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GRACE and the dance of the kilograms

By Graham Cogley

The GRACE satellites have transformed our understanding of how kilograms dance around on and beneath the Earth’s solid surface, but nobody would claim that analyzing what they are telling us is a simple job. A recent analysis by Riccardo Riva and co-authors exemplifies this point.

The problems start with a list of technical details to do with processing of the raw observables. “Observables” is jargon, short for “observable quantities”, but it is a valuable clue to how to think about the “inferables” that we are concerned about.

The point is that an “inferable”, such as relative sea-level change, may be quite some distance down the chain of reasoning from the observable, which in this case is the rate at which the two satellites are accelerating away from or towards each other. This rate depends directly on all the gravitational attractions they feel at the time of each measurement. We want to remove the technical noise so that we can infer the signal of the fluctuating gravity field experienced by the satellites, and so infer the transfers of mass that explain the gravitational fluctuations.

One of the technical details, for example, has to do with spatial resolution, which for GRACE is about 300 km. But the regions between which mass is being transferred generally have quite sharp boundaries, for example the coastline. The jargon for this part of the problem, “leakage”, is quite expressive. It hints that part of the signal we want has strayed out of our study region and into neighbouring regions.

Riva and co-authors have two study regions, the land and the ocean. Signal could be leaking either way across the coastline, but they argue that the oceanic signal of mass gain, expressed as relative sea-level change, is probably much smoother than the terrestrial signal of mass loss. So they simply define a 250-km wide buffer in the offshore waters and “unleak” all of its supposed signal back onto the landmasses.

There then follow a number of other corrections, including a correction for movements of mass within the solid Earth and a trial-and-error phase that seeks to undo the addition of some oceanic signal to the land signal during the unleaking phase.

Now the geophysical part of the problem can be addressed. Riva and co-authors reckon that +1.0 mm/yr of equivalent sea-level rise moved from the continental surfaces to the oceans between 2003 and 2009, give or take 0.4 mm/yr. This surprises me.

My estimate for the transfer from small glaciers (those other than the ice sheets) is about +1.2 mm/yr for the same period. Several recent estimates for the transfer from the Greenland Ice Sheet lie between about +0.5 and +0.7 mm/yr, and for the Antarctic Ice Sheet at about +0.5 mm/yr. (All of these abouts are partly because of the uncertainty of the measurements, or rather of the inferables, but also because of the difficulty of matching the different time spans of the analyses.) The glaciers, then, seem to be adding more than twice the mass to the ocean that is estimated by the Riva analysis.

It gets worse. Yoshihide Wada and co-authors, in a paper to appear shortly, argue that the mining of groundwater is running at present at a rate equivalent to +0.8 mm/yr. This addition is partly offset by the filling of reservoirs, estimated at —0.5 mm/yr over the past 50-60 years. The rate during the past decade is probably lower, because the frenzy of dam-building has abated somewhat recently. But it is not possible to get all of the continental surface contributions to add up to less than, say, +2.6 to +2.8 mm/yr, give or take perhaps 0.4 mm/yr.

What we have here is stark discord, well outside the error bars, between several “inferables”, and we haven’t even got to the sea-level rise due to thermal expansion and the estimated sea-level rise itself. This is a classic example of unsettled science in a context of settled science. We can draw a diagram to depict the water balance of the ocean, or write down a little equation. A balance is, after all, simple arithmetic. The boundary between the settled and unsettled parts of the problem lies somewhere beyond the diagram, and indeed beyond the signs, + or —, attached to the various terms in the equation. But at the moment it is definitely before we get to the first decimal digits of the numbers, at least one of which must be wrong.

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