THE CHOICE OF 2D PROBABILITY DISTRIBUTION FOR MAXIMUM FLOW AND VOLUME OF SNOW-MELT FLOOD - SELECTED PROBLEMS

The copula's theory to the 2D frequency analysis of snow-melt floods was developed in the paper. The flood incidents were described by 2D variable: the peak of discharge of snow-melt flood Q(max,f) and the volume of flood V-f. The random sample was set down on the base of measurement series of snow-melt floods at Wizna post in the Narew River for period 1966-2012. The aim of this paper is comparison of 2D probability distributions of varaiable (Q(max,f), V-f) estimated by 2D normal density function and copula's functions. Two copulas functions: elliptical Gaussian copula and Archimedean 1-parameters Gumbel-Hougaard copula were applied. To measure the distance between a continuous distribution function and the empirical distribution function the goodness-of-fit tests such as Kolmogorov-Smirnov (K-S), Anderson-Darling (A-D), Integrated Anderson-Darling (IA-D), Kuiper (K) statistics as well as Euclidean distance (L-2) were used. For 2D normal distribution with parameters estimated by MLM, the normality of marginals was assumed, and for copulas models the marginal frequency analysis was employed.