volume | PIER Journals

Abstract

The small slope approximation (SSA) and the Kirchhoff approach (KA) are applied to the prediction of microwave sea surface backscatter for both Ku and C bands for various wind speeds and incident angles. Numerical results are obtained assuming a non-directional surface wavenumber spectrum and compared with azimuthally averaged C- and Ku-band radar backscattering data. The KA can be obtained rigorously for a perfectly-conducting surface, whereas for a dielectric surface, either the KA of order one (KA1) or the stationary phase (SP) method can be used. Numerical results are obtained assuming a non-directional surface wavenumber spectrum and compared with azimuthally C and Ku bands radar backscattering data for incidence angles of interest for remote sensing. Since the SSA and KA formulations are expressed in polar coordinates, the backscattering coefficient is expressed in terms of surface height autocorrelation and its derivatives of one- and second- orders computed from integrating the sea spectrum multiplied by Bessel functions of the first kind. This allows to have for KA and first-order SSA (SSA-1), a single numerical integration over the radial distance instead of four, when the cartesian coordinates is chosen. Moreover, the azimuthal harmonic magnitudes of the backscattering coefficient according to the wind direction can be performed separately. For an isotropic sea surface assumed to be perfectly conducting where the KA is valid, the deviation between SSA and KA models is smaller than the one computed from the SP model for HH polarization. For the VV polarization, the difference is greater, since the polarization term of SSA is given by the small perturbation method, whereas for the KA approach, it is equal to the Fresnel coefficient. For an anisotropic sea surface, the comparison of KA with SSA-1 leads to the same conclusion. The isotropic part and the second azimuthal harmonic of the backscattering coefficient are also compared with empirical backscattering models CMOD2-I3 and SASS-II valid in C and Ku bands, respectively.

1. Beckmann, P. and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Part I: Theory, Pergamon Press, London, 1963.

2. Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing, Vol.II, Addison-Wesley, Reading, MA, 1982.

3. Olgilvy, J. A., Theory of Wave Scattering from Random Rough Surfaces, Adam Hilger, Bristol, Philadelphia, and New York, 1991.

4. Fung, A. K., C. Zuffada, and C. Y. Hsieh, "Incoherent bistatic scattering from the sea surface at L-band," IEEE Trans.Ge os. Rem.Sens., Vol. 39, No. 5, 1006-1012, 2001.
doi:10.1109/36.921418

5. Rice, S. O., "Reflection of electromagnetic wave from slightly rough surfaces," Symposium on the Theory of Electromagnetic Wave, 351-378, 1950.

6. Thorsos, E. I. and S. L. Broschat, "The validity of the perturbation theory approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acoust.Soc. Am., Vol. 86, No. 1, 261-277, 1989.
doi:10.1121/1.398342

7. Chevalier, B. and G. Berginc, "Small slope approximation method: scattering of a vector wave from 2D dielectric and metallic surfaces with Gaussian and non-Gaussian statistics," SPIE Scattering and Surface Roughness, Vol. III, 22-32, 2000.
doi:10.1117/12.401662

8. Bahar, E. and B. S. Lee, "Radar scatter cross section for two-dimensional random surfaces—full wave solutions and comparisons with experiments," Waves Random Media, Vol. 6, 1-23, 1996.
doi:10.1080/13616679609409792

9. Voronovich, A. G., "Wave scattering from rough surfaces," Springer Series on Wave Phenomena, Germany, 1994.

10. Voronovich, A. G., "Small slope approximation for electromagnetic wave scattering at a rough interface of two dielectric halfspaces," Waves Random Media, Vol. 4, 337-367, 1994.
doi:10.1088/0959-7174/4/3/008

11. Voronovich, A. G. and V. U. Zavorotny, "Theoretical model for scattering of radar signals in Ku- and C-bands from a rough sea surface with breaking waves," Waves Random Media, Vol. 11, 247-269, 2001.

12. Berginc, G., Y. Beniguel, and B. Chevalier, "Small slope approximation method: higher order contributions for scattering from 3-D surfaces," SPIE Scattering and surface roughness, Vol. II, 1999.

13. Berginc, G., Y. Beniguel, and B. Chevalier, "Extension of small-slope approximation method for 3-D scattering cross-section calculation of a rough convex object," PIERS Proceedings, Nantes, France, 582, 1998.

14. McDaniel, S. T., "Small-slope predictions of microwave backscatter from the sea surface," Waves Random Media, Vol. 11, 343-360, 2001.

15. Thorsos, E. I. and S. L. Broschat, "An investigation of the small slope approximation for scattering from rough surfaces, Part I: Theory," J.A coust.So c.A m., Vol. 97, No. 4, 2082-2093, 1995.

16. Broschat, S. L. and E. I. Thorsos, "An investigation of the small slope approximation for scattering from rough surfaces, Part II: Numerical studies," J. Acoust. Soc. Am., Vol. 101, No. 5, 2615-1625, 1997.
doi:10.1121/1.418502

17. Semyonov, B., "Approximate computation of scattering electromagnetic waves by rough surface contour," Radio Eng. Electron. Phys., Vol. 11, 1179-1187, 1966.

18. Bourlier, C., J. Saillard, and G. Berginc, "Theoretical study of the Kirchhoff integral from two-dimensional randomly rough surface with shadowing effect—application on the backscattering coefficient for a perfectly conducting surface," Waves Random Media, Vol. 11, 91-118, 2001.
doi:10.1088/0959-7174/11/2/302

19. Bourlier, C., J. Saillard, and G. Berginc, "Bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase and scalar approximation with shadowing effect—comparisons with experiments and application to the sea surface," Waves Random Media, Vol. 11, 119-147, 2001.
doi:10.1088/0959-7174/11/2/303

20. Bourlier, C., J. Saillard, and G. Berginc, "The shadowing function," Progress in Electromagnetic Research, J. A. Kong (ed.), Vol. 27, 226–287, EMW, Cambridge, 2000.

21. Bourlier, C., J. Saillard, and G. Berginc, "Study of the sea behavior," Progress In Electromagnetic Research, J. A. Kong (ed.), Vol. 27, 193–225, EMW, Cambridge, 2000.

22. Elfouhaily, T., B. Chapron, K. Katsaros, and D. Vandemark, "A unified directional spectrum for long and short wind-driven waves," Journal.Ge o.R es., Vol. 102, No. C7, 781-796, 1997.

23. Quilfen, Y., B. Chapron, T. Elfouhaily, K. Katsaros, and J. Tournadre, "Observation of tropical cyclones by high resolution scatterometry," Journal.Ge o.R es., Vol. 103, 7767-7786, 1998.
doi:10.1029/97JC01911

24. Bentamy, A., P. Queffeulou, Y. Quilfen, and K. Katsaros, "Ocean surface wind fields estimated from satellite active and passive microwave instruments," IEEE Trans.Ge osci.R emote Sens., Vol. 37, 2469-86, 1999.
doi:10.1109/36.789643

25. Wentz, F. J., S. Peteherich, and L. A. Thomas, "A model function for ocean radar cross section at 14.6 GHz," J. Geophys. Res., Vol. 89, 3689-3704, 1984.
doi:10.1029/JC089iC03p03689

26. Nghiem Fuk, S. V., K. Li, and G. Neumann, "The dependence of ocean backscatter at Ku-band on oceanic and atmospheric parameters," IEEE Trans.Ge osci.R emote Sens., Vol. 35, 581-600, 1997.
doi:10.1109/36.581972

27. Cox, C. and W. Munk, "Statistics of the sea surface derived from sun glitter," Journal Mar. Res., Vol. 13, 198-226, 1954.

28. Ellison, W., A. Balana, G. Delbos, K. Lamdaouchi, L. Eymard, C. Guillou, and C. Prigent, "New permittivity measurements of seawater," Radio Sci., Vol. 33, 639-648, 1998.
doi:10.1029/97RS02223

29. Fung, A. K. and K. K. Lee, "A semi-empirical sea-spectrum model for scattering coefficient estimation," IEEE Journal Oceanic Eng., Vol. 7, No. 4, 166-176, 1982.
doi:10.1109/JOE.1982.1145535

30. Yoshimori, K., K. Itoh, and Y. Ichioka, "Optical characteristics of a wind-roughened water surface: a two dimensional theory," Applied Optics, Vol. 34, No. 27, 6236-6247, 1995.
doi:10.1364/AO.34.006236

31. Appel, J. R., "An improved model of the ocean surface wave vector spectrum and its effects on radar backscatter," Journal Geo. Res., Vol. 99, No. C7, 1-21, 1994.

32. Lemaire, D., P. Sobieski, and A. Guissard, "Full-range sea surface spectrum in nonfully developed state for scattering calculations," IEEE Trans. Geosci. Remote Sens., Vol. 37, 1038-1051, 1999.
doi:10.1109/36.752222

33. Smith, B. G., "Lunar surface roughness, shadowing and thermal emission," J. Geophysical Research, Vol. 72, No. 16, 4059-4067, 1967.
doi:10.1029/JZ072i016p04059

34. Smith, B. G., "Geometrical shadowing of a random rough surface," IEEE Trans. Ant. Prop., Vol. 15, 668-671, 1967.
doi:10.1109/TAP.1967.1138991

35. Wagner, R. J., "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am, Vol. 41, No. 1, 138-147, 1966.
doi:10.1121/1.1910308

36. Bourlier, C., J. Saillard, and G. Berginc, "Effect of correlation between shadowing and shadowed points on the Wagner and Smith monostatic one-dimensional shadowing function," IEEE Trans.A nt.Pr op., Vol. 48, 437-446, 2000.
doi:10.1109/8.841905

37. Sancer, M. I., "Shadow-corrected electromagnetic scattering from a randomly rough surface," IEEE Trans. Ant. Prop., Vol. 17, 577-585, 1969.
doi:10.1109/TAP.1969.1139516

38. Abramovitz, M. and I. A. Segun, Handbook of Mathematical Functions, Dover Publications, 1972.

39. Fung, A. K., Microwave Scattering and Emission Models and Their Applications, Artech House, Boston, MA, 1994.

40. Voronovich, V., U. Zavorotny, and V. G. Irisov, "Sea-roughness spectrum retrieval from radar and radiometric measurements," Int.Ge os.and Remote Sensing Symp., IEEE, Piscataway, NJ, 3102–3104, 2000.

Prof. Christophe Bourlier

Dr. Gerard Berginc