These are some results from 19 GCMs. They were given the problem of showing what would happen to the global temperature and to global rainfall if the concentration of CO₂ were to increase by 1% per year. The CO₂ concentration would be doubled in 70 years. The temperature graph (a) shows a large range of possible values for the proposed changes and, on average, the models predict a temperature increase of about 1.8^oC for the doubling of CO₂. The range of the temperature results is from 0.8-3.0^oC, the result being given as 1.8^oC ± 1^oC not inspiring much confidence in the procedures.

   The graph (b) showing the predictions of rainfall are even less inspiring. Will it get wetter or drier if the concentration of CO₂ increases? We just don't know.

There are serious difficulties with large complex models and the quote from Goody & Yung's book; Atmospheric Radiation, sums up the situation.

Line-by-line calculations are often adopted as a standard against which to test certain approximations. Their value in a relative context is indisputable, but that should not be taken to mean that line-by-line calculations are necessarily of high absolute accuracy. This comment is relevant to an implicit assumption in much of the current literature: that more and more detailed physics encoded onto larger and larger computers will eventually yield accurate weather and climate predictions. This is more an article of faith than a demonstrable proposition. It is also possible to argue that numerical complexity hides or introduces its own sources of error, in addition to making it impossible to penetrate the algorithms of another investigator.

Another apt comment on modelling difficulties comes from William Kininmonth:

High powered computers allow us to carry out more complex modelling but the veracity of models relies on the specification of the individual interactions between the variables.

Weather forecasting models rely on initial specification of mass and momentum fields and, largely, the ability to conserve momentum (conservation of mass, although not of critical importance, is generally a basic specification). Within a few days of simulation the mass and momentum fields have diverged irreconcilably from the true evolution of the atmosphere as errors and computational uncertainty expand and propagate.

Climate forecasting is quite different from weather forecasting. It relies on an ability to conserve energy and to accurately reflect the transformation of energy within the climate system (solar radiation, sensible heat, latent energy, potential energy, terrestrial radiation, etc). Climate forecasting is a much more difficult task because of the exchange of energy and momentum between mediums, especially the gaseous and liquid fluids of the atmosphere and oceans. 

Although computing power might allow us to do modelling in powerful new ways the integrity of the models is only as good as the specifications of the interactions between the components. Climate models are severely limited in this respect, despite the access to powerful computers. 

And from Grant Petty:

Even now [2004], however, a fully comprehensive treatment of radiation and other physical processes remains too complex a problem for the most powerful computers to tackle for the entire atmosphere at once. General circulation models therefore continue to rely on grossly simplified representations of these processes, with the attendant risk of error in the model’s predictions. Finding ways to improve the accuracy and other physical parameterizations within the limits of available computing power is a major focus of current research in atmospheric science.

Grant W. Petty [A First Course in Atmospheric Radiation, Sundog Publishing, Wisconsin, (2004)]