More on the run-away greenhouse

I have previously discussed this
http://groups.google.com/group/soc.m...f7a852c240f001

here, and also http://groups.google.com/group/sci.a...f72c4284954030

here (and other posts in that thread).

My previous comments were essentially correct, but I feel the need to
expand on them.

- Venus and Earth

First, whether Venus ever did have a true run-away, and whether the
Earth will have. A planet in a run-away greenhouse state, with its
entire ocean entering the atmosphere, will surely be shrouded in
cloud, and the cloud will be extremely thick (optical depth 1,000) as
the atmosphere is almost pure water. The albedo of an infinite water
cloud, in a water-vapor atmosphere, to the spectrum of sunlight should
be about 0.5 .

I will here denote by Ie the current solar radiation recieved at
Earth, and express possible values in that unit. The SKI limit for
pure water is about 0.85 Ie, so with an albedo of 0.5 we have 1.7 Ie
for the run-away point. This was reached by Venus about 2 billion
years in the past, and will be reached by Earth about 5 billion years
in the future. So it seems the answer to my query is yes.

However, the points for both Venus and Earth can be delayed about a
billion years by the increased SKI limit caused by the other gases in
the atmosphere (i.e. N2). Note that a billion years ago is about the
latest that Venus could have lost its ocean, given the observed age of
the surface.

Gliese 581c, which was reported in the press as a possibly habitable
planet, has a solar input around 2.5 Ie, which is well above the run-
away point (in fact, the threshold is lower around M dwarfs as water
clouds have a lower reflectivity to the redder spectrum of light). So,
even if this planet is Earth-like, it will now resemble Venus.

- The surface temperature of a run-away planet

I said in my first post that the Earth after run-away should reach
about 700 K, according to the adiabat for pure water. To stabilise at
this temperature, however, it would need to radiate to space above the
SKI limit. Is this possible?

When more heat is added to this atmosphere, evaporation will thin the
cloud layer. It will shrink on both its top and bottom, though only
the top is relevant to the radiation balance. When the cloud top moves
to a higher temperature, the lapse rate in the region vacated (which
is still fairly optically thick) will rise to the dry adiabat, which
is much higher than the cloud lapse rate. This raises the temperature
of the effective radiating layer, allowing it to cool and thus
maintain balance. So the surface need not warm significantly for a
small change in solar radiation.

Eventually, if the sun brightened sufficiently, the cloud layer would
vanish altogether. The surface temperature could be computed at that
point by applying the dry adiabat down from the radiating layer. The
radiating layer will be (under Earth's gravity) about 100mb and 350 K,
and for a surface pressure of 500 bar (1 Earth ocean), we get ~1800 K.
That's hot enough to melt rock, but terrestrial planets will not reach
it, as the ocean will be lost soon after the run-away begins.

- Gas planets

The cloud layer of a planet experiencing a run-away qualitatively is
the same as that of a gas giant, so it seems appropriate to term these
gas planets. Many 'super-Earths' and even Earth-mass planets born with
a high percentage of volatiles will become permanent gas planets, as
they can't lose all their gas in any practical time. Indeed, as
simulations suggest that such planets may be born with 10% of water,
such a planet above the critical insolation will essentially be a gas
giant with extremely high metallicity.

Is Venus, then, currently a gas planet? I don't think I'd regard it as
one; it differs in the nature of its cloud layer from normal gas
planets, and it is a run-away only with respect to CO2. Nonetheless
its atmospheric structure strongly resembles one.

Andrew Usher