Venus Atmosphere Puzzle, one man's struggle with atmospheric physics Options

[qraal]

Hi All

This might seem like a really dumb question, but what's the mass of the Cytherean atmosphere per unit area?

At first pass I thought it was easy - same as for an isothermal atmosphere, Po/g, where Po is surface pressure and g is surface gravity. Simple. Except Venus doesn't come close to approximating an isothermal atmosphere. From a graph in Mark Bullock's PhD thesis (Hi Mark if you're visiting) I pulled the figures for Po and To as 92 bar and 735 K, while the left-side of the temperature curve was 250 K at 0.1 bar and 63 km. At about 210 K the temperature drop with altitude stops, then slowly rises into the Cytherean stratosphere.

Ok. My atmospheric physics is pretty limited - I 'modelled' that lapse rate pressure curve as a power law:

P/Po = (T/To)^n

and likewise for density, d/do = (T/To)^n.

Temperature, T, as a function of altitude, Z, I computed as T(Z) = To*(1-Z/(n.Zo)).

Zo = (k.T/m.g), where k is Boltzmann's constant and m is the molecular mass of the atmosphere.

These equations I then integrated between 210 K and 0.033 bar, 70 km, and 735 K and 92 bar, zero altitude.

The resulting equation is m = (n/(n+1))*(do.Zo)*(1 - (T/To))^(n+1) - a bit of simple algebra and the Gas equation shows that do.Zo = Po/g.

Thus the mass is lower than for a simple isothermal atmosphere by roughly (n/(n+1)). In this case n = 6.33, higher than the dry adiabat for CO2 which gives n = 4.45.

Now an adiabatic or polytropic atmosphere is an idealisation, but it seems odd to me that whenever Venus' atmospheric mass is discussed people always use the higher isothermal value. Have I missed something important in the physics, or is Venus's atmospheric mass just 86.4% of the usually quoted value?

[ljk4-1]

Venus Atmosphere Profile from a Maximum Entropy Principle

http://arxiv.org/abs/astro-ph/0609649

[rlorenz]

Venus Atmosphere Profile from a Maximum Entropy Principle

http://arxiv.org/abs/astro-ph/0609649

Hmm, interesting.

Without specifying the radiative deposition and emission profile, which the atmosphere
(at least, without the scary prospect of invoking clouds) cannot do much about, I
think this approach is not hugely different from saying the atmospheric temperature profile
with pressure or altitude is adiabatic (which for much of Venus, it is)

Rather more intriguing is the work by Ozawa ( Ozawa, H., and A. Ohmura,
Thermodynamics of a global-mean state of the atmosphere ––A state of maximum entropy increase, J. Clim., 10, 441–445, 1997)
which shows that given an opacity profile, the vertical structure of the (earth's) atmosphere
may adjust convectively to produce entropy at the maximum rate (so-called Maximum
Entropy Production principle, MaxEP).

Although the physical/thermodynamic foundations of the application of these ideas has
improved in recent years, it is still controversial (unloved by dynamicists) and really useful
applications have yet to be found...