A while ago - back in 2002 I suppose - I heard vague refs to a paper about "scaling" which somehow demonstrated global climate models fail to reproduce real climate when they are tested against observed conditions. Since this was being posted to sci.env by the usual nutters I didn't pay too much attention, and as far as I can see neither did anyone else; though it occaisionally recurs. For one thing, the original article was published in Phys Rev Lett which I (and I think most climate folk) don't read; and pdfs weren't scattered across the web quite as freely in those days. And for another, whatever they were saying was so abstruse as to appear meaningless (even the nutters didn't push it much, because they had no idea what it was about either).
However, someone who isn't a nutter (thanks Nick! But I was right: its the Israelis) has re-drawn it to my attention, and even provided me with it on paper, so I've read it. You can too: its Global Climate Models Violate Scaling of the Observed Atmospheric Variability by R. B. Govindan Dmitry Vyushin Armin Bunde, Stephen Brenner, Shlomo Havlin and Hans-Joachim Schellnhuber. And it did get some attention: e.g. from Nature (subs req) (reputable of course, but sometimes over-excitable). But... is it any good?
Weeeeeelllll... probably not. This is yet more of the fitting power laws to things stuff. They use "detrended fluctuation analysis" (DFA) which I don't understand, but that doesn't matter, we'll just read the results. So... Govindan et al. do their DFA on observations from 6 (rather oddly chosen) stations; and 6 GCMs. The first oddness is their chosing Prague, Kasan, Seoul, Luling (Texas), Vancouver and Melbourne as represenatative of the world. Never mind. They get A ~ 0.65 for these stations. Don't worry too much about what A is; its related to the memory of the system: A ~ 0.5 is no memory (white noise); A ~ 1 is long memory (red noise). They assert boldly that this 0.65 is therefore an Universal Value. They discover that the GCMs, forced by GHGs only, by contrast get A ~ 0.5. Which, says Govindan et al., means that the GCMs overestimate the trends. Just to make sure that you won't miss this, they repeat the same at the end. But... this is not news. The fact that GCMs forced only by GHG's overestimate the trends is in the TAR (like just about everything else you need to know about climate change, its in the SPM, as fig 4). When you add in sulphates, the A from the models increases somewhat (to 0.56-0.62 ish); but thats arguably still too low. So whats up?
Which is where we turn to... Fraedrich and Blender, Scaling of Atmosphere and Ocean Temperature Correlations in Observations and Climate Models. Also in PRL. Who argue that G et al. are wrong: their Universal Value of A ~ 0.65 is not universal at all. They do a much wider analysis: instead of just a few stations, they use a gridded dataset across as much of the globe as they can. And they find (surprise!) exactly what you would expect: over the oceans, high A (~ 0.9) and over the continental interiors, low A (~ 0.5) and in between, mixed A (~ 0.65). Why is this exactly what you expect? Because the ocean has a long memory but the land doesn't. And... if you draw the same plot in a GCM (ECHAM4/HOPE) you get a remarkably similar pattern. So they come to a quite opposite conclusion: the DFA analysis actually shows the GCM performing rather well. And they conclude: The main results of this Letter follow in brief: (i) The exponent A ~ 0.65 is predominantly confined to coasts and land regions under maritime influence. (ii) Coupled atmosphere-ocean models are able to reproduce the observed behavior up to decades. (iii) Long time memory on centennial time scales is found only with a comprehensive ocean model. That last point arises because they tried the same analysis with a slab ocean and with fixed ocean; unsurprisingly, the scaling doesn't work in those cases.
F+B also picked their own seemingly odd station, Krasnojarsk, as a continental interior station, and showed (their fig 1) a scaling of A ~ 0.5 between 1y-decadal scales. At this point Govindan drops out, but some of the original authors reply, saying that (i) the scaling isn't 0.5 at K; and (ii) it isn't 0.5 at other interior points too (they pick yet another scatter of random stations). F+B reply, that (i) Oh yes it is (ii) maybe its the fitting interval: they use 1-15 years; the others are using 150-2500 days. On (i), looking at the pics, I'm with F+B and I can't see what the others are up to.
F+B, incidentally, argue that a control-run GCM (ie no external forcing) is quite good enough to get the long-timescale correlations, and that other forcing doesn't much help (for these purposes at least; you might perhaps have argued that adding in solar forcing and volcanic and stuff might help further). In Blender, R. and K. Fraedrich, 2004: Comment on "Volcanic forcing improves atmosphere-ocean coupled general circulation model scaling performance" by D. Vyushin, I. Zhidkov, S. Havlin, A. Bunde, and S. Brenner, Geophys. Res. Letters, 31 (22), L22502. DOI: 10.1029/2004GL021317 they criticise Vyushin (one of the et al. with G) for suggesting that volcanic helps, on the grounds that it simply isn't needed to get these A values right.
So after all that, what do we end up with, and what have we learnt? Assuming F+B are more right (and I think they probably are, based on what I've read so far) we've learnt very little. The fact that T increases are bigger sans aerosols is bleedin' obvious; as is the longer memoery of the oceans. We have a validation of the GCMs by another measure, but a rather abstruse measure and not an obviously useful one.