported on 221 pesticides at 72 sites across the United States. Pesticides are difficult to measure, their concentrations often represent discrete snapshots in time, and capturing peak concentrations is expensive. Three types of regression models were developed to estimate daily concentrations for two selected pesticides at each of six National Water Quality Network for Rivers and Streams sites and included (1) a standard regression model that included surrogates and periodic functions (sine-cosine) of pesticide application use; (2) the seasonal wave with flow adjustment model that included a seasonal component and flow anomalies but excluded surrogates; and (3) the seasonal wave with flow adjustment model that included a seasonal component, flow anomalies, and surrogates. Because of low observation numbers, results from this study can be considered a pilot effort with the possibility that some models are overfit.

The use of continuously measured water-quality properties such as turbidity and specific conductance as surrogates for measuring suspended sediment and chloride concentrations, respectively, has applicability based on well supported theories. Pesticide concentrations, on the other hand, are not known to correlate well with such water-quality properties but instead with the timing of pesticide applications. The SEAWAVE-Q model was designed to represent the timing of pesticide applications by accounting for flow anomalies and including a more complex variable for seasonal patterns; thus, the base SEAWAVE-Q model dramatically improved pesticide concentration estimates when compared to standard regression models. In all site-pesticide-surrogate instances, generalized R² values increased by 3 to 56 percent (median of 25 percent) when compared to the standard surrogate regression models and thus improved the models by explaining more of the variability.

The addition of surrogate variables such as pH, specific conductance, turbidity, and water temperature to the base SEAWAVE-Q model to improve estimates of pesticide concentrations has no theoretical basis and is purely empirical. In general, the SEAWAVE-Q (with surrogates) model resulted in only modest improvements to model-performance values; generalized R² values increased by only 0 to 10 percent (median of 3 percent). In some instances, combinations of the variables produced more appreciative improvements in model results. In those instances, we hypothesize that the surrogates correlated with some unknown measure that directly relates to pesticide transport (such as turbidity’s relation to agricultural drainage pipes or water temperature’s relation to groundwater versus surface-water sources).

In all cases examined for this study, SEAWAVE-Q provided better estimates of daily pesticide concentrations than a standard surrogate regression modeling approach. The addition of surrogates to the base SEAWAVE-Q model tended to marginally improve estimates of pesticide concentrations but did help more in selected cases; however, this improvement came at a cost. The more complicated models incorporating surrogate variables had a greater likelihood of having missing observations because of sensor fouling or failure. The greater the number of surrogate variables included in a model, the greater the likelihood that one sensor would fail resulting in a missing observation for which estimates cannot be made. It may be desirable for situations where the addition of surrogates substantially improves estimated pesticide concentrations to simultaneously maintain a base SEAWAVE-Q model. This simpler model could be used to estimate concentrations for days with missing surrogates. These estimates would have greater uncertainty than those from the better model but could still provide usable estimates.

At the time of this investigation, SEAWAVE-Q is limited in temporal resolution to daily estimates. Pesticide concentrations can vary throughout the day, especially in smaller streams during storm events. As it stands, SEAWAVE-Q cannot estimate these short-term fluctuations, but refinements to the software to allow estimates at shorter time steps (such as hourly) may allow the SEAWAVE-Q model to better capture short term flow variability and its effect on pesticide concentrations.