Why do weather forecasts sometimes fail to predict accurately?
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To add to what other people wrote, we don’t have 100% accurate closed form solutions for forecast. Meaning even if we had perfect information of everything on Earth we can’t just plug it in an equation and get a forecast for a given time.
We must simulate interactions. Computers cannot simulate with infinite precision so we must divide time and space into intervals. Such divisions introduce errors that compound the longer we run a simulation.
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