Start Submission Become a Reviewer

Reading: Predicting areas of sustainable error growth in quasigeostrophic flows using perturbation al...

Download

A- A+
Alt. Display

Original Research Papers

Predicting areas of sustainable error growth in quasigeostrophic flows using perturbation alignment properties

Authors:

G. Rivière ,

Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, 75231 Paris Cedex 05, FR; GFDL Princeton University, Forrestal Campus, PO Box 308, NJ 08542 Princeton, US
X close

B. L. Hua

Laboratoire de Physique des Océans, IFREMER, BP 70, 29280 Plouzané, FR
X close

Abstract

A new perturbation initialization method is used to quantify error growth due to inaccuracies of the forecast model initial conditions in a quasigeostrophic box ocean model describing a wind-driven double gyre circulation. This method is based on recent analytical results on Lagrangian alignment dynamics of the perturbation velocity vector in quasigeostrophic flows. More specifically, it consists in initializing a unique perturbation from the sole knowledge of the control flow properties at the initial time of the forecast and whose velocity vector orientation satisfies a Lagrangian equilibrium criterion. This Alignment-based Initialization method is hereafter denoted as the AI method.

In terms of spatial distribution of the errors, we have compared favorably the AI error forecast with the mean error obtained with a Monte-Carlo ensemble prediction. It is shown that the AI forecast is on average as efficient as the error forecast initialized with the leading singular vector for the palenstrophy norm, and significantly more efficient than that for total energy and enstrophy norms. Furthermore, a more precise examination shows that the AI forecast is systematically relevant for all control flows whereas the palenstrophy singular vector forecast leads sometimes to very good scores and sometimes to very bad ones.

A principal component analysis at the final time of the forecast shows that the AI mode spatial structure is comparable to that of the first eigenvector of the error covariance matrix for a “bred mode” ensemble. Furthermore, the kinetic energy of the AI mode grows at the same constant rate as that of the “bred modes” from the initial time to the final time of the forecast and is therefore characterized by a sustained phase of error growth. In this sense, the AI mode based on Lagrangian dynamics of the perturbation velocity orientation provides a rationale of the “bred mode” behavior.

How to Cite: Rivière, G. and Hua, B.L., 2004. Predicting areas of sustainable error growth in quasigeostrophic flows using perturbation alignment properties. Tellus A: Dynamic Meteorology and Oceanography, 56(5), pp.441–455. DOI: http://doi.org/10.3402/tellusa.v56i5.14465
  Published on 01 Jan 2004
 Accepted on 20 Apr 2004            Submitted on 25 Apr 2003

References

  1. Barkmeijer , J. 1992 . Local error growth in a barotropic model . Tellus 44A , 314 – 323 .  

  2. Barnier , B. , Hua , B. L. and Leprovost , C. 1991 . On the catalytic role of high baroclinic modes in eddy-driven large-scale circulations . J. Phys. Oceanogr 21 , 976 – 997 .  

  3. Buizza , R. and Palmer , T. N. 1995 . The singular-vector structure of the atmospheric general circulation. J. Atmos. Sc i . 52 , 1434 – 1450 .  

  4. Buizza , R. , Tribbia , J. , Molteni , F. and Palmer , T. 1993 . Computation of optimal unstable structures for a numerical weather prediction model . Tellus 45A , 388 – 407 .  

  5. Farrell , B. F. 1990 . Small error dynamics and the predictability of atmospheric flows. J. Atmos. Sc i . 53 , 2409 – 2416 .  

  6. Farrell , B. F. and Ioannou , P. J. 1996 . Generalized stability theory. Part I: autonomous operators. J. Atmos. Sc i . 53 , 2025 – 2040 .  

  7. Frederilcsen , J. S. 1997 . Adjoint sensitivity and finite-time normal mode disturbances during blocking. J. Atmos. Sc i . 54 , 1144 – 1165 .  

  8. Frederilcsen , J. S. 2000 . Singular vectors, finite-time normal modes, and error growth during blocking. J. Atmos. Sc i . 57 , 312 – 333 .  

  9. Hamill , T. M. , Snyder , C. and Morss , R. E. 2000 . A comparison of probablistic forecasts from bred, singular-vector, and perturbed observation ensembles. Mon. Wea. Re v . 128 , 1835 – 1851 .  

  10. Houtelcamer , P. L. and Derome , J. 1995 . Methods for ensemble prediction. Mon. Wea. Re v . 123 , 2181 – 2196 .  

  11. Houtelcamer , P. L. and coauthors . 1996 . A system simulation approach to ensemble prediction. Mon. Wea. Re v . 124 , 1225 – 1242 .  

  12. Jimenez , J. , Wray , A. A. , Saffman , P. G. and Rogallo , R. S. 1993 . The structure of intense voracity in isotropic turbulence . J. Fluid Mech . 255 , 65 – 90 .  

  13. Lapeyre , G. , Klein , P. and Hua , B. L. 1999 . Does the traceur gradient vector align with the strain eigenvectors in 2D turbulence . Phys. Fluids A 11 , 3729 – 3737 .  

  14. Legras , B. and Vautard , R. 1996 . A guide to Lyapunov vectors. Proc. ECMWF Sem. on Predictability Vol. 1 , ECMWF, ReadingUnited Kingdom , 143 - 156 .  

  15. Leith , C. E. 1974 . Theoretical skill of Monte-Carlo forecasts. Mon. Wea. Re v . 102 , 409 – 418 .  

  16. Lorenz , E. N. 1965 . A study of the predictability of a 28-variable atmospheric model . Tellus 17 , 321 – 333 .  

  17. Mak , M. and Cai , M. 1989 . Local barotropic instability. J. Atmos. Sc i . 46 , 3289 – 3311 .  

  18. Molteni , E , Buizza , R. , Palmer , T. N. and Petroliagis , T. 1996 . The ECMWF ensemble prediction system: Methodology and validation . Quart. J. Roy. Meteor Soc . 122 , 73 – 120 .  

  19. Moore , A. M. and Mariano , A. J. 1999 . The dynamics of error growth and predictability in a model of the Gulf Stream. Part I: Singular vector analysis . J. Phys. Oceanogr 29 , 158 – 176 .  

  20. Moore , A. M. 1999 . The dynamics of error growth and predictability in a model of the Gulf Stream. Part II: Ensemble prediction . J. Phys. Oceanogr . 29 , 762 – 778 .  

  21. Patil , D. J. , Hunt , B. R. , Kalnay , E. , Yorke , J. A. and Ott , E. 2001 . Local low dimensionality of atmospheric dynamics . Phys. Rev. Lett . 86 , 5878 .  

  22. Rivière , G. , Hua , B. L. and Klein , P. 2003 . Perturbation growth in terms of barotropic alignment properties . Quart. J. Roy. Meteor Soc . 129 , 2613 – 2635 .  

  23. Schmitz , W. J. and Holland , W. R. 1986 . Observed and modeled mesoscale variability near the Gulf Stream and Kuroshio Extension . J. Geophys. Res . 91 , 9624 – 9638 .  

  24. Snyder , C. 1999 . Error growth in flows with finite-amplitude waves or coherent structures. J. Atmos. Sc i . 56 , 500 – 506 .  

  25. Snyder , C. and Joly , A. 1998 . Development of perturbations within a growing baroclinic wave . Quart. J. Roy. Meteor. Soc . 124 , 1961 – 1983 .  

  26. Snyder , C. and Hamill , T. M. 2003 . Leading lyapunov vectors of a turbulent baroclinic jet in a quasigeostrophic model. J. Atmos. Sc i . 60 , 683 – 688 .  

  27. Snyder , C. , Hamill , T. M. and Trier , S. B. 2003 . Linear evolution of error covariances in a quasigeostrophic model. Mon. Weather Re v . 131 , 189 – 205 .  

  28. Thompson , P. D. 1957 . Uncertainty of initial state as a factor in the predictability of large-scale atmospheric flow patterns . Tellus 9 , 275 – 295 .  

  29. Toth , Z. and Kalnay , E. 1993 . Ensemble forecasting at NMC: The generation of perturbations . Bull. Amer Meteor Soc . 74 , 2317 – 2330 .  

  30. Toth , Z. and Kalnay , E. 1997 . Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Re v . 125 , 3297 – 3319 .  

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

comments powered by Disqus