Awareness of the intensity of precipitation in different continuations as a design storm for a certain return period, in the design of hydraulic structures and operation of urban wastewater collection and extraction networks, floods and management and control and storage of water resources during floods and droughts, has always been important. Is; Therefore, maximum care should be taken in determining the intensity of precipitation with different continuity. Especially in the conditions of climate change, due to the change in the amount and temporal distribution of daily and annual precipitation, the maximum intensity of short-term precipitation has also changed; Therefore, simultaneous analysis of these three variables is important.Since precipitation is a multivariate phenomenon whose variables are dependent, the use of multivariate analysis also gives a more accurate interpretation than univariate analysis.In this regard, first, the data of maximum rainfall intensity in short-term continuities, maximum daily rainfall, and total annual rainfall were received from Isfahan synoptic station as a representative station of the Central Plateau region of Iran during the statistical period of 53 years (1967-2020) and the correlation between variables by three coefficients Kendall, Spearman and Pearson were eva‎luated; Significant positive correlation coefficients were obtained between pairs of variables. Then, among the 9 fitted distribution functions, the generalized Extreme value function on the maximum rainfall intensity with short-term continuity and total annual rainfall and the lognormal function on the maximum daily rainfall showed the best fit. Then, the five detailed functions of the Archimedean family, including Clayton, Frank, Gumbel-Hougaard, Ali-Mikhail-Haq, and Joe, were fitted to the variables in three bivariate, three asymmetric, and symmetric variables, and were sequenced using the maximum likelihood and hierarchical methods. Finally, the best fitted joint functions on the variables were selected using graphic fit tests (Q-Q plot) and numerical tests (NSE, RMSE, AIC, MLE). Thus in the bivariate model, the Clayton joint function for pairs of maximal precipitation intensity variables at short intervals of 10, 60, 120, and 180 minutes and the maximum daily precipitation and Frank joint function on pairs of maximum precipitation intensity variables at 30, 240, 360, and 540 continuities. Minutes and maximum daily precipitation showed the best fit, and in the case of three asymmetric and symmetric variables, the Frank joint function showed the best fit on all pairs of variables articulated to the third variable as well as the three variables together. Then, the results obtained from selected joint functions were used to estimate the common and conditional probabilities of two and three variables, and finally, the periodic, seasonal, and conditional returns of two and three variables were calculated and plotted as a criterion for designing hydraulic structures. In this way, by determining the turning point period or a certain season, different values of the pair of variables that result in that return period are obtained, and vice versa. Also, by determining the period of certain conditional returns, the maximum amount of rainfall intensity in short-term continuities was obtained. The results showed that during the conditional return period of three variables of 20 years, the maximum rainfall intensity in 10, 30, 60, 120, 180, 240, 360, and 540 minute continuities Will be respectively 40.3, 18.2, 12.3, 8, 6/1, 4.8, 3.9, and 3.1 (mm per hour). Comparing the results of bivariate with three variables, it was found that the maximum rainfall intensity in the short-term continuities of the bivariate conditional returns period of up to 7 years is greater than or equal to the maximum precipitation intensity in the short-term continuous durations of the variable conditional returns.

حميدرضا صفوي

محمدحسين گل محمدي، رامتين معيني