Parameterization of rainfall microstructure for radar meteorology and hydrology

A comprehensive general framework for the description and analysis of the microstructure of rainfall is presented. The microstructure of rainfall is parameterized in terms of the raindrop size distribution, which determines both the macroscopic physical properties of rainfall relevant for radar meteorology and hydrology and their relationships.To demonstrate that the definitions of rainfall related variables naturally lead to power law relationships, a rainfall parameterization based on the exponential raindrop size distribution is presented. The importance of the distinction between the properties of raindrops present in a volume of air and those of raindrops arriving at a surface is emphasized.A general formulation for the raindrop size distribution as a scaling law is derived, based on the ubiquitous power law relationships between rainfall related variables. The scaling law formulation is independent of any a priori assumption regarding the functional form of the raindrop size distribution and unifies all previously published parameterizations. It allows a separation of the effects of changes in the shape of the raindrop size distribution from those of changes in the rain rate. The values of the scaling exponents indicate whether it is the raindrop concentration or the characteristic raindrop size which controls the variability of the raindrop size distribution. The gap between the scaling law and traditional parameterizations is bridged by providing explicit expressions for the scaling law for all analytical distributions proposed in the literature.The scaling law formulation is verified experimentally using mean raindrop size distributions for various climatic settings (based on two classical parameterizations) and raw raindrop size distributions from The Netherlands. For the mean distributions the scaling procedure yields excellent results, for the raw distributions a residual amount of scatter about the mean curves remains, indicating that rain rate alone cannot explain all observed variability.As an example of the application of the scaling law, a new method for establishing power law radar reflectivity--rain rate relationships is derived. The method is applied to the mentioned mean and raw distributions. The large inter-event variability of the coefficients indicates that climatological radar reflectivity--rain rate relationships will be of little practical use.The Poisson homogeneity hypothesis, a fundamental assumption in radar meteorology, is tested on an extraordinary stationary time series of raindrop size distributions. The arrival rate fluctuations of the raindrops which contribute most to rain rate and radar reflectivity are found to behave according to Poisson statistics.Finally, perspectives for future research are presented.