Modeling Variability and Trends in Pesticide Concentrations in Streams1

Abstract

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.