Error covariance sensitivity and impact estimation with adjoint 4D‐Var: theoretical aspects and first applications to NAVDAS‐AR

This article presents the adjoint-data assimilation system (adjoint-DAS) approach to evaluate the forecast sensitivity with respect to the specification of the observation-error covariance (R-sensitivity) and background-error covariance (B-sensitivity) in a four-dimensional variational (4D-Var) DAS with a single outer-loop iteration. Computationally efficient estimates to the forecast impact of adjustments in the error covariance models are obtained by exploiting the mathematical properties of the R- and B-sensitivity matrices and their relationship with the observation sensitivity vector. An additional contribution of this work is that it establishes a synergistic link between various methodologies to analyze the DAS performance: observation sensitivity and impact assessment, error covariance sensitivity, and a posteriori diagnosis. The practical ability to obtain sensitivity information with respect to R- and B-parameters is presented with the adjoint versions of the Naval Research Laboratory Atmospheric Variational Data Assimilation System–Accelerated Representer (NAVDAS-AR) and the Navy Operational Global Atmospheric Prediction System (NOGAPS). The adjoint approach is used to provide guidance on the forecast impact of weighting the radiance data in the DAS according to observation-error variance estimates derived from an a posteriori diagnosis. The results indicate that information extracted from both error covariance diagnosis and sensitivity analysis is necessary to design parameter tuning procedures that are effective in reducing the forecast errors. Copyright © 2012 Royal Meteorological Society