Stochastic generator for rainfall with a Hawkes process marked by an extended generalized Pareto and a vine copula

A stochastic generator for rainfall is built from a Hawkes process, which is modeling the occurrence and serial correlation of non-zero rainfall values. Hawkes processes are suited to model intermittent signals, which is the case of rainfall at a fine enough observation frequency. This Hawkes process has a two-scale intensity function accounting for two orders of clustering in rainfall time series. The rainfall amount of each non-zero value is modeled by an extended generalized Pareto (EGP) distribution with the whole range of rainfall as support, from low to extreme values. New parametric EGP forms adapted to high frequency rainfall time series are defined. The Hawkes process only models the serial correlation of occurrences but not that of the amounts. A conditional version of the EGP is hence developed by adding a copula, modeling the temporal dependence of rainfall amounts. A subsettable canonical vine copula models this dependency for multiple time lags, while accounting for the intermittency of non-zero rainfall values. An application to a 40 yr time series of hourly rainfall in France is presented. Simulations from the model reproduce adequately the marginal distribution of rainfall, the temporal clustering of events, and the autocorrelation. The simulations are also able to reproduce the intensity-duration-frequency relation of the IDF extreme value model, showing that this stochastic generator is suitable for risk assessment of duration-dependent extremes.