Vol. 58
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2005-11-16
Forward Propagation Modeling Above Gaussian Rough Surfaces by the Parabolic Shadowing Effect
By
Progress In Electromagnetics Research, Vol. 58, 243-269, 2006
Abstract
In this paper, a fast method is presented to model the forward propagation above Gaussian rough surfaces and taking into account atmospheric refraction. The method is based on the Discrete Mixed Fourier Transform (DMFT) solved by the Parabolic Wave Equation, in which the Ament boundary condition with shadowing effect is used at grazing angle. In this model, for a bistatic configuration, the surface height PDF of the illuminated points is derived and it is introduced in the boundary condition. Examples demonstrate the capacities of the method to compute propagation factor above rough surfaces following Gaussian statistics and Gaussian height correlation and the proposed method is validated by comparison to a Monte Carlo approach.
Citation
Vincent Fabbro, Christophe Bourlier, and Paul Combes, "Forward Propagation Modeling Above Gaussian Rough Surfaces by the Parabolic Shadowing Effect," Progress In Electromagnetics Research, Vol. 58, 243-269, 2006.
doi:10.2528/PIER05090101
References

1. Patterson, W. L., "A dvanced refractive effects prediction system (AREPS), version 1.0 users manual," Technical document 3028, 92152-5001, 1998.

2. Levy, M. F. and K. H. Craig, "TERPEM propagation package for operational forecasting with EEMS," Proceedings of the 1996 Battelspace Atmospheric Conference, 497-505, 1996.

3. Rino, C. L. and H. D. Ngo, "Forward propagation in a half-space with an irregular boundary," IEEE Trans. Ant. and Prop., Vol. 45, 1340-1347, 1997.
doi:10.1109/8.623122

4. Ungan, B. U. and J. T. Johnson, "Time statistics of propagation over the ocean surface: A numerical study," IEEE Trans. Geo. and Rem. Sens., Vol. 38, 1626-1634, 2000.
doi:10.1109/36.851962

5. Lamar, M. T., R. S. Awadalla, and J. R. Kuttler, "An accelerated boundary integral equation scheme for propagation over the rough ocean surface," Radio Science, Vol. 37, No. 5, 2002.

6. Ament, W. S., "Toward a theory of reflection by a rough surface," IRE Proc., Vol. 41, 142-146, 1953.

7. Freund, D. E., N. E. Woods, H.-C. Ku, and R. S. Awadallah, "The effects of the shadowing on multipath radar propagation modeling," IEEE AP-S International Symposium and URSI National Radio Science Meeting, No. Session 58, 3-5, 2005.

8. Dockery, G. D. and J. R. Kuttler, "An improved-boundary algorithm for Fourier split-step solutions of the parabolic wave equation," IEEE Trans. Ant. and Prop., Vol. 44, No. 12, 1592-1599, 1996.
doi:10.1109/8.546245

9. Fock, V. A., "Solution of the problem of propagation of electromagnetic waves along the earth's surface by method of parabolic equations," J. Phys. USSR, Vol. 10, 13-35, 1946.

10. Hardin, R. H. and F. D. Tappert, "Application of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations," SIAM Rev., Vol. 15, 1973.

11. Kuttler, J. R. and R. Janaswamy, "Improved Fourier transform methods for solving the parabolic wave equation," Radio Science, Vol. 37, No. 2, 2002.
doi:10.1029/2001RS002488

12. Barrios, A. E., "Parabolic equation modeling in horizontally inhomogeneous environments," IEEE Trans. Ant. and Prop., Vol. 40, 791-797, 1992.
doi:10.1109/8.155744

13. Donohue, J. and J. R. Kuttler, "Propagation modeling over terrain using the parabolic wave equation," IEEE Trans. Ant. and Prop., Vol. 48, 260-277, 2000.
doi:10.1109/8.833076

14. Donohue, J. and G. D. Dockery, "Improved characterisation of low grazing angle sea clutter by the parabolic equation method," RTO SET Symposium on Low Grazing Angle Clutter, 1-30, 2000.

15. Leontovitch, A., "On the approximate boundary conditions for an electromagnetic filed on the surface of well-conducting bodies, investigations of propagation of radio waves," Academy of Science, 1948.

16. Bass, F. G. and I. M. Fuks, "Calculation of shadowing for wave scattering from a statistically rough surface," Sov. Radiophys., Vol. 7, 101-12, 1964.

17. Bass, F. G. and I. M. Fuks, Wave Scattering from Statistical ly Rough Surfaces, International Series in Natural Philosophy, C. B. Vesecky and J. F Vesecky (eds.), Pergamon, Oxford, 1979.

18. Kuznetsov, P. I., V. L. Stratonovich, and V. I. Tikhonov, "The duration of random function overshoots," Sov. Phys. Tech. Phys., Vol. 24, 1954.

19. Bourlier, C., G. Berginc, and J. Saillard, "Monostatic and bistatic statistical shadowing functions from one-dimensional stationary randomly rough surface according to the observation length: part I. Single scattering," Waves Random Media, Vol. 12, 145-174, 2002.
doi:10.1088/0959-7174/12/2/301

20. Wagner, R. J., "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am., Vol. 41, 138-147, 1966.
doi:10.1121/1.1910308

21. Smith, B. G., "Lunar surface roughness, shadowing and thermal emission," J. Geophys. Res., Vol. 72, 4059-4067, 1967.

22. Smith, B. G., "Geometrical shadowing of a random rough surface," IEEE Trans. Ant. and Prop., Vol. 5, 668-671, 1967.
doi:10.1109/TAP.1967.1138991

23. Beckman, P., "Shadowing of random rough surfaces," IEEE Trans. Ant. and Prop., Vol. 13, 384-88, 1965.
doi:10.1109/TAP.1965.1138443

24. Bourlier, C. and G. Berginc, "Shadowing function with single reflection from anisotropic Gaussian rough surface. application to Gaussian, Lorentzian and sea correlations," Waves Random Media, Vol. 13, 27-58, 2003.
doi:10.1088/0959-7174/13/1/303

25. Brokelman, R. A. and T. Hagfors, "Note of the effect of shadowing on the backscattering of waves from a random rough surface," IEEE Trans. Ant. and Prop., Vol. 14, 621-627, 1967.
doi:10.1109/TAP.1966.1138758

26. Brown, R. M. and E. V. Vegh., "New derivation for the rough- surface reflection coefficient and for the distribution of sea-wave elevations," IEE Proc., Vol. 131, 114-115, 1984.

27. Hurtaud, Y., "Contribution à l'étude de la propagation des ondes millimétriques au-dessus de la mer," Ph.D. thesis, 1987.

28. Eibert, T. F., "Irregular terrain wave propagation by a fourier split-step wide-angle parabolic wave equation technique for linearly bridged knife-eidges," Radio science, Vol. 37, No. 1, 1-5, 2002.
doi:10.1029/2000RS002560

29. Elfouhaily, T., B. Chapron, K. Katsaros, and D. Vandemark, "A unified directional spectrum for long and short wind-driven waves," J. Geo. Res., Vol. 102, No. C7, 781-796, 1997.

30. Bourlier, C. and G. Berginc, "Microwave analytical backscattering models from randomly rough anisotropic sea surface — Comparison with experimental data in C and Ku bands," Progress In Electromagnetic Research, Vol. 37, 31-78, 2002.