The depth - inversion problem in shallow water 1

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 twodimensional numerical wave tank, based on fully nonlinear potential flow theory. The first algorithm, DIA1, uses sets of values of wave celerity c, heightH , 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 (5070%) for the depth prediction in very shallow water, whereas the present methods are 3-10 times more accurate.