Analysis of the dependence of daily rainfall depth on wet spell duration across Europe

The statistical modelling of daily rainfall depth is commonly carried out independently from the rainfall occurrence process (dry/wet alternation). In this study, we investigate the effects of accounting for the dependence between rainfall depth (h) and wet spell duration (ws) using rain gauge data collected on 34 sites across Europe between 1971 and 2016. For each site, a set of conditioned haws sub-datasets was generated, and the two-parameter Polylog distribution was fitted on these sub-datasets. The results of the fittings highlight a good capability of the Polylog distribution to capture the statistical behavior of haws, as well as the presence of statistically significant differences in the various haws fittings obtained in some of the sites. This dependence has been quantified as "Weak" in about 13 sites (38%), and "Strong" in 9 sites (26%). The haws dependence was directly modelled for each site with a logarithmic function, showing how this approach is able to well reproduce the arithmetic and geometric means of the sub-samples (standard estimate errors of 0.62 and 0.42 mm, respectively). An attempt at explaining the spatial variability of the dependence through a penalized regression highlighted some key factors, such as longitude and distance from the shoreline; however, the selected features only partially explained the variability and the connection to climate factors. Overall, this research introduces a simple procedure to directly account for the haws dependence, which can provide a more robust modelling of the rainfall processes, as well as an improved understanding of the rainfall generating processes.