from first principles, coming up with an all-purpose algorithm or generally-applicable model is going to be harder than making it work for a single "use case".
for weather patterns, some parts of the country (speaking of the US here since that's where I'm familiar with) have fairly predictable cold front movements from west to east. others have ocean interactions, lake effects, etc.
I say 'washing machine' as it is a swirling mass of unpredictability. Yes there are obvious patterns that follow the seasons, but forecasts are required to be much more accurate than predicting the weather by patterns of the season.
They need to be accurate to each day, predicting temp, rainfall, wind etc. etc. The only way to do that is to try and predict how this chaotic system will progress over a period of time. Thats why all these weather agency talk about their new 'supercomputers' able to create more accurate forecasts. The processing power required to build these models is enormous.
No matter if you are forecasting locally or across the multiple states or countries, it still depends on forecasting the outcome of this chaotic system.
Like, for my purposes, I'd simply like to know the temperature trend for the next 3-5 days. Will each day's high be hotter or cooler than the previous?
Bonus points: what's the high temperature for the next 3 days (within say, 3°F).
Anecdotally, using these standards, this seems to be consistently wrong where I live for much of the summer. I don't pay attention in the other seasons as the weather is much milder.