Combining observations with a dynamical prior estimates an initial atmospheric state and its uncertainty. In a linear Gaussian update, analysis increments are with , where and are prior and observation error covariance matrices. Observation noise, sparse coverage and incorrect model or covariance assumptions can all leave forecast errors.
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Data assimilation is a technique used in various fields, such as meteorology, oceanography, environmental science, and engineering, to integrate real-time observational data into models to improve their accuracy and predictive capabilities. The primary goal of data assimilation is to provide a better estimate of the state of a system by merging observational data with model predictions.