Evaluation of statistical models: Perspective of water quality load estimation

The accurate representation of the load of water quality constituents, transported by rivers and streams, is crucial to understand the impact on the quality of the lakes, the behavior of the rivers and streams. Statistical models have been developed to predict the water-quality constituent loads from the available data of sampled con-centration (low-frequency/grab chemistry data) and continuous discharge (high frequency) at a particular sampled location and to further analyze trends and changes in water quality. However, the performance of statistical models to estimate water quality constituent loads depends on many aspects including the type of water quality constituent, sampling strategy and frequency, and the land use and areas of the watershed. This study evaluates the performance of a wide range of statistical models for the estimation of total suspended solids (TSS) and total phosphorus (TP) loads under various sampling scenarios and monitoring stations in Southern Ontario, Canada. Trends in TSS and TP concentrations and loads were further analyzed in major tributaries. The Weighted Regression on Time, Discharge, and Season Kalman Filter (WRTDS_K) model was found to be the most suitable model (p > 0.05 and Percentage Difference (%) (PDIFF) between +/- 20) for predicting TSS loads at most sampling stations and under most sampling scenarios, while, the Weighted Regression on Time, Discharge, and Season (WRTDS) model was found to be the most suitable model (p > 0.05 and flux bias statistics (FBS) between +/- 0.1) for predicting TP loads. The applied statistical models (LOADEST simple and curvilinear models, WRTDS, WRTDS_k, Beale's estimator, composite and interpolation models) have shown a limited potential to estimate load accurately at monitoring stations covering small drainage areas.