Modelling the dependence structure between two rainfall stations in Johor

Abstract

Rainfall data consist of zero and real rain values. In many rainfall models, the zero values are not seriously considered in the analysis, which may lead to the loss of some important information. Therefore, to preserve sufficient information, the effect of zero values needs to be examined before its omission from the analysis. In this study, a bivariate mixed model that consists of continuous and discrete distribution is employed to disclose the portion of zero values in the analysis where the possibility of no rain phenomenon characteristics in the data can be included. The rainfall data used are taken from two rainfall stations that are classified into three cases: data with only positive values (non-zero values) recorded at both stations, data with positive values recorded in either one of the stations and all data values including zeroes recorded at both rainfall stations. The interstation correlation coefficients of the bivariate mixed distribution under these three cases are then used to detect the importance of the zero values. Results show that the case, data with only positive values recorded at both stations is the best. In addition, the rainfall characteristics of two stations that are nearby and located in the same river basin can be different due to their different spatial conditions. However, one of the limitations of bivariate distribution is that all its univariate marginal distributions are assumed to be the same type of distribution, yet there are neighbouring stations that have different types of distributions. Hence, the Copula model is then proposed to describe the dependency between two stations without considering the effect of the marginal distributions. Based on the rainfall data that contain only non-zero values for both stations, Galambos distribution is found as the best Copula model in describing the dependencies between the two stations in Johor area. Lastly, the dependencies parameters of bivariate mixed distribution and Copula distribution are proposed as spatial weighting methods in estimating the rainfall values at unsampled location.