The North Atlantic general circulation west of 50°W determined by inverse methods

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Abstract
We review linear inverse theory in the context of its application to determining the general circulation of the ocean. Inverse methods are intimately related to least squares and rank deficient regression problems. Results are dependent upon the model assumed; in this paper all models are linear, geostrophic, and mass conserving, and they differ only in the initial reference pressure for the dynamic computations. We show how to compute the resolution of both the observations and the solutions, the degree of data independence, and the solution variance. To handle the underdetermined nature of the problem, we impose a conventional requirement of maximum simplicity relative to the initial model. More generally, the methodology provides a powerful technique for handling imperfect and noisy chemical and dynamical tracers and for assimilating a great variety of different information into dynamically consistent circulation schemes. In the latter part of the paper the methods are applied to the western North Atlantic west of the 50°W meridian. An attempt to use a full data set failed owing to the nonsynoptic nature of the observations. Two initial models were then applied to a reduced data set defined by seven boxes in which conservation of total mass and of four additional layers was required. Model I, which initially has a reference level at the bottom, leads to a large Gulf Stream transport (124 Sv) with an active recirculation zone to the south. Model II begins with a reference level at 2000 dbar and leads to a weaker Gulf Stream with recirculation zones on both sides. The southern recirculation breaks up into smaller scales. Both models yield a strong large‐scale gyre to the south of the Mediterranean salt tongue. The residual error is 2–3 Sv rms in both models, but it appears that systematic errors due to the seasonal variability probably exceed this value.