Local Data Assimilation in Specification of Open Boundary Conditions

Abstract

A data assimilation approach to specify open boundary conditions is proposed. The boundary values are determined from the solution of the special optimization problem: minimization of the difference between the model and reference boundary values under the integral constraints on the open boundary. These constraints represent the energy, momentum, and mass fluxes through the open boundary. Reference values represent the a priori knowledge about the boundary values. They might be derived from observations, results of another model run, or from another approach to the specification of open boundary conditions. Optimized open boundary conditions are presented in detail for the barotropic case and when only one integral constraint is considered: energy flux through the open boundary. It is shown that well-known radiation-type boundary conditions introduced by Reid and Bodine, and Flather, are special cases of the derived optimized conditions. The results of application of the proposed boundary conditions are demonstrated in the modeling of tidal and wind-driven circulation for a channel and for the northern part of the Adriatic Sea. The results of studies of the model predictions? sensitivity to errors in the reference values used in the boundary conditions are presented. The applications of optimized open boundary conditions show a significant reduction in errors when compared to the commonly used, nonoptimized schemes.