Oceanic Turbulence and Stochastic Models from Subsurface Lagrangian Data for the Northwest Atlantic Ocean

Milena Veneziani Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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Annalisa Griffa Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, and IOF/CNR, La Spezia, Italy

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Andy M. Reynolds Silsoe Research Institute, Silsoe, Bedford, United Kingdom

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Arthur J. Mariano Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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Abstract

The historical dataset provided by 700-m acoustically tracked floats is analyzed in different regions of the northwestern Atlantic Ocean. The goal is to characterize the main properties of the mesoscale turbulence and to explore Lagrangian stochastic models capable of describing them. The data analysis is carried out mostly in terms of Lagrangian velocity autocovariance and cross-covariance functions. In the Gulf Stream recirculation and extension regions, the autocovariances and cross covariances exhibit significant oscillatory patterns on time scales comparable to the Lagrangian decorrelation time scale. They are indicative of sub- and superdiffusive behaviors in the mean spreading of water particles. The main result of the paper is that the properties of Lagrangian data can be considered as a superposition of two different regimes associated with looping and nonlooping trajectories and that both regimes can be parameterized using a simple first-order Lagrangian stochastic model with spin parameter Ω. The spin couples the zonal and meridional velocity components, reproducing the effects of rotating coherent structures such as vortices and mesoscale eddies. It is considered as a random parameter whose probability distribution is approximately bimodal, reflecting the distribution of loopers (finite Ω) and nonloopers (zero Ω). This simple model is found to be very effective in reproducing the statistical properties of the data.

Corresponding author address: Milena Veneziani, RSMAS/MPO 4600 Rickenbacker Causeway, Miami, FL 33149. Email: cveneziani@rsmas.miami.edu

Abstract

The historical dataset provided by 700-m acoustically tracked floats is analyzed in different regions of the northwestern Atlantic Ocean. The goal is to characterize the main properties of the mesoscale turbulence and to explore Lagrangian stochastic models capable of describing them. The data analysis is carried out mostly in terms of Lagrangian velocity autocovariance and cross-covariance functions. In the Gulf Stream recirculation and extension regions, the autocovariances and cross covariances exhibit significant oscillatory patterns on time scales comparable to the Lagrangian decorrelation time scale. They are indicative of sub- and superdiffusive behaviors in the mean spreading of water particles. The main result of the paper is that the properties of Lagrangian data can be considered as a superposition of two different regimes associated with looping and nonlooping trajectories and that both regimes can be parameterized using a simple first-order Lagrangian stochastic model with spin parameter Ω. The spin couples the zonal and meridional velocity components, reproducing the effects of rotating coherent structures such as vortices and mesoscale eddies. It is considered as a random parameter whose probability distribution is approximately bimodal, reflecting the distribution of loopers (finite Ω) and nonloopers (zero Ω). This simple model is found to be very effective in reproducing the statistical properties of the data.

Corresponding author address: Milena Veneziani, RSMAS/MPO 4600 Rickenbacker Causeway, Miami, FL 33149. Email: cveneziani@rsmas.miami.edu

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  • Bauer, S., M. S. Swenson, A. Griffa, A. J. Mariano, and K. Owens, 1998: Eddy-mean flow decomposition and eddy-diffusivity estimates in the tropical Pacific Ocean. 1. Methodology. J. Geophys. Res, 103 , 3085530871.

    • Search Google Scholar
    • Export Citation
  • Bauer, S., M. S. Swenson, and A. Griffa, 2002: Eddy-mean flow decomposition and eddy-diffusivity estimates in the tropical Pacific Ocean. 2. Results. J. Geophys. Res.,107, 3154, doi:10.1029/2001JC000613.

    • Search Google Scholar
    • Export Citation
  • Berloff, P. S., and J. C. 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. S., and J. C. McWilliams, 2003: Material transport in oceanic gyres. Part III: Randomized stochastic models. J. Phys. Oceanogr, 33 , 14161445.

    • Search Google Scholar
    • Export Citation
  • Berloff, P. S., J. C. 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. S., T. K. Flesch, and B. L. Sawford, 1997: Turbulent dispersion with broken reflectional symmetry. J. Fluid Mech, 279 , 6999.

    • Search Google Scholar
    • Export Citation
  • Bower, A. S., and Coauthors, 2002: Directly measured mid-depth circulation in the northeastern North Atlantic Ocean. Nature, 419 , 603607.

    • Search Google Scholar
    • Export Citation
  • Bracco, A., J. H. LaCasce, and A. Provenzale, 2000: Velocity probability density functions for oceanic floats. J. Phys. Oceanogr, 30 , 461474.

    • Search Google Scholar
    • Export Citation
  • Bracco, A., E. P. Chassignet, Z. D. Garraffo, and A. Provenzale, 2003: Lagrangian velocity distributions in a high-resolution numerical simulation of the North Atlantic. J. Atmos. Oceanic Technol, 20 , 12121220.

    • Search Google Scholar
    • Export Citation
  • Brown, O. B., P. C. Cornillon, S. R. Emmerson, and H. M. Carle, 1986: Warm core rings: A statistical study of their behavior. Deep-Sea Res, 33 , 14591473.

    • Search Google Scholar
    • Export Citation
  • Brundage, W. L., and J. P. Dugan, 1986: Observations of an anticyclonic eddy of 18°C water in the Sargasso Sea. J. Phys. Oceanogr, 16 , 717727.

    • Search Google Scholar
    • Export Citation
  • Cheney, R. E., W. H. Gemmill, M. K. Shank, P. L. Richardson, and D. C. Webb, 1976: Tracking a Gulf Stream ring with SOFAR floats. J. Phys. Oceanogr, 6 , 741749.

    • Search Google Scholar
    • Export Citation
  • Cowen, R. K., K. M. M. Lwiza, S. Sponaugle, C. B. Paris, and D. B. Olson, 2000: Connectivity of marine populations: Open or closed? Science, 287 , 857859.

    • Search Google Scholar
    • Export Citation
  • Cowen, R. K., C. B. Paris, D. B. Olson, and J. L. Fortuna, 2003: The role of long distance dispersal versus local retention in replenishing marine populations. Gulf Caribb. Res, 14 (2) 129137.

    • Search Google Scholar
    • Export Citation
  • Davis, R. E., 1991: Observing the general circulation with floats. Deep-Sea Res, 38 , (Suppl.),. 531571.

  • Davis, R. E., 1998: Preliminary results from directly measuring mid-depth circulation in the tropical and South Pacific. J. Geophys. Res, 103 , 2461924639.

    • Search Google Scholar
    • Export Citation
  • Dutkiewicz, S., A. Griffa, and D. B. Olson, 1993: Particle diffusion in a meandering jet. J. Geophys. Res, 98 , 1648716500.

  • Elhmaidi, D., A. Provenzale, and A. Babiano, 1993: Elementary topology of two-dimensional turbulence from a Lagrangian view-point and single particle dispersion. J. Fluid Mech, 257 , 533558.

    • Search Google Scholar
    • Export Citation
  • Falco, P., A. Griffa, P-M. Poulain, and E. Zambianchi, 2000: Transport properties in the Adriatic Sea as deduced from drifter data. J. Phys. Oceanogr, 30 , 20552071.

    • Search Google Scholar
    • Export Citation
  • Figueroa, H. A., and D. B. Olson, 1989: Lagrangian statistics in the South Atlantic as derived from SOS and FGGE drifters. J. Mar. Res, 47 , 525546.

    • Search Google Scholar
    • Export Citation
  • Fratantoni, D. M., 2001: North Atlantic surface circulation during the 1990's observed with satellite-tracked drifters. J. Geophys. Res, 106 , 2206722093.

    • Search Google Scholar
    • Export Citation
  • Freeland, H., P. Rhines, and H. 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
  • Garraffo, Z. D., A. Griffa, A. J. Mariano, and E. P. Chassignet, 2001a: Lagrangian data in a high resolution numerical simulation of the North Atlantic. II: On the pseudo-Eulerian averaging of Lagrangian data. J. Mar. Syst, 29 , 177200.

    • Search Google Scholar
    • Export Citation
  • Garraffo, Z. D., A. J. Mariano, A. Griffa, C. Veneziani, and E. P. Chassignet, 2001b: Lagrangian data in a high resolution numerical simulation of the North Atlantic. I: Comparison with in-situ drifter data. J. Mar. Syst, 29 , 157176.

    • Search Google Scholar
    • Export Citation
  • Griffa, A., 1996: Applications of stochastic particle models to oceanographic problems. Stochastic Modeling in Physical Oceanography, R. Adler, P. Muller, and B. Rozovskii, Eds., Birkhäuser Verlag, 114–140.

    • Search Google Scholar
    • Export Citation
  • Inoue, H., 1986: A least-squares smooth fitting for irregularly spaced data: Finite-element approach using the cubic B-spline basis. Geophysics, 51 , 20512066.

    • Search Google Scholar
    • Export Citation
  • Joyce, T. M., 1984: Velocity and hydrographic structure of a Gulf Stream warm-core ring. J. Phys. Oceanogr, 14 , 936947.

  • Klein, H., and E. Mittelstaedt, 1992: Currents and dispersion in the abyssal Northeast Atlantic. Results from the NOAMP Field Program. Deep-Sea Res, 39 , 17271745.

    • Search Google Scholar
    • Export Citation
  • Krauss, W., and C. W. Boning, 1987: Lagrangian properties of the eddy fields in the northern Atlantic as deduced from satellite-tracked buoys. J. Mar. Res, 45 , 259291.

    • Search Google Scholar
    • Export Citation
  • LaCasce, J. H., 2000: Floats and f/H. J. Mar. Res, 58 , 6195.

  • Landau, L. D., and E. M. Lifshitz, 1981: Physical Kinetics.Vol. 10. Butterworth-Heinemann, 625 pp.

  • Lavender, K. L., R. E. Davis, and W. B. Owens, 2000: Mid-depth recirculation observed in the interior Labrador and Irminger Seas by direct velocity measurements. Nature, 407 , 6669.

    • Search Google Scholar
    • Export Citation
  • Leaman, K. D., and P. S. Vertes, 1996: Topographic influences on recirculation in the deep western boundary current: Results from RAFOS float trajectories between the Blake–Bahama Outer Ridge and the San Salvador “Gate.”. J. Phys. Oceanogr, 26 , 941961.

    • Search Google Scholar
    • Export Citation
  • Mariano, A. J., and O. B. Brown, 1992: Efficient objective analysis of heterogeneous and nonstationary fields via the parameter matrix. Deep-Sea Res, 39 , 12551271.

    • Search Google Scholar
    • Export Citation
  • Ollitrault, M., and A. Colin de Verdiere, 2002a: SOFAR floats reveal midlatitude intermediate North Atlantic general circulation. Part I: A Lagrangian descriptive view. J. Phys. Oceanogr, 32 , 20202033.

    • Search Google Scholar
    • Export Citation
  • Ollitrault, M., and A. Colin de Verdiere, 2002b: SOFAR floats reveal midlatitude intermediate North Atlantic general circulation. Part II: An Eulerian statistical view. J. Phys. Oceanogr, 32 , 20342053.

    • Search Google Scholar
    • Export Citation
  • Olson, D. B., 1980: The physical oceanography of two rings observed by the Cyclonic Ring Experiment. Part II: Dynamics. J. Phys. Oceanogr, 10 , 514528.

    • Search Google Scholar
    • Export Citation
  • Owens, W. B., 1984: A synoptic and statistical description of the Gulf Stream and subtropical gyre using SOFAR floats. J. Phys. Oceanogr, 14 , 104113.

    • Search Google Scholar
    • Export Citation
  • Owens, W. B., 1991: A statistical description of the mean circulation and eddy variability in the northwestern Atlantic using SOFAR floats. Progress in Oceanography, Vol. 28, Pergamon Press, 257–303.

    • 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
  • Patterson, S. L., 1985: Surface circulation and kinetic energy distributions in the Southern Hemisphere oceans from FGGE drifting buoys. J. Phys. Oceanogr, 15 , 865884.

    • Search Google Scholar
    • Export Citation
  • Pingree, R., and B. Sinha, 2001: Westward moving waves or eddies (storms) on the Subtropical/Azores front near 32.5°N? Interpretation of the Eulerian currents and temperature records at moorings 155 (35.5° W) and 156 (34.4° W). J. Mar. Syst, 29 , 239276.

    • Search Google Scholar
    • Export Citation
  • Poulain, P-M., 2001: Adriatic Sea surface circulation as derived from drifter data between 1990 and 1999. J. Mar. Syst, 29 , 332.

  • Poulain, P-M., and P. P. Niiler, 1989: Statistical analysis of the surface circulation in the California Current System using satellite-tracked drifters. J. Phys. Oceanogr, 19 , 15881603.

    • Search Google Scholar
    • Export Citation
  • Price, J. F., T. M. McKee, W. B. Owens, and J. R. Valdes, 1987: Site L SOFAR float experiment, 1982–85. Woods Hole Oceanographic Institution Tech. Rep. WHOI-97-52, 289 pp. [Available online at http://www.ntis.gov.].

    • Search Google Scholar
    • Export Citation
  • Priestley, M. B., 1981: Spectral Analysis and Time Series. Academic Press, 890 pp.

  • Provenzale, A., 1999: Transport by coherent barotropic vortices. Annu. Rev. Fluid Mech, 31 , 5593.

  • Provenzale, A., A. Babiano, and B. Villone, 1995: Single-particle trajectories in two-dimensional turbulence. Chaos, Solitons Fractals, 5 , 20552071.

    • Search Google Scholar
    • Export Citation
  • Rees, J. M., and E. M. Gmitrowicz, 1989: Dispersion measurements from SOFAR floats on the Iberian abyssal plain. Interim Oceanographic Description of the North-East Atlantic Site for the Disposal of Low-Level Radioactive Waste, Vol. 3, F. Nyffeler and W. Simmons, Eds., Nuclear Energy Agency, OECD, 64–67.

    • Search Google Scholar
    • Export Citation
  • Reynolds, A. M., 2002a: On Lagrangian stochastic modelling of material transport in oceanic gyres. Physica D, 172 , 124138.

  • Reynolds, A. M., 2002b: Lagrangian stochastic modeling of anomalous diffusion in two-dimensional turbulence. Phys. Fluids, 14 , 14421449.

    • Search Google Scholar
    • Export Citation
  • Reynolds, A. M., 2003a: Third-order Lagrangian stochastic modeling. Phys. Fluids, 15 , 27732777.

  • Reynolds, A. M., 2003b: On the application of nonextensive statistics to Lagrangian turbulence. Phys. Fluids, 15 , L1L4.

  • Richardson, P. L., 1980: Anticyclonic eddies generated near the Corner Rise seamounts. J. Mar. Res, 38 , 673686.

  • Richardson, P. L., 1993: A census of eddies observed in North Atlantic SOFAR float data. Progress in Oceanography, Vol. 31, Pergamon Press, 1–50.

    • Search Google Scholar
    • Export Citation
  • Riser, S. C., 1982: The quasi-Lagrangian nature of SOFAR floats. Deep-Sea Res, 29 , 15871602.

  • Riser, S. C., and H. T. Rossby, 1983: Quasi-Lagrangian structure and variability of the subtropical western North Atlantic circulation. J. Mar. Res, 41 , 127162.

    • Search Google Scholar
    • Export Citation
  • Risken, H., 1989: The Fokker–Planck Equation: Methods of Solution and Applications. Springer-Verlag, 472 pp.

  • Rossby, H. T., A. D. Voorhis, and D. Webb, 1975: A quasi-Lagrangian study of mid-ocean variability using long-range SOFAR floats. J. Mar. Res, 33 , 355382.

    • Search Google Scholar
    • Export Citation
  • Rossby, H. T., J. F. Price, and D. Webb, 1986: The spatial and temporal evolution of a cluster of SOFAR floats in the POLYMODE Local Dynamics Experiment (LDE). J. Phys. Oceanogr, 16 , 428442.

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

    • Search Google Scholar
    • Export Citation
  • Sawford, B. L., 1991: Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys. Fluids, A3 , 15771586.

  • Sawford, B. L., 1999: Rotation of trajectories in Lagrangian stochastic models of turbulent dispersion. Bound.-Layer Meteor, 93 , 411424.

    • Search Google Scholar
    • Export Citation
  • Schmitz Jr, W. J., 1985: SOFAR float trajectories associated with the Newfoundland Basin. J. Mar. Res, 43 , 761778.

  • Schmitz Jr, W. J., J. F. Price, P. L. Richardson, W. B. Owens, D. C. Webb, R. E. Cheney, and H. T. Rossby, 1981: A preliminary exploration of the Gulf Stream system with SOFAR floats. J. Phys. Oceanogr, 11 , 11941204.

    • Search Google Scholar
    • Export Citation
  • Sciremammano Jr., F., 1979: A suggestion for the presentation of correlations and their significance levels. J. Phys. Oceanogr, 9 , 12731276.

    • Search Google Scholar
    • Export Citation
  • Spall, M. A., P. L. Richardson, and J. F. Price, 1993: Advection and eddy mixing in the Mediterranean salt tongue. J. Mar. Res, 51 , 797818.

    • Search Google Scholar
    • Export Citation
  • Sundermeyer, M. A., and J. F. Price, 1998: Lateral mixing and the North Atlantic Tracer Release Experiment: Observations and numerical simulations of Lagrangian particles and passive tracer. J. Geophys. Res, 103 , 2148121497.

    • Search Google Scholar
    • Export Citation
  • Swenson, M. S., and P. P. Niiler, 1996: Statistical analysis of the surface circulation of the California Current. J. Geophys. Res, 101 , 2263122645.

    • Search Google Scholar
    • Export Citation
  • Taylor, G. I., 1921: Diffusion by continuous movements. Proc. London Math. Soc, 20 , 196212.

  • Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence. MIT Press, 300 pp.

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

    • Search Google Scholar
    • Export Citation
  • Zenk, W., K. S. Tokos, and O. Boebel, 1992: New observations of meddy movement south of the Tejo Plateau. Geophys. Res. Lett, 19 , 23892392.

    • Search Google Scholar
    • Export Citation
  • Zhang, H-M., M. D. Prater, and T. Rossby, 2001: Isopycnal Lagrangian statistics from the North Atlantic Current RAFOS floats observations. J. Geophys. Res, 106 , 1381713836.

    • Search Google Scholar
    • Export Citation
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