Editorial Type:
Article
Article Type:
Research Article

Empirically Evaluating Divergence Rates of Atmospheric Trajectories

Gidon Eshel Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois

Search for other papers by Gidon Eshel in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Feb 2006
DOI:
https://doi.org/10.1175/JAS3638.1
Page(s):
741–753
Restricted access

Abstract

Observed Northern Hemisphere divergence rates of phase-space trajectories initially emanating from neighboring points are estimated, using a simple, seasonal, weakly GCM-dependent linear method applied to Ertel potential vorticity on the 315-K isentrope. Using the same data and essentially the same method, atmospheric persistence, the rate of trajectory departure from an initial state, is also estimated. With the results applying only to the truncated state considered (comprising only a single variable observed at a single level), it is found that the time scale for divergence of two, initially reasonably similar, trajectories is about 4–6 days, between the time scales of cyclogenesis and blocking. It is also found that the time scale for divergence of a given trajectory from an earlier point along it is about 3–5 days.

Corresponding author address: Gidon Eshel, Dept. of the Geophysical Sciences, University of Chicago, 5734 S. Ellis Ave., Chicago, IL 60637. Email: geshel@uchicago.edu

Abstract

Observed Northern Hemisphere divergence rates of phase-space trajectories initially emanating from neighboring points are estimated, using a simple, seasonal, weakly GCM-dependent linear method applied to Ertel potential vorticity on the 315-K isentrope. Using the same data and essentially the same method, atmospheric persistence, the rate of trajectory departure from an initial state, is also estimated. With the results applying only to the truncated state considered (comprising only a single variable observed at a single level), it is found that the time scale for divergence of two, initially reasonably similar, trajectories is about 4–6 days, between the time scales of cyclogenesis and blocking. It is also found that the time scale for divergence of a given trajectory from an earlier point along it is about 3–5 days.

Corresponding author address: Gidon Eshel, Dept. of the Geophysical Sciences, University of Chicago, 5734 S. Ellis Ave., Chicago, IL 60637. Email: geshel@uchicago.edu

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

  • Alligood, K. T., T. D. Sauer, and J. A. Yorke, 1996: Chaos. Springer, 601 pp.

  • Brankovi, C., and T. N. Palmer, 1997: Atmospheric seasonal predictability and estimates of ensemble size. Mon. Wea. Rev., 125 , 859–874.

    • Search Google Scholar
    • Export Citation

  • Brankovi, C., T. N. Palmer, and L. Ferranti, 1994: Predictability of seasonal atmospheric variations. J. Climate, 7 , 217–237.

  • Buizza, R., A. Hollingsworth, F. Lalaurette, and A. Ghelli, 1999: Probabilistic predictions of precipitation using the ECMWF Ensemble Prediction System. Wea. Forecasting, 14 , 168–189.

    • Search Google Scholar
    • Export Citation

  • Charney, J. G., 1949: On a physical basis for numerical prediction of large-scale motions in the atmosphere. J. Atmos. Sci., 6 , 372–385.

    • Search Google Scholar
    • Export Citation

  • Charney, J. G., and N. A. Phillips, 1953: Numerical integration of the quasi-geostrophic equations for barotropic and simple baroclinic flows. J. Atmos. Sci., 10 , 71–99.

    • Search Google Scholar
    • Export Citation

  • Chen, W. Y., and H. M. Van den Dool, 1997: Atmospheric predictability of seasonal, annual, and decadal climate means and the role of the ENSO cycle: A model study. J. Climate, 10 , 1236–1254.

    • Search Google Scholar
    • Export Citation

  • DelSole, T., 2001: Optimally persistent patterns in time-varying fields. J. Atmos. Sci., 58 , 1341–1356.

  • Diks, C., 1999: Nonlinear Time Series Analysis. World Scientific, 209 pp.

  • Dirmeyer, P. A., 2003: The role of the land surface background state in climate predictability. J. Hydrometeor., 4 , 599–610.

  • Farrell, B. F., 1990: Small error dynamics and the predictability of atmospheric flows. J. Atmos. Sci., 47 , 2409–2416.

  • Farrell, B. F., and P. J. Ioannou, 2001: Accurate low-dimensional approximation of the linear dynamics of fluid flow. J. Atmos. Sci., 58 , 2771–2789.

    • Search Google Scholar
    • Export Citation

  • Fawcett, E. B., 1962: Six years of operational numerical weather prediction. J. Appl. Meteor., 1 , 318–332.

  • Fraedrich, K., and L. M. Leslie, 1987: Evaluation of techniques for the operational, single station, short-term forecasting of rainfall at a midlatitude station (Melbourne). Mon. Wea. Rev., 115 , 1645–1654.

    • Search Google Scholar
    • Export Citation

  • Germann, U., and I. Zawadzki, 2002: Scale-dependence of the predictability of precipitation from continental radar images. Part I: Description of the methodology. Mon. Wea. Rev., 130 , 2859–2873.

    • Search Google Scholar
    • Export Citation

  • Ghil, M., and A. W. Robertson, 2002: “Waves” vs. “particles” in the atmosphere’s phase-space: A pathway to long-range forecasting? Proc. Natl. Acad. Sci., 99 , (Suppl. 1). 2493–2500.

    • Search Google Scholar
    • Export Citation

  • Ghil, M., R. Benzi, and G. Parisi, 1985: Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics. North-Holland, 449 pp.

    • Search Google Scholar
    • Export Citation

  • Gutzler, D. S., and J. Shukla, 1984: Analogs in the wintertime 500 mb height field. J. Atmos. Sci., 41 , 177–189.

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437–471.

  • Kleeman, R., 2002: Measuring dynamical prediction utility using relative entropy. J. Atmos. Sci., 59 , 2057–2072.

  • Kruizinga, S., and A. H. Murphy, 1983: Use of an analogue procedure to formulate objective probabilistic temperature forecasts in the Netherlands. Mon. Wea. Rev., 111 , 2244–2254.

    • Search Google Scholar
    • Export Citation

  • Lin, C-L., T. Chai, and J. Sun, 2001: Retrieval of flow structures in a convective boundary layer using an adjoint model: Identical twin experiments. J. Atmos. Sci., 58 , 1767–1783.

    • Search Google Scholar
    • Export Citation

  • Lorenz, E. N., 1969: Atmospheric predictability as revealed by naturally occurring analogues. J. Atmos. Sci., 26 , 636–646.

  • Lorenz, E. N., 1975: Climatic predictability. The Physical Basis of Climate and Climate Modeling, B. Bolin et al., Eds., GARP Publication Series, Vol. 16, World Meteorological Organization, 132–136.

    • Search Google Scholar
    • Export Citation

  • Namias, J., 1951: General aspects of extended range forecasting. Compendium of Meteorology, T. F. Malone, Ed., Amer. Meteor. Soc., 802–813.

    • Search Google Scholar
    • Export Citation

  • Newman, M., P. D. Sardeshmukh, C. R. Winkler, and J. S. Whitaker, 2003: A study of subseasonal predictability. Mon. Wea. Rev., 131 , 1715–1732.

    • Search Google Scholar
    • Export Citation

  • Ott, E., 2002: Chaos in Dynamical Systems. 2d ed. Cambridge University Press, 478 pp.

  • Perry, J. N., R. H. Smith, I. P. Woiwod, and D. R. Morse, 2000: Chaos in Real Data. Kluwer, 226 pp.

  • Radinovic, D., 1975: An analogue method for weather forecasting using the 500/1000mb relative topography. Mon. Wea. Rev., 103 , 639–649.

    • Search Google Scholar
    • Export Citation

  • Saha, S., and H. M. Van den Dool, 1988: A measure of the practical limit of predictability. Mon. Wea. Rev., 116 , 2522–2526.

  • Schneider, T., and S. M. Griffies, 1999: A conceptual framework for predictability studies. J. Climate, 12 , 3133–3155.

  • Shapiro, R., 1958: Some observations of the persistence of the surface pressure distribution. J. Atmos. Sci., 15 , 435–439.

  • Van den Dool, H. M., 1987: A bias in skill in forecasts based on analogues and antilogues. J. Climate Appl. Meteor., 26 , 1278–1281.

  • Van den Dool, H. M., 1989: A new look at weather forecasting through analogues. Mon. Wea. Rev., 117 , 2230–2247.

  • Van den Dool, H. M., 1991: Mirror images of atmospheric flows. Mon. Wea. Rev., 119 , 2095–2106.

  • Van den Dool, H. M., 1994: Searching for analogues: How long must we wait? Tellus, 46 , 314–324.

  • Waliser, D. E., K. M. Lau, W. Stern, and C. Jones, 2003: Potential predictability of the Madden–Julian oscillation. Bull. Amer. Meteor. Soc., 84 , 33–50.

    • Search Google Scholar
    • Export Citation

  • Woodcock, F., 1980: On the use of analogues to improve regression forecasts. Mon. Wea. Rev., 108 , 292–297.

  • Woodgate, R. A., 1997: The effects of assimilation on the physics of an ocean model. Part II: Baroclinic identical-twin experiments. J. Atmos. Oceanic Technol., 14 , 910–924.

    • Search Google Scholar
    • Export Citation

  • Xue, Y., M. A. Cane, S. E. Zebiak, and T. N. Palmer, 1997: Predictability of a coupled model of ENSO using singular vector analysis. Part II: Optimal growth and forecast skill. Mon. Wea. Rev., 125 , 2057–2073.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 92 28 2
PDF Downloads 26 9 1