Evaluation of parameter interaction effect of hydrological models using the sparse polynomial chaos (SPC) method

Most of the commonly available sensitivity analysis methods cannot reliably compute the interaction effect. Even though the Sobol' type methods that use Monte Carlo simulation can evaluate the interaction effect, the result is either inaccurate or requires an extraordinary number of model runs to obtain a reasonable estimate. In this study, we evaluate the sparse polynomial chaos (SPC) method as a reasonable way to estimate the interaction effect. This method is evaluated on two mathematical test functions (Ishigami and Sobol' G) and two hydrologic models (HBV-SASK and SAC-SMA). Our results show the SPC method needs about a sample size of 30 to 70 times the number of dimensions of the parameter space to evaluate the interaction effects of hydrologic models. Our findings are significant for hydrologic simulation and model calibration, as we aim to improve the understanding of complex interactions among model components and to reduce model uncertainty.