volume | PIER Journals

Abstract

Radio refractivity values obtained for different heights (Ground surface, 50 m, 100 m and 150 m) over a tropical station, Akure, South-Western Nigeria using in-situ data over a period of five years has been investigated for chaos. Several chaos quantifiers such as entropy, Lyapunov exponent, recurrence plot were used. Determinism was detected in the time series studied at all the levels. Results obtained from the computation of radio refractivity show that the value of radio refractivity decreases with increasing altitude while chaotic quantifiers obtained at ground level and height 100m are found to be more chaotic than the other two levels (50 m and 150 m).

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

2. Bean, B. R. and E. J. Dutton, Radio Meteorology, Dover Publication Co., New York, 1968.

3. Campanharo, A. S. L. O., F. M. Ramos, E. E. N. Macau, and R. R. Rosa, M. J. A. Bolzan, L. D. A. Sa, "Searching chaos and coherent structures in the atmospheric turbulence above the Amazon forest," Phil. Trans. R. Soc. A, Vol. 366, 579-589, 2008.
doi:10.1098/rsta.2007.2118 Google Scholar

4. Cover, T. M. and J. A. Thomas, Elements of Information Theory, John Wiley and Sons, Inc., New York, 1991.

5. Eckmann, J. P., S. O. Kamphorst, and D. Ruelle, "Recurrence Plots of dynamical systems," Europhysics Letters, Vol. 5, 973-977, 1987.
doi:10.1209/0295-5075/4/9/004 Google Scholar

6. Falodun, S. E. and M. O. Ajewole, "Radio refractive index in the lowest 100-m layer of the troposphere in Akure, South Western Nigeria," Journal of Atmospheric and Solar-Terrestrial Physics, Vol. 68, No. 2, 236-243, 2006.
doi:10.1016/j.jastp.2005.10.002 Google Scholar

7. Fraser, A. M. and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Physical Review A, Vol. 33, No. 2, 1134-1140, 1986.
doi:10.1103/PhysRevA.33.1134 Google Scholar

8. Gallego, M. C., J. A. Garcia, and M. L. Cancillo, "Characterization of atmospheric turbulence by dynamical systems techniques," Bound. Lay. Meteorol., Vol. 100, 375-392, 2001.
doi:10.1023/A:1019236532730 Google Scholar

9. Hegger, R., H. Kantz, and T. Schreiber, "Practical implementation of nonlinear time series methods: The TISEAN package," Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 9, No. 2, 413-435, 1999.
doi:10.1063/1.166424 Google Scholar

10. Henderson, H. W. and R. Wells, "Obtaining attractor dimensions from meteorological time series," Adv. Geophys., Vol. 30, 205-327, 1988.
doi:10.1016/S0065-2687(08)60422-7 Google Scholar

11. Kaplan, J. L. and J. A. Yorke, "Chaotic behavior of multidimensional difference equations," Lect. Notes Math., Vol. 730, 204-227, 1979.
doi:10.1007/BFb0064319 Google Scholar

12. Kennel, M. B., R. Brown, and H. D. I. Abarbanel, "Determining embedding dimension for phase space reconstruction using a geometrical construction," Physical Review A, Vol. 45, 3403-3411, 1992.
doi:10.1103/PhysRevA.45.3403 Google Scholar

13. Kodba, S., M. Perc, and M. Marhl, "Detecting chaos from a time series," Eur. J. Phys., Vol. 26, 205-215, 2005.
doi:10.1088/0143-0807/26/1/021 Google Scholar

14. Lorenz, E. N., "Deterministic nonperiodic flow," J. Atmos. Sci., Vol. 20, 130-141, 1963.
doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 Google Scholar

15. Ogunjo, S. T., J. S. Ojo, A. T. Adediji, K. D. Adedayo, and J. B. Dada, "Chaos in radio refractivity over Akure, South-Western Nigeria," Book of Proceedings of the 5th National Annual Conference of the Nigerian Union of Radio Science (NURS), 59-63, 2013. Google Scholar

16. Rosenstein, M. T., J. J. Collins, and C. J. De Luca, "A practical method for calculating largest Lyapunov exponents from small data sets," Physica D, Vol. 65, 117-134, 1993.
doi:10.1016/0167-2789(93)90009-P Google Scholar

17. Wolf, A. S., J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov exponents from a short time series," Physica D, Vol. 16, 285-317, 1985.
doi:10.1016/0167-2789(85)90011-9 Google Scholar

18. Sano, M. and Y. Sawada, "Measurement of the Lyapunov spectrum from a chaotic time series," Phys. Rev. Lett., Vol. 55, 1082, 1985.
doi:10.1103/PhysRevLett.55.1082 Google Scholar

19. Siek, M. and D. P. Solomatine, "Nonlinear chaotic model for predicting storm surges," Nonlin. Processes Geophys., Vol. 17, 405-420, 2010.
doi:10.5194/npg-17-405-2010 Google Scholar

20. Strogatz, S. H., "Nonlinear Dynamics and Chaos," Addison-Wesley, Reading, 1994. Google Scholar

21. Tsonis, A. A. and J. B. Elsner, "Chaos, strange attractors and weather," Bull. Amer. Meteor. Soc., Vol. 70, 14-23, 1989.
doi:10.1175/1520-0477(1989)070<0014:CSAAW>2.0.CO;2 Google Scholar

22. Waelbroeck, H., "Deterministic chaos in tropical atmospheric dynamics," J. Atmos. Sci., Vol. 52, No. 13, 2404-2415, 1995.
doi:10.1175/1520-0469(1995)052<2404:DCITAD>2.0.CO;2 Google Scholar

23. Li, X., F. Hu, and G. Liu, "Characteristics of chaotic attractors in atmospheric boundary layer turbulence," Bound. Lay. Meteorol., Vol. 99, 335-345, 2001. Google Scholar

24. Zbilut, J. P., C. L. Webber, and Jr., "Embeddings and delays as derived from quantification of recurrence plots," Physics Letters A, Vol. 171, 199-203, 1992.
doi:10.1016/0375-9601(92)90426-M Google Scholar

25. Adediji, A. T., M. O. Ajewole, and S. E. Falodun, "Distribution of radio refractivity gradient and effective earth radius factor (k-factor) over Akure, South Western Nigeria," Journal of Atmospheric and Solar-Terrestrial Physics, Vol. 73, 2300-2304, 2011.
doi:10.1016/j.jastp.2011.06.017 Google Scholar

26. Adediji, A. T., M. O. Ajewole, S. E. Falodun, and O. R. Oladosu, "Radio refractivity Measurement at 150m altitude on TV tower in Akure, South West Nigeria," Journal of Engineering and Applied Sciences, Vol. 2, 1308-1313, 2007. Google Scholar

27. Segal, B., Measurement of tropospheric refractive index relevant to the study of anomalous microwave propagation --- Review and recommendations, CRC Report No. 1387, 1985.

28. ITU-R, , The refractive index: Its formula and refractivity data, 453-10, 2012.

Dr. Adekunle Titus Adediji

Dr. Samuel Toluwalope Ogunjo