A reduced-dynamics variational approach for the assimilation of altimeter data into eddy-resolving ocean models

A new method of assimilating sea surface height (SSH) data into ocean models is introduced and tested. Many features observable by satellite altimetry are approximated by the first baroclinic mode over much of the ocean, especially in the lower (but non-equatorial) and mid latitude regions. Based on this dynamical trait, a reduced-dynamics adjoint technique is developed and implemented with a three-dimensional model using vertical normal mode decomposition. To reduce the complexity of the variational data assimilation problem, the adjoint equations are based on a one-active-layer reduced-gravity model, which approximates the first baroclinic mode, as opposed to the full three-dimensional model equations. The reduced dimensionality of the adjoint model leads to lower computational cost than a traditional variational data assimilation algorithm. The technique is applicable to regions of the ocean where the SSH variability is dominated by the first baroclinic mode. The adjustment of the first baroclinic mode model fields dynamically transfers the SSH information to the deep ocean layers. The technique is developed in a modular fashion that can be readily implemented with many three-dimensional ocean models. For this study, the method is tested with the Navy Coastal Ocean Model (NCOM) configured to simulate the Gulf of Mexico.