Techniques of trend analysis for monthly water-quality data

Abstract

A set of statistical methods particularly well suited for evaluating time series of monthly water-quality data are presented. The Seasonal Kendall Test for trend is defined. It is a nonparametric test based on the differences between observations in the same month of different years. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation) it is robust by comparison with the parametric alternative of regression. The Seasonal Kendall Slope Estimator, a measure of trend magnitude, is defined. It is closely related to the Seasonal Kendall Test. It is an unbiased estimator of the slope of a linear trend and in comparison to linear regression has a considerably greater precision when the data are log-normally distributed but a moderately lesser precision when the data are normal. The flow-adjusted concentration is defined as the residual (actual minus the conditional expectation) concentration, based on some regression model of concentration as a function of river discharge. By testing these flow-adjusted concentration values for trend over time, one avoids the problem of identifying trends that are artifacts of the sequence of discharges observed. Rather, one is testing for changes in the relationship between concentration and discharge.