Climate extremes: not really about George Will

I really didn't want to say anything about George Will's recent Washington Post columns - RealClimate has links to the relevant discussions. I haven't read Will's columns for years, since before we canceled our Newsweek subscription. I had found his frequent clear misstatements annoying, and decided I was learning nothing from reading his opinions. So I've not made an exception in this case, I still haven't read what he actually wrote.

However, over at Andy Revkin's Dot Earth blog there have been several comments on the question of whether one or two (or 10) years of data can be considered strong evidence for a warming or cooling climate, and I thought I would add my own thoughts on that topic, somewhat relevant to the claims in Will's case.

Under normal circumstances the answer is simply no - climate is defined by the WMO and the IPCC as a statistical description of the weather averaged over 20 to 30 years. If you are just looking at the averaged quantities in that statistical description, then 1 or 2 years, or even a decade of aberrant weather is not enough to give us a clearly distinct climate, because you need that 20 or 30 year average and who's to say that the remaining years of the period won't pull the average back in the normal direction again?

But if you look beyond the average at standard deviation and the distribution of extreme weather, then there is reason to claim just one or two years as evidence for a change in climate. If under the old climate a particular weather event had only a 1 in 10,000 chance of occurring, then its presence even in a single year is strong evidence that climate has already changed and there's no need to wait 30 years to make the assertion. Any piece of data that is several sigma's away from the norm can be evidence of a change, whether warming or cooling.

So the extremely low ice events of the summers of 2007 and 2008 were well outside the statistical distribution previously observed, and therefore evidence of a change (unless our earlier estimates of natural variability were somehow too low). Whereas, a return to normal ice levels now is not evidence for or against any change, just as a return to rain in California or southern Australia wouldn't be evidence of a cooling climate, because those states remain within the expected statistical distributions of weather patterns for those regions.

It might help if scientists more clearly quantified extreme events (in terms of number of standard deviations from the norm) to give a better picture of what counts and what doesn't, as a single event or series of events that indicate changed climate.

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Discussion at Dot Earth

Discussion at Dot Earth continued with a response questioning the assumption of a normal distribution for the tail, and the effect such assumptions had in financial matters recently. My response on that:

No matter the exact form of the tail, the fact that an event is far into the tail does tell us it is something extreme, unusual, under the previously observed climate conditions. There are three possible reasons:

(1) Previous observations were too limited and the actual variability of the relevant measurement is much larger than we thought (i.e. WMO and IPCC's 30-year definition of climate is too short, climate is correlated for far longer periods than that - but then what do you call the average of weather at the 2- or 3-decadal scale?)

(2) The tail is so "fat" that these very extreme events are not really so unusual (but still, a 5-sigma event under a monotonically decreasing tail where 2 sigmas range has been observed over 30 years has to have a likelihood well under 1%; two of them in a row is that much less likely).

(3) The statistical distribution has changed due to a change in the underlying physical system - climate change.

By Occam's razor, (3) is the simplest explanation, barring evidence to the contrary. But it could of course still be wrong to jump to that conclusion from just a small number of extreme events. The more of them that pile up, though, well...

Assuming a near-normal distribution comes naturally from the central limit theorem, which strongly applies to climate variables that are obtained by averaging or adding many local (at some level-) independent values - global average surface temperature, for instance, or even the total sum of sea ice coverage. Inapplicability of the central limit theorem in this case implies large-scale correlated change - i.e., climate change, which gets us back to the same conclusion.

As to the comparison to the financial system - there is no fixed underlying "physical" system involved there, it is rather a self-referential system, one of Douglas Hofstadter's "strange loops". What financial models of risk failed to account for there was the same case where the central limit theorem fails - correlated change of the entire system as a whole. Our financial system has just been through its own (human-induced!) piece of "climate change". Not pretty.

Whatever the exact form of the distribution, normal or "fat", specifically quoting the quantitative number of standard deviations a particular event is different from past experience would always be useful.