Use of the Minimax Regret Approach for Robust Selection of Rainfall-Runoff Model Parameter Values Considering Multiple Events and Multiple Performance Indices

When hydrological simulation models are calibrated, the optimized parameter set based on a single event often does not show good accuracy for other events, even using the same performance measure. Therefore, this study improved the robust parameter set (ROPS) selection method for hydrological simulation models to consider multiple rainfall events by combining the Minimax Regret Approach (MRA) with Pareto optimums. A multi-event objective function, which is the linear combination of three weighting values and three Nash-Sutcliffe coefficients, was used and individually solved using a genetic algorithm. All available 63 multi-objective functions with weighting values based on three events were determined and then, the Pareto optimum was derived. These optimized parameter sets were considered as the ROPS candidates for the final selection. This study used two approaches. First, Nash-Sutcliffe efficiencies (NSEs) for the additional three rainfall events were used to identify the ROPS. Second, four performance indices, the NSE, the Peak Flow Error (PFE), the Root Mean Square Error (RMSE) and the Percent Bias (PBIAS), were used for the other three events. From the results, it can be concluded that the optimized parameter set from the best weighted multi-objective function using multiple events can simulate most rainfall events well with relatively high precision for both the NSE only and the four performance indices. Furthermore, it can be extended to combine multiple events from multiple sites.