Frequency analysis and rainfall-runoff simulation based on the tree sequence of the Vine copula

Rainfall-runoff simulation is one of the most important challenges in the management of water resources in each basin, considering the climatic changes and the increase of extreme values in recent years, especially in different regions of Iran. In this study, the rainfall and runoff values in the statistical period of 1993-2019 were used regarding the rainfall-runoff simulation in the Qale Shahrokh sub-basin in the Zayandeh-Rood Dam basin. In this study, the Vine copula-based simulation approach was used to simulate and joint frequency analysis the flow discharge in Qale Shahrokh station given by the rainfall in Chelgerd, Meyheh and Marghmalek stations. By analyzing the tree sequence of vine copulas and using internal rotated copulas, D-vine copula was selected as the best copula based on the studied statistics. By using the best copula and the conditional relationship c(u4|u1,u2,u3), the flow discharge simulation was done given by rainfall of the upstream stations. The simulation results showed an error rate equal to 18.57 (m3/s) based on the RMSE statistic and the efficiency of the model was 86% based on the NSE statistic. The results of the simulation of flow discharge values given by rainfall in the upstream stations showed that the proposed approach has simulated the average of observed values with high accuracy. By considering the condition of rainfall occurrence in the frequency analysis of flow discharge in Qale Shahrokh station, the joint return period curve and the conditional probability of occurrence in this sub-basin were obtained. Using this curve, it is possible to estimate the flow discharge values of the studied station with high accuracy along with different return periods and different probability of occurrence. Considering the fact that the proposed method is based on the condition of rainfall in the region as well as the marginal distribution according to the data, it has no implementation limitations and is somehow specific to the studied region.