Stationary and Nonstationary Generalized Extreme Value Models for Monthly Maximum Rainfall in Sabah

Abstract

Generalized Extreme Value (GEV) model is the combination of three types of distribution class namely Gumbel, Fréchet and Weibull distributions of the Extreme Value Theory (EVT). In hydrological studies, GEV model is widely applied in the modelling of extreme rainfall. The nature of hydrological variables is highly complex, especially with the changing climate and frequent occurrences of extreme events. As such, some rainfall models assume rainfall series as stationary, while some as nonstationary. In this study, GEV models based on stationary and nonstationary data are used to assess monthly maximum rainfall data within Sabah, Malaysia and performance comparison between both GEV models is conducted. Theoretically both stationary and nonstationary GEV models are based on the same foundation, however nonstationary GEV model allows the location and scale parameters to be expressed as cyclic function of time. In this study, the stationary and the nonstationary GEV models are individually fitted to rainfall data at selected stations. Monthly maximum rainfall is blocked, and the estimated location (μ), scale (σ) and shape (ξ) parameters are estimated by using Maximum Likelihood Estimation method. Performance of both GEV models are compared based on the Akaike Information Criterion, Bayesian Information Criterion and the likelihood ratio goodness of fit tests. Results showed that nonstationary GEV model is the best fit. The inclusion of cyclic covariates in the GEV model gives improvement on the stationary GEV model at the study region. It is also concluded that, Gumbel is identified as the significant distribution for monthly maximum rainfall in Sabah at 5% significance level.