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Re: atmospheric blanket / greenhouse effect



On 07/28/2003 03:10 PM, Robert Cohen wrote:
>> For a thick atmosphere, if you want a self-consistent theory, you
>> need to divide the atmosphere into layers and iterate your
>> argument. The Nth layer shields the N-1 lower layers as surely as
>> the first layer shields the surface. The effect is cumulative.
>> The radiation is _diffusing_ outwards.
>
> Yes, I agree with you,

:-)

> yet somehow I don't think I disagree with myself.

And maybe I don't disagree with you, either.
See below.

> Yes, it is better to divide the atmosphere into layers.

Agreed.

> My argument
> assumed a single layer which, as you point out, may not be a good
> approximation to the earth's atmosphere although I'd argue it is
> roughly correct. I'd also argue it is not even close to being
> correct for Venus. For Venus, one definitely needs to subdivide into
> layers in order to get such a hot surface temperature.
>

It depends on what "roughly correct" means.

The single-layer model is correct at the level of
dimensional analysis. But there's more to physics
than dimensional analysis.

Perhaps it's worth noting that diffusion is nonlinear.
-- For a process such as a wheel rolling uniformly
in the +x direction, things are linear. A million
microradians is the same as one radian.
-- For a random walk, things are *not* linear. A
million random one-micron steps are not equivalent
to a single one-meter step.

Or maybe you're implicitly claiming that the earth's
atmosphere is optically thin. That may be. That's
where this discussion began: I said I don't know
how high we have to go before the atmosphere becomes
optically thin. (We agree Venus must be very thick.)

Come to think of it, two lines of evidence suggest
that the Earth's atmosphere is not very optically
thick.
-- The night sky in the high desert is perceptibly
colder than the night sky in a humid locale, due
to radiative cooling. So certainly it is *sometimes*
thin.
-- The magnitude of the heat-trap effect (I can't
bring myself to call it the greenhouse effect) is
only about 35 degrees; if there were a huge
number of layers the effect would be bigger. This
is blatantly working backwards from the temperature
to get the "explanation" of the temperature, but
it tells us what ballpark we should be looking in.

I stand by my assertion that knowing the thickness
is important.