Other Applications (Continuation)

We have developed an algorithm for automatic derivation of the bathymetry in coastal seas using Sentinel-1 and TerraSAR-X satellite data.

Recently, the TanDEM-X mission successfully finished generating a new high-resolution topography worldwide. However, about 70% of the Earth is covered by oceans, where the sea floor topography cannot be measured by a single spaceborne Earth Observation technology today. With growing efforts in global shipping and offshore constructions like wind parks, the knowledge of bathymetry becomes increasingly important. Our algorithm can retrieve the bathymetry in continental shelf areas with water depths from about 100 to 10 meters. In these depths, the shoaling effect leads to swell waves becoming shorter when reaching shallower waters.

The developed algorithm is part of a maritime SAR processing chain designed to derive multiple L2 products like wind, sea state, ship detection or sea ice automatically and in Near Real Time (NRT). For the bathymetry retrieval, the land is masked out and the image is subdivided into a grid of square subscenes. In preparation for the FFT analysis, spectral contaminations like ships, wind parks, current boundaries or wind streaks are filtered out for an accurate sea state and wave length retrieval. Then we can retrieve the peak wave length for each subscene from the FFT spectra.

To calculate the water depth, the dispersion relation in intermediate depth waters must be solved, which requires the peak wave length and peak wave period as parameters. However, the wave period cannot be retrieved from SAR images. Measurement buoys for wave period data are very sparse, but can be used as input when available. We therefore use existing coarse datasets like General Bathymetric Charts of the Oceans (GEBCO) as first guess data on the water depth. The optimal peak wave period is determined with a root mean square deviation (RMSD) analysis comparing the depths at every grid point of the scene for a range of possible wave periods and using the one resulting in the smallest deviation. With this, the water depth can then be calculated at every grid point. Comparisons to existing bathymetry data yield an unbiased RMSD of about 12 meters for the full 10m to 100m range of depths or about 15% of the depth.

The presented method requires the presence of long swell waves and light to medium wind, hence, not every SAR acquisition of coastal waters is suitable for bathymetry derivation. For this application, TerraSAR-X is technically preferable due to its ability to detect wavelengths down to 30m, where Sentinel-1 requires longer wavelengths of 120m for bathymetry retrieval. However, TerraSAR-X data are only available when previously ordered while Sentinel-1 data are acquired constantly and freely accessible from the Copernicus data hub, which facilitates the retrieval of suitable scenes worldwide.

It is well known that stratified flows through a channel with a lateral contraction can generate Internal Solitary Waves (ISWs) when the flow speed is nearly critical (or transcritical) with respect to the linear long internal wave phase speed. These waves propagate in the upstream direction and may be arrested (or trapped) during the early stages of their lives (da Silva & Helfrich, 2008). Just as a compressible flow suddenly changes from a supersonic to subsonic state by going through a shock wave, a supercritical flow in a shallow canal can change into a subcritical state by going through a hydraulic jump. In supercritical (barotropic) flow conditions, obliquely oriented hydraulic jumps occur (e.g., Ippen and Harleman 1956), in analogy to shock waves in supersonic flows. Since disturbances generated in the supercritical flow cannot propagate directly upstream, they instead accumulate along a hydraulic jump oriented at an angle (known as the Mach angle) that is oblique to the flow direction. There is an equivalent phenomenon in stratified flows, which theory treats oblique internal hydraulic jumps as arrested, long, interfacial waves. However, such internal hydraulic features have not been previously reported in the oceanography literature, at least not as a long and recurring phenomenon (though the general concept has been applied to describe observed obliquity of tidal, internal hydraulic jumps at the Columbia River mouth; Honegger et al., 2017). Here we present, for the first time, Synthetic Aperture Radar (SAR) observations and analyses of recurring, oblique, internal hydraulic jumps at the Penghu Channel of the South China Sea. The Penghu Channel can be characterized as a relatively shallow channel (average depth 150m) with a lateral constriction, into which the combined steady and tidal currents may easily reach supercritical speeds at the minimum breath of the channel. The jumps were identified in the SAR image data archives from various missions (e.g. ERS, ENVISAT, TerraSAR-X, Sentinel-1) as recurring phenomenon. Jump occurrence is revealed by (i) SAR signatures of a sharp gradient in the surface currents and it is corroborated by (ii) the transition from supercritical to subcritical flow in the cross-jump direction via our knowledge of velocity and density measurements. Using a two-layer approximation, observed jump (Mach) angles are shown to lie within the theoretical bounds given by the critical internal long-wave (Froude) angle and the arrested maximum-amplitude internal bore angle, respectively. The jump’s orientation and associated uncertainty are estimated with a Radon transform technique. Variability of the jump angles is shown to be consistent with that expected from the two-layer model, applied to varying stratification and current speed over a range of tidal conditions and seasonal steady currents. Correspondence between the SAR observations and the remarkable simple theory demonstrates its utility in characterizing internal hydraulic phenomena. The crestlength extent and spatial coverage of the phenomenon (tens of crests up to 25km long) implies significant energy dissipation through mixing in the Channel. Energy budget considerations and implications to mixing are briefly discussed based on the SAR observations and our knowledge of the along-channel stratification.

The theory of radar imaging of internal waves developed by Alpers (1985) is based on weak hydrodynamic interaction theory and Bragg scattering theory. It is able to describe quite well the observed radar signatures of internal waves at L-band, but underestimates the strength of the modulation (modulation depth) at C-and X-band. Although this theory has also been applied for describing radar signatures of internal solitary waves (ISWs) at X-band (Romeiser and Graber, 2015), one has to use an unrealistic value of the relaxation rate, which is not supported by theory. The physical mechanism responsible for the enhanced modulation at C- and X-band is scattering at breaking surface wave, which has not been included in the conventional imaging theory. It is well known that ISWs often manifest themselves on the sea surface as bands of very strong roughness, which include breaking waves with wavelengths of the order of meters. Such bands are observed even when there is no wind and the sea is glassy. Obviously, the generation of roughness bands associated with breaking surface waves cannot be explained by weak hydrodynamic interaction theory, where the variable surface current associated with ISWs modulates “gently” the Bragg waves responsible for the radar backscattering, Furthermore, the radar backscattering at C-band and X-band from these roughness bands cannot be explained by Bragg scattering theory alone; it requires taking into account also radar backscattering from breaking waves, which, in contrast to Bragg scattering, is non-polarized scattering (Kudryavtsev et al., 2005). In this paper we analyze the relative contribution of scattering from breaking surface waves to the total radar backscattering (Bragg and non-polarized scattering). To this end, we have analyzed TerraSAR-X images acquired at HH and VV polarizations over the Strait of Gibraltar and Sentinel-1A images acquired at VV and VH polarizations over the South China Sea at low wind speeds. We show that backscattering from the leading ISW fronts is dominated by non-polarized scattering, while backscattering from the rear is a mixture of Bragg and non-polarized scattering. Furthermore, we have analyzed a TerraSAR-X image acquired at HH polarization in the Stripmap Mode with a resolution of 3 m over the Amazone Shelf showing sea surface signatures of small-scale, but strong ISWs propagating upstream. Due the narrow roughness bands and the high resolution of this SAR image, we were able to determine the azimuthal displacement of “sea spikes” (elements of very strongly enhanced radar backscatter) due to the motion of these scatter elements. We have estimated the velocity of these scatter elements associated with wave breaking from the azimuthal shifts in the SAR image and found that they result from breaking of waves with wavelengths of the order of 1 m.