  The modelling of the occurrence of rainfall dry and wet spells (ds and ws,
respectively) can be jointly conveyed using the inter-arrival times (it). While
the modelling of it 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 on 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 modelling of rainfall time characteristics at
station scale have been applied: i) a direct method (DM) that fits the discrete
Lerch distribution to it records, and 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 it are modelled by the Lerch distribution well.
Improved performances are obtained with the IM, thanks to the relaxation of the
assumption on the independence and identical distribution of the renewal times.
A further improvement on the fittings is obtained when the datasets are
separated into two periods, suggesting that the inferences may benefit for
accounting for the local seasonality.
