Extraction of intensity-duration for short-term extreme rainfalls from daily and yearly extreme rainfalls using copula functions

Understanding rainfall intensity in different regions, especially in the context of climate changes, is crucial for designing hydraulic structures like urban runoff collection systems. Therefore, a comprehensive examination of three variables, including daily and annual rainfall and the maximum intensity of short-term rainfall, is essential due to variations in the amount and temporal distribution of rainfall. In many regions, extreme rainfall intensities may not have been recorded, necessitating the estimation of maximum rainfall with durations less than 24 h by leveraging the correlation between maximum 24-h rainfall and annual rainfall. As precipitation is a multi-variable phenomenon with interdependent variables, employing multi-variable analysis provides a more accurate interpretation than single-variable analysis. To achieve this, this study utilized five copula functions from the symmetric Archimedean copula family to analyze the dependence structure between variables. The data for all three precipitation variables from the Isfahan synoptic station, representing the Central Plateau region of Iran, were collected over a 53-year period (1967–2020).Subsequently, the best marginal distribution functions were fitted to the variables. Then, using the maximum likelihood method and goodness of fit tests, the copula parameters and the best bivariate and trivariate copula functions were estimated respectively. Finally, the probabilities and periods of joint (AND and OR) and conditional returns of two and three variables were calculated and illustrated. Comparing the results of the bivariate and three-variables (maximum intensity of rainfall in short-term, maximum daily rainfall and average total annual rainfall) return periods, it was concluded that the three-variable conditional return period provides higher reliability for the long-term design of infrastructures.