Rainfall Modelling using Generalized Extreme Value Distribution with Cyclic Covariate

Jasmine Lee Jia Min,Syafrina Abdul Halim

doi:10.13189/ms.2020.080617

Abstract

Increased flood risk is recognized as one of the most significant threats in most parts of the world, resulting in severe flooding events which have caused significant property and human life losses. As there is an increase in the number of extreme flash flood events observed in Klang Valley, Malaysia recently, this paper focuses on modelling extreme daily rainfall within 30 years from year 1975 toyear 2005 in Klang Valley using generalized extreme value (GEV) distribution. Cyclic covariate is introduced in the distribution because of the seasonal rainfall variation in the series. One stationary (GEV) and three nonstationary models (NSGEV1, NSGEV2, and NSGEV3) are constructed to assess the impact of cyclic covariates on the extreme daily rainfall events. The better GEV model is selected using Akaike's information criterion (AIC), bayesian information criterion (BIC) and likelihood ratio test (LRT). The return level is then computed using the selected fitted GEV model. Results indicate that the NSGEV3 model with cyclic covariate trend presented in location and scale parameters provides better fits the extreme rainfall data. The results showed the capability of the nonstationary GEV with cyclic covariates in capturing the extreme rainfall events. The findings would be useful for engineering design and flood risk management purposes.

Highlights

Extreme value analysis of hydrological data allows interpreting historical data and making inference on future probabilities of occurrence of extreme events, such as floods due to extreme rainfalls
Due to the presence of the seasonal monsoon season in Malaysia, cyclic covariate trend is applied in the generalized extreme value (GEV) distribution in this study
In the case of extreme value variables, the Nonstationary generalized extreme value distribution (NSGEV) model is better in capturing the mean ad variance than GEV0

Summary

Introduction

Extreme value analysis of hydrological data allows interpreting historical data and making inference on future probabilities of occurrence of extreme events, such as floods due to extreme rainfalls. Statistical inference for hydrological time series such as extreme rainfall events normally relied on the assumption of stationarity [2]. Under the combined influences of climate change and variability or human intervention [3], the series often exhibits nonstationary features and will not likely satisfy stationary assumptions [4, 5]. Nonstationarity may affect both the severity and frequency of these extreme events [6]; the reality of nonstationary hydrometeorological extremes needs to be properly addressed. Nonstationary extreme value models with climatic covariates could be the valuable tools to assess future changes in extreme rainfall distribution and quantiles for engineering design and flood risk management purposes [7]

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Discussion

Conclusion