Latent process modelling of threshold exceedances in hourly rainfall series

Two features are often observed in analyses of both daily and hourly rainfall series. One is the tendency for the strength of temporal dependence to decrease when looking at the series above increasing thresholds. The other is the empirical evidence for rainfall extremes to approach independence at high enough levels. To account for these features, Bortot and Gaetan (Scand J Stat 41:606-621, 2014) focus on rainfall exceedances above a fixed high threshold and model their dynamics through a hierarchical approach that allows for changes in the temporal dependence properties when moving further into the right tail. It is found that this modelling procedure performs generally well in analyses of daily rainfalls, but has some inherent theoretical limitations that affect its goodness of fit in the context of hourly data. In order to overcome this drawback, we develop here a modification of the Bortot and Gaetan model derived from a copula-type technique. Application of both model versions to rainfall series recorded in Camborne, England, shows that they provide similar results when studying daily data, but in the analysis of hourly data the modified version is superior.