Two-Parameter Gamma Drop Size Distribution Models for Singapore

Abstract

Gamma model is fitted using the second, fourth, and sixth moments to model the rain drop size distribution (DSD) of Singapore. As the Joss distrometer measures the number of rain drops between the drop diameters from 0.3 to 5 mm, the truncated moment fitting between these drop diameter ranges is also used for modeling the DSD. Gamma DSD requires three-parameter estimation:N0, the intercept parameter; μ, the shape parameter; and Λ, the slope parameter. The aim of this paper is to find a suitable fixed μ and derive an appropriate μ-Λ relation for the tropical region in order to form a two-parameter gamma model. To find an appropriate μ value, observed DSDs are fitted with different μ values to estimate the rain rates, which are assessed by rain rate observations of the distrometer. Shape-slope relationships are fitted for different categories according to the rain rate and the number of drops. The derived μ-Λ relationships for the Singapore region are compared to the published results from two other regions, and the analysis is presented. Two-parameter gamma models are compared by retrieving the rain rate using the polarimetric radar variables. The effect of truncation on rain rate retrieval is also studied, and the use of the μ-Λ relationship for rain retrieval is recommended for the tropical region. The μ-Λ relation using the truncated moment method for the rain category R ≥ 5 mm/hr and rain counts ≥ 1000 drops retrieves the rain rates well compared to other μ-Λ relations.