A Bernoulli Inverse Method for Determining the Ocean Circulation

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  • 1 Hooke Institute for Atmospheric Research, Department of Atmospheric Physics, Clarendon Laboratory, Oxford OX1 3PU and Institute of Oceanographic Sciences, Wormley, Godalming, Surrey
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Abstract

A new inverse method for finding the large-scale ocean circulation is described. Unlike most previous methods it uses no horizontal gradient information, and is designed for widely spaced data. The method assumes that density, (linear) potential vorticity and Bernoulli function are all approximately conserved on a streamline, so that the Bernoulli function depends solely on density and potential vorticity, both of which are known from data. The requirement that Bernoulli functions should match at points where density and potential vorticity match then leads to a heavily overdetermined problem for the surface pressure field, solved by a singular-value decomposition.

The method is tested on an analytical solution due to Welander, and on the results of a numerical circulation model of Cox and Bryan, before use on climatological data, both over the main North Atlantic and over the beta triangle area. Analysis shows that for closely spaced data, the Bernoulli method reduces to beta-spiral dynamics, but with additional constraints from nonneighboring stations. The method, which is essentially nonlocal in character, as it depends on following flow streamlines, seems to be fairly robust both to noise in the data and to station spacing and selection.

Abstract

A new inverse method for finding the large-scale ocean circulation is described. Unlike most previous methods it uses no horizontal gradient information, and is designed for widely spaced data. The method assumes that density, (linear) potential vorticity and Bernoulli function are all approximately conserved on a streamline, so that the Bernoulli function depends solely on density and potential vorticity, both of which are known from data. The requirement that Bernoulli functions should match at points where density and potential vorticity match then leads to a heavily overdetermined problem for the surface pressure field, solved by a singular-value decomposition.

The method is tested on an analytical solution due to Welander, and on the results of a numerical circulation model of Cox and Bryan, before use on climatological data, both over the main North Atlantic and over the beta triangle area. Analysis shows that for closely spaced data, the Bernoulli method reduces to beta-spiral dynamics, but with additional constraints from nonneighboring stations. The method, which is essentially nonlocal in character, as it depends on following flow streamlines, seems to be fairly robust both to noise in the data and to station spacing and selection.

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