Assimilation studies of open-ocean flows .2. Error measures with strongly nonlinear dynamics

In a companion paper by Gunson and Malanotre-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.