Saturday, January 14, 2012

When Does a Greenhouse Run Away?

Over at Lumoville, an alleged professor of atmospheric science is claiming that a runaway greenhouse is impossible on Earth, so I thought I might try to discuss what the necessary and sufficient conditions for one are - Cliff Notes version.

The atmosphere, or rather some of the gases in the atmosphere, are fairly transparent to incoming visible radiation but opague to outgoing thermal radiation. This one way transport warms the Earth a good deal beyond what its temperature would be in their absence. The most important such gas is water vapor. Water vapor is the key, but not the only, player in runaway warming.
A tale of two feedbacks.

The blanket of water vapor around the Earth warms it. Suppose we warm the surface. That increases the amount of water vapor entering the atmosphere and consequently tends to warm it. That's a positive feedback, people, and positive feedbacks are unstable - a little bit of warming produces more warming, which in turn produces still more warming and so on to infinity. And vice-versa - cooling sets off still more cooling. If that were the whole story, we would either be condemned to chill or roast, unless we were prepared to believe in utterly improbable fine tuning.

As it turns out, there is a negative feedback which counteracts this effect. Increasing the amount of water vapor in the atmosphere increases convection, which increases rain, which removes water vapor from the atmosphere. There is a balance point between the positive and negative feedbacks which stabilizes the temperatures.
Convective Depth

What determines the balance point is mostly a matter of the depth of the convecting part of the atmosphere - that part of the atmosphere in which heat is tramsported upward more by convection than radiation. That depth depends on a few things, like the heat of the Sun, but importantly for our purposes, it depends on the amount of CO2 in the atmosphere. In the absence of water vapor, such as above the watervapor rainout level, CO2 is the principal source of radiative opacity for outgoing radiation. The temperature at the top of the radiating layer will be that required to balance incoming absorbed radiation. The temperature at the bottom of the convecting layer will be sufficient to support convection to the top of that convecting layer - some approximation of an adiabatic lapse rate.


Runaway occurs when the temperature at the bottom of the atmosphere reaches the boiling point of water. At that point, the condensation feedback ceases to operate and nothing can stop the temperature increase until the temperature at the bottom becomes high enough to radiate at frequencies that penetrate the water vapor - 1400 K or so.

Once that occurs, the die is cast. Water vapor at the top of the atmosphere will be dissociated by ionizing radiation, and the hydrogen will be lost to space. The oygen will be incorporated into the crust or into CO2, with most of the carbon in the Earth's crust being converted to CO2.

As the water is lost to space, the planet will cool somewhat, but the vastly increased load of CO2 will probably still keep surface temperatures at several hundred C. We will become like Venus, to which this scenario happened perhaps billions of years ago.

Correction and clarifications from experts solicited, as are questions from the less expert. It's clear from this that we are currently a long way from the runaway point, but it's non-trivial to calculate how dramatic an impact greenhouse gases make on the set point.

UPDATE: Wikipedia notes that there are somewhat different definitions of a runaway greenhouse effect about, some of which are less drastic than the Venusian style event I describe. I'm not sure which version Hansen thinks we are faced with. The milder ones are propelled by CO2 rather than water vapor, and are reversible (in geological time spans) by feedbacks in the carbon cycle.