These days, most spam-filtering programs rely on something called "Bayesian math" to determine whether a given item probably is or probably is not spam. It's not perfect, but it works better than pretty much any previous method. As it turns out, Bayes' Theorem applies to more than figuring out whether "Make Money Fast" is junkmail -- it may well be able to tell us the likely temperature increase from greenhouse gas accumulation.

James Annan is a researcher working on climate prediction for the Global Environment Modelling Research Program at Japan's Frontier Research Center for Global Change. In a paper to be published in *Geophysical Research Letters* (PDF), Annan and his colleague JC Hargreaves examine a variety of detailed predictions of "climate sensitivity" -- the amount of temperature increase coming from a doubling of atmospheric CO2 concentrations from pre-industrial levels (from roughly 280ppm to roughly 560ppm). Most projections of the temperature increase give a range of 1.5°C to 4.5°C, with a decent chance of 6° or higher -- and anything that high being an utter catastrophe.

But, as Annan puts it in his weblog,

We made the rather elementary observation that these above estimates are based on essentially independent observational evidence, and therefore can (indeed must) be combined by Bayes' Theorem to generate an overall estimate of climate sensitivity. [...] The question that these previous studies are addressing is not

"What do we estimate climate sensitivity to be"

but is instead

"What would we estimate climate sensitivity to be, if we had no information other than that considered by this study."

So what is Bayes' Theorem?

Bayes' Theorem is a mathematical method of determining the likelihood of uncertain events given a mix of potentially-limited data. As a general rule, the more data added to the mix, the better the result; you can see an example of this in the improved accuracy of spam filters during the "training" period, as they add more examples to their determinations.

By combining the results from multiple well-grounded predictions of climate sensitivity, Annan and Hargreave came up with what they argue is a more accurate prediction of climate sensitivity probability. They argue that a temperature increase above 4.5°C is almost entirely unlikely to occur (the paper says <5%, but on his blog Annan argues that it's far lower than that), and the greatest probability is a 3°C increase at 560ppm. This lines up well with most predictions, even those with less data or a much greater temperature range, adding to the authors' confidence.

A few things to keep in mind:

This may seem like they've just confirmed the conventional wisdom that a roughly 3°C increase is the most likely, and on the surface they have. But much more important is the reduction of the likelihood of potentially-catastrophic increases. The difference between extremes can often be a problem when trying to plan for possible outcomes; by constraining the possible results, it becomes somewhat easier to plan mitigation and response.

That said, this is not an upper-limit on warming, simply an arguably better model of what would result from a doubling of pre-industrial greenhouse gases. If we continue on our present course, or fail to reduce carbon emissions swiftly enough, we could easily blow past 560ppm -- and the corresponding 3°C increase. If this model tells us that we won't necessarily see disaster this century, it doesn't mean that we're off the hook.

Finally, it's important to remember that a Bayesian calculation is only as good as its inputs. A spam filter based on clicking the "junk" button on random items won't work as well as one based on careful assignment of status. If any of the models used by Annan and Hargreave turn out to be mistaken or seriously inaccurate, their Bayesian combination will also be off.

Annan notes that the referees for the journal were extremely tough on this paper, and relying on a universal mathematical formula instead of a climate-specific models is likely off the radar of most atmospheric scientists. It will be very interesting to watch the reactions of climate scientists to this paper -- in particular, what the folks at RealClimate have to say. I don't think we should toss out the "what happens if we hit +6°C" scenarios just yet, but I find this to be a very interesting perspective on how we think about the climate to come.