Efficient Inverse Modeling of Barotropic Ocean Tides

Abstract

A computationally efficient relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described. The GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations (SWEs). 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. Once this matrix is factored representers can be calculated rapidly. 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. 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. While the dynamical calculations involve elevations alone, depth-averaged currents can be directly assimilated into the tidal model with this approach. The efficient representer calculation forms the basis for the Oregon State University (OSU) Tidal Inversion Software (OTIS). 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. Approximate GI solution methods, based on using a reduced set of representers, allow very large datasets to be inverted. OTIS regional and local GI tidal modeling (with grids containing up to 105 nodes) require only a few hours on a common desktop workstation. Use of OTIS is illustrated by developing a new regional-scale (1/6°) model of tides in the Indonesian Seas.