volume | PIER Journals

Abstract

In this paper we present seasonal results of the effective earth radius factor distribution in South Africa using recently (2007-2009) acquired radiosonde data from the South African Weather Service (SAWS) for seven locations in South Africa. Two data modeling methods are used to formulate the solution for the distribution of the effective earth radius factor. The seasonal effective earth radius factor statistics obtained from the radiosonde measurements are then interpolated, gridded and presented in contour maps to cover the rest of the country for the four seasons defined by ITU-R recommendation P.453-12. The Integral of Square Error is used to check the performance of the data modeling techniques while the Root Mean Square Error is used to compare the performance of the different interpolation methods used.

1. Cost 255 Final Report, , Radio wave propagation modelling for Satcom services at Ku-band and above, European Space Agency, SP-1252, March 2002.

2. Ayantunji, B. G., P. N. Okeke, and J. O. Urama, "Diurnal and seasonal variation of surface refractivity over Nigeria," Progress In Electromagnetics Research B, Vol. 30, 201-222, 2011.

3. Adenugba, D. A., "A Vb.Net class library and client application for radio refractivity," International Journal of Computer Applications, Vol. 33, No. 3, November 2011.

4. Asiyo, M. O. and T. J. Afullo, "Statistical estimation of fade depth and outage probability due to multipath propagation in South Africa," Progress In Electromagnetics Research B, Vol. 46, 251-274, 2013.

5. Adediji, A. T. and M. O. Ajewole, "Vertical profile of the radio refractivity gradient in Akure, South-West Nigeria," Progress In Electromagnetics Research C, Vol. 4, 157-168, 2008.

6. Chaudhary, N. K., D. K. Trivedi, and R. Gupta, "The impact of k-factor on wireless link in Indian semi-desert terrain," Int. J. Advanced Networking and Applications, Vol. 2, No. 4, 776-779, 2011.

7. Nel, J. W., S. J. Erasmus, and S. Mare, "The establishment of a radio refractivity database for Southern Africa," IEEE, TH0219-6/88/0000-0144, 1988.

8. Ajayi, G. O., "Physics of the troposphere radio-propagation," International Centre for Theoretical Physics, Internal Report No. IC/89/23.

9. Freeman, R. L., Radio System Design for Telecommunications, 3rd Ed., Wiley-Interscience, John Wiley & Sons Inc., New York, 2007.

10. Adediji, A. T., M. O. Ajewole, S. E. Falodun, and O. R. Oladosu, "Radio refractivity measurement at 150m altitude on TV tower at Akure, South-West Nigeria," Journal of Engineering and Applied Sciences, Vol. 2, No. 8, 1308, 2007.

11. ITU-R, , The radio refractive index: Its formula and refractivity data, ITU-R Recommendation P.453-12, 2012.

12. Al-Ansari, K., A. A. Abdulhadi, and R. Kamel, "Statistical analysis of refractivity in UAE," International Symposium on Rainfall Rate and Radio Wave Propagation, 2007.

13. Palmer, A. J. and D. C. Baker, "Predicting the long-term average of the effective earth radius factor for South Africa using ground based observations," SAIEE Africa Research Journal, Vol. 97, No. 2, 182-185, June 2006.

14. Palmer, A. J., A novel empirical model of the k-factor for radio propagation in Southern Africa for communication planning applications, Ph.D. Thesis, University of Pretoria, South Africa, November 2003.

15. Palmer, A. J. and D. C. Baker, "A novel semi-empirical model of the effective earth radius factor," IEEE Transactions on Broadcasting, Vol. 52, No. 4, 557-565, December 2006.
doi:10.1109/TBC.2006.884737

16. Serdega, D. and G. Ivanovs, "Refraction seasonal variation and that in°uence on to GHz range microwaves availability," Electronics and Electrical Engineering, Vol. 6, No. 78, ISSN 1392-1215, 2007.

17. Parsons, J. D., The Mobile Radio Propagation Channel, John Wiley and Sons, ISBN 0-470-84152-4, 2000.

18. Adediji, A. T. and M. O. Ajewole, "Variation of radio refractivity and effective earth radius factor (k-factor) over Akure, South Western Nigeria," IEEE, 978-1-4244-5118-0/11, 2011.

19. Odedina, P. K. and T. J. Afullo, "On the k-factor distribution and diffraction fading for Southern Africa," SAIEE Africa Research Journal, Vol. 97, No. 2, June 2006.

20. ITU-R, , Propagation data and prediction methods required for the design of terrestrial line-of-sight systems, ITU-R Recommendation P.530-14, 2012.

21. Odedina, P. K. and T. J. Afullo, "Effective earth radius factor characterization for line-of-sight paths in Botswana," IEEE AFRICON Proceedings, 227-232, 2004.

22. Odedina, P. K. and T. J. Afullo, "Effective earth radius factor measurement and modeling for radio link design in Botswana," SAIEE Africa Research Journal, Vol. 99, No. 3, 2008.

23. Fulgence, D., Effective earth radius distribution for Central Africa: Rwanda and north-western Tanzania, M.S. Thesis, National University of Rwanda, August 2012.

24. Silverman, B. W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1986.

25. Sheather, S. J., Density estimation, Vol. 19, No. 4, 588-597, Statistical Science, 2004.

26. Zucchini, W., "Applied Smoothing Techniques, Part 1: Kernel Density Estimation,", October 2003.

27. Froehlich, D. F. and M. Rahman, "A note on the choice of the smoothing parameter in the kernel density estimate," BRAC University Journal, Vol. VI, No. 1, 59-68, 2009.

28. Sain, S. R., Adaptive kernel density estimation, Ph.D. Thesis, Rice University, Houston, Texas, August 1994.

29. Faraway, J. J. and M. Jhun, "Bootstrap choice of bandwidth for density estimation," American Statistical Association Journal, Vol. 85, No. 412, 1990.
doi:10.1080/01621459.1990.10474983

30. Raykar, V. C. and R. Duraiswami, Very fast optimal bandwidth selection for univariate kernel density estimation, Perceptual Interfaces and Reality Laboratory of Maryland University, June 28, 2006.

31. Haithcoat, T., Spatial interpolation, University of Missouri, Columbia, 1987.

32. Bohling, G., "Kriging," Kansas Geological Survey, C&PE 940, October 19, 2005.

33. Johnston, K., J. M. Hoef, K. Krivoruchko, and N. Lucas, "Using ArcGIS geostatistical analyst," GIS by ESRI, USA, 2001.

34. Odedina, P. K. and T. J. Afullo, "Use of spatial interpolation technique for the determination of the geoclimatic factor and fade calculation for South Africa ," Proceedings of IEEE AFRICON Conference, Namibia, September 26-28, 2007.

35. Azpurua, M. and K. Dos Ramos, "A comparison of spatial interpolation methods for estimation of average electromagnetic field magnitude," Progress In Electromagnetics Research M, Vol. 14, 135-145, 2010.
doi:10.2528/PIERM10083103

37. Bello-Pineda, J. and J. L. Hernandez-Stefanoni, "Comparing the performance of two interpolation methods for creating a digital bathymetric model of the Yucatan submerged platform," Pan-American Journal of Applied Aquatic Sciences, Vol. 2, No. 3, 247-254, 2007.

38. Boer, E. P. J., K. M. de Beurs, and A. W. Hartkamp, "Kriging and thin plate splines for mapping climatic variables," International Journal of Applied Earth Observation and Geoinformation, Vol. 3, No. 2, 146-154, 2001.
doi:10.1016/S0303-2434(01)85006-6

39. Janis, M. J. and S. M. Robeson, "Determining the spatial representativeness of air-temperature records using variogramnugget series," Physical Geography, Vol. 25, No. 6, 513-530, 2004.
doi:10.2747/0272-3646.25.6.513

40. LeMay, Jr., N. E., Variogram modeling and estimation, M.S. Thesis in Applied Mathematics, University of Colorado, Denver, 1998.

41. Hammer, O., Paleontological Statistics Version 2.17 Reference Manual, Natural History Museum, University of Oslo, 1999-2002.

Mr. Abraham M. Nyete

Prof. Thomas Joachim Odhiambo Afullo