A multivariate balance operator for variational ocean data assimilation

It is common in meteorological applications of variational assimilation to specify the error covariances of the model background state implicitly via a transformation from model space where variables are highly correlated to a control space where variables can be considered to be approximately uncorrelated. An important part of this transformation is a balance operator which effectively establishes the multivariate component of the error covariances. The use of this technique in ocean data assimilation is less common. This paper describes a balance operator that can be used in a variable transformation for oceanographic applications of three- and four dimensional variational assimilation. The proposed balance operator has been implemented in an incremental variational data assimilation system for a global ocean general-circulation model. Evidence that the balance operator can explain a significant percentage of background-error variance is presented. The multivariate analysis structures implied by the balance operator are illustrated using single-observation experiments.