An Efficient Data-Driven Variance-Based Global Sensitivity Analysis for Identifying Dominant Factors that Control Unusual Hydrological Events

During the past decades, several distributed and semi-distributed process-based hydrologic models have been developed for simulating water flow dynamics at a range of spatio-temporal scales. Modelling complex hydrologic processes and their interaction with human inevitably introduces a considerable uncertainty associated with forcings, model parameters, and model structure. Adequate characterization of uncertainty is vital to draw appropriate inferences about the system’s behaviour to support decision making. The Global Sensitivity Analysis (GSA) has proven to be a promising tool for quantifying the model output uncertainty through apportioning the uncertainty to different sources. The sampling-based strategy is a common, yet computationally demanding, approach to GSA. By running a model using various configurations of (randomly generated) parameter values, this strategy provides modellers with desired sensitivity indices. However, due to typically large number of parameters, long run times, and limited computational budget, this strategy may not be efficient. In this study, we introduce a new data-driven variance-based GSA technique to alleviate the computational burden associated with GSA of the computationally intensive models. In particular, we incorporate the copula models in the setting of variance-based GSA. Our proposed GSA technique does not require re-running the model as it uses a sample of pre-existent model runs to capture the joint probability distribution of the model parameters and responses. Based on the learned probability model, our method can effectively estimate different types of variance-based sensitivity indices. This method enables the user to efficiently conduct GSA for cases in which the properties of input-output distributions and of the underlying response surface are unknown and only a (small) sample of the input-output space is available. We demonstrate the utility of the proposed method by conducting numerical experiments using a physically-based model, Variable Infiltration Capacity (VIC) with 18 parameters, in Bow Basin, Alberta, Canada. Using the depth functions, we first extracted critical time periods with unusual events, which represent most of the hydrological variability. Next, we applied the proposed GSA method to efficiently identify key factors that significantly influence the simulation of these hydrologically unusual events. Results and insights gained through this study provide valuable information for parameter identifiability analysis, model calibration, and diagnostic testing.