Cloud albedo and the run-away greenhouse
Andrew Usher
here:
Here I will discuss how clouds affect the run-away onset and climates
on the lower side of it. I will also end this post with some general
discussion of habitable planets.
- The albedo of water clouds
At mid- to far-infrared (>2.5 microns) water clouds are nearly
blackbodies. But little solar energy is in that range. In the UV to
near-infrared, one can assume water droplets to be nearly non-
absorbing scatterers. It can easily be calculated that in any
reasonable cloud, scattering by droplets exceeds that by the gas;
conversely, absorption by water vapor within the cloud dominates
absorption by the liquid.
The albedo of a cloud thus depends highly on the atmosphere in which
it is embedded. A pure water-vapor atmosphere gives the lowest
figures.
In the evaluation of the run-away point, we may assume, as stated in
the last post, that the cloud is infinitely thick and in a pure water
atmosphere. In this case, computing the albedo requires knowing only
the properties at the cloud top. I assume a density of 1% by mass, a
droplet radius of 10 microns, and a cloud-top pressure of 5 mb (sat.
at 267 K, approximately equal to the SKI limit for Earth gravity). I
do not have access to good cross-sections so I can only estimate them
from graphs. Nevertheless it is clear that albedo changes rapidly with
wavelength, from nearly 1 below 500nm to nearly 0 above 900nm.
This gives approximately 0.5 bolometric for the Sun's spectrum, which
is what I guessed in the last post. For an M5 star, about 0.2 is
correct, and at A0, 0.8; this is a huge range.
- Comparison to gas planets
The calculation above shows that even a cloud-filled atmosphere will
be somewhat bluish. A cloud-free atmosphere will be more so on account
of having a lower albedo at every wavelength. It seems to me that
Uranus and Neptune are probably as blue as possible, and that
increasing their mole fraction of CH4 would actually make them whiter
by thickening the cloud layer.
The varying albedo with stellar temperature must be accounted for when
calculating the effective temperatures of extrasolar giant planets.
For example, the threshold distance for a giant to have water clouds
will vary about 2:1 (insolation-adjusted) between an A-type and an M-
type star.
- The run-away point
Calculation with the albedos mentioned above gives the run-away
insolation as 1.7 Ie for the solar-type star, 1.06 Ie for the M5 star,
and 4.25 Ie for the A0 star. In spite of that range, the nature of the
run-away should be the same in all cases.
It may be asked if the transition to the run-away will be sudden or
gradual. The gradual transition is that often alluded to in the
literature, such as Kasting's 'moist greenhouse', and is computed with
cloud-free or constant-albedo models. But it appears to be incorrect,
at least most of the time.
Let us take an atmosphere with a substantial pressure of N2 (~1 bar).
I define the 'maximum greenhouse point' to be that at which the amount
of IR escaping from the surface directly to space is negligible. This
is about 310K for Earth's gravity, and changes ~10K for each doubling.
Above this point this radiation to space can't be further increased by
raising surface temperature (until after the run-away).
Now the total pressure will hardly change at the maximum greenhouse
point, yet the albedo of clouds will be much greater due to the low
mixing ratio of H2O. If the ratio of liquid water to gaseous water is
about 10 times higher, the albedo will jump from 0.5 to 0.8,
approximately, for an infinite cloud.
Since a continuous cloud layer must be optically thick (being fully
convective), and the cloud-albedo feedback goes the wrong way, the
atmosphere below the run-away point _can not_ have a complete cloud
cover. Thus the jump from partial to complete cloud cover, the actual
run-away, must be sharp. Kasting was wrong, at least for any planet
with a significant pressure of non-condensible gas.
- The cloud-albedo feedback
The run-away point for Earth or Venus is about 1.7 Ie. Yet, the
maximum with Earth's current albedo is no more than 1.3 Ie before
outgoing radiation would have to reach an impossible level. Thus, the
albedo must increase before Earth reaches that limit, and continue to
increase until the run-away point. The only way that can happen is
through clouds.
Let me state that again: the cloud cover must continuously increase as
the run-away point is approached. There is no way around this; no
actual modeling is needed to show it. Through the same calculation, we
can compute the minimum tropical cloud cover just before the run-away.
Taking the average cloudless albedo (surface + Rayleigh) to be 0.2,
this will be (0.5 - 0.2)/(0.8 - 0.2) = 0.5; as this assumes no cloud
greenhouse effect, actual values must be higher.
The figure will also be higher for hotter stars, but nearly the same
for cooler stars.
This may well have relevance to global-warming models; all the models
used by climate scientists to produce their alarmist figures use a
positive cloud feedback, which, according to the above, is impossible.
A negative feedback will likely make sensitivity no larger than 1.5 K,
which is what I would guess anyway based on historical temperatures.
- The super-tropical climate
I give this name to the climate above the maximum-greenhouse point but
below the run-away point. As the name suggests, it should exhibit the
features of Earth's tropical climates, only more so. The atmosphere is
optically thick to thermal IR and thus latent heat is the principal
means of cooling.
What would the surface temperature be in this regime? That is hard to
figure without modeling. It is certainly higher than the maximum-
greenhouse temperature, but how much higher? My guess is not much, if
no other greenhouse gases are important, as increasing surface
temperature would only result in more convection, and thus clouds. For
comparison, take a tide-locked ocean planet - while the temperature
will be nearly constant between day and night, the convection won't!
So, I reckon 320K is a good estimate of surface temperatures just
before the run-away point on Earth. That is, Earth will remain
habitable up until that point, 4-5 billion years hence.
These climates will be recognisable yet have the most 'extreme'
weather possible (in terrestrial terms) due to their extreme
convection. This will be especially so around hotter stars. One could
have insolation of 4 Ie around an A-type star in such a climate -
though cloud cover would be very high, when the sun did get through to
the ground, it would feel the full strength of 4x Earth's illumination
(well - likely less due to Rayleigh scattering).
- The habitable zone
This, the run-away greenhouse, signals the inner edge of the habitable
zone. So for our Sun, at present, the inner edge is 1/sqrt(1.7) ~ 0.77
AU. The outer edge is much harder to define, but it seems evident that
Mars is outside it.
We can judge by the Earth's history that a planet with a global ocean
will, when it reaches the limits of habitability, go through 'snowball
earth' cycles between iceball and super-greenhouse. A planet too dry
for a global ocean (like Mars) will reach a steady state, but that
will probably have no permanent liquid water and might actually be
less favorable to life than 'snowball earth' cycles.
It appears that Earth may be close to the center of the HZ and near
optimal to remain habitable for most of the Sun's main-sequence life.
Andrew Usher
Rodney Blackall
<3a44b38b-4116-4378...@t54g2000hsg.googlegroups.com>,
Andrew Usher <k_over...@yahoo.com> wrote:
> The albedo of a cloud thus depends highly on the atmosphere in which
> it is embedded. A pure water-vapor atmosphere gives the lowest
> figures.
It should be remembered that a significant fraction of Earth's clouds are
made up of ice crystals and that these vary in form with temperature.
> In the evaluation of the run-away point, we may assume, as stated in
> the last post, that the cloud is infinitely thick and in a pure water
> atmosphere. In this case, computing the albedo requires knowing only
> the properties at the cloud top. I assume a density of 1% by mass, a
> droplet radius of 10 microns, and a cloud-top pressure of 5 mb (sat.
> at 267 K, approximately equal to the SKI limit for Earth gravity). I
> do not have access to good cross-sections so I can only estimate them
> from graphs. Nevertheless it is clear that albedo changes rapidly with
> wavelength, from nearly 1 below 500nm to nearly 0 above 900nm.
It should be rememered that cloud top pressures above Earth very rarely fall
below 250 mb (the most vigourous tropical and semi-tropical thunderstorms).
300 mb is a good gues for cirrus cloud tops.
It is almost impossible to keep water droplets supercooled below -40.
--
Rodney Blackall (retired meteorologist)(BSc, FRMetS, MRI)
Buckingham, ENGLAND
Using Acorn SA-RPC, OS 4.02 with ANT INS and Pluto 3.03j
Andrew Usher
wrote:
> > The albedo of a cloud thus depends highly on the atmosphere in which
> > it is embedded. A pure water-vapor atmosphere gives the lowest
> > figures.
>
> It should be remembered that a significant fraction of Earth's clouds are
> made up of ice crystals and that these vary in form with temperature.
Yes, but that effect is much smaller in terms of albedo. Anyway I'm
computing clouds warmer than that.
> > In the evaluation of the run-away point, we may assume, as stated in
> > the last post, that the cloud is infinitely thick and in a pure water
> > atmosphere. In this case, computing the albedo requires knowing only
> > the properties at the cloud top. I assume a density of 1% by mass, a
> > droplet radius of 10 microns, and a cloud-top pressure of 5 mb (sat.
> > at 267 K, approximately equal to the SKI limit for Earth gravity). I
> > do not have access to good cross-sections so I can only estimate them
> > from graphs. Nevertheless it is clear that albedo changes rapidly with
> > wavelength, from nearly 1 below 500nm to nearly 0 above 900nm.
>
> It should be rememered that cloud top pressures above Earth very rarely fall
> below 250 mb (the most vigourous tropical and semi-tropical thunderstorms).
> 300 mb is a good gues for cirrus cloud tops.
The tropical tropopause can reach about 100mb. The tropopause in a
pure water-vapor atmosphere would indeed be about 5mb due to IR
opacity.
> It is almost impossible to keep water droplets supercooled below -40.
Who said anything about that? 267 K is -6 C.
Andrew Usher
Andrew Usher
59:3323).
Although it uses an unrealistic constant-albedo model, it otherwise
confirms my conjectures. Specifically, it shows that the transition to
the run-away is sharp, not gradual; that maximum tropical temperatures
just before the run-away are around 320 K, and that the tropopause
temperature remains nearly constant as the run-away is approached
(i.e. the stratosphere remains dry).
The authors admit that their model does not give the correct threshold
because of the simplification (I calculated it approximately). There
is no ocean circulation; if it were implemented, it (along with cloud
cover) would slightly lower tropical temperatures and raise those at
the poles (about 300 K in their model when the tropics are 320 K).
The threshold temperature, 315-320 K in this model, will be increased
by undersaturation of the atmosphere (a drier world than Earth) or by
non-condensible greenhouse gases, and as stated before, vary about +10
K for each doubling of gravity. Realistic Earth-like planets will have
between 0.35 and 2 g, giving between -15 and +10 K correction.
So:
Conclusion 1. Earth will remain habitable for 4-5 billion years.
Conclusion 2. Venus must have experienced a run-away, likely no more
than 2 billion years ago.
Conclusion 3. Before this, Venus was habitable with temperatures not
exceeding 320 K.
Andrew Usher
BradGuth
Since them acidic clouds do a damn fine job of reflecting most of the
solar energy (especially of the IR spectrum), why is the planet Venus
itself so geothermally driven as being surface hot and clearly
geologically active?
~ Brad Guth Brad_Guth Brad.Guth BradGuth
Andrew Usher
> Since them acidic clouds do a damn fine job of reflecting most of the
> solar energy (especially of the IR spectrum),
They actually reflect least in the IR.
> why is the planet Venus
> itself so geothermally driven as being surface hot and clearly
> geologically active?
It is hot because of its atmosphere (as I have been discussing
in the other thread
http://groups.google.com/group/sci.astro/browse_thread/thread/1fb47f97f7b20a3a#
), not geothermal activity.
Andrew Usher