Editorial Type:
Article
Article Type:
Research Article

On the Possibility of Singular Low-Frequency Spectra and Lévy Law Persistence Statistics in the Planetary-Scale Turbulent Circulation

J. A. Viecelli Lawrence Livermore National Laboratory, Livermore, California

Search for other papers by J. A. Viecelli in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Mar 1998
DOI:
https://doi.org/10.1175/1520-0469(1998)055<0677:OTPOSL>2.0.CO;2
Page(s):
677–689
Restricted access

Abstract

Long-time integrations of general circulation models with constant forcing and idealized models of turbulent rotating discrete vortex flows in a planar dish have consistently yielded red ultralow-frequency spectra. A red spectrum having an integrable fractional-exponent singularity at the frequency origin is associated with occasional long-lasting random persistence intervals described by probability distributions with Lévy law tails, suggesting this type of persistence distribution may be relevant to the planetary scale turbulence. Decade-length records of 200-mb wind velocity fluctuations from North American 12-h radiosonde data are examined for the presence of Lévy statistics, and the convergence properties of errors in means and variances computed from finite length time-series samples containing random persistence intervals governed by Lévy probability laws are compared with the convergence properties corresponding to the low-frequency white-noise hypothesis. Some implications for estimating climatic means and variances are discussed.

Corresponding author address: Dr. J. A. Viecelli, Lawrence Livermore National Laboratory, Livermore, CA 94550.

Abstract

Long-time integrations of general circulation models with constant forcing and idealized models of turbulent rotating discrete vortex flows in a planar dish have consistently yielded red ultralow-frequency spectra. A red spectrum having an integrable fractional-exponent singularity at the frequency origin is associated with occasional long-lasting random persistence intervals described by probability distributions with Lévy law tails, suggesting this type of persistence distribution may be relevant to the planetary scale turbulence. Decade-length records of 200-mb wind velocity fluctuations from North American 12-h radiosonde data are examined for the presence of Lévy statistics, and the convergence properties of errors in means and variances computed from finite length time-series samples containing random persistence intervals governed by Lévy probability laws are compared with the convergence properties corresponding to the low-frequency white-noise hypothesis. Some implications for estimating climatic means and variances are discussed.

Corresponding author address: Dr. J. A. Viecelli, Lawrence Livermore National Laboratory, Livermore, CA 94550.

Save
Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Branstator, G., 1990: Low frequency patterns induced by stationary waves. J. Atmos. Sci.,47, 629–648.

  • Charles, B. N., 1959: Lag correlations of upper winds. J. Meteor.,16, 83–86.

  • Durst, C. S., 1954: Variation of wind with time and distance. Geophysical Memoirs No. 93, Met. Office, London.

  • Ellsaesser, H. W., 1960: Wind variability, Air Weather Service Tech. Rep. AWS TR 105-2, 99 pp.

  • Eubanks, T. M., J. A. Steppe, J. O. Dickey, and P. S. Callahan, 1985:A spectral analysis of the Earth’s angular momentum budget. J. Geophys. Res.,90, 5385–5404.

  • Feller, W., 1967: An Introduction to Probability Theory and Its Applications. Wiley and Sons, 461 pp.

  • Gnedenko, B. V., and A. N. Kolmogorov, 1954: Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, 264 pp.

  • Hansen, A. R., and A. Sutera, 1995: The probability density distribution of the planetary-scale atmospheric wave amplitude revisited. J. Atmos. Sci.,52, 2463–2472.

  • Hoerling, M. P., and M. Ting, 1994: Organization of extratropical transients during El Niño. J. Climate,7, 745–766.

  • Horel, J. D., and J. M. Wallace, 1981: Planetary-scale atmospheric phenomena associated with the Southern Oscillation. Mon. Wea. Rev.,109, 813–829.

  • Hurst, H. E., 1951: Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civil Eng.,116, 770–799.

  • ——, 1957: A suggested statistical model of some time series which occur in nature. Nature,180, 494.

  • James, I. N., and P. M. James, 1989: Ultra-low-frequency variability in a simple atmospheric circulation model. Nature,342, 53–55.

  • Jones, R. E., 1975: Estimating the variance of time averages. J. Appl. Meteor.,14, 159–163.

  • ——, 1976: A note on estimating the variance of time-averages. J. Appl. Meteor.,15, 514–515.

  • Keppenne, C. L., and M. Ghil, 1992: Adaptive filtering and prediction of the Southern Oscillation Index. J. Geophys. Res.,97, 20449–20454.

  • Kimoto, M., and M. Ghil, 1993a: Multiple flow regimes in the Northern Hemisphere winter. Part I: Methodology and hemisphere regimes. J. Atmos. Sci.,50, 2625–2643.

  • ——, and ——, 1993b: Multiple flow regimes in the Northern Hemisphere winter. Part II: Sectorial regimes and preferred transitions. J. Atmos. Sci.,50, 2645–2673.

  • Klafter, J., G. Zumofen, and M. F. Schlesinger, 1993: Fractal description of anomalous diffusion in dynamical systems. Fractals,1, 389–404.

  • Kumar, A., and M. P. Hoerling, 1995: Prospects and limitations of seasonal atmospheric GCM predictions. Bull. Amer. Meteor. Soc.,76, 335–345.

  • Lau, N.-C., 1981: A diagnostic study of recurrent meteorological anomalies appearing in a 15-year simulation with a GFDL general circulation model. Mon. Wea. Rev.,109, 2287–2311.

  • Longuet-Higgins, M. S., 1968: The eigenfunctions of Laplace’s tidal equations over a sphere. Philos. Trans. Roy. Soc. London,A262, 511–607.

  • Madden, R. A., 1976: Estimates of natural variability of time averaged sea level pressure. Mon. Wea. Rev.,104, 942–952.

  • ——, 1979: Observations of large-scale traveling Rossby waves. Rev. Geophys. Space Phys.,17, 1935–1949.

  • ——, 1981: A quantitative approach to long-range prediction. J. Geophys. Res.,86, 9817–9825.

  • Nitsche, G., and J. M. Wallace, 1994: Is there evidence of multiple equilibria in planetary wave amplitude statistics? J. Atmos. Sci.,51, 314–322.

  • Ramage, C. S., 1993: Forecasting in meteorology. Bull. Amer. Meteor. Soc.,74, 1863–1871.

  • Rosen, R. D., and D. A. Salstein, 1983: Variations in atmospheric angular momentum on global and regional scales and the length of day. J. Geophys. Res.,88, 5451–5470.

  • Shapiro, L., 1982: Hurricane climatic fluctuations. Part II: Relation to large-scale circulation. Mon. Wea. Rev.,110, 1014–1023.

  • Shea, D. J., and R. A. Madden, 1990: Potential for long-range prediction of monthly mean surface temperatures over North America. J. Climate,3, 1444–1451.

  • Trenberth, K. E., 1984a: Some effects of finite sample size and persistence on meteorological statistics. Part I: Autocorrelations. Mon. Wea. Rev.,112, 2359–2368.

  • ——, 1984b: Some effects of finite sample size and persistence on meteorological statistics. Part II: Potential predictability. Mon. Wea. Rev.,112, 2369–2379.

  • Tsonis, A. A., and J. B. Elsner, 1995: Testing for scaling in natural forms and observables. J. Stat. Phys.,81, 869–880.

  • Viecelli, J. A., 1993: Statistical mechanics and correlation properties of a rotating two-dimensional flow of like-sign vortices. Phys. Fluids,A5, 2484–2501.

  • ——, 1994: Persistence of Lagrangian trajectories in rotating two-dimensional turbulence. J. Atmos. Sci.,51, 337–352.

  • Yoder, C. F., J. G. Williams, and M. E. Parke, 1981: Tidal variations of earth rotation. J. Geophys. Res.,86, 881–891.

  • Zwiers, F. W., 1987: A potential predictability study conducted with an atmospheric general circulation model. Mon. Wea. Rev.,115, 2957–2974.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 329 89 55
PDF Downloads 52 29 4