volume | PIER Journals

Abstract

The paper describes the modelling of the average rainfall rate distribution measured at different locations in South Africa. There are three major aspects this paper addresses: to develop a rainfall rate model based on the maximum likelihood method (ML); to develop contour maps based on rainfall rate at 0.01% percentage of exceedence; and re-classification of the ITU-R and Crane rain zones for the Southern Africa region. The work presented is based on five-minute rainfall data converted to one-minute equivalent using a newly proposed hybrid method. The results are mapped and compared with conventional models such as the ITU-R model, Rice-Holmberg, Moupfouma and Crane models. The proposed rainfall rate models are compared and evaluated using root mean square and chi-square (χ²) statistics. Then re-classification of the rain zone using ITU-R and Crane designations is suggested for easy integration with existing radio planning tools. The rainfall rate contour maps at 0.01% percentage of exceedence are then developed for South Africa and its surrounding islands.

1. Collin, R. E., Antennas and Radiowave Propagation, 401-402, McGraw Hill, ISBN 0-07-Y66156-1, 1995.

2. Goldhirsh, J., "Yearly variations of rain-rate statistics at wallops island and their impact on modeled slant path attenuation distributions," IEEE Transaction on Antennas and Propagation, Vol. 31, No. 6, 918-921, November 1983.
doi:10.1109/TAP.1983.1143155 Google Scholar

3. Crane, R. K., Electromagnetic Wave Propagation Through Rain, Wiley Interscience, 1996.

4., ITU-R: Characteristics of Precipitation for Propagation Modeling, Recommendation P.837-4. ITU-R Recommendations, P Series, International Telecommunications Union, 2007.

5. Rice, P. and N. Holmberg, "Cumulative time statistics of surface-point rainfall rate," IEEE Transactions on Communications, Vol. 21, 1772-1774, October 1973. Google Scholar

6. Moupfounma, F. and L. Martin, "Modelling of the rainfall rate cumulative distribution for the design of satellite and terrestrial communication systems ," International Journal of Satellite Communications, Vol. 13, No. 2, 105-115, 1995.
doi:10.1002/sat.4600130203 Google Scholar

7. Ajayi, G. O. and E. B. C. Ofoche, "Some tropical rainfall rate characteristics at ile-ife for microwave and millimeter wave application," Journal of Climate and Applied Meteorology, Vol. 23, 562-567, 1983. Google Scholar

8. Owolawi, P. A., T. J. Afullo and S. B. Malinga, "Effect of rainfall on millimeter wavelength radio in Gough and Marion Islands," PIERS Online, Vol. 5, No. 4, 328-335, 2009.
doi:10.2529/PIERS080906044944 Google Scholar

9. Owolawi, P. A., T. J. Afullo and S. B. Malinga, "Rainfall rate characteristics for the design of terrestrial links in South Africa," Proceedings of Southern Africa Telecommunication Networks and Applications Conference (SATNAC) , 1-76, September 2008. Google Scholar

10. Fashuyi, M. O., P. A. Owolawi and T. J. Afullo, "Rainfall rate modeling for LOS radio systems in South Africa," South African Institute of Electrical Engineering Journal, Vol. 42, No. 1, 74-81, March 2006. Google Scholar

11. Owolawi, P. A. and T. J. Afullo, "Rainfall rate modeling and its worst month statistics for millimetric LOS links in South Africa," Radio Science, Vol. 42, 2007. Google Scholar

12. Owolawi, P. A., T. J. Afullo and S. B. Malinga, "Effect of worst-month distribution on radio link design in South Africa," 11th URSI Commission F Triennial Open Symposium on Radio Wave Propagation and Remote Sensing , 55-61, Rio de Janeiro, October 2007. Google Scholar

13. Mulangu, C. T., P. A. Owolawi and T. J. O. Afullo, "Rainfall rate distribution for LOS radio system in Botswana," Proceedings of 10th Southern Africa Telecommunication, Networks and Application Conference (SATNAC), September 2007. Google Scholar

14. Owolawi, P. A., "Rain rate and rain drop size distribution models for line-of-sight millimetric systems in South Africa," M.Sc. Dissertation, Department of Electrical and Electronics Engineering, University of KwaZulu Natal, Durban, 2006. Google Scholar

15. Seeber, R. J., "N model vir die bepaling van die punt-reenintensitverdeling vir die voorspelling van mikrogolf-reenverswakking in Suidelike Afrika," South African Institute of Electrical Engineering Journal, 67-75, June 1995. Google Scholar

16. 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 of Electrical, Electronics and Computer Engineering, University of KwaZulu Natal, Durban,South Africa, 2010. Google Scholar

17. Emiliani, L. D., J. Agudelo, E. Gutierrez, J. Restrepo and C. Fradique-Mendez, "Development of rain-attenuation and rain-rate maps for satellite system design in the Ku and Ka bands in Colombia," IEEE Antennas and Propagation Magazine, Vol. 46, No. 6, 54-68, December 2004.
doi:10.1109/MAP.2004.1396736 Google Scholar

18. World Meteorological Organization: World Distribution of Thunderstorm Days, No. 21, TP. 21, WMO/OMM, 1953.

19. World Meteorological Organization: World Meteorological Organi-zation Climatological Normal (CLINO) for Climate and Climate Ship Stations for the Period 1931-1960, WMO/OMM, No. 117, TP. 52, Geneva, 1962.

20. Dutton, E. J., H. T. Dougherty, R. F. Martin, and Jr., "Prediction of European rainfall and link performance coefficients at 8 to 30 GHz," NTIS Rep., ACC-ACO-16-17, 1974. Google Scholar

21. Wong, R. K. W., "Weibull distribution, iterative likelihood techniques and hydrometeorlogical data," Journal of Applied Meteorology, Vol. 16, 1360-1364, 1977.
doi:10.1175/1520-0450(1977)016<1360:WDILTA>2.0.CO;2 Google Scholar

22. Wilks, D. S., "Rainfall intensity, the Weibull distribution and estimation of daily surface runoff," Journal of Applied Meteorology, Vol. 28, 52-58, 1977. Google Scholar

23. Evans, M., N. Hastings and B. Peacock, Statistical Distributions,2nd edition, John Wiley and Sons Inc. New York, 1993.

24. Walack, C., Hand-book on Statistical Distributions for Experimen-talists, Internal Report SUF-PFY/96-01, 2007.

25. Eckhard, L., A. S. Werner and A. Markus, "Lognormal distributions across the sciences: Key and clues," BioScience, Vol. 51, No. 5, May 2001. Google Scholar

26. Suhaila, J. and A. A. Jemain, "Fitting daily rainfall amount in Malaysia using the normal transformer distribution," Journal of Applied Science, Vol. 7, No. 14, 2007. Google Scholar

27. Thom, H. C., "A note on the gamma distribution," Monthly Weather Review, Vol. 86, 117-122, 1958.
doi:10.1175/1520-0493(1958)086<0117:ANOTGD>2.0.CO;2 Google Scholar

Dr. Pius Adewale Owolawi