Gary D. Egbert

TL;DR: In this paper, a relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described, where the GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations.

Abstract: Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

TL;DR: Satellite altimeter data from Topex/Poseidon is used to map empirically the tidal energy dissipation and shows that approximately 1012 watts—that is, 1 TW, representing 25–30% of the total dissipation—occurs in the deep ocean, generally near areas of rough topography.

TL;DR: In this paper, a general mathematical framework for Jacobian computations arising in electromagnetic (EM) geophysical inverse problems is developed, which is based on the discrete formulation of the forward problem and divides computations into components (data functionals, forward and adjoint solvers, model parameter mappings).

TL;DR: In this article, the authors show that all of the statistical assumptions usually used in estimating transfer functions for geomagnetic induction data fail at periods from 5 min to several hours at Geomagnetic mid-latitudes.