The question posed in this post is; whether it is better to use satellite gravimetry or satellite altimetry to determine a marine geoid?

Satellite Gravimetry

Major Missions: GOCE (ESA), GRACE (NASA)

How it works: GOCE uses a gradiometer which is comprised of six accelerometers that measure differences in the gravity field. GRACE measures gravity by measuring the distance between the two satellites which varies with fluctuations in the gravity field.

Satellite Altimetry

Major Missions: Skylab (NASA), GOES-3 (NASA), Seasat (NASA), Geosat (NASA), ERS missions (ESA), TOPEX/Poseidon (NASA), Jason satellites (NASA),

How it works: An altimeter emits electromagnetic radiation in the microwave bandwidth at a near-nadir direction. The radiation is reflected off the earth’s surface (or the ocean surface) and back to the satellite. By measuring the travel time the distance between the satellite and the target can be calculated.

Gravity and Geometry

By reading the short introductions above, it would be reasonable to disregard satellite altimetry for geoid determination, and for the geoid over solid terrain you would be right, but over the oceans satellite altimetry becomes an important and necessary part in geoid determination. This is due to the dynamic nature of the oceans and the limitations of gravity missions.

The major problem with satellite gravimetry is that only the low frequency features of the geoid can be measured through space based techniques, for now anyway. Just with the shear surface volume of our oceans supplementing these satellite missions with higher frequency measurements through airborne and shipborne gravity measurements is just not practical. Luckily geodesists and hydrographers already had a way of geoid determination that can supplement the satellite based observations. To do this they used equation 1 below where h is the geodetic height, N is the geoid-ellipsoid separation, ζ is the dynamic sea topography and e is the error. This means that by measuring h with satellite altimetry and combining this data with tidal and dynamic sea models you can determine the geoid-ellipsoid separation value. This is why some of the earlier altimetry missions where designed to have geodetic missions, the newer missions all have exact repeat missions which have a lower density of measurement but can measure temporal data better.

Equation 1: *h = N + ζ + e*

This method of course depends on having accurate dynamic sea models. However as gravity missions started in the early 2000s it was determined that you could combine the low frequency data from the satellite gravimetry with the high frequency data from the altimetry missions. This is done using Equation 2 where N_REF is the long wavelength geoid from the gravimetry missions, ΔN is the high frequency residuals in the geoid-ellipsoid data, ζ _MDT is the mean dynamic topography, and ζ(t) is the time varying sea surface topography (this includes tides, dynamic atmospheric effects, wind, etc.). By assuming that N_REF, ζ _MDT, and ζ(t) are all long wavelength features then the slope of ΔN can be measured through comparing h from one observation to another, given that they were subsequent measurements.

Equation 2: *h = N_REF + ΔN + ζ _MDT + ζ(t) + e*

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