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Tides are of course not just a source of noise. With data taken from moving platforms (e.g., ships, Lagrangian drifters, satellites) spatial and temporal variations are aliased, rendering a simple filtering scheme untenable, and again requiring accurate maps of tidal fields. For a fixed observation site, such as a semipermanent mooring, tides can be removed by filtering of time series. Here the tides are often seen as a nuisance that must be removed from the data prior to studies of longer period oceanographic variations. Knowledge of tides is of value in many scientific studies as well. As a result, for many practical applications in the marine environment (e.g., shipping and modeling of pollution dispersal) accurate maps of tidal currents or elevations are often indispensable. Use of OTIS is illustrated by developing a new regional-scale (1/6°) model of tides in the Indonesian Seas.Ī large fraction of the variance in many oceanographic variables is due to tides.

OTIS regional and local GI tidal modeling (with grids containing up to 10 5 nodes) require only a few hours on a common desktop workstation. Approximate GI solution methods, based on using a reduced set of representers, allow very large datasets to be inverted. OTIS includes software for generating grids, prior model covariances, and boundary conditions for time stepping the nonlinear shallow water equations to generate a first guess or prior solution for preliminary processing of TOPEX/Poseidon altimeter data for solution of the GI problem and for computation of posterior error bars. The efficient representer calculation forms the basis for the Oregon State University (OSU) Tidal Inversion Software (OTIS). While the dynamical calculations involve elevations alone, depth-averaged currents can be directly assimilated into the tidal model with this approach. This allows rational assumptions about errors in the SWE, with soft momentum balance constraints (e.g., to account for inaccurate parameterization of dissipation), but holds mass conservation constraints.

By retaining the first-order SWE system (defined in terms of both elevations and currents) in the definition of the discretized GI penalty functional, complete generality in the choice of dynamical error covariances is retained. Once this matrix is factored representers can be calculated rapidly. To make representer computations efficient, the SWEs are solved in the frequency domain by factoring the coefficient matrix for a finite-difference discretization of the second-order wave equation in elevation.

The GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations (SWEs). A computationally efficient relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described.