Tellus A Dynamic Meteorology and Oceanography · 2010 · 37 citations · 44 references
Parameter EstimationEngineeringVariational Data AssimilationEarth ScienceData AssimilationError CovariancesState EstimationNumerical Weather PredictionUncertainty QuantificationUncertainty EstimationBackground CovarianceEstimation TheoryStatisticsHybrid ApproachGeographyInverse ProblemsHybrid MethodRobust ModelingLand Data AssimilationStatistical InferenceShort-term Variability
Data assimilation combines observational data with the governing dynamics of the system. The study aims to merge the strengths of 4D‑Var and ensemble methods into a single hybrid framework. The hybrid method identifies the subspace of dominant 4D‑Var error‑reduction directions, removes them from the background covariance via a Galerkin projection, replaces them with low‑rank Hessian‑inverse estimates of analysis error, and iteratively updates the covariance to capture the “error of the day.” Numerical experiments on a nonlinear model show that the hybrid approach yields accurate error covariance estimates and improves 4D‑Var analysis outcomes.
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. These directions are then removed from the background covariance through a Galerkin-type projection, and are replaced by estimates of the analysis error obtained through a low-rank Hessian inverse approximation. The updated error covariance in one window can be used as the background covariance for the next window thus better capturing the ‘error of the day’. The numerical results for a non-linear model demonstrate how the hybrid method leads to a good estimate of the true error covariance, and improves the 4D-Var analysis results.
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