Reference ellipsoids and geoids are typically used to compute estimates (e.g. sea surface height with respect to WGS-84 ellipsoid) and can be included as additional information. Most are specific to the ocean.
The reference ellipsoid is an arbitrary reference surface that is a rough approximation of the Earth’s shape, which is basically a sphere ‘flattened’ at its poles. The length of one of the axes at the equator is chosen so that the ellipsoid coincides with mean sea level at this latitude. It is the first-order definition of the non-spherical shape of the Earth as an ellipsoid of revolution.
The marine geoid is the shape of the sea surface assuming the complete absence of perturbing forces (tides, wind, currents, etc.). The geoid reflects the Earth’s gravitational field (it is an equipotential surface) and varies in height by as much as 100 metres over distances of several thousand kilometres due to uneven mass distribution within the planet’s crust, mantle and core. Other, less pronounced irregularities are also visible over smaller distances. These reflect the ocean bottom topography.
The Mean Sea Surface represents the sea level due to constant phenomena. It is the sum of the geoid and the Mean Dynamic Topography (that includes the permanent stationary component of ocean dynamic topography).
The Mean Sea Surface is computed from altimetry, averaging data over several years.
Sea level anomalies (also called sea surface height anomalies) are sea surface heights with respect to the Mean Sea Surface (MSS). It is not to be confused with what is usually called ‘Mean Sea Level’ ( MSL), which is a measure of the sea level variations over time (see Applications: Ocean: Mean Sea Level).
A mean profile can also be used, which is the mean of the sea surface along the tracks of a specific satellite (whereas MSS can be computed from several satellites)
This mean circulation is not produced directly from altimetry data, which rather provide the mean sea surface, consisting of the marine geoid plus the sea elevation due to the mean oceanic. We, therefore, have to combine altimetry data with other data (in-situ, gravimetric satellites, etc), to determine the geoid precisely, and by subtracting it, compute the mean circulation.
The relation between those three reference surfaces (each one referenced to a Reference ellipsoid) can be formalized as follow:
Quantities computed from altimetric heights can be thus defined:
Sea Surface Height (SSH) is the sea surface height with respect to the Reference ellipsoid
Dynamic topography (or Absolute Dynamic Topography, ADT; sometimes called Sea Surface Topography — which can be misleading with Sea Surface Temperature, however) is the sea surface height with respect to the geoid
Sea Level Anomalies (SLA, also called SSHA, Sea Surface Height Anomalies) is the sea surface height with respect to a Mean Sea Surface or a Mean profile
So, SSH = (Altitude – Range – corrections) = geoid + ADT = MSS + SLA/SSHA = geoid + MDT + SLA/SSHA
Bathymetry is the measurement of the ocean depths. Although is has no direct use in altimetry data processing, it can be useful in shallow water (since ocean altimetry is not as effective there), or for comparing with ocean features such as currents.
Bathymetry can be computed using among other things altimetry sea surface height measurements (via the geoid).