[extropy-chat] A Bayesian Looks at Climate Change

[Hal Finney]

I ran into an amazing blog entry from last month which sheds new light
on global warming from an unusual perspective:
http://julesandjames.blogspot.com/2006/03/climate-sensitivity-is-3c.html
The blog entry is by James Annan and describes a paper he coauthored with
J.C. Hargreaves that is being published in Geophysical Research Letters:
http://www.jamstec.go.jp/frcgc/research/d5/jdannan/GRL_sensitivity.pdf

It looks at the question of how sensitive the climate is to changes in CO2
level.  Specifically, how much of a temperature increase, in degrees C,
would we expect if CO2 levels doubled from their pre-industrial baseline?

This is a major question in climatology and has been analyzed from a
number of different directions, with reasonably consistent results:
generally 1.5-4.5 degrees C, with possibly as much as 6C or even higher
seen in some studies, and 3C generally the most likely level.

To put this into perspective, doubling CO2 is about what we expect to do.
An increase of 1.5C would be challenging; 3C very difficult; and 6C a
catastrophic, mass-extinction, end of the world situation.  Hence knowing
the likelihood of the more extreme possibilities is very important.

I'll mention BTW that James Annan got a bit of fame last year when he
offered to bet global warming skeptics that warming would occur.  For a
while he got no takers, and it was a good story: skeptics are afraid
to bet!  Then some guy took him up on it, and it wasn't such a good story
any more, just two people who disagreed.  James also plays the FX idea
futures game where, ironically, the predictions err if anything in the
opposite direction, predicting generally more dire and extreme outcomes
than mainstream science.  So he is what I would consider a clueful guy
(where I define "clueful" as "familiar with Robin Hanson's work"!).

But back to his paper.  Given all these results, Annan and Hargreaves did
a simple, obvious but astonishing thing.  I'll quote from his blog entry:

> So all these diverse methods generate pdfs [probability distribution
> functions] for climate sensitivity that peak at about 3C, but which
> have a long tail reaching to values as high as 6C or beyond at the 95%
> confidence level (and some are even worse). As a result, it's been widely
> asserted that we cannot reasonably rule out such a high value.
>
> So, what did we do that was new? People who have read this post will
> already have worked out the answer. 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. Just like the engineer and physicist in my little story,
> an analysis based on a subset of the available data does not actually
> provide a valid 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."
>
> The answers to these two questions are simply not equivalent
> at all. In their defence - and I don't want people to think I'm
> slamming the important early work in this area - at the time of
> the first estimates, the various distinct strands of evidence had
> not been examined in anything like so much detail, so arguably
> the first few results could be considered valid at the time
> they were generated. However, with more evidence accumulating,
> this is clearly no longer the case.
>
> When we combined some of the most credible and solidly-grounded
> (in our opinion) estimates arising from different observational
> evidence, we found that the resulting posterior pdf was
> substantially narrower than any of the observationally-based
> estimates previously presented. It's inevitable that such a
> narrowing would occur, but we were surprised by how substantial
> the effect was and how robust it was to uncertainties in the
> individual constraints. I suppose with hindsight this is obvious
> but we admit it did rather take us by surprise. As recently
> as last summer, I was happily talking about values in the 5-6C
> region as being plausible, even if the 10C values always seemed
> pretty silly.

The bottom line is that when you combine all these different papers
using Bayesian analysis, you get that climate sensitivity is 3 +/- 0.5
degrees C, an astonishingly narrow estimate given the state of knowledge
in the field.

Annan mentions, "The paper didn't exactly sail through the refereeing
process..."  I can imagine that Geophysical Research Letters does not
see a lot of papers about Bayes theorem!  But this methodology is the
foundation, at least in principle, for the kinds of rational, quantitative
probability estimates that are so necessary in science.

I can't help wondering whether there may be other fields which are ripe to
have the same techniques applied.  Any time you have a variety of results
which are derived by independent means, Bayes provides the framework
for combining the data and updating the probability distribution.
This should be part and parcel of the toolbox of the working scientist,
yet as Annan's experience shows it is actually quite foreign to journals
of the hard sciences.

This sounds like a great paper and a substantial step forward in our
understanding of the likely situation we will face with regard to climate
change if we don't undertake large scale mitigation projects.  A 3C
sensitivity value is not exactly good news, but at least it means that we
are not looking at sterilizing the planet or some such.  And by reducing
uncertainty it should help policy makers to make rational choices.

Hal