Joint frequency analysis of rainfall characteristics using copula functions (Case study: Kasiliyan watershed)

Recently, copula functions have attracted great attention of hydrologists as a practical tool for multivariate frequency analysis of climatological phenomena. In this study, we focus on the joint frequency analysis of two dependent characteristics of rainfall, including depth (mm) and duration (hr) using copulas for 522 events recorded in Sangdeh rain gauge station located in Kasiliyan watershed. To join the marginal distributions and constructing the joint distribution, seven copulas including Clyton, Ali-Mikhail-Haq, Farlie-Gumbel-Morgenstern, Frank, Galambos, Gumbel-Hougaard and Placket were used and evaluated. By comparing the mentioned parametric copulas with an empirical copula, we found that the Placket is the the best fitted copula on the considered variables. Finally, the joint probabilities, joint return periods and conditional joint return periods were calculated and plotted. For example, joint probability values for two events with duration of 12 and 24 (hr) given rainfall depth that exceeds 15 (mm) were calculated as 0.2663 and 0.7693, respectively. Also, conditional return period was calculated equal to 9.19 year for an event with depth of 30 (mm), given rainfall duration that exceeds 24 (hr) and equal to 14.94 year for an event with duration of 24 (hr), given rainfall depth that exceeds 30 (mm).