An alternative to measuring sea surface height to extreme precision, which would require knowing the satellite height to extreme precision along with all the other phenomena affected the RF signal propagation, is to measure the sea height relative to fixed objects.
For example, if the local sea height is measured with respect to the nearly simultaneously measured land height, then it could be easier to infer variations in the local sea height.
Hmmmm...that assumes gravity propagates like light--but we really don't understand much about gravity. Still looking for gravity waves, and trying to understand gravity as part of the fabric of space. So I don't know if your assumption about "conservation" nor your analogy to light apply here. Great minda are working on the problem!
With respect to 'erhaps the "squared" exponent in the denominator of Newton's Law is not exactly 2.0,' this exponent usually occurs because there is conservation in an expanding sphere. For example, a pulse of light emitted from a point source and spreading uniformly in all directions is effectively spreading on the surface of an expanding sphere. Since the surface area of this sphere is proportional to r^2.000000..., we have a 1/r^2 law for the intensity of light.
A different exponent would require a different method of propagation.
Land-based lasers are used to measure the altitude of the satellites which use RADAR to measure the sea surface height. But the land-based lasers are themselves experiencing vertical movement due to the solid earth tides caused by lunar and solar grivity. They may also be experiencing long-term horizontal and vertical movement due to tectonic plate movement. I have no doubt that all of these factors, and plenty more, are build into the model that is used to calibrate the system and to correct the raw data. I think NASA is probably the most trusted part of the US government, and rightly so. But NASA also has to constantly worry about funding, so it may be difficult for administrators to admit the limitations of their systems. (e.g. warnings of engineers not taken seriously by administrators prior to Challenger disaster) There may be a temptation for NASA administrators and NASA press correspondents to use "typical" values instead of "worst case" values.
A lot of the literature I have read talks about "precision", but precision is not the same thing as accuracy.
The satellites Jason-1 and Jason-2 are part of the much larger "geodetic infrastructure". The National Research Council issued a report in 2010 entitled "Precise Geodetic Infrastructure - National Requirements for a Shared Resource". I bought a copy online, and it is fascinating reading. But the following statement gave me pause: "Modern geodesy delivers precision to one part per billion, and precision of one part per trillion can be envisioned in the foreseeable future.".
Presision, maybe, but I can't help wondering about accuracy, which depends upon having a stable reference point. If every part of the earth is moving, then all calibration must be performed with respect to an imaginary reference point, such as the earth's center of mass. After all of the available data is factored into the model, aren't we still left with a lot of assumptions?
@Bob: And the moon's gravity causes not only ocean tides, but also the so-called "solid earth tide" which causes the land under your feet to rise and fall tens of centimeters every 12 hours.
Keeping this in mind, it's amazing to me that we don't have more Earthquakes than we do. So if we went ~4 billion years back in time when the Moon had just formed and was much closer to the Earth than it is today, how big would the sea and earth tides have been then?
@Bill: It's naive and irresponsible, IMO, to think the Sun's output has been constant over the years...
Surely we know it's not been constant. Did you see my book review of Alone in the Universe by John Gribbin. People talk about the Earth inhabiting the "Goldilocks Band" that's warm enough to have liquid (none-ice) water yet cool enough that the water doesn't boil off. As I recall, Gribbin presented lots of evidence for variations in the sun's temperature/outout over time showing the the Goldilocks Band moved in or out over time and that Earth was lucky to have always remained within the extreme end points.