Editorial Type:
Article
Article Type:
Research Article

Spectra, Spatial Scales, and Predictability in a Quasigeostrophic Model

Rebecca E. Morss National Center for Atmospheric Research,* Boulder, Colorado

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Chris Snyder National Center for Atmospheric Research,* Boulder, Colorado

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Richard Rotunno National Center for Atmospheric Research,* Boulder, Colorado

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Print Publication:
01 Oct 2009
DOI:
https://doi.org/10.1175/2009JAS3057.1
Page(s):
3115–3130
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Abstract

Results from homogeneous, isotropic turbulence suggest that predictability behavior is linked to the slope of a flow’s kinetic energy spectrum. Such a link has potential implications for the predictability behavior of atmospheric models. This article investigates these topics in an intermediate context: a multilevel quasigeostrophic model with a jet and temperature perturbations at the upper surface (a surrogate tropopause). Spectra and perturbation growth behavior are examined at three model resolutions. The results augment previous studies of spectra and predictability in quasigeostrophic models, and they provide insight that can help interpret results from more complex models. At the highest resolution tested, the slope of the kinetic energy spectrum is approximately at the upper surface but −3 or steeper at all but the uppermost interior model levels. Consistent with this, the model’s predictability behavior exhibits key features expected for flow with a shallower than −3 slope. At the highest resolution, upper-surface perturbation spectra peak below the energy-containing scales, and the error growth rate decreases as small scales saturate. In addition, as model resolution is increased and smaller scales are resolved, the peak of the upper-surface perturbation spectra shifts to smaller scales and the error growth rate increases. The implications for potential predictive improvements are not as severe, however, as in the standard picture of flows exhibiting a finite predictability limit. At the highest resolution, the model also exhibits periods of much faster-than-average perturbation growth that are associated with faster growth at smaller scales, suggesting predictability behavior that varies with time.

Corresponding author address: Dr. Rebecca E. Morss, NCAR, P.O. Box 3000, Boulder, CO 80307. Email: morss@ucar.edu

Abstract

Results from homogeneous, isotropic turbulence suggest that predictability behavior is linked to the slope of a flow’s kinetic energy spectrum. Such a link has potential implications for the predictability behavior of atmospheric models. This article investigates these topics in an intermediate context: a multilevel quasigeostrophic model with a jet and temperature perturbations at the upper surface (a surrogate tropopause). Spectra and perturbation growth behavior are examined at three model resolutions. The results augment previous studies of spectra and predictability in quasigeostrophic models, and they provide insight that can help interpret results from more complex models. At the highest resolution tested, the slope of the kinetic energy spectrum is approximately at the upper surface but −3 or steeper at all but the uppermost interior model levels. Consistent with this, the model’s predictability behavior exhibits key features expected for flow with a shallower than −3 slope. At the highest resolution, upper-surface perturbation spectra peak below the energy-containing scales, and the error growth rate decreases as small scales saturate. In addition, as model resolution is increased and smaller scales are resolved, the peak of the upper-surface perturbation spectra shifts to smaller scales and the error growth rate increases. The implications for potential predictive improvements are not as severe, however, as in the standard picture of flows exhibiting a finite predictability limit. At the highest resolution, the model also exhibits periods of much faster-than-average perturbation growth that are associated with faster growth at smaller scales, suggesting predictability behavior that varies with time.

Corresponding author address: Dr. Rebecca E. Morss, NCAR, P.O. Box 3000, Boulder, CO 80307. Email: morss@ucar.edu

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  • Barros, V. R., and A. Wiin-Nielsen, 1974: On quasi-geostrophic turbulence: A numerical experiment. J. Atmos. Sci., 31 , 609–622.

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

    • Search Google Scholar
    • Export Citation

  • Blumen, W., 1978: Uniform potential vorticity flow: Part I. Theory of wave interactions and two-dimensional turbulence. J. Atmos. Sci., 35 , 774–783.

    • Search Google Scholar
    • Export Citation

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

  • Boer, G. J., 2003: Predictability as a function of scale. Atmos.–Ocean, 41 , 203–215.

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

  • Boffetta, G., and S. Musacchio, 2001: Predictability of the inverse energy cascade in 2D turbulence. Phys. Fluids, 13 , 1060–1062.

  • Boffetta, G., A. Celani, A. Crisanti, and A. Vulpiani, 1997: Predictability in two-dimensional decaying turbulence. Phys. Fluids, 9 , 724–734.

    • Search Google Scholar
    • Export Citation

  • Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci., 28 , 1087–1095.

  • Cho, J. Y. N., and Coauthors, 1999: Horizontal wavenumber spectra of winds, temperature, and trace gases during the Pacific Exploratory Missions: 1. Climatology. J. Geophys. Res., 104 , 5697–5716.

    • Search Google Scholar
    • Export Citation

  • Dewan, E. M., 1979: Stratospheric wave spectra resembling turbulence. Science, 204 , 832–835.

  • Errico, R., 1985: Spectra computed from a limited area grid. Mon. Wea. Rev., 113 , 1554–1562.

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

  • Held, I. M., R. T. Pierrehumbert, S. T. Garner, and K. L. Swanson, 1995: Surface quasi-geostrophic dynamics. J. Fluid Mech., 282 , 1–20.

    • Search Google Scholar
    • Export Citation

  • Hoyer, J-M., and R. Sadourny, 1982: Closure modeling of fully developed baroclinic instability. J. Atmos. Sci., 39 , 707–721.

  • Juckes, M., 1994: Quasigeostrophic dynamics of the tropopause. J. Atmos. Sci., 51 , 2756–2768.

  • Koshyk, J. N., and K. Hamilton, 2001: The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere–stratosphere–mesosphere GCM. J. Atmos. Sci., 58 , 329–348.

    • Search Google Scholar
    • Export Citation

  • 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 , 1041–1058.

  • 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.

  • Lilly, D. K., 1989: Two-dimensional turbulence generated by energy sources at two scales. J. Atmos. Sci., 46 , 2026–2030.

  • Lindborg, E., 1999: Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech., 388 , 259–288.

    • Search Google Scholar
    • Export Citation

  • Lindborg, E., 2006: The energy cascade in a strongly stratified fluid. J. Fluid Mech., 550 , 207–242.

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

  • Mathieu, J., and J. Scott, 2000: An Introduction to Turbulent Flow. Cambridge University Press, 384 pp.

  • McWilliams, J. C., and J. H. S. Chow, 1981: Equilibrium geostrophic turbulence 1: A reference solution in a β-plane channel. J. Phys. Oceanogr., 11 , 921–949.

    • Search Google Scholar
    • Export Citation

  • Metais, O., and M. Lesieur, 1986: Statistical predictability of decaying turbulence. J. Atmos. Sci., 43 , 857–869.

  • Morss, R. E., K. A. Emanuel, and C. Snyder, 2001: Idealized adaptive observation strategies for improving numerical weather prediction. J. Atmos. Sci., 58 , 210–232.

    • Search Google Scholar
    • Export Citation

  • Morss, R. E., J. Demuth, and J. K. Lazo, 2008: Communicating uncertainty in weather forecasts: A survey of the U.S. public. Wea. Forecasting, 23 , 974–991.

    • Search Google Scholar
    • Export Citation

  • Nastrom, G. D., and K. S. Gage, 1985: A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42 , 950–960.

    • Search Google Scholar
    • Export Citation

  • NRC, 2006: Completing the Forecast: Characterizing and Communicating Uncertainty for Better Decisions Using Weather and Climate Forecasts. National Academies Press, 124 pp.

    • Search Google Scholar
    • Export Citation

  • Pierrehumbert, R. T., I. M. Held, and K. L. Swanson, 1994: Spectra of local and nonlocal two-dimensional turbulence. Chaos, Solitons Fractals, 4 , 1111–1116.

    • Search Google Scholar
    • Export Citation

  • Roads, J. O., 1985: Temporal variations in predictability. J. Atmos. Sci., 42 , 884–903.

  • Rotunno, R., and J-W. Bao, 1996: A case study of cyclogenesis using a model hierarchy. Mon. Wea. Rev., 124 , 1051–1066.

  • Rotunno, R., and C. Snyder, 2008: A generalization of Lorenz’s model for the predictability of flows with many scales of motion. J. Atmos. Sci., 65 , 1063–1076.

    • Search Google Scholar
    • Export Citation

  • Simmons, A. J., and A. Hollingsworth, 2002: Some aspects of the improvement in skill of numerical weather prediction. Quart. J. Roy. Meteor. Soc., 128 , 647–677.

    • Search Google Scholar
    • Export Citation

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

  • Snyder, C., and T. M. Hamill, 2003: Leading Lyapunov vectors of a turbulent baroclinic jet in a quasigeostrophic model. J. Atmos. Sci., 60 , 683–688.

    • Search Google Scholar
    • Export Citation

  • Snyder, C., T. M. Hamill, and S. B. Trier, 2003: Linear evolution of error covariances in a quasigeostrophic model. Mon. Wea. Rev., 131 , 189–205.

    • Search Google Scholar
    • Export Citation

  • Straus, D. M., 1989: Baroclinic instability and wave-wave interactions in quasi-geostrophic error growth. J. Atmos. Sci., 46 , 2380–2403.

    • 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

  • Tulloch, R., and K. S. Smith, 2006: A theory for the atmospheric energy spectrum: Depth-limited temperature anomalies at the tropopause. Proc. Natl. Acad. Sci. USA, 103 , 14690–14694.

    • Search Google Scholar
    • Export Citation

  • Tulloch, R., and K. S. Smith, 2009: Quasigeostrophic turbulence with explicit surface dynamics: Application to the atmospheric energy spectrum. J. Atmos. Sci., 66 , 450–467.

    • Search Google Scholar
    • Export Citation

  • Tung, K. K., and W. W. Orlando, 2003: The k−3 and k−5/3 energy spectrum of atmospheric turbulence: Quasigeostrophic two-level model simulation. J. Atmos. Sci., 60 , 824–835.

    • 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

  • Vannitsem, S., and C. Nicolis, 1997: Lyapunov vectors and error growth patterns in a T21L3 quasigeostrophic model. J. Atmos. Sci., 54 , 347–361.

    • Search Google Scholar
    • Export Citation

  • VanZandt, T. E., 1982: A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Lett., 9 , 575–578.

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