A modeling study of rainfall rate‐reflectivity relationships

Power law models that relate rainfall rate and radar reflectivity factor are the principal topic of this paper. Two interrelated problems associated with these models are examined: (1) estimation of parameters of power law models, and (2) assessment of the accuracy of rainfall rate estimates derived from power law models. A statistical model of raindrop processes is used for analysis of both problems. The model provides explicit representations of power law model parameter estimates and the error of rainfall rate‐reflectivity relationships in terms of simple representations of raindrop processes. These results are used to examine issues related to parameterization of algorithms for radar rainfall estimation including (1) bounds on power law model parameter estimates, (2) climatological variability of power law model parameters, (3) seasonal variability of power law model parameters, and (4) multiplicative bias in radar rainfall estimates. Empirical analyses are carried out using drop size data from a number of sites. Detailed analyses are carried out for a data set from North Carolina.