Power analysis and trend detection for water quality monitoring data. An application for the Greater Yellowstone Inventory and Monitoring Network

An important consideration for long term monitoring programs is determining the required sampling effort to detect trends in specific ecological indicators of interest. To enhance the Greater Yellowstone Inventory and Monitoring Network’s water resources protocol(s) (O’Ney 2006 and O’Ney et al. 2009 [under review]), we developed a set of tools to: (1) determine the statistical power for detecting trends of varying magnitude in a specified water quality parameter over different lengths of sampling (years) and different within-year collection frequencies (monthly or seasonal sampling) at particular locations using historical data, and (2) perform periodic trend analyses for water quality parameters while addressing seasonality and flow weighting.

A power analysis for trend detection is a statistical procedure used to estimate the probability of rejecting the hypothesis of no trend when in fact there is a trend, within a specific modeling framework. In this report, we base our power estimates on using the seasonal Kendall test (Helsel and Hirsch 2002) for detecting trend in water quality parameters measured at fixed locations over multiple years. We also present procedures (R-scripts) for conducting a periodic trend analysis using the seasonal Kendall test with and without flow adjustment. This report provides the R-scripts developed for power and trend analysis, tutorials, and the associated tables and graphs. The purpose of this report is to provide practical information for monitoring network staff on how to use these statistical tools for water quality monitoring data sets.