The application of the hybrid copula-GARCH approach in the simulation of extreme discharge values

Abstract

Abstract Statistical analysis and simulation of annual maximum discharge values, while considering the corresponding maximum daily rainfall, provide a comprehensive view of flood management. This research presents the application of copula functions for simulating and modeling two variables of annual maximum discharge and corresponding precipitation. In this research, the performance of copula-based models and ARCH-based models including VAR-GARCH, copula, and copula-GARCH models was then evaluated to simulate the annual maximum discharge values. The simulation results of all three models were evaluated using NSE and NRMSE statistics. According to the 95% confidence intervals, the accuracy of all three models was confirmed. The correlation results of the studied pair variables confirmed the possibility of using copula-based models. The results of simulations revealed that a higher accuracy of the copula-GARCH approach compared with two models copula and VAR-GARCH. Considering 76% efficiency (NSE = 0.76) of the copula-GARCH approach, the results indicated 20 and 2.7% improvements in the performance of the proposed approach compared to both VAR-GARCH and copula models. The results also illustrated that by combining nonlinear ARCH models with copula-based simulations, the reliability of simulation results increased. The results obtained in this study suggest that the proposed method is very effective for increasing the certainty of frequency analysis of two variables. Because the copula-GARCH approach simulates the average values, the first and third quarters, as well as the amplitude of changes of 5 and 95% of the data better than the other two models. Graphical abstract Violin plot of AMD series in copula scale

Keywords

• ARCH models
• ARMA
• Frequency analysis
• Gumbel-Hougaard
• Heteroscedasticity