Abstract
Several inverse models have recently been put forward for obtaining estimates of the unknown reference velocities on the basis of the balances for momentum, vorticity, heat and salt of the large scale geostrophic circulation in the ocean. Notable forerunners are the inverse method proposed by Wunsch (1978) and the β-spiral method of Stommel and Schott (1977). These have first been applied in strictly adiabatic versions in the North Atlantic (see also Wunsch and Grant 1982, Schott and Stommel 1978). Both approaches can be extended to diabatic conditions. For the β-spiral model the consideration of the diffusion terms in the balances for tracers and vorticity are conceptionally simple (e.g. Olbers et al. 1985, Bigg 1985). Also Wunsch’s method has been generalized in this respect (see e.g. Wunsch 1984). We should also mention Hogg’s model (Hogg 1987) which is an inversion of the advective-diffusive balances on two isopycnals subject to the geostrophic constraint between the isopycnals. The model was applied in the central North Atlantic.
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References
Bigg, G.R., 1985, ‘The beta spiral method’, Deep Sea Res., 32, 465–484
Cheney, R.E., Marsh, J.G. and B.D. Beckley, 1983, ‘Global mesoscale variability from collinear tracks of Seasat altimeter data’, J. Geophys. Res., 88, 4343–4354
Cox, M.D. and K. Bryan, 1984, ‘A numerical model of the ventilated thermocline’, J. Phys. Oceanogr., 14, 674–687
Daniault, N. and Y. Menard, 1985, ‘Eddy kinetic energy distribution in the Southern Ocean from altimetry and FGGE drifting buoys’, J. Geophys. Res., 90, 11877–11889
Gordon, A.L., Molinelli E. and T. Baker, 1978, ‘Large-Scale Relative Dynamic Topography of the Southern Ocean’, Journal of Geophysical Res., 83, 3023–3031
Gordon, A.L., Molinelli E. and T. Barker, 1982, ‘Southern Ocean atlas’, Columbia University Press.
Gregg, M.C., 1987, ‘Diapycnal Mixing in the Thermocline: A Review’, J. Geophys. Res., 92, 5249–5286
Hellermann, S. and M. Rosenstein, 1983, ‘Normal monthly wind stress over the world ocean with error estimates’, J. Phys. Oceanogr., 13, 1093–1104
Hogg, N.G., 1987, ‘At least squares fit of advective-diffusive equations to Levitus Atlas data’, J. Mar.. Res., 45, 347–375
Holloway, G., 1989, ‘Parametrisation of small-scale processes’, this book
Levitus, S., 1982, ‘Climatological atlas of the world ocean’, NOAA Tech. Pap., 3, 173
McDougall, T.J., 1987, ‘Neutral Surfaces’, J. Phys. Oceanogr., 17, 1950–1963
McWilliams, J.C., Holland, W.R. and J.H.S. Chow, 1978, ‘A description of numerical Antarctic Circumpolar Currents’, Dyn. Atmos. Oceans, 2, 213–291
Montgomery, R.B., 1938, ‘Circulation in upper layers of southern North Atlantic deducted with use of isentropic analysis’, Pap. Phys. Oceanogr. Meteorol., 2, 55
Müller, P., Olbers, D. and J. Willebrand, 1978, ‘The IWEX spectrum’, J. Geophys. Res., 83, 479–500
Munk, W.H., 1966, ‘Abyssal recipes’, Deep Sea Res., 13, 707–730
Nowlin jr., W.D. and J.M. Klinck, 1986, ‘The Physics of the Antarctic Circumpolar Current’, Reviews of Geophysics, 24, 469–491
Olbers, D.J., Wenzel, M. and J. Willebrand, 1985, ‘The inference of North Atlantic circulation patterns from climatological hydrographic data’, Review of Geophysics, 23, 313–356
Olbers, D., 1989, ‘A geometrical interpretation of inverse problems’, this book
Pedlosky, J., 1979, ‘Geophysical fluid dynamics’, Springer Verlag, 624pp.
Schott, F. and H. Stommel, 1978, ‘Beta spirals and absolute velocities from different oceans’, Dep. Sea Res., 25, 961–1010
Solomon, H., 1971, ‘On the representation of isentropic mixing in ocean circulation models’, J. Phys. Oceogr., 1, 233–234
Stommel, H. and F. Schott, 1977, ‘The beta spiral and the determination of the absolute velocity field from hydrographic station data’, Deep Sea Res., 24, 325–329
Tarantola, A., 1986, ‘Inverse problem theory’, Elsevier, 335pp.
Veronis, G., 1972, ‘On properties of seawater defined by temperature, salinity, and pressure’, J. Mar. Res., 30, 227–255
Wenzel, M., 1986, ‘Die mittlere Zirkulation des Nordatlantik auf der Grundlage klimatologischer hydrographischer Daten’, Berichte Institut für Meereskunde Kiel, 157, 109pp
Wolff, J.-O. and D.J. Olbers, 1988, ‘The Dynamical Balance of the Antarctic Circumpolar Current Studied with an Eddy Resolving Quasigeostrophic Model’, submitted for publication
Wunsch, C., 1978, ‘The general circulation of the North Atlantic west of 50°W determined from inverse methods’, Rev. Geophys., 16, 583–620
Wunsch, C., 1984, ‘An eclectic Atlantic Ocean circulation model, I, The meridional flux of heat’, J. Phys. Oceanogr., 14, 1712–1733
Wunsch, C., 1989, ‘Tracer inverse problems’, this book
Wunsch, C. and B. Grant, 1982, ‘Towards the general circulation of the North Atlantic Ocean’, Frog. Oceanogr., 11, 1–59
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© 1989 Kluwer Academic Publishers
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Olbers, D., Wenzel, M. (1989). Determining Diffusivities from Hydrographic Data by Inverse Methods with Applications to the Circumpolar Current. In: Anderson, D.L.T., Willebrand, J. (eds) Oceanic Circulation Models: Combining Data and Dynamics. NATO ASI Series, vol 284. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1013-3_3
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DOI: https://doi.org/10.1007/978-94-009-1013-3_3
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