View source for Talk:Bathymetry German Bight from X-band radar

=Review by Andrea Taramelli (January 2013)=


There exists an extensive literature on the analysis of radar images of patterns of well developed swell at the sea surface. The refraction of long swell at a water depth smaller than 50 m is caused by the influence of underwater topography in the coastal areas. The X-band radar is able to image the sea surface with a resolution up to 1 m and individual water waves with wavelengths down to 20m are delectable. 


==Early developments==
The fact that under water bottom topographic features become visible on radar images has started to be an innovative issue since the 80’s. Early research was conducted by de Loor and Brunsveld van Hulten<ref>de Loor, G.P. and Brunsveld van Hulten, H.W.  1978. Microwave measurements over the North Sea. Boundary Layer Meteorol. 13: 113- 131</ref><ref>de Loor, G.P. 1981. The observation  of tidal patterns, currents, and bathymetry with SLAR imagery of the sea. IEEE J. Oceanic Eng. OE-6: 124-129</ref> with signatures of underwater sand waves on K band (36 GHz) real aperture radar (RAR) from an aircraft over the North Sea. Later, similar evidence were also found on radar images obtained by other systems like Seasat L band (1.2 GHz) synthetic aperture radar (SAR) (Fu and Holt, 1982<ref>Fu, L.L. and Holt, B.  1982. Seasat views oceans and sea ice with synthetic aperture radar. JPL Publ. 81-120, 200 pp., Jet Propulsion Lab., Pasadena, Calif.</ref>; Lodge, 1983<ref>Lodge, D.S.W. 1983. Surface expressions of bathymetry on SEASAT synthetic aperture radar images. International Journal of Remote Sensing 4: 639-653</ref>; Alpers, 1985<ref>Alpers, W. 1985. Theory of radar imaging of internal waves. Nature 314(6008): 245-247</ref>). Since the penetration depth of microwaves in seawaters is only of the order of millimeters to centimeters, the bottom topography at depths of ten meters can be reconstructed via surface effects. The imaging mechanism is a two-step process: first the spatial variations of the water depth lead to a modulation of the tidal flow. The resulting surface current gradients give rise to hydrodynamic modulation of the surface roughness, which can be detected by the radar system.

Quantitative models for radar signatures of underwater bottom topography were presented starting from mid 80’s (Alpers and Hennings, 1984<ref name=AH>Alpers, W., and Hennings, I. 1984. A theory of the imaging mechanism of underwater bottom topography by real and synthetic aperture radar. J. Geophys. Res. 89: 10,529-10,546</ref>; Shuchman et al., 1985<ref>Shuchman, R.A., Lyzenga, D.R. and Meadows, G.A. 1985. Synthetic aperture radar imaging of ocean-bottom topography via tidal-current interactions: theory and observations Int. J. Remote Sensing 6: 1179-1200</ref>). In these investigations the current modulation is described by a continuity equation, the wave-current interaction by weak hydrodynamic interaction theory in the relaxation time approximation (Alpers and Hasselman, 1978<ref>Alpers, W. and Hasselmann, K. 1982. Spectral signal to clutter and thermal noise properties of ocean wave imaging synthetic aperture radars. Int. J. Remote Sens. 3: 423–446</ref>; Hughes, 1978<ref>Hughes, B. A. 1978, The effect of internal waves on surface wind waves, 2. J. Geophys. Res. 83, 455</ref>; Plant, 1982<ref>Plant, W.J. 1982. A relationship between wind stress and wave slope, J. Geophys. Res. 87: 1961-1967</ref>; Plant, 1986<ref>Plant, W.J. 1986. A two-scale model of short wind-generated waves and scatterometry. J. Geophys. Res. 91: 10,735-10,749</ref>), and the interaction between radar signal and sea surface by Bragg scattering theory (Venezuela, 1978<ref>Valenzuela, G.R. 1978. Theories for the interaction of electromagnetic and ocean waves - A review. Boundary Layer Meteorol. 13: 61-85</ref>). This approach assumes the backscattered power to be proportional to wave height spectral density of the short Bragg waves, that is, of ocean waves wavelength comparable to the radar wavelength. Basically it predicts that the relative deviation of the backscattered power from its equilibrium value is proportional to the local current gradient and the so-called relaxation time of the Bragg waves. On the basis of this definition a strong dependency between predictions of the model (Alpers and Hennings, 1984<ref name=AH/>) and measurements has been found only at relatively low microwave frequencies like 1 GHz (L band), while observed modulation depth at higher frequencies like 10 Ghz (X band) are underestimated by the models as much as 2 orders of magnitude. Further developments of the Radar modeling system (Romeiser et al., 1994<ref>Romeiser, R., Schmidt, A. and Alpers, W.  1994. A three-scale composite surface model for the ocean wave-radar modulation transfer function. J. Geophys. Res. 99: 9785-9801</ref>; Romeiser et al., 1997<ref>Romeiser, R., Alpers, W. and Wismann, V.  1997. An improved composite surface model for the radar backscattering cross section of the ocean surface, 1, Theory of the model and optimization/validation by scatterometer data, J. Geophys. Res. 102: 25,237-25,250</ref>) have shown that composite surface models are able to predict a similar radar signature at L and X band for surface current patterns over internal waves, that appears to be in good agreement with experimental results.

==SAR Inversion Methodology==
The method to retrieve the bottom topography from X-SAR scene is based on the inversion of the wave shoaling and refraction relationships in shallow waters.  The basic theory of these methods is the retrieval of the bathymetry from the changing wave characteristics deduced from the SAR data, assuming a model of wave propagation on the irregular sea bottom (Brush, 2011<ref>Brusch, S. 2011. High Resolution Wind and Bathymetry Maps from Synthetic Aperture Radar to increase Ship Safety and Ship Traffic Monitoring from Space. Doctorate Dissertation at the Universität Hamburg</ref>).
Wave shoaling is the effect of increasing wave height when the surface wave approaches shallow waters. When the wave reaches shallow waters it slows down gradually and the wavelength reduces. As the wave energy is roughly constant, the reduction of the wave speed is balanced by the growth in height. Wave refraction is the change of direction of the wave front due to the fact that waves propagate faster in deep than in shallow water. The consequence is that the wave front upon approaching the coast rotates up to become parallel to the bathymetric line.

A method was developed for tracking wave rays influenced by bathymetry, depending on changing of swell wavelength and direction. In addition, the individual breaking waves leave a signature in high-resolution SAR images, which allows to determine the height of breaking waves. Analysis of the SAR image spectra allows to obtain the peak wavelength, direction and height of wave systems. The extraction of the wave parameters from SAR can be performed by exploiting low orbit satellite SAR sensors as COSMO SkyMed and TerraSAR-X by fitting the known relationship between the spectrum energy of the SAR scene and the Significant Wave Height (Brush et al., 2011<ref>Brush, S., Held, P., Lehner, S., Rosenthal, W. and Pleskachevsky, A. 2011. Underwater Bottom-Topography in coastal areas from TerraSAR-X data. International Journal of Remote Sensing 32: 4527-4543</ref>; Li et al., 2010<ref>Li, X., Lehner, S. and Rosenthal, W. 2010. Investigation of Ocean Surface Wave Refraction Using TerraSAR-X Data, IEEE Transaction on Geoscience and Remote Sensing 48 : 830 - 840</ref>).

A crucial point in this process is the selection of the X-SAR dataset used for the bathymetry retrieval, that necessarily consists of SAR images with well developed swell in the coastal area. Significant periods have to be selected from large datasets collected all year around and selection criteria must be adopted to focus on periods when this kind of events are more probable to occur. Selection criteria based on wind statistics allow to focus on specific periods of the year when strong winds are known to blow in a large area surrounding the study site.

==References==
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