Even with a totally deterministic model, you can't predict weather very far out because it's chaotic. In other words, you'd need to measure the parameters with arbitrarily high accuracy, which even an advanced AI can't do. To oversimplify, if you need one more bit of accuracy in the measurements for each hour you forecast, it's impossible to get enough accuracy to forecast a week out.

For a detailed discussion of chaos and weather prediction, see: http://www.ecmwf.int/sites/default/files/Chaos%20and%20weath... The "trick" for dealing with chaos is to do a bunch of predictions with perturbed values. If they all end up the same, then the forecast is probably okay. If they vary widely, then you know not to assign much accuracy to the forecast.