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 metho d. Here the estimation of error covariances for the estimated boundary and initial conditions and interior fields, in the presence of strong ly nonlinear dynamics, is investigated. The evaluation of the full err or covariance matrix for the estimated control variables from the inve rse Hessian matrix is presented along with its dependence upon the deg ree of nonlinearity in the dynamics. Major new results here obtained a re the availability of off-diagonal covariances, the successful calcul ation of error covariances for all boundary and initial conditions, an d the estimation of errors for interior fields. The role of the Hessia n matrix is assessed in gauging the sensitivity of the estimated bound ary and initial conditions to the data.