Barrett is not a climate scientist
According to a search of 22,000 academic journals, there is a "JC Barrett" listed as a co-author of a single research paper on cloud densification published 13 years ago.
In an article published in 1994 in the New Scientist he suggested that the lowest 30 metres of the troposphere already contains all the CO2 necessary to absorb all the radiation reflected and emitted back by the earth's surface at most infra-red wavelengths, except for the "window" between 7.5 and 14 micrometres, through which radiation escapes back into space.  Other scientists strongly disagree with him. 
He was one of the keynote speakers at the conference in Leipzig in November 1995 organized by the European Academy for Environmental Affairs and the Science and Environmental Policy Project (SEPP) which resulted in the Leipzig Declaration on Global Climate Change. At that conference he said that even if the level of CO2 would double, that would result in a temperature increase of only 0.07°C what cannot justify the commotion about global warming. 
Currently he is a member of the Scientific Advisory Forum of the Scientific Alliance.
- Jack Barrett, "Structure and Bonding (Basic Concepts In Chemistry)," Wiley-RSC, April 19, 2002, ISBN 0471224790
- Jack Barrett, "Atomic Structure and Periodicity," Wiley-RSC, December 13, 2002, ISBN 0471444685
- DeSmogBlog research on Barrett.