A posteriori error covariances in variational data assimilation

摘要

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 (background, observation, and model errors). A numerical algorithm is developed to construct an a posteriori cov-ariance operator of the analysis error using the Hessian of an auxiliary optimal control problem based on the tangent linear model constraints.