A Comparative Study on DDF Curve with Bivariate and Univariate Model

DDF(or IDF) curve is consisted with rainfall depth(or intensity), duration and frequency, and it is useful to see how rainfall changes in various conditions. Furthermore, recently, multivariate frequency analysis is applied to hydrology because of its scalability. In this study, to obtain DDF curve, rainfall quantile is estimated by both of univariate and bivariate(rainfall depth and duration) frequency analysis. For bivariate model, three copula models which are Frank, Gumbel-Hougaard, and Joe, are used in this study. Copula model has been studied widely for various fields, and it is flexible for marginal distribution than other conventional bivariate models. Hourly recorded data(1961~2010) of Seoul weather station from Korea Meteorological Administration (KMA) is applied for frequency analysis, and inter-event time definition is used for identification of rainfall events. For estimate parameters of copula models, maximum pseudo-likelihood estimation method which is semi-parametric method is used. Gumbel distribution is examined and used for rainfall depth, and generalized extreme value (GEV) distribution is examined and used for duration. As a result, 4 DDF curves are obtained (univariate, 3 copula models). In compared to univariate model, rainfall quantile of bivariate model unaffected by duration. In detail, Frank model shows closest trend along the duration, and Joe model doesn`t show the little changes along the duration. Change of rainfall quantile from bivariate model along the duration is less significant than univariate model as varying nonexceedance probability.