Oceanography The Official Magazine of
The Oceanography Society
Volume 26 Issue 02

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Volume 26, No. 2
Pages 68 - 79

Nonlinear Internal Waves in Synthetic Aperture Radar Imagery

Christopher R. Jackson José C.B. da Silva Gus Jeans Werner Alpers Michael J. Caruso
Article Abstract

Synthetic aperture radar (SAR) has contributed significantly to the study and understanding of oceanic nonlinear internal waves. Although they travel within the ocean’s interior, currents associated with internal waves produce variations in ocean surface roughness that is readily detectable by SAR. This paper will first review the morphology of nonlinear internal wave signatures in SAR imagery and then examine the information that can be extracted from those signatures, including the determination of wave type and an estimation of phase speed.


Jackson, C.R., J.C.B. da Silva, G. Jeans, W. Alpers, and M.J. Caruso. 2013. Nonlinear internal waves in synthetic aperture radar imagery. Oceanography 26(2):68–79, https://doi.org/10.5670/oceanog.2013.32.


Ablowitz, M.J., and D.E. Baldwin. 2012. Nonlinear shallow ocean-wave soliton interactions on flat beaches. Physical Review E 86(3), 036305, https://doi.org/10.1103/PhysRevE.86.036305.

Alpers, W. 1985. Theory of radar imaging of internal waves. Nature 314:245–247, https://doi.org/10.1038/314245a0.

Apel, J.R., J.R. Holbrook, A.K. Liu, and J.J. Tsai. 1985. The Sulu Sea internal soliton experiment. Journal of Physical Oceanography 15(12):1,625–1,651, https://doi.org/10.1175/1520-0485(1985)​015<1625:TSSISE>2.0.CO;2.

Brandt, P., R. Romeiser, and A. Rubino. 1999. On the determination of characteristics of the interior ocean dynamics from radar signatures of internal solitary waves. Journal of Geophysical Research 104(C12):30,039–30,045, https://doi.org/10.1029/1999JC900092.

da Silva, J.C.B., S.A. Ermakov, and I.S. Robinson. 2000. Role of surface films in ERS SAR signatures of internal waves on the shelf: 3. Mode transitions. Journal of Geophysical Research 105(C10):24,089–24,104, https://doi.org/10.1029/2000JC900053.

da Silva, J.C.B., S.A. Ermakov, I.S. Robinson, D.R.G. Jeans, and S.V. Kijashko. 1998. Role of surface films in ERS SAR signatures of internal waves on the shelf: 1. Short-period internal waves. Journal of Geophysical Research 103(C4):8,009–8,031, https://doi.org/10.1029/97JC02725.

da Silva, J.C.B., and K.R. Helfrich. 2008. Synthetic aperture radar observations of resonantly generated internal solitary waves at Race Point Channel (Cape Cod). Journal of Geophysical Research 113, C11016, https://doi.org/​10.1029/2008JC005004.

da Silva, J.C.B., A.L. New, and J.M. Magalhaes. 2011. On the structure and propagation of internal solitary waves generated at the Mascarene Plateau in the Indian Ocean. Deep Sea Research Part I 58:229–240, https://doi.org/10.1016/j.dsr.2010.12.003.

Dokken, S.T., R. Olsen, T. Wahl, and M.V. Tantillo. 2001. Identification and characterization of internal waves in SAR images along the coast of Norway. Geophysical Research Letters 28:2,803–2,806, https://doi.org/​10.1029/2000GL012730.

Egbert, G.D., and S.Y. Erofeeva. 2002. Efficient inverse modeling of barotropic ocean tides. Journal of Atmospheric and Oceanic Technology 19:183–204, https://doi.org/​10.1175/1520-0426(2002)019<0183:EIMOBO>​2.0.CO;2.

Ermakov, S.A., S.G. Salashin, and A.R. Panchenko. 1992. Film slicks on the sea surface and some mechanisms of their formation. Dynamics of Atmospheres and Oceans 16(3):279–304, https://doi.org/10.1016/0377-0265(92)90010-Q.

Ewing, G. 1950. Slicks, surface films and internal waves. Journal of Marine Research 9:167–187.

Farmer, D.M., and L. Armi. 1988. The flow of Mediterranean Water through the Strait of Gibraltar, the flow of Atlantic water through the Strait of Gibraltar. Progress in Oceanography 2:1–105, https://doi.org/​10.1016/0079-6611(88)90055-9.

Fu, L.L., and B. Holt. 1982. Seasat Views Oceans and Sea Ice With Synthetic Aperture Radar. JPL Publication 81-120, National Aeronautics and Space Administration, Jet Propulsion Laboratory, Pasadena, CA, 204 pp. Available online at: http://southport.jpl.nasa.gov/reports/seasat/seasat.pdf (accessed July 16, 2013).

Hsu, M.K., and A.K. Liu. 2000. Nonlinear internal waves in the South China Sea. Canadian Journal of Remote Sensing 26:72–81.

Hyder, P., D.R.G. Jeans, E. Cauquil, and R. Nerzic. 2005. Observations and predictability of internal solitons in the Northern Andaman Sea. Journal of Applied Ocean Research 27:1–11, https://doi.org/10.1016/j.apor.2005.07.001.

Jackson, C.R. 2004. An Atlas of Internal Solitary-like Waves and Their Properties, 2nd ed. Global Ocean Associates, Alexandria, VA, 560 pp. Available online at: http://www.internalwaveatlas.com (accessed July 16, 2013).

Jackson, C.R. 2009. An empirical model for estimating the geographic location of nonlinear internal solitary waves. Journal of Atmospheric and Oceanic Technology 26:2,243–2,255, https://doi.org/10.1175/2009JTECHO638.1.

Jackson, C.R., J.C.B. da Silva, and G. Jeans. 2012. The generation of nonlinear internal waves. Oceanography 25(2):108–123, https://doi.org/10.5670/oceanog.2012.46

Jeans, G., M. Calverley, W. Jeffery, C. Jackson, V. Vlasenko, and A.R. Osborne. 2012. Worldwide internal soliton criteria. Paper presented at Oceanology International 2012, London, UK, March 14–15, 2012.

Kadomtsev, B.B., and V.I. Petviashvili. 1970. On the stability of solitary waves in weakly dispersive media. Soviet Physics, Doklady 15:539–541. 

Kudryavtsev, V., D. Akimov, J.A. Johannessen, and B. Chapron. 2005. On radar imaging of current features: 1. Model and comparison with observations. Journal of Geophysical Research 110, C07016, https://doi.org/​10.1029/2004JC002505.

Li, X., P. Clemente-Colon, and K.S. Friedman. 2000. Estimating oceanic mixed-layer depth from internal wave evolution observed from RADARSAT-1 SAR. Johns Hopkins APL Technology Digest 21:130–135.

Liu, A.K., Y.S. Chang, M.-K. Hsu, and N.K. Liang. 1998. Evolution of nonlinear internal waves in the East and South China Seas. Journal of Geophysical Research 103(C4):7,995–8,008, https://doi.org/10.1029/97JC01918.

Lorenzzetti, J.A., and F.G. Dias. 2013. Internal solitary waves in the Brazilian SE continental shelf: Observations by synthetic aperture radar. International Journal of Oceanography 2013, 403259, https://doi.org/10.1155/2013/403259.

Mercier, M.J., M. Mathur, L. Gostiaux, T. Gerkema, J.M. Magalhães, J.C. da Silva, and T. Dauxois. 2012. Soliton generation by internal tidal beams impinging on a pycnocline: Laboratory experiments. Journal of Fluid Mechanics 704:37–60, https://doi.org/10.1017/jfm.2012.191.

Miles, J.W. 1977. Obliquely interacting solitary waves. Journal of Fluid Mechanics 79:157–169, https://doi.org/10.1017/S0022112077000081.

Osborne, A.R., J.R. Brown, T.L. Burch, and R.I. Scarlet. 1977. The influence of internal waves on deepwater drilling operations. Paper presented at the Offshore Technology Conference, May 2–5, 1977, Houston, TX.

Osborne, A.R., and T.L. Burch. 1980. Internal solitons in the Andaman Sea. Science 208:451–460, https://doi.org/10.1126/science.208.4443.451.

Porter, D.L., and D.R. Thompson. 1999. Continental shelf parameters inferred from SAR internal wave observations. Journal of Atmospheric and Oceanic Technology 16:475–487, https://doi.org/​10.1175/1520-0426(1999)016<0475:

Robinson, I.S. 2010. Discovering the Ocean from Space: The Unique Applications of Satellite Oceanography. Springer, 638 pp.

Romeiser, R., and W. Alpers. 1997. An improved composite surface model for the radar backscattering cross section of the ocean surface: Part 2. Model response to surface roughness variations and the radar imaging of underwater bottom topography. Journal of Geophysical Research 102(C11):25,251–25,267, https://doi.org/10.1029/97JC00191.

Sethian, J.A. 1999. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, 2nd ed. Cambridge University Press, 378 pp.

Shroyer, E. 2008. Varicose waves. (Box in Small-scale processes in the coastal ocean by J.N. Moum, J.D. Nash, and J.M. Klymak.) Oceanography 21(4):28, https://doi.org/​10.5670/oceanog.2008.02

Wang, C., and R. Pawlowicz. 2012. Oblique wave‐wave interactions of nonlinear near‐surface internal waves in the Strait of Georgia. Journal of Geophysical Research 117, C06031, https://doi.org/10.1029/2012JC008022.

Zabusky, N.J., and M.A. Porter. 2010. Soliton. Scholarpedia 5(8):2068, https://doi.org/​10.4249/scholarpedia.2068.

Zhao, Z., V. Klemas, Q. Zheng, and X.-H. Yan. 2004. Remote sensing evidence for baroclinic tide origin of internal waves in the northeastern South China Sea. Geophysical Research Letters 31, L06302, https://doi.org/10.1029/2003GL019077.