Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation

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Hessian‐based model reduction for large‐scale systems with initial‐condition inputs (2008, methodology): “In [17], POD was used in a large-scale inverse problem setting to define a reduced space for the initial condition in which to solve the data assimilation problem.”
On the Sensitivity Equations of Four-Dimensional Variational (4D-Var) Data Assimilation (2008, methodology): “The verification of the SOA model included a Taylor series test (Daescu and Navon 2007) and a Hessian symmetry test using pairs of random vectors.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “[31, 36, 37]) Navon et al proposed a dual-weighted POD method, where the weights assigned to each snapshot were derived from an adjoint related to the optimality system of a variational data assimilation problem in meteorology.”
A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation (2008, methodology): “Evaluation of the Hessian matrix of the 4DVAR cost functional in the reduced space is feasible using a second-order adjoint model (Daescu and Navon 2007) and may be used to provide statistical information on the analysis errors.”