Evaluation of cluster‐based rectangular pulses point process models for rainfall

This technical note presents a comparison of cluster‐based point rainfall models using the historical hourly rainfall data observed between 1949 and 1976 at Denver, Colorado. The Denver data are used to analyze the performance of three classes of models, namely, the Bartlett‐Lewis model, the geometric Neyman‐Scott model and the Poisson Neyman‐Scott model. The original formulation of the structure of each model, as well as the modified description developed in order to improve the zero depth probability, is considered in this study. Rodriguez‐Iturbe et al.(1987a) concluded that it is unlikely that empirical analysis of rainfall data can be used to choose between the Bartlett‐Lewis model and the Neyman‐Scott model. In a subsequent paper, Rodriguez‐Iturbe et al. (1987b) argued that the choice of the distribution of the number of cells per storm for the Neyman‐Scott model, either geometric or Poisson, has no general bias effect on the stochastic structure. Some investigators (e.g., Burlando and Rosso, 1991), however, reported results contradictory to those of the previous authors. In light of these observations this note investigates the performance of the cluster‐based models. For the Denver data the geometric Neyman‐Scott model yields better results compared to the Poisson Neyman‐Scott model. Moreover, the Bartlett‐Lewis model is shown to be very sensitive to the sets of moment equations used in the parameter estimation. This sensitivity is not observed in the Neyman‐Scott scheme and is believed to be a drawback for applying the Bartlett‐Lewis model in hydrologic simulation studies.