Why the AMO Overshoots

I’ve had a bit of off-line feedback on my previous post Spin Snow, not Sea Ice, the AMO is Real!, so I thought I’d try to correct any misconceptions arising from my clumsy presentation.

1. I am only attempting to explain general climate trends, not annual variation in the weather. In particular, I am assuming that the SST (e.g. as measured by satellite) correlates with the heat stored in ocean surface waters (to 100-200m depth, say).  Hence I don’t model “heat” and “temperature” separately.  Over periods of less than a decade, the SST may be determined more by atmospheric variability (including cloud cover) than heat loss from the ocean.   Additionally, there will be different patterns of Atlantic SST variability at different latitudes.  (Since the underlying cycle is of more and less heat lost at high latitudes over decadal timescales, the idealised model would be of an alternately steeper and shallower temperature gradient from (steadily warming) low latitudes to high latitudes – though we can’t rule out heat transfer between the hemispheres as well).

2. Although I have used the term “AMO” (Atlantic Multi-Decadal Oscillation), this (i.e. apparently cyclic variation in the Atlantic sea surface temperature (SST)) is just one measure (another affected is the NAO/NAM, see previous post).  Since the Arctic exchanges water with the Pacific via the Bering Strait as well with the Atlantic via the Fram Strait and Barents Sea, the mechanism itself requires another name, so perhaps “AMO” should be read as the Arctic Multi-decadal Oscillation!  I only modelled the Arctic and the Atlantic, but the Pacific waters cooled by flow of surface currents to the Arctic would be affected much the same as the Atlantic, so I don’t think the extra complexity is required for a proof of principle.

3. Which brings me onto the final point: I’m only attempting a proof of principle, in particular in my graphics.  All I was setting out to do was represent what I perceive to be the logical consequence of coupling between the temperatures of the Arctic and the North Atlantic and Pacific.

In actual fact, I suspect the heat exported to the Arctic varies with a higher power of the Atlantic temperature and not linearly.  The point is that less and thinner Arctic sea ice at the start of winter allows more cold deep water formation which is accompanied by the dispersal of more heat because there’s more of it and also because the surface water was initially warmer.  Introducing a square function leads (as well as to a more chaotic system) to a shortening of the AMO cycle in a warming world.  E.g.:

Any fool can produce an oscillation in a spreadsheet, so why do I think the AMO mechanism is real and important?

1. We keep being told that the Arctic is warming faster than predicted by the climate models. This means it is dissipating more heat than predicted – by radiation into space, by evaporating water that falls as snow or rain and so on.  The climate involves net heat gain at low latitudes, heat transport in the atmosphere and oceans and heat loss at high latitudes.  If the Arctic is warmer than would be expected for steady global warming, then what we’re going to get is unsteady warming (as in the 1930s-40s, see previous post).

2. The criteria exist for an oscillating system – the temperature of the Arctic depends on that of the North Atlantic (and the North Pacific) and vice versa (i.e. there is a negative feedback loop) and there are delays in the system.  These arise because the rate of surface water flow to the Arctic (and deep water flow back) is variable and adjusts only slowly.  There needs to be a relatively large temperature difference between the North Atlantic (NA) (please read North Pacific too) and the Arctic to generate a sufficiently strong current to cool the NA. As every MBA student knows (e.g. from the Beer Game) any negative feedback loop with delays results in an oscillating system.

The system round Antarctica is somewhat different – the coldest area is land and water can flow freely from warmer areas to colder ones (i.e. those with seasonal sea-ice and hence deep cold water formation). This is not to say there aren’t oscillations down there, just that they’re not the same (or, probably, as extreme).

3. The AMO mechanism is that, as the NA warms, the Arctic warms too (because there’s always a current from the NA), reducing the amount of insulating sea ice (and multi-year ice is thicker and a better insulator than first year ice) and therefore increasing its capacity to drain heat (by creating new ice and cold deep water) from the NA.  The critical point – the delay in the system – is that warming and cooling takes some years, so the Arctic will continue to warm even as it starts to cool the NA, and will cool (forming more multi-year ice) even as the NA starts to warm.

4. It seems to me – and my incredibly simplified modelling supports this – that the Arctic will keep warming until it cools the NA, however warm the NA gets (of course, the NA can also lose heat in different ways).  Until, that is, first, the capacity of the Arctic to dissipate heat is reached, and then the system breaks – when the Arctic gets so warm it can no longer generate an overturning circulation.

And once the Arctic has warmed enough to cool the NA, it will overshoot (this could already have happened in the current cycle if the summer sea ice minimum has already been reached), because the NA will still be warm enough to warm the Arctic even while it (the NA) is cooling, albeit at a slower and slower rate until the process reverses.  For similar reasons, the Arctic will also overshoot in the reverse phase, i.e. it will continue to cool even after the NA has started warming again.

5. A rough calculation suggests a net oceanic transfer of heat to the Arctic of 60TW or ~2*10^21J/yr [1], which luckily is compatible with the figures I calculated in my previous post The Earth is a Fridge.  Now, the IPCC estimates that the oceans have gained on average ~14*10^22J between 1961 and 2003 (including ~8*10^22J from 1993-2003) because of global warming (the blue bars are 1961-2003, the burgundy bars 1993-2003):

That is, the oceans have been gaining heat at a rate of around 3*10^21J/yr on average (and around 8*10^21J/yr from 1993-2003).  Let’s attribute 1 or 2*10^21J/yr to the NH which after all is mostly land.

It seems to me at least plausible that an overshooting strengthening of the AMO by more than 50% from its 2*10^21J/yr average – and remember it will be strongest when there is no sea-ice at all in summer, which is still some way from the case – could pump heat out of the northern oceans at a faster rate than they are gaining it by GW (this is all very approximate, proof of principle stuff, but note that a 50% volume increase oceanic circulation in the positive phase of the AMO would be 50% more water containing more heat – conceivably 4*10^21J/yr, perhaps, rather than 2*10^21J/yr).  That is, the AMO could create some cooling for a period.  Of course, this would be followed up by even faster warming, then an even stronger reaction, until the system reaches its capacity as I mentioned earlier, after which we’d just see steady warming.

I conclude with a final figure from the IPCC (panel (a) is mislabelled, the graph shows just the minimum sea-ice extent each year, not the anomalies in it):

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Reference

[1] “Modelling Arctic Ocean heat transport and warming episodes in the 20th century caused by intruding Atlantic Water”, Wang Jia et al, Chinese Journal of Polar Science, Dec 2008.