Analysis of joint and conditional return periods for several dependent characteristics of runoff hydrograph using copula functions (Case study: Kasiliyan watershed)

Recently, the use of copula functions as a practical and flexible tool for constructing joint probability distribution of multivariate hydrologic phenomena, such as flood, has attracted great attention of hydrologists. The main objective of this study is to extract and analysis of the joint and conditional return periods of some dependent characteristics of runoff hydrograph, including runoff volume, peak discharge, base time and time to peak discharge. These characteristics extracted from 60 flood events recorded in Valikbon hydrometric station, located in outlet of Kasiliyan reference watershed during 1975-2007. Three copulas, including Clyton, Ali-Mikhail-Haq and Frank were considered for constructing the joint distribution of the paired hydrograph characteristics. The Frank copula was selected as the best copula for constructing the joint distribution from paired characteristics of runoff volume and peak discharge of hydrograph and also runoff volume and base time of hydrograph. While the Clyton copula was recognized as the best copula for other two dependent characteristics, namely time of peak discharge and base time of hydrograph. After constructing joint distributions, several valuable information such as joint probability, joint and conditional return periods were calculated and plotted.