Multi-scale trend analysis of water quality using error propagation of generalized additive models

Effective stewardship of ecosystems to sustain current ecological status or mitigate impacts requires nuanced understanding of how conditions have changed over time in response to anthropogenic pressures and natural variability. Detecting and appropriately characterizing changes requires accurate and flexible trend assessment methods that can be readily applied to environmental monitoring datasets. A key requirement is complete propagation of uncertainty through the analysis. However, this is difficult when there are mismatches between sampling frequency, period of record, and trends of interest. Here, we propose a novel application of generalized additive models (GAMs) for characterizing multi-decadal changes in water quality indicators and demonstrate its utility by analyzing a 30-year record of biweekly-to-monthly chlorophyll-a concentrations in the San Francisco Estuary. GAMs have shown promise in water quality trend analysis to separate long-term (i.e., annual or decadal) trends from seasonal variation. Our proposed methods estimate seasonal averages in a response variable with GAMs, extract uncertainty measures for the seasonal estimates, and then use the uncertainty measures with mixed-effects meta-analysis regression to quantify inter-annual trends that account for full propagation of error across methods. We first demonstrate that nearly identical descriptions of temporal changes can be obtained using different smoothing spline formulations of the original time series. We then extract seasonal averages and their standard errors for an a priori time period within each year from the GAM results. Finally, we demonstrate how across-year trends in seasonal averages can be modeled with mixed-effects meta-analysis regression that propagates uncertainties from the GAM fits to the across-year analysis. Overall, this approach leverages GAMs to smooth data with missing observations or varying sample effort across years to estimate seasonal averages and meta-analysis to estimate trends across years. Methods are provided in the wqtrends R package.