Filtering of Altimetric Sea Surface Heights with a Global Approach

The geoid models from GRACE and soon GOCE in combination with sea surface geometry data from satellite altimetry allow to obtain a precise estimate of the absolute dynamic sea surface topography with rather high spatial resolution. However, this requires

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Filtering of Altimetric Sea Surface Heights with a Global Approach A. Albertella, X. Wang, and R. Rummel

Abstract The geoid models from GRACE and soon GOCE in combination with sea surface geometry data from satellite altimetry allow to obtain a precise estimate of the absolute dynamic sea surface topography with rather high spatial resolution. However, this requires the combination of data with fundamentally different characteristics and different spatial resolutions. One of the central objectives must be to get altimetric data and the geoid spectrally consistent without loss of precision and/or resolution. Therefore it is necessary to find a representation common to the geoid model and to altimetry that allows to obtain spectral consistency by filtering the altimetric data. We try to design a filter for the altimetric data, using the spectral characteristics of the satellite gravimetric geoid, considering a “global” approach. It consists of the extension of the altimetric sea surface height so as to cover all of the Earth’s surface and the representation of the data in terms of spherical harmonic functions. The effect of the extension of the data to the land areas is studied in detail.

32.1 Introduction Accurate and high resolution knowledge of the geoid offers the possibility in combination with an altimetric ocean surface of a determination of the Dynamic Ocean Topography (DOT). The altimetric

A. Albertella () Institut für Astronomische und Physicalische Geodäsie, Technische Universität München, Munich, Germany e-mail: [email protected]

mean sea surface is computed using the profiles from different altimetric satellites. With the geoid models as produced by the gravimetric satellite missions GRACE and GOCE this possibility becomes reality. In the studies by Ganachaud et al. (1997) and Wunsch and Gaposchkin (1980) in situ hydrographic data and a circulation model derived from altimetry and geoid information are combined to derive a global estimate of the absolute oceanic general circulation. Even though the limited spatial resolution and accuracy of the geoid models at that time limit the possibilities of DOT computation, the two estimates exhibit nicely large scale general circulation. In constructing a geoid model, one truncates its spectrum at a certain maximum degree L. For all degrees less or equal to L one has the coefficients of the model together with their error (commission error). The signal for degrees greater than L is not modeled, but its expected average size is identified as omitted signal (omission error). In Losch et al. (2002) it is shown, based on an analysis in the Southern Ocean, that the introduction of the omission error in the geoid error model produces discrepancies in the solution. In particular, such effects are present on the long (well known) scales. If the analysis is performed in a local region, the combination of the altimetric data and the geoid height could be inconsistent with the hydrographic estimate of the ocean circulation, also due to the inaccuracy of model