Estimating open-ocean boundary conditions : sensitivity studies

Abstract

The problem of estimating boundary and initial conditions for a regional open-ocean model is addressed here. With the objective of mimicking the SYNOP experiment in the Gulf Stream system, a meandering jet is modeled by the fully nonlinear barotropic vorticity equation. Simulated observations of current velocity are taken using current meters and acoustic tomography. Twin experiments are 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. At the minimum, the error covariance matrix of the estimated control variables can be evaluated from the inverse Hessian of the cost function. The first major scientific objective of this work is the estimation of initial and boundary conditions for the model from sparse interior data. First the vorticity initial conditions are used as control variables and the boundary conditions are kept fixed. The jet-like flow is found to induce strong dependence of the model/data misfit upon the specified boundary conditions. Successively, the boundary values of streamfunction and vorticity are included among the control variables and estimated together with the initial conditions. Experiments are performed with various choices of scaling and first guess for the control variables, and various observational strategies. The first major new result obtained is the successful estimation of the complete set of initial and boundary conditions, 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, even when noise is added. It is found that information from the observations is communicated to the boundaries by advection of vorticity and by the instantaneous domain-wide connections in the streamfunction field due to the elliptic character of the Poisson equation. The second major scientific objective is the estimation of error covariances in the presence of strongly nonlinear dynamics. The evaluation of the full error covariance matrix for the estimated control variables from the inverse Hessian matrix is investigated along with its dependence upon the degree of nonlinearity in the dynam1cs. Further 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 the interior fields of streamfunction and vorticity. The role of the Hessian matrix is assessed in gauging the sensitivity of the estimated boundary and initial conditions to the data. Also, the importance is stressed of retaining off-diagonal structure of the Hessian to obtain more accurate error estimates.