### Harry Potter and the Polar Amplification of Global Warming

Yes at last some science again. The title is a forlorn attempt to draw in hordes of eager new readers... :-)

So... we all know that the poles are due to get warmer than the rest of the planet under global warming, but do we know why? Before answering why, I should point out that only the northern polar regions show general warming at present, and that this is exactly what the climate models "predict". This is generally (and I would say correctly) ascribed mostly to the moderating influence of the vast southern ocean. But it may also be partly because there is very little scope for ice-albedo feedback over Antarctica: its snow-covered now, and most of it will stay that way under any plausible warming. Unlike, say, bits of Siberia or Alaska, which (if you warm them a bit) will lose some seasonal snowcover. The only bit of "antarctica" which can participate in ice-albedo feedback is the seasonal sea ice; and this has only been measured well since 1979.

But on to the paper I wanted to blog: V A Alexeev et al, Climate Dynamics (2005) 24: 655-666. If you want the technical details, you can read the paper, so I'll assume that what you want is a superficial overview. If so, read on :-)

In fact, if you want a truely superficial overview, the answer is something like the sum of:

In a bit more detail... they start off with a simple "Budyko-Sellers" type EBM (energy balance model):

with T the temperature, D the (latitudinal) diffusion coefficient, A and B are a linear param of OLR, Q is 1/4 the solar constant, S is a heating function and a(x) is the albedo. Tune up A and B and you have a a simple model. a(x) is simple too: a(x) = 0.3 is T > -10 oc and 0.6 otherwise (at least to start with; it gets enven simpler later). "T" is interpreted as annual and zonally averaged temperature, "x" is latitude.

So, fine: take the model, run it; then add something: 4 w/m2 to the RHS and look at the changes to T. And you discover... general warming (of course) and polar amplification of the warming (because the albedo, a, is T-dependent).

Well, this is what you wanted to see and built the model accordingly: an ice-albedo feedback is enough to give polar amplification. But by itself its a bit dull. So they modify the model to remove the T-dependent-albedo (ie, its now fixed) and they discover... no polar amplification. As expected. T rises uniformly. This too is dull.

But, aha! they say, the model is too simple, since we know that if the air is warmer there will be more moisture (notice carefully avoids saying the air will contain more moisture...) so the same winds will carry more energy polewards. So its fair to make the diffusion coefficient linearly dependent on the temperature, to rather crudely simulate that effect. And, ta-da, when you do that, you then recover the polar amplification. And if you split the forcing into tropics and not-tropics, you discover that the forcing flows out of the tropics polewards, but not so much from the extra-tropics tropics-wards. Which is about what you expect on flow-of-energy grounds.

However, it has sort-of been deliberately built in. So, instead, they do much the same thing in two different aqua-planet GCMs: turn off albedo changes, force in tropics only; force in extra-tropics only; and force globally. And that gives you polar amplification. And the global tends to be the sum of the other two (ie, its sort-of linear, with the albedo fixed). And looking at the GCM diags, the mechanism is apparently similar to the simple EBM case (actually the clouds help a bit too, but they get amplification even with the clouds fixed).

So we end up with: polar amplification is:

Sadly they don't really tell you which influence is bigger in the real world. The thing that they don't mention, but folk often do, is the idea that the greenhouse effect of CO2 is bigger in the polar regions because its colder, hence less H2O, hence CO2 increases "can have a bigger effect". I don't think thats true, and they dont even bother mentioning it, so presumably they agree.

So... we all know that the poles are due to get warmer than the rest of the planet under global warming, but do we know why? Before answering why, I should point out that only the northern polar regions show general warming at present, and that this is exactly what the climate models "predict". This is generally (and I would say correctly) ascribed mostly to the moderating influence of the vast southern ocean. But it may also be partly because there is very little scope for ice-albedo feedback over Antarctica: its snow-covered now, and most of it will stay that way under any plausible warming. Unlike, say, bits of Siberia or Alaska, which (if you warm them a bit) will lose some seasonal snowcover. The only bit of "antarctica" which can participate in ice-albedo feedback is the seasonal sea ice; and this has only been measured well since 1979.

But on to the paper I wanted to blog: V A Alexeev et al, Climate Dynamics (2005) 24: 655-666. If you want the technical details, you can read the paper, so I'll assume that what you want is a superficial overview. If so, read on :-)

In fact, if you want a truely superficial overview, the answer is something like the sum of:

- Ice-albedo feedback
- Forcing in the tropics warms the globe. Forcing in the extra-tropics warms the extra-tropics only. Hence, global forcing warms the extra-tropics more.

In a bit more detail... they start off with a simple "Budyko-Sellers" type EBM (energy balance model):

d/dx D(1-x^2) d/dx T(x) = A + B T(x) - Q S(x) (1 - a(x))

with T the temperature, D the (latitudinal) diffusion coefficient, A and B are a linear param of OLR, Q is 1/4 the solar constant, S is a heating function and a(x) is the albedo. Tune up A and B and you have a a simple model. a(x) is simple too: a(x) = 0.3 is T > -10 oc and 0.6 otherwise (at least to start with; it gets enven simpler later). "T" is interpreted as annual and zonally averaged temperature, "x" is latitude.

So, fine: take the model, run it; then add something: 4 w/m2 to the RHS and look at the changes to T. And you discover... general warming (of course) and polar amplification of the warming (because the albedo, a, is T-dependent).

Well, this is what you wanted to see and built the model accordingly: an ice-albedo feedback is enough to give polar amplification. But by itself its a bit dull. So they modify the model to remove the T-dependent-albedo (ie, its now fixed) and they discover... no polar amplification. As expected. T rises uniformly. This too is dull.

But, aha! they say, the model is too simple, since we know that if the air is warmer there will be more moisture (notice carefully avoids saying the air will contain more moisture...) so the same winds will carry more energy polewards. So its fair to make the diffusion coefficient linearly dependent on the temperature, to rather crudely simulate that effect. And, ta-da, when you do that, you then recover the polar amplification. And if you split the forcing into tropics and not-tropics, you discover that the forcing flows out of the tropics polewards, but not so much from the extra-tropics tropics-wards. Which is about what you expect on flow-of-energy grounds.

However, it has sort-of been deliberately built in. So, instead, they do much the same thing in two different aqua-planet GCMs: turn off albedo changes, force in tropics only; force in extra-tropics only; and force globally. And that gives you polar amplification. And the global tends to be the sum of the other two (ie, its sort-of linear, with the albedo fixed). And looking at the GCM diags, the mechanism is apparently similar to the simple EBM case (actually the clouds help a bit too, but they get amplification even with the clouds fixed).

So we end up with: polar amplification is:

- Ice-albedo feedback
- Forcing in the tropics warms the globe. Forcing in the extra-tropics warms the extra-tropics only. Hence, global forcing warms the extra-tropics more.

Sadly they don't really tell you which influence is bigger in the real world. The thing that they don't mention, but folk often do, is the idea that the greenhouse effect of CO2 is bigger in the polar regions because its colder, hence less H2O, hence CO2 increases "can have a bigger effect". I don't think thats true, and they dont even bother mentioning it, so presumably they agree.

## 2 Comments:

Desperately searching for something about the Polar Amplification Effect and came across you...

You may, in fact, have just saved my bacon. Fingers crossed this comes up in the exam!

Glad to hear it. More recently, there is also this from RealClimate.

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