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 Lc and Lt, simultaneously measured at a number of locations xi (i = 1, ..., N) in the direction of wave propagation (e.g., using remote sensing techniques), to predict the depth variation h(xi). The second algorithm, DIA2, uses spatial wave asymmetry s2/s1 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