Vol. 36

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2014-06-12

Variations in Non-Linearity in Vertical Distribution of Microwave Radio Refractivity.

By Adekunle Titus Adediji and Samuel Toluwalope Ogunjo
Progress In Electromagnetics Research M, Vol. 36, 177-183, 2014
doi:10.2528/PIERM14041606

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).

Citation


Adekunle Titus Adediji and Samuel Toluwalope Ogunjo, "Variations in Non-Linearity in Vertical Distribution of Microwave Radio Refractivity.," Progress In Electromagnetics Research M, Vol. 36, 177-183, 2014.
doi:10.2528/PIERM14041606
http://www.jpier.org/PIERM/pier.php?paper=14041606

References


    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.

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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.

    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

    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

    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

    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

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

    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

    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

    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.

    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

    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

    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.

    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.