Vector Generalized Additive Models for Extreme Rainfall Data Analysis: A case study in South Korea

Abstract

Extreme value theory (EVT) is the branch of statistics concerned with inference about the tails of the distribution function. Accurate estimation of the year return levels of climate extremes is a critical step in the projection of future climate and in engineering design for disaster response. The study of non-stationary behavior in the extremes is important to analyze data in environmental sciences, climate, finance, or sports. The largest order statistics is an extension of the block maxima approach that is used in extreme value modeling. However, in Korea, the scientific literature usually has used the method based on fitting a distribution to an annual maximum. We focus on daily rainfall amounts data sets collected from the Korea Meteorological Administration for Seoul, Busan and Daegu, from 1961 to 2020. First, we fit the GEV df to block maxima data, i.e., annual maximum rainfall. Second, we use the top 10 annual precipitation events. We model, in which both mean and scale parameters of extreme value distribution are modeled as linear or smooth functions of covariate, YEAR, using the vector generalized linear models (VGLMs) and vector generalized additive models (VGAMs).