See the second half of this cousin comment. But a short summary (with a bit of additional info):

First, I see a philosophical difference between input uncertainty and calculation noise; the mathematical tools you need to attack each problem are different. The first can be solved through sampling (or a number of other different ways); the second can be solved with increased precision (or a number of other different ways). Importantly, sampling does not seem to me to be a promising approach to solving the calculation noise problem, because the errors may be systematic instead of random. In chaotic systems, this problem seems especially important.

Second, it seems common for both weather models and climate models to use simulation time steps of about 10 minutes. If you want to predict 6 days ahead, that's 864 time steps. If you want to predict 60 years ahead, that's over 3 million time steps.