Predictability of Rotating Stratified Turbulence

K. Ngan McGill University, Montreal, Quebec, Canada

Search for other papers by K. Ngan in
Current site
Google Scholar
PubMed
Close
,
P. Bartello McGill University, Montreal, Quebec, Canada

Search for other papers by P. Bartello in
Current site
Google Scholar
PubMed
Close
, and
D. N. Straub McGill University, Montreal, Quebec, Canada

Search for other papers by D. N. Straub in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Although predictability represents one of the fundamental problems in atmospheric science, gaps in our knowledge remain. Theoretical understanding of the inverse error cascade is limited mostly to homogeneous, isotropic turbulence, whereas numerical simulations have focused on highly complex numerical weather prediction models. These results cannot be easily reconciled.

This paper describes selected aspects of the predictability behavior of rotating stratified turbulence. The objective is to determine how the predictability varies with scale when the dynamics are more realistic than the idealized models that underlie the classical picture of predictability and yet are free of the parameterizations that complicate interpretation of NWP models. Using a numerical model of the nonhydrostatic Boussinesq equations, it is shown that the predictability decay, as diagnosed by the relative error, is slower for subsynoptic flow. The dependence on the deformation radius, differences between balanced and unbalanced modes, and implications for NWP models are discussed.

* Current affiliation: Met Office, Exeter, Devon, United Kingdom

Corresponding author address: K. Ngan, Met Office, Exeter, Devon, EX1 3PB, United Kingdom. Email: keith.ngan@metoffice.gov.uk

Abstract

Although predictability represents one of the fundamental problems in atmospheric science, gaps in our knowledge remain. Theoretical understanding of the inverse error cascade is limited mostly to homogeneous, isotropic turbulence, whereas numerical simulations have focused on highly complex numerical weather prediction models. These results cannot be easily reconciled.

This paper describes selected aspects of the predictability behavior of rotating stratified turbulence. The objective is to determine how the predictability varies with scale when the dynamics are more realistic than the idealized models that underlie the classical picture of predictability and yet are free of the parameterizations that complicate interpretation of NWP models. Using a numerical model of the nonhydrostatic Boussinesq equations, it is shown that the predictability decay, as diagnosed by the relative error, is slower for subsynoptic flow. The dependence on the deformation radius, differences between balanced and unbalanced modes, and implications for NWP models are discussed.

* Current affiliation: Met Office, Exeter, Devon, United Kingdom

Corresponding author address: K. Ngan, Met Office, Exeter, Devon, EX1 3PB, United Kingdom. Email: keith.ngan@metoffice.gov.uk

Save
  • Anthes, R. A., Y-H. Kuo, D. P. Baumhefner, R. M. Errico, and T. W. Bettinge, 1985: Predictability of mesoscale atmospheric motions. Adv. Geophys., 28B , 159–202.

    • Search Google Scholar
    • Export Citation
  • Asselin, R. A., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100 , 487–490.

  • Babiano, A., C. Basdevant, and R. Sadourny, 1985: Structure functions and dispersion laws in two-dimensional turbulence. J. Atmos. Sci., 42 , 941–949.

    • Search Google Scholar
    • Export Citation
  • Bartello, P., 1995: Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atmos. Sci., 52 , 4410–4428.

    • Search Google Scholar
    • Export Citation
  • Basdevant, C., B. Legras, R. Sadourny, and M. Béland, 1981: A study of barotropic model flows: Intermittency, waves and predictability. J. Atmos. Sci., 38 , 2305–2326.

    • Search Google Scholar
    • Export Citation
  • Boer, G. J., 1994: Predictability regimes in atmospheric flow. Mon. Wea. Rev., 122 , 2285–2295.

  • Boer, G. J., and T. G. Shepherd, 1983: Large-scale two-dimensional turbulence in the atmosphere. J. Atmos. Sci., 40 , 164–184.

  • Boffetta, G., A. Celani, A. Crisanti, and A. Vulpiani, 1997: Predictability in two-dimensional decaying turbulence. Phys. Fluids, 9 , 722–734.

    • Search Google Scholar
    • Export Citation
  • Boffetta, G., M. Cencini, M. Falcioni, and A. Vulpiani, 2002: Predictability: A way to characterize complexity. Phys. Rep., 356 , 367–474.

    • Search Google Scholar
    • Export Citation
  • Daley, R., 1981: Predictability experiments with a baroclinic model. Atmos.–Ocean, 19 , 77–89.

  • Daley, R., 1993: Atmospheric Data Analysis. Cambridge University Press, 472 pp.

  • Durran, D. R., 1989: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, 465 pp.

  • Errico, R., and D. Baumhefner, 1987: Predictability experiments using a high-resolution limited-area model. Mon. Wea. Rev., 115 , 488–504.

    • Search Google Scholar
    • Export Citation
  • Gage, K., 1979: Evidence for a k−5/3 law inertial range in mesoscale two-dimensional turbulence. J. Atmos. Sci., 36 , 1950–1954.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic, 662 pp.

  • Hamilton, K., Y. O. Takahashi, and W. Ohfuchi, 2008: Mesoscale spectrum of atmospheric motions investigated in a very fine resolution global general circulation model. J. Geophys. Res., 113 , D18110. doi:10.1029/2008JD009785.

    • Search Google Scholar
    • Export Citation
  • Kleeman, R., and A. Majda, 2005: Predictability in a model of geophysical turbulence. J. Atmos. Sci., 62 , 2864–2879.

  • Koshyk, J. N., K. Hamilton, and J. D. Mahlman, 1999: Simulations of the k−5/3 mesoscale spectral regime in the GFDL SKYHI general circulation model. Geophys. Res. Lett., 26 , 843–846.

    • Search Google Scholar
    • Export Citation
  • Kraichnan, R. H., 1970: Instability in fully developed turbulence. Phys. Fluids, 13 , 569–575.

  • Leith, C. E., 1971: Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sci., 28 , 145–161.

  • Leith, C. E., and R. H. Kraichnan, 1972: Predictability of turbulent flows. J. Atmos. Sci., 29 , 1041–1057.

  • Lilly, D. K., 1972: Numerical simulation studies of two-dimensional turbulence: II. Stability and predictability studies. Geophys. Astrophys. Fluid Dyn., 4 , 1–28.

    • Search Google Scholar
    • Export Citation
  • Lilly, D. K., 1983: Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40 , 749–761.

  • Lorenz, E. N., 1969: The predictability of a flow which possesses many scales of motion. Tellus, 21 , 289–307.

  • Majda, A. J., and P. Embid, 1998: Averaging over fast gravity waves for geophysical flows with unbalanced initial data. Theor. Comput. Fluid Dyn., 11 , 155–169.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 2008: Irreducible imprecision in atmospheric and oceanic simulations. Proc. Natl. Acad. Sci. USA, 104 , 8709–8713.

    • Search Google Scholar
    • Export Citation
  • Métais, O., and M. Lesieur, 1986: Statistical predictability of decaying turbulence. J. Atmos. Sci., 43 , 857–869.

  • Ngan, K., and T. G. Shepherd, 1997: Chaotic mixing and transport in Rossby-wave critical layers. J. Fluid Mech., 334 , 315–351.

  • Ngan, K., P. Bartello, and D. N. Straub, 2008: Dissipation of synoptic-scale flow by small-scale turbulence. J. Atmos. Sci., 65 , 766–791.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., 2000: Predicting uncertainty in forecasts of weather and climate. Rep. Prog. Phys., 63 , 71–116.

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2nd ed. Springer, 710 pp.

  • Rawlins, F., S. P. Ballard, K. J. Bovis, A. M. Clayton, D. Li, G. W. Inevarity, A. C. Lorenc, and T. J. Payne, 2007: The Met Office global four-dimensional variational data assimilation scheme. Quart. J. Roy. Meteor. Soc., 133 , 347–362.

    • Search Google Scholar
    • Export Citation
  • Riley, J. J., and M-P. Lelong, 2000: Fluid motions in the presence of stable stratification. Annu. Rev. Fluid Mech., 32 , 613–657.

    • Search Google Scholar
    • Export Citation
  • Riley, J. J., R. W. Metcalfe, and M. A. Weissman, 1981: Direct numerical simulation of homogeneous turbulence in density-stratified fluids. Proc. Workshop on Nonlinear Properties of Internal Waves, La Jolla, CA, American Institute of Physics, 79–112.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132 , 3019–3032.

  • Takahashi, Y. O., K. Hamilton, and W. Ohfuchi, 2006: Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys. Res. Lett., 33 , L12812. doi:10.1029/2006GL026429.

    • Search Google Scholar
    • Export Citation
  • Thompson, P. D., 1957: Uncertainty of the initial state as a factor in the predictability of large scale atmospheric flow patterns. Tellus, 9 , 275–295.

    • Search Google Scholar
    • Export Citation
  • Tribbia, J. J., and D. P. Baumhefner, 2004: Scale interactions and atmospheric predictability: An updated perspective. Mon. Wea. Rev., 132 , 703–713.

    • Search Google Scholar
    • Export Citation
  • Vallis, G. K., 1983: On the predictability of quasi-geostrophic flow: The effects of beta and baroclinicity. J. Atmos. Sci., 40 , 10–27.

    • Search Google Scholar
    • Export Citation
  • Van Tuyl, A., and R. M. Errico, 1989: Scale interaction and predictability in a mesoscale model. Mon. Wea. Rev., 117 , 495–517.

  • Vukicevic, T., and R. M. Errico, 1990: The influence of artificial and physical factors upon predictability estimates a complex limited-area model. Mon. Wea. Rev., 118 , 1460–1482.

    • Search Google Scholar
    • Export Citation
  • Waite, M. L., and P. Bartello, 2006a: Stratified turbulence generated by internal gravity waves. J. Fluid Mech., 546 , 313–339.

  • Waite, M. L., and P. Bartello, 2006b: The transition from geostrophic to stratified turbulence. J. Fluid Mech., 568 , 89–108.

  • Wiggins, S., 1990: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, 672 pp.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 186 35 1
PDF Downloads 147 29 5