We know how pressure, temperature, humidity and sunshine work to create weather, and we have very complicated simulations that rely on field data collected by stations and satellites.
An example:
There’s a beach. A sunny beach with cold water in front of it. When the sun shines on the sand, it gets hot very quickly and heats up the air above it, but the water stays cold. Warm air rises up, and the surrounding air fills the “hole” the rising air has left. This air comes from the cold water, and moving air is what we call wind. Now, depending on how sunny it is, we can calculate how much warmer the beach will get than the water, and then get the wind speed out of that. How do we know how sunny it is? Through satellite pictures that show clouds, and through sensors at the ground.
There’s lots and lots of complicated models and atmospheric mechanisms, but with those we can predict many many things. Since we have loads of data, experience and computing power, we can do large simulations that predict roughly up to two weeks. That roughness adds up though for each day, because one cloud or one degree can already make the difference, but most models are accurate up to three days.
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