The depth-inversion problem in shallow water

Two Depth Inversion Algorithms (DIAs) were developed and validated using on results of computations for the shoaling of periodic waves over mild slopes, in a two-dimensional numerical wave tank, based on fully nonlinear potential flow theory. The first algorithm, DIA1, uses sets of values of wave celerity c, height H, and spatial wavelengths L-c and L-t, simultaneously measured at a number of locations x(i) (i = 1,..., N) in the direction of wave propagation (e.g., using remote sensing techniques), to predict the depth variation h(x(i)). The second algorithm, DIA2 uses spatial wave asymmetry s(2)/s(1) calculated from wave phase, instead of H. Results indicate that state-of-the-art depth inversion methods based on the linear dispersion relation may lead to large errors (50-70%) for the depth prediction in very shallow water, whereas the present methods are 3-10 times more accurate.