These days, really fast computers.
The Americans have the Global Forecast System (GFS). The Europeans have the European Center for Medium-Range Weather Forecasts (ECMWF).
Other countries run less powerful systems, and other systems exist that are used only in the next 1-3 days.
All of them run a *ton* of physics and math calculations. Experience has taught us that if, say, a super typhoon were to move into the North Pacific near Japan, five days later the weather pattern will change in a relatively predictable way in the U.S.
From this you can at least get a broad idea of whether or not it’ll be warm in a certain region, and maybe even if it will be rainy. This idea is called [teleconnections](https://www.cpc.ncep.noaa.gov/data/teledoc/teleintro.shtml).
Out to 14 days, you’re relying more on past history and hoping the math gets you close. But weather is unpredictable, and little errors in the Day 2 forecast spiral into huge errors by Day 5.
Meteorologists try to work around this by running a whole bunch of 14-day forecasts, then using the average, and/or discarding a few because the forecast is unreasonable (in their opinion).
This gets you… closer, but the nature of the problem means it will still be significantly wrong a lot of the time.
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