Adjoint sensitivity of the model forecast to data assimilation system error covariance parameters

The development of the adjoint of the forecast model and of the adjoint of the data assimilation system (adjoint‐DAS) makes feasible the evaluation of the local sensitivity of a model forecast aspect with respect to a large number of parameters in the DAS. In this study it is shown that, by exploiting sensitivity properties that are intrinsic to the analyses derived from a minimization principle, the adjoint‐DAS software tools developed at numerical weather prediction centres for observation and background sensitivity may be used to estimate the forecast sensitivity to observation‐ and background‐error covariance parameters and for forecast impact assessment. All‐at‐once sensitivity to error covariance weighting coefficients and first‐order impact estimates are derived as a particular case of the error covariance perturbation analysis. The use of the sensitivity information as a DAS diagnostic tool and for implementing gradient‐based error covariance tuning algorithms is illustrated in idealized data assimilation experiments with the Lorenz 40‐variable model. Preliminary results of forecast sensitivity to observation‐ and background‐error covariance weight parameters are presented using the fifth‐generation NASA Goddard Earth Observing System (GEOS‐5) atmospheric DAS and its adjoint developed at the Global Modeling and Assimilation Office.