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

In 2010, many areas of Victoria, particularly the northeastern region, were severely affected by heavy rainfall causing major flooding throughout the region. Rainfall intensity, duration and its severity are classified as important variables in the field of hydrology and water resource management. However, rainfall characteristics are often multidimensional and hence require the joint modelling of several random variables. 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 individual behaviour of the two variables must be characterized by the same parametric family of univariate distributions. However, in reality the variables do not have to have the same type of marginal distribution. In the past decade, Copula models, introduced by A. Sklar in 1959, were introduced to circumvent this limitation and have been successfully applied in various fields such as Civil, Mechanical, Offshore engineering in drought and flood analysis. This paper aims to study and model the joint distribution of rainfall severity and duration in northeastern Victoria using copulas. The selected rain gauge stations selected for this study are based in the flood areas that historically have large amounts of rain per year. Monthly rainfall data for a 100 year period, supplied by Australian Bureau of Meteorology (BOM), for 12 rain gauge stations situated in northeast Victoria are used in the analysis. The data is first transformed into appropriate indices by a transformation known as the Standard Precipitation Index (SPI) and these indices are subsequently used to generate the rainfall intensity and duration. The resulting intensity and duration data are fitted using the family of Archimedean copulas. The final estimated models are applied to analyse various rainfall events in Victoria and to derive the expected return periods.