AFAIK one of the biggest problem in numeric simulations is critical phenomena, where depending on a tiny difference in current state, something either happens o

AFAIK one of the biggest problem in numeric simulations is critical phenomena, where depending on a tiny difference in current state, something either happens or doesn't happen. Critical phenomena include phase changes such as water freezing or condensing (clouds). Obviously that's a problem for weather forecasts. For a long-term climate model, it might work to average out (over space and time) some critical phenomema and assume a steady function from e.g. average air temperature to ice cap size and cloud cover. (source: wrote some homework-grade numerical simulations, physics major.)