Multivariate Flood Frequency Analysis Based On Copula Functions

Based on theories and methods of multivariate flood frequency, using flood data in the north of Shaanxi as study area, A new multivariate flood frequency analysis method-Copula function were used to establish joint probability distribution and conditional probability distribution of flood characteristics variables of in the north of Shaanxi and analyzed flood probability in different combination of Flood characteristics variables in order to provid the basis for flood control and water engineering design, construction and management in the north of Shaanxi. To abtained the main conclusions were given in the following:(1) Flood characteristics of peak and volume in research area subject to P-III-type distribution and duration are subject to lognormal distribution.(2)There is a good correlation between every two flood Characteristics of variables. Kendall rank correlation coefficient and Spearman rank correlation coefficient of flood peak and flood volume in every station are great than 0.7; Kendall rank correlation coefficient and Spearman rank correlation coefficient of flood peak and flood duration,flood peak and flood volume in most stations are great than 0.6,and only a very small number of stations is between 0.4 ~ 0.6;The results show that the order of the correlation between the flood characteristic variables is: peak and volume, volume and the duration, peak and duration.(3)Copula has a good fitting effect for the flood measured data in the studied area. For joint probability distribution function.,the best fit Copula for two variables of peak and volume, peak and duration of the joint probability distribution function is Gumbel-Hougaard (GH) Copula; The best fit Copula for two variables of volume and duration of the joint probability distribution function in different stations is Gumbel-Hougaard (GH) Copula and Clayton Copula; The best fit Copula for three variable of peak, flood volume and duration of the joint probability distribution function in different stations are Clayton Copula,Frank Copula and Gumbel-Hougaard (GH) Copula。(4)According to selected the best copula between different variables in every stations,it established joint probability distribution and over probability distribution between peak and volume, peak and duration, volume and duration and abtained the corresponding joint probability distribution plot, over probability distribution plot and the current return period contour; Meanwhile, the three variables joint probability distribution and over probability distribution among peak, volume and duration were established and draw the corresponding joint probability distribution plot, over probability distribution plot and the current return period contour; Select the maximum measured value of every station characteristics variables of peak, volume and duration and calculated the joint probability and over probability of two variables and three variables,and joint probability were greater than over probability and the corresponding joint return period is less than the over return period. From this, when the characteristics of the variable exceeds the measured maximum value that the probability of flood events was smaller and don't occurred easily.(5)Established the conditional probability distribution of peak and volume, peak and duration, volume and duration and drawn the conditional return period under given conditions; Established the conditional probability distribution of peak and volume and duration and drawn the conditional return period under given conditions;According to the established the conditional probability distribution between different characteristics of variables , the probability of occurrence of floods under different conditions were caculated;The conditional probability distribution plot shows that the conditional return period that the conditions were equal to specific value was less than the conditional return period that the conditions were less than or equal to specific value.