After looking at this post, Ryan Maue suggested that I do a further analysis of humidity trends using the ERA Interim data set of ECMWF. This is the most up to date information, although it covers a much shorter period than the ERA 40 data I used in the earlier analysis. The results are that over the 19 year period from 1989 to 2007 there are no significant trends in specific humidity (q) in this data set. Current theory would say that q should be increasing. Thus between the ERA 40 data, and the ERA Interim data there is no confirmation of the theory, and in fact many of the trends are negative, particularly over the NH mid latitudes, but not significant.
The data for this study is from the ERA interim data set downloaded from the ECMWF servers.
The results can be found here.