Equivalence between the Kalman filter and 4D-Var
Experiment with one observation at time t0 + T
- Initial conditions:
- Linear case with one observation at t0 + T and no model error
Analysis increment of the Kalman filter
- Here L ? L(t0,t0 + T) is the propagator of the linear system
Analysis increment of 4D-Var
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- Analysis increments are identical at the end of the assimilation interval