Estimating the Optimal Spatial Complexity of a Water Quality Model Using Multi-Criteria Methods

Discretizing the landscape into multiple smaller units appears to be a necessary step for improving the performance of water quality models. However there is a need for adequate falsification methods to discern between discretization that improves model performance and discretization that merely adds to model complexity. Multi-criteria optimization methods promise a way to increase the power of model discrimination and a path to increasing our ability in differentiating between good and bad model discretization methods. This study focuses on the optimal level of spatial discretization of a water quality model, the Alpine Hydrochemical Model of the Emerald Lake watershed in Sequoia National Park, California. The 5 models of the watershed differ in the degree of simplification that they represent from the real watershed. The simplest model is just a lumped model of the entire watershed. The most complex model takes the 5 main soil groups in the watershed and represents each with a modeling subunit as well as having subunits for rock and talus areas in the watershed. Each of these models was calibrated using stream discharge and three chemical fluxes jointly as optimization criteria using a Pareto optimization routine, MOCOM-UA. After optimization the 5 models were compared for their performance using model criteria not used in calibration, the variability of model parameter estimates, and comparison to the mean of observations as a predictor of stream chemical composition. Based on these comparisons, the results indicate that the model with only 2 terrestrial subunits had the optimal level of model complexity. This result shows that increasing model complexity, even using detailed site specific data, is not always rewarded with improved model performance. Additionally, this result indicates that the most important geographic element for modeling water quality in alpine watersheds is accurately delineating the boundary between areas of rock and areas containing either soil or talus. This delineation can be done with existing satellite remote sensing capabilities. This conclusion could prove useful in regionalizing alpine water quality models similar to the AHM.