In a companion paper by Gunson and Malanotte‐Rizzoli [this issue], the problem of estimating boundary and initial conditions for a regional open‐ocean model from sparse data is addressed using the adjoint method. Here the estimation of error covariances for the estimated boundary and initial conditions and interior fields, in the presence of strongly nonlinear dynamics, is investigated. The evaluation of the full error covariance matrix for the estimated control variables from the inverse Hessian matrix is presented along with its dependence upon the degree of nonlinearity in the dynamics. Major new results here obtained are the availability of off‐diagonal covariances, the successful calculation of error covariances for all boundary and initial conditions, and the estimation of errors for interior fields. The role of the Hessian matrix is assessed in gauging the sensitivity of the estimated boundary and initial conditions to the data.

The problem of estimating boundary and initial conditions for a regional open‐ocean model is addressed here. With the objective of mimicking the Synoptic Ocean Prediction (SYNOP) experiment in the Gulf Stream system, a meandering jet is modeled by the fully nonlinear barotropic vorticity equation. Simulated velocity observations are taken using current meters and acoustic tomography; twin experiments are then performed in which the adjoint method is used to reconstruct the flow field. The estimated flow is forced to resemble the true flow by minimizing a cost function with respect to some control variables. First, the vorticity initial conditions are used as control variables, and the boundary conditions are specified. The strong flow is found to induce strong dependence of the model/data misfit upon the specified boundary conditions. Second, the boundary values of stream function and vorticity are then included among the control variables. Various choices of a priori information about the control variables are employed, using various observational strategies. The major new result obtained is the successful estimation of the complete set of initial and boundary conditions, which is necessary to integrate the vorticity equation forward in time. From a time‐invariant first guess for the boundary conditions the assimilation is able to create temporal variations at the boundaries that make the interior flow match well the velocity observations.

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