An Adjoint Ocean Model Using Finite Elements: An Application to the South Atlantic

Abstract

A new inverse model to study the large-scale ocean circulation and its associated heat and freshwater budget is developed. The model relies on traditional assumptions of mass, heat, and salt conservation. A three-dimensional velocity field that is in steady state and obeys geostrophy is derived. Using this flow field, the steady-state advection–diffusion equations for temperature and salinity are solved and the corresponding density is calculated. An optimization approach is used that adjusts reference velocities to get model parameters close to observations so that the velocities are in geostrophic balance with the model density field. In order to allow a variable spatial resolution, the finite-element method is used. The mesh is totally unstructured and the three-dimensional elements are tetrahedra. Climatological hydrographic data, observations of sea surface height (SSH) from satellite altimetry, and wind data are assimilated in the model. The advantages of the finite-element method make it possible to use an easy representation of the model parameters on the tetrahedra. It is not difficult to find the adjoint form of the discrete equations. The unstructured mesh agrees well with the complex geometry of the bottom topography. The model is applied to the South Atlantic. First model results show that the upper-level circulation corresponds to the circulation known from literature. The volume transport through Drake Passage is constrained to be 130 Sv. The transports of water masses, heat, and salt across the open boundaries (Drake Passage, 30°S, 20°E) are in agreement with the literature. The formation rate of bottom water is 13.0 Sv and the heat transport across 30°S to the north is 0.64 PW.