Variational parameter estimation for a two‐dimensional numerical tidal model

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Abstract
It is shown that the parameters in a two‐dimensional (depth‐averaged) numerical tidal model can be estimated accurately by assimilation of data from tide gauges. The tidal model considered is a semi‐linearized one in which kinematical non‐linearities are neglected but non‐linear bottom friction is included. The parameters to be estimated (bottom friction coefficient and water depth) are assumed to be position‐dependent and are approximated by piecewise linear interpolations between certain nodal values. The numerical scheme consists of a two‐level leapfrog method. The adjoint scheme is constructed on the assumption that a certain norm of the difference between computed and observed elevations at the tide gauges should be minimized. It is shown that a satisfactory numerical minimization can be completed using either the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) quasi‐Newton algorithm or Nash's truncated Newton algorithm. On the basis of a number of test problems, it is shown that very effective estimation of the nodal values of the parameters can be achieved provided the number of data stations is sufficiently large in relation to the number of nodes.

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