Estimation of boundary values in a North Atlantic circulation model using an adjoint method

A 1° × 1° resolution version of the MIT-GCM in the North Atlantic is used to test whether open-boundary conditions can be constrained by observations inside the domain using an adjoint method. In this preliminary feasibility study, the model is run during 1993 with a simplified vertical mixing physics. It is constrained by monthly SST fields, monthly climatological θ, S fields and TOPEX/POSEIDON altimetry. The adjoint model is built using automatic differentiation software. The method aims at bringing the model’s trajectory to consistency with data, by adjusting the initial θ, S fields, the time-varying atmospheric forcing fields and the time-varying open-boundary values. An originality of the work is the ‘nested approach’, which uses optimized fields from a global, coarser resolution model for the open-boundary conditions and for the prior estimates of the surface conditions adjustments. A solution is obtained after 75 iterations. This study shows that significant changes can be obtained on the open-boundary values, and that a general improvement in the circulation is achieved in the constrained solution, mainly in the Gulf Stream and equatorial regions. Changes at the open boundaries are characterized by a large temporal variability and small spatial scales. Large local adjustments are found close to the bottom and are likely unrealistic. There, the method tends to compensate for some model’s deficiencies by computing large corrections on the open-boundary values. The analysis of the cost function gradients with respect to the controls allows us to explore the local consistency between the constraints from the different data sets. This study suggests that no fundamental difficulty emerges when constraining open-boundary values. Its extension to a longer run with complete mixing physics can be envisaged.