7.4 Data Assimilation
Data assimilation optimally combines observations with model forecasts to produce the best estimate of the atmospheric state.
Methods
4D-Var
Minimizes cost function over time window using adjoint model. Used by ECMWF.
EnKF
Ensemble Kalman Filter: uses ensemble spread to estimate error covariance.
Hybrid
Combines variational and ensemble approaches. State of the art.
Analysis Equation
$$\mathbf{x}^a = \mathbf{x}^b + \mathbf{K}(\mathbf{y}^o - H(\mathbf{x}^b))$$
Analysis = Background + Kalman Gain × Innovation