Robust Parameter Estimation Framework of a Rainfall-Runoff Model Using Pareto Optimum and Minimax Regret Approach

Abstract

This study developed a robust parameter set (ROPS) selection framework for a rainfall-runoff model that considers multi-events using the Pareto optimum and minimax regret approach (MRA). The calibrated parameter sets based on the Nash-Sutcliffe coefficient (NSE) for two events were derived using a genetic algorithm. We generated 41 combinations for weighting values between two events for the multi-event objective function and derived 41 Pareto optimum points that were considered as the ROPS candidates. Then, two different approaches for parameter selection were proposed to determine the ROPS among the candidates: one uses NSE only and the other uses four performance measures (NSE, peak flow error, root mean square error and percentage of bias). In the NSE-only method, five events, including two events from the calibration set and three events from the evaluation set, were used, and the ROPS was selected based on the regrets of both the calibration and the evaluation sets. In the multiple (i.e., four) performance measure method, only three events from the evaluation set were used and the ROPS was determined based on the regrets of twelve different cases, including three events with four measures. As a result, while single- and multi-event optimizations produced satisfying results for the calibration events, the optimized parameters from the single-event calibration do not perform well for another event, even one with the same criteria, such as NSE. The results of this study suggest that the optimized parameter set from the well-weighted objective function can successfully simulate not only hydrographs in general but also others, such as peak flow. In addition, the ROPS can be selected by considering the multiple performance measures of multiple validation events, as well as the NSE only of multiple calibration and validation events. Note that the study provides a framework that could be performed reasonably well with a limited number of events. While the computational resources might not be a limiting factor these days, it is still valuable to have such a tool for several reasons: one could utilize it for an operational decision making support tool, as the full searches for an optimal set of parameters might not be performed in the operational facility. It could also be used in a situation where one has a limited number of good-quality observational data for some reason.