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).
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.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.
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.
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.