With satellite altimetry there have been two types of missions, geodetic missions (GM) and exact repeat missions (ERM). GM altimetry has a very high density of measurements that is due to its very long repeat orbit, this makes it particularly useful for deriving short wavelength features such as the variations in the geoid that are not measured through satellite gravimetry. ERM altimetry has a short repeat orbit which allows it to observe the temporal variations in the ocean topography, however this is at a cost of density.
Picture from the IAG 2006 geoid school presentation
The only two satellites to observe GM altimetry were ERS-1 and GEOSAT, which combined comprise of about two and a half years of observations. This is unfortunate as the technology difference between those two missions and what we have today is vastly different in many ways, particularly in the accuracy of altimetry measurements and orbits. This means that we only have precise measurements for ERM altimetry and have to interpolate the data within the areas without measurements. To perform the interpolation we can use the data from the GM altimetry, although dated, to provide a more rigorous solution then without it.
Now obviously this is not ideal due to the limited accuracy of the legacy data, however, we can apply the knowledge gained since then to reduce some of the errors from the estimated satellite position and the reduction of time elements such as tides. These are both parameters that are actually determined with the use of measurements from satellite gravimetry (which came at a later date) as well as satellite altimetry from more recent years. This means that the more recent observations are not only contributing to the established measurements of the geoid but also towards the interpolated values.
This just goes to show you that you should always keep legacy measurements because you might want to re-process with future knowledge.
SANSÒ, F., & SIDERIS, M. G. (2013). Geoid determination: theory and methods.
The question posed in this post is; whether it is better to use satellite gravimetry or satellite altimetry to determine a marine geoid?
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.
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
To learn more follow the link to the image source or wait for a future post!