Modeling Variability and Trends in Pesticide Concentrations in Streams¹

Abstract

A parametric regression model was developed for assessing the variability and long‐term trends in pesticide concentrations in streams. The dependent variable is the logarithm of pesticide concentration and the explanatory variables are a seasonal wave, which represents the seasonal variability of concentration in response to seasonal application rates; a streamflow anomaly, which is the deviation of concurrent daily streamflow from average conditions for the previous 30 days; and a trend, which represents long‐term (inter‐annual) changes in concentration. Application of the model to selected herbicides and insecticides in four diverse streams indicated the model is robust with respect to pesticide type, stream location, and the degree of censoring (proportion of nondetections). An automatic model fitting and selection procedure for the seasonal wave and trend components was found to perform well for the datasets analyzed. Artificial censoring scenarios were used in a Monte Carlo simulation analysis to show that the fitted trends were unbiased and the approximate p‐values were accurate for as few as 10 uncensored concentrations during a three‐year period, assuming a sampling frequency of 15 samples per year. Trend estimates for the full model were compared with a model without the streamflow anomaly and a model in which the seasonality was modeled using standard trigonometric functions, rather than seasonal application rates. Exclusion of the streamflow anomaly resulted in substantial increases in the mean‐squared error and decreases in power for detecting trends. Incorrectly modeling the seasonal structure of the concentration data resulted in substantial estimation bias and moderate increases in mean‐squared error and decreases in power.

A new approach for continuous estimation of baseflow using discrete water quality data: Method description and comparison with baseflow estimates from two existing approaches

“…Flow anomalies (FA) are dimensionless, orthogonal time series calculated from measured daily discharge that describe the variability in stream discharge at different time scales (e.g. 1 day, 30 days, 1 year; Vecchia et al, 2008). Flow anomalies have been found to be correlated to the observed variability of concentrations of pesticides and nutrients in other studies (Vecchia et al, 2008;Ryberg et al, 2010), and therefore were expected to add significant explanatory power to the regressions used to predict SC.…”

Antecedent flow conditions and nitrate concentrations in the Mississippi River basin

“…In this study, a statistical model is used to quantify the unexplained variability in nitrate concentration after filtering out these effects. This unexplained variability is the deviation of the observed log nitrate concentration from the log nitrate concen- tration predicted by a statistical model (based on contemporaneous daily mean flow, season, and trend), herein referred to as nitrate anomalies (Vecchia et al, 2008). To evaluate if antecedent flow conditions can help to explain variations in nitrate concentrations, we tested whether nitrate anomalies were significantly (alpha = 0.05) related to a measure of antecedent flow conditions.…”

“…Many studies show that antecedent moisture conditions influence nutrient export from river basins (Burt and Worrall, 2009;Garrett, 2012;Macrae et al, 2010;Soulsby et al, 2003;Vecchia et al, 2008;Lucey and Goolsby, 1993). Commonly, studies document increased nutrient export following a prolonged dry period (Foster and Walling, 1978;Macrae et al, 2010), though some studies have observed the opposite effect when considering only more recent antecedent conditions (Creed and Band, 1998;Macrae et al, 2010;Welsch et al, 2001).…”

Flow‐covariate prediction of stream pesticide concentrations

“…; N, let LF t ¼ log F t ð Þ. 2) Short-term flow anomaly [8]. For flow F t , the short-term flow anomaly SF t is defined as …”