An Investigation of the Slope-Shape Relation for Gamma Raindrop Size Distribution

作者：Chu Yen Hsyang^*; Su Ching Lun

来源：Journal of Applied Meteorology and Climatology, 2008, 47(10): 2531-2544.

DOI：10.1175/2008JAMC1755.1

The gamma drop size distribution (DSD) has been widely used in the meteorological community for years to model observed DSD. It has been found that the relation between the slope (Lambda) and shape (mu) parameters of the gamma DSD can be empirically described by a polynomial of second degree. In this article, on the basis of disdrometer-measured DSDs from seven independent precipitation events associated with different weather systems, an empirical mu-Lambda relation that is slightly different from those reported by other scientists is obtained by best fitting a quadratic polynomial to observed data. In addition to the empirical relation, a mu-Lambda relation is derived based on theoretical relations between gamma DSD moments and Lambda and mu. It is shown that the derived mu-Lambda relation is independent of the order of the moment of the gamma DSD. The key factor dominating the mu-Lambda relation is the ratio of the number density parameter N(D-m) to total number density of the raindrop M-0, where D-m is the mean diameter of the DSD. It is further shown that the skewness and the variance of the DSD determine the magnitude of the ratio N(D-m)/M-0 that governs the slope of the mu-Lambda relation. A comparison between the derived and the empirical mu-Lambda relations shows that their behaviors are very similar, especially for large rainfall rates characterized by smaller Lambda and mu values. Moreover, the ratio N(D-m)/M-0 bears a weak relation to the rainfall rate R. Nevertheless, the square of the ratio M-0/N(D-m) is closely related to the ratio R/M-0 and their relation can also be described by a second-degree polynomial. Considering this property, the authors examine the validity of the various mu-Lambda relations by simulating the relations between R/M-0 and [M-0/N(D-m)](2). A comparison between observed and simulated results shows that the relation generated from the derived mu-Lambda relation bears the best resemblance to the observed one in both magnitude and shape.

• 出版日期2008-10-28
• 单位中央民族大学