Bathymetric survey and current field observation

This Microwave radar techniques uses using local gravity wave dispersion Special challenge in coastal protection management is provided by the management of sandy coastlines. Here humans interact with the dynamic processes of the ocean with the shore line and undertake measures for their stabilization by measures such as beach nourishment. The interference of humans with nature must be attended by intense observations. The increase of sand to the coastal system means the survey of the sand’s residence on the one side, but on the other side the observation of the forces causing erosion, transport and deposition of sand. For this it is not enough to acquire time series of physical parameters at single observation points. It requires area mapping observations to identify the response within the system and to assign the process to their origins, either occasional forcing by storms or to continuous forcing by the tidal cycle, for instance. We will point out in the following the methods of radar hydrography allowing area covering and continuous survey of the forcing as well as the response of the bathymetry. The area of investigation is List West at the north end of the Island Sylt in the German bight. In the current paragraph we present the assessment of the bathymetry and the current field by imaging the wave backscatter using marine radar.

Time series of these images are inversed locally where the linear wave theory is valid and the surface wave dispersion holds. The algorithm used is known as “Dispersive Surface Classificator” (DiSC). The method has been developed at the Radar Hydrography Department of Helmholtz-Zentrum Geesthacht and is licensed as commercial product by Vision 2 Technology GmbH, partner of the Geesthachter Innovations- und Technologie-Zentrum (GITZ). The method is based on the linear wave theory that allows, by tracking of wave crest in space and time, the determination of the parameters water of depth and current vector. The dispersion relation of sea-surface waves is derived from the Eulerian equations of motion, the continuity equation and the dynamic and kinematic boundary conditions at the sea surface and the sea floor.


A detailed description of the derivation of the dispersion relation is given in Senet et al., (2001[5]). The analysis of the image sequences of the inhomogeneous wave field provides a set of physical parameters on a local spatial scale. The basic idea of the method is that, in shallow waters, the waves vary their propagation (phase speed and wave number) locally and thus impresses the local bathymetry into the image series. The same mechanism acts via the local current that may be assessed by the DiSC as well.

The water depth and the current vector are free parameters influencing the shape of the dispersion shell in the wave-number frequency domain. An important characteristic of this application is that the radar has not to be calibrated, as the wave height is not influencing the wave dispersion. From the three dimensional radar observation the three dimensional power spectra in wavenumber -frequency domain is calculated by a Fourier Transformation. Next the shape of the actual effective dispersion is deduced by fitting the detected power values to a plane approximating the dispersion. Deviations from the undisturbed dispersion are used to determine the local water depth and current vector, Senet et al., (2007[6]). The local results are composed in spatial hydrographic-parameter maps.

The method is illustrated in figure 1 and the main steps of analysis are the following:
• preservation of the complex-valued 3D FFT image spectrum,
• filtering techniques of complex spectrum to separate the wave signal from noise, in contrast to the global method that the power spectrum is filtered
• directional and dispersion separation of the complex-valued spectrum into spectral bins at 2D wavenumber planes of constant frequency,
• 2D inverse Fast Fourier Transformation(2D FFT-1) of the spectral bins, yielding complex-valued, one-component spatial maps in the spatio-frequency domain,
• calculation of spatial maps of local wavenumbers from the one-component images of constant frequency,
• composition of the one-component local wavenumber maps of constant frequency to local 3D spectra and
• calculation of spatial hydrographic-parameter maps from the local 3Dspectra.


The result of the DiSC is the instantaneous local depth, the bathymetry, and the estimation of the current field. Figure 2a and 2b illustrate the bathymetries averaged over a tidal cycle each before and after a storm (wind conditions 8-9 Bft.). The two maps have common reference, corrected by gauge measurements.

The difference of the sediment volume between the beginning and end of the storm, which under the conditions could be considered as the sediment net increase of the area of investigation, is estimated in 50.000m3, with ±10% of accuracy for each grid cell, under the assertion that the accuracy of the method is higher than 90% per cell as it is given in Flampouris et al., (2007[7]). In general, the assumption of the constant difference between two periods, of the mean sea level, is not strong enough and decreases the accuracy of the calculation.

Fig. 3 illustrates an example of the current field in the same area as above. The wind conditions are approximately 5 Beaufort and the date of the data acquisition is the 12th July of 2001. The false current values, which are too high close to the shore and over the shoal at the north west corner of the observation area, indicate grid cells for which the linear dispersion is not valid.

The method to scan the surface current field horizontally has been developed in the group of Radar Hydrography. It uses two coherent radar devices to produce high resolution current vector maps. In analogy to ADCP this method is named Radar Doppler Current Profiler. It consists by two radar systems, where the one antenna is permanently looking 45° ahead and the other 45° towards the stern and an intersection angle about 90°, see the two brown arrows directed south west in figure 1. While no long waves are acting the radial Doppler speeds are the sum of the wind friction and the surface current. By the Doppler relation we calculate the radial velocities from the backscattered signal for each range bin (length ~7.5m). Integrating the radar observations over a second, the radial speed results in an accuracy of 1,5 cm/s. The ship’s movements are compensated under the use of a PDGPS. The local impact of the actual wind friction is compensated by additional measurements from the stopped ship with the antenna looking in all wind directions with 10° steps. An automatic quality control rejects routinely faulty data. The post processing procedure is to compose the full surface current vector by merging the two components into a geo-coded grid with the grid distance up to 10 m. Figure 4 shows an example of a geo-coded RDCP current map with a grid resolution 100m during ebbing. An eddy with a diameter of about one nautical mile shows the outflow directed westward on the northern side of the gully and a counter current directed eastward on the south side. Comparison of the ADCP currents (see Fig. 5), which has been acquired during the same ship track, and the RDCP calculated arrows closed by the ship demonstrates that this new scanning method fits. Figures 6.a) and b), show the speed and direction of the surface current field within the tidal gully ‘Lister Tief’. This is overlaid by a current modulation due to the change in the cross section over submerged sand dunes, which interact with the ebb current in a way that we observe acceleration over the crest of the dunes and slowing down where the cross section is widening. The ADCP profile in figure 5 states these features in a vertical cross section map. The mentioned areas with acceleration and deceleration over the sand dunes are visible in the horizontal as well as in the vertical (up and down slide) speed components.

A model to estimate the bottom shear stress (BSS) was developed to assess the impact of the current field to the sand regime. As input this model needs the surface current, the bathymetry and the grain size of the sediment. Under the prediction of homogeneous water column, rough sea floor and no swell condition the impact of the tidal currents to the sea bottom is received.
The base of the model is the Taylor-Law which shows that we can calculate the current velocity in any depth of the water column when we know the velocity in another certain depth. So when we know the surface current vector field we know the velocity within the water layer close to the bottom.
The RDCP provides the surface water speed in a broad stripe parallel to the ship course.
The ADCP provides a vertical section to show the rotation of the current vector with increasing depth.
The bathymetry data provides the local water depth and the terrain slope. The slope is important for the form drag component of the shear stress equation, which dominates the resulting stress.
The rough sea floor condition is necessary for the calculation of the near bottom current. Over a smooth bed the change of the current velocity would be linear instead of logarithmic.
Two options to display the bottom shear stress have been chosen: 1st the absolute value of the resulting shear stress and 2nd the difference between this value and the critical bottom shear stress. The second option is helpful in localizing areas where bed motion is initialized with high probability. Up to now we can show the initiation but there cannot be made any suggestion about the transposition of the material. So we can only talk about potential erosion or deposition. The homogeneous water column was verified by repeated CTD measurements in the area.