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

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Dobrindt, U. and Schröter, J. (2003): An Adjoint Ocean Model Using Finite Elements: An Application to the South Atlantic , Journal of atmospheric and oceanic technology, vol. 20, no. 3, pp. 392-407 .
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Abstract:

A new inverse model to study the large scale ocean circulation and its associated heat and fresh waterbudget is developed. The model relies on traditional assumptions of mass, heat and salt conservation.A 3-dimensional velocity field which 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 correspondingdensity is calculated. An optimization approach is used that adjusts reference velocities to get modelparameters close to observations and that the velocities are in geostrophic balance with the modeldensity field. In order to allow a variable spatial resolution, the finite element method is used. The mesh istotally unstructured and the 3-dimensional elements are tetrahedra.Climatological hydrographic data, observations of sea surface height (SSH) from satellite altimetry and winddata are assimilated in the model. The advantages of the finite element method make it possible to use aneasy representation of the model parameters on the tetrahedra. It is not difficult to find the adjoint form of thediscrete equations. The unstructured mesh agrees well with the complex geometry of the bottomtopography.The model is applied to the South Atlantic. First model results show, that the upper-level circulationcorresponds to the circulation known from literature. The volume transport through Drake Passage isconstrained to be 130 Sv. The transports of water masses, heat and salt across the open boundaries(Drake Passage, 30S, 20E) are in agreement with the literature. The formation rate ofbottom water is 13.0 Sv and the heat transport across 30S to the north is 0.64 PW.

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