Wagging the "Fat Tail" of Climate Catastrophe

How much should we pay to avoid the tiny risk of total destruction?

Ronald Bailey | February 10, 2009

How much should we pay to prevent the tiny probability of human civilization collapsing? That is the question at the center of an esoteric debate over the application of cost-benefit analysis to man-made climate change. Harvard University economist Martin Weitzman raised the issue by putting forth a Dismal Theorem arguing that some consequences, however unlikely, would be so disastrous that cost-benefit analysis should not apply.

The danger, according to Weltzman, lurks at the tails of risk probability distribution. The most common probability distribution is the famous "bell curve." In a normal distribution, about two-thirds of values are within about one standard deviation of the mean. For example, among American males the average height is 5 feet 9 inches, and one standard deviation is about 3 inches. This means that two-thirds of American men are between 5 feet 6 inches and 6 feet in height. 95 percent of men fall within two standard deviations—between 5 feet 3 inches and 6 feet 3 inches—and 99 percent are within three standard deviations.

So there's a 99 percent chance that the next guy you see walking down the street will stand over 5 feet and under 6 feet 6 inches in height. As one moves further and further from the mean height, one finds fewer and fewer men who are outside the ever widening height criteria. The probability that you will meet a man who is over 12 feet tall (26 standard deviations from the mean) is essentially nil.

Climate computer models try to estimate future temperatures given the accumulation of greenhouse gases in the atmosphere. In 2007, the United Nations Intergovernmental Panel on Climate Change's (IPCC) Fourth Assessment Report (4AR) estimated that increases in average global temperature for the next 100 years will fall within a likely range of 1.1 to 6.4 degrees Celsius. An increase of 6.4 degrees would be bad enough, but what if it was too low?

In fact, Weitzman contends that the uncertainties surrounding future man-made climate change are so great that there is some probability that total catastrophe will strike. Statisticians often refer to the extreme right-hand and left-hand sides of a bell-shaped probability distribution as its "tails." In the case of adult male height, the tails eventually go to zero—in other words, there are no adult males under 21 inches tall (17 standard deviations) and none over 9 feet tall (14 standard deviations). Weitzman argues that the probability distribution of high-impact low-probability climate catastrophes has a built-in tendency to be fat tailed: Their tails never fall to zero. His claim is somewhat analogous to arguing that the probability distribution for future temperatures never completely rules out the possibility of meeting the moral equivalent of a 12 foot tall man.

Weitzman focuses on equilibrium climate sensitivity. Climate sensitivity is defined as the global average surface warming that follows a doubling of atmospheric carbon dioxide concentrations. The IPCC 4AR finds that climate sensitivity is "likely to be in the range 2 to 4.5 degrees Celsius with a best estimate of 3 degrees, and is very unlikely to be less than 1.5 degrees. Values substantially higher than 4.5 degrees Celsius cannot be excluded." Without going into detail, Weitzman assumes that uncertainties over values higher than 4.5 degrees Celsius can yield fat tails of catastrophic climate change.

Consequently, Weitzman spins out scenarios in which there could be a 5 percent chance that global average temperature rises by 10 degrees Celsius (20 degrees Fahrenheit) by 2200 and a 1 percent chance that it rises by 20 degrees Celsius (36 degrees Fahrenheit). Considering that the globe's average temperature is now about 15 degrees Celsius (59 degrees Fahrenheit), such massive increases would utterly transform the world and likely wreck civilization. Surely people should just throw out cost-benefit analysis and pay the necessary trillions of dollars to avert this dire possibility, right?

Then again, perhaps Weitzman is premature in declaring the death of cost-benefit analysis. Yale University economist William Nordhaus certainly thinks so and has written a persuasive critique of Weitzman's dismal conclusions. First, Nordhaus notes that Weitzman assumes that societies are so risk averse that they would be willing to spend unlimited amounts of money to avert the infinitesimal probability that civilization will be destroyed. Nordhaus then shows that Weitzman's dismal theorem implies that the world would be willing to spend $10 trillion to prevent a one-in-100 billion chance of being hit by an asteroid. But people do not spend such vast sums in order to avoid low probability catastrophic risks. For example, humanity spends perhaps $4 million annually to find and track possibly dangerous asteroids.

Nordhaus also notes that catastrophic climate change is not the only thing we might worry about. Other low probability civilization destroying risks include "biotechnology, strangelets, runaway computer systems, nuclear proliferation, rogue weeds and bugs, nanotechnology, emerging tropical diseases, alien invaders, asteroids, enslavement by advanced robots, and so on." As Nordhaus adds, "Like global warming, all of these have deep uncertainty—indeed, they may have greater uncertainty because there are fewer well-understood constants in the biological and technological world than in the geophysical world. So, if we accept the Dismal Theorem, we would probably dissolve in a sea of anxiety at the prospect of the infinity of infinitely bad outcomes." If we applied Weitzman's analysis to our individual lives, none of us would ever get out of bed for fear of dying from a slip in the shower or a car accident on the way to work.

Weitzman's analysis also assumes that humanity will not have the time to learn about any impending catastrophic impacts from global warming. But mid-course corrections are possible with climate change. People would notice if the average temperature began to increase rapidly, for example, and would act to counteract it by cutting emissions, deploying low-carbon technologies, or even engaging in geo-engineering. And while other low probability calamities, such as the entire Earth being transformed into strange matter by strangelets produced in high energy physics experiments, don't allow for learning, "there is no point in revising our views about strangelets in the microsecond after we discover that the calculations of the physicists are wrong." And yet, we do not shut down such experiments.

On the crucial issue of climate sensitivity, climate researcher James Annan at Japan's Frontier Research Center for Global Change asks if the uncertainties Weitzman talks about aren't just a reflection of our current ignorance, rather than some inherent feature in the climate system itself. Isn't climate sensitivity an imprecisely known constant about which climate scientists can learn more, eventually converging toward a point estimate? If climate sensitivity turned out to be low, that would mean that future climate disasters were less likely. So instead of spending vast sums of money to cut carbon dioxide emissions, a better strategy would be fund research that aims to more closely specify climate sensitivity.

At the end of his critique of Weitzman's Dismal Theorem, Nordhaus investigates what combination of factors would actually produce a real climate catastrophe. He defines a catastrophic outcome as one in which world per capita consumption declines by at least 50 percent below current levels. Since output is projected to grow substantially over the coming century, this implies a decline that is at least 90 percent below the projected baseline. In contrast, the most extreme climate scenario presented by the gloomy Stern Review had people living in 2200 making do with only 9 times current per capital consumption instead of 13 times current consumption.

Nordhaus ran a number of scenarios through the Dynamic Integrated Model of Climate and Economics (DICE), his integrated assessment model. Integrated assessment models like DICE combine scientific and socio-economic aspects of climate change to assess policy options for climate change control. DICE would produce a catastrophic result only if temperature sensitivity was at 10 degrees Celsius, economic damage occurred rapidly at a tipping point of 3 degrees Celsius, and nobody took any action to prevent the catastrophic chain of events. Interestingly, even when setting all of the physical and damage parameters to extreme values, humanity still had 80 years to cut emissions by 100 percent in order to avoid disaster.

Finally, in his 2008 book, A Question of Balance: Weighing the Options on Global Warming Policies, Nordhaus shares the results of running the cost-benefit analysis through the DICE-2007 model. He found that the optimal policy trajectory is one where the world gradually increases the price of emitting carbon dioxide over the next century at a rate in real terms of 2 to 3 percent per year. Nordhaus concludes that the world should impose a tax of $27 per ton of carbon (or $7.40 per ton of carbon dioxide since burning 1 ton of carbon produces 3.67 tons of carbon dioxide). This tax is equivalent to about 9 cents per gallon of gasoline and 1 cent per kilowatt hour of electricity. The tax should increase to $90 per ton by 2050 and $200 per ton in 2100.

Following this carbon price trajectory, the DICE-2007 model estimates that carbon dioxide emissions would be cut 25 percent from what they would otherwise have been in 2050 and be 45 percent lower than otherwise in 2100. The result would be an increase in global mean temperature relative to today of 1.9 degrees Celsius for 2100 and 2.7 degrees Celsius for 2200.

Comments

|2.10.09 @ 3:17PM|#

That's the essential question posed by Harvard economist Martin Weitzman, who argues that the potential consequences of global warming are so dire that a cost-benefit analysis should not be applied to any proposed solution.

Not sure how we can apply infinite resources to both preventing global warming and preventing an asteroid strike.

D.A. Ridgely|2.10.09 @ 3:32PM|#

Finally, the question must be asked: Why hasn't anyone ever done an analysis of the fat tailed probability that bad government policy will cause a civilization wrecking catastrophe?

If we promise to hire enough research assistants to help stimulate the economy, I'll bet we can get some government money to study the question now!

stuartl|2.10.09 @ 3:46PM|#

....such as the entire Earth being transformed into strange matter by strangelets produced in high energy physics experiments, don't allow for learning, "there is no point in revising our views about strangelets in the microsecond after we discover that the calculations of the physicists are wrong." And yet, we do not shut down such experiments.

Some have tried.

mark|2.10.09 @ 4:03PM|#

Very well-reasoned article. Unfortunately, the alarmists will have their short-term victories in the next year or two; I just hope their ideas are discredited soon.

DADIODADDY|2.10.09 @ 4:21PM|#

Can we have just enough Global Warming so I don't have to wear this stupid Christmas sweater with the reindeer on it anymore? Please...

|2.10.09 @ 4:23PM|#

I just hope their ideas are discredited soon.

I hope so too. People who appreciate the severity of climate change aren't actually people who want it to happen.

DADIODADDY|2.10.09 @ 4:40PM|#

Come on man, I really hate this sweater.

|2.10.09 @ 4:52PM|#

As one moves further and further from the mean height, one finds fewer and fewer men who are outside the ever widening height criteria. The probability that you will meet a man who is over 12 feet tall (26 standard deviations from the mean) is essentially nil.

But! If you do meet a twelve foot tall man, he will snatch you up and, holding you by one leg, bite off your head!

|2.10.09 @ 4:57PM|#

Weitzman assumes that societies are so risk averse that they would be willing to spend unlimited amounts of money to avert the infinitesimal probability that civilization will be destroyed.

There was once a time I would have laughed at this.

|2.10.09 @ 5:05PM|#

And, after he bites your head off, he'll grind your bones to make his bread.

|2.10.09 @ 5:27PM|#

I don't know. I've met a lot of environmentalist activists who seem to be secretly anticipating the end of the world, having to survive together in the post-apocalyptic wasteland, tending their organic farm within a small commune, hunting a gathering, dreading up eachother's hair; God knows they spend enough time thinking about it. It's a kind of fetish.

DannyK|2.10.09 @ 5:40PM|#

I dunno, you're putting an awful lot of weight on the calculations of a single Yale economist. I remember looking at that PDF you linked to and finding a double-handful of false assumptions. And you're also setting up a false choice between spending nothing and "infinite resources" to address climate change.

To use the usual example, people buy fire insurance because there's a small chance that their house will burn down and they'll lose everything. You won't pay an infinite amount for that insurance, but you'll pay something.

Just look at Australia this week for an example of how devastating climate change could be for an entire country. If this really is due to climate change, then their lovely wildfire/drought/flooding combination may become the new norm for Australia.

To return to your human height example, they'll have moved to the Land of the Giants for the forseeable future. And that will be very bad.

|2.10.09 @ 6:11PM|#

If this really is due to climate change, then their lovely wildfire/drought/flooding combination may become the new norm for Australia.

That's a pretty big "if", there. With its friend, the equally big "may."

Reminding me of a previous hobbyhorse, that any sentence containing the word "may" can be rewritten with "may or may not" without changing its meaning. Hence:

If this really is due to climate change, then their lovely wildfire/drought/flooding combination may or may not become the new norm for Australia.

Sounds to me like they probably don't have much to worry about.

You won't pay an infinite amount for that insurance, but you'll pay something.

And this Yalie tool is apparently arguing that you should pay an infinite amount for that insurance. Hence, we mock him.

|2.10.09 @ 6:18PM|#

Uh, the Yalie tool is Nordhaus, who is arguing that you shouldn't pay an infinite amount for that insurance.

|2.10.09 @ 6:43PM|#

"That's the essential question posed by Harvard economist Martin Weitzman, who argues that the potential consequences of global warming are so dire that a cost-benefit analysis should not be applied to any proposed solution."

I wonder how he squares this with the fact that the potential consequences of going to hell are so dire that a cost-benefit analysis should not be applied to any proposed solution. I suggest a 100% income tax, with all the proceeds going to the Catholic church to avoid people going to hell.

Neu Mejican|2.10.09 @ 6:56PM|#

I wonder what process Nordhaus used to validate DICE.

In particular, I wonder how the validation process for Nordhaus's DICE is different than the one used on climate models used by climatologists.[what cross validation techniques is he using to verify his assumptions?]

This
http://sedac.ciesin.columbia.edu/mva/DICE/DICEDET.html

gives me a bunch of dead links.

Chad|2.10.09 @ 6:58PM|#

Ron, after having written all that, why don't you see that cost/benefit analysis just isn't a useful tool for this problem? It is obvious that the outcome of the analysis is more dependant on the assumptions you make (discount rates, economic and population growth rates, chances of catastrophy, "arbitrary" values placed on misery, species loss, risk, etc) than it is on the actual phenomenon of climate change.

The differences in conclusion between a Nordhaus or Copenhagen Consensus analysis and Stern's analysis almost completely boil down to a philosophical debate about the appropriate discount rate rather than anything to do with what they are studying. That's quite telling.

Any time that you discover that the outcome of your model is more sensitive to its assumptions than the data you feed it, you can rapidly conclude that the analysis just isn't providing very useful information.

The science is over. Climate change is happening, and largely man-made. It will be somewhere between a mild annoyance and the apocalypse, centered on really bad. What are you going to do about it?

And as another point to all you libertarians:

To the extent that carbon taxes offset income taxes, it is OK if carbon taxes are too high. As long as they aren't so high that the dead-weight loss on the carbon tax is higher than that on the income tax, we would still be coming out ahead.

jgr|2.10.09 @ 7:12PM|#

I'm willing to reduce the carbon footprint by one Environmental Protection Agency and I'll even throw in Al Gore.

|2.10.09 @ 8:19PM|#

DannyK: In re fire insurance--I believe that Nordhaus thinks that he is calculating the appropriate premium for an AGW policy and that Weitzman's proposed premium is way too high.

Chad: In re dependence upon assumptions--that's a good part of the argument that Nordhaus is making against Weitzman's Dismal Theorem.

However, I do take your point about the philosophical differences being at the center of the discussion.

Finally, of course, what is at stake between Nordhaus and Weitzman is precisely the question of what we should do about AGW - what are the appropriate policies to handle whatever is coming.

Note to all: Just hours after the column was submitted to my editors, I received a copy of Weitzman's new reply to Nordhaus criticisms. I haven't had a chance to read it yet.

Neu Mejican|2.10.09 @ 8:47PM|#

More indepth discussions of this paper are available here.

http://julesandjames.blogspot.com/2007/10/weitzmans-dismal-theorem.html

and here

http://theamericanscene.com/2008/01/04/weitzman-formalism-run-amok

Ron,
I would be interested in Weitzman's response to Nordhaus, are you planning on posting it in an update perhaps.

|2.10.09 @ 11:34PM|#

Numbers pulled out of ass alert!

I hear that the yearly cost of climate (non-uber catastrophic) change around 2100 will be about 3.8 trillion U$D. The global domestic product will be around 550 Trillion U$D.

So barring the unexpected, the costs of only adaptation aren't all that extreme. This is the upper limit of predictable costs. But if all the silly internet numbers are to be believed in other related categories, investing in climate change mitigation has a benefit ration of 20:1. That is this the costs of mitigation with some unavoidable adaptation would be the equivalent value pa of under 200 billion U$D pa. And would have the added benefit of avoiding any unforeseen potential super climate disaster.

Or my math of unsourced intardweb numbers is just plain bad.

|2.10.09 @ 11:37PM|#

Ron B said:
"Finally, of course, what is at stake between Nordhaus and Weitzman is precisely the question of what we should do about AGW - what are the appropriate policies to handle whatever is coming."

How about by not coddling the fossil fuel industries with subsidies and market protections.

That, and the bizarre expectations that coal will still be cheap wtih CO2 sequestration.

|2.11.09 @ 4:14AM|#

Nordhaus example does his argument a disservice by invoking
"a one-in-100 billion chance of being hit by an asteroid.
this understates the odds by a factor of a million for a mere catsatrophe, and a hundred or more relative to the prospect of a mass extinction

There are roughly 100 significant asteroid impact strictures on the extant crust of the Earth, and perhaps ten times as many have been plowed under by subduction .

Divide the age of the Earth by that order of magnitude , and again by a human lifetime and the odds on a catastrophic hit sduring yours are closer to 1 in 64,000

|2.11.09 @ 10:10AM|#

NM: Thanks for the additional links. Actually, I linked to the Annan discussion in my column and I did read through the American Scene blog as well. But more information is always better and other readers may find them of interest.

Sam-Hec: I suspect that the numbers you cite come from Nordhaus. I linked to his book in which he describes his analysis in the column. See also my column describing his earlier calculations here.

I don't believe you will find a single word from me in favor of "coddling" fossil fuels.

Russell Seitz: You're right, but I believe that Nordhaus' point was that IF the asteroid danger was ONLY 1 in 100 billion, then the Dismal Theorem would imply that we should spend $10 trillion to avoid it.

BTW, I think we should spend more than $4 million. On the other hand, as I reported from the Global Catastrophic Risks conference, the good news is that NASA already believes that it has accounted for 80 percent of possibly civilization wrecking asteroids.

|2.11.09 @ 11:53AM|#

Regardless of what the IPCC says, the conclusion that we are warming at all is questionable, let alone at a catastrophic rate. There is plenty of evidence that the Earth has recently been warmer in the past than it is now - Viking farmsteads on Greenland and mines in the Alps revealed by retreating ice (for instance), when industrial CO2 emissions certainly weren't the cause. The natural causes of the previous warmings and coolings are still operative today, even if we don't understand or acknowledge them. In addition, we know that most of the official surface temperature measurements have been corrupted by urbanization, the Urban Heat Island effect, and incompetence: http://www.surfacestations.org/

Neil Craig|2.11.09 @ 12:02PM|#

One weakness of Weitzman's argument is that it makes no allowance for the way in which action in one direction will increase the risk of a catastrophic result in another. For example anyboy worried they might grow to short could take growth hormone to prevent this which would make some sense if it didn't increrase that chance they would end up to short.

The possibility that doing what the Greens want would leave us so over-regulated & be so destructive of innovation that it might produce a diferent catastrophe is credible - indeed considering countries which have adopted all the shibboleths of "environmentalism" are right now heading into a depression unrivaled since at least 1929 (& countires like China & India where Ludditism is not encouraged aren't) makes this catastrophe an odds on bet. Equally in the 1970s the Greens were worried about a new global ice age & one would expect measures to prevent warming would tend to encourage cooling (though to be fair to them their cure at the time for an ice age was less air travel & more Ludditry which is exactly the same as their cure for warming). Avoiding the miniscule threat of 1 catastrophe by increasing 1 greater one & one leading one makes no sense.

|2.11.09 @ 1:33PM|#

I was searching for a simple and non-technical explanation of the Dismal theorem.I found this explanation as an excellent piece for the layman.

DADIODADDY|2.11.09 @ 1:42PM|#

STILL GOT THAT FUCKING SWAETER ON GUYS/GALS...

Neu Mejican|2.11.09 @ 1:43PM|#

Ron,

Oops, missed that link in the column.

I do think the logic of this is being over thought.

The science says...what we are doing will create some predictable problems, we should do less of it to avoid those problems. This is no different, in essence, than recognizing that lead pipes are a bad idea and moving to copper or PVC instead.

The flaw I see in Nordhaus's thinking is the idea that we will move to less carbon intensive energy as we advance just because we are advancing. Without the society recognizing that dumping huge amounts of co2 into the atmosphere is something that is undesirable, that factor won't be taken into account in future advances.

As for the probability of catastrophic problems from c02, they are 100% certain at some future point in time (undeterimined, but probably 2 or 3 centuries) if we continue to dump at the same increasing rate we dump today. That gives us plenty of time to respond to avoid the catastrophic consequences. The arguments about the more near term needs deal with disagreements about what costs are acceptable to avoid smaller scale problems.

FWIW, one of the assumptions that goes into this is that the things that will reduce co2 emissions are a drag on the economy. Amory Lovins makes a good case that this assumption is not only unproven, but exactly backwards.

Many of the steps we can take to reduce c02 emissions are economically sensible. Many will result in less government involvement in people's lives...for instance replacing the income tax with a carbon tax reduces government involvement in employment, could be managed with something much smaller than the IRS.

Yadda yadda

|2.11.09 @ 3:07PM|#

Expounding a little on what NM says,
If global temps reach 5 degrees C higher than preindustrial temps, it doesn't matter when, then Methane Hydrates will begin bubbling huge amounts of methane out the of the depths and into the atmosphere, warming things up. Rumor suggests that these methane emissions might form clouds which could explode as they mix with oxygen and are ignited by lightning.

This may very well end terrestrial civilization.

Via the Methane, temps will rise even faster. Soon Hydrogen sulfide gas, a toxic, ozone eroding, greenhouse gas, will also begin bubbling out of the depths. Breathing it will kill much aerobic life on earth. The ozone layer will be destroyed, killing most surface life left.

Land animals and plants have survived this in the past. But not without being radically changed. The last time it happened the process took tens of thousands of years. We seem to be going at a whole lot faster.

|2.11.09 @ 7:21PM|#

For Brad, the commenter referencing the idea that "the earth has been warmer in the past", and citing viking farmlands and mines in the alps as evidence:

What you're thinking of is the Medieval Warming Period. The MWP is constantly trotted out as evidence that the global temperatures have been higher in the past without major problems and that therefore climate science doesn't really understand what's going on.

The problem with this reasoning is that there's basically no evidence (certainly no scientific consensus) that the MWP affected temperatures anywhere outside of the Northern Atlantic region.

It wasn't a period where the GLOBAL temperatures were higher, it was a period where the temperatures _in one region_ were higher.

So whatever conditions were like in the MWP, it's not particularly relevant to discussion of global mean temperatures to say that one particular region of the planet was warmer at one point.

|2.11.09 @ 9:01PM|#

PKS,
To be fair, that is not entirely true. Th effects were felt throughout the whole north atlantic basin. And the temperature swing was measurable in the rest of the northern hemisphere. But the southern hemisphere was not measurably changed. The MWP is still a poor comparison of human climate adaptability, as it progressed more slowly than now.

Chad|2.11.09 @ 10:17PM|#

"Divide the age of the Earth by that order of magnitude , and again by a human lifetime and the odds on a catastrophic hit sduring yours are closer to 1 in 64,000"

Given the relationship between large temperature swings and mass extinctions in the fossil records, the odds of catastrophy in the span of our lifetimes due to climate change is much, much higher than 1/64000.

Indeed, its closer to certain that 1/64000.

TokyoTom|2.12.09 @ 3:59AM|#

Ron, Marty Weitzman has given me permission to use his draft response to Nordhaus, so I`ve put up a digest of it here:

Snakes & fat tails; Weitzman responds to Nordhaus

It seems to me that Weitzman isn`t saying we should abandon CBA, but simply that CBA can`t really tell us with any confidence whether and how to price carbon. Nordhaus concluded decades agao that we should price carbon; the implication of Weitzman is that we both ought to invest in better determining climate risks and probably ought to price carbon a bit higher to reflect potentially large downside risks.

Regards,

Tom

Neu Mejican|2.12.09 @ 10:16AM|#

TokyoTom,

Thanks for posting that response.

My quick take...Winner Weitzman by TKO.

|2.12.09 @ 4:42PM|#

The IPCC derives its range of projected temperature increases by assuming that carbon dioxide caused the bulk of the extant climate warming and then extrapolating the past by use of what it calls story lines about future conditions. In spite of what Al Gore says, the science about carbon dioxide being the culprit is not settled.

The procedural problem that I see with Weitzman's use of the IPCC ranges of projected temperatures is that the IPCC cannot calculate, or even estimate accurately, the probability of occurrence of any of the story lines that they use to project an envelope of future climate temperature. Therefore, the probability of occurrence of any particular future temperature regime is unknown.

|2.12.09 @ 6:39PM|#

An 'assumption' well founded on now basic physics is not a mere assumption.

Without the heat retaining ability of CO2, the Earth would naturally return to 33 degrees centigrade below 0. Add CO2, and the global mean temperature increases, not linearly, but still it increases.

|2.12.09 @ 7:53PM|#

If you believe Wikipedia...

Naturally occurring greenhouse gases have a mean warming effect of about 33 °C (59 °F), without which Earth would be uninhabitable. On Earth the major greenhouse gases are water vapor, which causes about 36-70 percent of the greenhouse effect (not including clouds); carbon dioxide (CO2), which causes 9-26 percent; methane (CH4), which causes 4-9 percent; and ozone, which causes 3-7 percent.

...then the 33°C is from the present temperature, not 0, and it comprises all GHG, not just CO2.

So the actual decline in temperature due to removing the heat retaining capability of CO2 is closer to 10 or 12°F from present day temps.

At least your 33 was good enough for a successful search!

|2.12.09 @ 9:20PM|#

I did make a booboo there. BUt:
"In the absence of the greenhouse effect and an atmosphere, the Earth's average surface temperature[7] of 14 °C (57 °F) could be as low as −18 °C (−0.4 °F), the black body temperature of the Earth.[8][9][10]" Also from wikipedia.
http://en.wikipedia.org/wiki/Greenhouse_effect
14-33=-18
Still fracking cold.

And it is worth noting that the much ballyhooed water vapor contribution wont be possible as temperatures drop, because the water wont be able to unprecipitate. The methane wont be able to escape from the icy shell that covers the Earth, so scratch that. All others have too small an effect to matter by that point. It would be to cold for us to care.

|2.12.09 @ 9:30PM|#

But if the marginal change is the removal of CO2's warming effect, then the decrease in temperature is between 3°C and 8°C -- not 33°C and not even reducing the 14°C present temp to a freezing average.

I do find it striking that the black-body temperature of earth is 0°F. Someone should tell Herr Fahrenheit's heirs that his reference points were ahead of their time.

|2.12.09 @ 9:52PM|#

no.
IF the planet magically loses CO2's effect, OR Methane's effect, OR Ozone's influence, THEN the planet ALSO consequently loses the greenhouse effect of water vapor. This is because water vapor can't maintain itself with out any one of those other temperature forcings.

At best Ozone would stick around. The blue Earth would be snow white.

|2.12.09 @ 10:00PM|#

Given that the lion's share of warming due to CO2 increases shows up mostly in cold winter nights, I would expect the cooling to show up mostly in cold winter nights as well, thus merely making cold ice colder.

Your claim that some massive cascade occurs after a loss of a very few degrees in average temps requires a bit more of an argument.

|2.12.09 @ 10:05PM|#

The blackbody temp of the earth is 248.573ºK.
The actual temp of the earth is ~287ºK (due to the greenhouse effect)

287º-14º=273º(0ºF) !=248º

|2.12.09 @ 10:14PM|#

273°K is 0°C, not 0°F.

The entirety of my knowledge of the black-body temperature of the earth is from your bolded Wikipedia quote above.

could be as low as −18 °C (−0.4 °F), the black body temperature of the Earth

If that 255°K is wrong, and it should be your later 248°K, then I apologize for getting Herr Fahrenheit's heirs all excited.

|2.12.09 @ 10:18PM|#

OKay,
Magically losing just Ozone's greenhouse effect might only put us back into a geologically-contemorary Ice Age, and not an Ice Ball Earth. Losing current levels of methane's greenhouse effect likely also be a notably chillier Ice age. But the key point stands:

Water vapor is not self maintaining; to persist as a greenhouse gas it needs other more persistent temperature forcings. CO2 is the most persistent, and the most common greenhouse gas. CO2 is the control valve for water vapor.

|2.12.09 @ 10:21PM|#

"273°K is 0°C, not 0°F."
DAMMIT!

287º-14º=273º(-32ºF) !=248º
gah. @_@,

|2.12.09 @ 10:29PM|#

I got the 248k number from the blackbody section of wikipedia:
http://en.wikipedia.org/wiki/Black_body

obviously a discrepancy needs to be resolved somewhere.

Nowthen, back to watching ANIME!!

TokyoTom|2.13.09 @ 5:29AM|#

Ron, allow me a few further notes:

1. As you know Nordhaus has advocated based on CBA that we implement carbon pricing for a decade or two now; Weitzman is in effect saying that CBA doesn't tell us enough about the risks we face and that we should add an insurance component to the carbon price.

2. Surely people should just throw out cost-benefit analysis and pay the necessary trillions of dollars to avert this dire possibility, right? Nowhere does Weitzman suggest this.

3. But mid-course corrections are possible with climate change. People would notice if the average temperature began to increase rapidly, for example, and would act to counteract it by cutting emissions, deploying low-carbon technologies, or even engaging in geo-engineering.

This is basically balderdash and you should know it. The climate cannot turn on a dime. The enormous inertia in the climate makes "mid-course corrections" for all practical purposes impossible within a 50-100 year period.

|2.13.09 @ 5:05PM|#

Sam-Hec and MikeP

I often distrust Wikipedia and in this case, I find that most publications agree that water vapor contributes between 90 and 95 % of the heat holding of the atmosphere. Carbon dioxide accounts for about 85% of the remainder, leaving less than 6% divided among the other gases. I think that the calculation differs because water vapor is highest in the zones where solar radiation is the highest. Those zones are between the two Tropics, Cancer and Capricorn.

Evaporation of water from the oceans probably controls both the temperature and the water content of the atmosphere. The oceans absorb solar radiation and though they may radiate some heat, most of their heat loss is through evaporation of water vapor. As the vapor mixes with cooler air, water vapor condenses and releases heat to the atmosphere.

I realize that IPCC claims that increasing warmth in the atmosphere will lead to increased water vapor in the atmosphere, which will increase the heat retention by the atmosphere. However, that is unproven. Attempts to demonstrate an increasing concentration of water vapor in the atmosphere have failed. I also would point out that increased solar radiation at the surface of the earth would also lead to an increase in the water vapor concentration in the atmosphere. Again, we have no evidence that it is happening.

It is not necessarily true that the water vapor in the air is not self-maintaining. It seems likely to me that the increasing temperature of the air and oceans has caused the increased concentration of carbon dioxide in the air. That is because warm water retains less carbon dioxide than cold water so an ocean being warmed by an increase in solar radiation would release carbon dioxide. Remember, the quantity of carbon dioxide dissolved in the oceans exceeds the quantity of carbon dioxide in the atmosphere by a couple of orders of magnitude, i.e. by at least 100 times.

It actually sounds like Sam-Hec is arguing that we should maintain or increase the concentration of carbon dioxide in the air so as to forestall an ice age. He might have a good point. I say that because all of human experience indicates that a warm climate is good for the life on Earth and that cold climate is bad for life on Earth.

My main point was that we cannot know the probability of any future climate because we cannot know the probability of occurrence of any of the IPCC's story lines. For example, one of the story lines is business as usual. That means we continue for the next 100 years increasing the emissions of carbon dioxide at the rates that we have for the past 150 years. Now, I would think that the probability of such a thing is low, because supplies of fossil fuels will become harder to find and therefore more expensive, which should lead to development of alternative sources of energy. But, I don't know. Furthermore, neither does anyone else. Therefore, we cannot assign a probability to the occurrence of such a thing. That leads to the conclusion that we cannot calculate the probability of any future temperature regime even if the carbon dioxide-induced hypothesis is correct. Personally, I think the probability that the carbon dioxide-induced warming hypothesis is true to be miniscule.

|2.13.09 @ 9:11PM|#

Snorbert,
For most purposes of casual internet discussion, Wikipedia is just fine.

" Attempts to demonstrate an increasing concentration of water vapor in the atmosphere have failed."
Please Google Search 'Water Vapor Increase'. There are a number of credible observations to the contrary.

"I also would point out that increased solar radiation at the surface of the earth would also lead to an increase in the water vapor concentration in the atmosphere. Again, we have no evidence that it is happening. "

Yes we have no evidence of increased solar radiation at the earth's surface. Partly due to the lack of increased average solar radiation over the past 60 years; and we hear/read of Solar Dimming due to the increasing sooty gunk in our atmosphere. So some other temperature forcing must be responsible, neh?

If CO2 were leaving the oceans and going atmospheric due to warmer oceans, then there should be less CO2 in the oceans. Instead, CO2 is increasing in the oceans. Additionally the new atmospheric CO2 would have a particular isotope (fairly high in carbon and oxygen isotope) instead the atmospheric CO2 isotope change is consistent with burning fossil fuels (higher in oxygen isotopes and lower in carbon isotopes). The only other way to get CO2 emissions like this is a Great Basalt Flood...I think we would have noticed this by now.

"It actually sounds like Sam-Hec is arguing that we should maintain or increase the concentration of carbon dioxide in the air so as to forestall an ice age."

Actually I think we need to halt and lower CO2 to between 250 and 350ppm in the short term (geologically speaking). In the long term though, I do see carbon as a valuable tool to control the climate for the enrichment of human civilization. Interesting new article on doing just that:
http://www.azocleantech.com/Details.asp?newsID=4619

|2.13.09 @ 9:20PM|#

p.s.
Snorbert,
I thank you for your thoughtful and civil comment.

Also when I said:
"The only other way to get CO2 emissions like this is a Great Basalt Flood"
I meant wrt to scale. Not isotope proportions; which incidentally would be be low isotopes ratios in both elements for volcanic CO2

|2.13.09 @ 10:49PM|#

Back to the main question posed by Ron Bailey:

How much to pay to fix global warming?

I just came across an article on what (supposedly) the consensus is among economists:
http://tinyurl.com/cx64o6