An Ensemble Approach to Weak-constraint Four-dimensional Variational Data Assimilation

This article presents a framework for performing ensemble and hybrid data assimilation in a weak-constraint four-dimensional variational data assimilation system (w4D-Var). A practical approach is considered that relies on an ensemble of w4D-Var systems solved by the incremental algorithm to obtain flow-dependent estimates to the model error statistics. A proof-of-concept is presented in an idealized context using the Lorenz multi-scale model. A comparative analysis is performed between the weak- and strong-constraint ensemble-based methods. The importance of the weight coefficients assigned to the static and ensemble-based components of the error covariances is also investigated. Our preliminary numerical experiments indicate that an ensemble-based model error covariance specification may significantly improve the quality of the analysis.