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It is also possible to formulate the 4DVar problem with the model acting as a weak constraint. We then search for a model solution close to the measurements that “almost” satisfies the dynamical model and its initial and boundary conditions. The concept of the model being a “weak constraint” as opposed to “strong constraint” was introduced by Sasaki (1970b). An early weak-constraint assimilation study is the one byBennett and McIntosh (1982 who solved the weak-constraint variational inverse problem for an ocean tidal model.

Weak Constraint 4DVar