Knowledge of the gravity field, and more specifically of the geoid is of foremost importance to use altimetry data in oceanography.

Dynamic topography and altimetry

Dynamic topography is the sea level driven by thermodynamic processes in the ocean. It includes a “static” part (taking into account features like the main currents, etc.), and a variable part. Altimetry gives access to the sea surface height with respect to an ellipsoid reference. However, this sea surface height includes features from several different sources: geoid, ocean variability, main currents, etc.
SSH = Geoid height + dynamic topography
= Mean Sea Surface + Sea Level Anomalies
= (Geoid height + Mean Dynamic Topography) + Sea Level Anomalies Variations of the Sea Surface Height can be computed (Sea Level Anomalies, i.e. sea surface height with respect to the Mean Sea Surface), using long period of altimetry data to define a mean sea surface or a mean profile under the satellite track.


Geoid, MSS, MDT and SLA data are not immediately compatible. Meaning:
– they must be referenced on the same surface (Reference ellipsoid),
– they must be homogeneous with respect to tides
– and, last but not least, their spectral content must be the same. If one data include small-scale phenomena and not the other, the addition will miss some information (and the same for a comparison between different datasets)

GOCE and GOCE User Toolbox

GOCE (Gravity Field and Steady-State Ocean Circulation) is an ESA mission dedicated to the determination of the Earth’s gravity field and the geoid height at a spatial resolution of 100 km with unprecedented accuracy.
The GOCE User Toolbox (GUT) is a compilation of tools for the utilisation and analysis of GOCE Level 2 products. GUT supports applications in Geodesy, Oceanography and Solid Earth Physics. GUT consists of a series of advanced computer routines that carry out the required computations. It may be used on Windows PCs, UNIX/Linux Workstations, and Mac.

Data used

“A priori” data provided with GUT v1.1, including GOCE EGM_GOC_2 Level-2 Spherical Harmonic Potential Product File (DIRECT SOLUTION – First HPF Delivery) data, MSS_CNES_CLS10, MDT_CNES_CLS_09, and also gridded and along-track SLA from Aviso


We will use both GUT and BRAT to compute a MDT then use it with altimetry data.

GUT processing: create a satellite-only MDT

GOCE spherical harmonics data are provided with GUT. Once retreived, you can compute a geoid, then you have to harmonize this geoid with the Mean Sea Surface you wish to use. Once done, you can subtract the two and get a Mean Dynamic Topography.

The steps to follow to calculate the mean dynamic topography in spatial domain are:
Compute a geoid from GOCE spherical harmonics data
Step 1: Create a geoid height, into the same reference system as the MSS
gut geoidheight_gf -InFile GO_CONS_EGM_GOC_2__20091101T000000_20100110T235959_0002.HDR -Ellipse TOPEX -T mean-tide -OutFile
Grid adaption between geoid and MSS
Step 2: Interpolate the MSS file onto the same grid as the geoid height
gut adapt_gf -InFile -Gf -OutFile
Subtraction of geoid from MSS
Step 3: Subtract both files by typing:
gut subtract_gf -InFileLhs -InFileRhs -OutFile
Masking the Difference
Step 4: Remove the values on continents by typing:
gut landmask_gf -InFile -InLsmFile -OutFile
Filtering in space domain (at 2°)
Step 5 : Filter the resulting file by typing:
gut filter_gf -InFile -Fhan 2 -OutFile

Note that a built-in workflow within GUT enables you to do the same in one instruction:
gut geoidheight_gf –InFile GO_CONS_EGM_GOC_2__20091101T000000_20100110T235959_0002.HDR -Ellipse TOPEX -R 0.5:359.5,-89.5:89.5 -I 1:1 –OutFile
It was split in different steps here to highlight the important points of the processing.

GUT is using BRAT Display as a viewer, so you can use directly this by entering “BratDisplay” in a command window.

BRAT processing:

BRAT can be used several ways in combination with GUT. For example:
– to compute SLA, either from GDRs or from higher level datasets, along-track or gridded, or extract them from pre-computed datasets
– to compute geostrophic velocities, and plot them (See Data Use Case on Geostrophic velocities)
– to compute Kinetic energy from those (or from similar GUT outputs)
– to overlay on other altimetry data or data available within altimetry datasets (e.g. bathymetry)
– to select/edit relevant data (editing in particular) by using thresholds, or flag values, etc.

fig 1. Compute a geoid from GOCE spherical harmonics data

fig 2.Grid adaption between geoid and MSS

fig 3. Subtraction of geoid from MSS

fig 4. Masking the Difference

fig 5. Resulting MDT after filtering in space domain (at 2°)

Dynamic topography and altimetry

Once your MDT computed, you can use again GUT to add it to different SLAs computed within BRAT.
The main point to remember is that you must compute SLA in m (the same than MDT), and adapt the SLA grid to the MDT one (using the adapt_gf workflow)



adt_sm printemps04_sm
fig 6. Jason-2 SLA added to the above computed MDT
fig 7. Geostrophic velocities computed from this Dynamic Topography over the Gulf Stream region using BRAT (see relevant Data Use Case).