Power analysis for National Park Service lake chemistry data from 2008 to 2011

Harrod Starcevich, Leigh Ann

Statistical power analysis for Sierra Nevada Network lake chemistry monitoring data. The Sierra Nevada Network (SIEN) of the National Park Service identified lake chemistry as one of its Vital Signs for long-term monitoring. Since 2008, chemistry metrics at 24 or 25 SIEN lakes have been monitored each year to provide data for status and trend estimation. Status estimation occurs annually, and trend estimation will occur every five years. The goal of this current work is to analyze the data from the surveys conducted in 2008 through 2011, identify covariates that would improve trend estimation and variance components estimation, and update the analysis of the power to detect trend. For outcomes with non-zero estimates of year-to-year variation, the highest power to detect trend is found for Mg, Na, and pH. Despite the relatively-high year-to-year variation observed in the Mg measurements, the random-slope variation and residual variation are very small for this outcome and acceptable power to detect large trend (4% annually) is attained. The lowest power is observed in indicators with high random-slope variation or variance components with a large magnitude. Even with the assumption of no year-to-year variation for the nitrate trends, the power to detect trends in nitrates is very low due to the large magnitude of the other measurable variance components. Previous work with Sierra Nevada lakes pilot data indicates that nitrates exhibit considerable year-to-year variation as well. Additional years of monitoring will improve the ability to obtain estimates of year-to-year variance for all outcomes of interest. In several cases, the variance components obtained in this exercise are quite similar to those obtained from pilot data sets for the 2008 power analysis. However, for most outcomes, the random slope variance is estimated to be much larger than the pilot data indicated. The new estimates of random-slope variation are often an order of magnitude larger than the previous estimates and impact the power to detect population-level trends. The estimates of the variation of site-level slopes may improve with time and more accurate estimation of long-term trend within a site. However, the larger variation may simply indicate a more heterogeneous sample than was used for the previous power analysis.