The Application of Two-Dimensional Copulas in Simulation of Flood Discharge Outlet

In this study, using the copula-based approach, the simulation of the flood discharge in the Karun River has been studied. In this regard, the flood in 11/30/2008 of the Karun River was used. Using the Nakagami and generalized Pareto marginal distributions, various copula functions were investigated, and the results showed the superiority of the Clayton copula with a parameter value of . According to Clayton copula and marginal distributions, the analysis of the frequency of occurrence of the pair variable of inflow and outflow hydrographs was carried out, and the results led to the presentation of a typical curve regarding the estimation of different values ​​of the outflow hydrograph corresponding to the values ​​of the inflow hydrograph. This curve can simulate the output values ​​of the hydrograph with different probability and based on the input values. Copula-based simulation, according to the conditional density of copula functions showed that the correlation coefficient of the simulated values ​​is 7% higher than the observed values. The accuracy and certainty of simulating the output values ​​of the hydrograph was also confirmed according to the violin plot. The results of this research showed that the copula-based simulation model has a high efficiency in simulating the output flow of the flood hydrograph. The results of the copula-based simulation, based on the root mean square error and Nash-Sutcliffe statistics, showed an error rate of 35.93 cubic meters per second and an efficiency of 0.96, respectively. The conditional density used in this research led to the presentation of a proposed equation regarding the simulation of the flood hydrograph outlet under the condition of the occurrence of the flood hydrograph inlet in the study area with an efficiency of 66%.