Sea level fingerprints

Why does a melting ice sheet make the sea fall near itself and rise most on the far side of the world?

Everyone carries a bathtub model of the ocean: add water anywhere, the level rises everywhere by the same amount. So it is worth asking what the ocean has that a bathtub does not. Two things — it is huge enough for gravity to vary across it, and it sits on ground that moves. Once those are in, the bathtub prediction fails so badly that melting Greenland makes the sea fall along Greenland's own coast. How can losing ice raise sea level globally and lower it locally?

Start with the ice sheet as a mass rather than as a water supply. Greenland holds enough ice to raise global mean sea level by roughly seven metres, and all that mass has gravity. It pulls the surrounding ocean toward itself, and seawater, being free to move, piles up in response. The sea surface near a great ice sheet stands measurably higher than it otherwise would — not because of anything the ice does when it melts, but simply because it is there.

Now ask what happens when some of it leaves. The attraction weakens, and the water that had been held near the ice sheet relaxes away. That is a local fall, and it is not a subtle competition between two effects: near the ice sheet the loss of gravitational pull dominates completely, so within roughly two thousand kilometres the sea surface drops even as the world's oceans gain water.

A second local effect points the same way. Remove kilometres of ice and the ground beneath rebounds — elastically and immediately, not the millennial creep of the last ice age. The land goes up while the sea goes down, and what a tide gauge records is the difference between them.

Now follow the water. It went somewhere, and the total is conserved. If the near field loses while the global mean gains, arithmetic forces the far field to gain more than the global mean. Published gravitationally self-consistent calculations put that far-field maximum at roughly 1.2 to 1.3 times the global mean for a Greenland source — so a metre of global average rise from Greenland delivers something closer to 1.3 metres to the tropical Pacific. Antarctic loss produces the mirror image, hitting northern hemisphere coasts hardest.

A third effect is smaller but real: moving that much mass shifts the Earth's rotation pole slightly, and the ocean adjusts to the changed spin. Each source — Greenland, West Antarctica, Alaskan glaciers, groundwater depletion — produces its own pattern. That is why they are called fingerprints, and why in principle a set of coastal records can be read backwards to say which reservoir the water came from.

Now the honest part. This has been solid theory for a century, but detecting the patterns in real data is hard, because a coastline's record is dominated by tides, currents, wind, local subsidence and the leftover deformation from the last ice age. Convincing observational detection in satellite altimetry is recent, and the field is still arguing about how much of the signal is unambiguously fingerprint rather than ocean dynamics. The theory is not in dispute; the extraction is.

Where this sits next to its neighbours: the collection's piece on isostatic rebound is this same load problem answered by the solid Earth instead of by the sea surface, and the two land at opposite fixed points in time. Rebound from the last ice age is still running ten thousand years after its cause; the gravitational fingerprint of today's melt appears essentially the instant the ice is gone. And they are entangled in practice — the slow one is the largest correction that must be removed before the fast one can be seen.

The refinement that ties everything together is that "sea level" at a coast is a relative measurement — the gap between a moving sea surface and moving ground. Three things move it: the total volume of water, the shape of the gravity field, and the elevation of the land. The bathtub model keeps only the first.

Two corrections worth making explicitly. First, none of this says melting Greenland is good news for Greenland — the falling local sea level is a consequence of a process that raises sea level for almost everyone else, and the far field that gains the most includes low island states with no part in causing it. Second, the near-field fall is not a small effect to be waved at: close to the ice margin it is several times the global mean in magnitude, with the opposite sign, which is why a tide gauge in the wrong place is actively misleading about global change.

• How the fingerprints of different sources are separated in practice, and why the correction for past ice-age deformation dominates the error budget.
• What the pattern implies for which coastlines should plan for more than the headline global figure.

Every term the collection defines is gathered in the glossary.