Estimates of Analysis and Forecast Error Variances Derived from the Adjoint of 4D-Var

AbstractA method is presented in which the adjoint of a four-dimensional variational data assimilation system (4D-Var) was used to compute the expected analysis and forecast error variances of linear functions of the ocean state vector. The power and utility of the approach are demonstrated using the Regional Ocean Modeling System configured for the California Current system. Linear functions of the ocean state vector were considered in the form of indices that characterize various aspects of the coastal upwelling circulation. It was found that for configurations of 4D-Var typically used in ocean models, reliable estimates of the expected analysis error variances can be obtained both for variables that are observed and unobserved. In addition, the contribution of uncertainties in the model control variables to the forecast error variance was also quantified. One particularly powerful and illuminating aspect of the adjoint 4D-Var approach to the forecast problem is that the contribution of individual obser...