Monday, May 10, 2010

Explaining Long Tail Climate Risk

In this post, I review a paper from last year in Geophysical Research Letters by Urban and Keller of Penn State University.  The paper (which is free!) explores the reasons for why there is a long tail of probability of very high climate sensitivity, and what might be done about it.  (Given that, if the climate sensitivity were very high, life might get pretty unpleasant, it would be good to know one way or the other).

One caveat before we get going: in reading my writings about very recent climate science papers, readers should be aware that a) these are areas where the science is not settled, and any given paper may turn out to be off on the wrong track, and b) I am not a climate scientist, and thus I may introduce some additional risk of misinterpreting a paper or misunderstanding its context.  Caveat lector!   My goal in blogging about these things is to understand these issues for myself, and also to try to use such gifts for scientific analysis and exposition as I may have to make the issues clearer for non-specialists to whom the primary literature is not very accessible, but who nonetheless care a lot and would like to be informed.

First, let's remind ourselves what we are talking about.  I posted the other day a graph from the 2007 Roe and Baker Science paper which serves to illustrate the situation pretty well:

These are various estimates of what scientists call the probability density function of the climate sensitivity. The climate sensitivity is how much the planet will warm up (on average) as a result of a doubling of the concentration of CO2 in the air. This isn't known, but the graph shows how probable each possible value is, with x-axis being the climate sensitivity, and the y-axis indicating the amount of probability in each one degree (Celsius) range of the x-axis.  The most likely value is around 3oC (5oF), but it's not certain that's actually the value.  The "long-tail" is the region to the right - you can see that, depending on which estimate you like, there is around a 10% chance of a climate sensitivity between 5oC and 6oC, around a 5% chance of a climate sensitivity between 6oC and 7oC, and so on.  These are fairly disastrous values.

Ok, so why don't scientists know?  We've already increased CO2 from 280ppm to about 388ppm:

So that's an increase of about 39% - about a factor 1.4.  And we know that in response, global temperatures have risen about 0.75oC (see p10 here for example, or this).  It happens that 1.4 is very close to the square root of two (1.414), so if we rise another factor of 1.4 from here, that would be a doubling of CO2. And if the first factor of 1.4 gave us 0.75oC in warming, then why can't we guess that another similar multiple will give us another 0.75oC, and figure that the climate sensitivity is thus 1.5oC?  Why do the scientists think it's most likely to be around 3oC and maybe even 6oC or 7oC?  And why are they so uncertain?

The answer is the difficulty of knowing how the ocean enters the picture.  The ocean is thermally connected to the atmosphere, so that as the atmosphere warms due to more heat-trapping gases in it, the oceans warm too.  However, the oceans have a huge thermal mass, compared to the atmosphere, so that they don't warm up that quickly.  In the meantime, they drain heat off from the atmosphere and mean that the full effects of global warming are not yet experienced.  There is more warming "in the pipeline".

However, it is poorly understood exactly how fast the oceans are taking up heat.  The physics that governs heat uptake by the oceans is not well understood enough to predict this theoretically (think chaotic turbulence), and of course experimentally measuring the temperature changes over the entire global ocean is a difficult science project.  This lack of knowledge translates into a lack of certainty about the climate sensitivity.  As Urban and Keller put it:
A given surface air temperature change is consistent with either a relatively large heating which is penetrating rapidly into the oceans and delaying some of the surface warming (i.e., a high climate sensitivity and a high ocean diffusivity), or a relatively small heating which is penetrating slowly into the oceans so the surface warming is quickly experienced (i.e., a low climate sensitivity and a low ocean diffusivity).
The "diffusivity" here is how rapidly the ocean adjusts its temperature to a change in the input from the atmosphere.  Diffusivity is basically a measure of how quickly heat flows through a given object divided by the thermal mass of the object.  A highly diffusive material (say copper) will quickly adopt the temperature of its environment, whereas a low diffusive material (say wood) will only slowly adopt the temperature of the environment (at least in the center of the object).

A very, very rough analogy to the climate sensitivity uncertainty might be this: suppose you wake-up to find yourself locked in a sealed windowless room with walls of an unknown material.  The only contents of the room are a bed and a thermometer.  Your first day in the room, the temperature is stable and comfortable.  However, on the morning of the second day, you notice the temperature is rising quickly - you fear there may be a fire going on outside, but you can't tell - all you can see is the rise in the temperature inside the room.  If that's all you know, you can't distinguish between two situations - a) it's very hot outside the room, but the walls insulate well, and b) it's only a little warm outside the room, but the walls are thin and so you are feeling the consequences of that immediately.  In the first case, you are in much more trouble than the second case (assuming no fire brigade, etc, etc).

A better analogy would be this: suppose that you know the sealed windowless room has fairly thin walls (but you are kept from touching them by, oh, say an electric fence) but that there is also a decent sized swimming pool taking up most of the area of the floor.  You don't know how much heat is going into the swimming pool, so again you can't distinguish between the cases that a) the temperature outside the room is really hot, but right now we are protected by the swimming pool absorbing most of the heat, and b) the swimming pool absorbs heat slowly, but the temperature outside the room is not that bad.  Again, in the short term, the two situations seem similar, but a) is much worse news in the long term.

This is the issue explored by the Urban and Keller paper.  They use experiments with toy 1-dimensional computer models to show that observations of the ocean heat diffusivity would be complementary to observations of the global surface temperature change.  If we knew both well, the uncertainty in the climate sensitivity would be much lower.  The key figure is this one:

The x-axis in each of these graphs is the climate sensitivity (in oC) and the y-axis is the ocean diffusivity (in cm2/s if you really want to know).  In the model world, the true climate sensitivity/diffusivity is shown by the cross, but if you only get to measure the surface temperature, you are in the situation shown in the top panel - the solid lines enclose 5% of the probability around the average, the heavy dashes 50% of the probability, and the dotted lines 95% of the probability.  So in this world, with no information about ocean heat uptake, you can't distinguish at all between low sensitivity/low diffusivity and high sensitivity/high diffusivity.  In the second panel, you have a good measurement of ocean heat uptake, and none about surface temperature.  But in the third panel you have decent measurements of both, and now you can bound the situation and produce a climate sensitivity estimate that is quite close to the true one.

I guess the good news in the second room is this: if the swimming room is taking up most of the heat at present, you might hope that it will continue to do so for a while longer, and you at least have some breathing room while you try to figure out what to do.


Tom Bennion said...


Many thanks for this. I practice environment law in New Zealand and the law here asks the courts to assess adverse effects which are "low probability but high potential impact". I have been told that this long tail of probability for climate sensitivity exists but have never seen it explained so well.

Are there any good comparative risk analyses out there on climate change? For example the risk large parts of the globe become uninhabitable on a wet bulb basis versus risk of death by car crash (one you have used), heart attack, cancer etc.

We argue in courts all the time about the risk of contaminants etc from industrial activities and the levels of risk we are concerned about are far far less than for climate change. But how certain are we about these long tail probabilities? How do they stack up beside, say, EPA standards for uptake of lead by humans.

Tom Bennion

Stuart Staniford said...

"how certain are we about these long tail probabilities"?

That's an excellent question Tom, but it seems we'd fairly quickly get dragged into basic existential questions about the meaning of probability. What does it mean to be "certain" of a probability, since the latter is fundamentally an estimate of our ignorance?

If we think about things like "what's the probability Stuart will live past 2050?", that's something that actuarial tables will express an opinion on, and since we have a large population of prior experience on which to base estimates, we might be willing to grant that the resulting probability was "correct". However, obviously, if I supplied additional information on my health status, diet, exercise habits, etc, all of those might cause the estimate to change. So even there, probability being "correct" means something like "the available information about the subject has been processed and compared to prior populations according to current best practices and an estimate of the probability prepared accordingly."

In the case of the global climate, we have no prior planets/civilizations to compare too, and instead these probability estimates are being made by doing things like running large ensembles of climate models, or making theoretical mathematical estimates of the possibilities. The methods of doing this are not long-established, but instead are being innovated for the specific purpose of clarifying our ignorance of this particular one-time large-scale experiment.

So I'd say that these estimates have to be, in some sense, less certain. Nonetheless, presumably the opinion of leading scientists expressed in leading journals in the last few years is as good as is presently available.

I would imagine in a court at the end of the day, it would come down to what your experts were willing to attest to, and the credibility of those experts?