[Vision2020] Realclimate.org: Albedo of Solar Panels: Popular Book "Superfreakonomics" Fails Basic Math on this Issue

[Ted Moffett]

I am returning to a previous question posed on Vision2020, regarding the
albedo effect of solar panels... I wrote on 4/08/09 that I would have to
research the question to attempt an answer.

Recently on Realclimate.org this issue received a detailed analysis, in
response to data (astonishingly misleading) presented in the popular
science/statistical analysis book, authored in part by Steven Levitt,
"Superfreakonomics."  Apparently this book presents egregious distortions
of basic math regarding the albedo impact of massive solar panel deployment:

http://www.realclimate.org/index.php/archives/2009/10/an-open-letter-to-steve-levitt/#more-1488

 An open letter to Steve Levitt
Filed under:

   - Communicating
Climate<http://www.realclimate.org/index.php/archives/category/communicating-climate/>
   - Reporting on
climate<http://www.realclimate.org/index.php/archives/category/communicating-climate/reporting-on-climate/>

— 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:

[image: GoogleElec]<http://www.realclimate.org/wp-content/uploads/GoogleElec1.png>

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:

[image: Globe] <http://www.realclimate.org/wp-content/uploads/Globe.png>

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:

[image: GoogleSand]<http://www.realclimate.org/wp-content/uploads/GoogleSand1.png>

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 log2(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:

[image: WasteHeatWiki]<http://www.realclimate.org/wp-content/uploads/WasteHeatWiki.png>

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<http://www.realclimate.org/index.php/archives/2009/10/why-levitt-and-dubner-like-geo-engineering-and-why-they-are-wrong/>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…

[image: GoogleMap]<http://www.realclimate.org/wp-content/uploads/GoogleMap1.png>

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
 Comments (pop-up) (578) <http://www.realclimate.org/?comments_popup=1488>
-------------------------------------
On 4/8/09, Ted Moffett <starbliss at gmail.com> wrote:


> I would have to research this issue to attempt an answer.  I am not sure of
> the albedo of the areas you describe that might be covered with solarpanels, nor what the
> albedo of large areas of solar panels is in comparison.
>
> There are proposals to block solar energy via huge numbers of
> micro-mirrors in space or sulfur compounds injected into the upper
> atmosphere, to mimic the cooling effects of volcanoes.  If the Earth had
> numerous volcanoes, or a one or two very powerful ones, exploding, this
> would cool the climate temporarily.  If a large asteroid hits, which
> currently is beyond human technology to stop, though in the future humans
> may have space technology waiting to deflect them, we will have global
> warming that is unimaginable at first (or so some experts say due to heated
> debris that would spread over the globe from the explosive impact), then a
> global winter due to sunlight being blocked.  Don't worry, be happy!  "Dust
> in the wind..." as the Kansas song goes...
>
> As to the methane hydrate in permafrost, also in areas in the oceans and
> some lakes, that warming could destabilize, if the process of methane
> releases from these deposits accelerates in a feedback mechanism due to a
> warming climate... Let's not go there.  Consider that methane hydrates
> contain double or more of the carbon contained in all traditional fossil
> fuels: oil, coal, natural gas.  There are efforts to exploit methane
> hydrates as an energy source, which is potentially huge.
>
> One of the primary theories as to a main cause of the Paleocene-Eocene
> Thermal Maximum, about 55-56 million years ago, when temperatures in the
> oceans and the atmosphere were up to 8 degrees C. warmer than now, and there
> were no polar ice caps, is a methane pulse from methane hydrate releases.
> You can read about this at the website below, though I found errors in the
> text compared to the graphs.  Note the first graph shows an increase in
> methane to about 16000 ppbv, while the text claims the graph shows an
> increase to 1600 ppvb.  An error in editing, I suppose?  Or do I have this
> wrong?
>
> http://www.falw.vu/~renh/methane-pulse.html
>
> Ted Moffett
>
>  On 4/7/09, donald edwards <donaledwards at hotmail.com> wrote:
>>
>>
>> Ted, would you be in a position to ponder a guess as to what effect at
>> countering the lost reflective properties of the melted ice by covering half
>> the states of Nevada, Utah, Arizona and California in reflective solar
>> panels would have; besides the obvious power gains.
>>
>> I mean, would it make a difference in stopping the current melting by
>> reflecting more heat back into space than is possible without any ice to
>> mirror it off rather than the current system of accelerated melting by cause
>> and effect?  Wouldn't this also help avoid the already started cotastrophe
>> of the melting permafrost releasing methane?
>>
>> Just wondered about this before.  Thanks,
>>
>> Don
>>
>>
>>
>>
>>
>>
>>
>
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