Relationships between Tracer Ages and Potential Vorticity in Unsteady Wind-Driven Circulations

Hong Zhang Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland

Search for other papers by Hong Zhang in
Current site
Google Scholar
PubMed
Close
,
Thomas W. N. Haine Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland

Search for other papers by Thomas W. N. Haine in
Current site
Google Scholar
PubMed
Close
, and
Darryn W. Waugh Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland

Search for other papers by Darryn W. Waugh in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The relationships between different tracer ages and between tracer age and potential vorticity are examined by simulating barotropic double-gyre circulations. The unsteady model flow crudely represents aspects of the midlatitude, middepth ocean circulation including inhomogeneous and anisotropic variability. Temporal variations range in scale from weeks to years, although the statistics are stationary. These variations have a large impact on the time-averaged tracer age fields. Transport properties of the tracer age fields that have been proved for steady flow are shown to also apply to unsteady flow and are illustrated in this circulation. Variability of tracer ages from ideal age tracer, linear, and exponential transient tracers is highly coordinated in phase and amplitude and is explained using simple theory. These relationships between different tracer ages are of practical benefit to the problem of interpreting tracer ages from the real ocean or from general circulation models. There is also a close link between temporal anomalies of tracer age and potential vorticity throughout a significant fraction of the domain. There are highly significant anticorrelations between ideal age and potential vorticity in the subtropical gyre and midbasin jet region, but correlation in the central subpolar gyre and eastern part of the domain is not significant. The existence of the relationship is insensitive to the character of the flow, the tracer sources, and the potential vorticity dynamics. Its structure may be understood by considering the different time-mean states of the tracer age and potential vorticity, the different tracer sources and sinks, and the effect of variability in the flow. Prediction of the correlation without knowledge of the time-mean fields is a harder problem, however. Detecting the correlation between potential vorticity and tracer age in the real ocean will be difficult with typical synoptic oceanographic transect data that are well-sampled in space, but sparse in time. Nevertheless, it is reasonable to suppose the correlation exists in some places.

Corresponding author address: Dr. Hong Zhang, Department of Earth and Planetary Sciences, The Johns Hopkins University, 301 Olin Hall, 3400 N. Charles St., Baltimore, MD 21218. Email: hong.zhang@jhu.edu

Abstract

The relationships between different tracer ages and between tracer age and potential vorticity are examined by simulating barotropic double-gyre circulations. The unsteady model flow crudely represents aspects of the midlatitude, middepth ocean circulation including inhomogeneous and anisotropic variability. Temporal variations range in scale from weeks to years, although the statistics are stationary. These variations have a large impact on the time-averaged tracer age fields. Transport properties of the tracer age fields that have been proved for steady flow are shown to also apply to unsteady flow and are illustrated in this circulation. Variability of tracer ages from ideal age tracer, linear, and exponential transient tracers is highly coordinated in phase and amplitude and is explained using simple theory. These relationships between different tracer ages are of practical benefit to the problem of interpreting tracer ages from the real ocean or from general circulation models. There is also a close link between temporal anomalies of tracer age and potential vorticity throughout a significant fraction of the domain. There are highly significant anticorrelations between ideal age and potential vorticity in the subtropical gyre and midbasin jet region, but correlation in the central subpolar gyre and eastern part of the domain is not significant. The existence of the relationship is insensitive to the character of the flow, the tracer sources, and the potential vorticity dynamics. Its structure may be understood by considering the different time-mean states of the tracer age and potential vorticity, the different tracer sources and sinks, and the effect of variability in the flow. Prediction of the correlation without knowledge of the time-mean fields is a harder problem, however. Detecting the correlation between potential vorticity and tracer age in the real ocean will be difficult with typical synoptic oceanographic transect data that are well-sampled in space, but sparse in time. Nevertheless, it is reasonable to suppose the correlation exists in some places.

Corresponding author address: Dr. Hong Zhang, Department of Earth and Planetary Sciences, The Johns Hopkins University, 301 Olin Hall, 3400 N. Charles St., Baltimore, MD 21218. Email: hong.zhang@jhu.edu

Save
  • Allaart, M. A. F., H. Kelder, and L. C. Heijboer, 1993: On the relation between ozone and potential vorticity. Geophys. Res. Lett., 20 , 811814.

    • Search Google Scholar
    • Export Citation
  • Chang, K. I., M. Ghil, K. Ide, and C. A. Lai, 2001: Transition to aperiodic variability in a wind-driven double-gyre circulation model. J. Phys. Oceanogr., 31 , 12601286.

    • Search Google Scholar
    • Export Citation
  • Cox, M. D., 1985: An eddy resolving numerical model of the ventilated thermocline. J. Phys. Oceanogr., 15 , 13121324.

  • Danielsen, E. F., 1968: Stratospheric-tropospheric exchange based on radioactivity, ozone and potential vorticity. J. Atmos. Sci., 25 , 502518.

    • Search Google Scholar
    • Export Citation
  • Deleersnijder, E., J. Campin, and E. J. M. Delhez, 2001: The concept of age in marine modeling, Part I. Theory of preliminary model results. J. Mar. Syst., 28 , 229267.

    • Search Google Scholar
    • Export Citation
  • Delhez, E. J. M., E. Deleersnijder, A. Mouchet, and J-M. Beckers, 2003: A note on the age of radioactive tracers. J. Mar. Syst., 38 , 277286.

    • Search Google Scholar
    • Export Citation
  • Doney, S. C., W. J. Jenkins, and J. L. Bullister, 1997: A comparison of ocean tracer dating techniques on a meridional section in the eastern North Atlantic. Deep-Sea Res., 44A , 603626.

    • Search Google Scholar
    • Export Citation
  • England, M. H., 1995: The age of water and ventilation timescales in a global ocean model. J. Phys. Oceanogr., 25 , 27562777.

  • England, M. H., and E. Maier-Reimer, 2001: Using chemical tracers to assess ocean models. Rev. Geophys., 39 , 2970.

  • Figueroa, H. A., 1994: Eddy resolution versus eddy diffusion in a double gyre GCM. Part II: Mixing of passive tracers. J. Phys. Oceanogr., 24 , 387402.

    • Search Google Scholar
    • Export Citation
  • Fine, R. A., M. Rhein, and C. Andrie, 2002: Using a CFC effective age to estimate propagation and storage of climate anomalies in the deep western North Atlantic Ocean. Geophys. Res. Lett., 29 .2227, doi:10.1029/2002GL015618.

    • Search Google Scholar
    • Export Citation
  • Ghil, M., Y. Feliks, and L. U. Sushama, 2002: Baroclinic and barotropic aspects of the wind-driven ocean circulation. Physica D, 167 , 135.

    • Search Google Scholar
    • Export Citation
  • Haine, T. W. N., and S. L. Gray, 2001: Quantifying mesoscales variability in ocean transient tracer fields. J. Geophys. Res., 106 , 1386113878.

    • Search Google Scholar
    • Export Citation
  • Haine, T. W. N., and T. M. Hall, 2002: A generalized transport theory: Water-mass composition and age. J. Phys. Oceanogr., 32 , 19321946.

    • Search Google Scholar
    • Export Citation
  • Hall, T. M., and R. A. Plumb, 1994: Age as a diagnostic stratospheric transport. J. Geophys. Res., 99 , 10591070.

  • Hall, T. M., and T. W. N. Haine, 2002: On ocean transport diagnostics: The idealized age tracer and the age spectrum. J. Phys. Oceanogr., 32 , 19871991.

    • Search Google Scholar
    • Export Citation
  • Hall, T. M., T. W. N. Haine, and D. W. Waugh, 2002: Inferring the concentration of anthropogenic carbon in the ocean from tracers. Global Biogeochem. Cycles, 16 .1131, doi:10.1029/2001GB001835.

    • Search Google Scholar
    • Export Citation
  • Hall, T. M., D. W. Waugh, T. W. N. Haine, P. E. Robbins, and S. Khatiwala, 2004: Reduced estimate of anthropogenic carbon in the Indian Ocean due to mixing and time-varying air-sea CO2 disequilibrium. Global Biogeochem. Cycles, 18 .GB1031, doi:10.1029/2003GB002120.

    • Search Google Scholar
    • Export Citation
  • Holzer, M., and T. M. Hall, 2000: Transit-time and tracer-age distribution in geophysical flows. J. Atmos. Sci., 57 , 35393558.

  • Jia, Y., and K. J. Richards, 1996: Tritium distributions in an isopycnic model of the North Atlantic. J. Geophys. Res., 101 , 1188311901.

    • Search Google Scholar
    • Export Citation
  • Jiang, S., F. F. Jin, and M. Ghil, 1995: Multiple equilibria, periodic, and aperiodic solutions in a wind-driven, double-gyre shallow-water model. J. Phys. Oceanogr., 25 , 764786.

    • Search Google Scholar
    • Export Citation
  • Keffer, T., 1985: The ventilation of the world’s oceans: Maps of the potential vorticity field. J. Phys. Oceanogr., 15 , 509523.

  • Khatiwala, S., M. Visbeck, and P. Schlosser, 2001: Age tracers in an ocean GCM. Deep-Sea Res., 48A , 14231441.

  • Klatt, O., and Coauthors, 2002: Repeated CFC sections at the Greenwich Meridian in the Weddell Sea. J. Geophys. Res., 107 .3030, doi:10.1029/2000JC000731.

    • Search Google Scholar
    • Export Citation
  • Lary, D. J., M. P. Chipperfield, J. A. Pyle, W. A. Norton, and L. P. Riishøjgaard, 1995: Three dimensional tracer initialization and general diagnostics using equivalent PV latitude-potential-temperature coordinates. Quart. J. Roy. Meteor. Soc., 112 , 187210.

    • Search Google Scholar
    • Export Citation
  • Leovy, C. B., C-R. Sun, M. H. Hitchman, E. E. Remsberg, J. M. Russell III, L. L. Gordley, J. C. Gille, and L. V. Lyjak, 1985: Transport of ozone in the middle stratosphere: Evidence for planetary wavebreaking. J. Atmos. Sci., 42 , 230244.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite volume, incompressible Navier-Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102 , 57535766.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., J. Nilsson, and D. Jamous, 2001: Entry, flux, and exit of potential vorticity in ocean circulation. J. Phys. Oceanogr., 31 , 777789.

    • Search Google Scholar
    • Export Citation
  • Meacham, S. P., 2000: Low-frequency variability in the wind-driven circulation. J. Phys. Oceanogr., 30 , 269293.

  • Morgenstern, O., and A. Marenco, 2000: Wintertime climatology of MOZAIC ozone based on the potential vorticity and ozone analogy. J. Geophys. Res., 105 , D12,. 1548115494.

    • Search Google Scholar
    • Export Citation
  • Musgrave, D. L., 1990: Numerical studies of tritium and helium-3 in the thermocline. J. Phys. Oceanogr., 20 , 344373.

  • Pedlosky, J., 1996: Ocean Circulation Theory. Springer-Verlag, 453 pp.

  • Richards, K. J., Y. Jia, and C. F. Rogers, 1995: Dispersion of tracers by ocean gyres. J. Phys. Oceanogr., 25 , 873887.

  • Robbins, P. E., and W. J. Jenkins, 1998: Observations of temporal changes of 3H-4He age in the eastern North Atlantic thermocline: Evidence for change in ventilation? J. Mar. Res., 56 , 11251161.

    • Search Google Scholar
    • Export Citation
  • Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 378 pp.

  • Schlosser, P., J. L. Bullister, R. Fine, W. J. Jenkins, R. Key, J. Lupton, W. Rother, and W. M. Smethie Jr., 2001: Transformation and age of water masses. Ocean Circulation and Climate, G. Siedler, J. Church, and J. Gould, Eds., Academic Press, 431–454.

    • Search Google Scholar
    • Export Citation
  • Schoeberl, M. R., and Coauthors, 1989: Reconstruction of the constituent distribution and trends in the Antarctic polar vortex from ER-2 fight observations. J. Geophys. Res., 94 , 1681516845.

    • Search Google Scholar
    • Export Citation
  • Steinfeldt, R., 2004: Ages and age spectra of Eastern Mediterranean Deep Water. J. Mar. Syst., 48 , 6781.

  • Steinfeldt, R., and M. Rhein, 2004: Spreading velocities and dilution of North Atlantic Deep Water in the tropical Atlantic based on CFC time series. J. Geophys. Res, 109 .C03046, doi:10.1029/2003JC002050.

    • Search Google Scholar
    • Export Citation
  • Talley, L., 1988: Potential vorticity distribution in the North Pacific. J. Phys. Oceanogr., 18 , 89106.

  • Thiele, G., and J. L. Sarmiento, 1990: Tracer dating and ocean ventilation. J. Geophys. Res., 95 , 93779391.

  • Warner, M. H., J. L. Bullister, D. P. Wisegarver, R. H. Gammon, and R. F. Weiss, 1996: Basin-wide distributions of chlorofluorocarbons CFC-11 and CFC-12 in the North Pacific: 1985–1989. J. Geophys. Res., 101 , 2052520542.

    • Search Google Scholar
    • Export Citation
  • Waugh, D. W., M. K. Vollmer, R. F. Weiss, T. W. N. Haine, and T. M. Hall, 2002: Transit time distributions in Lake Issyk-Kul. Geophys. Res. Lett., 29 .2231, doi:10.1029/2002GL016201.

    • Search Google Scholar
    • Export Citation
  • Waugh, D. W., T. M. Hall, and T. W. N. Haine, 2003: Relationships among tracer ages. J. Geophys. Res., 108 .3138, doi:10.1029/2002JC001325.

    • Search Google Scholar
    • Export Citation
  • Waugh, D. W., T. W. N. Haine, and T. M. Hall, 2004: Transport times and anthropogenic carbon in the subpolar North Atlantic Ocean. Deep-Sea Res., 51 , 14751491.

    • Search Google Scholar
    • Export Citation
  • Willebrand, J., S. G. H. Philander, and R. C. Pacanowski, 1980: The oceanic response to large-scale atmospheric disturbances. J. Phys. Oceanogr., 10 , 411429.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 2002: Oceanic age and transient tracers: Analytic and numerical solutions. J. Geophys. Res., 107 .3048, doi:10.1029/2001JC000797.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 289 115 10
PDF Downloads 72 21 4