The Runaway Greenhouse Effect

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About

This is a qualitative demonstration of the runaway greenhouse effect. It is intended to provide a general idea of how such a process works. It is thought that the planet Venus once had oceans like Earth. Owing to Venus's closer proximity to the Sun, and the fact that the Sun has heated up since the beginning of the solar system, these oceans have since evaporated. The process for this is the runnawy greenhouse effect.

What you see in the simulation is solar radiation transfered from the sun to the planet (yellow dots), and infrared radiation from the planet to space (red dots). The atmosphere has three components a non-greenhouse gas (like N2) in green, a non-condensible greenhouse gas (like CO2) in black, and a condensible greenhouse gas (like H2O) in blue. The gauge on the right gives the temperature of the planet at equilibrium for a given composition of the atmosphere. The sliders below allow you to alter the solar constant (move the planet closer to the sun), and release/remove CO2 from the atmosphere. It is assumed CO2 is released by volcanism.

In this model, the planets temperature is determined by balancing the outgoing flux of the planet with the incoming flux from the sun. The presence of greenhouse gasses in the atmosphere causes the planet to heat up. The greenhouse gases absorb radiation from the planet and reflect it back to the surface, returning that energy. Here, there is a feedback between the temperature of the planet and the amount of water in the atmosphere. Thus, as the temperature rises, more water vapor is deposited in the atmosphere which causes the temperature to rise further. At a certain value of the solar constant, known as the Kombayashi-Ingersoll limit, the the ocean goes from stable to unstable. This is because around this limit, the temperature is extremely sensitive to changes in the solar constant.

What about Venus?

This model does not perfectly describe what is believed to have happened to Venus. It is thought that Venus posessed a water ocean and then as the sun heated up (as it transitioned into its main cycle), the Kombayashi-Ingersoll limit was exceeded and the ocean evaporated. After this, the water in the atmosphere was broken apart by UV radiation and the resultant H2 escaped from the planet. With no more water, the reactions that bind CO2 to rocks couldn't take place, and the atmosphere filled up with CO2 to its current state.

Assumptions

First and foremost, this is a one dimensional model for a static atmosphere. For this model, we have assumed that the sun emits in the visible spectrum (represented by yellow photons), and the planet emits in the infrared (represented by red photons). Both are assumed to be perfect blackbodies. We have then assumed that the visible light does not interact with the atmosphere, whereas the presence of CO2 (black particles) and H2O (blue particles) absorbed in the infrared, and emit isotropically. All absorbtion processes are assumed to be "gray" that is, without a dependance on wavelength.

For the temperature profile of the atmosphere, I have made the Eddington approximation, where flux increases linearly with optical depth. I have assumed that both greenhouse species, CO2 and H2O, have the same absorbtion cross section. These approximations have the same qualitative effects as more complicated models.

I have assumed that the pressure at the surface of the planet is equal to the saturation pressure of water, in order to determine the concentration of H2O in the atmostphere.

Sources

Thermometer picture: http://clipartion.com/free-clipart-15368/ (Accessed 5/3/2016)
Anderw P. Ingersol, The Runaway Greenhouse: A History of Water on Venus, Journal of the Atmospheric Sciences, Volume 26, November 1969
Raymond T. Pierrehumbert, Principles of Planetary Climate Cambridge University Press, 2011/
Shinchi Nakajima, Yoshi-Yuki Hayashi, Yutaka Abe, A Study on the "Runaway Greenhouse Effect" with a One-Dimensional Radiative-Convective Equilibrium Model Journal of the Atmospheric Sciences, Vol. 49, 1992.