Part B: Sensitivity Analysis in Nonlinear Variational Data Assimilation: Theoretical Aspects and Applications

Abstract

This chapter presents the mathematical framework to evaluate the sensitivity of a model forecast aspect to the input parameters of a nonlinear four-dimensional variational data assimilation system (4D-Var DAS): observations, prior state (background) estimate, and the error covariance specification. A fundamental relationship is established between the forecast sensitivity with respect to the information vector and the sensitivity with respect to the DAS representation of the information error covariance. Adjoint modeling is used to obtain first- and second-order derivative information and a reduced-order approach is formulated to alleviate the computational cost associated with the sensitivity estimation. Numerical results from idealized 4D-Var experiments performed with a global shallow water model are used to illustrate the theoretical concepts.

Keywords: Estimation theory, atmospheric data assimilation, error statistics, sensitivity analysis, adjoint model, large-scale optimization, Hessian matrix, second-order derivative information, order reduction, variational data assimilation, background estimate, error covariance, DAS representation, shallow water model, error statistics, information-redundancy, suboptimal weighting, a priori estimates, data thinning, super-obbing.