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?

[qraal]

Hi ngunn & MichaelT

As you might've guessed I have performed a numerical integration using a variable 'g' and the results are similar. Atmospheric mass only differs slightly between the two (<1%).

My real puzzle is why integration of the density equation, r = ro(T/To)^(Cp/(Cp-Cv)), didn't give the mass as Po/g. Constant lapse rate, as used in the International Earth Atmosphere, still gives Po/g after numerical integration - but I must've made a stupid assumption somewhere when I derived an analytical solution that differed so strongly. Over the temperature range in question, for Earth, Cp/Cv is practically constant, and only begins to differ from 1.4 for temperatures over 350 K.

That being said the Venus model is doing ok, but I've discovered the learning curve on modelling atmospheric absorption of solar radiation is quite steep. The (z,T) curve for Venus rapidly approaches a dT/dz of ~0 at a certain altitude, I guess due to increased heat gain from radiation. Now I could throw in an empirical fit, just like VIRA, but I'd like to read more of my references and come to some understanding of what's going on. I'm guessing that the atmosphere is becoming stable against convection forming an isothermal 'lid' just like the temperate zone tropopause on Earth.

If so there should be some literature around on just how that works, at least for Earth, and by extrapolation for Venus too.

Adam Crowl aka qraal

[MichaelT]

If so there should be some literature around on just how that works, at least for Earth, and by extrapolation for Venus too.

Adam Crowl aka qraal

On Earth the absorption of UV radiation by the ozone layer is mainly responsible for the increasing temperature in the stratosphere, and, thus for the existence of the tropopause (dT/dz = 0). So there should be plenty of literature around on how that radiation absorption works on our planet.

Michael

[qraal]

Hi Michael

There's quite a lot of literature, but nothing giving a general overview - yet.

I've got a set of course notes about the issue I need to read in depth.

Don, the cloud chemistry and advective processes are complex but simpler than Earth in some ways. Must be because of a lack of Coriolis forces and insignificant surface friction effects. Ralph Lorenz has some papers of relevance on atmospheres self-organising to run at the Carnot limit.

Adam

On Earth the absorption of UV radiation by the ozone layer is mainly responsible for the increasing temperature in the stratosphere, and, thus for the existence of the tropopause (dT/dz = 0). So there should be plenty of literature around on how that radiation absorption works on our planet.

Michael