Haaaaang on.....
I think people posting here are confusing "modeling the weather" with "forecasting the weather".
While the point of the former is to do a better job of the latter, you can forecast the weather for most purposes to an acceptable level of error with the naked eye, a couple of instruments that have been around in essentailly the same form for several hundred years and a bit of knowledge.
The addition of com links to other people doing the same stuff elsewhere makes life even easier of course, as does a radar setup of the right kind in the right place. Satelite pix are the ultimate bees knees.
Not perfect by any means, but good enough for most purposes.
It is my understanding that modeling the weather requires so much digital oomph that the further out you try and predict it the more likely it is that it is already happening by the time you get the answer.
My next door neighbour uses a rock hanging from a string outside his kitchen window to forecast the weather. If he looks out and the rock is wet, it's raining. If it's not wet, it's not raining. If his window is broken, it's windy.