Weather forecasts are based on models and extrapolation based on a lot of factors. I'm not too certain but I think that the smallest weather model cell size is about two miles squared or perhaps cubed - I don't know how the models work.

Weather forecast distribution is by "news". News is deployed at mostly fixed intervals.

Anecdote: In Yeovil, Somerset, UK. The topography here (its quite hilly here in a county with some fairly famous "levels") means that it can be pissing down with rain on one side of the town and be dry on the other side and so on.

Weather forecasting is a quite hard problem. The really hard problem is delivering it.