Using Mutual Information for Global Sensitivity Analysis on Watershed Modeling

Abstract

Global sensitivity analysis (GSA) often is applied to assess the sensitivity of model outputs to their inputs using ensemble simulations. However, increasing model complexity and the associated computational cost have limited the use of most GSA approaches for process-based watershed models. We propose to use mutual information (MI) as a computationally efficient GSA method for watershed modeling. Such MI computed from several hundred realizations usually can capture nonlinear relationships between inputs and outputs of interest. We perform MI-based watershed sensitivity analyses in studies of the Portage River Watershed in Ohio and the American River Watershed in Washington. In these studies, MI is used to evaluate the sensitivity of river discharges simulated by the Soil and Water Assessment Tool to no less than 20 SWAT parameters for each watershed. Our MI-based sensitivity analyses achieved convergence with about 300–500 realizations, a small fraction of the ensemble size (i.e., several thousands) required by the Sobol method. Nevertheless, the two-dimensional MI yields similar sensitivity ranking compared to Sobol's total-order sensitivity indices, especially for sensitive parameters. Our study thus sheds new light on the use of MI as an affordable GSA method for computationally intensive models such as the hyperresolution, watershed hydrobiogeochemical models.