A Stochastic Raindrop Time Distribution Model

Abstract

A disdrometer simultaneously measuring time of arrival and size of raindrops was set up in the Paris, France, area. Data collected over a period of 25 months (May 1992 to May 1994) are presented and analyzed to derive a long-term temporal model governed by a renewal process whose survival law is a Bi-Pareto law of the third kind. The model thus found allows nearly nine orders of magnitude of the time intervals between raindrops to be mathematically represented at the same time using only six parameters. The analysis presented here does not consider rainfall intensity and the nature of rain (convective, stratiform, etc.) as classification parameters. This approach, which may at first sight seem objectionable, is justified by the quality of the statistical inferences that can be made from the model. Two such applications are described?namely, the prediction of the total fallen-water height and the conversion between various rain gauge integration times, which are often necessary for telecommunications purposes (for which only limited models are currently available). Since this kind of temporal data is rare, a comparison is also made with published data having the finest possible temporal resolution from the point of view of the fractal properties of rain, namely, its fractal dimension. A fairly good agreement was found with these other results and at the same time leads to a deeper insight into the fractal nature of rain. This model provides a very satisfactory statistical representation of rain but does not intend to provide a physical interpretation of the observed temporal behavior of rain, which remains to be done.