A very simple model for the water vapour feedback on climate change

Climate sensitivity is often said to be doubled by water vapour feedback. We expect the distribution of relative humidity to change little under climate change from simple physical arguments, which are confirmed by the most detailed physical models we have, and consistent with the limited observational evidence. A substantial positive feedback on climate change is then to be expected, and an approximate doubling is well established numerically. However, a physical explanation for the size of this effect is conspicuously lacking. We consider an idealized numerical model of Simpson's. Its counter‐intuitive result –that OLR does not change as climate warms –is shown to be more general than often thought, though clearly not applicable to our planet as it stands. However, with certain physical approximations a ‘partly‐Simpsonian’ generalization can be derived: that the component radiated by water vapour does not change as the climate system warms, while that radiated by everything else increases following Planck's Law. While still not quantitatively accurate, this does provide a physical explanation for the general size of the water vapour feedback, as well as for its robustness in GCMs. The partly‐Simpsonian approach also provides a physical explanation for the well‐established fact that, in water‐vapour‐dominated regions of the spectrum, the heat radiated by the climate system is a function primarily of relative humidity, not temperature. © Crown Copyright 2010. Published by John Wiley & Sons, Ltd.