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

Impact of robustness of hydrological model parameters on flood prediction uncertainty

“…This is equivalent to only consider NS in our research: using Zone 3 parameters to analyse uncertainty. However, the results in our study show the trade‐offs between robustness and NS , which cannot be revealed when robustness is not considered as in Kim et al ().…”

“…In the research by Kim et al (), robustness is not considered as a criterion to select model parameters to analyse hydrological simulation uncertainty. This is equivalent to only consider NS in our research: using Zone 3 parameters to analyse uncertainty.…”

“…However, in this research, multiple flood events were calibrated individually without evaluating the overall robustness and objectives. In recent years, a Minimax‐Regret approach was used for hydrological model calibration with multiple flood events (Kim, Chung, Won, & Gil, ). This Minimax‐Regret approach is able to explore the solutions with the best performances in the worst cases and can hedge against the most influential, worst and critical situations.…”

“…This Minimax‐Regret approach is able to explore the solutions with the best performances in the worst cases and can hedge against the most influential, worst and critical situations. Although Kim et al () considered multiple data sets, hydrological model parameter robustness was not taken into consideration. Most recently, Dakhlaoui, Ruelland, Tramblay, and Bargaoui () analysed the robustness of three hydrological models in hydrological simulation under climate variability, but hydrological model parameter robustness is not explicitly quantified.…”

Towards an Efficient Rainfall–Runoff Model through Partitioning Scheme

“…In recent years, many efforts have been made to identify, measure and reduce the uncertainty of parameters in CRR models. For example, in many studies multi-objective approach is deployed to reduce uncertainty in the parameter estimation [12][13][14], in some papers attempts have also been made to estimate the uncertainty parameter using methods such as the Generalize Likelihood Uncertainty Estimation (GLUE) and Sequential Uncertainty Fitting Procedure (SUFI) [15][16][17][18][19]. Furthermore, in several other studies, hybridization methods by combining hydrologic predictions from multiple competing models are applied to overcome the model structural uncertainty [20][21][22].…”