• Babiano, A., C. Basdevant, P. Le Roy, and R. Sadourny, 1987: Single-particle dispersion, Lagrangian structure function and Lagrangian energy spectrum in two-dimensional incompressible turbulence. J. Mar. Res., 45 , 107131.

    • Search Google Scholar
    • Export Citation
  • Berloff, P., and J. McWilliams, 1999a: Large-scale, low-frequency variability in wind-driven ocean gyres. J. Phys. Oceanogr., 29 , 19251949.

    • Search Google Scholar
    • Export Citation
  • Berloff, P., and J. McWilliams, 1999b: Quasigeostrophic dynamics of the western boundary current. J. Phys. Oceanogr., 29 , 26072634.

  • Berloff, P., and J. McWilliams, 2002: Material transport in oceanic gyres. Part II: Hierarchy of stochastic models. J. Phys. Oceanogr., 32 , 797830.

    • Search Google Scholar
    • Export Citation
  • Berloff, P., J. McWilliams, and A. Bracco, 2002: Material transport in oceanic gyres. Part I: Phenomenology. J. Phys. Oceanogr., 32 , 764796.

    • Search Google Scholar
    • Export Citation
  • Borgas, M., and B. Sawford, 1994: Stochastic equations with multifractal random increments for modeling turbulent dispersion. Phys. Fluids, 6 , 618633.

    • Search Google Scholar
    • Export Citation
  • Borgas, M., T. Flesch, and B. Sawford, 1997: Turbulent dispersion with broken reflectional symmetry. J. Fluid Mech., 332 , 141156.

  • Bower, A., and S. Lozier, 1994: A closer look at particle exchange in the Gulf Stream. J. Phys. Oceanogr., 24 , 13991418.

  • Box, G., G. Jenkins, and G. Reinsel, 1994: Time Series Analysis: Forecasting and Control. Prentice Hall, 598 pp.

  • Bracco, A., J. LaCasce, and A. Provenzale, 2000: Velocity pdfs for oceanic floats. J. Phys. Oceanogr., 30 , 461474.

  • Colin de Verdiere, A., 1983: Lagrangian eddy statistics from surface drifters in the eastern North Atlantic. J. Mar. Res., 41 , 375398.

    • Search Google Scholar
    • Export Citation
  • Davis, R., 1987: Modeling eddy transport of passive tracers. J. Mar. Res., 45 , 635666.

  • Figueroa, H., 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
  • Figueroa, H., and D. Olson, 1994: Eddy resolution versus eddy diffusion in a double gyre GCM. Part I: The Lagrangian and Eulerian description. J. Phys. Oceanogr., 24 , 371386.

    • Search Google Scholar
    • Export Citation
  • Freeland, H., P. Rhines, and T. Rossby, 1975: Statistical observations of the trajectories of neutrally buoyant floats in the North Atlantic. J. Mar. Res., 33 , 383404.

    • Search Google Scholar
    • Export Citation
  • Gardiner, C., 1983: Handbook of Stochastic Processes for Physics, Chemistry and the Natural Sciences. Springer-Verlag, 442 pp.

  • Griffa, A., 1996: Applications of stochastic particle models to oceanographic problems. Stochastic Modelling in Physical Oceanography, R. Adler et al., Eds., Birkhauser, 467 pp.

    • Search Google Scholar
    • Export Citation
  • Griffa, A., K. Owens, L. Piterbarg, and B. Rozovskii, 1995: Estimates of turbulence parameters from Lagrangian data using a stochastic particle model. J. Mar. Res., 53 , 371401.

    • Search Google Scholar
    • Export Citation
  • Jiang, S., 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
  • Kaneda, Y., T. Ishihara, and K. Gotoh, 1999: Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. Phys. Fluids, 11 , 21542166.

    • Search Google Scholar
    • Export Citation
  • Karlin, S., and H. Taylor, 1975: A first course in stochastic processes. Academic Press, 557 pp.

  • Krauss, W., and C. Böning, 1987: Lagrangian properties of eddy fields in the northern North Atlantic as deduced from satellite-tracked buoys. J. Mar. Res., 45 , 259291.

    • Search Google Scholar
    • Export Citation
  • LaCasce, J., and A. Bower, 2000: Relative dispersion in the sub-surface North Atlantic. J. Mar. Res., 58 , 863894.

  • Luhar, A., M. Hibberd, and P. Hurley, 1996: Comparison of closure schemes used to specify the velocity PDF in Lagrangian stochastic dispersion models for convective conditions. Atmos. Environ., 30 , 14071418.

    • Search Google Scholar
    • Export Citation
  • Lumpkin, R., and P. Flament, 2001: Lagrangian statistics in the central North Pacific. J. Mar. Syst., 29 , 141155.

  • Lumpkin, R., A-M. Treguier, and K. Speer, 2002: Lagrangian eddy scales in the northern Atlantic Ocean. J. Phys. Oceanogr., 32 , 24252440.

    • Search Google Scholar
    • Export Citation
  • Maurizi, A., and S. Lorenzani, 2001: Lagrangian time-scales in homogeneous non-Gaussian turbulence. Flow, Turb. Combust., 67 , 205216.

    • Search Google Scholar
    • Export Citation
  • Pasquero, C., A. Provenzale, and A. Babiano, 2001: Parameterization of dispersion in two-dimensional turbulence. J. Fluid Mech., 439 , 279303.

    • Search Google Scholar
    • Export Citation
  • Piterbarg, L., 2001: The top Lyapunov exponent for a stochastic flow modeling the upper ocean turbulence. SIAM Appl. Math., 62 , 777800.

    • Search Google Scholar
    • Export Citation
  • Pope, S., 1994: Lagrangian PDF methods for turbulent flows. Annu. Rev. Fluid Mech., 26 , 2363.

  • Reynolds, A., 2002: On Lagrangian stochastic modelling of material transport in oceanic gyres. Physica D, 172 , 124138.

  • Risken, H., 1989: The Fokker–Planck Equation. Springer-Verlag, 472 pp.

  • Roberts, M., and D. Marshall, 2000: On the validity of downgradient eddy closures in ocean models. J. Geophys. Res., 105 , 2861328627.

    • Search Google Scholar
    • Export Citation
  • Rodean, H., 1996: Stochastic Lagrangian Models of Turbulent Diffusion. Amer. Meteor. Soc., 79 pp.

  • Rupolo, V., B. Hua, A. Provenzale, and V. Artale, 1996: Lagrangian velocity spectra at 700 m in the western North Atlantic. J. Phys. Oceanogr., 26 , 15911607.

    • Search Google Scholar
    • Export Citation
  • Sawford, B., 1991: Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys. Fluids A, 3 , 15771586.

  • Siegel, A., J. Weiss, J. Toomre, J. McWilliams, P. Berloff, and I. Yavneh, 2001: Eddies and vortices in ocean basin dynamics. Geophys. Res. Lett., 28 , 31833187.

    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., 1993: Some historical remarks on the use of nonlinear viscosities. Large Eddy Simulation of Complex Engineering and Geophysical Flows, B. Galperin and S. Orszag Eds., Cambridge University Press, 3–36.

    • Search Google Scholar
    • Export Citation
  • Stammer, D., 1998: On eddy characteristics, eddy transports, and mean flow properties. J. Phys. Oceanogr., 28 , 727739.

  • Taylor, G., 1921: Diffusion by continuous movement. Proc. London Math. Soc., 20 , 196212.

  • Thomson, D., 1987: Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech., 180 , 529556.

    • Search Google Scholar
    • Export Citation
  • Visbeck, M., J. Marshall, T. Haine, and M. Spall, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27 , 381402.

    • Search Google Scholar
    • Export Citation
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Material Transport in Oceanic Gyres. Part III: Randomized Stochastic Models

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  • 1 Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
  • | 2 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California
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Abstract

Transport models are required for simulating the subgrid-scale transport by mesoscale eddies, which are typically not resolved in coarse-grid representations of the ocean circulation. Here, a new transport model from the class of stochastic models is formulated and its performance is tested against an eddy-resolving solution of the ocean circulation. The new approach overcomes drawbacks of the standard Markov models by broadening the range of simulated motions and by allowing transitions from one type of motion to another. The stochastic transport models yield random motion of individual passive particles, and the probability density function of the particle population may be interpreted as the concentration of a passive tracer. The models are developed for simulating observed transports of material by turbulent flows in the presence of coherent fluid structures, and they use only few internal parameters characterizing particular type of turbulence. The idea of stochastic randomization is introduced in the hierarchy of inhomogeneous and nonstationary stochastic models, and it is illustrated with the first kinematic-time parameter in the second-order Markov model. The principal property of the randomized stochastic hierarchy is its capability to simulate a broad range of intermediate-time, nondiffusive, single-particle dispersion behaviors involving a variety of timescales and length scales. This property is missing in the standard, nonrandomized hierarchy of Markov models which, as shown in a previous study, introduces errors in Lagrangian velocity correlation function and the corresponding material spreading process. The randomization implies that the parameter is represented by a probability distribution rather than a fixed average value. The probability distribution represents different populations of mesoscale fluctuations coexisting within a geographical region. The randomization effects are first studied in a homogeneous situation. Then, the performance of the inhomogeneous stochastic model is tested against passive tracer transport simulated by the fluid-dynamic, eddy-resolving ocean model. It is shown that the randomized model performs systematically better than the nonrandomized one, although only modestly so in some transport measures. Also, systematic differences are found between the direct solution of the stochastic model and the corresponding diffusion process with the eddy diffusivity estimated from the stochastic model. A local algorithm is proposed for estimating all the model parameters.

Corresponding author address: Pavel S. Berloff, Woods Hole Oceanographic Institution, MS#29, Woods Hole, MA 02543. Email: pberloff@whoi.edu

Abstract

Transport models are required for simulating the subgrid-scale transport by mesoscale eddies, which are typically not resolved in coarse-grid representations of the ocean circulation. Here, a new transport model from the class of stochastic models is formulated and its performance is tested against an eddy-resolving solution of the ocean circulation. The new approach overcomes drawbacks of the standard Markov models by broadening the range of simulated motions and by allowing transitions from one type of motion to another. The stochastic transport models yield random motion of individual passive particles, and the probability density function of the particle population may be interpreted as the concentration of a passive tracer. The models are developed for simulating observed transports of material by turbulent flows in the presence of coherent fluid structures, and they use only few internal parameters characterizing particular type of turbulence. The idea of stochastic randomization is introduced in the hierarchy of inhomogeneous and nonstationary stochastic models, and it is illustrated with the first kinematic-time parameter in the second-order Markov model. The principal property of the randomized stochastic hierarchy is its capability to simulate a broad range of intermediate-time, nondiffusive, single-particle dispersion behaviors involving a variety of timescales and length scales. This property is missing in the standard, nonrandomized hierarchy of Markov models which, as shown in a previous study, introduces errors in Lagrangian velocity correlation function and the corresponding material spreading process. The randomization implies that the parameter is represented by a probability distribution rather than a fixed average value. The probability distribution represents different populations of mesoscale fluctuations coexisting within a geographical region. The randomization effects are first studied in a homogeneous situation. Then, the performance of the inhomogeneous stochastic model is tested against passive tracer transport simulated by the fluid-dynamic, eddy-resolving ocean model. It is shown that the randomized model performs systematically better than the nonrandomized one, although only modestly so in some transport measures. Also, systematic differences are found between the direct solution of the stochastic model and the corresponding diffusion process with the eddy diffusivity estimated from the stochastic model. A local algorithm is proposed for estimating all the model parameters.

Corresponding author address: Pavel S. Berloff, Woods Hole Oceanographic Institution, MS#29, Woods Hole, MA 02543. Email: pberloff@whoi.edu

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