# Geodesy & Geophysics

# Overview of Satellite Altimetry

Due to the complexity of the Continuous Vertical Datum for Canadian Waters (CVDCW) project, this will become clearer as I write more about it, it was necessary to form a (semi) multidisciplinary team to tackle the problems that the project faced. This team is comprised of the Canadian Hydrographic Service (CHS) and the Canadian Geodetic Survey (CGS).

The CVDCW combines the Canadian Gravimetric Geoid Model of 2013 (CGG2013), from the CGS, and ocean models of the sea surface topography, from the CHS, to obtain a Hydrographic Vertical Separation Surface (HyVSEP) that can reduce geodetic heights to a number of vertical water datums, primarily chart datum. This is done using eq. 1 where N is the geoid undulation from CGG2013, DOT is the Dynamic Ocean Topography, and sep(MSS-tidal level) is the difference between the Mean Sea Surface (MSS) and the tidal level or vertical water datum desired.

There are three measurements that therefore must be made to calculate the HyVSEP, all found on the right side of the equation. Each of these measurements, of course, have an uncertainty value associated with them, however, what Robin et al (2014) does not seem to address is that all three of these measurements for offshore modeling is reliant on *satellite altimetry*.

What then is satellite altimetry and how is it a key part in three separate measurements?

Typically, satellite altimetry is a form of microwave remote sensing (RADAR) that is found on special scientific satellites; SKYLAB, GEOS-3, SEASAT-1, Topex/Poseidon, GEOSAT, ERS-1&2, GFO, ENVISAT-1, Jason 1&2 (Jason 3 was launched January 2016 and has an altimeter); but is sometime found in the form of laser remote sensing particularly if polar regions are the target area; ICESat, Cryosat-2.

Unlike the InSAR method used in the RADARSAT missions, satellite altimetry is a nadir facing sensor which yields a much smaller footprint. Satellite altimetry can therefore achieve a much higher precision and accuracy because of the lower incident angle and through atmospheric corrections that are determined through measuring the atmospheric conditions with a Radiometer, which can only be utilized properly with a nadir sensor.

Image: JASON-2 satellite

There have been two different types of satellite altimetry missions, Geodetic Missions (GM) which has a non-repeating or very long repeat orbit, allowing for a more dense coverage and Exact Repeat Missions (ERM) which has a short repeat time and allows for the time modeling of time variant features. In total there has been 60 years of ERM data but less than 2.5 years of GM data as only ERS-1 and Geosat had GM orbits (Sanso and Sideris, 2013). This causes an issue for using satellite altimetry for geodetic purposes as the ERS-1 and Geosat altimetry data is not as accurate as modern altimetry data. The largest cause of this uncertainty is from the orbit determination of the satellite itself; Geosat used Doppler and ERS-1 used SLR (as well as PRARE until its malfunction early into the mission).

There has been effort to ‘re-process’ the data through remove-restore and crossover adjustment techniques which try to define a more accurate orbital model to the position of the satellite as well as combing the GM data with the more rigorous ERM data. I might have a future post that gets into more detail about this but for now it is just important to know that any surface solutions from satellite altimetry are a combination of GM and Interpolated ERM data.

There are many other considerations into determining accuracy that I won’t go into for this post but I do encourage you to check out the further readings if you are as interested in it as I am.

Now to get onto the meat of this post; how satellite altimetry is (probably) used simultaneously for all three measurements.

The first and most obvious measurement is in the tide models. Satellite altimetry measures the distance between the satellite and the instantaneous sea surface (Δh), averaged over time this produces a Mean Sea Surface (MSS) and can be used to determine various water level definitions such as LLWLT which is used for chart datum in Canada. A distinct advantage of satellite altimetry over its more traditional counterpart, tide gauges, is that the measurements are not in relationship to a fixed point but rather in relationship to the geo-center, the center of mass of the earth, which allows the data to be free from the effects of crustal motion.

The second measurement is the geoid measurement. The geoid, an equipotential surface, is a lumpy reference surface, also known as a datum, that represents Mean Sea Level (MSL). If the oceans where static then the geoid would coincide with the MSS but as they are dynamic they differ by a value called the *dynamic ocean topography *(DOT), ζ*.* The geoid undulation, N, is the separation value of the Geoid and the Ellipsoid and is used for terrestrial applications to convert geodetic heights to orthometric heights. For marine applications the geoid undulation is not useful on its own as it has no relation to the sea surface. Please read my post on the difference between using satellite gravimetry and satellite altimetry for geoid determination here.

As can be seen in the figure, the difference between the Ellipsoid and MSS can be calculated using the geoid undulation, N, and the DOT, ζ. The DOT is the third measurement that is needed for the HyVSEP. The DOT value can be reduced through the removal of tidal corrections (the first measurement), 75% of signal variance, and dynamic atmospheric corrections, 10% of signal value. The rest of the signal is from wind and other high frequency effects which can be modeled. The primary method of determining DOT, that I have read, is through the reduction of MSS and N, with N also being a function of DOT and MSS.

It has been my observation that all three measurements are co-dependent on each other so it will be interesting to see how the CHS and CGS handled this, but significantly more reading is required to fully understand how they’ve approached the problem so expect more posts on the matter in weeks to come.

Further Readings

SANSÒ, F., & SIDERIS, M. G. (2013). *Geoid determination: theory and methods.*

SEEBER, G. (2003). *Satellite geodesy: foundations, methods, and applications*. New York, Walter de Gruyter.

JASON MISSIONS

JASON-1: http://sealevel.jpl.nasa.gov/missions/jason1/jason1factsheet/

JASON-2: https://www.nasa.gov/mission_pages/ostm/spacecraft/index.html

# Re-Processing Old Altimetry Data

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.

Further Reading:

SANSÒ, F., & SIDERIS, M. G. (2013). *Geoid determination: theory and methods.*

# Satellite Gravimetry v. Altimetry for Geoid Determination

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*

To learn more follow the link to the image source or wait for a future post!