Comparative Study of Singapore’s Drop Size Distribution for Fixed µ

Modified gamma model with moment estimators is used to model the rain Drop Size Distribution (DSD) of Singapore (1°20’N, 103°41’E). Gamma model parameters N0, µ and Λ are determined through measured data for ten different averaged rain rates. The estimates from the method of moments are obtained by equating a sufficient number of measured moments to the corresponding theoretical moments. The estimated parameters show that the gamma model parameter µ varies very slowly compared to the other two parameters. This slow varying parameter varies between 3.03 and 9.30 for rain rates from 1.50mm/hr to 147.70mm/hr for the tropical region of Singapore. In this paper, an attempt is made to simplify the modified gamma model with moment estimator by keeping this slow varying parameter µ as a constant. This study is performed using various constant µ values of 3, 4.58 and 5 to model rain drop size distribution along with the calculated µ values based on the measured DSD for all the considered rain rates. Fixed µ models deviate more from measured DSD for the lower three rain rates, except µ=4.58 which models well only at 4.99mm/hr. Root mean square errors (RMSE) are calculated to compare modeled DSD with the measured data. RMSE calculations along with rain drop size distributions show that modified gamma model can be used to model Singapore’s DSD with fixed µ=4.58 and µ=5 for all the rain rates from 99.55mm/hr to 147.70mm/hr and µ=3 for all the rain rates from 23.29mm/hr to 76.15mm/hr. Results show that there is no fixed µ value that can be used for the entire range of rainfall rate