Abstract
The structural organization of initially random errors evolving in a barotropic tangent linear model, with time-dependent basic states taken from analyses, is examined for cases of block development, maturation and decay in the Southern Hemisphere atmosphere during April, November, and December 1989. The statistics of 100 evolved errors are studied for six-day periods and compared with the growth and structures of fast growing normal modes and finite-time normal modes (FTNMs). The amplification factors of most initially random errors are slightly less than those of the fastest growing FTNM for the same time interval. During their evolution, the standard deviations of the error fields become concentrated in the regions of rapid dynamical development, particularly associated with developing and decaying blocks. We have calculated probability distributions and the mean and standard deviations of pattern correlations between each of the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. The mean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases with increasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but not always, gives the largest mean pattern correlation with error fields. Corresponding pattern correlations with the fast growing normal modes of the instantaneous basic state flow are significant but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increase further when the time interval is increased beyond six days.
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References
Anderson, J. L., 1991: The robustness of barotropic unstable modes in a zonally varying atmosphere.J. Atmos. Sci.,48, 2393–2410.
Anderson, J. L., 1993: The climatology of blocking in a numerical forecast model.J. Climate,6, 1041–1056.
Anderson, J. L., 1996: Selection of initial conditions for ensemble forecasts in a simple perfect model framework.J. Atmos. Sci.,53, 22–36.
Arnoldi, W. E., 1951: The principle of minimized iterations in the solution of the matrix eigenvalue problem.Quarterly of Applied Mathematics,9, 17–29.
Bengtsson, L., 1981: Numerical prediction of atmospheric blocking: A case study.Tellus,33, 19–24.
Borges, M. D., and D. L. Hartmann, 1992: Barotropic instability and optimal perturbations of observed nonzonal flows.J. Atmos. Sci.,49, 335–354.
Buizza, R. and F. Molteni, 1996: The role of finite-time barotropic instability during transition to blocking.J. Atmos. Sci.,53, 1675–1697.
Buizza, R., P. Houtekamer, Z. Toth, G. Pelerin, Mozheng Wei, and Y. Zhu, 2005: A comparison of the ECMWF, MSC and NCEP global ensemble prediction systems.Mon. Wea. Rev., in press.
CMB, 1989: Climate Monitoring Bulletin, Southern Hemisphere, No. 39 April; No. 46, November; No.47, December 1989, National Climate Centre, Bureau of Meteorology, Australia.
Colucci, S. J. and D. P. Baumhefner, 1992: Initial weather regimes as predictors of numerical 30-day mean forecast accuracy.J. Atmos. Sci.,49, 1652–1671.
Coughlan, M. L., 1983: A comparative climatology of blocking action in the two hemispheres.Australian Meteorological Magazine,31, 3–13.
de Pondeca, M. S. F. A., A. Barcilon, and X. Zou, 1998a: An adjoint sensitivity study of the efficacy of modal and nonmodal perturbations in causing model block onset.J. Atmos. Sci.,55, 2095–2118.
de Pondeca, M. S. F. A., A. Barcilon, and X. Zou, 1998b: The role of wave breaking, linear instability, and PV transports in model block onset.J. Atmos. Sci.,55, 2852–2873.
Errico, R. M., T. Vukicevic, and K. Raeder, 1993: Examination of the accuracy of a tangent linear model.Tellus,45A, 462–477.
Farrell, B. F., 1989: Optimal excitation of baroclinic waves.J. Atmos. Sci.,46, 1193–1206.
Frederiksen, J. S., 1982: A unified three-dimensional instability theory of the onset of blocking and cyclogenesis.J. Atmos. Sci.,39, 970–982.
Frederiksen, J. S., 1984: The onset of blocking and cyclogenesis in Southern Hemisphere synoptic flows: Linear theory.J. Atmos. Sci.,41, 1116–1131.
Frederiksen, J. S., 1997: Adjoint sensitivity and finite-time normal mode disturbances during blocking.J. Atmos. Sci.,54, 1144–1165.
Frederiksen, J. S.; 1998: Precursors to blocking anomalies: The tangent linear and inverse problems.J. Atmos. Sci.,55, 2419–2436.
Frederiksen, J. S., 2000: Singular vectors, finite-time normal modes and error growth during blocking.J. Atmos. Sci.,57, 312–333.
Frederiksen, J. S., and R. C. Bell, 1990: North Atlantic blocking during January 1979: Linear theory.Quart. J. Roy. Meteor. Soc.,116, 1289–1313.
Frederiksen, J. S., and G. Branstator, 2001: Seasonal and intraseasonal variability of large-scale barotropic modes.J. Atmos. Sci.,58, 50–69.
Frederiksen, J. S., M. A. Collier, and A. B. Watkins, 2004: Ensemble prediction of blocking regime transitions.Tellus,56A, 485–500.
Goldhirsch, I., S. A. Orszag, and B. K. Maulik, 1987: An efficient method for computing leading eigenvalues and eigenvectors of large asymmetric matrices.J. Sci. Computing.,2, 33–58.
Held, I. M., 1983: Stationary and quasi-stationary eddies in the extratropical troposphere: Theory.Large Scale Dynamic Processes in the Atmosphere, B. J. Hoskins and R. P. Pearce, Eds., Academic Press, 127–167.
Houtekamer, P. L., and J. Derome, 1995: Methods for ensemble prediction.Mon. Wea. Rev.,123, 2181–2196.
Kimoto, M., H. Mukougawa, and S. Yoden, 1992: Mediumrange forecast skill variation and blocking transition: A case study.Mon. Wea. Rev.,120, 1616–1627.
Lacarra, J. F., and O. Talagrand, 1988: Short-range evolution of small perturbations in a barotropic model.Tellus,40A, 81–95.
Legras, B., and R. Vautard, 1996: A guide to Liapunov vectors.Proc. of a Seminar Held at ECMWF on Predictability, 4–8 September 1995, Vol. I, 143–156.
Lejenas, H., 1984: Characteristics of southern hemisphere blocking as determined from a time series of observational data.Quart. J. Roy. Meteor. Soc.,110, 967–979.
Lorenz, E. N., 1965: A study of the predictability of a 28-variable atmospheric model.Tellus,17, 321–333.
Molteni, F., and T. Palmer, 1993: Predictability and finitetime instability of the northern winter circulation.Quart. J. Roy. Meteor. Soc.,119, 269–298
Molteni, F., R. Buizza, T. Palmer, and T. Petroliagis, 1996: The ECMWF ensemble prediction system: Methodology and validation.Quart. J. Roy. Meteor. Soc.,122, 73–119
Mu, M., and W. Duan, 2003: A new approach to studying ENSO predictability: Conditional nonlinear optimal perturbation.Chinese Sci. Bull.,48, 1045–1047.
Mu, M., W. S. Duan, and B. Wang, 2003: Conditional nonlinear optimal perturbation and its applications.Nonlinear Process in Geophysics,10, 493–501.
Noar, P. F., 1983: Numerical modelling of blocking with reference to June 1982.Australian Meteorological Magazine,31, 37–49.
Noone, D., and I. Simmonds, 1998: Similarity of “fastgrowing perturbations” and an illustrative experiment with ensemble forecasting.Australian Meteorological Magazine,47, 5–19.
Palmer, T. N., 1993: Extended-range atmospheric prediction and the Lorenz model.Bull. Amer. Meteor. Soc.,74, 49–65.
Saad, Y., 1992:Numerical Methods for Large Eigenvalue Problems. Halsted Press-John Wiley & Sons Inc., 346pp.
Simmons, A. J., J. M. Wallace, and G. W. Branstator, 1983: Barotropic wave propagations and instability, and atmospheric teleconnection patterns.J. Atmos. Sci.,40, 1363–1392.
Szunyogh, I., E. Kalnay, and Z. Toth, 1997: A comparison of Lyapunov and Optimal vectors in a low-resolution GCM.Tellus,48A, 200–227.
Tibaldi, S., and F. Molteni, 1990: On the operational predictability of blocking.Tellus,42A, 343–365.
Tibaldi, S., P. Ruti, and M. Maruca, 1995: Operational predictability of winter blocking at ECMWF: An update.Ann. Geophysicae,13, 305–317.
Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: the generation of perturbations.Bull. Amer. Meteor. Soc.,174, 2317–2330.
Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method.Mon. Wea. Rev.,125, 3297–3319.
Tribbia, J., and D. Baumhefner, 1993: On the problem of prediction beyond the deterministic range.Proc. NATO Workshop on Predictions of Interannual Climate Variations, S. Shukla, Ed., NATO ASI Series, Springer-Verlag, 251–265.
van Loon, H., 1956: Blocking action in the Southern Hemisphere, Part I.Notos,5, 171–177.
Veyre, P., 1991: Direct prediction of error variances by the tangent linear model: A way to forecast uncertainty in the short range?Proc. ECMWF Workshop on New Developments in Predictability, Reading, UK, 65–86.
Wei, Mozheng, 2000: Quantifying local instability and predictability of chaotic dynamical systems by means of local metric entropy,International Journal of Bifurcation and Chaos,10, No. 1, 135–154.
Wei, Mozheng, and Z. Toth, 2003: A New Measure of Ensemble Performance: Perturbation versus Error Correlation Analysis (PECA).Mon. Wea. Rev.,131, 1549–1565.
Whitaker, J. S., and A. Barcilon, 1992: Type B cyclogenesis in zonally varying flow.J. Atmos. Sci,49, 1877–1892.
Wright, A. D. F., 1974: Blocking action in the Australian region. Tech. Rep., No. 10, Bureau of Meteorology, Australia, 29pp.
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Wei, M., Frederiksen, J.S. Finite-time normal mode disturbances and error growth during Southern Hemisphere blocking. Adv. Atmos. Sci. 22, 69–89 (2005). https://doi.org/10.1007/BF02930871
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DOI: https://doi.org/10.1007/BF02930871