IDF relationships using bivariate copula for storm events in Peninsular Malaysia

Abstract

► We derive IDF points of convective storms by using the copula method. ► The correlation between storm intensity and duration is negative and moderate. ► The Frank and Gaussian copula are suitable for storms in Peninsular Malaysia. ► We compare the results with the IDF curves from the univariate approach. ► The IDF points from both methods are in agreement with each other. Intensity–duration–frequency (IDF) curves are used in many hydrologic designs for the purpose of water managements and flood preventions. The IDF curves available in Malaysia are those obtained from univariate analysis approach which only considers the intensity of rainfalls at fixed time intervals. As several rainfall variables are correlated with each other such as intensity and duration, this paper aims to derive IDF points for storm events in Peninsular Malaysia by means of bivariate frequency analysis. This is achieved through utilizing the relationship between storm intensities and durations using the copula method. Four types of copulas; namely the Ali–Mikhail–Haq (AMH), Frank, Gaussian and Farlie–Gumbel–Morgenstern (FGM) copulas are considered because the correlation between storm intensity, I , and duration, D , are negative and these copulas are appropriate when the relationship between the variables are negative. The correlations are attained by means of Kendall’s τ estimation. The analysis was performed on twenty rainfall stations with hourly data across Peninsular Malaysia. Using Akaike’s Information Criteria (AIC) for testing goodness-of-fit, both Frank and Gaussian copulas are found to be suitable to represent the relationship between I and D . The IDF points found by the copula method are compared to the IDF curves yielded based on the typical IDF empirical formula of the univariate approach. This study indicates that storm intensities obtained from both methods are in agreement with each other for any given storm duration and for various return periods.