On the representation of hyetograph characteristics by stochastic rainfall models

Two stochastic models of the rainfall process, belonging to different categories, are compared in terms of how well they reproduce certain hyetograph characteristics. The first is the scaling model of storm hyetograph, which belongs to the category of storm-based models. The second is the Bartlett–Lewis rectangular pulse model, the most widespread among the category of point process models. The scaling model is further developed introducing one more parameter to better-fit historical data. The Bartlett–Lewis model is theoretically studied to extract mathematical relationships for the intra-storm structure. The intercomparison is based on the storm hyetographs of a data set from Greece and another one from USA. The different storms are identified in each data set and classified according to their duration. Both models are fitted using the characteristics of storms. The comparison shows that the scaling model of storm hyetograph agrees well with the structure of historical hyetographs whereas the Bartlett–Lewis rectangular pulse model exhibits some discrepancies in either its original version or its random parameter version. However, it is shown that the performance of the Bartlett–Lewis model is significantly improved, and becomes comparable to that of the scaling model, by introducing a power-law dependence of its cell related parameters (duration and rate of arrivals) on the storm duration.