Two-Parameter Gamma Drop Size Distribution Models for Singapore

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.

[1]  Emmanouil N. Anagnostou,et al.  Comparison of Raindrop Size Distribution Estimates From X-Band and S-Band Polarimetric Observations , 2007, IEEE Geoscience and Remote Sensing Letters.

[2]  Y. H. Lee,et al.  Comparative Study of Singapore ’ s Drop Size Distribution for Fixed μ , 2008 .

[3]  Toshiaki Kozu,et al.  Rainfall Parameter Estimation from Dual-Radar Measurements Combining Reflectivity Profile and Path-integrated Attenuation , 1991 .

[4]  V. Chandrasekar,et al.  Examination of the μ–Λ Relation Suggested for Drop Size Distribution Parameters , 2007 .

[5]  Witold F. Krajewski,et al.  Comparison of Drop Size Distribution Measurements by Impact and Optical Disdrometers , 2001 .

[6]  D. Narayana Rao,et al.  On the variability of the shape‐slope parameter relations of the gamma raindrop size distribution model , 2006 .

[7]  Guifu Zhang,et al.  An Evaluation of a Drop Distribution-Based Polarimetric Radar Rainfall Estimator , 2003 .

[8]  Guifu Zhang,et al.  The Shape–Slope Relation in Observed Gamma Raindrop Size Distributions: Statistical Error or Useful Information? , 2003 .

[9]  Guifu Zhang,et al.  Polarimetric Radar Estimators Based on a Constrained Gamma Drop Size Distribution Model , 2004 .

[10]  K. Beard,et al.  A New Model for the Equilibrium Shape of Raindrops , 1987 .

[11]  Guifu Zhang,et al.  Errors in Estimating Raindrop Size Distribution Parameters Employing Disdrometer and Simulated Raindrop Spectra , 2009 .

[12]  Alexander V. Ryzhkov,et al.  Analysis of Video Disdrometer and Polarimetric Radar Data to Characterize Rain Microphysics in Oklahoma , 2008 .

[13]  D. Short,et al.  Evidence from Tropical Raindrop Spectra of the Origin of Rain from Stratiform versus Convective Clouds , 1996 .

[14]  Guifu Zhang,et al.  A method for estimating rain rate and drop size distribution from polarimetric radar measurements , 2001, IEEE Trans. Geosci. Remote. Sens..

[15]  Rafael F. Rincon,et al.  Microwave link dual-wavelength measurements of path-average attenuation for the estimation of drop size distributions and rainfall , 2002, IEEE Trans. Geosci. Remote. Sens..

[16]  Carlton W. Ulbrich,et al.  Rainfall Microphysics and Radar Properties: Analysis Methods for Drop Size Spectra , 1998 .

[17]  Yee Hui Lee,et al.  Truncated Gamma Drop Size Distribution Models for Rain Attenuation in Singapore , 2010, IEEE Transactions on Antennas and Propagation.

[18]  Axel Seifert,et al.  On the shape-slope relation of drop size distributions in convective rain , 2005 .

[19]  V. N. Bringi,et al.  Analysis of aircraft hydrometeor spectra and differential reflectivity (ZDR) radar measurements during the Cooperative Convective Precipitation Experiment , 1984 .

[20]  Carlton W. Ulbrich,et al.  Drop size spectra and integral remote sensing parameters in the transition from convective to stratiform rain , 2006 .

[21]  Paul L. Smith.  Raindrop Size Distributions: Exponential or Gamma—Does the Difference Matter? , 2003 .

[22]  C. Ulbrich.  Natural Variations in the Analytical Form of the Raindrop Size Distribution , 1983 .