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.

翻译：降雨干持续期和湿持续期（分别简称ds和ws）的发生可通过到达间隔时间（it）进行联合建模。虽然利用到达间隔时间建模具有优势——仅需单次拟合即可描述所有降雨时间特征（包括湿链和干链，即持续期概念的扩展），但关于更新过程时间独立同分布的假设会隐式地将无记忆特性赋予推导出的湿持续期，这在某些情况下可能不成立。本研究在站点尺度上应用了两种不同的降雨时间特征建模方法：i) 直接方法（DM），将离散Lerch分布拟合至it记录，并从it分布推导出ws和ds（以及相应的链）；ii) 间接方法（IM），分别将Lerch分布拟合至ws和ds记录，放宽了更新过程的假设。该研究对欧洲六个具有广泛降雨格局特征站点的应用结果显示：即使当it能够通过Lerch分布良好建模时，几何分布并不总能合理重现ws频率。由于放宽了更新过程时间独立同分布的假设，IM方法获得了更优的表现。当数据集按两个时段划分时，拟合效果进一步改善，表明考虑局部季节性将有利于推断。