使用 Gamma 分布函數之總體水物法的水物終端速度參數化

Abstract

終端速度是雲物理學中的一個重要物理參數，對水物碰撞合併、重力沉降與凝結或蒸發的通風效應估算有密切關聯。本研究的目的旨在改進使用 gamma 粒徑分布函數的多矩量總體水物法模式中的水物終端速度參數式。針對雨滴部分，本研究基於 Böhm (1992) 的理論值進行參數化，並與 Gunn 與 Kinzer (1949) 比對以驗證參數式之可靠性；另有使用包含本研究參數式的數個參數法進行一維簡單重力沉降模式做數值動力測試。新的參數法相較於目前 WRF 模式中常見使用的終端速度參數式與前人研究成果之參數式更加準確。冰相水物的部分，本研究基於 Böhm (1989, 1992) 的理論值，除了冰相粒子大小與密度外，使用橢圓體近似得額外考慮冰晶形狀的影響。由於實驗研究資料仍不夠完備，冰晶參數法較難與目前實驗相互比對；但本研究將 Böhm (1989) 與目前較新亦較完整，由 Mitchell 與 Heymsfield (2005) 提出的架構進行比較。

Terminal velocity is a key parameter in cloud microphysical processes, including collision coalescence/accretion/aggregation, gravitational sedimentation, ventilation effect of hydrometeors’ condensation/vaporization, etc. The goal of this study is to improve the terminal velocity parameterization for multi-moment hydrometeor microphysical schemes using gamma function as particle size distribution (PSD), which is the most common form of PSD in current bulk microphysical schemes. For raindrops, the semi-theoretical calculation of fall speed suggested by Böhm (1992) was used as the base of the parameterization. The results were compared with the experimental result of Gunn and Kinzer (1949) to check the liability of the parameterization. The new parameterization showed better accuracy compared with earlier formulas, including those used in the WRF model. For ice particles, the new parameterization can well approximate the fall speeds from the calculation framework of Böhm (1989, 1992) which considered not only the size and density dependence but also the shape of ice particles using spheroidal approximation. Verification of ice hydrometeors’ fall speed is difficult because of the lack of comprehensive measurement data. Nevertheless, a comparison was made against the currently most comprehensive parameterization of Mitchell and Heymsfield (2005) that is based on a somewhat different analytical framework. A simple 1-D sedimentation dynamics test for raindrop terminal velocity is conducted to examine the behavior and usability of our parameterization formula.