Altimetry measures the distance between satellite and sea surface. This distance minus the satellite position gives the "sea surface eight" (see Altimetry: How it works?).
However, numerous perturbations have to be taken into account, and corrections need to be subtracted to take into account various physical phenomena:

• propagation corrections: the altimeter radar wave is perturbated during atmosphere crossing
  • ionospheric correction
  • wet tropospheric correction
  • dry trosphospheric correction
• ocean surface correction for the sea state which directly affects the radar wave: electromagnetic bias.
• geophysical corrections for the tides (ocean, solid earth, polar tides, loading effects)
• atmospheric corrections for the ocean's response to atmospheric dynamics: inverse barometer correction (low frequency), atmospheric dynamics correction (high frequency).

 In addition, SSH is calculated for each altimetric measurement considered as valid according to the criteria (per threshold, per spline, per statistic on the ground track) applied either to the main altimetric parameters, the geophysical corrections or the SSH directly. These criteria may vary from one mission to the next depending on the altimeters' characteristics. For more information on how they are defined, refer to the Cal/Val validation reports for each satellite's relative cycle.
The precise references for the corrections and orbits used when calculating the mean sea level are given in the table below. They are mostly contained in 'GDR' altimetric products for the Jason-1 and Jason-2 missions. However, for the Topex/Poseidon mission, the MGDR products are rather old, and more recent corrections, compatible with the standards used for the Jason missions, have therefore been used.

To calculate MSL, the global or basin MSL time series must be distinguished from the regional maps of MSL slopes. In both cases, these calculations are available mission by mission for the period of the mission being considered, or by combining several altimetry missions covering the entire altimetric period.

Time series for each mission

With regard to the calculation of MSL time series for each mission (Topex/Poseidon, Jason-1, Jason-2), a mean grid of sea level anomalies (SLA=SSH-MSS) of 2°x2° must first be calculated for each cycle (~10 days) in order to distribute the measurements equally across the surface of the oceans. The global or basin mean for each grid is calculated by weighting each box according to its area, in order to give less significance to boxes at high latitudes which cover a smaller area. This then gives the time series per cycle, which is then filtered with a low-pass filter in order to remove signals of less than 2 months or 6 months, and the annual and semi-annual periodic signals are also adjusted. The MSL slope is deduced from this series using a least squares method.

Time series combining missions

The global MSL for the entire altimetric period is calculated by combining the time series from all three Topex/Poseidon, Jason-1 and Jason-2 missions before filtering out the periodic signals. The three missions are linked together during the ?verification? phases of the Jason-1 and Jason-2 missions in order to calculate very precisely the bias in global MSL between these missions. It was decided to connect Topex/Poseidon and Jason-1 to Jason-1's cycle 11 (May 2002) by applying a bias of 6.69 cm to Jason-1's MSL. Similarly, Jason-2's MSL was connected to Jason-1's MSL on Jason-2's cycle 11 (October 2008) by applying a bias of 7.43 cm to Jason-2's MSL and also by adding the bias between Jason-1 and Topex/Poseidon. The global MSL reference series is obtained by filtering out the periodic signals for the entire altimetric period.

Maps for each mission

The regional MSL slopes for each mission are estimated using SLA grids for each cycle and each mission as defined above for the time series. The regional slopes are estimated using the least squares method at each grid point after adjusting the periodic signals (annual and semi-annual). The map of these points is deduced from the slope grid, as well as the map of the corresponding formal adjustment error.

Maps combining missions

Lastly, the regional MSL slopes for the entire altimetric period are calculated using Ssalto/Duacs multi-mission gridded data, which not only enable the slopes to be estimated at a good resolution (1/3 of a degree on a Mercator grid), but also enable the local MSL slopes above 66° to be estimated using data contributed by the ERS-2 and Envisat missions. To estimate the regional slopes, the same methodology is used as for the grids for each mission.

MSL measured using altimetry incorporates variations in the geoid. However, these interannual or long-term variations directly affect the estimate of the MSL slope and must therefore be corrected. Regional estimates of these variations are currently available owing to the GRACE mission, although only since 2002. They cannot therefore be used to calculate regional and global MSL slopes for the entire altimetric period. Consequently, the results described here only take into account the global impact of the postglacial rebound (glacial isostatic adjustment, or GIA) which is ultimately just one of the contributing factors to geoid variations. The GIA correction is only applied to the global MSL time series, and has been estimated as approximately -0.3 mm/year [Peltier, 2006] . The global MSL slope is therefore higher after this correction has been applied.

• Ablain, M., S. Philipps, 2006, Topex/Poseidon 2005 annual validation report, Topex/Poseidon validation activities, 13 years of T/P data (GDR-Ms)
• Carrère, L. and F. Lyard, 2003: Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing ? comparison with observations, Geophys. Res. Lett., 30(6), 1275.
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• Labroue, S., P. Gaspar, J. Dorandeu, F. Mertz, OZ. Zanifé, 2006, Overview of the Improvements Made on the Empirical Determination of the Sea State Bias Correction, 15 years of progress in radar altimetry Symposium, Venice, Italy, 2006
• Ray, R., 1999: A Global Ocean Tide model from Topex/Poseidon Altimetry, GOT99.2. Rapport n° NASA/TM-1999-209478, Goddard Space Flight Center Ed., NASA, Greenbelt, MD, USA. pp. 58.
• Scharroo, R., J. Lillibridge, and W.H.F. Smith, 2004: Cross-calibration and long-term monitoring of the Microwave Radiometers of ERS, Topex, GFO, Jason-1 and Envisat. Marine Geodesy, 97.
• Wahr, J. W., 1985, "Deformation of the Earth induced by polar motion," J. Geophys. Res. (Solid Earth), 90, 9363-9368.