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. Wh...

/pdf/efficient-inverse-modeling-of-barotropic-ocean-tides-2awn93pupi.pdf

Efficient Inverse Modeling of Barotropic Ocean Tides

▪ Abstract The 100 kyr quasiperiodic variation of continental ice cover, which has been a persistent feature of climate system evolution throughout the most recent 900 kyr of Earth history, has occurred as a consequence of changes in the seasonal insolation regime forced by the influence of gravitational n-body effects in the Solar System on the geometry of Earth's orbit around the Sun. The impacts of the changing surface ice load upon both Earth's shape and gravitational field, as well as upon sea-level history, have come to be measurable using a variety of geological and geophysical techniques. These observations are invertible to obtain useful information on both the internal viscoelastic structure of the solid Earth and on the detailed spatiotemporal characteristics of glaciation history. This review focuses upon the most recent advances that have been achieved in each of these areas, advances that have proven to be central to the construction of the refined model of the global process of glacial isos...

GLOBAL GLACIAL ISOSTASY AND THE SURFACE OF THE ICE-AGE EARTH: The ICE-5G (VM2) Model and GRACE

GLOBAL GLACIAL ISOSTASY AND THE SURFACE OF THE ICE-AGE EARTH: The ICE-5G (VM2)

The GRACE satellite mission, scheduled for launch in 2001, is designed to map out the Earth's gravity field to high accuracy every 2–4 weeks over a nominal lifetime of 5 years. Changes in the gravity field are caused by the redistribution of mass within the Earth and on or above its surface. GRACE will thus be able to constrain processes that involve mass redistribution. In this paper we use output from hydrological, oceanographic, and atmospheric models to estimate the variability in the gravity field (i.e., in the geoid) due to those sources. We develop a method for constructing surface mass estimates from the GRACE gravity coefficients. We show the results of simulations, where we use synthetic GRACE gravity data, constructed by combining estimated geophysical signals and simulated GRACE measurement errors, to attempt to recover hydrological and oceanographic signals. We show that GRACE may be able to recover changes in continental water storage and in seafloor pressure, at scales of a few hundred kilometers and larger and at timescales of a few weeks and longer, with accuracies approaching 2 mm in water thickness over land, and 0.1 mbar or better in seafloor pressure.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB02844

Time variability of the Earth's gravity field: Hydrological and oceanic effects and their possible detection using GRACE

During the 1990s, a large number of new tidal atlases were developed, primarily to provide accurate tidal corrections for satellite altimetry applications. During this decade, the French tidal group (FTG), led by C. Le Provost, produced a series of finite element solutions (FES) tidal atlases, among which FES2004 is the latest release, computed from the tidal hydrodynamic equations and data assimilation. The aim of this paper is to review the state of the art of tidal modelling and the progress achieved during this past decade. The first sections summarise the general FTG approach to modelling the global tides. In the following sections, we introduce the FES2004 tidal atlas and validate the model against in situ and satellite data. We demonstrate the higher accuracy of the FES2004 release compared to earlier FES tidal atlases, and we recommend its use in tidal applications. The final section focuses on the new dissipation term added to the equations, which aims to account for the conversion of barotropic energy into internal tidal energy. There is a huge improvement in the hydrodynamic tidal solution and energy budget obtained when this term is taken into account.

https://hpiers.obspm.fr/combinaison/documentation/articles/Modelling_Ocean_Tides_Lyard_FES2004.pdf

Modelling the global ocean tides: modern insights from FES2004

The static deformation of an elastic half-space by surface pressure is reviewed. A brief mention is made of methods for solving the problem when the medium is plane stratified, but the major emphasis is on the solution for spherical, radially stratified, gravitating earth models. Love-number calculations are outlined, and from the Love numbers, Green's functions are formed for the surface mass-load boundary-value problem. Tables of mass-load Green's functions, computed for realistic earth models, are given, so that the displacements, tilts, accelerations, and strains at the earth's surface caused by any static load can be found by evaluating a convolution integral over the loaded region.

W. E. Farrell

Papers

Deformation of the Earth by surface loads