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

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  • 1 Shimane University, Matsue, Shimane, Japan
  • | 2 National Institute of Information and Communications Technology, Koganei, Tokyo, Japan
  • | 3 Shimane University, Matsue, Shimane, Japan
  • | 4 The Institute of Statistical Mathematics, Minato-ku, Tokyo, Japan
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Abstract

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 μ while rain parameter relations such as k–Ze relations from those models using different μ values are very close to each other, indicating the stability of the model against the variation of μ 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.

Corresponding author address: Toshiaki Kozu, 1060 Nishikawatsu, Matsue, Shimane 690-8504, Japan. Email: kozu@ecs.shimane-u.ac.jp

Abstract

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 μ while rain parameter relations such as k–Ze relations from those models using different μ values are very close to each other, indicating the stability of the model against the variation of μ 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.

Corresponding author address: Toshiaki Kozu, 1060 Nishikawatsu, Matsue, Shimane 690-8504, Japan. Email: kozu@ecs.shimane-u.ac.jp

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