2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 48 Number 2, February 2000

Table of Contents for this issue

Complete paper in PDF format

Propagation Modeling Over Terrain Using the Parabolic Wave Equation

Denis J. Donohue, Member, IEEE and J. R. Kuttler

Page 260.

Abstract:

We address the numerical solution of the parabolic wave equation over terrain using the Fourier/split-step approach. The method, referred to as a shift map, generalizes that of Beilis and Tappert, who introduced a coordinate transformation technique to flatten the boundary. This technique is extended to a wide-angle form, allowing larger propagation angles with respect to the horizon. A new impedance boundary condition is derived for electromagnetic waves incident on a finitely conducting surface that enables solution of the parabolic wave (PWE) using the previously developed mixed Fourier transform. It is also shown by example that in many cases of interest, the boundary may be approximated by discrete piecewise linear segments without affecting the field solution. A more accurate shift map solution of the PWE for a piecewise linear boundary is, therefore, developed for modeling propagation over digitally sampled terrain data. The shift-map solution is applied to various surface types, including ramps, wedges, curved obstacles, and actual terrain. Where possible, comparisons are made between the numerical solution and an exact analytical form. The examples demonstrate that the shift map performs well for surface slopes as large as 10-15 ° and discontinuous slope changes on the order of 15-20 °. To accommodate a larger range of slopes, it is suggested that the most viable solution for general terrain modeling is a hybrid of the shift map with the well-known terrain masking (knife-edge diffraction) approximation.

References

  1. S. Ramo, J. R. Whinnery and T. Van Duzer, Fields and Waves in Communication Electronics, New York: Wiley, 1984.
  2. J. R. Kuttler and G. D. Dockery, "Theoretical description of the parabolic approximation/Fourier split-step method of representing electromagnetic propagation in the troposphere", Radio Sci., vol. 26, pp.  381-393, 1991.
  3. G. D. Dockery and J. R. Kuttler, "An improved impedance boundary algorithm for Fourier split-step solutions of the parabolic wave equation", IEEE Trans. Antennas Propagat., vol. 44, pp.  1592-1599, Mar./Apr.  1996.
  4. V. A. Fock, "Solution of the problem of propagation of electromagnetic waves along the earth's surface by method of parabolic equations", J. Phys. USSR, vol. 10, pp.  13-35, 1946.
  5. F. B. Jensen, W. A. Kuperman, M. B. Porter and H. Schmidt, Computational Ocean Acoustics, New York: AIP, 1994.
  6. J. R. Kuttler and J. D. Huffaker, "Solving the parabolic wave equation with a rough surface boundary condition", J. Acoust. Soc. Amer., vol. 94, pp.  2451-2454, 1993.
  7. S. Ayasli and M. B. Carlson, "SEKE: A computer model for low-altitude radar propagation over irregular terrain", MIT/Lincoln Lab. Project Rep., Cambridge, MA, CMT-70, 1985 .
  8. L. B. Dozier, "PERUSE: A numerical treatment of rough surface scattering for the parabolic wave equation", J. Acoust. Soc. Amer., vol. 75, pp.  1415-1432, 1984.
  9. A. Beilis and F. D. Tappert, "Coupled mode analysis of multiple rough surface scattering", J. Acoust. Soc. Amer., vol. 66, pp.  811-826, 1979.
  10. D. J. Donohue, "Propagation modeling over terrain by coordinate transformation of the parabolic wave equation", in Proc. 1996 IEEE Antennas Propagat. Int. Symp., Baltimore, MD, July 1996, p.  44. 
  11. F. D. Tappert and L. Nghiem-Phu, "A new split-step Fourier algorithm for solving the parabolic wave equations with rough surface scattering", J. Acoust. Soc. Amer. Suppl., vol. 77, p.  S101, 1985.
  12. D. Rouseff and T. E. Ewart, "Effect of random sea surface and bottom roughness on propagation in shallow water", J. Acoust. Soc. Amer., vol. 98, pp.  3397-3404, 1995.
  13. A. E. Barrios, "A terrain parabolic equation model for propagation in the troposphere", IEEE Trans. Antennas Propagat., vol. 42, pp.  90-98,  Jan.  1994.
  14. C. L. Rino and H. D. Ngo, "Forward propagation in a half-space with an irregular boundary", IEEE Trans. Antennas Propagat., vol. 45, pp.  1340-1347, Sept.  1997.
  15. D. J. Thomson and N. R. Chapman, "A wide-angle split-step algorithm for the parabolic equation", J. Acoust. Soc. Amer., vol. 74, pp.  1848-1854, 1983.
  16. D. J. Donohue and J. R. Kuttler, "Modeling radar propagation over terrain", JHU/APL Tech. Dig., vol. 18, pp.  279-287, 1997.
  17. R. C. Johnson, and H. Jasik, Eds., "Antenna Engineering Handbook", McGraw-Hill, New York, 1984. pp. 19.6-19.7.
  18. M. H. Newkirk, "Recent advances in the tropospheric electromagnetic parabolic equation routine (TEMPER) propagation model,"in 1997 Battlespace Atmosph. Conf., J. Richter, Ed., San Diego, CA: Office Dir. Defense Res. Engrg., SPAWAR, 1998.
  19. R. O. Schmidt, "Multiple emitter location and signal parameter estimation", IEEE Trans. Antennas Propagat., vol. 34, pp.  276-280, Mar.  1986.
  20. D. A. McNamara, C. W. I. Pistorius and J. A. G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction, Norwood, MA: Artech House, 1990.
  21. C. A. Balanis, Advanced Engineering Electromagnetics, New York: Wiley, 1989.
  22. R. J. McArthur and D. H. O. Bebbington, "Diffraction over simple terrain obstacles by the method of parabolic equations", in Inst. Elect. Eng. Proc. Int. Conf. Antennas Propagat., 1991, pp.  824-827. 
  23. R. J. McArthur, "Propagation modeling over irregular terrain using the split-step parabolic equation method", in Inst. Elect. Eng. Proc. Radar, 1992, pp.  54-57. 
  24. T. B. A. Senior and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, London: U.K.: IEE Press, 1995.