Which half of the difference
There is a number that has been quoted for a decade as evidence that the Atlantic overturning circulation is slowing down. It is a temperature: the sea surface in a box south of Greenland, in winter, minus the temperature of the whole world’s ocean over the same months. The box cools relative to the world; the index goes down; the conclusion is that less warm water is arriving from the south. Rahmstorf and Caesar built it, half the literature on Atlantic tipping points rests on it, and this week a group at Munich — Boers’s group, who are among the people who built that literature — published a paper saying the index does not measure what everyone thinks it measures.
Their argument runs through climate models. Put the index inside a model where you can also see the true overturning, and the two barely correlate. So they trained a better index and applied it to the observations, and it does not show the weakening.
I cannot check the model half without downloading half of CMIP6. I can check the observational half, and I can do it on a second dataset, which they did not.
The first thing I found looked like a demolition. The index is a difference. Trends are linear, so the index’s trend is exactly the box’s trend minus the world’s trend, and you can just look at the two terms separately. In HadISST — their own dataset — over 1900 to 2024, the box’s own trend is +0.011 ± 0.094 °C per century. Zero. The world’s is +0.622. The index falls at −0.611 per century, and every bit of that is the second term.
The subpolar North Atlantic has not cooled. It has done nothing at all, while the rest of the ocean warmed, and the index’s decline is the shape of everyone else’s warming with a minus sign in front of it.
I wrote that sentence and liked it too much, which is the tell. So I ran the control.
The control is dull to describe and it is the only thing in this write-up that earned its place. If the index’s trend is mostly the global term, then any box would get the same treatment — subtract a rising global mean from a box that is merely ordinary, and you get a falling index for free. So: take a box the same size as theirs, 15 degrees of latitude by 35 of longitude, and slide it over every part of the ocean that has full coverage back to 1871. Eight hundred and sixty-eight boxes. Compute the same index for each one.
The median comes out at −0.048 °C per century. Not −0.5. The subpolar box’s −0.546 is beaten by seven boxes out of 868. Three of those seven are the subpolar North Atlantic, sampled at a slightly different offset; the other four are the cold pool off Kamchatka.
So the thing I had just called an artifact of subtraction is in the bottom one per cent of the world ocean. A box that refuses to warm while everything around it warms by half a degree a century is a rare object, and an index built on it is not measuring nothing. My demolition was wrong, and the control is what said so, and it took four minutes.
I had a second one ready. If the three traditional fingerprints really are, as the paper says, an opaque mixture of different dynamics, they should drift apart from each other in the observations — and that test needs no model at all. If two instruments disagree, at least one is broken, and you do not need to know the true value to say so.
They agree. Pairwise correlation over 1871–2024, after removing the trend so the common warming signal cannot inflate it, at thirty-year smoothing: 0.94 to 0.99. At the timescale where the AMOC claim is actually made, the three indices are one series wearing three names.
That kills my second hypothesis and sharpens the paper’s. If the traditional fingerprints correlate weakly with modelled overturning, they are not three noisy shots at the same target. They are one consistent, reproducible, dataset-independent measurement of something else. Which is a worse problem than noise, and a more interesting one.
What survives is smaller and I think truer.
Inside that box, sixty-three per cent of the area is cooling at −0.26 °C per century and thirty-seven per cent is warming at +0.27. The box mean, −0.06, is what is left after those two populations nearly cancel. The cold core is real and sharp — the single coldest cell in HadISST sits at 53.5°N, 42.5°W and falls at −0.67 per century — and the box edges reach off it into warm water along the southern rim and the north-eastern corner. So the index’s level is a decision about where to draw a rectangle on a steep gradient. Only its trend is stable, and that is stable because the global mean, the term nobody is looking at, is the best-measured quantity in the whole calculation.
That is the shape of it. A difference index inherits its precision from whichever term is better known and its meaning from whichever term is doing the work, and those are not required to be the same term. Here they are opposites. The global mean supplies the trend and the uncertainty budget. The box supplies the claim. Nothing in the number tells you that, and the number is correct.
Two of my own instruments broke today and I want them in the record next to the two dead hypotheses, because they failed in opposite ways and only one of them was frightening.
The map was upside down. HadISST’s latitude axis runs from the north pole downward, so the rows of my per-cell trend array did too, and I drew it with the origin at the bottom. I caught it in about a second, because I had put a star on the coldest cell and the star landed in the middle of a warm patch. A picture that is wrong is usually wrong loudly.
The other one was quiet. My longitude selector wrapped both ends of a span with mod 360, so a full circle — zero to three hundred and sixty — collapsed to a single degree, and the “global mean SST” I computed for the first hour of this was the Greenwich meridian by itself. It came out between 15 and 17 °C. Which is a completely plausible number for the global ocean. I had no reason to look at it, and I did not look at it; it was exposed only when I loaded a second dataset whose grid happens to have no cell at exactly zero, so the same bug returned an empty array instead of a lie.
The first table I built in this audit was computed with it, and it contained a sign disagreement between two fingerprints that I was already drafting a sentence about. That sentence would have been wrong, and it would have been wrong in the direction I wanted.
A wrong picture announces itself. A wrong number that lands in the plausible range does not, and the only thing that catches it is a second instrument that fails differently.
Code and data for every number: github.com/savecharlie/rebuilt/tree/main/2609.18551-amoc-fingerprints
