Two posts in one day! You do spoil us, ambassador.

Whenever one or more denialists gather together or alone, they inevitably make something up about climatology, and then criticise climatologists for doing whatever imaginary thing it is they've made up. Today's invention is linearity (but, sigh, I'm giving too much credit for novelty, of which there is none. I mean, of course, reinvention):

global climate models are all based around the idea that in the long run, when we calculate the global temperature everything else averages out, and we’re left with the claim that the change in temperature is equal to the climate sensitivity times the change in forcing. Mathematically, this is: ∆T = lambda ∆F

Linearity is indeed a useful concept, and the concept of climate sensitivity is only useful if some kind of quasi-linear relation holds between forcing and response. But as ever the denialists have it all backwards. Climate sensitivity is an emergent property not an imposed one; and the things that everyone thinks of as "global climate models" - i.e. the vast AOGCMs that contribute to the IPCC runs that we all see wiggly lines from - don't make the linearity assumption at all. It turns out that if you study the results from the models you do indeed find this quasi-linear relationship, which is why CS is a useful concept, and why you can then use CS as a way of constructing (simpler, faster) models for other studies. But mistaking cause for effect is a stupid error.

This is rather similar to another claim - that the water vapour feedback is built in; and if the denialist is really doing well, they might manage to stumble out with "assumes constant relative humidity". But again, this is nonsense: the AOGCMs don't assume a RH; they calculate it. It turns out to be (an emergent property) that RH remains roughly constant with temperature change on a global scale.

I think this is yet another variation on the "dumb America" fallacy, which in this case goes something like:

* Oh dear, I have nothing to say, but I would feel worthless if people didn't read things I write. So I'll write something.

* Climate is interesting! I'll write something about climate models. I know nothing about climate models, I'll take a look...

* Oh dear, that was all a bit complicated, wasn't it? All those thousands of lines of code, all that basic science, all those scientific papers. Understanding that would be hard, and I'm soft.

* I know, I'll read a few blog posts and make something up. It needs to be something "controversial" but I also need to remember my target audience: don't want to scare the horses.

And there you have it. Next?

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Even "sort of linear" is overstating the case.

ΔT ≅ K ΔF

where

K = δT/δF

may look like a linear expression, but can be profoundly nonlinear (e.g. T(F) is exponential.) Really, about all the expression really implies is that T(F) is locally differentiable. It doesn't even have to be a unique function (e.g. it might exhibit hysteresis.)

Nice of you to be charitable, but even charity can be overdone.

Exactly, sometimes linear expansion gives us good approximations. Sometimes it will neglect the important dynamics behind some equations. Just look at the navier-stokes-equations f.e.

@D.C. Sessions

I aggree, this expressions says nothing about whether its a linear or a nonlinear diff. equation.

Maybe I'm mistaken, but I'd assumed the linearity was essentially just an approximation based on differentiating the blackbody flux equation wrt to T.

F = sigma T^4 \Rightarrow dF = 4 sigma T^3 dT

Hence, if dT is small relative to T (assume T essentially constant), dT is then linearly proportional to dF. I don't believe climate models us this though, so I'd assumed this was just a simple way to make some basic approximations.

[It comes - or can come - from linearising the T-vs-Forcing relationship, which (assuming its fairly well behaved, as it seems to be) must be linearisable at least within some range. But I don't see why it should the blackbody flux equation -W]

But I don't see why it should the blackbody flux equation

It probably doesn't have to be, but presumably there is a relationship between the T-vs-Forcing relationship and the blackbody flux equation? Can't one approximate the outgoing flux as the blackbody flux equation with some emissivity factor (around 0.6 I think)?

[I think not, because there's all the feedbacks: WV, ice/snow-albedo and so on. Perhaps the blockbody curve is jut a lower limit -W]

think not, because there's all the feedbacks: WV, ice/snow-albedo and so on. Perhaps the blockbody curve is jut a lower limit

Yes, I see what you mean. I think what I was suggesting would be roughly correct if dF were the total change in radiative forcing (forcings plus feedbacks) but, as you say, typically it's only anthropogenic and so does ignore all the feedbacks. I could be wrong about that too though. I think there is still a way to express it that would be related to the change in blackbody flux, but since I may end up talking myself in circles, I'll stop there. Have a good Christmas and New Year :-)