Data assimilation
= Data assimilation
Combining observations with a dynamical prior estimates an initial atmospheric state and its uncertainty. In a linear Gaussian update, analysis increments are $K(y-Hx_b)$ with $K=BH^T(HBH^T+R)^{-1}$, where $B$ and $R$ are prior and observation error <covariance matrices>. Observation noise, sparse coverage and incorrect model or covariance assumptions can all leave forecast errors.