Bivariate frequency analysis of rainfall intensity and depth using copula functions (Case study: Chehelchai Watershed, GorganRood, Golestan)

Rainfall as an input factor for flood modeling and design of hydraulic structures has great importance. Rainfall frequency analysis is a major task for water resources planners and hydrologists. Considering this fact that hydrological phenomena including rainfall are multivariate (intensity-depth-duration) terms, joint modeling of several random variables would be required. Considering the importance of two rainfall characteristics including intensity and depth in flood management and design of hydraulic structures, in this research, copula function was used for the analysis of dependency structure of these two variables. For this purpose, 40 years recorded rainfall data in Minoodasht hydrometry station located on Chehelchay River in Gorganrood watershed was used. In order to determine the allowable risk of structure failure against rainfall, its univariate return period was compared with estimated joint return period through selected copula. In this study, Frank copula led to the best results in bivariate modeling of rainfall intensity and depth, according to goodness of fit tests. Associated return period was estimated by Frank copula to improve allowable structural risk estimation in comparison to univariate return period. For example, an incident with the intensity of rainfall equal to 45.43 mm/h and its depth of 168.61 mm for 100 years’ univariate return period is 53 years in "or" case and 954 years in "and" case for bivariate joint return period. Comparison of bivariate analysis with univariate analysis indicates the difference the outcome of these tow methods. As due to the lack of consideration of all effective features in the phenomenon, the univariate analysis of hydrological events would not be a comprehensive analysis, therefore, the multivariate analysis of hydrological events is recommended.