MSS :overview


SPACE OCEANOGRAPHY MEAN SEA SURFACE
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CLS_SHOM98.2 mean sea surface

OBJECTIVES

The CLS_SHOM MSS must be accurate along and close to the satellite ground tracks of the oceanic dedicated altimetric missions (T/P, ERS, GEOSAT.... JASON, ENVISAT, GFO).
The CLS_SHOM MSS must contain the short wavelength of the geoid undulations at the vicinity of the satellite ground tracks.
The CLS_SHOM MSS should be the reference for calculating and merging homogeneously Sea Level Anomalies.

PERSPECTIVES

The CLS_SHOM MSS will be used for merging present altimeter data and futur data of Jason, ENVISAT, and GFO.
The MSS should be determined over a longer period by a reference to 5 year TOPEX/Poseidon Mean Profile.
Our processing and gridding methode will be adapted for gravity anomalie and vertical deflection calculations.

METHOD

Data used

Three-year T/P mean profile (Cycles 11 to 121, NASA-JGM-3 orbit).
Two-year ERS-1 mean profile (Merging phase C and G, DPAF orbit).
Two-year GEOSAT mean profile (Cycles 1 to 44, years 87 and 88).
ERS-1 geodetic phase (two 168-day non repeat subcycles).

Reference frame of the data/MSS

Because TOPEX/POSEIDON mean profile is the more precise of our set of data, we have chosen to reference all the other satellite measurements to it (see table below). Thus, the MSS height would be related to the T/P ellipsoid , on the T/P frame.

TOPEX/POSEIDON Earth reference ellipsoid caracteristics:

a= 6378136.3 m

1/f= 298.257

GM= 398600.4415 km3/s

TOPEX/POSEIDON frame:

The T/P sea surface height were calculated using the NASA Precise Orbit Determination (based on the JGM-3 model , Tapley et al., (1996 ), the Mean Sea Surface is based on the same standards. These standards -called "Nominal"- were first defined at the beginning of the T/P missions. They are described in details in: Tapley et al., 1994 (TABLE 6).
Then the POD has been revisited, some of the modifications are presented in: Marshall et al., 1995 (TABLE 17).
Note that 2 minors changes are not mentionned in that last paper (N. Zelensky, pers. comm., 1999):

Model	Nominal POD	New (current) POD
Earth tides	k3=0	k3=0.093
Geocenter tidal variation	none	T/P Ray'94 tides

For more details, please contact N. Zelensky,

Preprocessing and Processing

	Mean Profile T/P	Mean Profile ERS-1	Mean Profile GEOSAT	Geodetic Phase ERS-1
Periods	1993-94-95 (cy 11 to 121)	92/11 - 93/11 (phase C) 95/05 - 96/05 (phase G)	86/11 - 88/11 (cy 1 to 44)	94/04 - 94/09 (phase E) 94/10 - 95/03 (phase F)
Remarks	Reference for all observations	Merging phases C and G	introduce interannual variability>	provide high resolution
Spatial resolution at the equator	315 km	~ 80 km	160 km	~ 8 km
Global coverage (latitude limits)	66°	82°	72°	82°
Processing particularities		adjustement of E/E Xover differencies removing oceanic variability adjustement to T/P mean profile	adjustement to T/P mean profile	adjustement of E/E Xover differencies removing oceanic variability adjustement to T/P mean profile
RMS of crossover differencies before processing	1.66 cm	2.55 cm	6.54 cm	~13.0 cm
Internal accuracy between 66°N and 66°S	1.2 cm	1.6 cm	2.0 cm	6.5 cm
Accuracy related from T/P between 66°N and 66°S	1.2 cm	2.0 cm	3.2 cm	6.5 cm
Accuracy beyond 66°N and 66°S		4.8 cm	3.2 cm	10.0 cm

Griding or Estimation Method

Inverse method, based on a suboptimal interpolation technique (e.g., Bretherton et al., 1976). Measurement noise and large scale errors along the satellite ground tracks are taken into account (e.g., Le Traon et al., 1998b).

OBSERVATIONS:

Residuals of the Mean Heights to the EGM96 geoid (Lemoine et al., 1996)
Data noise: Measurement errors
Large scale errors (e.g. residual orbit errors)
Error due to a bad oceanic variability reduction

METHOD:

For each grid point in the first calculation grid (0.25°x0.25°):

data are collected in the 200 km radius bubble
the bubble mean height is calculated and subtracted, to center the observations
the observation covariance matrix is inverted
a subgrid estimation (1/16° x 1/16°) is processed, using this covariance matrix, providing estimates and estimation errors if the ocean depth is below 10 meters (depth calculation is based on ETOPO5 bathymetric files).
The bubble mean and the EGM96 geoid are added back to the estimates.

Extrapolating along the coast

The MSS has been calculated in ocean areas where depth is greater than 10 meters, in order to ensure a better quality of the surface. Moreover the purpose of this surface calculation was not to provide a geoid estimation at the global level, implying a continuity between the mean sea level, and the geoid over land. However the MSS grid should be interpolated by users. Local interpolation schemes are usually based on polynomial interpolants spanning over several grid points. Thus, near the coast in areas where the bathymetry is still lower than 10 meters, the surface can not be interpolated. Consequently, the surface has been extrapolated toward the land (approximately over a distance of one degree) by cubic spline interpolation. The extrapolation ensures a continuity of the MSS gradients, as shown in the mapping of the Mediterranean sea.

NOTE that grid points (1/16° x 1/16°) where the MSS is valid and the associated estimation error is not valid (value = 999.999) correspond to islands or shoreline/coastal areas where the MSS has been extrapolated.

VALIDATION

In order to validate and improve the MSS calculation, several tests were performed:

Look at the differencies between the T/P, ERS-1, and Geosat mean profiles heights and corresponding interpolated values of the MSS.
Compare the MSS gradients with the along track mean profiles to verify the restitution of the short vawelengths of the geoid.
Compare the CLS_SHOM v. 98.2 MSS to MSS calculated with other dataset (e.g. GEOSAT geodetic dataset), in particular the OSU95 MSS (Yi, 1995) and the GRGS MSS (Cazenave et al., Mazzega et al.,1996).
Analyse the impact of using the CLS_SHOM v. 98.2 MSS to reference satellite data (instead of using the classical method of referencing SLA to a mean profile).
Analyse the impact of using the CLS_SHOM v. 98.2 MSS to calculate the geoid cross-track errors, instead of the OSU95 MSS.

Surfaces	Satellite	Mean of height differencies (cm)	standard deviation (cm)	Mean of gradient differencies (cm/km)	standard deviation (cm/km)
OSU95	T/P ERS-1 GEOSAT 168(scy:1) 168(scy:10)	-0.39 0.12 -0.20 -0.49 0.70	3.64 5.34 4.94 8.80 9.68	0 0 0 0 0	0.15 0.29 0.28 0.86 0.87
GRGS	T/P ERS-1 GEOSAT 168(scy:1) 168(scy:10)	-2.21 -2.73 -2.26 -1.95 -2.00	5.11 6.65 6.72 8.95 9.44	0 0 0 0 0	0.42 0.48 0.49 0.91 0.91
CLS_SHOM	T/P ERS-1 GEOSAT 168(scy:1) 168(scy:10)	-0.13 -0.17 -0.27 0.05 0.29	1.29 2.08 4.06 7.12 7.26	0 0 0 0 0	0.11 0.15 0.18 0.80 0.78

Difference between MSS	Mean (cm)	Standard deviation (cm)
OSU95 - GRGS	-3.32	10.68
CLS_SHOM - OSU95	0.05	10.43
CLS_SHOM - GRGS	-3.09	10.18

FIRST CONCLUSIONS

The validation tests performed are not independant:

1) we have compared the MSS value to the mean profiles used to estimate the surface, it is an internal quality test ;

2) we have looked at the differences with other MSS, it is an external relative test (we do not know the absolute precision of the other MSS).
Because the T/P and ERS-1 mean profiles are accurate, and because the differences of these profiles with the CLS_SHOM v. 98.2 MSS are low (~2 cm rms), we can conclude that the accuracy of the MSS under the satellite ground tracks is good, and the short wavelength well represented (slope differences below 2mm/km). Note that in area where few T/P or ERS-1 mean profile data can constrain the MSS estimation, we assume that the accuracy treshold should be of the order of the geodetic data precision, i.e., 6.5 cm rms.
MSS differences indicate that the OSU MSS is less accurate than the CLS_SHOM v. 98.2 MSS. Visual comparisons clearly show the trackiness contaminating the OSU MSS. While comparisons between the GRGS and CLS_SHOM v. 98.2 MSS reveal the so called "orange skin effect". The CLS_SHOM v. 98.2 MSS seems to well reproduce the geoid short wavelength along the satellite ground tracks, but might be smoother than the GRGS MSS in between (note that the CLS_SHOM v. 98.2 MSS does not contain GEOSAT geodetic data which provide higher spatial resolution).
The CLS_SHOM v. 98.2 MSS have a really homogeneous oceanic signal content. This was one of the main objective of the work: by referencing to the T/P mean profile, and by reducing the oceanic variability of the ERS-1 data, the oceanic content of the CLS_SHOM v. 98.2 MSS is the mean height of the ocean during 1993-94-1995.
The impact of the use of the MSS to reference SLA has been inferred. It shows that using the MSS does not degrade the SLA: 2 cm rms differences are observable in some areas with the SLA classically referenced to the mean profiles. These differences are either caused by MSS biases (like geographical correlated errors) or mean profile accuracy (near the cost and the island the mean profiles are less precise).
The impact of the use of the CLS_SHOM v. 98.2 MSS instead of the OSU95 MSS for the geoid cross track error has been evaluated. RMS differences at crossover points of the T/P mean profile corrected using in the correction the CLS_SHOM v. 98.2 or OSU95 MSS are 1.5 and 1.8 cm rms respectively. CLS_SHOM v. 98.2 is thus more accurate at the track vicinity.