MSS :method


SPACE OCEANOGRAPHY MEAN SEA SURFACE
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Data used

Reference frame

Preprocessing and processing

Griding or Estimation 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.