Mathematical and physical basis of general circulation models of climate

This paper is a review; firstly of the mathematical and scientific assumptions underpinning general circulation models (GCMs) and of the criteria that should be satisfied by those models; secondly of the computational methods and the interpretation of results using concepts of non-linear dynamics and statisitical techniques; thirdly of future developments and some of the associated mathematical questions arising from ever more climate change processes being integrated into the GCMs.