volume | PIER Journals

Abstract

The Doppler spectral characteristics of electromagnetic backscattered echoes from dynamic nonlinear surfaces of finite-depth sea is investigated with the second-order small-slope approximation (SSA-II). The revised nonlinear hydrodynamic choppy wave model (CWM) combining with an experiment-verified shoaling coefficient is utilized to model the finite-depth sea wave profiles, and the simulated surfaces of finite-depth sea show steeper crests and more flat troughs as depth decreases. First, Comparison of the Doppler spectra for linear sea surfaces and nonlinear choppy sea surfaces shows that nonlinear hydrodynamic effect greatly enhances the Doppler shift and the Doppler spectrum bandwidth, and the predicted results agree well with the rigorous numerical model data. The Doppler spectra of backscattered echoes from finite-depth sea with different depths are further evaluated. At small incident angles, the Doppler shifts and the spectra bandwidths are much lower for shallower sea, and the opposite situation can be gradually observed for increased incident angles. This indicates that the nonlinear wave-wave interactions among waves occur more frequently in finite-depth sea and the long waves will be suppressed while shorter wind waves will be boosted in shallower water. Moreover, the dependence of the Doppler spectral characteristics on polarization is also discussed.

1. Kurrant, D. J. and E. C. Fear, "Extraction of internal spatial features of inhomogeneous dielectric objects using near-field reflection data," Progress In Electromagnetics Research, Vol. 122, 197-221, 2012.
doi:10.2528/PIER11092105 Google Scholar

2. Chen, H., M. Zhang, and H.-C. Yin, "Facet-based treatment on microwave bistatic scattering of three-dimensional sea surface with electrically large ship," Progress In Electromagnetics Research, Vol. 123, 385-405, 2012.
doi:10.2528/PIER11101108 Google Scholar

3. Yang, W., Z.-Q. Zhao, C.-H. Qi, W. Liu, and Z.-P. Nie, "Iterative hybrid method for electromagnetic scattering from a 3-D object above a 2-D random dielectric rough surface," Progress In Electromagnetics Research, Vol. 117, 435-448, 2011. Google Scholar

4. Baussard, A., M. Rochdi, and A. Khenchaf, "PO/Mec-based scattering model for complex objects on a sea surface," Progress In Electromagnetics Research, Vol. 111, 229-251, 2011.
doi:10.2528/PIER10083005 Google Scholar

5. Ji, W.-J. and C.-M. Tong, "Bistatic scattering from two-dimensional dielectric ocean rough surface with a PEC object partially embedded by using the G-SMCG method ," Progress In Electromagnetics Research, Vol. 105, 119-139, 2010.
doi:10.2528/PIER10041101 Google Scholar

6. Luo, W., M. Zhang, Y.-W. Zhao, and H. Chen, "An efficient hybrid high-frequency solution for the composite scattering of the ship on very large two-dimensional sea surface," Progress In Electromagnetics Research M, Vol. 8, 79-89, 2009.
doi:10.2528/PIERM09050103 Google Scholar

7. Fabbro, V., "Apparent radar cross section of a large target illuminated by a surface wave above the sea," Progress In Electromagnetics Research, Vol. 50, 41-60, 2005.
doi:10.2528/PIER04050502 Google Scholar

8. Zhang, M., Y.-W. Zhao, H. Chen, and W.-Q. Jiang, "SAR imaging simulation for composite model of ship on dynamic ocean scene," Progress In Electromagnetics Research, Vol. 113, 395-412, 2011.
doi:10.2528/PIER11071501 Google Scholar

9. Chen, H., M. Zhang, D. Nie, and H. C. Yin, "Robust semi-deterministic facet model for fast estimation on EM scattering from ocean-like surface ," Progress In Electromagnetics Research B, Vol. 18, 347-363, 2009.
doi:10.2528/PIERB09100508 Google Scholar

10. Nie, D. and M. Zhang, "Bistatic scattering analysis for two-dimensional rough sea surfaces using an angular composite model," Int. J. Remote Sens., Vol. 32, No. 24, 9661-9672, 2011.
doi:10.1080/01431161.2011.574160 Google Scholar

11. Mouche, A. A., B. Chapron, N. Reul, and F. Collard, "Predicted Doppler shifts induced by ocean surface wave displacements using asymptotic electromagnetic wave scattering theories," Waves Random Complex Media, Vol. 18, No. 1, 185-196, 2008.
doi:10.1080/17455030701564644 Google Scholar

12. Zavorotny, V. U. and A. G. Voronovich, "Two-scale model and ocean radar Doppler spectra at moderate- and low-grazing angles," IEEE Trans. Antennas Propag., Vol. 46, No. 1, 84-92, 1998.
doi:10.1109/8.655454 Google Scholar

13. Rino, C. L., T. L. Crystal, A. K. Koide, H. D. Ngo, and H. Guthart, "Numerical simulation of backscattering from linear and nonlinear ocean surface realizations," Radio Sci., Vol. 26, No. 1, 51-71, 1991.
doi:10.1029/90RS01687 Google Scholar

14. Creamer, D. B., F. Henyey, R. Schult, and J. Wright, "Improved linear representation of sea surface waves," J. Fluid Mech., Vol. 205, 135-161, 1989.
doi:10.1017/S0022112089001977 Google Scholar

15. Toporkov, J. V. and G. S. Brown, "Numerical simulations of scattering from time-varying, randomly rough surfaces," IEEE Trans. Geosci. Remote Sens., Vol. 38, No. 4, 1616-1625, 2000.
doi:10.1109/36.851961 Google Scholar

16. Johnson, J. T., J. V. Toporkov, and G. S. Brown, "A numerical study of backscattering from time-evolving sea surfaces: Comparison of hydrodynamic models," IEEE Trans. Geosci. Remote Sens., Vol. 39, No. 11, 2411-2420, 2001.
doi:10.1109/36.964977 Google Scholar

17. Soriano, G., M. Joelson, and M. Saillard, "Doppler spectra from a two-dimensional ocean surface at L-band," IEEE Trans. Geosci. Remote Sens., Vol. 44, No. 9, 2430-2437, 2006.
doi:10.1109/TGRS.2006.873580 Google Scholar

18. Nouguier, F., C. A. Guérin, and G. Soriano, "Analytical techniques for the Doppler signature of sea surfaces in the microwave regime II: Nonlinear surfaces," IEEE Trans. Geosci. Remote Sens., Vol. 49, No. 12, 4920-4927, 2011.
doi:10.1109/TGRS.2011.2153207 Google Scholar

19. Nouguier, F., C. A. Guérin, and B. Chapron, "Choppy wave model for nonlinear gravity waves," J. Geophys. Res. (JGR) --- Oceans, Vol. 114, No. C09012, 1-16, 2009. Google Scholar

20. Barrick, D. E. and B. J. Lipa, "The second-order shallow-water hydrodynamic coupling coe±cient in interpretation of HF radar sea echo," IEEE J. Ocean. Eng., Vol. 11, No. 2, 310-315, 1986.
doi:10.1109/JOE.1986.1145187 Google Scholar

21. Lipa, B. J. and D. E. Barrick, "Extraction of sea state from HF radar sea echo: Mathematical theory and modeling," Radio Sci., Vol. 21, No. 1, 81-100, 1986.
doi:10.1029/RS021i001p00081 Google Scholar

22. Holden, G. J. and L. R. Wyatt, "Extraction of sea state in shallow water using HF radar," Proc. Inst. Elect. Eng. F --- Radar Signal Process., Vol. 139, No. 2, 175-181, 1992.
doi:10.1049/ip-f-2.1992.0021 Google Scholar

23. Qi, C., Z. Zhao, W. Yang, Z.-P. Nie, and G. Chen, "Electromagnetic scattering and Doppler analysis of three-dimensional breaking wave crests at low-grazing angles ," Progress In Electromagnetics Research, Vol. 119, 239-252, 2011.
doi:10.2528/PIER11062401 Google Scholar

24. Luo, W., M. Zhang, C. Wang, and H.-C. Yin, "Investigation of low-grazing-angle microwave backscattering from three-dimensional breaking sea waves," Progress In Electromagnetics Research, Vol. 119, 279-298, 2011.
doi:10.2528/PIER11062607 Google Scholar

25. 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, No. 3, 247-269, 2001. Google Scholar

26. Soriano, G. and M. Saillard, "Modelization of the scattering of electromagnetic waves from the ocean surface," Progress In Electromagnetics Research, Vol. 37, 101-128, 2002.
doi:10.2528/PIER01111800 Google Scholar

27. Berginc, G., "Small slope approximation method: A further study of vector wave scattering from two-dimensional surfaces and comparison with experimental data," Progress In Electromagnetics Research, Vol. 37, 251-287, 2007. Google Scholar

28. Li, X.-F. and X.-J. Xu, "Scattering and Doppler spectral analysis for two-dimensional linear and nonlinear sea surfaces," IEEE Trans. Geosci. Remote Sens., Vol. 49, No. 2, 603-611, 2011.
doi:10.1109/TGRS.2010.2060204 Google Scholar

29. McCormick, M. E., Ocean Engineering Wave Mechanics, John Wiley & Sons Inc, New York, 1973.

30. Hasselmann, K., et al. "Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP)," Dtsch. Hydrogr. Z. Suppl., Vol. 12, No. A8, 1-95, 1973. Google Scholar

31. Miche, M., "Mouvements ondulatoires de la mer en profondeur constante ou décroissante. forme limite de la houle lors de son d'eferlement. Application aux digues marines," Ann. Ponts Chaussées, Vol. 114, 25-78, 1944. Google Scholar

32. Tsang, L., J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, John Wiley & Sons Inc., New York, 2001.

33. Romeiser, R. and D. R. Thompson, "Numerical study on the along-track interferometric radar imaging mechanism of oceanic surface currents ," IEEE Trans. Geosci. Remote Sens., Vol. 38, No. 1, 446-458, 2000.
doi:10.1109/36.823940 Google Scholar

Prof. Ding Nie

Prof. Min Zhang

Dr. Xupu Geng

Dr. Ping Zhou