Vol. 46
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2012-11-25
Obtaining Raindrop Size Model Using Method of Moment and Its Applications for South Africa Radio Systems
By
Progress In Electromagnetics Research B, Vol. 46, 119-138, 2013
Abstract
In this paper, the Raindrop Size Distribution (DSD) modeling and analysis are presented. Drop sizes are classified into different rain types, namely: drizzle, widespread, shower and thunderstorm. The gamma and Lognormal distribution models are employed using the method of moments estimator, considering the third, fourth and sixth order moments. The results are compared with the existing raindrop size distribution models such as the three parameter lognormal distribution proposed by Ajayi and his colleagues and Singapore's modified gamma and Lognormal models. This is then followed by the implementation of the proposed raindrop size distribution models on the computation of the specific rain attenuation. Finally, the paper suggests a suitable raindrop size distribution model for the region with its expressions. The proposed models are very useful for the determination of rain attenuation for terrestrial and satellite systems.
Citation
Senzo Jerome Malinga, and Pius Adewale Owolawi, "Obtaining Raindrop Size Model Using Method of Moment and Its Applications for South Africa Radio Systems," Progress In Electromagnetics Research B, Vol. 46, 119-138, 2013.
doi:10.2528/PIERB12070806
References

1. Ajayi, G. O., S. Feng, S. M. Radicella, and B. M. Reddy, "Handbook on Radio Propagation Related to Satellite Communications in Tropical and Subtropical Countries," ICTP, 1996.

2. Crane, R. K., Electromagnetic Wave Propagation through Rain, John Wiley, 1996.

3. Das, S., A. Maitra, and A. K. Shukla, "Rain attenuation modelling in the 10-100 GHz frequency using drop size distributions for different climate zones in tropical India," Progress In Electromagnetics Research B, Vol. 25, 211-224, 2010.
doi:10.2528/PIERB10072707

4. Chen, K.-S., C.-Y. Chu, and Y.-C. Tseng, "A semi-empirical model of rain attenuation at Ka-band in Northern Taiwan," Progress In Electromagnetics Research M, Vol. 16, 213-223, 2011.

5. Mandeep, J. S. and J. E. Allnut, "Rain attenuation prediction at Ku-band in South East Asia countries," Progress In Electromagnetics Research, Vol. 76, 65-74, 2007.
doi:10.2528/PIER07062605

6. Berne, A. and R. Uijlenhoet, "A stochastic model of range profiles of raindrop size distributions: Application to radar attenuation correction," Geophys. Res. Lett., Vol. 32, L10803, 2005, doi:10.1029/2004GL021899.
doi:10.1029/2004GL021899

7. Jameson, A. R. and A. B. Kostinski, "What is a raindrop size distribution?," Bulletin of the American Meteorological Society,, Vol. 82, 1169-1177, 2001.
doi:10.1175/1520-0477(2001)082<1169:WIARSD>2.3.CO;2

8. Owolawi, P. A., "Characteristics of rain at microwave and millimetric bands for terrestrial and satellite links attenuation in South Africa and surrounding islands,", Ph.D. Dissertation, School KwaZulu Natal, Durban, South Africa, Jul. 2010.
doi:10.1175/1520-0477(2001)082<1169:WIARSD>2.3.CO;2

9. Uijlenhoet, R., J. A. Smith, and M. Steiner, "Microphysical structure of extreme precipitation as inferred from ground-based raindrop spectra," Journal of the Atmospheric Sciences, Vol. 60, 1220-1238, 2003.
doi:10.1175/1520-0469(2003)60<1220:TMSOEP>2.0.CO;2

10. Laws , J. O. and D. A. Parsons, "The relation of raindrop-size to intensity," Trans. Amer. Geophys. Union, Vol. 24, 452-460, 1943.
doi:10.1029/TR024i002p00452

11. Marshall, J. S. and W. M. Palmer, "The distribution of raindrops with size," Journal of Meteorology, Vol. 5, 165-166, 1948.
doi:10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2

12. Quimpo , R. G. and A. B. Brohi, "On the frequency distribution of raindrop sizes," Journal of Irrigation and Drainage Engineering, Vol. 112, No. 2, 119-127, May 1986.
doi:10.1061/(ASCE)0733-9437(1986)112:2(119)

13. Owolawi, P. A., "Raindrop size distribution model for the prediction of rain attenuation in Durban," PIERS Online, Vol. 7, No. 5, 516-523, 2011.

14. Maaciel, L. R. and M. S. Assis, "Tropical rainfall drop size distribution," International Journal of Satellite Communications, Vol. 8, 181-186, 1990.
doi:10.1002/sat.4600080310

15. Kumar , L. S., Y. H. Lee, and J. T. Ong, "Truncated gamma drop size distribution models for rain attenuation in Singapore," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 4, Apr. 2010.
doi:10.1109/TAP.2010.2042027

16. Kumar , L. S., Y. H. Lee, and J. T. Ong, "Two-parameter gamma drop size distribution models for singapore," IEEE Transactions on Geoscience and Remote Sensing, Vol. 549, No. 4, Sep. 2011.

17. Jassal, B. S., A. K. Verma, and L. Singh, "Raindrop size distribution and attenuation for Indian climate," Indian Journal of Radio and Space Physics, Vol. 23, No. 3, 193-196, Jun. 1994.

18. Tharek, A. R. and J. Din, "Rainfall drop size distribution measurements in Malaysia," Proc. URSI Comm. F. 1992 Symposium Wave Propagation and Remote Sensing, 1.2.1-1.2.5, Ravenscar, North Yorkshire, UK, Jun. 8-12, 1992.

19. Ajayi, G. O. and R. L. Olsen, "Modelling of tropical raindrop size distribution for microwave and millimeter wave applications," Radio Science, Vol. 20, 193-202, 1985.
doi:10.1029/RS020i002p00193

20. Ajayi, G. O. and A. Adimula, "Variations in raindrop size distribution and specific attenuation in a tropical environment," URSI Comm. F Symposium, 811-814, La Londe-less Maures, France, Sep. 1989.

21. Sevruk, B. and W. R. Hamon, International Comparison of National Precipitation Gauges with a Reference Pit Gauge, WMO Instrument and Observing Methods Rep., No. 17, 111, 1984, [Available from World Meteor. Org., Case Postale 2300, CH-1211, Geneva, Switzerland].

22. Sevruk, B., "Wind induced measurement error for high-intensity rains," Proc. International Workshop on Precipitation Measurement, WMO Tech. Document 328, 199-204, 1989, [Available online at http://www.wmo.ch].

23. Groisman, P. Y. and D. R. Legates, "The accuracy of united states precipitation data," Bull. Amer. Meteor. Soc., Vol. 75, 215-227, 1994.
doi:10.1175/1520-0477(1994)075<0215:TAOUSP>2.0.CO;2

24. Ne·spor, V. and B. Sevruk, "Estimation of wind-induced error of rainfall gauge measurements using a numerical simulation," J. Atmos. Oceanic Technol., Vol. 16, 450-464, 1999.
doi:10.1175/1520-0426(1999)016<0450:EOWIEO>2.0.CO;2

25. Sevruk, B., M. Ondras, and B. Chvila, "The WMO precipitation measurement intercomparisons," Atmos. Res., Vol. 92, 376-380, 2009.
doi:10.1016/j.atmosres.2009.01.016

26. Fiser, O., M. Schoenhuber, and P. Pesice, "First results of DSD measurement by video distrometer in the Czech republic in 1998-1999," Studia Geophysica et Geodetica, Vol. 46, No. 3, 485-505, 2002.
doi:10.1023/A:1019591002211

27. Adimula, I. A. and G. O. Ajayi, "Variation in raindrop size distribution and specific attenuation due to rain in Nigeria," Ann. Telecom., Vol. 51, No. 1-2, 87-93, 1996.

28. 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 Transactions on Antennas and Propagation, Vol. 50, 1420-1424, Oct. 2002.

29. Afullo, T. J. O., "Raindrop size distribution modeling for radio link design along the eastern coast of South Africa," Progress In Electromagnetics Research B, Vol. 34, 345-366, 2011.

30. Mandeep, J. S. and K. Tanaka, "Effect of atmospheric parameters on satellite links," Int. Journal Millimeter Wave, Vol. 28, No. 10, 789-795, 2007.
doi:10.1007/s10762-007-9269-x

31. Kumar, L. S., Y. H. Lee, J. X. Yeo, and J. T. Ong, "Tropical rain classification and estimation of rain from Z-R (reflectivity-rain rate) relationships," Progress In Electromagnetics Research B, Vol. 32, 107-127, 2011.
doi:10.2528/PIERB11040402

32. Gunn, R. and G. D. Kinzer, "The terminal velocity of fall for water droplets in stagnant air," Journal Atmos. Sci., Vol. 6, No. 4, 243-248, 1949.

33. Vivekanandan, J., G. Zhang, and E. Brandes, "Polarimetric radar rain estimators based on constrained gamma drop size distribution model," J. Appl. Meteorology, Vol. 43, No. 2, 217-230, 2004.
doi:10.1175/1520-0450(2004)043<0217:PREBOA>2.0.CO;2

34. Kozu, T. and K. Nakamura, "Rainfall parameter estimation from dual-radar measurements combining reflectivity profile and path-integrated attenuation," J. Atmos. Oceanic Tech., Vol. 8, No. 2, 259-270, 1991.
doi:10.1175/1520-0426(1991)008<0259:RPEFDR>2.0.CO;2

35. Ulbrich, C. W., "Natural variation in the analytical form of the raindrop size distribution," J. Climate Appl. Meteoro., Vol. 22, 1764-1775, 1983.
doi:10.1175/1520-0450(1983)022<1764:NVITAF>2.0.CO;2

36. Timothy, K. I., S. Sharma, M. Devi, and A. K. Barbara, "Tropical raindrop size distribution (RDS): Prediction and modeling its effects on microwave propagation," Proceedings of 9th International Conference on Antennas and Propagation, 244-248, Eindhoven, The Netherlands, Apr. 4-7, 1995.

37. Pan, W., P. Leung, W. Huang, and W. Liu, "On interval estimation of the coefficient of variation for three-parameter Weibull, lognormal and gamma distribution: A simulation-based approach," European Journal of Operational Research, Vol. 164, 367-377, 2005.
doi:10.1016/j.ejor.2003.04.005

38. 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.

39. Ong, J. T., K. I. Timothy, T. Kozu, J. W. F. Goddard, J. Eastment, C. Wilson, and J. Tan, "Studies on tropical rainfall structure with RAL S-band radar, TRMM PR and radiosonde-inter comparison," Proc. --- European Geophysical Society, XXVI General Assembly, France, Mar. 2001.

40. Jiang, H., M. Sano, and M. Sekine, "Weibull raindrop-size distribution and its application to rain attenuation," IEE Proc., Microwave, Antenna Propagation, Vol. 144, No. 3, 197-200, Jun. 1997.
doi:10.1049/ip-map:19971193

41. Yeo, T. S., P. S. Kooi, M. S. Leong, and L. W. Li, "Tropical raindrop size distribution for the prediction of rain attenuation of microwaves in the 10-40 GHz band," IEEE Transactions on Antennas and Propagation, Vol. 49, No. 1, 80-82, Jan. 2001.
doi:10.1109/8.910533

42. International Telecommunication Union "Specific attenuation model for rain for use in prediction methods,", Recommendation ITU-R, P.838-3, Geneva, 2005.

43. Willmott, C. J. and K. Matsuura, "Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance," Climate Research, Vol. 30, 79-82, Dec. 2005.
doi:10.3354/cr030079

44. Olsen, R., D. Rogers, and D. Hodge, "The aRb relation in the calculation of rain attenuation," IEEE Transactions on Antennas and Propagation, Vol. 26, No. 2, 318-329, 1978.
doi:10.1109/TAP.1978.1141845

45. Da Silva Mello, L. and M. S. Pontes, "Unified method for the prediction of rain attenuation in satellite and terrestrial links," Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No. 1, Jun. 2012.