I knew someone would bring this up.
Climate models are physical models, not statistical models. They don't depend on data to make predictions. Scientists compare model output to data to test accuracy of the model but the tweaks they make are related to the modeling of physical processes and are not statistical in nature.
They don't depend on initial conditions to make predictions. You could set the initial conditions anywhere and the model would eventually converge on the same answer in the end. The closer your initial conditions are to reality the faster it converges but in the end it will.
Climate models can easily be more accurate than weather models. As an analogy consider flipping a coin. I can't tell you accurately whether the next flip will come up heads or tails however I can tell you the results of flipping a coin 1000 times with pretty good accuracy. Weather is what you get with each coin flip, climate is the results of 1000 coin flips.
Here are a couple of FAQ's on climate models for your edification:
http://www.realclimate.org/index.php/archives/2008/11/faq-on-climate-models/http://www.realclimate.org/index.php/archives/2009/01/faq-on-climate-models-part-ii/ 
