Many characteristics of the ocean circulation are reflected in the mean dynamic topography (MDT). Therefore observing the MDT provides valuable information for evaluating or improving ocean models. Using this information is complicated by the inconsistent representation of MDT in observations and ocean models. This problem is addressed by a consistent treatment of satellite altimetry and geoid height information on an ocean model grid. The altimetric sea surface is expressed as a sum of geoid heights represented by spherical harmonic functions and the mean dynamic topography parameterized by a finite element method. Within this framework the inversion and smoothing processes are avoided that are necessary in step-by-step approaches, such that the normal equations of the MDT can be accumulated in a straightforward way. Conveniently, these normal equations are the appropriate weight matrices for model-data misfits in least-squares ocean model inversions.Two prototypes of these rigorously combined MDT models, with an associated complete error description including the omission error, are developed for the North Atlantic Ocean and assimilated into a 3D-inverse ocean model. Preprint submitted to ElsevierJuly 26, 2011The ocean model solutions provide evidence that satellite observations and oceanographic data are consistent within prior errors.

Citation:Becker, S., J. M. Brockmann, and W.-D. Schuh (2014), Mean dynamic topography estimates purely based on GOCE gravity field models and altimetry, Geophys. Res. Lett., 41, 2063Lett., 41, -2069Lett., 41, , doi:10.1002 Abstract The quality of mean dynamic topography (MDT) models derived from an altimetric mean sea surface and a gravity field model mainly depends on the spatial resolution and accuracy of the particular gravity field model. We use an integrated approach which allows for estimating the MDT and its (inverse) covariance matrix on a predefined grid which is one of the requirements for ocean data assimilation. The quality and accuracy of the MDT directly reflects the quality and accuracy of the used gravity field model. For the first time, MDT estimates along with its full error covariance matrix based on Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) data can be provided. We demonstrate the progress accomplished with GOCE processing and the valuable contribution of the GOCE gravity field models regarding the estimation of the MDT by showing results based on altimetric observations of Jason-1 and Envisat in combination with different GOCE gravity field models for the North Atlantic.

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topographythe difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. However, the calculation of the mean dynamic topography from satellite based gravity field models and altimetric sea surface height measurements is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches Becker, 2012). Within this combination method the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e. the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which makes it best suitable for ocean data assimilation. Meanwhile, we made significant improvements regarding the used data sets. In this paper we focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.

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