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Based on the composite surface scattering model, the analytical formulas for Doppler shift and bandwidth of radar echoes return from time-varying sea surface are derived. In our derivations, the influences of the tilt modulation, the shadow and the curvature of large-scale undulating waves are all taken into account for achieving more reasonable results. Comparisons between the theoretical results and direct numerical simulations demonstrate that the analytical formulas can significantly improve the simulated results. And the effects of the tilt modulation, the shadow and the curvature on Doppler spectral properties are discussed in detail. From the simulated results, it is found that the predicted Doppler shifts are always larger in HH-polarization than in VV-polarization due to the tilt modulation of large-scale waves. In addition, at low-grazing angles, the shadow of large-scale waves results in a rapid increase of the predicted Doppler shift, and on the contrary maks the bandwidth narrower.
[1] Johnson J T, Burkholder R J, Toporkov J V, Lyzenga D R, Plant W J 2009 IEEE Trans. Geosci. Remote Sensing 47 1641
[2] Chapron B, Collard F, Ardhum F 2005 J. Geophys. Res. 110 C07008
[3] Johannessen J A, Kudryavtsev V, Akimov D, Eldevik T, Winther N, Chapron B 2005 J. Geophys. Res. 110 C07017
[4] Kudryavtsev V, Akimov D, Johannessen J A, Chapron B 2005 J. Geophys. Res. 110 doi: 10.1029/ 2004JC002505
[5] Crombie D D 1955 Nature 175 681
[6] Barrick D E 1977 Radio Sci. 12 415
[7] Bass F G, Fuks I M, Kalmykov A I, Ostrovsky I E, Rosenberg A D 1968 IEEE Trans. Antennas Propagat. 16 560
[8] Wright J W, Keller W C 1971 Phys. Fluids 14 466
[9] Mouche A, Chapron B, Reul N, Collard F 2008 Waves Random and Complex Media 18 185
[10] Zhang Y H, Wang Y H, Guo L X 2010 Chin. Phys. B 19 054103
[11] Wang Y H, Zhang Y M 2011 IEEE Trans. Geosci. Remote Sensing 49 1071
[12] Guo L X, Wang R, Wang Y H, Wu Z S 2008 Acta Phys. Sin. 57 3464 (in Chinese) [郭立新, 王蕊, 王运华, 吴振森 2008 物理学报 57 3464]
[13] Toporkov J V, Brown G S 2000 IEEE Trans. Geosci. Remote Sensing 38 1616
[14] Johnson J T, Toporkov J V, Brown G S 2001 IEEE Trans. Geosci. Remote Sensing 39 2411
[15] Soriano G, Joelson M, Saillard M, Marseille P C 2006 IEEE Trans. Geosci. Remote Sensing 44 2430
[16] Wang Y H, Zhang Y M, He M X, Zhao C F 2012 IEEE Trans. Geosci. Remote Sensing 50
[17] Zavorotny V U, Voronovich A G 1998 IEEE Trans. Antennas Propagat 46 84
[18] Voronovich A G, Zavorotny V U 1998 Waves Random Media 8 41
[19] Ulaby F T, Moore R K, Fung A K 1982 Microwave Remote Sensing. Vol. II (Reading, MA: Addision- Wesbey)
[20] Klein L A, Swift C T 1977 IEEE Trans. Antennas Propagat 25 104
[21] Smith B G 1967 Journal of Geophysical Research 72 4059
[22] Keller W C, Plant W J 1994 J. Geophys. Res. 99 9751
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[1] Johnson J T, Burkholder R J, Toporkov J V, Lyzenga D R, Plant W J 2009 IEEE Trans. Geosci. Remote Sensing 47 1641
[2] Chapron B, Collard F, Ardhum F 2005 J. Geophys. Res. 110 C07008
[3] Johannessen J A, Kudryavtsev V, Akimov D, Eldevik T, Winther N, Chapron B 2005 J. Geophys. Res. 110 C07017
[4] Kudryavtsev V, Akimov D, Johannessen J A, Chapron B 2005 J. Geophys. Res. 110 doi: 10.1029/ 2004JC002505
[5] Crombie D D 1955 Nature 175 681
[6] Barrick D E 1977 Radio Sci. 12 415
[7] Bass F G, Fuks I M, Kalmykov A I, Ostrovsky I E, Rosenberg A D 1968 IEEE Trans. Antennas Propagat. 16 560
[8] Wright J W, Keller W C 1971 Phys. Fluids 14 466
[9] Mouche A, Chapron B, Reul N, Collard F 2008 Waves Random and Complex Media 18 185
[10] Zhang Y H, Wang Y H, Guo L X 2010 Chin. Phys. B 19 054103
[11] Wang Y H, Zhang Y M 2011 IEEE Trans. Geosci. Remote Sensing 49 1071
[12] Guo L X, Wang R, Wang Y H, Wu Z S 2008 Acta Phys. Sin. 57 3464 (in Chinese) [郭立新, 王蕊, 王运华, 吴振森 2008 物理学报 57 3464]
[13] Toporkov J V, Brown G S 2000 IEEE Trans. Geosci. Remote Sensing 38 1616
[14] Johnson J T, Toporkov J V, Brown G S 2001 IEEE Trans. Geosci. Remote Sensing 39 2411
[15] Soriano G, Joelson M, Saillard M, Marseille P C 2006 IEEE Trans. Geosci. Remote Sensing 44 2430
[16] Wang Y H, Zhang Y M, He M X, Zhao C F 2012 IEEE Trans. Geosci. Remote Sensing 50
[17] Zavorotny V U, Voronovich A G 1998 IEEE Trans. Antennas Propagat 46 84
[18] Voronovich A G, Zavorotny V U 1998 Waves Random Media 8 41
[19] Ulaby F T, Moore R K, Fung A K 1982 Microwave Remote Sensing. Vol. II (Reading, MA: Addision- Wesbey)
[20] Klein L A, Swift C T 1977 IEEE Trans. Antennas Propagat 25 104
[21] Smith B G 1967 Journal of Geophysical Research 72 4059
[22] Keller W C, Plant W J 1994 J. Geophys. Res. 99 9751
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