Superposition of the Neyman–Scott Rectangular Pulses Model and the Poisson White Noise Model for the Representation of Tropical Rain Rates

Abstract

A point process model for tropical rain rates is developed through the derivation of the third moment expression for a combined point process model. The model is a superposition of a Neyman?Scott rectangular pulse model and a Poisson white noise process model. The model is scalable in the temporal dimension. The derivation of the third moment for this model allows for the inclusion of the skewness parameter, which is necessary to adequately represent rainfall intensity. Analysis of the model fit to tropical tipping-bucket rain gauge data ranging in temporal scale from five min to one day indicates that it can adequately produce synthesized rainfall having the statistical characteristics of rain rate over the range of scales tested. Of special interest is the model?s capability to accurately preserve the probability of extreme tropical rain rates at different scales. In addition to various hydrological applications, the model also has many potential uses in the field of meteorology, such as the study and development of radar rain rate algorithms for the tropics, which need to parameterize attenuation due to heavy rain.