Applying different methods to model dry and wet spells at daily scale in a large range of rainfall regimes across Europe

The modeling of the occurrence of a rainfall dry spell and wet spell (ds and ws, respectively) can be jointly conveyed using interarrival times (its). While the modeling has the advantage of requiring a single fitting for the description of all rainfall time characteristics (including wet and dry chains, an extension of the concept of spells), the assumption of the independence and identical distribution of the renewal times it implicitly imposes a memoryless property on the derived ws, which may not be true in some cases. In this study, two different methods for the modeling of rainfall time characteristics at the station scale have been applied: (i) a direct method (DM) that fits the discrete Lerch distribution to it records and that then derives ws and ds (as well as the corresponding chains) from the it distribution and (ii) an indirect method (IM) that fits the Lerch distribution to the ws and ds records separately, relaxing the assumptions of the renewal process. The results of this application over six stations in Europe, characterized by a wide range of rainfall regimes, highlight how the geometric distribution does not always reasonably reproduce the ws frequencies, even when its are modeled well by the Lerch distribution. Improved performances are obtained with the IM thanks to the relaxation of the assumption of the independence and identical distribution of the renewal times. A further improvement of the fittings is obtained when the datasets are separated into two periods, suggesting that the inferences may benefit from accounting for the local seasonality.