Devoted readers will remember my interview of Nathan Urban in week302—week305 of This Week’s Finds. We talked about how he estimated the probability that global warming will cause the biggest current in the North Atlantic to collapse.
Now he and a bunch of coauthors have a new paper using paleoclimate data and some of the same mathematical techniques to estimate of how much the Earth will warm if we double the amount of CO2 in the atmosphere:
• A. Schmittner, N.M. Urban, J.D. Shakun, N.D. Mahowald, P.U. Clark, P.J. Bartlein, A.C. Mix and A. Rosell-Melé, Climate sensitivity estimated from temperature reconstructions of the last glacial maximum, Science, 2011.
The average global temperature rise when we double the amount of CO2 in the atmosphere is called the climate sensitivity.
The paper claims that the “likely” (66% probability) climate sensitivity is between 1.7 and 2.6 °C. They say it’s “very likely” (90% probability) that the climate sensitivity is between 1.4 and 2.8 °C. Their best estimate is around 2.2 or 2.3 °C.
If true, this is good news, because other studies suggest 3 °C as the best estimate, 2 to 4.5 °C as the “very likely” range, and a chance of even higher figures.
On the other hand, Nathan and his collaborators predict a significantly higher climate sensitivity on land. Here’s a graph of the probability density for various possible values
As you can see, their analysis easily allows for warming of 3 to 4 °C on land if we double the amount of CO2.
The best summary of the paper is this new interview of Nathan Urban by the blogger ‘thingsbreak’:
• Thingsbreak, Interview with Nathan Urban on his new paper “Climate sensitivity estimated from temperature reconstructions of the last glacial maximum”, Planet 3.0, 24 November 2010.
So, check that out if you want more details but aren’t quite ready for the actual paper! There’s a lot of important stuff I haven’t said here.
Azimuth 
Two corrections: It’s Michael Tobis, not Tobin. Also, although he’s the main blog editor, the interview was conducted by “thingsbreak”, the proprietor of The Way Things Break blog.
Another correction, or at least clarification:
In our study, “climate sensitivity” is a global average quantity, and we don’t consider separate land or ocean sensitivities.
The green curve in the figure shows the global climate sensitivity if we analyze only land temperature data. This is different from “climate sensitivity on land”.
However, the land and ocean do warm by different amounts in response to doubled CO2, so you could define separate land and ocean sensitivities.
Ok, I don’t know if this is actually clearer, but the point is that we’re estimating a global sensitivity using different subsets of data, rather than estimating local sensitivities that apply to different parts of the Earth.
How does he get a probability distribution for something that has never occured before (sudden rise in CO2)? I haven’t read the paper yet.
I think I understand from the interview. He is estimating a parameter called “climate sensitivity” which relates warming to CO2 level. Apparently there is reason to believe that he can get a reasonable estimate of the parameter from the prehistoric data, and apply it to a model of our current climate.
We assume that the climate sensitivity to CO2 can be encoded in a certain physical relationship between temperature and the infrared radiation that the Earth emits to space. We’re effectively estimating the strength of this relationship from past changes in CO2 and temperature, assuming that the relationship is the same in the past and today. Then, continuing to assume this relationship holds, we can infer what the temperature change would be from a rise in CO2.
Unfortunately the climate sensitivity cannot be perfectly represented by this simple temperature-radiation relationship, and so there are limitations to our study.
Is climate sensitivity independent of ice albedo etc.? I won’t be surprised if it’s smaller during glaciation than without ice caps.
Why do you think that? There’s an ice albedo feedback effect: when it gets warmer ice melts making the Earth darker, so it absorbs more heat and it gets warmer. This effect increases the climate sensitivity and it’s substantial. But when it gets warm enough for ice caps to completely vanish I’d expect this effect to diminish. (Not disappear, since it still snows.)
Snowball Earth needs a huge greenhouse to get out of the trap. But that’s an extreme case. Methinks the ice albedo feedback thing can be turned around: With ice the ground doesn’t warm as easily (or, as quick) as without. (Of course the warm would come anyhow – the time scale is crucial and complicates things.)
I’m not sure where (if) I read about possible variability of climate sensitivity, perhaps Hansen.
I just had a look at Hansen’s Storms book, which has an excellent index. On p. 46 he says
(His fig. 30 seems to tell my Snowball Earth example is wrong.) On p.234, regarding a paper by Zachos, Zeebe, Dickens (2009) on the PETM, Hansen is
There are different ways of defining “climate sensitivity”, which depend on what you choose to hold fixed in your hypothetical CO2-doubling experiment. Our definition doesn’t include the albedo feedback of the big LGM continental ice sheets.
On Google+, Timothy Chase pointed out this article about the paper we’re talking about here:
• Michael Marshall, CO2 may not warm the planet as much as thought, New Scientist, 24 November 2011.
and he quoted this part:
Over on Google+, Nick Barnes points out this discussion of the paper we’re talking about here:
• James Annan, More on Schmittner, James’ Empty Blog, 24 November 2011.
and Pedro J. Hdez points out this:
• dana1981, Schmittner et al. (2011) on climate sensitivity – the good, the bad, and the ugly, Skeptical Science, 27 November 2011.
A quote from the latter:
Florifulgurator,
There is no obvious relationship between climate sensitivity and how it should vary with the base climate. One might intuitively expect a different ice albedo feedback from the LGM to pre-industrial vs. pre-industrial-2xCO2 (though as Nathan Urban mentioned, ice sheets are imposed as changed boundary conditions, or forcings, and thus do not necessarily mean an enhanced albedo feedback).
But the ice-albedo feedback is rather small globally, with the exception of possible bifurcation points into a snowball regime. The water vapor feedback tends to be much more important, and that increases at higher temperatures (though, so does the negative lapse rate feedback). The Planck radiative feedback is also non-linear. Clouds might also behave differently between climate states and no one really understands those effects.
Thus, whether climate sensitivity is higher at the LGM or in a greenhouse world really requires a highly model and parameter-dependent answer.
I went through the paper pretty carefully.
Why are the tails so thin on all those PDFs ?
Except for the Land PDF they drop down to the 1e-17 level very rapidly. Doesn’t this modify the Land contributions when you work out the Markov chain reconstruction using Bayes rule?
Aren’t we sitting in the ice-age corner of the climate energy potential well using data from the Last Glacial Maximum? How does this translate to climate sensitivity in a warmer climate when we are almost on the other side of the well currently? It seems like the sensitivity is bumping up against the latent heat of fusion for making lots of sea-ice when we are working in an ice-age climate.
The tails are thin because the likelihood of the data in those areas of parameter space is very small, under the likelihood function we assumed. The land and ocean contributions modify each other when combining the two data sources, but the ocean data are more influential on the final result.
Your second set of questions have to do with state-dependence of climate sensitivity. We should expect some state dependence, but it’s not clear how much (this may be rather model-dependent).
Our model does not completely ignore state dependence: it shouldn’t predict exactly the same warming for a CO2 doubling starting from glacial or interglacial states. For example, we have an interactive sea ice model, and its sea ice (and associated temperature changes) will do different things in response to increased CO2 depending on what state you start from.
However, to conclude something about modern CO2 changes from paleo CO2 changes, we do have to assume that there is some physics in common between glacial and interglacial states. Our methodology assumes that glacial and interglacial states obey the same relationship between temperature and outgoing longwave radiation.
Thanks Dr. Urban for the reply,
I posted an analysis of your paper at Judith Curry’s Climate Etc. blog and attached your comments.
As you probably know, she is interested in the uncertainty aspects of climate science modeling and usually gets a good discussion going.
A few remarks on your analysis:
Fat tails of climate sensitivity are most common in analyses using short-term transient data. They may diminish in paleo studies when transient effects are less important. However, they can reappear in the guise of forcing uncertainties, especially if you use a linearized model when forcing uncertainty includes zero or negative forcings. You’ll get a ratio distribution that hits a divide-by-zero.
The Markov chain algorithm is an adaptive Metropolis Markov chain Monte Carlo (MCMC) algorithm. It is not a HMM.
The default prior for the paper is bounded uniform on the range 0.26 to 8.37 K (the range of the ensemble members), as we state on the paper. We also considered a prior that is bounded uniform in feedback factor instead of ECS (see the SOM).
The thin tails are almost certainly not a result of Monte Carlo sampling. I also tried the analysis where I evaluated the posterior directly on a 1D grid, without sampling (fixing the error variances so I only had to consider ECS uncertainty). I got a similar result as the MCMC analysis.
Why should the climate sensitivity be assumed to be a constant? With all the individual feedback effects kicking at various points I would have assumed a varying sensitivity as more likely.
What does one climate sensitivity measurement of a cold world really imply when it is so removed from today’s climate?
Climate sensitivity probably isn’t constant. It’s often separated into “fast” feedbacks (atmospheric scale) and slower feedbacks (carbon cycle, cryosphere); sometimes the slower feedbacks are omitted from the definition of climate sensitivity. Depending on the time scale you’re interested in, a constant climate sensitivity may be a reasonable zeroth-order approximation (although it’s somewhat artificial, since it’s the infinite time limit and so in principle should include all timescales).
Your second question is aimed at the state-dependence of climate sensitivity, which I discuss somewhat above and in my interview.