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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.

## Ice-Albedo Feedback, and Temperature Bifurcation Structure

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:

$\displaystyle \frac {Q (1-\alpha (T_{s}))}{4} = \sigma T_{s}^4$

where Ts is the surface temperature, and the other terms are defined as before. I will focus this discussion on the ice-albedo feedback, since the extent to which a planet is covered in ice will be intimately connected to temperature.  One can intuit that changing the ratio of ice surface to land/ocean surface, in response to climate change, will modify a planets reflectivity to sunlight and amplify the initial cause of the change.  One can also speak of albedo changes due to desertification or re-forestation, for example.  However, the ice-albedo feedback is a common example of thinking about surface albedo changes, and one that also enters prominently into the “snowball Earth” issue that I want to shed light on (and has broader connections to planetary habitability as one moves farther away from a star).  To move forward with the discussion, I work under two assumptions: