Errors in bathymetric retrievals using linear dispersion in 3-D FFT analysis of marine radar ocean wave imagery

The phenomenon of ocean wave-shoaling, and the associated reduction of ocean wave phase speed with decreased water depth, provides useful information for inferring water depth D (bathymetry) in coastal environments. One strategy for relating D to phase speed C and wave-vector K of long wavelength ocean waves involves using the one-dimensional (1-D) linear (gravity wave) dispersion relationship C ²=g*tanh(KD)/K. In principle, this approach has limitations because the approach is based on a WKB approximation, so it cannot be applied when D varies appreciably over the wavelength of a shoaling wave. Also, the approach is restricted to waves that have small wave height. The author uses a set of marine radar image sequences and applies this linear approximation, using a 3-D FFT analysis of 88 sets of image sequences spaced half an hour apart. The author inverts the dispersion relation to solve for D. Depths between 3.6 and 5.8 m were tested, for root mean square (RMS) wave heights offshore between 8 and 3 m. The author shows that for low to moderate wave heights, the approach does generally retrieve the correct depth in water depths of 5 m and greater for moderate wave RMS heights. However, an increase in the RMS wave height from 1 m to 3.5 m produced a much poorer depth estimate, proving the need for an application of a nonlinear wave model to the problem. The errors also increase with shallower depths as expected, as the error dependence on depth and wave height is determined