Weather forecasting models are inherently chaotic, with small initial errors potentially leading to significant inaccuracies. However, the European Centre for Medium-Range Weather Forecasts (ECMWF) has managed to achieve high accuracy in predicting weather up to 15 days in advance. The key to this success is the 4-dimensional variational data assimilation (4D-Var) technique, employed since 1997. This method integrates real-time observations into the models, significantly reducing the impact of the butterfly effect. By minimizing sensitivity to initial conditions, 4D-Var not only enhances weather predictions but also finds applications in other time-series forecasting systems.
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