On optimal solution error covariances in variational data assimilation

Abstract

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find some unknown parameters of the model. The equation for the error of the optimal solution is derived through the statistical errors of the input data. The covariance operator of the optimal solution error is obtained using the Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints.