Holger Dambeck writes in Der Spiegel:

Climate researchers use some of the most powerful computers in the world to run their models. Still, the sheer amount of data that must be crunched mandates that many details are simply left out. How accurate are the results?
“Give me ten parameters, and I’ll simulate an elephant for you. Give me one more, and he’ll wag his tail.” The saying sums up the problem with many models. Models allow you demonstrate anything and everything, as long as there are enough knobs to turn. The real test of how good a model really is comes when you compare it to reality.
But when it comes to climate change, researchers are faced with a practically insoluble problem: We won’t know for sure until the end of the century whether climate predictions for the year 2100 are correct or not. But with climate scientists around the world warning of the dangerous consequences of climate change, it becomes apparent that we can hardly afford to wait that long.
Climate models, of course, are not completely a matter of faith. They describe real, physical processes in the Earth’s atmosphere. Differential equations describe how wind, temperature and air pressure develop in connection with each other. The impact of water — in the form of moisture or clouds, made up of liquid drops or ice crystals — as well as the role of greenhouse gases like CO2 is taken into account.
Dramatically Simplified
How do all these equations work together? The same way one would expect from physics class: Temperature goes up when warm air moves around or when rising pressure compresses air. Such changes in temperature in turn affect atmospheric pressure which then drives air masses. The Earth’s rotation plays a role as well. This interplay between temperature, pressure and air circulation is reflected in the equations that drive climate prediction models.
But all these processes must be dramatically simplified for even supercomputers to produce results in a reasonable amount of time. “You have to limit yourself to the processes you think are most important,” says Marco Giorgetta of the Max Planck Institute for Meteorology in Hamburg.

The rest here.