The increase (decrease) in specific humidity under a global warming (cooling) situation represents the most powerful climate feedback as a response to radiative perturbations, effectively doubling the sensitivity of Earth’s climate.
The absorption of longwave radiation goes up as the logarithm of water vapor concentrations, so like CO2, the fractional change in water vapor is more important than the absolute changes. Most of the water vapor feedback occurs in the upper tropical troposphere, and most of the water vapor feedback occurs in the longwave component of the spectrum (at the poles, there is a significant shortwave component as well).
The water vapor increases in the atmosphere come from the fact that the partial pressure of atmospheric water vapor can increase as a function of temperature (following the Clausius-Clapeyron equation). C-C provides an upper limit to the saturation pressure, which as a result of circulation patterns, is not what is actually observed (i.e., global relative humidity is well under 100%) so understanding how water vapor increases also requires knowing how incremental changes in water vapor actually follow with the C-C equation. Here we are in 2009 where observations and models produce a roughly constant relative humidity (globally averaged) in climate change situations, suggesting increases of saturation pressure about 7%/degree K of warming.
In a recent issue of Science, Andrew Dessler and Steve Sherwood provide a perspectives article (subscription required for full text) briefly summarizing some history and current state of understanding behind the water vapor feedback. The authors seem confident that this feedback is well understood, and observational, theoretical, and model-based understanding has improved remarkably over the last few decades. As it stands, there is no reason to doubt the general description of a powerful positive feedback due to humidity increases as the globe warms, which now has strong support from a large and growing body of literature.
Humidity is largely controlled by the large-scale wind and temperature fields, which can be calculated explicitly in climate models; the dependance of the overall water vapor feedback on microphysical interactions (which must be paramaterized) is comparatively small, so the strength of the water vapor feedback associated with cloud microphysical processes is unlikely to exceed a few percent.