Estimation of N*0 for the Two-Scale Gamma Raindrop Size Distribution Model and Its Statistical Properties at Several Locations in Asia

Toshiaki Kozu Shimane University, Matsue, Shimane, Japan

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Kazuhiro Masuzawa KOA Corporation, Ina, Nagano, Japan

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Toyoshi Shimomai Shimane University, Matsue, Shimane, Japan

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Nobuhisa Kashiwagi The Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan

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Abstract

An automatic estimation method is developed to detect stepwise changes in the amplitude parameter of the normalized raindrop size distribution (DSD) N*0. To estimate N*0, it is also assumed that the variation of three DSD parameters follows the two-scale gamma DSD model; this is defined as a DSD model in which one DSD parameter is fixed, the second is allowed to vary rapidly, and the third is constant over a certain space or time domain and sometimes exhibits stepwise transitions. For this study, it is assumed that N*0 is the third DSD parameter. To estimate this stepwise-varying parameter automatically, a non-Gaussian state-space model is used for the time series of log10N*0. The smoothed time series of log10N*0 fit well to the stepwise transition of log10N*0 when it was assumed that the state transition probability follows a Cauchy distribution. By analyzing the long-term disdrometer data using this state-space model, statistical properties for log10N*0 are obtained at several Asian locations. It is confirmed that the N*0 thus estimated is useful to improve the rain-rate estimation from the measurement of radar reflectivity factor.

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

Abstract

An automatic estimation method is developed to detect stepwise changes in the amplitude parameter of the normalized raindrop size distribution (DSD) N*0. To estimate N*0, it is also assumed that the variation of three DSD parameters follows the two-scale gamma DSD model; this is defined as a DSD model in which one DSD parameter is fixed, the second is allowed to vary rapidly, and the third is constant over a certain space or time domain and sometimes exhibits stepwise transitions. For this study, it is assumed that N*0 is the third DSD parameter. To estimate this stepwise-varying parameter automatically, a non-Gaussian state-space model is used for the time series of log10N*0. The smoothed time series of log10N*0 fit well to the stepwise transition of log10N*0 when it was assumed that the state transition probability follows a Cauchy distribution. By analyzing the long-term disdrometer data using this state-space model, statistical properties for log10N*0 are obtained at several Asian locations. It is confirmed that the N*0 thus estimated is useful to improve the rain-rate estimation from the measurement of radar reflectivity factor.

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

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