DG dR dG

For example, if R represents the concentration of water vapor on Earth, or of methane on Titan, and if R varies as a function of temperature, then the feedback would influence G through the OLR. Writing OLR = OLR(T, R(T), A), then the feedback parameter is dOLR dR

assuming the albedo to be independent of temperature in this case. Now, since OLR increases with T and OLR decreases with R, the feedback will be destabilizing ($ < 0) if R increases with T. (One might expect R to increase with T because Clausius-Clapeyron implies that the saturation vapor pressure increases sharply with T, making it harder to remove water vapor by condensation, all other things being equal). Note that in this case the water vapor feedback does not lead to a runaway, with more water leading to higher temperatures leading to more water in a never-ending cycle; the system still attains an equilibrium, though the sensitivity of the equilibrium temperature to changes in a control parameter is increased.

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