A study of the raindrop size distribution along the eastern coast of South Africa (Durban) is presented. The Biweight kernel estimator based on distometer measurement is used to determine the best estimate of the measured raindrop size probability distribution function (pdf). The best kernel estimator, which results in the lowest integral square error (ISE), is used to measure the closeness of the estimated lognormal and gamma pdf of raindrop size to the measured raindrop size distribution. It is established that the optimised lognormal pdf slightly outperforms the optimised gamma pdf in terms of the mean ISE and the RMSE values, with mean ISE values of 0.026 for lognormal and 0.04 for gamma distributions, respectively, and corresponding mean RMSE values of 0.073 and 0.081, respectively. The method-of-moments gamma and lognormal distributions are observed to be worse estimators of the measured pdf than the two optimized distributions. The N(D) distributions using the optimised l gnormal and gamma distributions for the region are compared with those for different tropical regions, namely, India, Singapore, Nigeria, Indonesia, and Brazil. While the Indian lognormal N(D) model gives the highest peak for low raindrop sizes for all rain rates, Durban's gamma and lognormal models exhibit the widest raindrop size spread over all rain rates ranging from 1-120 mm/h. Finally, the specific attenuation due to rain using the Durban models are compared against the ITU-R models and actual measurements over a 19.5 GHz LOS link; the results indicate a need for further work involving both distrometer and radio link measurements for rain rates exceeding 30 mm/h in the eastern coast of South Africa.
2. Afullo, , T. J. and P. K. Odedina, "Effective earth radius factor measurement and modeling for radio link design in Botswana," SAIEE Res. J., Vol. 99, No. 3, 77-86, 2008.
3. Ajayi, , G. O. and R. L. Olsen, "Modeling of a tropical raindrop size distribution for microwave and millimeter wave applications," Radio Sci. J., Vol. 20, No. 20, 193-202, 1985.
4. Ajayi, , G. O., S. Feng, S. M. Radicella, and B. M. Reddy, Handbook on Radiopropagation Related to Satellite Communications in Tropical and Subtropical Countries, 2-14, ICTP Press, , Trieste, 1996.
5. Best, A. C., "Empirical formulae for the terminal velocity of waterdrops falling through the atmosphere," Quart. J. Roy Met. Soc., Vol. 76, 302-311, 1950.
6. Cerro, , C., , B. Codina, J. Bech, and J. Lorente, "Modeling raindrop size distribution and Z(R) relations in the western Mediterranean area," Journal of Applied Meteorology, Vol. 36, No. 11, 1470-1479, 1997.
7. Crane, , R. K., "The rain range experiment --- propagation through a simulated rain environment," IEEE Trans. Antennas & Propagation, Vol. 22, No. 2, 321-328, 1974.
8. Distromet System, The Joss-Waldvogel Distrometer Handbook,, Basel, Switzerland, 2000.
9. Fashuyi, , M. O. , T. J. Afullo, and , "Rain attenuation prediction and modeling for line-of-sight Links on terrestrial paths in South Africa ," Radio Sci. J.,, No. RS5006, 2007.
10. Fiser, , O., , M. Schonhuber, and P. Presice, "First results of DSD measurement by videodistrometer in the Czech Republic in 1998--1999," Stud. Geophys. Geod. , Vol. 46, 485-505, 2002.
11., "Geppert: The Lognormal Distribution, Engr 323 Notes,", 2011.
12., "Specific rain attenuation model for rain for use in prediction models," Recommend. 838-3, ITU-R P Series, 2005.
13. Kerr, , D. E., Propagation of Short Radio Waves, MIT Radiation laboratories Series, McGraw-Hill Book Company, 1951.
14. Kumar, , L. S., Y. H. Lee, and J. T. Ong, "Truncated gamma drop size distribution models for rain attenuation in Singapore,", Vol. 58, No. 4, 1325-1335, 2010.
15. Maitra, A., "Rain attenuation modelling from measurements of rain drop size distribution in the Indian region," IEEE Ant. & Prop. Letters, Vol. 3, 180-181, 2004.
16. Marshall, , J. S. , W. M. Palmer, and , "The distribution of raindrops with size," J. Meteor., Vol. 5, 165-166, 1948.
17. Marzuki, M., T. Kozu, T. Shimomai, W. L. Randeu, H. Hashiguchi, and Y. Shibagaki, "Diurnal variation of rain attenuation obtained from measurement of raindrop size distribution in equatorial Indonesia ," IEEE Trans. Ant. & Prop., Vol. 57, No. 9, 1191-1196, 2009.
18. Mulangu, , C. T. and T. J. O. Afullo, "Variability of the propagation coe±cients due to rain for microwave links in Southern Africa," Radio Sci. J., No. RS3006, 2009,.
19. Odedina, M. O. and T. J. Afullo, "Determination of rain attenuation from electromagnetic scattering by spherical raindrops: Theory and experiment," Radio Sci. J., No. RS1003, 2010.
20. Olsen, , R. L., , D. V. Rogers, and D. B. Hodge, "The aRb relation in the calculation of rain attenuation," IEEE Trans. Antennas Propag., Vol. 26, No. 2, 547-556, 1978.
21. Ong, J. T. and Y. Y. Shan, "Raindrop size distribution models for Singapore | comparison with results from different regions," Proc. 10th Intl. Conf. on Ant. & Prop., Vol. 436, 2.281-2.285, 1997.
22. Sayama, , S. , M. Sekine, and , "Influence of raindrop size distribution on the di®erential reflectivity up to submillimeter wavelength of 0.96 mm," Int. J. Infrared & Millimetric Waves, Vol. 23, No. 5, 775-784, 2002.
23. Silverman, , B. W., Density Estimation for Statistics and Data Analysis, Chapman & Hall, ISBN 0-412-24620-1, 1990.
24. Tenorio, , R. S, M. C. da Silva Moraes, and L. C. B. Molion, "Raindrop size distribution over north-eastern coast of Brazil," 11th URSI Open Symposium on Radio Ware Propagation & Remote Sensing , 2007.
25. Timothy, K. I, , J. T. Ong, and E. B. L. Choo, "Raindrop size distribution using method of moments for terrestrial and satellite communication applications in Singapore ," IEEE Trans. Ant. & Prop., Vol. 50, No. 10, 1420-1424, 2002.
26. Ulbrich, , C. W., "Natural variations in the analytical form of the raindrop size distribution," Journ. Climate & Applied Meteorology, Vol. 22, 1764-1775, 1983.
27. Wang, M. A. , J. Din, and , "Comparison of the raindrop size distribution in tropical region," Proceedings of 2004 RF and Microwave Conference, 2004.
28. Owolawi, , P. A., "Rainfall rate probability density evaluation and mapping for the estimation of rain attenuation in South Africa and surrounding islands ," Progress In Electromagnetics Research, Vol. 112, 155-181, 2011.
29. Kumar, , L. S., , Y. H. Lee, J. X. Yeo, and J. T. Ong, "Tropical rain classi¯cation and estimation of rain from Z-R (reflectivity - rain rate) relationships," Progress in Electromagnetics Research B, Vol. 32, 107-127, 2011.