Optimized open boundary conditions in a primitive equation ocean model
This study addresses the problem of data assimilation in the specification of open boundary conditions for limited area models. Optimization techniques are presented which are based on combining data available on the open boundary with the physics of the hydrodynamic model. Previous studies have examined this approach for the barotropic mode [ Shulman and Lewis 1995, 1996; Shulman 1997]. This study expands this approach to the baroclinic case. As with the barotropic condition, the boundary conditions have the physical interpretation as special linearizations of the Bernoulli equation for each normal mode. Due to the complexity of decomposing variables into normal modes with varying bathymetery, two alternative approaches are presented. The first is a simplification of the optimized open boundary condition based on normal modes. The second uses empirical orthogonal functions instead of normal modes. In all the approaches, two schemes are used to provide reference values and energy flux estimates. The boundary conditions are tested in several simulations. The simulations use an idealized channel open on one end, a enclosed rectangular open on one end, and the Monterey Bay area. The models are tested with tidal forcing and wind forcing. The optimized boundary conditions are compared to two non-optimized conditions: a simple coupling condition for the channel and rectangular tests, and a radiation condition for the Monterey Bay tests. The results of these tests and comparisons of the different approaches are presented.