Calculation of Compound Hazard Probability using Convolution of Distributions

The hazard produced by natural phenomena on infrastructure and urban populations has been widely studied. Researchers recognise that the danger posed by these phenomena depends on their extreme values. Most researchers focus on the extremes of natural phenomena considered in isolation, one variable at a time. What is relevant in hazard studies is, however, coincident extremes of several climatic variables, i.e. the presence of compound extremes. The peak value of these extremes seldom coincide, but off-peak values located in the tail of the distributions are often concurrent and can lead to catastrophic events. The problem is complicated by the presence of correlations between these variables. This paper presents a robust methodology to solve the problem based on the convolution of distributions. To illustrate the methodology, the case of a cyclone landing close to a coastal city is discussed, and its probability of flooding and recurrence period is calculated.