Time-series model, statistical methods, and software documentation for R–QWTREND—An R package for analyzing trends in stream-water quality

As part of a U.S. Geological Survey water-quality study started in 2018, in cooperation with the International Joint Commission, North Dakota Department of Environmental Quality, and Minnesota Pollution Control Agency, a publicly available software package called R–QWTREND was developed for analyzing trends in stream-water quality. The R–QWTREND package is a collection of functions written in R, an open source language and a general environment for statistical computing and graphics. The package uses a parametric time-series model to express logarithmically transformed concentration in terms of flow-related variability, trend, and serially correlated model errors. Flow-related variability captures natural variability in concentration on the basis of concurrent and antecedent streamflow. The trend identifies systematic changes in concentration in terms of potential step trends, piecewise monotonic trends, or user-specified trends. Maximum likelihood estimation is used to estimate model parameters and determine the best-fit trend model. This report describes the time-series model and statistical methodology behind R–QWTREND and provides formal documentation for installing and using the package.