Dear Mr. Levitt,

The problem of global warming is so big that solving it will require creative thinking from many disciplines. Economists have much to contribute to this effort, particularly with regard to the question of how various means of putting a price on carbon emissions may alter human behavior. Some of the lines of thinking in your first book, Freakonomics, could well have had a bearing on this issue, if brought to bear on the carbon emissions problem. I have very much enjoyed and benefited from the growing collaborations between Geosciences and the Economics department here at the University of Chicago, and had hoped someday to have the pleasure of making your acquaintance. It is more in disappointment than anger that I am writing to you now.

I am addressing this to you rather than your journalist-coauthor because one has become all too accustomed to tendentious screeds from media personalities (think Glenn Beck) with a reckless disregard for the truth. However, if it has come to pass that we can’t expect the William B. Ogden Distinguished Service Professor (and Clark Medalist to boot) at a top-rated department of a respected university to think clearly and honestly with numbers, we are indeed in a sad way.

By now there have been many detailed dissections of everything that is wrong with the treatment of climate in Superfreakonomics , but what has been lost amidst all that extensive discussion is how really simple it would have been to get this stuff right. The problem wasn’t necessarily that you talked to the wrong experts or talked to too few of them. The problem was that you failed to do the most elementary thinking needed to see if what they were saying (or what you thought they were saying) in fact made any sense. If you were stupid, it wouldn’t be so bad to have messed up such elementary reasoning, but I don’t by any means think you are stupid. That makes the failure to do the thinking all the more disappointing. I will take Nathan Myhrvold’s claim about solar cells, which you quoted prominently in your book, as an example.



As quoted by you, Mr. Myhrvold claimed, in effect, that it was pointless to try to solve global warming by building solar cells, because they are black and absorb all the solar energy that hits them, but convert only some 12% to electricity while radiating the rest as heat, warming the planet. Now, maybe you were dazzled by Mr Myhrvold’s brilliance, but don’t we try to teach our students to think for themselves? Let’s go through the arithmetic step by step and see how it comes out. It’s not hard.

Let’s do the thought experiment of building a solar array to generate the entire world’s present electricity consumption, and see what the extra absorption of sunlight by the array does to climate. First we need to find the electricity consumption. Just do a Google search on “World electricity consumption” and here you are:

Now, that’s the total electric energy consumed during the year, and you can turn that into the rate of energy consumption (measured in Watts, just like the world was one big light bulb) by dividing kilowatt hours by the number of hours in a year, and multiplying by 1000 to convert kilowatts into watts. The answer is two trillion Watts, in round numbers. How much area of solar cells do you need to generate this? On average, about 200 Watts falls on each square meter of Earth’s surface, but you might preferentially put your cells in sunnier, clearer places, so let’s call it 250 Watts per square meter. With a 15% efficiency, which is middling for present technology the area you need is

2 trillion Watts/(.15 X 250. Watts per square meter)

or 53,333 square kilometers. That’s a square 231 kilometers on a side, or about the size of a single cell of a typical general circulation model grid box. If we put it on the globe, it looks like this:

So already you should be beginning to suspect that this is a pretty trivial part of the Earth’s surface, and maybe unlikely to have much of an effect on the overall absorbed sunlight. In fact, it’s only 0.01% of the Earth’s surface. The numbers I used to do this calculation can all be found in Wikipedia, or even in a good paperbound World Almanac.

But we should go further, and look at the actual amount of extra solar energy absorbed. As many reviewers of Superfreakonomics have noted, solar cells aren’t actually black, but that’s not the main issue. For the sake of argument, let’s just assume they absorb all the sunlight that falls on them. In my business, we call that “zero albedo” (i.e. zero reflectivity). As many commentators also noted, the albedo of real solar cells is no lower than materials like roofs that they are often placed on, so that solar cells don’t necessarily increase absorbed solar energy at all. Let’s ignore that, though. After all, you might want to put your solar cells in the desert, and you might try to cool the planet by painting your roof white. The albedo of desert sand can also be found easily by doing a Google search on “Albedo Sahara Desert,” for example. Here’s what you get:

So, let’s say that sand has a 50% albedo. That means that each square meter of black solar cell absorbs an extra 125 Watts that otherwise would have been reflected by the sand (i.e. 50% of the 250 Watts per square meter of sunlight). Multiplying by the area of solar cell, we get 6.66 trillion Watts.

That 6.66 trillion Watts is the “waste heat” that is a byproduct of generating electricity by using solar cells. All means of generating electricity involve waste heat, and fossil fuels are not an exception. A typical coal-fired power plant only is around 33% efficient, so you would need to release 6 trillion Watts of heat to burn the coal to make our 2 trillion Watts of electricity. That makes the waste heat of solar cells vs. coal basically a wash, and we could stop right there, but let’s continue our exercise in thinking with numbers anyway.

Wherever it comes from, waste heat is not usually taken into account in global climate calculations for the simple reason that it is utterly trivial in comparison to the heat trapped by the carbon dioxide that is released when you burn fossil fuels to supply energy. For example, that 6 trillion Watts of waste heat from coal burning would amount to only 0.012 Watts per square meter of the Earth’s surface. Without even thinking very hard, you can realize that this is a tiny number compared to the heat-trapping effect of CO2. As a general point of reference, the extra heat trapped by CO2 at the point where you’ve burned enough coal to double the atmospheric CO2 concentration is about 4 Watts per square meter of the Earth’s surface — over 300 times the effect of the waste heat.

The “4 Watts per square meter” statistic gives us an easy point of reference because it is available from any number of easily accessible sources, such as the IPCC Technical Summary or David Archer’s basic textbook that came out of our “Global Warming for Poets” core course. Another simple way to grasp the insignificance of the waste heat effect is to turn it into a temperature change using the standard climate sensitivity of 1 degree C of warming for each 2 Watts per square meter of heat added to the energy budget of the planet (this sensitivity factor also being readily available from sources like the ones I just pointed out). That gives us a warming of 0.006 degrees C for the waste heat from coal burning, and much less for the incremental heat from switching to solar cells. It doesn’t take a lot of thinking to realize that this is a trivial number compared to the magnitude of warming expected from a doubling of CO2.

With just a little more calculation, it’s possible to do a more precise and informative comparison. For coal-fired generation,each kilowatt-hour produced results in emissions of about a quarter kilogram of carbon into the atmosphere in the form of carbon dioxide. For our 16.83 trillion kilowatt-hours of electricity produced each year, we then would emit 4.2 trillion kilograms of carbon, i.e. 4.2 gigatonnes each year. Unlike energy, carbon dioxide accumulates in the atmosphere, and builds up year after year. It is only slowly removed by absorption into the ocean, over hundreds to thousands of years. After a hundred years, 420 gigatonnes will have been emitted, and if half that remains in the atmosphere (remember, rough estimates suffice to make the point here) the atmospheric stock of CO2 carbon will increase by 210 gigatonnes, or 30% of the pre-industrial atmospheric stock of about 700 gigatonnes of carbon. To get the heat trapped by CO2 from that amount of increase, we need to reach all the way back into middle-school math and use the awesome tool of logarithms; the number is

(4 Watts per square meter) X log 2 (1.3)

or 1.5 Watts per square meter. In other words, by the time a hundred years have passed, the heat trapped each year from the CO2 emitted by using coal instead of solar energy to produce electricity is 125 times the effect of the fossil fuel waste heat. And remember that the incremental waste heat from switching to solar cells is even smaller than the fossil fuel waste heat. What’s more, because each passing year sees more CO2 accumulate in the atmosphere, the heat trapping by CO2 continues to go up, while the effect of the waste heat from the fossil fuels or solar cells needed to produce a given amount of electricity stays fixed. Another way of putting it is that the climate effect from the waste heat produced by any kind of power plant is a one-off thing that you incur when you build the plant, whereas the warming effect of the CO2 produced by fossil fuel plants continues to accumulate year after year. The warming effect of the CO2 is a legacy that will continue for many centuries after the coal has run out and the ruins of the power plant are moldering away.

Note that you don’t actually have to wait a hundred years to see the benefit of switching to solar cells. The same arithmetic shows that even at the end of the very first year of operation, the CO2 emissions prevented by the solar array would have trapped 0.017 Watts per square meter if released into the atmosphere. So, at the end of the first year you already come out ahead even if you neglect the waste heat that would have been emitted by burning fossil fuels instead.

So, the bottom line here is that the heat-trapping effect of CO2 is the 800-pound gorilla in climate change. In comparison, waste heat is a trivial contribution to global warming whether the waste heat comes from solar cells or from fossil fuels. Moreover, the incremental waste heat from switching from coal to solar is an even more trivial number, even if you allow for some improvement in the efficiency of coal-fired power plants and ignore any possible improvements in the efficiency of solar cells. So: trivial,trivial trivial. Simple, isn’t it?

By the way, the issue of whether waste heat is an important factor in global warming is one of the questions most commonly asked by students who are first learning about energy budgets and climate change. So, there are no shortage of places where you can learn about this sort of thing. For example, a simple Google search on the words “Global Warming Waste Heat” turns up several pages of accurate references explaining the issue in elementary terms for beginners. Including this article from Wikipedia:

A more substantive (though in the end almost equally trivial) issue is the carbon emitted in the course of manufacturing solar cells, but that is not the matter at hand here. The point here is that really simple arithmetic, which you could not be bothered to do, would have been enough to tell you that the claim that the blackness of solar cells makes solar energy pointless is complete and utter nonsense. I don’t think you would have accepted such laziness and sloppiness in a term paper from one of your students, so why do you accept it from yourself? What does the failure to do such basic thinking with numbers say about the extent to which anything you write can be trusted? How do you think it reflects on the profession of economics when a member of that profession — somebody who that profession seems to esteem highly — publicly and noisily shows that he cannot be bothered to do simple arithmetic and elementary background reading? Not even for a subject of such paramount importance as global warming.

And it’s not as if the “black solar cell” gaffe was the only bit of academic malpractice in your book: among other things, the presentation of aerosol geoengineering as a harmless and cheap quick fix for global warming ignored a great deal of accessible and readily available material on the severe risks involved, as Gavin noted in his recent post. The fault here is not that you dared to advocate geoengineering as a solution. There is a broad spectrum of opinion among scientists about the amount of aerosol geoengineering research that is justified, but very few scientists think of it as anything but a desperate last-ditch attempt, or at best a strategy to be used in extreme moderation as part of a basket of strategies dominated by emissions reductions. You owed it to your readers to present a fair picture of the consequences of geoengineering, but chose not to do so.

May I suggest that if you should happen to need some friendly help next time you take on the topic of climate change, or would like to have a chat about why aerosol geoengineering might not be a cure-all, or just need a critical but informed opponent to bounce ideas off of, you don’t have to go very far. For example…

But given the way Superfreakonomics mangled Ken Caldeira’s rather nuanced views on geoengineering, let’s keep it off the record, eh?

Your colleague,

Raymond T. Pierrehumbert

Louis Block Professor in the Geophysical Sciences

The University of Chicago