Improved fitting of the Bartlett-Lewis Rectangular Pulse Model for hourly rainfall

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Abstract
This paper examines the applicability of the Bartlett-Lewis Rectangular Pulse Model to rainfall taken from a site in Elmdon, Birmingham, UK. The approach used is to assess the performance of the model in terms of characteristics of the precipitation process, incorporating monthly seasonality. Analytical expressions are derived to complement those presented in Rodriguez-Iturbe et al. (1987). As in that paper, the shortcomings of the simple Poisson process are reduced by the use of a Bartlett-Lewis process. Different methods of parameter estimation are examined. The characteristic features of the time distribution of rainfall events, however, can be well approximated only by optimization and this enables an improved identification of the model parameters.