# Current and Bathymetry Mapping in Bays, Harbors, and Nearshore Regions

Our marine radar product line allows the extraction of surface currents from time the dependence of images of ocean wave patterns, processed using 3D Fast Fourier Transform analyses. A typical wave pattern image is shown below at roughly 6-m pixel size, and consecutive patterns collected at 1.85 second intervals shown in the movie demonstrate their translation across the scene.

One snips a square of pixels 2N; on a side, typically 32 to 64, from each of the series and submits it to 3D-FFT analysis. We find that the image intensity energy lies on the hyperbola of revolution defined by the deep water dispersion relation for gravity waves, Ω²=gK. A plot of this function in the KxKyΩ plane is demonstrated below. More specifically, the FFT analysis using 32 rotations at a 1.85-sec period, integrating for 59.2 seconds, provides slices at 0.0169 Hz spacing on the vertical axis in deep water.

For shallow water, the dispersion parabola of revolution is now defined by the shallow water approximation: ²=gK TANH(KD), where D is the local mean depth. The effect is to flatten the dispersion surface as is shown below.

Finally, in the presence of currents the dispersion rule is modified so that the surface of revolution is tilted in the direction of the current, as is shown below.

We have conducted experiments using these methods in shallow water where the depth dependence is retrieved, and examples of 3D FFT spectra are shown below, effectively horizontal slices through the surface above. The yellow circle represents the intersection with the ? axis of the shallow water surface (2nd cased above) at a 0.0169 Hz increment, with only a subset shown of the total of 16. The red circle represents the deep water dispersion relation. Applying this same analysis to deep water currents would shift the red circle off the origin in each case.

Refer to our 2001 paper on the subject for more information.