Study on Proper Sample Size for Multivariate Frequency Analysis for Rainfall Quantile

For a given rainfall event, it can be characterized into some properties such as rainfall depth (amount), duration, and intensity. By considering these factors simultaneously, the actual phenomenon of rainfall event can be explained better than univariate model. Recently, applications of multivariate analysis for hydrological data such as extreme rainfall, drought and flood events are increasing rapidly. Theoretically, sample size on 2-dimension sample space needs n-square sample size if univariate frequency analysis needs n sample size. Main object of this study is to estimate of appropriate sample size of bivariate frequency analysis (especially using copula model) for rainfall data. Hourly recorded data (1961~2010) of Seoul weather station from Korea Meteorological Administration (KMA) is applied for frequency analysis and three copula models (Clayton, Frank, Gumbel) are used. Parameter estimation is performed by using pseudo-likelihood estimation and estimated mean square error (MSE) on various sample size by peaks over threshold (POT) concept. As a result, estimated thresholds of rainfall depth are 65.4 mm for Clayton, 74.2 mm for Frank, and 76.9 mm for Gumbel, respectively