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## The Water Vapor Feedback and Runaway Greenhouse

In previous posts, I have outlined in a few steps the interplay between the radiation balance of a planet, its temperature structure, and the feedback mechanisms that gives freedom for the climate to depart from its reference norm. In the ice-albedo post for example, we have seen a bifurcation structure in which removing enough CO2 (or lowering the sunlight a planet receives) can plunge the planet into a runaway ice-covered state. In this post, I’ll consider the “hot end” of a similar type of bifurcation, although now we enter a regime in which no ice exists and a significant fraction of the atmosphere is composed of water vapor. This would be typical of any ocean planet that becomes sufficiently hot to make water vapor a dominant constituent of the air. More traditional applications of the “water vapor feedback” to the global warming issue will be discussed.

In the previous post, I discussed the simplest of energy balance models that can yield insight into the temperature of a planet. I will elaborate on the arguments presented there to include a temperature-dependent albedo, $\alpha = \alpha(T)$, which allows the rate at which a planet absorbs starlight to depend itself on the climate state. We will again ignore the existence of a greenhouse effect in this discussion, and write the energy balance as before:
$\displaystyle \frac {Q (1-\alpha (T_{s}))}{4} = \sigma T_{s}^4$