Pressure on Venus

I’ve written before about the Runaway greenhouse process on Venus. In the case of Venus, this was an entirely natural process and such a process is unlikely to take place on Earth as we have locked much of our CO2 into carbonate rocks. It is, however, illustrative of how the greenhouse effect can significantly influence the climate on a terrestrial planet.

I recently became aware of a post on the Watts up with that website claiming that the reason Venus has such a high surface temperature is because of the extremely high pressure. There are lots of equations and graphs and quite a convincing argument, but it is simply wrong. The reason I thought I would write about this is that when I saw that post I remembered a senior Professor in an Earth Science department at a US university telling me the same thing a few years ago. At the time I thought, “that’s interesting”, but didn’t think any more of it. If a professor of Earth science can get it wrong, no wonder it’s easy enough to make it seem as though the argument makes sense.

So why is it wrong. Basic atmospheric modelling is not all that difficult. To model an atmosphere you need an equation of state relating pressure, density and temperature. Typically you would use something like
EoS
where P is the pressure, ρ is the density, T is the temperature, mH is the mass of a hydrogen atom, and μ is the mean molecular weight. On Earth, the most common molecule in the atmosphere is N2 so μ ~ 28, while on Venus it is CO2 so μ ~ 44.

Atmospheres will settle into a state of hydrostatic equilibrium. This means that the downward force of gravity will be balanced by an upward pressure force. This allows us to write
HydroEquil
where g is the acceleration due to gravity (9.8 m s-2 on Earth and 8.9 m s-2 on Venus) and z is the height in the atmosphere. We can solve the above equation to write
AtmosEquation
where Po is the pressure at the base of the atmosphere. The term kT/μmHg is known as the scaleheight and tells you the vertical distance over which the pressure drops by a factor of 1/e (1/2.72). It increases with temperature and so the hotter the atmosphere, the slower the pressure drops with height.

Now we have a set of equations that essentially allow us to solve a basic atmospheric structure problem. However, there are two things we don’t know. What is T and what is Po? Where does the temperature come from? Well it comes from the balance between the amount of energy that the planet receives from the Sun and the amount it re-radiates into space. The temperature of the planet must be such that it re-radiates as much energy back into space as it receives. The pressure at the base of the atmosphere is related to the atmospheric density through the equation of state. The atmospheric density depends on how much atmospheric material there is in the atmosphere. I’ve kind of implied that it is simple, but in truth it is not that simple. The planet’s temperature depends on the composition of the atmosphere. To solve the problem properly, you need to include the influence of the atmosphere on the incoming and outgoing radiation. This will determine the equilibrium planetary temperature and the variation of temperature with height. You also need to iterate until the density structure gives the correct total mass. However, what determines the pressure profile in the atmosphere is the temperature of the atmosphere and the amount of material in the atmosphere (i.e., the density). The pressure does not determine the temperature. If there was no incoming energy, the atmosphere would lose energy, the temperature would drop, the scale height would decrease and the atmosphere would collapse onto the surface of the planet. When it was cold enough, the molecules would become liquids or solids and the atmosphere would disappear. In other words to have a steady atmospheric pressure, you need incoming energy from the Sun. To re-iterate, the temperature determines the pressure, the pressure does not determine the temperature.

So the reason Venus has a high surface temperature is not because of the high pressure. The reason it has a high pressure is because of the high temperature and density. We can illustrate this by considering the Earth. Atmospheric pressure at sea level is 105 Pa. Atmospheric density at sea level is about 1.2 kg m-3. The atmosphere is primarily nitrogen so μ = 28, mH = 1.67 x 10-27 kg, and k = 1.38 x 10-23 m2 kg s-2. If I plug these numbers into the equation of state shown at the beginning of the post I get T = 338 K. So, the Earth’s temperature is because of our atmospheric pressure, not because of the energy we receive from the Sun! No, clearly this is wrong. If the temperature and density determine the pressure, I can then use the density and pressure to calculate the temperature. It doesn’t mean that the pressure determines the temperature, it just means there’s a relationship between pressure, density and temperature.

Given that I’ve linked to the post on the Watts up with that website, this would normally appear as a comment. I’ll be interested to see if it does indeed appear as such. It’s clear that claiming that the high surface temperature on Venus is due to its high pressure is wrong. Anyone who understands physics would accept this and the author of the post claiming this should recognise this and be willing to acknowledge their mistake. I would have much more time for those who are skeptical of man-made climate change if they were willing to accept when they are wrong. That is essentially the scientific process. Mis-using a set of equations to make a spurious claim is not.

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