Frequency analysis of floods with joint functions, case study: Zayandehrood Dam

Analyzing the frequency of floods and understanding the probability of their occurrence, as well as the return period of this phenomenon, is crucial for reservoir management. Flood occurrences are inherently multivariate, and the use of classical multivariate functions for their analysis is limited. Therefore, it is recommended to employ copula functions for multivariate flood frequency analysis. These functions combine the distribution functions of univariate variables while considering the correlation between them. In the case of this phenomenon, the variables of peak discharge, flood volume, and flood duration are utilized. This study was conducted using statistical data from the Zayandehrood dam. The best function for each variable was determined based on goodness-of-fit criteria. The correlation between each pair of variables was calculated, and the copula function was selected using Akaike, NSE, and RMSE criteria. For the peak dischargeflood volume relationship, Joy's copula function was chosen, while the peak discharge-flood duration and flood volume-flood duration relationships used the AMH function. Subsequently, the univariate and combined return periods were calculated and can be used for risk estimation.