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

Abstract

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.

General water-quality conditions, long-term trends, and network analysis at selected sites within the Ambient Water-Quality Monitoring Network in Missouri, water years 1993–2017

“…Water-quality and discharge data for the analysis period were obtained from the USGS NWIS database (U.S. Geological Survey, 2020) for use in two USGS hydrologic data analysis packages, EGRET (Hirsch and De Cicco, 2015) and R-QWTREND (a parametric statistical time-series model for detecting trends; Vecchia and Nustad, 2020), that were written for the R statistical software (R Core Team, 2020). Data retrieved from NWIS included discharge data and all water-quality data for the 15 constituents of interest for 1993-2017.…”

“…Discharge-adjusted water-quality trends were analyzed at 58 sites within the AWQMN in Missouri. A statistical time-series model R-QWTREND, developed by the USGS, was used for analyzing complex discharge-related trends in water-quality constituents (Vecchia and Nustad, 2020). R-QWTREND characterizes discharge-related variability at multiple time scales to manage variable discharge resulting from long-and short-term climatic variation so that concentration trends are detected independent of trends in discharge (Nustad and Vecchia, 2020).…”

“…The model also can interpret censored data, but no more than 25 percent of the dataset can be censored. Analyses can be performed with datasets that do not meet the minimum criteria, but the model errors could be highly biased (Vecchia and Nustad, 2020) and should be interpreted with caution. Datasets for the selected constituents at sites used in this study that did not meet the minimum criteria of 60 observations or exceeded 25 percent censored were not used for trend analysis.…”

“…Trend models were developed for the study following steps and default package programming as documented in Vecchia and Nustad (2020) with a minor modification. Prior to outlier identification, imputation of censored values occurs in R-QWTREND's preprocessing script, prepQWdata.…”

“…The R-QWTREND program uses Gaussian maximum likelihood estimation to fit the model parameters, chooses the best trend model, and determines the significance levels (probability [p]-values) associated with the trends (Vecchia and Nustad, 2020). For this study, results were compared with all nested model results (null [no trend], single-period trend, and two-period trend), and determined to be statistically significant when the "attained significance level" (p-value) was less than the pre-defined threshold of significance (alpha=0.05).…”