Modelling rainfall severity and duration in north-eastern Victoria using Copulas

Since 2010, there have been many areas in Victoria, particularly in the north-eastern provinces, that were badly affected by heavy rain causing major flooding. Rainfall duration and severity are commonly regarded as important variables in the field of hydrology and water resource management which affect flooding intensity. However, rainfall characteristics are often multidimensional and hence require the joint modelling of several random variables. The selected rain gauge stations are located in the flood areas that historically have large amounts of rain per year. Monthly rainfall data for an 81 year period were supplied by the Australian Bureau of Meteorology (BOM) for 2 rain gauge stations in north-eastern Victoria. Traditionally, the pair-wise dependence between variables such as intensity, duration, and severity has been described using the classical family of bivariate distributions. The main restriction of this approach is that the marginal distribution of each of the two random variables must be characterized by the same parametric family of univariate distribution. However in reality the variables do not have the same marginal distribution. In the past decade, Copula models were introduced to circumvent this limitation. Copulas have also been successfully applied to various multivariate simulation studies in civil, mechanical, offshore engineering and flood frequency analysis. In this paper, we will first discuss the Standard Precipitation Index, (SPI) which was developed to quantify rainfall severity and duration. Secondly, estimation of univariate marginal distributions were performed and followed by the identification of the generator and parameter of appropriate copulas and, finally, the determination of the joint probability distributions are obtained. In our research, the bivariate rainfall distributions were obtained using the family of Archimedean Copulas such as Gumbel-Houggaard and Clayton family of copulas. The models are then used to describe various rainfall events in Victoria and various goodness of fit tests will be performed. This study aims to model the joint distributions of rainfall severity and duration in north-eastern Victoria and then to apply the results in considering various aspects of recent flooding that occurred in north-eastern Victoria.