Modelling multivariate extreme flood events

Abstract

Cost benefit analysis, and other measures of economic risk, needs to take account of several characteristics of flood events if a realistic assessment of flood damage is to be made. Crucial characteristics might typically include the peak flow, the total volume of water above some threshold, and the duration of the inundation. The last mentioned is of particular importance for rice crops in Asia. Realistic modelling of these floods typically requires fitting a tri-variate extreme value distribution with a carefully chosen dependence structure. Two approaches are compared. The first utilises copulas, which are multivariate uniform distributions. To begin with, the marginal distributions of the variables are estimated and then transformed to uniform distributions. Then the dependence structure, in this transformed space, is modelled by one of a large variety of possible analytic models or a non-parametric form. The second approach is to fit conditional distributions using regression type methods, such as an empirical Gibbs sampler. The empirical Gibbs sampler is particularly flexible as the variance of the conditional distributions can easily be related to the values of the other variables. Comparisons will be made of the ability of the various models to approximate known distributions. Practical cases will include the annual flood on the Mekong. Non-stationarity, and possible links with climatic indicators, such as El Nino, will be explored.