Computer simulations. Over time we have developed several different mathematical models for how the atmosphere behaves. These models are used to generate the daily weather forecast as well as seasonal predictions and long term climate forecasts.
The issue is that the weather/atmosphere is a chaotic system highly dependent upon initial conditions, and the data we collect doesn’t cover the entire atmosphere. So we have to make assumptions and interpolate to fill in the gaps. This means that the further out into the future you run your model, the more it is going to diverge from reality, which is why we are constantly taking new measurements and rerunning the models, so they we stay close to reality
Now, for the longer term predictions, we don’t need the level of detail that we need for tomorrow’s forecast. We are just looking for general trends. So we just run the models several times, adjusting the inputs based on historical data, current conditions and experience, to come up with a range of statistically likely outcomes.
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