A consistent rainfall parameterization based on the exponential raindrop size distribution

There exists an impressive body of experimental evidence confirming the exi stence of power law relationships between various rainfall related variable s. Many of these variables (such as rain rate, radar reflectivity factor an d kinetic energy flux density) have a direct relevance for hydrology and re lated disciplines (hydrometeorology, soil erosion). There is one fundamenta l property of rainfall which ties all these variables together, namely the raindrop size distribution. It is the purpose of this article to explain (1 ) that there exist two fundamentally different forms of the raindrop size d istribution, (2) how various hydrologically relevant rainfall variables are related to both these forms, and (3) how the coefficients of power law rel ationships between such rainfall variables are determined by the parameters of these two forms of the raindrop size distribution. The classical expone ntial raindrop size distribution is used as an example of a family of raind rop size distributions. Three groups of rainfall related variables are cons idered, namely properties of individual raindrops (size, speed, volume, mas s, momentum and kinetic energy), rainfall integral variables (raindrop conc entration, raindrop arrival rate, liquid rainwater content, rain rate, rain fall pressure, rainfall power and radar reflectivity factor) and characteri stic Sizes (median-volume diameter, volume-weighted mean diameter and mean- volume diameter). Six different consistent sets of power law relationships between these rainfall related variables and rain rate are presented, based on different assumptions regarding the rain rate dependence of the paramet ers of the raindrop size distribution. (C) 1999 Elsevier Science B.V. All r ights reserved.