Copula based analysis of rainfall severity and duration: A case study

The main objective of this study is to investigate the joint distribution of rainfall severity and rainfall duration in the state of Victoria, Australia, based on monthly rainfall data from selected rain-gauge stations which are located in the north-eastern and south-western parts of the state, during the period from 1950 to 2010. Traditional approach for considering the joint distribution of rainfall characteristics using standard bivariate modeling presents some limitations that can be circumvented by using Copula models. Archimedean and extreme-value copulas will be used to obtain the bivariate distribution of rainfall severity and duration. The Standard Precipitation Index (SPI), which is employed extensively to quantify rainfall severity, will be discussed in detail. Several goodness of fit tests will be performed to find the best fitting copulas and the results will be summarized. The final fitted copulas will then be applied to obtain the joint and conditional return periods from a minimum of two years to one hundred years of rainfall events in Victoria.