Forward Sensitivity Approach to Dynamic Data Assimilation

Abstract

The least squares fit of observations with known error covariance to a strong-constraint dynamical model has been developed through use of the time evolution of sensitivity functions—the derivatives of model output with respect to the elements of control (initial conditions, boundary conditions, and physical/empirical parameters). Model error is assumed to stem from incorrect specification of the control elements. The optimal corrections to control are found through solution to an inverse problem. Duality between this method and the standard 4D-Var assimilation using adjoint equations has been proved. The paper ends with an illustrative example based on a simplified version of turbulent heat transfer at the sea/air interface.