A copula-based analysis of flood phenomena in Victoria, Australia

The issue of floods in Australia is receiving increased researchers’ attention. Floods normally occur when some part of the country experiences high level of precipitation for a certain period of time. Natural disaster protection plans, which have flood mitigation projects, intensified the studies of rainfall modelling due to urgent need in water resource management. As a result, statistical analysis of rainfall is becoming increasingly important resulting from the unpredictable climactic condition prevailing in many parts of the world. This research presents a statistical analysis of rainfall characteristics over Victoria, Australia. Traditional approaches in building multivariate distributions pose some limitations especially in the field of hydrology. This is due to the fact that hydrological variables are highly dependent and do not always satisfy the traditional modelling assumptions. Copulas are regarded as one of the best tools in assisting statisticians in constructing joint distribution of multivariate random variables with different types of marginal distributions. Copulas also provide a compliant procedure where the dependence structure between the variables can be consistently preserved. Four hydrologic applications are presented using several copula-based approaches: (1) joint rainfall characteristics modelling using the parametric family of copulas, (2) applications on Beta kernel copula analysis using parametric and nonparametric marginal distributions, (3) comparison studies between parametric and nonparametric copulas, and (4) studies of return periods.<br><br>