Estimation of Raindrop Size Distribution and Rainfall Rate from Polarimetric Radar Measurements at Attenuating Frequency Based on the Self-Consistency Principle

A method for estimating three parameters of a gamma raindrop size distribution (DSD) model and the rainfall rate from polarimetric radar at attenuating frequency was developed. The algorithm was developed based on the self-consistency principle but was expanded to consider the attenuation effect by describing the interrelation between polarimetric measurements along the range profile. The proposed method does not require any assumptions of relation among DSD parameters or simplifications of equations that describe the relation between the axis ratio and diameter of raindrops, which have been used in previous studies. Moreover, the proposed algorithm needs no external reference data such as two-dimensional video disdrometer measurements for attenuation corrections because it retrieves the co-polar and differential specific attenuation from the interrelation among the polarimetric measurements. The performance of this algorithm was evaluated by comparison with optical disdrometers and a weighing precipitation gauge. The evaluation of the algorithm showed that the retrieved three DSD parameters of raindrops, reflectivity, and differential reflectivity from actual C-band polarimetric radar data have fairly good agreement with those obtained by surface measurements. Moreover, rainfall rates retrieved using this algorithm have comparable precision with those estimated from the specific differential phase, and outperform those estimated through the so-called Z-R relation, particularly during heavy rainfall. Furthermore, the effects of raindrop temperature and shape parameter on the retrieval of the rainfall rate were examined. The results show that for radar operating at C-band, a raindrop temperature error of 10 degrees C may be negligible in rainfall rate estimations, whereas a shape parameter error of 2 may increase the error of the rainfall rate estimation by 10 %.