Determining the Mean, Large-Scale Circulation of the Atlantic with the Adjoint Method

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Abstract
A new model approach based on the adjoint formalism and aimed at assimilating large sets of hydrographic data is presented. The goal of the model calculations is to obtain the mean, large-scale ocean circulation together with coefficients of iso- and diapycnal mixing and air-sea heat and freshwater fluxes. The final, optimal solution is required to be consistent with the principle of geostrophy and must predict realistic distributions of temperature and salinity. The model covers the entire Atlantic and has realistic topography. Model resolution is nonuniform and ranges from 2.5° to 10° horizontally and from 60 m to 500 m in the vertical. Model velocities are initialized with geostrophic flows calculated from original hydrographic station data; initial air-sea heat fluxes and mixing coefficients are taken from the literature. Mass, heat, and salt budgets are satisfied exactly, and for given boundary conditions and model flows the model temperature and salinity distributions are calculated. Then horizontal flows and the air-sea fluxes are modified automatically (in directions provided by the adjoint model) until deviations between model temperatures and salinities and their measured counterparts (data) are minimized while keeping the vertical shear of the horizontal velocities (as given by the initial geostrophic flows) largely unchanged. Model results show that the simulated temperature and salinity fields can indeed be brought to close agreement with the observed distributions. Modifications to the initial horizontal flows needed to achieve this agreement are found to consist mainly of constant velocity shifts (reference velocity) in the vertical profiles. The final, optimal flow field thus is consistent with geostrophic dynamics, and the present model can be regarded as a new approach to the classical problem of calculating reference velocities from hydrographic data. Meaningful results are found for air-sea heal fluxes and for the vertical velocities w.

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