Depth inversion in shallow water based on nonlinear properties of shoaling periodic waves |
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| Institution: | 1. Graduate Institute of Hydrological and Oceanic Sciences, National Central University, Taoyuan 320, Taiwan;2. Tainan Hydraulics Laboratory, Tainan 709, Taiwan;3. International Wave Dynamics Research Center, National Cheng-Kung University, Tainan 701, Taiwan;1. Department of Marine Technology, Amirkabir University of Technology, Hafez Ave. No. 424, Tehran, Iran;2. Department of Civil Engineering, Pardis Branch, Islamic Azad University, Tehran, Iran;1. United States Geological Survey, Pacific Coastal and Marine Science Center, 400 Natural Bridges Drive, Santa Cruz, CA 95060, USA;2. School of Earth and Environment, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia;3. Theiss Research, El Granada, CA 94018, USA;4. Woods Hole Oceanographic Institution, 266 Woods Hole Rd., Woods Hole, MA 02543, USA;5. Center for Applied Coastal Research, University of Delaware, 301 Du Pont Hall, Newark, DE 19716, USA;6. Department of Geoscience, San Francisco State University, 1600 Holloway Ave., San Francisco, CA 94132, USA |
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| Abstract: | Two depth inversion algorithms (DIA) 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 (FNPF) 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 DIAs, 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, root-mean-square (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 DIAs—have rms-errors 5 to 10 times larger. |
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