I was just looking at the weather app on my phone and started thinking about this
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I’d split it into two main categories: experience and computer modeling.
Hundreds of years of watching the weather around the world has allowed experts to see how weather patters tend to move. Thus a lot of the time they can look and see that the weather over there is headed their way. And, if its doing so-and-so over there, when it gets here it is likely to do thus-and-such.
Second, Today’s computers are powerful enough to run a finite element analysis on the Earth’s entire atmosphere. This is where the atmosphere is broken up into a huge number of “boxes”. Then physics rules are applied to all the boxes. A simplified example of one of the physics rules is that the total mass of the atmosphere stays the same (see note). Thus if 100 kg of air moves out of one of the boxes, this 100 kg must show up somewhere in the other boxes. By applying much more complicated rules and keeping track of what’s in each and every box, powerful computers can make predictions of the future weather.
Note: Saying the total mass of the atmosphere doesn’t change is an oversimplification. Water can move between the oceans/lakes and the atmosphere, changing the total mass of the atmosphere. This is just one of the complications that must be included in the computer model.
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