This post is a summary, review and commentary of the classic paper by Andrew Ingersoll titled The Runaway Greenhouse: A History of Water on Venus. The paper shows how a simple radiative transfer model can reproduce the runaway greenhouse effect due to water that we see on Venus.

Abstract: Radiative-convective equilibrium models of planetary atmospheres are discussed for the case when the infrared opacity is due to a vapor in equilibrium with its liquid or solid phase. For a grey gas, or for a gas which absorbs at all infrared wavelengths, equilibrium is impossible when the solar constant exceeds a critical value. Equilibrium therefore requires that the condensed phase evaporates into the atmosphere.

Moist adiabatic and pseudoadiabatic atmospheres in which the condensing vapor is a major atmospheric constituent are considered. This situation would apply if the solar constant were supercritical with respect to an abundant substance such as water. It is shown that the condensing gas would be a major constituent at all levels in such an atmosphere. Photodissociation of water in the primordial Venus atmosphere is discussed in this context.

The model the Ingersoll uses is the plane-parallel atmosphere in radiative equilibrium with a convective troposphere. This model has been used to accurately predict the thermal structure of the Earth’s stratosphere and the Earth’s mean surface temperature (Manabe and Wetherald - 1967). The atmospheric composition is assumed. Then also assuming a constant solar flux, the atmospheric temperature profile is computed. In the cases where an atmospheric constituent is dependent upon the temperature, interesting effects occur.

The stated purpose of the paper is “to show that when the amount of an absorbing gas in the model atmosphere is determined by its vapor pressure, singularities may result, which represent not only a failure of the model, but also signal a profound change in the physical system which the model represents.” That is, they wish to understand the interesting effects when considering the atmospheres of Earth and Venus.

The singularities occur if there is the possibility of a feedback, in this case, where the opacity of the atmosphere depends on the surface temperature. If there is a molecule at the surface in the solid or liquid phase that is in equilibrium with the gaseous state in the atmosphere. There exists a value of the solar flux, called the critical value, where solar fluxes above this value indicate that equilibrium of the molecule between the solid or liquid phase and the gaseous phase is impossible. Equilibrium is therefore possible when the solar flux is below the critical value. Every infrared-active substance has its own critical value. Infrared-active substances are the only important ones because the others do not absorb the Earth’s outgoing longwave radiation.

Water is subcritical on Earth because we see it in both the liquid, solid, and gaseous phases at the surface. (Technically we don’t actually see the water vapor at the surface, but it’s there.) Carbon dioxide is supercritical on Venus since there is a large amount of CO2 in the atmosphere, but apparently none at the surface.

He uses the grey model, which just means that he assumes that the absorption coefficient does not depend on the frequency of the radiation. This is obviously not true, but it is an okay assumption for such a crude model. There is quite a bit of discussion of the particulars of his model that I’ll skip here, and jump right to the conclusion. If you’re interested, it’s a good paper to read, and is included in the references. In fact, that’s it for summarizing the paper. The good stuff is over with. He discusses possible applications to Venus, but if you read the title of the paper you can see where that’s going.

The paper shows a very good application of a simple radiative transfer model to explain the atmospheric composition of Venus. The writing is clear and straightforward even for someone without a background in radiation. A familiarity with scientific literature in general will probably be necessary to gain any insights from the paper, so this is not something that the general public could read and fully understand. A great way to understand this paper better is to actually do it! The actual code is simple to write, and all one needs is a text such as Thomas and Stamnes or Bohren and Clothiaux to help get you started.

This paper also shows for how long the greenhouse effect has been known about, and in particular that carbon dioxide is a greenhouse gas. Yet, there are still people who deny the existance of the greenhouse effect. If there were no greenhouse effect the Earth would be much cooler than it is today. So when I hear anyone deny the existance of the effects of greenhouse gases, I smile, nod my head, and silently judge them. So don’t be one of those people, okay?

References:
Bohren, C. F. and E. E. Clothiaux, 2006. Fundamentals of Atmospheric Radiation. Wiley-VCH.
Ingersoll, A.P., 1969. The runaway greenhouse: A history of water on Venus. J. Atmos. Sci. 26 (1969), 1191–1198.
Manabe, S. and R. T. Wetherald, 1967. Thermal equilibrium of the atmosphere with a given distribution of relative humidity. J. Atmos. Sci., 24, 241-259.
Thomas, G. E. and K. Stamnes, 1999. Radiative transfer in the atmosphere and ocean. Cambridge University Press.

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