Depth inversion in shallow water based on nonlinear properties of shoaling periodic waves 1

Two depth inversion algorithms applicable to coastal waters are developed, calibrated, and validated based on results of computations of periodic waves shoaling over mild slopes, in a two-dimensional numerical wave tank based on fully nonlinear potential flow theory. In actual field situations, these algorithms would be used to predict the cross-shore depth variation h based on sets of values of wave celerity c and length L, and either wave height H or left-right asymmetry s2=s1, simultaneously measured at a number of locations in the direction of wave propagation, e.g., using video or radar remote sensing techniques. In these depth inversion algorithms, an empirical relationship, calibrated for a series of computations in the numerical wave tank, is used to express c as a function of relative depth koh and deep water steepness koHo. To carry out depth inversion, wave period is first predicted as the mean of observed L=c values, and Ho is then predicted, either based on observed H or s2=s1 values. The celerity relationship is finally inverted to predict depth h. The algorithms are validated by applying them to results of computations for cases with more complex bottom topography and different incident waves than in the original calibration computations. In all cases, rms-errors for the depth predictions are found to be less than a few percent, whereas depth predictions based on the linear dispersion relationship—which is still the basis for many state-of-the-art depth inversion algorithms—have rms-errors 5 to 10 times larger.