Frequency analysis of rainfall events with a Copula under non-stationary condition

This study investigated a bivariate non-stationary frequency analysis based on the rainfall events. Hourly rainfall data from 1973 to 2020 of the Korea Meteorological Administration stations in South Korea were adopted. Rainfall events were created by converting hourly rainfall data by setting the Inter Event Time Definition (IETD) to 12 hours. There are three characteristics of rainfall event: rainfall depth, duration, and intensity. Among them, rainfall depth and intensity were selected as variables for frequency analysis. The return period of a rainfall event that occurs only when both two variables are greater than the threshold is called T_and, and is calculated using Freund's bivariate exponential distribution. The minimum T_and of the annual maximum (AM) was taken as the threshold, and extreme rainfall events were extracted using the Peaks-Over-Threshold (POT) method. The return period was obtained using the generalized Pareto distribution (GPD). As a result of estimating parameters by the Maximum Likelihood Estimate (MLE) method, trend of the scale parameter of the GPD was investigated when the shape parameter fixed. Non-stationary model of the GPD was developed using six nonlinear regression equations selected through R-squared (R^2) and Akaike Information Criterion (AIC). The non-stationary GPDs of the two variables are combined through the Copula models to obtain one return period and probability rainfall. Using the bivariate non-stationary frequency analysis method is expected to prevent water disasters at rainfall increasing regions in South Korea.
Acknowledgments
This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1A2C1007447) and by Korea Environment Industry & Technology Institute(KEITI) through Aquatic Ecosystem Conservation Research Program(or Project), funded by Korea Ministry of Environment(MOE) (2022003050007).