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Why do small errors in weather models grow over time?

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Weather forecasting Doppler radars, such as this one operated by the U.S. National Weather Service at New Underwood, South Dakota, extract the Doppler frequency shift of the echo produced by a moving target by noting how much the frequency of the received signal differs from the frequency of the signal that was transmitted.

Small errors in weather models grow over time primarily because the atmosphere is a complex, chaotic system. In numerical weather prediction, models calculate future conditions by taking initial measurements and solving physics-based equations in iterative steps.123

Because the atmosphere is chaotic, it exhibits the butterfly effect, where even infinitesimal differences in initial conditions—such as a tiny rounding error—can lead to dramatically different outcomes over time. As models perform these calculations, small errors inevitably creep into the data. These errors do not remain static; they accumulate and grow exponentially as the simulation progresses.123

Eventually, these compounded errors become so significant that they swamp the original forecast, rendering it invalid. This creates a "horizon of predictability," an impassable barrier beyond which even the most precise initial measurements cannot guarantee an accurate long-term forecast. Consequently, while models are highly effective for short-term predictions, the inherent nonlinearity of atmospheric processes limits the accuracy of extended forecasts.23