In the same way. Atmosphere is divided into cells with various variables and supercomputer then calculate the relations and effects between the cells. Though it is very much just an educated guess for the longer periods of time.
Weather models are quite precise and good these days, but in the end they are still just models, an approximations and representations of reality. Basically only forecast you should look at is for the 3 days, maybe for a week at maximum.
This article has some great explanations too: https://letstalkscience.ca/educational-resources/stem-in-context/why-weather-so-hard-predict
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