In short: they cannot, at least not reliably. Source: my mother is a meteorologist, she has studied in Russia and worked for years in a weather station in Kasakstan or however you write it in English, before we moved to Germany and she had to redo her masters because of accreditation issues.
Here’s the thing: Meteorologists measure lots of different kinds of data. They then use different models to predict weather conditions. However, none of them can be entirely accurate, since to achieve that you would have to know all the different states of all the atoms in the air, and even then it would be very sensitive to initial conditions, even small changes would influence the outcome drastically. So they measure lots, calculate different models and combine that data for a rough prediction.
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