Comparative Analysis of Multivariate Copula Models for Extreme Rainfall Simulation in Pahang, Malaysia

Abstract

Extreme rainfall events, often occurring at a regional scale, imply a degree of interdependence among several variables within the same locality. To replicate this dependency structure, a joint probability analysis utilizing multivariate approach is required. Conventional multivariate probabilistic distributions inherently imply that all variables adhere to the same distribution, which is realistically untrue. Alternatively, this study utilized the copula theory; a robust statistical method that enables the separate modelling of joint distributions and univariate marginals, thereby allowing for the simultaneous modelling and simulation of annual maximum daily rainfall data obtained from three rainfall stations in Pahang. From the modelling perspective, the efficacy of four distinct copula models was illustrated and the goodness-of-fit test indicates that the Gumbel copula is the superior model, followed by the Frank, Clayton, and Skew-t copulas, in that sequence. Moreover, the simulated data was able to be reverted back into meaningful value, allowing direct comparison to be done in terms of mean and variance of simulated and empirical values. The finding suggests all copula models successfully produced simulation outcomes that closely mimic the empirical distributions and characteristics of the observed extreme rainfall. These findings establish the basis for subsequent research on spatial and risk analysis of extreme events, which is essential for effective decision-making and catastrophe mitigation.