The characteristics of raindrop size distribution and optimal moment estimator

Accurate measurements of raindrop size distributions are important for many meteorological applications, including not only estimation of rainfall, cloud model initialization and verification but also rain microphysics. Therefore, the understanding of the DSDs information is an important issue to reduce the error for radar rainfall estimation.

To obtain the DSD theoretically, the gamma distribution was used for DSDs model and calculation of the N0 (mm-1-mm-3), Ë (mm-1), and ì (shape parameter). The DSDs parameters of gamma distribution were retrieved and various moments of observed DSD were used to estimate DSDs parameters. The appropriate combinations of DSDs moment were used to estimate DSD gamma parameters.

The characteristics of DSDs, best fitted DSD model, and the application of the various gamma functions based on moment scheme were examined. In order to find out the optimal DSD estimator, each moment estimator was analyzed and compared with power law estimator. The fractional standard error (FSE) was used to assess the quantitative performance between the retrieved rainfall rate-reflectivity and observed one. As a result, the estimators of M234, M246, M346, and M456 were similar to observed ones, while there were large errors on M012 moment and MP moment. The middle moment estimators are better than those of low and high moments in this study and M456 which is larger moment estimator gave the lowest FSE on rainfall rate and reflectivity. The results suggest that M456 estimator needs to be further investigated in future studies for the best DSD estimation.