Characterization of ERA5 daily precipitation using the extended generalized Pareto distribution

Both mean and extreme precipitation are highly relevant and a probability distribution that models the entire precipitation distribution therefore provides important information. Very low and extremely high precipitation amounts have traditionally been modeled separately. Gamma distributions are often used to model low and moderate precipitation amounts and extreme value theory allows to model the upper tail of the distribution. However, difficulties arise when making a link between upper and lower tail. One solution is to define a threshold that separates the distribution into extreme and non-extreme values, but the assignment of such a threshold for many locations is not trivial. 

Here we apply the Extended Generalized Pareto Distribution (EGPD) used by Tencaliec & al. 2019. This method overcomes the problem of finding a threshold between upper and lower tails thanks to a transition function (G) that describes the transition between the empirical distribution of precipitation and a Pareto distribution. The transition cumulative distribution function G has to be constrained by the upper tail and lower tail behavior. G can be estimated using Bernstein polynomials.

EGPD is used here to characterize ERA-5 precipitation. ERA-5 is a new ECMWF climate re-analysis dataset that provides a numerical description of the recent climate by combining a numerical weather model with observations. The data set is global with a spatial resolution of 0.25° and currently covers the period from 1979 to present.

ERA-5 daily precipitation is compared to EOBS, a gridded dataset spatially interpolated from observations over Europe, and to CMORPH, a satellite-based global precipitation product. Simultaneous occurrence of extreme events is assessed with a hit rate. An intensity comparison is conducted with return levels confidence intervals and a Kullback Leibler divergence test, both derived from the EGPD.

Overall, extreme event occurrences between ERA5 and EOBS over Europe appear to agree. The presence of overlap between 95% confidence intervals on return levels highly depends on the season and the probability of occurrence.