Cunningham, S.A.
(2000)
Circulation and volume flux of the North Atlantic using synoptic hydrographic data in a Bernoulli inverse.
*Journal of Marine Research*, 58 (1), 1-35.
(doi:10.1357/002224000321511188).

## Abstract

A new formulation of the Bernoulli inverse is used to determine the circulation and flux of the North Atlantic from synoptic CTD observations. The inverse assumes that the compressible Bernoulli function, modified potential temperature and salinity are conserved on streamlines in steady, geostrophic, hydrostatic, mass and density conserving flow. Crossings between CTD stations in the distribution of modified potential temperature versus salinity define a set of streamlines. The Bernoulli function is conserved along streamlines and the difference in the Bernoulli function at each crossing is related to the contribution of the unknown sea-surface height (SSH) to the Bernoulli function. These crossings form a set of overdetermined simultaneous linear equations which we solve using a singular value decomposition. A covariance matrix of the SSH solution gives a good estimate of the SSH solution error. From the SSH we calculate a barotropic reference velocity which is added to the baroclinic velocity from the observed density distribution giving the total geostrophic velocity. The inverse is tested using output from the Ocean Circulation and Climate Advanced Model (OCCAM) where the SSH is known a priori: the mean SSH error is 2.2 cm, corresponding to a velocity error of ~1 cm/s for stations separated by 300 km. Inverses of the CTD data have a significantly smaller mean SSH error of 1.2 cm which corresponds to a velocity error of ~0.5 cm/s. Solutions are sensitive to the inclusion of deep crossings which result from observational error as a consequence of small meridional salinity gradients in North Atlantic Deep Water. The inverse is better than a classical dynamic height analysis of the data, by which we mean that the variance of the inverse circulation at depth is greater than the error variance. In the upper ocean (shallower than ?2 = 36.873 which is the top of the Labrador Sea Water) the North Atlantic Current and west wind drift transport 35 ± 4 Sv eastward between 39N and 54N. In the eastern North Atlantic the North Atlantic Current turns northward, west of 20W, with a flux of 14 ± 3 Sv into the Iceland Basin west of the Rockall-Hatton Plateau. The depth-integrated flux of the subpolar gyre in the Irminger Basin is 16 ± 6 Sv fed equally from sources in the western North Atlantic and from flow which crosses the Reykjanes Ridge east to west from the eastern North Atlantic. The circulation at the depth of the Labrador Sea Water is a mid-depth minimum and is generally dominated by error estimates. However, the flux west to east across the Mid-Atlantic Ridge is 3 ± 2 Sv. A simple estimate of the mean flushing time of the Labrador Sea Water layer in the eastern North Atlantic is ~16 years. At depth, over the Porcupine Abyssal Plain the inverse puts in place a basin scale cyclonic circulation and we note agreement with mean circulation rates of 1 to 2 cm/s derived from current meters.

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