A Detection of Applicable Copula using Goodness of Fit Tests for Bivariate Rainfall Frequency Analysis

The copula model is broadly applied and studied in a hydrological field. The copula model is easier and more flexible to construct multivariate model than conventional multivariate model. Because of above statement and characteristic of the copula model which is a kind of distribution, in the hydrological field the copula model is frequently studied for multivariate frequency analysis. When the copula model is applied for frequency analysis, choosing applicable copula model is difficult yet. In this study, to detect applicable copula model Cramer-von-Mises and Kolmogorov-Smirnov tests, which are suggested by Genest et al. (2009), are applied. For estimation of copula parameter, maximum pseudo-likelihood estimation method and Kendall's tau estimation method are applied. Rainfall data recorded by five weather stations, which are Seoul, Chuncheon, Gangneung, Wonju, and Chungju and managed by Korea Meteorological Administration (KMA), are applied for frequency analysis. For bivariate frequency analysis, amount (total depth) and duration are selected and applied. Frank, Gumbel-Hougaard, Joe, and Clayton families are applied (Joe, 1997; Nelsen 1999). A critical value is rejected on p-value 5%. A rejection rate and p-value of copulas are compared.