 The principle of altimetry
(Credits CNES/D. Ducros)

## Satellite-to-surface distance: Range

Radar altimeters on board the satellites transmit signals at high frequencies (over 1,700 pulses per second) to Earth and receive the echoes from the surface (the ‘waveform’). They are analysed to derive a precise measurement of the time taken to make the round trip between the satellite and the surface. These time measurements, scaled to the speed of light (the speed at which electromagnetic waves travel), yields the range R measurements (see From radar pulse to altimetry measurements for Further details).
However, as electromagnetic waves travel through the atmosphere, they can be decelerated by water vapour or ionisation. Once these phenomena have been corrected for, the final range can be estimated with great accuracy (see dataprocessing).
The ultimate aim is to measure surface height relative to a terrestrial reference frame. This requires independent measurements of the satellite’s orbital trajectory, i.e. exact latitude, longitude and altitude coordinates.

## Satellite Altitude

The critical orbital parameters for satellite altimeter missions are altitude, inclination and period. The altitude of a satellite depends upon a number of constraints (e.g. inclination, atmospheric drag, gravity forces acting on the satellite, area of the world to be mapped, etc). The period, or ‘repeat orbit’ is the time needed for the satellite to pass over the same position on the ground, uniformly sampling the Earth’s surface. Inclination gives the highest latitude at which the satellite can take measurements.

The altitude of a satellite (S) is the satellite’s distance with respect to an arbitrary reference (e.g. the reference ellipsoid, a rough approximation of the Earth’s surface). It depends upon a number of constraints (e.g. inclination, atmospheric drag, gravity forces acting on the satellite, area of the world to be mapped, etc). The satellite can be tracked in a number of ways so as to measure its altitude with the greatest possible accuracy and thus determine its precise orbit, accurate to within 1 or 2 cm. The main techniques used are:
– Doppler shift, to accurately determine the satellite’s velocity on its orbit, using dynamic orbitography models to deduce the satellite’s trajectory relative to Earth (e.g. DORIS, or PRARE instruments),
– GPS or similar systems can also be used,
– laser tracking is also used, often for calibration.

## Surface height

The surface height (H), is the satellite’s distance at a given instant from the reference surface, so:

(corrected) Height = Altitude – (corrected) Range.

For the ocean, the sea surface height (or SSH) integrates effects such as:

• The sea surface height which would exist without any perturbing factors (wind, currents, tides, etc.). This surface, known as the geoid, is determined by gravity variations around the world, which are in turn due to major mass and density differences on the seafloor. For example, a denser rock zone on the seafloor would deform sea level by tens of metres, and be visible as a hill on the geoid.
• The ocean circulation, or dynamic topography, which comprises
• the permanent stationary component (permanent circulation linked to Earth’s rotation, permanent winds, etc.). The mean effect is of the order of one metre.
• and a highly variable component (due to wind, eddies, seasonal variations, etc.).

To derive the dynamic topography, the easiest way would be to subtract the geoid height from SSH. In practice, mean sea level is subtracted instead, to yields the variable part (sea level anomalies) of the ocean signal.