Joint probability analysis for estimation of extremes

Conditions required to cause flooding often involve more than one source variable such as large waves combined with a high sea level causing coastal flooding, or high river flow combined with a high sea level causing river flooding. In order to estimate the probability of flooding, one needs to know not only the high and extreme values of each variable, but also their likelihood of occurring simultaneously. This work summarises the terminology and the types of method available for joint probability analysis, and discusses the issues associated with data selection and event definition. It then describes the development and testing of methods for incorporation of temporal dependence into an approach involving Monte Carlo simulation. An illustration study shows the effect of introducing firstly short-term clustering, then seasonality and long-term trend. Three further case studies are used to illustrate some key points in the appropriate use and interpretation of joint probability methods.