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Friday, October 30, 2009

Real Climate: An open letter to Steve Levitt by Raypierre

An open letter to Steve Levitt

— raypierre @ 29 October 2009

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.. . .

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