A STOCHASTIC RAINDROP TIME DISTRIBUTION MODEL

A disdrometer simultaneously measuring time of arrival and size of rai ndrops was set up in the Paris, France, area. Data collected over a pe riod 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 fou nd allows nearly nine orders of magnitude of the time intervals betwee n raindrops to be mathematically represented at the same time using on ly six parameters. The analysis presented here does not consider rainf all intensity and the nature of rain (convective, stratiform, etc.) as classification parameters. This approach, which may at first sight se em objectionable, is justified by the quality of the statistical infer ences that can be made from the model. Two such applications are descr ibed-namely, the prediction of the total fallen-water height and the c onversion between various rain gauge integration times, which are ofte n necessary for telecommunications purposes (for which only limited mo dels are currently available). Since this kind of temporal data is rar e, a comparison is also made with published data having the finest pos sible temporal resolution from the point of view of the fractal proper ties of rain, namely, its fractal dimension. A fairly good agreement w as found with these other results and at the same time leads to a deep er insight into the fractal nature of rain. This model provides a very satisfactory statistical representation of rain but does not intend t o provide a physical interpretation of the observed temporal behavior of rain, which remains to be done.