You didn't read those FAQ's I cited did you? Here is a quote from one of them:
If left to run on their own, the models will oscillate around a long-term mean that is the same regardless of what the initial conditions were. Given different drivers, volcanoes or CO2 say, they will warm or cool as a function of the basic physics of aerosols or the greenhouse effect.The basic physics that drive the climate and are incorporated into climate models is not chaotic in nature. For a given set of inputs (simulated insolation, simulated changes in greenhouse gases, simulated volcanic eruptions, etc.) they will produce a given output. Using PDEs doesn't change that.
Climate models and weather models have a lot in common since they model basically the same thing, just on different time scales and different physical scales. Weather models are detailed to catch the differences in local effects and to pinpoint local weather more accurately. But climate models incorporate things that weather models ignore because they have miniscule effects of the short time scales in which weather models operate. BTW, if weather forecasters want to make accurate forecasts I imagine they're running their models more often than once a week. Daily would make more sense to me.
When I said climate models don't depend on data I meant that is not an input to the climate model run. Of course the output of climate models is compared to real world data. That's how they get tested. So far they're better than any other method we have. Here is a comparison of model output to real world data up to the end of 2011:
http://www.realclimate.org/index.php/archives/2012/02/2011-updates-to-model-data-comparisons/There are links to earlier comparisons in the article.
I agree with you on the tipping points issue. Things like the Arctic sea ice disappearing or permafrost melting leading to massive increases in methane may cause drastic changes but they are not included in climate models because we don't know enough about them to reliably model them yet. I note that either of those two tipping points would lead to even worse effects so climate models if anything are conservative in their projections.
BTW, on the Arctic sea ice issue, the head of the polar ocean physics group a the University of Cambridge said that the added heat from sea ice loss is equivalent to the warming from about 20 years of CO2 emissions.
