Why does the stratosphere cool when the troposphere warms?

This post is obsolete and wrong in many respects. Please see this more recent post for links to the answer.

14/Jan/05: This post was updated in the light of my further education in radiation physics.

25/Feb/05: Groan…and again.

Recent discussions of climate change (MSU Temperature Record, ACIA) have highlighted the fact that the stratosphere is cooling while the lower atmosphere (troposphere) and surface appear to be warming. The stratosphere lies roughly 12 to 50 km above the surface and is marked by a temperature profile that increases with height. This is due to the absorbtion by ozone of the sun’s UV radiation and is in sharp contrast to the lower atmosphere. There it generally gets colder as you go higher due to the expansion of gases as the pressure decreases. Technically, the stratosphere has a negative ‘lapse rate’ (temperature increases with height), while the lower atmosphere’s lapse rate is positive.

(New. A brief discussion of the greenhouse effect is useful here. You can read the technical reasons below, but the key point for this discussion is that increasing greenhouse gases increases the temperature gradient from the surface.

[Technical digression: Imagine an atmosphere with multiple isothermal layers that only interact radiatively. At equilibrium each layer can only emit what it absorbs. If the amount of greenhouse gas (GHG) is low enough, each layer will basically only see the emission from the ground and so by Stefan-Boltzmann you get for the air temperature (Ta) and the ground temperature (Tg) that 2 Ta4 = Tg4 , i.e. Ta=0.84 Tg for all layers (i.e. an isothermal atmosphere). On the other hand, if the amount of GHGs was very high then each layer would only see the adjacent layers and you can show that the temperature in the top layer would approximate 0.84n Tg (n+1)-1/4 Tg, (see note) where n is the number of layers - much colder than the low GHG case. Hence the increased GHG steepens the surface-to-top temperature gradient.]

In the case of the Earth, the solar input (and therefore long wave output) are roughly constant. This implies that there is a level in the atmosphere (called the effective radiating level) that must be at the effective radiating temperature (around 252K). This is around the mid-troposphere ~ 6km. Since increasing GHGs implies an increasing temperature gradient, the temperatures must therefore ‘pivot’ around this (fixed) level. i.e. everything below that level will warm, and everything above that level will cool.

Even though the stratosphere has an opposite lapse rate to the troposphere because of the ozone absorption, the effect of increasing GHGs is the same, i.e. since it is above the effective radiating level, it will cool. The cooling will be greatest as you go higher. In the troposphere, there are important other effects that change the temperature, cheifly moist convection, and that smears out the temperature changes you expect from a pure radiative atmosphere. So while the troposphere does warm as a function of increasing GHGs, the maximum change is not at the surface, but actually in the mid-troposhere. End new)

To be sure, this is a very rough picture and where other feedbacks are important (due to clouds, convection, dynamics etc.) the picture locally can be significantly different from this one-dimensional cartoon. Nonetheless, at the global mean level, this is the dominant effect.

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