On Analysis Error Covariances in Variational Data Assimilation

On Analysis 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 the initial condition function (analysis). The equation for the analysis error is derived through the errors of the input data (background and observation errors). This equation is used to show that in a nonlinear case the analysis error covariance operator ...

A posteriori error covariances in variational data assimilation

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 covariance...

On deterministic error analysis in variational data assimilation

The problem of variational data assimilation for a nonlinear evolution model is considered to identify the initial condition. The equation for the error of the optimal initialvalue function through the errors of the input data is derived, based on the Hessian of the misfit functional and the second order adjoint techniques. The fundamental control functions are introduced to be used for error a...

A Hybrid Approach to Estimating Error Covariances in Variational Data Assimilation

Data Assimilation (DA) involves the combination of observational data with the underlying dynamical principles governing the system under observation. In this work we combine the advantages of the two prominent DA systems, the 4D-Var and the ensemble methods. The hybrid method described in this paper consists of identifying the subspace spanned by the major 4D-Var error reduction directions. Th...

Modeling Retrieval Error Covariances for Global Data Assimilation