The Other Half of the Global Warming Problem

For reasons I have discussed in earlier posts,  I am skeptical of the claim that global warming on the scale suggested by the IPCC projections is a serious problem that needs to be dealt with. In this post, I want to look at the other side of the problem. If one accepts the conventional view that it is a serious enough problem to justify the cost of the sharp reduction in the use of fossil fuels needed to substantially reduce it, can it be done?

The reason I suspect it cannot is that preventing global warming faces a public good problem at several levels. Consider first the individual level. One might argue that if global warming is going to make me worse off, that is a reason for me to reduce my use of fossil fuels in order to prevent it. The problem is that although it is a reason, it is a very weak reason, because I would be bearing all of the cost—driving less, or being colder in winter and hotter in summer, or paying more to get my electricity from solar power instead of from natural gas—while receiving only a tiny fraction of the benefit. As with other public goods, one would expect it to be underproduced and, since this is a public good for an enormous public, drastically so.

One popular solution to a public good problem is to have the good produced by government. Have the government hold down the production of CO2 by a carbon tax or a cap and trade system, subsidize the development of technologies for recyclable power, and in various other ways force its citizens to modify their behavior to reduce global warming.

One problem with this solution is that we have no good way of making a government act in the interest of those it rules, in part due to another public good problem. Anything I do to make government do the right things—figuring out which politician supports good policies and voting for him or contributing to his campaign, writing books or op-eds defending good policies and criticizing bad—is itself producing a public good for a large public, since almost all of the benefit of good policies goes to other people. Public goods, especially for large publics, are underproduced, which explains why many voters—about half of them, judging by the highly unscientific experiment of asking students in classes I teach—do not even know the name of the congressman who represnts them, and almost no voter knows enough about all of the relevant issues to have a sound basis for deciding how to vote. That outcome is referred to in the public choice literature as rational ignorance. It is rational to be ignorant when information costs you more than it is worth to you.

If we have no way of making government consistently act in the national interest, we cannot count on government action to deal with global warming, even if it is in our interest to do so. And even if we did have a reliable way of controlling our government, we would still face a second level of public good problem. Controlling global warming is a public good not only at the individual level but at the national level, since if the U.S. holds down its emission of CO2, any benefit is shared with all other countries, whether or not they hold down theirs. Hence even a U.S. government that did act in the interest of its population might choose not to deal with global warming unless it could somehow arrange for most other countries to do so as well. Such an agreement among many beneficiaries of a public good is hard to arrange. It is even harder when, as in this case, the benefits are very unevenly distributed. Even if global warming produces net costs, which for the purposes of this post I am assuming, the costs to some countries will be larger than to others and some countries, most obviously in cold regions, will probably benefit.

I have just offered reasons, at several levels, why nothing will be done to prevent global warming, even if it is worth preventing. Readers may reasonably ask how I can explain the fact that things are being done. The U.S. House passed a cap and trade bill some years ago, although it never made it through the Senate, and it looks as though there will be renewed attempts to get a carbon tax or something similar in the near future. The current administration has subsidized a variety of activities, such as biofuels and the development of electric automobiles, on the theory that they reduce global warming. Similar policies have been employed by a number of other countries, many of which committed themselves some years back to specified future reductions in carbon emissions.

The answer is that while such policies are not worth doing, politically speaking, as a way of reducing global warming, they may be politically profitable in other ways. A loan guarantee to a company whose investors support the current administration, for instance, is a private good, or a public good with a very small public, from the standpoint of those investors, and one they will be willing to pay for in campaign donations or other ways of rewarding the politicians responsible for it. A carbon tax provides a new way of getting money into the hands of government, where it can be used to buy votes or reward supporters. Cap and trade, along the lines of the actual bill passed by the House, generates valuable assets—permits permitting the emission of a set amount of carbon dioxide. Those assets can be, in the House bill were, allocated to politically favored groups. In all of these ways, the campaign against global warming provides rhetorical support for politicians doing things they would like to do, but things that, absent that support, might cost them votes.

Consider as an analogous case Obama’s stimulus program. Very likely Obama believed his own rhetoric, believed that it would bring down unemployment. But supposed he didn’t. As long as other people believed it, the stimulus made political sense for him, since it gave him a convincing excuse to spend large amounts of borrowed money. If he didn’t believe it he had to worry a little about the failure of unemployment to come down as predicted—but, as the most recent presidential election demonstrates, that problem can be overcome. He succeeded in getting reelected by a comfortable margin, despite the striking difference between what he predicted and what happened.

My conclusion is that there may be no practical way of using political mechanisms to slow or prevent global warming, even if it is worth doing. Public support for doing it will be used by politicians to do things they want to do, many of which will impose substantial costs, which is why they need the warming rhetoric to let them do them. The things they do are unlikely to be well designed to prevent global warming, since that will not be the reason they are being done. I offer as one piece of evidence the biofuels program. Part of the original justification for it was the claim that it would reduce CO2 emissions. At this point, a fair number of environmental leaders and organizations have conceded that it will not. It does, however, raise the price of corn, which makes it politically attractive to politicians who want farmers to vote for them, and there is no sign as yet that it is going to go away.

Air and Sea: A Very Simple Model

Thinking about recent arguments on climate, I have been trying to work out the logic of the air/sea interaction in order to make sense of the pattern of warming. My current conclusion is that, on a very simple model, what we observe is qualitatively about what we would expect if at some point around the year 2000 net energy input to the system had for some reason declined. The purpose of this post is to sketch the argument and see if people commenting see anything wrong with it.

My model is a very simple one. The whole atmospheric system is one object with uniform temperature, the sea  another object with uniform temperature. The atmosphere gains heat via net radiation input from the sun, loses it via conduction to the sea. At any instant the temperature of the atmosphere is atmospheric heat/atmospheric heat capacity, and similarly for the sea.

If atmospheric temperature were constant for a sufficiently long time the two temperatures would approach equality, but atmospheric temperature has been rising due to net energy input from the sun. Heat loss to the sea by conduction is proportional to the temperature difference between atmosphere and sea. If the net input from the sun had been constant  for a sufficiently long time, the equilibrium of the system would be a constant temperature difference between atmosphere and sea. That gives a constant net heat increase for the atmosphere (radiation in, conduction out) and for the sea (conduction in). Atmosphere and sea are warming at the same rate because if atmosphere warmed faster the temperature difference would be increasing which would increase heat flow from atmosphere to sea which would decrease the rate of warming of the atmosphere, increase that of the sea, until the two equalized. I am ignoring the fact that as the whole system warmed it would radiate more out to space. For simplicity I assume that that effect is small over the range of temperatures I will be looking at, so we can assume constant net radiative input. I am ignoring the fact that if the process went on long enough the sea would boil. I'm looking at much shorter time period than that—decades not millenia.

Now assume that something changes, reducing net radiative input just enough so that heat coming into the atmosphere via radiation is just equal to heat leaving the atmosphere via conduction. The atmosphere stops warming. But it's still warmer than the sea—that's why it is losing heat via conduction. And since it is still losing heat by conduction, the sea continues to warm. Gradually that warming reduces the temperature difference, reducing the rate of heat transfer from atmosphere to sea, slowing the rate at which the sea is warming. If net radiative input remains constant, atmospheric temperatures will gradually start to go up again. If, on the other hand, net radiative input from the sun declines at the same rate at which heat transfer by conduction is declining, atmospheric temperature will remain constant, sea temperature will continue to rise but at a declining rate. 

Figure 1 is a graph of atmospheric temperature taken from skepticalscience, a pro-warming site (i.e. one that argues that AGW exists and is a very serious problem that needs to be dealt with):

Figure 1

eyeballing it, temperatures appear to flatten out sometime between 1998 and 2002 and remain roughly constant thereafter.

Figure 2 is the same graph of ocean heat that I discussed in a previous post.

Figure 2

Eyeballing it, the rate of warming appears to decline about 2003.

This is a very simple model and a very simple description of the graphs. Since both graphs have a lot of noise, a simple description may be the best we can do. As should be obvious, my point is only qualitative. I have not made any calculation of how large the heat flow should be from atmosphere to sea as a function of temperature difference and I have not offered data on the actual size of the temperature difference over time. 

All of that would require a much more elaborate analysis. My point is only that the observed pattern of atmospheric temperature going flat followed by ocean warming slowing but not stopping is the pattern one would expect if net radiative input dropped. It is thus consistent with the idea of a pause in warming, not in the sense of temperature increase of the whole system going to zero—the sea is still warming—but of the temperature increase of the system slowing in the way to be expected if atmospheric warming stopped.

Two questions for commenters:

1. Have I made any mistake in my analysis of the simple model? The only problem I see is that the drop in rate of warming on Figure 2 looks too abrupt—on my model it ought to be a gradual change. But it's a noisy graph.

2. Are there obvious ways in which making the model more realistic would change the conclusion? In particular, are there obvious improvements which would justify the claim, discussed in my earlier post, that there is no pause because the "missing heat" is going into the ocean? I take that as meaning that what has changed is not the net radiative input from the sun but the conductive loss to the sea, that the flattening of atmospheric temperature is due to an increase in the latter not a decrease in the former.

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P.S. A couple of people commenting on this (one on G+) argue that I have the heat flow backwards, that the input from the sun mostly goes to the land and sea and is then transferred up to the atmosphere rather than going in the other direction as in my model. I have not yet figured out the implications for making sense of the data, assuming they are correct.

What is Wrong with Global Warming Anyway?

The argument for large and expensive efforts to prevent or reduce global warming has three parts, in principle separable: Global temperature is trending up, the reason is human activity, and the consequences of the trend continuing are very bad. Almost all arguments, pro and con, focus on the first two. The third, although necessary to support the conclusion, is for the most part ignored by both sides.

The usual argument to show that an increase in global temperatures by a few degrees centigrade over the next century would be a catastrophe, or at least a very bad thing, consists of pointing out specific bad effects: rising  sea level increasing the risk of flooding in very low lying areas, rising temperature making particular areas less suited to growing the crops they now grow. But an increase in global temperature would also have good effects, as should be obvious to anyone who has ever spent a winter in Chicago, not to mention Alaska or Siberia. The question is not whether there are any bad effects but whether there are net bad effects, whether the increased risk of flooding in Bangladesh does or does not outweigh the opening of a sea route north of Asia and the increase in the habitable area of Canada and Siberia.

The answer, I think, is that nobody knows if the net effects would be good or bad, and probably nobody can know. We are talking, after all, about effects across the world over a century. How accurately could somebody in 1900 have predicted what would matter to human life in 2000? What reason do we have to think we can do better?

Should we, for instance, assume that Bangladesh will still be a poor country a century hence, or that it will by then have followed the path blazed by South Korea, Taiwan, Singapore and Hong Kong—and so be in a position to dike its coast, as Holland did several centuries ago, or move housing some miles further inland, at a cost that can be paid out of petty change? Should we assume that population increase makes agricultural land more valuable and the expansion of the area over which crops can be grown more important, or that improvements in crop yield make it less? While there may be people who believe that they know the answer to such questions, the numbers required to justify such belief are at best educated guesses, in most cases closer to pure invention. Someone who wants to prove that global warming is bad can make high estimates for the costs, low estimates for the benefits, and so prove his case to his own satisfaction. Someone with the opposite agenda can reverse the process and prove his case equally well.

If we cannot calculate in any detail what the actual consequences of global warming and associated costs and benefits will be, an alternative is to ask whether we have any reason to expect, a priori, that costs will be larger than benefits. There are, I think, two answers.

The first is that any change, whether warming or cooling, is presumptively bad, because current human activity is optimized against current conditions. Farmers grow crops suited to the climate where they are growing them; a change in climate will require a costly change in what they grow and how they grow it. Houses are designed for the climate they are built in and located in places not expected, under current circumstances, to flood. Putting it in economic terms, we have born sunk costs based on the current environment, and a change in that environment will eliminate some of the quasi-rents that we expected as the return for those costs.

This is a real argument against rapid change. But the global warming controversy involves changes over not a year or a decade  but a century. Over a century, most farmers will change the crop they find it most profitable to grow multiple times; if average temperatures are trending up, those changes will include a shift towards crops better suited to slightly warmer weather. Over a century, most houses will be torn down and replaced; if sea level is rising, houses currently built on low lying coastal ground will be rebuilt a little farther inland—not much farther if we are talking, as the IPCC estimates suggest we should be, about a rise of a foot or two. Hence the presumption that change is bad is a very weak one for changes as slow as those we have good reason to expect from global warming.

It is hard to see any other reason to expect gobal warming to make us, on net, worse off. The earth and its climate were not, after all, designed for our convenience, so there is no good reason to believe that their current state is optimal for us. It is true that our species evolved to survive under then existing climatic conditions but, over the period for which humans have existed, climate has varied by considerably more than the changes being predicted for global warming. And, for the past many thousands of years, humans have lived and prospered over a range of climates much larger than the range that we expect the climate at any particular location to change by.

If we have no good reason to believe that humans will be substantially worse off after global warming than before, we have no good reason to believe that it is worth bearing sizable costs to prevent global warming.

Readers who reject this conclusion are invited to offer reasons why we should expect the negative effects of global warming to outweigh the positive. Readers on the other side, inclined to post comments attacking me for being so credulous as to accept the reality of anthropogenic global warming, are free to do so but should not expect any response from me, since that is not the argument I am at the moment interested in having.

Two Problems With the 1% Claim

A number of news stories claim that a recent paper by Lovejoy proves that the probability that the warming of the past century is entirely due to natural causes is less than one percent. I find the conclusion plausible enough, but, so far as I can tell, there is no way that it can be derived in the way Lovejoy is said to have derived it.

The first problem, probably the fault of the reporters not of Lovejoy himself, is the misinterpretation of what the confidence result produced by classical statistics means. If you analyze a body of data and reject the null hypothesis at the .01 level, that means that if the null hypothesis is true, the probability that the evidence against it would be as strong as it is is less than .01—the probability of the evidence conditional on the null hypothesis. That does not imply that the probability that the null hypothesis is true given that the evidence against it is that strong is less than .01—the probability of the null hypothesis conditional on the evidence. The two sound similar but are in fact entirely different. 

My standard example is to imagine that you pull a coin out of your pocket, toss it without inspecting it, and get heads twice. The null hypothesis is that it is a fair coin, the alternative hypothesis that it is a double headed coin. The chance of getting two heads if it is a fair coin is only .25. It does not follow that, after getting two heads, you should conclude that the probability is .75 that the coin is double headed. For previous discussions of this issue see this one in the contest of World of Warcraft and this in the context of DNA analysis of mummies.

The second problem is that, so far as I can tell, there is no way Lovejoy could have calculated the probability that natural processes would produce 20th century warming from the data he was using, which consisted of a reconstruction of world temperature from 1500 to the present. The paper is sufficiently complicated so that I may be misinterpreting it, but I think his procedure went essentially as follows:

Assume that changes in global temperature prior to 1880 were due to random natural causes. Use the data from 1500 to 1875 to estimate the probability distribution of natural variation in global temperature. Given that distribution, calculate the probability that natural variation would produce as much warming from 1880 to 2008 as occurred. That probability is less than .01. Hence reject the assumption that warming from 1880 on was entirely due to natural causes at the .01 level.

The problem with this procedure is that data from 1500 on can only give information on random natural processes whose annual probability is high enough so that their effect can be observed and their probability calculated within that time span. Suppose there is some natural process capable of causing a global temperature rise of one degree C in a century whose annual probability is less than .001. The odds are greater than even that it will not occur even once in Lovejoy's data. Hence he has no way of estimating the probability that such a process exists. The existence of such a process would provide an explanation of 20th century warming that does not involve human action. So he cannot estimate, from his data, how likely it is that natural processes would have produced observed warming, which is what he is claiming to do. 20th century warming would, in that case, be what Taleb refers to as a Black Swan event. If one swan in a thousand is black, the observer looks at five hundred swans, finds all of them white, and concludes, incorrectly, that the probability of a black swan is zero.

How does Lovejoy solve that problem? If I correctly read the paper, the answer is:

Stated succinctly, our statistical hypothesis on the natural variability is that its extreme probabilities ... are bracketed by a modified Gaussian...

In other words, he is simply assuming a shape for the probability distribution of natural events that affect global climate. Given that assumed shape, he can use data on the part of the distribution he does observe to deduce the part he does not observe. But he has no way of testing the hypothesis, since it is a hypothesis about a part of the curve for which he has no data.

If I am correctly reading the paper—readers of this post are welcome to correct me if they think I am not—that means that Lovejoy has not only not proved what reporters think he has, he has not proved what he thinks he has either. A correct description of his result would be that the probability that natural processes would produce observed warming, conditional on his assumption about the shape of the probability distribution for natural processes that affect global temperature, is less than .01.

One obvious question is whether this problem matters, whether, on the basis of data other than what went into Lovejoy's paper, one can rule out the possibility of natural events capable of causing rapid warming that occur too infrequently for their probability to be deduced from the past five hundred years of data. I think the answer is that we cannot. The figure below is temperature data deduced from a Greenland ice core. It shows periods of rapid warming, some much more rapid than what we observed in the 20th century, occurring at intervals of several thousand years. During one of them, "The temperature increased by more than 10°C within 40 years." The temperature shown is local not global—we do not have the sort of paleoclimate reconstructions that would be needed to spot similar episodes on a global scale. But the fact that there are natural sources of very rapid local warming with annual frequency below .001 is an argument against ruling out the possibility that such sources exist for global warming as well.

In my next post, I pointed out that not only was it possible that there existed a low probability process capable of producing rapid warming whose cause and hence  probability was independent of the higher probability processes Lovejoy observed, it appears to have actually happened—certainly Lovejoy believes it did. AGW itself is a black swan in precisely the sense discussed above.

AGW, Considered as a Black Swan

In my previous post I took issue with Lovejoy's claim to show, by statistical analysis of global temperature data since 1500, that the probability that natural processes would produce the amount of warming observed in the period 1880 to 2008 was less, probably much less, than one in a hundred. My complaint was not with his conclusion, which might well be true, but with his argument.

In order to calculate the probability that what happened would happen as a result of natural causes of temperature change, Lovejoy needed a probability distribution showing what the probability was of a natural cause producing any given temperature change. He could estimate that distribution by looking at changes over the period from 1500 to 1880 on the (plausible) assumption that humans had little effect on global temperature over that period. But that data could not tell him the probability distribution for events rare enough to be unlikely to show up in his data, for instance some cause of warming that occurred with an annual probability of only .001.

His solution to that problem was to assume a probability distribution, more precisely a range of possible distributions, fit it with the data he had and deduce from it the probability of the rare large events that might have provided a natural cause for 20th century warming. That makes sense if those events are a result of the same processes as the more frequent events, just less likely versions of them—just as flipping a coin and getting eight heads in a row is a result of the same processes that give you four, five, or six heads in a row. But it makes no sense if there are rare large events that are produced by some entirely different process, one whose probability the observed events tell us nothing about—if, for instance, you got four heads in a row by sheer luck, forty heads in a row because someone had slipped you a two headed coin. The forty heads, or the hypothetical rare cause of large warming, would be a black swan, an event sufficiently rare that it had not been observed and so was left out of the calculation.

It occurred to me, after considering a response by Lovejoy and a comment on the Google+ version of my post, that not only was such a black swan event possible in the context of climate, one had occurred. AGW itself is a black swan, a cause of rapid warming whose probability cannot be deduced by looking at the distribution of climate change from the period 1500 to 1880.

If the point is not clear, imagine that Lovejoy wrote his article in 1880. Since warming due to human activity had not yet occurred, there would be no reason for him to distinguish between causes of warming and natural causes of warming. He would interpret the results of his calculations as showing that the probability of warming by a degree C over the next 128 years was less, probably much less, than .01. He would be assuming away the possibility of some cause of substantial warming independent of the causes of past warming, one whose probability could not be predicted from their probability distribution.

That cause being, of course, greenhouse gases produced by human action.

Global Warming, Carbon Taxes, and Public Choice

In earlier posts I argued that global warming is probably real, probably anthropogenic, and will probably impose real but not catastrophic, costs. This raises an obvious question: What, if anything, should we do about it?

If I were dictator of the world, the answer would be fairly obvious. Impose a tax on activities that create greenhouse gases designed to reflect the marginal cost they create. That's the standard economic solution, due to Pigou, for problems of negative externalities. Since the tax brings in additional revenue, combine it with a corresponding reduction in whatever taxes currently have the largest adverse effects.

I do not, in fact, support such carbon taxes. The reason is that I do not believe that, if imposed, they would fit the pattern described above.

To begin with, they would not be based on a realistic estimate of the marginal costs; insofar as they would be based on anything, judging by the ongoing arguments over Kyoto and similar proposals, they would be based on some target level of emissions. If, as seems likely, the level of taxes needed to substantially slow global warming was much higher than the marginal damage done, the result would be to buy lower temperature at a price much higher than it was worth, making the net situation worse, not better.

I offer as further evidence the arguments I have been having over at Brian's "Backseat Driving" blog with people who are absolutely convinced that global warming would have catastrophic consequences but curiously unwilling to support that conviction with anything more than handwaving arguments. Judging by casual observation, they are the norm, not the outliers, of their movement.

Furthermore, I think it unlikely that income from carbon taxes would be used to reduce other taxes. The clear evidence here is the repeated pattern with regard to wars. New taxes are introduced as an emergency measure for a war, retained long after the war is over; there is always some politically profitable way to spend the money. In the case of carbon taxes, I am confident that they would be used as an additional source of revenue, perhaps with the argument that the money was needed to ameliorate the effects of whatever global warming continued to occur.

Finally, I suspect that widespread acceptance of the catastrophist view of global warming would result in quite a lot more than carbon taxes. It would provide a new justification for politically motivated interferences in a wide range of human activities. Anyone who questioned such policies would be labelled a denialist, accused of wanting Bangladeshis to drown and African children to starve. Again, look at the ongoing exchanges on Brian's blog.

Hence I conclude that serious efforts to combat global warming would have large costs, costs justified only if there were good reason to be confident that not taking such efforts would have catastrophic effects.

For the benefit of Brian and his friends, I think it might be useful to clarify the relevant terminology, as deduced from their and my usage:

Denialist: (1) Someone who refuses to accept the current scientific evidence on the existence and causes of global warming.

Denialist: (2) Someone who refuses to reject the current scientific evidence on the likely future scale of the effects of global warming.

Catastrophist: Someone who rejects the current scientific evidence on the likely future scale of the effects of global warming, preferring to believe that sea level will go up much more than current estimates predict, and that global warming will result in large increases in frequency, violence, or both of hurricanes as well as other large climatic changes, all of them adverse.

Global Warming: Confusing Moral and Practical Arguments

In controversies over global warming, one issue that keeps coming up is whether it is anthropogenic, whether if the world is getting warmer it is our fault. So far as I can tell, the question stated in that way is almost entirely irrelevant to the controvery; it reflects a confusion between moral and practical arguments.

Suppose the cause of global warming is not human action but changes in solar activity or some other external factor. Suppose also that the consequences of global warming will be catastrophic. Finally suppose that there is something we can do to prevent global warming, say raising the albedo of the earth with orbital mirrors, high altitude pollution, or whatever. Isn't the argument for doing it precisely the same as if we were causing the warming? Hence isn't "whose fault is it" a wholly irrelevant distraction?

Of course, the questions of causation and prevention are not unrelated. If we are causing global warming that suggests one possible way of preventing it—stop whatever we are doing that causes it. But doing that may be, indeed very likely is, enormously costly, perhaps more costly than letting global warming happen. It might even be impossible, if what we have already done is enough to cause long run catastrophe even if we don't do any more of it. And even if we are causing it and could stop doing so, there might be better solutions.

Concerning Global Warming More Generally

I should add that I am taking no position here on the other usual questions about global warming. I do not know if it is happening, although it seems likely enough. I do not know if, if it is happening, it is due to human action, although that again seems a plausible enough guess. And it is not all clear to me that, if it happens, it will be a bad thing, let alone a catastrophe.

The crucial fact for me is that the more persuasive predictions of bad effects are well into the future; at one point the estimate was a sea level rise of half a meter to a meter over the next century. In my view, the next century is sufficiently uncertain so that it makes little sense to take expensive precautions against risks that far off. By the time the risk arrives, if it arrives, we may have already wiped outselves out in some other way. If we have not wiped ourselves out, our lives may have changed in a way that eliminates or even reverses the problem; communting via virtual reality produces little CO2. If we are still around and the problem is still around, we are likely to have a level of technology and wealth that will make possible a range of solutions well beyond what we are currently considering.

All of these are reasons why I think a persuasive case for doing something about global warming requires evidence, not yet available, of serious negative effects in the fairly near future. But that conclusion does not depend on whether whatever is happening to the climate is or is not our fault.

Land Gained and Lost: A Fermi Estimate

Climate change affects the amount of land usable by humans in at least three different ways. Land is lost through sea level rise. Land is lost because it becomes too hot for human use. Land is gained because it becomes warm enough for human use. Exact calculations of the size of all three effects, if possible at all, would require much more expertise and effort than I am bringing to the problem so what I offer are Fermi estimates, numbers based on very crude approximations. For all three estimates I will be assuming warming of 3°C above current temperatures and sea level rise of .6 m above present sea level, roughly what the latest IPCC report projects for the end of the century under SSP3-7.0.

Land Lost to Sea-level Rise

The amount of land lost equals the length of coastline times the amount by which it shifts in. For the total length of the world’s coastline I found a figure of 356,000 km. The amount by which coastline shifts in with a given amount of sea level rise depends on the slope of the coastal land. I came across a figure of a hundred feet of shift for every foot of sea level rise in a book discussing the situation on the U.S. Atlantic coast; since I do not have figures for every coast in the world, I will use that.

60m coastline shift x 356,000 km of coastline = 21,436 km²

That is my very approximate estimate of land lost to sea level rise.

Land Lost to Rising Temperature

How much does temperature rise in hot parts of the world with 3° more of global warming? Figure SPM.5b of the latest IPCC report[1] shows a map of projected average temperature change due to a 4° increase relative to 1850-1900 in average global temperature, roughly 3° relative to current temperature. Parts of the Earth that are both hot and densely populated appear to warm by a little less than the global average. Table 11.SM.2 shows the effect of different levels of global warming on maximum temperatures. It looks from that as though 3° of global warming would raise the maximum temperature of the relevant regions[2] by about 3°. So if we knew at what temperature, average or maximum, the Earth’s surface becomes too hot for human habitation, we could conclude that any area currently within three degrees of that would, with our assumed level of global warming, become too hot for humans.

The simplest approach to doing this is to compare a map of global temperature (Figure1 ) to a map of population density (Figure 2) and see at what temperature population density goes to close to zero. Comparing the two maps we observe that while the coldest areas of the globe are essentially empty, the hottest are not; some, such as the Philippines, Senegal, and Malaysia, are densely populated. If there is a temperature at which the Earth’s surface becomes unliveable, these maps do not show it. Our estimate of the amount of land lost by the direct effect of heating, calculated in this way, is zero.

We may be able to do a little better by looking at data on cities. The hottest city, by average temperature, is Assab, Eritrea, at 30.5°C, with several others nearly that warm. Hence we can conclude that any city whose average temperature after climate change is less than 30.5° will not be unliveably hot while cities whose temperature is higher than that might be. There are 28 cities with an average temperature of 28°C or more. Their a combined population is about 33 million, which is roughly .7% of the urban population of the world. If we use urban population ratio as a very rough proxy for total population ratio and that as a very rough proxy for land ratio and calculate.7% of the non-arctic land area of Earth, we get 

149 million km² (Land area) – 5.5 million (Antarctica) - .8 million (Greenland) = 143 million km²

143 million km² x.007 = 1 million km²

That gives us a very approximate upper bound for the amount of land that becomes unlivable due to global temperature increasing by three degrees. It is only an upper bound because we do not know that a city would be unliveable at an average temperature of 31°, only that there are no cities that hot.

Both of these calculations are based on average temperature. Arguably what habitability depends on is be maximum temperature. If it gets unendurably hot during a summer day, the fact that winter nights are cold is little compensation.

Figure 3 is the equivalent of Figure 1 for maximum temperatures. The highest temperature regions it shows include densely populated parts of India as well as more sparsely populated parts of Africa and Arabia. Insofar as one can tell from that map, there are no places large enough to show on the map where maximum temperatures are too high for human habitation. It is possible that some would be that hot after an additional three degrees of warning but the combined evidence of Figures 2 and 3 suggests not, since some of the hottest regions are densely populated.

I have been defining usable land as land humans can live on. While there are parts of Earth that seem crowded, average land per person is about five acres, so human populations are not limited by the amount of space to put them in. They might, however, be limited by not enough land to feed them, so it might make more sense to define usable land as land suitable for growing crops.

Is there any significant amount of land that is too hot to grow crops? So far as I can tell, there is not. Maps showing yield of various crops can be found online; some regions with high average and maximum temperatures show substantial yields. The yields shown are averaged over countries, but a map of agriculture in India shows crops being grown across areas within India of both high average and high maximum temperature.

My conclusion from these calculations is that there is probably no substantial amount of land area that will become either uninhabitable or unable to grow crops solely because of temperature with global warming of 3°C.

This does not mean that there is no area that will become either uninhabitable or unable to grow crops as a result of global warming, only that there is no area where it will happen solely because of temperature. Looking at Figure 2, one observes a wide region of northern Africa with almost nobody living there — the Sahara. That area is less hot than some populated regions, so temperature is not the entire reason it is empty, but it can be, almost surely is, part of the reason, so increased temperature might expand it.

On the other hand, the latest IPCC report suggests the possibility that climate change might have the opposite effect:

Some climate model simulations suggest that under future high-emissions scenarios, CO2 radiative forcing causes rapid greening in the Sahel and Sahara regions via precipitation change (Claussen et al., 2003; Drijfhout et al., 2015). For example, in the BNU-ESM RCP8.5 simulation, the change is abrupt with the percentage of bare soil dropping from 45% to 15%, and percentage of tree cover rising from 50% to 75%, within 10 years (2050-2060) (Drijfhout et al., 2015). However, other modelling results suggest that this may  be a short-lived response to CO2 fertilization (Bathiany et al., 2014).

In summary, given outstanding uncertainties in how well the current generation of climate models capture land-surface feedbacks in the Sahel and Sahara, there is low confidence that an abrupt change to a greener state will occur in these regions before 2100 or 2300.

Figuring out all consequences of climate change for the amount of land available for human use is a much more complicated problem than I am trying to solve.

Land Gained Due to Rising Temperature

Human land use at present is limited by cold, not heat, as shown on Figure 2 above — the equator is populated, the polar regions are not. It follows that global warming, by shifting temperature contours towards the poles, should increase the amount of land warm enough for human habitation. Making Antarctica habitable would require a lot more than three degrees of global warming and the southernmost land masses north of it are already inhabited, so any land gains from warming will be in the northern hemisphere.

Figure 11.SM.1 of the sixth IPCC report shows minimum temperature of areas such as North America and Northern Asa going up by between 2 and 3.4 degrees per degree of global warming. Since warming is greater in colder climates, I take 3 degrees per degree as a reasonable guess for the increase in temperature in the northern part of those zones. It follows that three degrees of global warming will increase the temperature in the colder parts of those zones by about nine degrees. To estimate how much land will shift from not quite habitable to at least barely habitable we need two numbers — what length of the contour dividing barely habitable from not quite habitable is over land and how far a nine degree increase in temperature will shift it.

It seems likely that habitability depends more on minimal temperature than on average temperature. Figure 4 shows temperatures in January, which should be close to the minimum, with contours every five degrees — much more precise information than Figure 1 provides for average temperatures. Combining the temperature information on Figure 4 with the population density information on Figure 2, the border of habitability appears to be at about -15°C. Nine degrees of warming will raise the January temperature of land currently at -24° to -15°, so shift the land between those two contours from not quite habitable to barely habitable. I estimate the distance between the -15° and -25° contours to average about 800 km, making the distance between -15° and -24° about 720 km, and the length over land of those contours to total about 15,000 km. Hence the area between them is about 10,800,000 km².

This land is being warmed from not quite habitable to at least barely habitable, from a population density of less than two per square km to a population density of more than two but in some areas less than ten. At the same time, the land a little farther south is being warmed from barely habitable to more than barely habitable, and the land south of that …  . Combining those effects, 10.5 million square km is a rough estimate of the increase in fully usable land.

The analysis so far has used population density as the measure of habitability. As I suggested earlier, it may make more sense to use the ability to grow crops. Crop production maps for Canada and Russia show crops growing in about the same areas that appear habitable by population density, so I have not tried to redo the calculation on that basis.

Conclusion

On the basis of these calculations, I find, for the effect of climate change by the end of the century under SSP3-7.0:

Loss of usable land by flooding due to sea level rise: 21,436 km²

Loss of usable land due to the direct effect of warming: Probably close to zero, with one calculation giving an upper bound of one million km².

Increase of usable land due to the direct effect of warming: 10.8 million km².

All of these numbers are very approximate but they imply a large net increase, due to climate change, in the amount of land usable by humans — more than twice the area of the United States. They also imply that nearly five hundred times as much land is gained through warming as is lost through sea level rise, which makes it odd that only the latter is commonly included in discussions of the effects of climate change.

P.S. Two commenters on this in different places asked why I didn't discuss other work along these lines and one of them provided a link to “Climate change impacts on global agricultural land availability” by Xiao Zhang and Ximing Cai 2011 Environ. Res. Lett. 6. It is a more elaborate analysis than mine, focusing on the amount of arable land and trying to take account of a  wider range of constraints including soil quality and humidity. It finds increases in some regions, decreases in others, with the net effect, not including land not available because of population increase, ranging from -.8 million km² to +1.2 million km². Details of their analysis are difficult to extract from the article — I could not tell, for example, whether the effect of CO₂ fertilization on the water requirement of plants is one of the effects they take into account. The analysis in this chapter is less sophisticated but much easier for the reader to audit, to figure out what I am doing and whether to trust the result.

A similar calculation is done in Ramankutty N et al 2002,  “The global distribution of cultivable lands: current patterns and sensitivity to possible climate change,” Global Ecol. Biogeogr. 11 377–92. That article explicitly takes account of the reduction in water requirements due to CO₂ fertilization. The authors conclude “In the GCM-simulated climate of 2070–99, we estimate an increase in suitable cropland area of 6.6 million km².” Since I am estimating land warm enough for human use and they are estimating land suitable for cultivation, taking account of a variety of constraints, it is not surprising that their figure is lower than mine. The Sahara, for example, is warm enough for human use — there are densely populated regions that are warmer — but not suitable for cultivation.

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This is a draft of a chapter for a book I am working on. I am looking for two sorts of comments:

1. Easy ways of doing my calculations better. There are obviously ways I could make my results more accurate by more complicated calculations but since I don't really care if the real number is twice mine or half it, that isn't worth doing. On the other hand, if there are ways just as easy but smarter, giving a more reliable result, I am interested.

2. Major mistakes. My conclusions are pretty dramatic and I want to know if they are, for some reason, wildly wrong.

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[1] This and other references to IPCC figures in this chapter are to IPCC AR6 WGI Full Report.

[2] SAS, EAS, SEA, and CAF in the table.

 

Global Warming, British Snow, and Filtered Evidence

In a recent online exchange, one poster suggested that the unseasonably cold weather in Britain was evidence against global warming. The response from another was that it was actually evidence in favor, that global warming meant more energy in the weather system, which led to greater variability, hence extremes in both directions.

Neither I nor the poster who made that argument knows enough about the physics of climate to judge whether that claim is or is not true; I am not sure anyone does. Suppose, however, that it is. We then have a serious problem for the ordinary citizen who is trying to figure out from the information that reaches him how seriously to take worries about global warming, who to believe. To see why, consider a simple back of the envelope calculation.

There are at least two features of the weather likely to show up in news stories: temperature and rainfall. Under our assumption, either unusually cold or unusually hot weather, either unusually dry or unusually wet seasons, count as evidence for global warming. Casual evidence for global warming need not be, usually is not, global, nor need it concern an entire year. An unusually hot summer in Australia or North America makes the news, just as an unusually cold winter in Britain does.

So how many different chances are there, each year, to generate evidence in favor of global warming? We have two weather variables, each of which can go in two directions. We have winter, summer, spring, and fall in which it can happen—although stories about temperature in spring and fall will be less striking than winter or summer—and a single month might also generate its own story. For simplicity, let's say there are five relevant time periods in a year. For further simplicity, let's say there are twenty geographical regions sufficiently salient so that unusual weather in one of them will be noticed. Multiply it out and we have four hundred different opportunities each year for the weather to turn out—somewhere, sometime—in a way that will generate a news story seen as evidence in favor of global warming. Whether or not global warming is real and significant, weather is notoriously variable, so we can be pretty sure that some of those four hundred will happen, giving the casual observer reason to believe that global warming is affecting the weather.

What about evidence in the other direction? Under our assumption, unusual weather in any direction counts as evidence in favor, so for evidence against we need usual weather. There are lots of opportunities for that too. But usual weather is not newsworthy—I don't remember any stories last winter, or the winter before, reporting that Britain was having about the usual amount of snow. The news media, for obvious reasons, filter in favor of the unusual, of man bites dog not dog bites man. If all unusual weather counts as evidence on one side of the argument, that side is going to look much stronger than it is.

The problem is not limited to this particular controversy. For an older and arguably more important example, consider religion. If a mother prays for the recovery of her dying child and the child recovers, everyone she knows and many people she doesn't know hear about it. If she prays and the dying child dies, that is likely to get much less attention. Death, after all, is what usually happens to dying people. In this case too, the evidence is filtered in favor of the unusual—and the unusual, in almost any direction, is going to look like evidence in favor,of religion, evidence that something beyond us is intervening.

James Hanson Gets it Partly Right

A recent piece by James Hanson proposes the formation of a centrist political party organized around the issue of global warming. The policy he proposes is a carbon tax charged to producers of fossil fuels, with the revenue returned to the population as a fixed amount per capita which he calls a dividend. Otherwise known as a demogrant.

There are several things I found interesting about the proposal. One is that, given his factual beliefs—that global warming due to the burning of fossil fuel imposes very large net costs—he has the economics right. His proposal makes much more sense than what politicians who talk about global warming have actually been pushing, which has ranged from electric auto subsidies to the mandated use of biofuels. If burning fossil fuels  produces large net externalities, the sensible way of taking account of them is to include those costs in the price of fuel and let individuals in a market society adjust to them.

Another thing I found interesting was the way in which his proposal was targeted at the political center. Conservatives and libertarians, even ones who agree with Hanson about the dangers of global warming, are unlikely to approve  either of a tax that goes to increase government spending or of extensive regulation. They might prefer that revenues from a carbon tax go to reduce other taxes or to reduce the deficit, but distributing the money to the population is at least better than sending it to Washington. 

Those left of center might prefer that the revenues from a carbon tax go to help the poor. But while a  demogrant is not a very efficient form of income redistribution, it does on net transfer from the rich to the poor, since the rich consume, on average, more fossil fuel than the poor and so pay more of the tax. The net effect of his proposal is to reduce the production of CO2 in what economists view as the least costly way of doing so without doing anything that either the left or the right would object very strongly to. The right gets the market, the left gets some mild redistribution, and earth stays cool. It is a policy that should be popular with people on both left and right who agree with Hanson about the dangers of global warming.

One other thing I liked about the Hanson essay is that he argues in favor of nuclear power. As I pointed out some time back, nuclear power is the one substitute for fossil fuel that produces no CO2 and can be expanded almost without limit. That does not prove it should be expanded—for one thing, it is currently a more expensive source of power than fossil fuel. But it does mean that people worried about global warming ought to be biased in favor of nuclear power—and Hanson is.

 

There are, however, two things wrong with his proposal. The first is that, on the historical evidence, creating a third party in the U.S. political system and making it a serious competitor to the existing parties is extremely hard, so hard that it has been more than a hundred and fifty years since the last time it happened. If global warming were really producing, here and now, the sorts of catastrophes its prophets warn of, that might be enough to make it possible, but it isn't.

The second is that Hanson, like many other people, takes it for granted that global warming will have large net negative effects. For reasons I have discussed in earlier posts, I don't. So far as I can see, global warming on the scale suggested by the IPCC reports, about three degrees Centigrade and a foot or two of sea level rise over a century, is at least as likely to produce net positive effects as net negative, probably more likely. That might not be true if the  trend was continued for several more centuries but, given how rapidly technological change is altering the world, I think any predictions more than a century out, probably any predictions even that far out, should be viewed with extreme skepticism.

My past posts on global warming.

Mann v. Hansen: They Aren't All the Same

My interest in the global warming controversy centers mostly on the question, largely although not entirely economic, of what the net effect for humans would be of global warming on the scale suggested by past IPCC projections; for details see my previous posts on the subject. I have, however, also been an observer, mostly from a safe distance, of the ongoing war between proponents of the conventional view of global warming and critics. For anyone else interested in observing it, I suggest the RealClimate blog for the former side and Anthony Watt's What's Up With That for the latter. They represent the more reasonable range of their respective factions. For the less reasonable range, a sample of both sides can be found on the Usenet group alt.global-warming.

One not surprising feature of the argument is that each side tends to demonize everyone on the other side. That is a mistake. Some people hold a position for good reasons, some for bad. Some supporters of a position are honest, some are not. And that is true both of correct positions and of incorrect ones, given that most such disputes are over questions complicated enough so that there are good arguments for both sides.

I was reminded of this point by a recent link on WUWT to a paper coauthored by James Hansen, who has been a prominent supporter of the idea that global warming is a very serious problem and strong measures should be taken to deal with it. The paper is a defense of nuclear energy, both on the grounds that it results in many fewer deaths than conventional energy sources and on the grounds that it does not produce CO2, hence shifting to nuclear energy would reduce global warming.

That is interesting because, while the second point is clearly true and the first may well be, it is not a position popular with environmentalists. I pointed that out in an old post on this blog, and ended with:

I am sure there are people who are both seriously worried about global warming and in favor of nuclear power. But how many of them are there? How many high profile spokesmen or organizations have taken that position?

 I now have at least one example.

This is the second time I have noticed Hansen getting something right. The first was a video of a talk he gave on how to control global warming. It was in favor of what economists call a pigouvian tax, in this case a tax on putting CO2 in the air, as a superior alternative to more direct forms of regulation. Given his underlying assumption—that global warming produces large net negative externalities—he had the economics right. In that case as well, although not as clearly, he was going against the consensus of "his side," most of whose members, in my experience, support a range of more direct regulations and many of whom disapprove of the idea of allowing firms to "buy the right to pollute."

I offer, as a contrast to Hansen, another prominent figure on the same side of the dispute, Michael Mann, most famous for his role in the hockey stick controversy, the argument over whether features of a graph of global temperature in an article he co-authored were real or were artifacts of an error in the statistical procedure he used to produce it. That particular controversy is complicated enough so that I have no strong opinion on it, although I do have the opinion of one statistician I know that there was a real problem with the analysis. 

But I also observed, mostly via arguments on the Usenet group, a less important controversy over a simpler issue, the claim by Mann, his university, and his supporters, that he was a "Nobel winning scientist."

[Later addition: Tim Lambert in the comments points out that the university web page claimed Mann won a Nobel prize (along with others), but specifies the peace prize, hence does not describe him as a "Nobel winning scientist."  The claim on Mann's facebook page was similar. 

So I don't have evidence that Mann or the university described him as a "Nobel winning scientist," merely that they (falsely) claimed he had won a Nobel prize. On the other hand, a quick google finds lots of stories by supporters, including stories of interviews with Mann, which do describe him as a "Nobel winning scientist," which seems unlikely if he made any effort to correct those who so described him.]

That claim was bogus twice over. To begin with, the Nobel prize in question was the Peace Prize, so even if Mann had won it, the description, although literally true, would be misleading. But in fact, the prize did not go to him, it went to the IPCC. His claim was based on a certificate from the IPCC, sent to a substantial number of people, crediting them with work that helped the organization win the prize. 

Doing work, along with others, that helps an organization win the Peace Prize does not make you a Nobel prize winning scientist, as should have been obvious to anyone not blindly partisan—but wasn't to a considerable number of people who were. Mann's university, many of his supporters, and (I think) Mann himself, finally abandoned the claim after someone got in touch with the Nobel committee and got the response that the prize had been given to the IPCC, not to Mann et. al., and he was thus not a Nobel winner. That does not tell me whether the hockey stick is or isn't bogus, but it does tell me something about Mann that makes me very reluctant to trust anything he writes.

I could, I suppose, make longer lists of good guys and bad guys on both sides of this and other controversies—Pachauri, the head of the IPCC, would be on the same list as Mann, for his role in the Himalayan glacier controversy. So would some people on my side of other issues. But I think two examples are sufficient to make the point.

Nordhaus on Global Warming

A correspondent points me at the work of Nordhaus and Boyer, attempting to estimate the externality from CO2 production and the appropriate response. I have not read the printed version, but there is a webbed version available. A number of things strike me:

1. Their conclusion is that 

"current approaches, such as the Kyoto Protocol, are highly inefficient, with abatement costs approximately ten times their benefits in reduced damages."

2. In order to get even that result, they depend on including costs from a very uncertain estimate of the risk that global warming will result in low probability catastrophes of one sort or another: 

"this approach is taken because of the finding of the first-generation studies that the impacts on market sectors are likely to be relatively limited."

Or in other words, without including the costs from such catastrophic risks, global warming doesn't seem to be a serious problem.

3. They estimated the cost from low probability catastrophes by asking a lot of experts how likely they thought it was that there would be a catastrophe, assuming a given rise in global temperature, that would reduce world GNP by at least 25%.

Even if one takes seriously the output of that sort of procedure, there is a striking asymmetry in their approach. They do not appear to have asked any experts what the chance is that preventing global warming would cause a catastrophe—or, to put it differently, that global warming will prevent one. Yet, as I keep pointing out, earth's climate was not designed for us, hence there is no a priori reason to assume that large negative results due to a few degrees of warming are more likely than large positive ones.

This is a striking illustration of my general critique of the "add up the externalities" approach to policy issues. Possible changes can have both positive and negative effects. If you want to conclude that something should be prevented, you focus on the negative effects, ignore or minimize the positive ones, and claim to have an objective argument to support your conclusion. That is precisely what Nordhaus and Boyer have done. The only surprising part is that, even after doing that, they still got only a weak version of the (presumably) desired conclusion.

This leaves me wondering what the pro-global warming view of Nordhaus and Boyer is. Their conclusion  weakens the case for something like the Kyoto protocol--and that conclusion hinges on a procedure that cannot, I think, be defended. Correct that error and their work appears to provide no support for any substantial effort to prevent global warming.

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P.S. After writing this, it occurred to me that there is one respect in which I am being too hard on Nordhaus and Boyer. Suppose we limit "catastrophes" to changes that are not only unlikely and very large, but also very fast. Then there really is some asymmetry to the situation. Humans are currently optimized against the current environment, making any change presumptively negative. I have argued in the past that that is not a strong argument with regard to changes that occur slowly—for example three degrees of warming in a century—since humans will in any case be changing what they do in many ways over so long a period. But that argument would not apply to a change that occurred over only a few years.

If, for instance, climate change makes Europe unbearably cold but adds an equal amount of acceptable land elsewhere, say in northern Canada, and does it in only a couple of years, there will be a very large net cost.

So they would have a legitimate case if they limited their category of catastrophes to rapid ones—but, so far as I can tell from what they wrote, they did not.

Have Past IPCC Temperature Projections/Predictions Been Accurate?

Arguments for or against doing things to slow climate change depend on what will happen if we don’t, a question the IPCC reports try to answer. That makes it important to know how reliable their predictions are. The latest report runs to almost four thousand pages, largely of detailed analysis depending on multiple scholarly articles for each step — Chapter 7, to pick one at random, has fifty editors and about nine hundred articles in its list of references. Someone with infinite time, energy and expertise might be able to go through all of the calculations that produced the predictions in the reports in order to see if they were done correctly, but that is not a practical option.

There is an alternative. The climate system is too complicated to make predictions on the basis of theory alone, hence the IPCC project largely consists of sophisticated curve fitting, picking a form for the relationship among observables suggested by physical theory, choosing parameters for the relationships, how strong each effect is, by finding the values that best fit historical data.  With enough tweaking of the models and adjusting of parameters that process can fit past data, but that does not tell you whether the models fit the real system well enough to correctly predict future data. As someone is supposed to have said, with enough parameters you can fit the skyline of New York.

The solution, for both the researcher who wants to know if his model is right and someone else trying to decide whether to believe him, is to test the model against data that were not used in creating it. We do not know the future, the future eventually becomes the past, so a model constructed in 1990 can be tested in 2021 against data that did not exist when the model was constructed.

The past reports are webbed. Back in 2014 I looked at each to see what someone who read it would expect future temperature to do and reported the results on my blog. If you would like to check my conclusions about what each report implied for yourself you can find links to the reports here.

What the IPCC Predicted

The executive summary of the first report (1990) contains:

Under the IPCC Business-as-Usual (Scenario A) emissions of greenhouse gases, the average rate of increase of global mean temperature during the next century is estimated to be about 0.3°C per decade (with an uncertainty range of 0.2°C to 0.5°C).

The graph shown for the increase is close to a straight line at least from 2000 on, so it seems reasonable to ask whether the average increase from 1990 to the present is within that range. 

Figure 18 from the Second Assessment Report (1995) shows the future temperature through 2020. Through that date, it rises steadily at about .14°C/decade.[1]

From the Third Assessment Report (2001):[2]

For the periods 1990 to 2025 and 1990 to 2050, the projected increases are 0.4 to 1.1°C and 0.8 to 2.6°C, respectively.

For the former period, that implies an increase of from .11 to .31 °C/decade.

The Fourth Assessment Report (2007) has[3]

For the next two decades a warming of about 0.2°C per decade is projected for a range of SRES emissions scenarios.

What Happened

When I did the calculations in 2014, I found that the IPCC had predicted high four times out of four, twice by enough so that actual warming was below the bottom of the predicted range. That looked like evidence that we should not put much weight on their predictions of future temperature.

We now have seven years more data, so I did it again. As of September of 2021, when I am writing this, the last year whose temperature is shown on the NASA page I am using is 2018; I have redone the calculations accordingly. Here are the results:

The first IPCC report was released in 1990. From then to 2018, global temperature rose .38°C for an average of .14°C/decade, well below the predicted range.

The second report was released in 1995. From then to 2018, temperature rose by .37°C, for an average rate of growth of .16 °C, a little higher than the prediction.

 

The third report was released in 2001. From then to 2018, temperature rose by .29°C for an average of .17°C/decade, towards the lower end of the predicted range.

 

The fourth report was released in 2007. From then until 2018, temperature rose by .18 degrees, .16°C/decade, below the predicted .2°C.

 

The predictions look better now than they did in 2014, high three times out of four, low once, and only once has actual warming been below the predicted range. They are still running a little high but the results look consistent with random error. That makes it at least possible that the IPCC researchers are now modeling the climate system well enough to produce reasonable estimates of its future behavior.

It is possible but far from certain because the test they passed is not a very strong one. A theory that correctly predicted the outcome of next year’s elections, including every house seat, every senate seat, and the total votes for each party, would be a very good theory indeed, since doing that well by chance is very unlikely, so we would have good reason to trust its future predictions. A theory which correctly predicted which party will end up with a senate majority after the 2022 election would be better than one that got it wrong but not much better, since one can get the right answer half the time by flipping a coin.

The IPCC reports rely on complicated models and a lot of data. One way to judge how impressive their results are, how much evidence that they have done a good job of modelling climate, is to compare their results with those of much simpler models. The simplest is the assumption that global temperature never changes. The IPCC did a little worse than that model in 1990, since it predicted warming from then to 2018 of .3°/decade and the actual value,  .14°/decade, was closer to zero. But they did much better than that model the next three times.

The next simplest model is a straight line. From 1910, about when current warming started, to 1990, when the first IPCC report came out, warming was .11 °C/decade. The rate of warming from 1990 to 2018 was .14 °C/decade, so the straight-line prediction made in 1990 predicts about 79% of warming from then to 2018. The ratio of the IPCC prediction to what actually happened was 250% for the 1990 prediction, 81% for the 1995, 125% for the 2001 and 2007 predictions.[4] So predicting that the rate of warming would continue at its average level as of 1990 does much better than the 1990 prediction, about as well as the three later ones.

One test of how good the IPCC models are is to see how well each of them did at predicting warming from then to now. The first report fails that test, the next three pass it; actual warming was within their predicted range although not equal to their best guess. That is evidence that those models can be expect to give correct predictions in the future but not very strong evidence. 

It is, however, much better than the evidence was in 2014.

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[1] The figure is on page 323 of Climate Change 1995 The Science of Climate Change. When I did my calculations in 2014 I thought it was .13°/decade but measuring the graph more carefully I now think it is .14.

[2] Page 60 of Climate Change 2001 Synthesis Report.

[3] Page 7 of Climate Change 2007 Synthesis Report.

[4] I am defining each of the IPCC predictions as the predicted value if there is one or the center of the range if there isn’t.