2010-09-07
Shape Slope Parameter Distribution Modelling of Electromagnetic Scattering by Rain Drops
By
Progress In Electromagnetics Research B, Vol. 25, 191-209, 2010
Abstract
Gamma model parameters using 2nd, 3rd and 4th moments are calculated from the drop size data of Singapore. The gamma model is simplified into two parameter model by finding a relation between the shape and slope parameters, μ and Λ. Due to the poor correlation found between μ and Λ, the drop size data is filtered based on their rain rates before a good correlation between the two parameters can be found. The μ-Λ relations are then fitted for the different ranges of rain rate filtering. Scatter plots of μ and Λ are plotted with constant median volume diameter (D0) lines. The μ-Λ relations for the different rain types for the tropical island of Singapore are proposed and compared with the μ-Λ relations from three other countries of different climatic zones. T-Matrix calculations are performed to find the polarimetric variables at S-band by using the gamma DSD calculated from the Singapore's drop size data. The calculated differential reflectivity and horizontal reflectivity are used along with the best μ-Λ relations to find the gamma model parameters. The retrieved rain rate using polarimetric variables is compared with the distrometer's measured rain rate. Results show a good agreement between the retrieved rain rate and the measured rain rate. Therefore, the proposed shape slope relationship is found to be suitable for rain rate retrieval.
Citation
Lakshmi Sutha Kumar, Yee Hui Lee, and Jin Teong Ong, "Shape Slope Parameter Distribution Modelling of Electromagnetic Scattering by Rain Drops," Progress In Electromagnetics Research B, Vol. 25, 191-209, 2010.
doi:10.2528/PIERB10072101
References

1. Mandeep, J. S., "Equatorial rainfall measurement on Ku-band satellite communication downlink," Progress In Electromagnetics Research, Vol. 76, 195-200, 2007.
doi:10.2528/PIER07070901        Google Scholar

2. Zhang, G., J. Vivekanandan, and E. Brandes, "A method for estimating rain rate and drop size distribution from polarimetric Radar measurements," IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 4, 830-840, Apr. 2001.
doi:10.1109/36.917906        Google Scholar

3. Ulbrich, C. W., "Natural variation in the analytical form of the raindrop size distribution," J. Climate Appl. Meteor., Vol. 22, No. 10, 1764-1775, 1983.
doi:10.1175/1520-0450(1983)022<1764:NVITAF>2.0.CO;2        Google Scholar

4. Gurvich, A. S. and V. Kan, "Structure of air density irregularities in the stratosphere from spacecraft observations of stellar scintillation: 1. Three-dimensional spectrum model and recovery of its parameters," Atmospheric and Oceanic Physics, Vol. 39, No. 3, 300-310, 2003.        Google Scholar

5. Brandes, E. A., G. Zhang, and J. Vivekanandan, "An evaluation of a drop distribution based polarimetric radar rainfall estimator," Journal of Applied Meteorology, Vol. 42, No. 5, 652-660, 2003.
doi:10.1175/1520-0450(2003)042<0652:AEOADD>2.0.CO;2        Google Scholar

6. Zhang, G., J. Vivekanandan, E. Brandes, R. Menegini, and T. Kozu, "The shape-slope relation in observed gamma raindrop size distributions: Statistical error or useful information?," Journal of Atmospheric and Oceanic Technology, Vol. 20, No. 8, 1106-1119, 2003.
doi:10.1175/1520-0426(2003)020<1106:TSRIOG>2.0.CO;2        Google Scholar

7. Seifert, A. K., "On the shape-slope relation of drop size distributions in convective rain," Journal of Applied Meteorology, Vol. 44, No. 7, 1146-1151, 2005.
doi:10.1175/JAM2254.1        Google Scholar

8. Moisseev, D. N. and V. Chandrasekar, "Examination of μ-Λ relation suggested for drop size distribution parameters," Journal of Atmospheric and Oceanic Technology, Vol. 24, No. 5, 847-855, 2007.
doi:10.1175/JTECH2010.1        Google Scholar

9. Anagnostou, M. N., E. N. Anagnostou, J. Vivekanandan, and F. L. Ogden, "Comparison of raindrop size distribution estimates from X-band and S-band polarimetric observations," IEEE Geosci. Remote Sens. Lett., Vol. 4, No. 4, 601-605, Oct. 2007.
doi:10.1109/LGRS.2007.903061        Google Scholar

10. Cao, Q., G. Zhang, E. Brandes, T. Schuur, A. Ryzhkov, and K. Ikeda, "Analysis of video disdrometer and polarimetric radar data to characterize rain microphysics in Oklahoma," Journal of Applied Meteorology, Vol. 47, No. 8, 2238-2255, 2008.
doi:10.1175/2008JAMC1732.1        Google Scholar

11. Cao, Q. and G. Zhang, "Errors in estimating raindrop size distribution parameters employing disdrometer and simulated raindrop spectra," Journal of Applied Meteorology and Climatology, Vol. 48, No. 2, 406-425, 2009.
doi:10.1175/2008JAMC2026.1        Google Scholar

12. Rao, T. N., N. V. P. Kirankumar, B. Radhakrishna, and D. N. Rao, "On the variability of the shape-slope parameter relations of the gamma raindrop size distribution model," Geophysical Research Letters, Vol. 33, L22809, 2006, doi:10.1029/2006GL028440.        Google Scholar

13. Brawn, D. and G. Upton, "On the measurement of atmospheric gamma drop-size distributions," Atmos. Sci. Let., Vol. 9, No. 4, 245-247, 2008.
doi:10.1002/asl.198        Google Scholar

14. Munchak, S. J. and A. Tokay, "Retrieval of raindrop size distribution from simulated dual-frequency radar measurements," Journal of Applied Meteorology and Climatology, Vol. 47, No. 1, 223-239, 2008.
doi:10.1175/2007JAMC1524.1        Google Scholar

15. Atlas, D. and C. W. Ulbrich, "Drop size spectra and integral remote sensing parameters in the transition from convective to stratiform rain," Geophysical Research Letters, Vol. 33, L16803, 2006, doi:10.1029/ 2006GL026824.        Google Scholar

16. Tokay, A., D. A. Short, C. R. Williams, W. L. Ecklund, and K. S. Gage, "Tropical rainfall associated with convective and stratiform clouds: intercomparison of disdrometer and profiler measurements," Journal of Applied Meteorology, Vol. 38, No. 3, 302-320, 1999.
doi:10.1175/1520-0450(1999)038<0302:TRAWCA>2.0.CO;2        Google Scholar

17. Caracciolo, C., F. Porcu, and F. Prodi, "Precipitation classification at mid-latitudes in terms of drop size distribution parameters," Advances in Geosciences, Vol. 16, 11-17, 2008.
doi:10.5194/adgeo-16-11-2008        Google Scholar

18. Gunn, R. and K. D. Kinzer, "The terminal velocity of fall for water droplets in stagnant air," J. Metero., Vol. 6, No. 4, 243-248, 1949.
doi:10.1175/1520-0469(1949)006<0243:TTVOFF>2.0.CO;2        Google Scholar

19. Smith, P. L., "Raindrop size distributions: Exponential or gamma --- Does the difference matter?," Journal of Applied Meteorology, Vol. 42, No. 7, 1031-1034, 2003.
doi:10.1175/1520-0450(2003)042<1031:RSDEOG>2.0.CO;2        Google Scholar

20. Ulbrich, C. W. and D. Atlas, "Rain microphysics and radar properties: Analysis methods for drop size spectra," Journal of Applied Meteorology, Vol. 37, No. 9, 912-923, 1998.
doi:10.1175/1520-0450(1998)037<0912:RMARPA>2.0.CO;2        Google Scholar

21. Tokay, A., A. Kruger, and W. F. Krajewski, "Comparison of drop size distribution measurements by impact and optical disdrometers," Journal of Applied Meteorology, Vol. 40, No. 11, 2083-2097, 2001.
doi:10.1175/1520-0450(2001)040<2083:CODSDM>2.0.CO;2        Google Scholar

22. Thurai, M., G. J. Huang, V. N. Bringi, W. L. Randeu, and M. Schonhuber, "Drop shapes, model comparisons, and calculations of polarimetric radar parameters in rain," Journal of Atmospheric and Oceanic Technology, Vol. 24, No. 6, 1019-1032, Jun. 2007.
doi:10.1175/JTECH2051.1        Google Scholar

23. Beard, K. V. and C. Chuang, "A new model for the equilibrium shape of raindrops," J. Atmos. Sci., Vol. 44, No. 11, 1509-1524, 1987.
doi:10.1175/1520-0469(1987)044<1509:ANMFTE>2.0.CO;2        Google Scholar