Bivariate Frequency Analysis of Annual Maximum Rainfall Event Series in Seoul, Korea

Abstract

The return period of a rainfall event is estimated by the frequency analysis for a given rainfall duration. Thus, it is possible to derive different return periods with different rainfall durations for a given rainfall event. The longest derived return period is generally cited to represent the rainfall event. However, it is not clear if the longest derived return period is a representative measure of the given rainfall event. In this study, as a solution for this problem, a bivariate frequency analysis was introduced. As a first step, annual maximum rainfall events were selected by applying a bivariate exponential distribution. As an application, a total of 1,534 rainfall events observed in Seoul, Korea, over the last 46 years were analyzed. The annual maximum rainfall event series were then analyzed by applying a bivariate logistic model. The results were also compared with those from a conventional univariate frequency analysis. The findings of this study are summarized as follows: (1) the bivariate exponential distribution satisfactorily represented the duration and total rainfall depth data of all independent rainfall events, and the annually estimated parameters of the bivariate exponential distribution were more reasonable with respect to annual changes in the climatic conditions than those for the entire data period; (2) by using the bivariate logistic model, the return period was able to be assigned to each annual maximum rainfall event; and (3) rainfall quartiles of the univariate frequency analysis were bigger than those from the bivariate frequency analysis for rather short return periods of less than 30 years, but smaller for rather long return periods exceeding 100 years, primarily attributable to the smaller variance of the univariate annual maximum series.