利用中壢特高頻同向散射雷達觀測的降水回波資訊，結合理論推導和長期地面雨滴譜儀資料，研究大氣垂直速度對於反演出的伽瑪雨滴粒徑分布中之斜率參數Λ和形狀參數μ之間的影響。在理論推導的過程中經由漸進式的導入和誤差修正，將可直接由雷達觀測的降水終端速度和都卜勒頻譜寬得到μ和Λ值，結果顯示隨者大氣垂直上升速度的增加，反演出的μ和Λ值也有跟著變大的趨勢。此外大氣垂直速度對於降水回波中的終端速度和雨滴粒徑分布寬度也具有很強的關聯性，隨者大氣垂直上升速度的增加，降水終端速度有變大的趨勢而雨滴粒徑分布寬度則有變小的趨勢。而上述特性成因有可能為強烈的上升氣流在某一雷達體積內將小粒徑的雨滴撐住和帶離而造成原始的雨滴粒徑分布改變，導致雨滴粒徑分布有截斷的情況出現。利用地面雨滴譜儀資料經由特意的截斷雨滴粒徑分布的數值計算結果與雷達反演出的結果相比有良好的一致性，此一物理特性也正好說明了由雷達資料所反演出空中的結果與由雨滴譜儀得到地面的結果彼此之間，其μ和Λ散佈的差異性。

伽瑪雨滴粒徑分布中之斜率參數Λ和形狀參數μ之間的關係藉由長期地面雨滴譜儀觀測的資料也已完成分析與研究。其中發現降水終端速度與斜率參數Λ或形狀參數μ之間存在一指數型態的經驗關係，而根據此經驗關係式，進一步可得到μ和Λ的數學解析關係式，在降雨率大於5的情況下，μ和Λ的經驗式與解析式之間有良好的一致性。此外發現ln(No)、μ和Λ的機率密度函數可分別用對數常態分布、伽瑪分布與對數常態分布描述之。而根據其統計特性，伽瑪雨滴粒徑分布將可被模擬出來並獲得相對應的μ和Λ間之關係式，利用其相關物理限制條件小心地濾除資料後，可發現利用此一方式獲得的μ和Λ的關係式與地面雨滴譜得到的μ和Λ的經驗關係式相當地吻合，此一結果可說明伽瑪雨滴粒徑分布參數的統計特性在決定μ和Λ的經驗關係中扮演了相當關鍵的角色。此外從豐富的地面雨滴譜儀數據來看，μ-Λ經驗關係式的特徵確實代表了雨滴下落過程中碰撞破碎與聚合之間的平衡。

With a theoretical derivation and long-term ground-based disdrometer measurements, we investigate vertical wind effect on the relation between slope (Λ) and shape (μ) parameters of the Gamma rain drop size distribution (DSD) estimated from the precipitation echoes of the Chung-Li VHF coherent scatter radar. We derive approximate equations to estimate μ and Λ from radar-measured precipitation terminal velocity and Doppler spectral width. The result shows that there is a tendency for the estimated μ and Λ values to increase with the increase of the upward wind velocity. In addition, the terminal velocity and the spread of the DSD estimated from the precipitation echoes bear a strong relation to the vertical air velocity. With increasing upward vertical air velocity, the terminal velocity tends to be large and the spread of the DSD has a tendency to be small. The dependence of the estimated μ and Λ values on the vertical wind velocity is very likely caused by the updraft that can support and carry away the smaller rain drops in the original drop size distribution in the radar volume, leading to a truncated DSD that is characterized by specific μ and Λ values. Numerical calculations of the intentionally truncated disdrometer-measured DSDs are in good agreement with the radar observations. These results can account for the difference in the patterns of μ-Λ scatter distributions between radar estimation in the air and disdrometer measurement on the ground.

On the basis of disdrometer-measured rain drop size distribution (DSD) for the period from 2000 to 2008, the relation between shape (μ) and slope (Λ) parameters of the Gamma DSD are analyzed and investigated. We find that the empirical relation between the shape (or slope) parameter and the precipitation terminal velocity (VT) can be well described by an exponential function. With the help of the empirical μ-VT or Λ-VT relation, we derive an analytical μ–Λ relation and find that it almost perfectly matches the empirical 2nd order polynomial of the disdrometer-measured DSDs with rainfall rates greater than 5 mm hr-1. It is found that the probability density functions of ln(No), μ and Λ can be described by lognormal, Gamma and lognormal functions, respectively. With these statistical properties, the Gamma DSD is simulated and the empirical 2nd order polynomial of the corresponding μ–Λ relation can thus be obtained. After carefully sifting realistic data from the randomly generated DSD data based on physical constraints, the μ–Λ relation of the simulated Gamma DSDs is in good agreement with that of the disdrometer measurement. These results suggest that the statistical property of the Gamma DSD parameters plays crucial roles in determining the empirical μ–Λ relation. In addition, judging from the rich ground-based DSD data, the characteristics of the empirical relationship of μ–Λ relation represent the balance between the breakup and coalescence of raindrops and the aggregation process during their falling process.

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