Earlier quoted context omitted.
You know less than you think you do. GPS is not part of the measurement suite in OP, but better than 1.8 cm vertical resolution from GPS has been possible since the late 1990s, using after the fact orbit determination. It is now routine to get sub-cm vertical accuracy in GPS measurements [1, fig. 3, magenta line]. The horizontal displacements are known to about a mm. These displacements are known so accurately that y…
> You know less than you think you do. Not clear how this ad-hominem enhances your argument. >If you don’t know how they did the measurement, why are you so sure it is wrong? I'm not "so sure", I'm just skeptical. I find it hard to believe that one can estimate the net ice loss over a huge and dynamic body of ice with an accuracy better than 0.001%, using any type of measurements conceivable. You are saying that some…
Yes, that is correct. The mass of Antartica, whatever that might mean, is not required in itself. Percent error in estimating that is not relevant. Remember that we are interested in mass changes only.
The GRACE measurement is based on explaining the relative position of a pair of orbiting spacecraft by mass changes in 4500 "mascons" -- equal-area spherical caps that blanket the globe (see figs 2 and 3 of [1]). The fundamental observation is the range and relative velocity of the pair of spacecraft, which can be very accurately determined. The mass within each mascon has an analytically-known relationship to these observations (eqs. 8, 9 of [1] - relating mass sigma to acceleration a).
It's a monthly measurement -- you accumulate a month's worth of orbits, and solve a least-squares problem to fit the range-rate data with the masses. This can also be viewed as maximum a posteriori estimation in the conventional way. See equation 13 of [1].
I hope this clarifies why it does not matter what the ice underneath is doing. The ice has mass, and therefore it affects the gravitational potential that the satellites operate in.
You are correct to be surprised. The measurement is surprising, and it has been revolutionary. Hundreds of papers have been published using it, and it has received scrutiny and undergone improvements for more than a decade. Three independent groups (JPL, UTexas, DLR) have worked on the full retrieval over this time. Lots of what we know about groundwater withdrawals, ice sheets, and more recently deep ocean currents, is based on this measurement.
There is an attribution issue at ice/water boundaries (sec. 6 of [1]). It is due to mixed pixels -- a mascon that is part water, part ice. The mass change observed at the mascon should not be spread evenly over the whole pixel. It is split in constrained way based on errors and priors. But as [1] explains, this is not an "order of magnitude" type error, it's just a correction.
[1] https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/201...
But to repeat -- the fundamental result of the OP does not rely on GRACE (nor does it rely on GPS). It relies on ice sheet velocity models.