For a quantitative interpretation of the radar signatures, we need to know some radar parameters and environmental parameters. The frequency of the ERS-1 SAR is 5.3 GHz (C band), the polarization is VV, and the incidence angle is about 23°. The Rhine plume image was acquired during an ascending overpass, looking to the right, as indicated by the red arrows. The backscattered power detected by the SAR is basically proportional to the intensity of ocean waves with wavelengths of about 7 cm which propagate in and against this direction. The satellite's heading was 344° i.e., North is 16° clockwise from the vertical axis of the image.

According to weather observations at Hoek van Holland, the wind speed was about 11 m/s from 210°. In principle, this information could also be retrieved from the SAR image itself, using a wind retrieval tool.

The time of the SAR image acquisition was 2:07 hours before high water in Hoek van Holland. According to a current atlas, the tidal currents at this phase are quite small and converge in the test area, making the water level rise. At the Rhine plume front itself we expect some current shear and convergence, since certain circulation patterns, including a slow rotation, must be established to maintain a clear separation between a freshwater lens and the ambient seawater for some time.

We will now have a closer look at the region marked by the white square.

In order to determine the current variations at the front, we will now try to reproduce this observed radar signature with a numerical SAR imaging model, which can simulate theoretical SAR signatures of a given current field. For example, we can try a simple convergent current pattern (modeled by a hyperbolic tangent function) as given by the blue line, and we obtain the simulated SAR signature given by the red line. The radar imaging model M4S simulates such radar signatures by computing the spatial variations of the surface wave spectrum, which result from hydrodynamic wave - current interaction, converting the resulting wave spectra into Doppler spectra of the backscattered radar signal, and generating expectation-value SAR signatures from the Doppler spectra according to SAR imaging theory.

This animation shows results of test simulations with pure current shears in the vicinity of the front. Assuming a cyclonal rotation of the Rhine plume, we expect a (small) positive current in y direction on the left and a (small) negative current on the right of the front. This would result in a dark signature! However, even if we reverse the shear current pattern, the simulated SAR signatures are much smaller than the observed one, even for unrealistically strong current shears. We conclude that the current shear at the front cannot be the dominant source of the observed SAR signature.

Better agreement between model results and observations is obtained with a pure convergence at the front, as shown in this animation, which illustrates the iterative current field optimization procedure. Hydrodynamic modulation of the surface waves by convergent currents appears to be the main source of the observed bright SAR signature of the Rhine plume front. According to M4S, the current component normal to the front changes by about 0.4 m/s within about 20 m. This would be the main information extracted from the given SAR image by using MARSAIS tools. However, quantitative results obtained in this context are somewhat questionable, since the model validation is very difficult.

Finally, we can have another look at the effect of shear currents in combination with the best-fit solution for the convergent cross-front current component. The dependence of the simulated SAR signature on the current shear is still quite weak. Accordingly, we will usually not be able to determine the strength of shear currents at oceanic fronts from their SAR signatures.