Refinements to an Optimized Model-Driven Bathymetry Deduction Algorithm

In this paper we describe a numerical algorithm which deduces characteristics of the bottom bathymetry given free surface elevation records dense in space but sparse in time. The method makes use of the Levenberg-Marquardt numerical optimization scheme in conjunction with a time-domain nonlinear model. Iteration occurs until the mismatch between the free surfaces of the data and model are minimized; the bathymetry is adjusted in order to achieve this minimum. The sensitivity measure is a by-product of the calculation, and determines the invertibility of the system. Due to convergence concerns, we limit ourselves to deduction of bathymetric profile parameters. Tests of the system using monochromatic, irregular and groupy waves show favorable results; the latter is particularly notable given the difficulty standard inversion methods have had with groupy waves. A two-stage system is also outlined, in which a simple parameterization for a nearshore bar is developed and utilized. The first stage determines the mean profile, while the second stage determines the bar characteristics using the first stage results as the initial iterate. To extend the method's capabilities further, the use of phase speed records is discussed.