Four out of the last 15 posts on this blog have been related to climate change, which is probably a higher ratio than Andrew would like. But lots of people keep responding to them, so the principle “give the people what they want” suggests that another one won’t hurt too much. So, here it is. If you haven’t read the other posts, take a look at Andrew’s thoughts about forming scientific attitudes, and my thoughts on Climategate and my suggestions for characterizing beliefs. And definitely read the comments on those, too, many of which are excellent.
I want to get a graphic “above the fold”, so here’s the plot I’ll be talking about.
I have a PhD in physics, and although much of what I do at work is statistical data analysis and some engineering-type modeling I still have a physicists’ outlook in general. I don’t think a really simple physical model can tell us exactly what the doubling the amount of carbon dioxide in the atmosphere will do…but I do think it can tell us a lot. So, let’s take a look.
Carbon dioxide absorbs and re-radiates infrared radiation. It can’t help but do so. I’d stake my life on it, and I mean that sincerely. Doubling or tripling the amount of carbon dioxide in the atmosphere will definitely affect the radiation balance of the earth. Nobody credible would (or does) disagree with that. The whole debate comes down to: what is the magnitude of the effect. For simplicity, I’ll just talk about the “climate sensitivity”, which is usually defined as the change in global-average temperature if the carbon dioxide concentration is doubled from its pre-industrial level and is held indefinitely at that higher concentration.
I do not claim to be more than a mediocre physicist, but even I can easily follow the calculation that doubling the amount of CO2 in the atmosphere, IF NOTHING ELSE CHANGED, would increase the temperature by between 1C and 2C. (There’s an excellent discussion in John Harte’s “Consider a Spherical Cow”, or at least in the 1988 edition). The reason for that factor-of-two range is the crudity of the specific calculation I have looked at, it’s not inherent: a more careful calculation can give a much more precise estimate for what would happen if the CO2 concentration were doubled and nothing else changed. I don’t think Hal Lewis or Freeman Dyson or any other credible physicist would disagree substantially with the estimate.
But nobody thinks that nothing else would change. One thing that many people agree will change is the amount of water vapor in the atmosphere: if the earth and air warm slightly, the air can hold slightly more water vapor, and the evaporation rate will be slightly higher at a given humidity. Since water vapor is a greenhouse gas — an even more potent one than CO2, per molecule — this would amplify the warming over what you would get from CO2 alone. So, a simple model is: more CO2 -> some warming -> more water vapor -> more warming. This is called “feedback”, but note that this isn’t a feedback
It’s worth noting that at this level of abstraction — not worrying about the spatial distribution of heat or water vapor, but just drawing a sphere outside the earth’s atmosphere and looking at how much energy flows in (from the sun) and how much flows out (from reflected sunlight and from heat radiated from the earth and atmosphere) — there are only a few parameters that are needed to describe the system: what is the solar intensity; what is the average temperature of the earth; what is the earth’s albedo; and a few parameters to describe the atmosphere. This simple calculation is good for some purposes, but it’s limited in what it can tell you. If you want to calculate what will happen to a car if it is in a collision, you can determine things like the post-collision speed of the car with a very simple model that involves only a few parameters…but if you want to know what will happen to a person in the car, that’s a whole different level of complexity.
Anyway: the model that considers only CO2 and water vapor suggests substantial climate sensitivity. So is it “game over”? No, because (1) the amount of water vapor to expect is hard to estimate, and (2) other feedbacks could work the opposite direction from the water vapor one. You only have a few choices, though, if you want to find negative feedbacks. You have to find either a mechanism that increases the albedo, or one that substantially decreases the heat-trapping capacity of the atmosphere even though it has extra CO2 and water vapor in it. I don’t think anybody seriously thinks there is anything to be found in the latter category, so most of the controversy is in the albedo.
For example, if we’ve got extra water vapor in the atmosphere, maybe that will lead to more cloudiness, which would increase the albedo. For people who think climate sensitivity is over-estimated by the IPCC, clouds are almost always one of the things they emphasize, since there aren’t many other ways ways of increasing the albedo. If the cloudiness effect happens and is big enough, the effect of more clouds could even surpass the effect of the water vapor, and the climate sensitivity (as defined) could even be a bit lower than the effect of CO2 alone, though it would still be positive. (Note that we would have a more humid, cloudier earth, which would imply changes is weather and precipitation patterns, so one might say that the climate is sensitive to CO2…but the global average temperature change would be low, and that’s the definition of climate sensitivity that I am talking about).
There are ways of testing the hypothesis that higher temperatures will lead to more cloudiness. For instance you can look at the level of cloudiness when it is cool compared to when it is warm — in winter versus summer, for instance — to help gauge how much cloudier it will be, if any, if the atmosphere warms a little. Or you can try to use physics to model cloud formation and destruction…but now you’re trying to model what happens to the driver inside the crashing car, rather than just what happens to the car; it’s a lot more complicated and nobody really trusts these models. (This is the sort of thing Freeman Dyson has in mind when he says cloudiness is only calculated through fudge factors in the models). The uncertainties in the effect of clouds (negative feedback) and the amount of atmospheric water vapor (positive feedback) are two of the biggest uncertainties in predicting climate sensitivity. There are other feedbacks in both directions, such as desertification (negative), and melting of ice and snow (positive), but these are not as important as water vapor and clouds on a global scale, though they can be very important for local climate.
Putting it all together, obviously just from my point of view: “zero” or a very low number (or a negative number) is an idiot’s estimate for the likely value of climate sensitivity. Such a value _could_ happen, if feedback effects worked out just exactly right, but there’s no reason to expect them to work out just exactly right. The default estimate — the one it should take substantial evidence to move you away from, if you follow the physics — is somewhere in the range of 0.5C to 6C for a doubling of CO2. If someone wants to claim the number is outside that range, well, I agree that it could be but you will have to have some really good evidence, or think of a big effect that has been overlooked somehow. If we think of it from a Bayesian statistics standpoint, then on physical grounds I have a prior estimate that puts most of the probability between 0.5C and 6C for climate sensitivity. (In an earlier draft of this paragraph, I had a range from 1C to 5C instead. I wouldn’t want to be forced to defend to the death every feature of the prior.)
Finally, we get to the graphic. Each of these probability distributions is supposed to summarize the belief of a different person. In blue, we have an “anthropogenic climate change denier.” This is someone who just doesn’t believe that doubling of atmospheric CO2 could have any substantial impact on the global mean temperature. I don’t know if any such people think the effect could be negative, but maybe they do; if they don’t, then just move all of that negative probability into the low positive range somewhere. At any rate, these people are convinced that there is just the right amount of negative feedback to cancel out the known effect of CO2 and the expected effect of water vapor.
In orange, we have a certain type of skeptic. This person thinks low values of climate sensitivity are quite likely. This hypothetical skeptic thinks “experts” (as represented by the IPCC, I’ll get to them, below) are very overcertain in their estimates. But the skeptic also thinks the experts are much more likely to overestimate the sensitivity than to underestimate it.
In red, we have the “consensus” estimate of the Intergovernmental Panel on Climate Change (IPCC). Actually, it’s possible that in their reports they give a statistical distribution, in which case it certainly won’t exactly match the one shown: I based the red curve purely on the IPCC statement that the climate sensitivity is unlikely to be less than 2C, and that values over 4.5C can’t be excluded but don’t provide a very good fit to data.
The purple dotted curve represents what I am calling my “prior distribution,” explained above. I think that if I knew only the physics calculations discussed above, plus the fact that very high climate sensitivity probably isn’t consistent with data from the past 50 years, the dotted purple curve would represent my distribution. It’s hard to return myself to that “state of innocence” though, as Andrew calls it: in fact, I didn’t think hard about that “prior distribution” until I was already aware of a lot of predictions, data, controversy, and so on.
One thing worth noting: the IPCC curve is only narrower than the “Phil prior” by about a factor of 1.5. One way to interpret this is that the IPCC folks don’t actually trust their models very much: all that modeling, and they can only narrow the distribution a little bit compared to what a beginning climate modeler might get from a really simple model. This is worth noting because a standard critique of the climate modeling community is that they “believe their models” too much. And I happen to agree with the critique! The modelers only believe their models a bit, but even that bit is too much, I think. Still, it is clear that the modelers (or at least the IPCC consensus process) are allowing that there is lots of uncertainty.
And, finally, the solid purple line…that’s about where I am now. I’ve given weight to the experts (as represented by the IPCC), but knowing the general truth that everyone, experts and non-experts alike, tends to be overcertain, I have a wider distribution than the IPCC, so I’ve got a non-negligible bit of probability down there at very low values of climate sensitivity. I even agree with the “skeptical” view that the experts are more likely to be overestimating the sensitivity than to be underestimating it, although I think both are possible.
But I think the hypothetical “skeptic” curve puts way too much probability on very low values — not as bad as the “denier”, but still, this is someone who is unjustifiably convinced that negative feedbacks will come close to counteracting the effects of CO2.
(By the way, none of the lines are supposed to go below zero, or even go to zero, at 6C, but the drawing software I used has done some funny stuff there and it doesn’t seem worth fixing. Oh, and each of the curves is intended to have the same integral — unity — but since this is just a by-hand sketch, they probably don’t).
Above, I’ve opened my soul, as it were, to discuss why I believe what I believe. Part of my belief, actually a substantial part, is informed by a very simple physical model that I believe is useful in spite of its simplicity, that shifts my prior well away from 0 as a reasonable estimate of climate sensitivity. What if you don’t have the physics background to evaluate such a model for yourself? Then, you’re more or less forced to choose who you care to believe: deniers, skeptics, “experts,” journalists, bloggers, friends…
In a comment on Andrew’s entry about forming attitudes on scientific issues I said this:
When it comes to anthropogenic climate change, if someone wants to allocate some probability to the chance that the skeptics have it right, I think that’s a very reasonable thing to do. Make it 90% mainstream, 10% skeptics, or even 75% mainstream, 25% skeptics if you are are heavily inclined towards the skeptical camp. But there are people out there who are 90-10 the other way! If you are an expert climate modeler and you think your colleagues have the science wrong, that’s one thing. If you’re just some schmoe who only knows what he reads in the papers, and you choose to assign a 90% or 95% probability to the conclusions of the small band of skeptics…where does that come from? Do you really think the experts in a field get it wrong 90% or 95% of the time?
I think I’ll leave it there.