Raindrop size distributions and radar reflectivity–rain rate relationships for radar hydrology

摘要

The conversion of theradar reflectivity factor Z(mm6m-3) to rain rate R(mm h-1 )is a crucial step in the hydrological application of weather radarmeasurements. It has been common practice for over 50 years now to take for thisconversion a simple power law relationship between Z andR. It is the purpose of this paper to explain that the fundamental reason forthe existence of such power law relationships is the fact that Zand R are related to each other via the raindropsize distribution. To this end, the concept of the raindrop sizedistribution is first explained. Then, it is demonstratedthat there exist two fundamentally different forms of the raindrop sizedistribution, one corresponding to raindrops present in avolume of air and another corresponding to those arriving at a surface. It isexplained how Z and R are defined in terms of both theseforms. Using the classical exponential raindrop size distribution as an example,it is demonstrated (1) that the definitions of Z and Rnaturally lead to power law Z–R relationships, and (2)how the coefficients of such relationships are related to the parameters of theraindrop size distribution. Numerous empirical Z–R relationshipsare analysed to demonstrate that there exist systematic differences in thecoefficients of these relationships and the correspondingparameters of the (exponential) raindrop size distribution between differenttypes of rainfall. Finally, six consistent Z–R relationshipsare derived, based upon different assumptions regarding the rain rate dependenceof the parameters of the (exponential) raindrop sizedistribution. An appendix shows that these relationships are in fact specialcases of a general Z–R relationship that followsfrom a recently proposed scaling framework for describing raindrop sizedistributions and their properties. style="line-height: 20px;">Keywords: radar hydrology, raindrop size distribution, radar reflectivity–rain rate relationship