Raindrop Size Distribution Modeling from a Statistical Rain Parameter Relation and Its Application to the TRMM Precipitation Radar Rain Retrieval Algorithm

A generalized method is presented to derive a "two scale'' raindrop size distribution (DSD) model over a spatial or temporal domain in which a statistical rain parameter relation exists. The two-scale model is generally defined as a model in which one DSD parameter is allowed to vary rapidly and the other is constant over a certain space or time domain. The existence of a rain parameter relation such as the radar reflectivity-rainfall rate (Z-R) relation over a spatial or temporal domain is an example of such a two-scale DSD model. A procedure is described that employs a statistical rain parameter relation with an assumption of the gamma DSD model. An example using Z-R relations obtained at Kototabang, West Sumatra, is presented. The result shows that the resulting two-scale DSD model expressed by conventional DSD parameters depends on the assumed value of parameter m while rain parameter relations such as k-Ze relations from those models using different m values are very close to each other, indicating the stability of the model against the variation of m and the validity of this method. The result is applied to the DSD model for the Tropical Rainfall Measuring Mission (TRMM) precipitation radar 2A25 (versions 5 and 6) algorithm. The derivation procedure of the 2A25 DSD model is described. Through the application of this model, it has become possible to make a logically well-organized rain profiling algorithm and reasonable rain attenuation correction and rainfall estimates, as described in an earlier paper by Iguchi et al.