The basis of IPCC predictions is that any moderate warming caused by increased CO2 levels is enhanced by more evaporation from the oceans. Water vapour is itself a strong greenhouse gas and this increase results in a large “positive feedback” boosting climate sensitivity to a doubling of CO2 as high as 6C.
This is all just theory however, so it is important to observe whether water vapour in the atmosphere has actually increased or not in response to increasing CO2. The data shown below are from the NASA NVAP  project based on radiosonde, TIROS,TOVS & SSM/I satellite based data. This data was kindly brought to my attention by Ken Gregory .
The data from NVAP shows little change in water vapour from 1988 until 2001 at all levels in the atmosphere. If anything a small decrease in the important upper atmospheric layers in the detail shown below Fig1b.
If we now integrate all layers to get the total water vapour column we then get figure 2:
There is no evidence whatsoever in NVAP of any increase in water vapour in the atmosphere during the period 1988 – 2001 during which time CO2 levels increased by ~30 ppm (10%) and temperature anomalies by ~0.3C. The data show some reduction in water vapour in the radiative crucial upper layers of the atmosphere. Based on this data water vapour feedback looks to be small or even negative.
This result is evidence against significant positive feedback from water vapour to CO2 radiative forcing. Small changes in water vapour can completely offset (or enhance) any change in CO2 radiation flux to space. The evidence does not support any trend increase in water vapour with either surface temperature or CO2.
1. http://eosweb.larc.nasa.gov/project/nvap/table_nvap.html see also http://www.leif.org/EOS/2012GL052094-pip.pdf
2. Ken Gregory points out that our water vapour values calculated by the Fortran program supplied give slightly higher values than that quoted in the new paper: Weather and Climate Analyses Using Improved Global Water Vapor Observations. The reason for this is currently unknown. However that paper also shows no increase in water vapour from 19880 until 2010.