# Processing Mean Sea Level with altimetry data

Altimetry measures the distance between satellite and sea surface. This distance minus the satellite position gives the "sea surface height" (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.

# Corrections & models

| Jason-2 | Jason-1 geodetic orbit | Jason-1 repetitive orbit | Envisat | Saral | Topex/Poseidon |
---|---|---|---|---|---|---|

Orbit | CNES POE-D standards | GSFC POE (09/2008), | ||||

Mean Sea Surface (MSS) | MSS_CNES_CLS2011 (with 20 years reference) | |||||

Dry troposphere | ECMWF model computed from gaussian grids | ERA-Interim model | ||||

Wet troposphere (composite*) | Jason-2 radiometer (AMR) | Jason-1 radio<br/>meter (JMR) (no composite algorithm) | Jason-1 radiometer (JMR for cycles <228 and JMR Replacement Product for cycles 228 to 259) | Enhanced MWR + composite algorithm [Ollivier, et al. 2012] | Saral/AltiKa radiometer (no composite algorithm) | TMR with drift correction [Scharoo et al. 2004] and empirical correction of yaw maneuvers [T/P 2005 annual validation report] |

Ionosphere | Filtered (iterative method) dual-frequency altimeter range measurements (SLOOP project) | - before cy65: Filtered (iterative method) dual-Frequency altimeter range measurements (SLOOP project) | GIM | Filtered (iterative method) dual-frequency altimeter range measurements (for TOPEX) and Doris (for Poseidon) | ||

Sea State Bias | Non parametric SSB [Tran, et al. 2012] | Non parametric SSB compatible enhanced MWR | Hybrid SSB, same method as in [Scharroo et al., 2013] | Non parametric SSB (for TOPEX) [Tran, 2010], BM4 formula (for Poseidon). | ||

Ocean tide and loading tide | GOT4.8 | |||||

Solid Earth tide | Elastic response to tidal potential [Cartwright and Tayler, 1971], [Cartwright and Edden, 1973] | |||||

Pole tide | [Wahr, 1985] | |||||

Combined atmospheric correction | High Resolution Mog2D Model [Carrère and Lyard, 2003] + inverse barometer computed from ECMWF model (rectangular grids) | High Resolution Mog2D Model [Carrère and Lyard, 2003] + inverse barometer computed from ERA-Interim model | ||||

Specific corrections | Jason-2 / T/P global MSL bias | Jason-1 geodetic/Jason-1 repetitive bias | Jason-1 / T/P global MSL bias | - Bias for side-B period | None | - Doris/Altimeter ionospheric bias, |

# Method for calculating regional and global MSL slopes

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 1°x3°, (1° along the latitudinal axis, 3° along the longitudinal axis) 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 latitude and its area covering the ocean, in order to give less significance to boxes at high latitudes which cover a smaller area and to boxes that overlap land. 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.

Unlike other missions, Envisat's cycles are 35-day long. However, in order to have approximately a temporal sampling close to Jason-1 mission (around 10 days), Envisat's MSL shown here is not performed on a cyclic basis but on a 250 tracks basis (around 9 days). The curve is then filtered with a 2 (dots) and 6 months (lines) cut off frequency for a better readability. During the first year (cycles 9 to 22) Envisat MSL global trend is not consistent to other flying satellites. This unexplained behavior is under investigation. Results plotted here are obtained after cycle 22 (beginning of 2004).

### 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 subtracting a bias of 5.46 cm to Jason-1's MSL. This bias is computed as the difference of the averages of the global MSL between the two missions on a common period over a few cycles centered on the cycle 11 of Jason-1:

**Corrected MSL ** (Jason-1) = **MSL** (Jason-1) - **bias** (Jason-1, T/P)

Similarly, Jason-2's MSL was connected to Jason-1's MSL on Jason-2's cycle 11 (October 2008) by subtracting a bias of -7.34 cm to Jason-2's MSL and also by taking into account the bias between Jason-1 and Topex/Poseidon:

**Corrected MSL** (Jason-2) = **MSL** (Jason-2) - **bias** (Jason-2, Jason-1) - **bias **(Jason-1, T/P)

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.

# Taking into consideration variations in the geoid

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.

# Corrections & models references

- 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.
- Cartwright, D. E., R. J. Tayler, 1971, "New computations of the tide-generating potential," Geophys. J. R. Astr. Soc., 23, 45-74.
- Cartwright, D. E., A. C. Edden, 1973, "Corrected tables of tidal harmonics," Geophys. J. R. Astr. Soc., 33, 253-264.
- Gaspar, P., and F. Ogor, 1996, Estimation and analysis of the sea state bias of the new ERS-1 and ERS-2 altimetric data, (OPR version 6). Technical Report. IFREMER/CLS Contract n° 96/2.246 002/C. (CLS/DOS/NT/96.041).
- Labroue S., 2007 : RA2 ocean and MWR measurement long term monitoring, 2007 report for WP3, Task 2 - SSB estimation for RA2 altimeter. Contract 17293/03/I-OL. CLS-DOS-NT-07-198, 53pp. CLS Ramonville St. Agne
- 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 - Ollivier, A., Y. Faugere, M. Ablain, N. Picot, P. Femenias, et J. Benveniste. "Envisat ocean altimeter becoming relevant for mean sea level trend studies."
*Marine Geodesy*, 2012: vol 35. - 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., Lillibridge, J., 2005: Non-parametric sea-state bias models and their relevance to sea level change studies, in
*Proceedings of the 2004 Envisat and ERS Symposium*, Eur.Space Agency Spec. Publ., ESA SP-572, edited by H.Lacoste and L. Ouwehand. - 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.
- Tran, N., S. Philipps, J-C. Poisson, S. Urien, E. Bronner, et N. Picot. "Oral : Impact of GDR-D standards on SSB corrections.", pdf, Aviso. 28 Septembre 2012.
- Tran, N., S. Labroue, S. Philipps, E. Bronner, and N. Picot, 2010 : Overview and Update of the Sea State Bias Corrections for the Jason-2, Jason-1 and TOPEX Missions.
*Marine Geodesy, accepted*. - USO correction: more information about this Envisat correction is available on http://earth.esa.int/pcs/envisat/ra2/auxdata/
- Wahr, J. W., 1985, "Deformation of the Earth induced by polar motion," J. Geophys. Res. (Solid Earth), 90, 9363-9368.