Formulation and optimization of the probability matching method for radar reflectivity and rain rate in the Darwin region

The focus of this paper is the estimation of rainfall from radar and rain-gauge networks. This study has further developed the probability matching method by introducing formulae by which radar reflectivity and rain rate relationships can be parametrised by assuming they fit known probability distributions. It is shown that rain rate (R) and radar reflectivity (Z) are basically log-normally distributed; hence respective population means and standard deviations provide the required probability distributions. A probability matching technique is developed based on this assumption. In practice the use of truncated log-normal distributions is found to be necessary to give the best fit in the development of Z-R relations. Results presented for the Darwin region indicate reasonable agreement between rainfall values obtained with this approach and those employing traditional power law relationships and empirically based probability matching methods. The effects of threshold values are also evaluated using an error process analysis and an optimisation algorithm to minimise the nonlinear object function of rainfall estimation. The optimised thresholds for the truncated log-normal distributions of radar reflectivity and rainfall in Darwin, Australia, are found to be around 21 dBZ and 1.2 mm h-1 respectively.