Wednesday, December 06, 2006

Shine on shine on Monckton's moon......

There has been much ado about Monckton's folly, aka "Apocalypse Cancelled" which first appeared in the Sunday Telegraph, complete with instructions to the unlettered, aka discussion, calculations and references. The overnight shift at Rabett Labs (we are growing stuff again, and it does take forever and two days) is extremely grateful to Monckton of Brenchley, for otherwise we might be doing productive things while we wait for the paint to dry.

Now Eli is an old and crafty Rabett (how the hell do you think you get to be an old Rabett with all them bears and program managers out there trying to get your grants, aka cheese), and he knows that when people start to wade through dense pack, they very seldom get far, and the really juicy stuff is oft hid at the back, where only the ghoulies and the ghillies go, so he started on page 30, where Monckton describes his M model (the references start on 34).

With the rest of the fun bunch, he steps through the standard Stefan-Boltzmann argument about the temperature of an atmosphere lacking earth. It actually is standard stuff that you can find all over the net. A nice example is this dry lab at the Colorado School of Mines. The calculation Monckton does starts on pg 10 of the dry lab, but there is much other information there that you might be interested in. Pretty much the same thing occurs in all the "M Models" (blame him for that, not me). The temperature of the Earth without an atmosphere would be given, on average by
If you use standard values for the solar constant, the albedo (alpha), and the Stefan Boltzman constant (sigma) you get T~ (255K) [UPDATE: that's a ~ for approximately, not a negative sign].

Monckton then notes that the average global temperature (surface, sea, whatever) is about 15 C or 288 K and then says that the greenhouse effect is ~ (30K), not the ~ (20 K) referred to in the IPCC TAR and elsewhere. He gets quite huffy about this.

So dear friends, we ask, why is 255 K the right answer to the wrong question?

Well it turns out to be interesting. In his calculation for the earth without an atmosphere, Monckton uses the average albedo of the earth with an atmosphere, about .31. That includes clouds (not there if you don't have an atmosphere), water (tends to go away in a vacuum), and ice to some extent, but surely not grass.

What value of the albedo SHOULD you use when the atmosphere ain't there: The Moon's albedo might be a good estimate or maybe that of Mars:
Astronomers have determined the visual albedos of our planets. From NASA’s planetary sites, the brightest is Venus with an albedo of 0.65. That means 65% of incoming sunlight is reflected from the cloud-covered planet. The remaining 35% contributes to the heat energy of Venus. Mercury, at 0.11, has the lowest planetary albedo. Earth’s albedo is 0.37; Mars is 0.15; Jupiter, 0.52; Saturn, 0.47; Uranus, 0.51; Neptune 0.41. Pluto’s albedo varies from 0.5 to 0.7.

It should be pointed out that these planetary albedos are averages. Taking Earth as an example, clouds vary from 0.4 to 0.8, snow varies from 0.4 to 0.85, forests vary from 0.04 to 0.1, grass is about 0.15, and water varies from 0.02 with the Sun directly overhead to 0.8 at low levels of incidence. So the Earth’s albedo varies, and depends on the extent of cloudiness, snowfall, and the Sun’s angle of incidence on the oceans. With an average albedo of 0.37, 63% of incoming solar energy contributes to the warmth of our planet. It’s obvious that if cloud cover were to decrease significantly, the Earth’s surface temperature would increase, contributing to other factors of global warming such as the amounts of greenhouse gasses.

Our Moon’s average albedo is 0.12.
So you plug a Mars like 0.15 in for alpha, and turn the crank and you get a warm 268 K, about 13 K higher than if you used the 0.31 albedo typical of an Earth with an atmosphere. And, as you can see, this gives a greenhouse warming of 20 K, and a lot of Monckton's arguments go down the drain.

UPDATE: We can gain another insight into the problem by looking at the Earth's Radiation Budget. Below (you may have to open the figure up in a new window) you can see that of the incoming ~ 342 W/m^2 about 102 are reflected in the atmosphere (the albedo of ~ .3), and about 15 W/m^2 are absorbed IN the atmosphere. If you look down at the bottom, about 160 of the 185 W/m^2 that make it to the surface are absorbed, which yields a surface albedo of 15/185 ~ 0.08. That makes sense. The earth, with all its water and green stuff should absorb more visible radiation than say the shining Moon.

However, let us be honest (why, why you ask...:because I am going to get a cheap publication out of this) Monckton was not the first to make this mistake, and I even know lots of textbooks on atmospheric chemistry that include the same error.


C W Magee said...

Isn't the vapour pressure of H2O low enough at 255 for us to assume that ice wouldn't sublimate apperciably? If so, then we can use the albedo of ice, which makes the earth wicked cold- like a Paul Hoffman wet dream, only flash-frozen. Not great for Rabetts, but ideal for lemmings.

_Arthur said...

Is the heat coming from the Earth's core negligible in the calculation of the surface temp, in the absence of atmosphere ?

jre said...

Great post -- brief, clear and on target!
I think there's a typo in your equation graphic, though. Put a "4" in the crook of your radical, so it reads T=(S(1-alpha)/4 sigma)^.25, and everything will be just poifect!

Anonymous said...

To me the greenhouse effect is the temperature difference between the surface of the Earth and the blackbody temperature of Earth as seen from space, and that one is ~30 K. This is not the same as the difference in temperature between an Earth with and without an atmosphere. So there I would have to give Moncton right, although this is only a matter of definitions. It will not change anything about the expected future warming.

Anonymous said...

Also, up near the top you've got a T-255 that should be T=255. Fix that or you'll be farther off than Monckton!

Arthur, I don't have the reference at hand but have seen it mentioned many times. The upshot is that it is a truly small term, negligible for these purposes.

EliRabett said...

Thanks for the comments. I've tried corrected the blunders such as the fourth root(It was 3 AM here, but then again, bunnies have red eyes). The ~ was a tilde, not a negative sign, but I tried to make that clear. Probably I'll go back and take them out an use "about".

Lab Lemming and Tomas Palm raise interesting points. For Lab Lemming, I've added a diagram of the radiation budget which shows that the albedo of the earth's surface alone is about 10%, actually lower than that of Mars or the Moon.

Thomas Palm's question is what is the temperture of the Earth viewed from space. He gives the right answer to that question. The other question you could ask is what would the temperature of the surface be if there were no greenhouse gases (CO2, H2O, etc.) in the atmosphere. That is the answer I gave.

In any case this clear up the issue.

24601 said...

On a quick scan I couldn't find Monckton's reference to this issue. Can you please point me to where he mentioned it? Cheers.

Anonymous said...

Thomas Palm said...

"To me the greenhouse effect is the temperature difference between the surface of the Earth and the blackbody temperature of Earth as seen from space, and that one is ~30 K"

Actually, though lots of references Wikipedia and others) say just that about the greenhouse effect, that don't make it so.

The greenhouse effect (due to gases which absorb IR radiation: H2O, CO2 and chlorofuorocarbons, for ex) and the albedo (affected by both IR absorbing-gases like H20 and other stuff like sulfate aerosols) are quite distict phenomena.

The fact that the two phenomena are often mistakenly considered part of the same "greenhouse effect" is undoubtedly due to the fact that water vapor plays such a large role both in the absorption of IR emitted by the earth and in reflecting visible radiation from the sun.

Besides, that Monckton has used the average albedo of the earth with an atmosphere to calculate the temp of the earth without an atmosphere ain't a matter of "choice of definition of greenhouse".

It's mixing apples and oranges -- complete nonsense.

Anonymous said...

To be honest, I expected a more substantive point made about Monckton's calculation than "he's oversimplified things a bit", but then oversimplification and tendentiousness are staples on blogs.

Monckton made a simplification to perhaps show how much contribution the atmosphere makes to the overall heat budget of the earth, without trying to work out what albedo the earth would have without oceans (which make the Earth darker) or cryosphere (which make it lighter) or a living, breathing biophere that unfortunately has Lambert in it.

The only point to be made is that all simplifications of climate which attempt to reduce measurement down to one number (the mean temperature, whatever that means) can be shown to be oversimplifications. But such oversimplifications are rife in climate science (such as the diagram Rabbett reproduced) and pretty much most of them cannot be justified except as an appeal to the lack of computing power available and the amount of time we have to wait for results.

I must admit I did expect slightly more in the way of debunking that Lambert led me to believe when I followed the link from Doltoid, but once again, to disappointment.

I don't think Monckton is guilty of oversimplification any more than any researcher in climate science is guilty of reducing variables and complexity in order to make a first-order approximation.

I suspect that the mere repitition of "Monckton is wrong" is all that is actually happening here.

EliRabett said...

Moinckton jumped up and down on his high horse on this one.