volume | PIER Journals

Abstract

Within the framework of the composite surface scattering model, analytical formulas for Doppler shift and bandwidth of radar echoes backscattered from time-varying sea surface are derived in the forms of three-dimensional integrals. In our derivations, the influences of the tilt modulation (TM), the hydrodynamic modulation (HM), the shadow and the curvature of large-scale undulating waves are all taken into account for achieving more reasonable results. Comparisons between our theoretical curves and the results obtained directly by exact numerical method demonstrate that our formulas can improve the simulated results. On the other hand, the simulations by our formulas can also help to estimate the effects of the TM, the HM, and the shadow of large-scale waves on Doppler behaviors individually. We find that the predicted Doppler shifts are always larger in HH-polarization than in VV-polarization due to the TM. Meanwhile, the simulations also show that the predicted Doppler shifts for both HH- and VV-polarizations would become larger when the HM is considered. In addition, at low-grazing angles (LGA), the shadow effect results in a rapid increase in the predicted Doppler shift, and on the contrary makes the bandwidth narrower.

1. Crombie, D. D., "Doppler spectrum of sea echo at 13.66 Mc./s.," Nature, Vol. 175, 681-682, 1955.
doi:10.1038/175681a0

2. Bass, F. G., I. M. Fuks, A. I. Kalmykov, I. E. Ostrovsky, and A. D. Rosenberg, "Very-high frequency radiowave scattering by a disturbed sea surface. Part II: Scattering from an actual sea surface," IEEE Trans. Antennas Propagat., Vol. 16, 560-568, 1968.
doi:10.1109/TAP.1968.1139244

3. Wright, J. W. and W. C. Keller, "Doppler spectra in microwave scattering from wind waves," Phys. Fluids, Vol. 14, 466-474, 1971.
doi:10.1063/1.1693458

4. Zavorotny, V. U. and A. G. Voronovich, "Two-scale model and ocean radar Doppler spectra at moderate- and low-grazing angles," IEEE Trans. Antennas Propagat., Vol. 46, 84-92, 1998.
doi:10.1109/8.655454

5. Nie, D., M. Zhang, X.-P. Geng, and P. Zhou, "Investigation on Doppler spectral characteristics backscattered echoes from non-linear surface of finite-depth sea," Progress In Electromagnetics Research, Vol. 130, 169-186, 2012.

6. Qi, C., Z. Zhao, W. Yang, Z. 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

7. Soriano, G., M. Joelson, M. Saillard, and P. C. Marseille, "Doppler spectra from a two-dimensional ocean surface at L-band," IEEE Trans. Geosci. Remote Sensing, Vol. 44, 2430-2437, 2006.
doi:10.1109/TGRS.2006.873580

8. Fuks, I. M. and A. G. Voronovich, "Radar backscattering from Gerstner's sea surface," Waves in Random Media, Vol. 12, 321-339, 2002.
doi:10.1088/0959-7174/12/3/305

9. Toporkov, J. V. and G. S. Brown, "Numerical simulations of scattering from time-varying randomly rough surfaces," IEEE Trans. Geosci. Remote Sensing, Vol. 38, 1616-1625, 2000.
doi:10.1109/36.851961

10. Johnson, J. T., J. V. Toporkov, and G. S. Brown, "A numerical study of back-scattering from time-evolving sea surfaces: Comparison of hydrodynamic models," IEEE Trans. Geosci. Remote Sensing, Vol. 39, 2411-2420, 2001.
doi:10.1109/36.964977

11. Hayslip, A. R., J. T. Johnson, and G. R. Baker, "Further numerical studies of back-scattering from time-evolving nonlinear sea surfaces," IEEE Trans. Geosci. Remote Sensing, Vol. 41, 2287-2293, 2003.
doi:10.1109/TGRS.2003.814662

12. Saillard, M., P. Forget, G. Soriano, M. Joelson, P. Broche, and P. Currier, "Sea surface probing with L-band Doppler radar: Experiment and theory," C. R. Physique, Vol. 6, 675-682, 2005.
doi:10.1016/j.crhy.2005.06.008

13. Hisaki, Y., "Doppler spectrum of radio wave scattering from ocean-like moving surfaces for finite illuminated area," Int. J. Remote Sensing, Vol. 24, 3075-3091, 2003.
doi:10.1080/01431160210153057

14. Nouguier, F., C. A. Guerin, and G. Soriano, "Analytical techniques for the Doppler signature of sea surfaces in the microwave regime --- I: Linear surfaces," IEEE Trans. Geosci. Remote Sensing, Vol. 49, No. 12, 4856-4864, 2011.
doi:10.1109/TGRS.2011.2152848

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

16. Wang, Y. H. and Y. M. Zhang, "Investigation on Doppler shift and bandwidth of backscattered echoes from a composite sea surface," IEEE Trans. Geosci. Remote Sensing, Vol. 49, 2287-2293, 2011.

17. Wang, Y. H., Y. M. Zhang, M. X. He, and C. F. Zhao, "Doppler spectra of microwave scattering fields from nonlinear oceanic surface at moderate- and low-grazing angles," IEEE Trans. Geosci. Remote Sensing, Vol. 50, No. 4, 1104-1116, 2012.
doi:10.1109/TGRS.2011.2164926

18. Pidgeon, V. W., "Doppler dependence of radar sea return," J. Geophys. Res., Vol. 73, 1333-1341, 1968.
doi:10.1029/JB073i004p01333

19. Valenzuela, G. R. and M. B. Laing, "Study of Doppler spectra of radar sea echo," J. Geophys. Res., Vol. 75, 551-563, 1970.
doi:10.1029/JC075i003p00551

20. Plant, W. J., "A model for microwave Doppler sea return at high incidence angles: Bragg scattering from bound, tilted waves," J. Geophys. Res., Vol. 102, 21131-21146, 1997.
doi:10.1029/97JC01225

21. Lamont-Smith, T., "Doppler spectra of laboratory wind waves at low grazing angle," Waves in Random Media, Vol. 10, 33-41, 2000.
doi:10.1088/0959-7174/10/1/303

22. Romeiser, R. and D. R. Thompson, "Numerical study on the along-track interferometric radar imaging mechanism of oceanic surface currents," IEEE Trans. Geosci. Remote Sensing, Vol. 38, 446-458, 2000.
doi:10.1109/36.823940

23. Alpers, W. and K. Hasselmann, "The two-frequency microwave technique for measuring ocean-wave spectra from an airplane or satellite," Boundary Layer Meteorol, Vol. 13, 215-230, 1978.
doi:10.1007/BF00913873

24. Alpers, W., D. B. Ross, and C. L. Rufenach, "On the detectability of ocean surface waves by real and synthetic aperture radar," J. Geophys. Res., Vol. 86, 6481-6498, 1981.
doi:10.1029/JC086iC07p06481

25. Fisz, M., Probability Theory and Mathematical Statistics, Krieger Pub. Co., 1980.

26. Keller, W. C. and W. J. Plant, "Microwave backscatter from the sea: Modulation of received power and Doppler bandwidth by long waves," J. Geophys. Res., Vol. 99, 9751-9766, 1994.
doi:10.1029/94JC00082

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

28. Voronovich, A. G. and V. U. Zavorotny, "Curvature effects in the composite model for low-grazing-angle rough-surface scatter," Waves in Random Media, Vol. 8, 41-52, 1998.

29. Smith, B. G., "Lunar surface roughness: Shadowing and thermal emission," J. Geophys. Res., Vol. 72, 4059-4067, 1967.
doi:10.1029/JZ072i016p04059

Professor Yunhua Wang

Dr. Yan-Min Zhang

Professor Li-Xin Guo