Fixed points, stable manifolds, weather regimes, and their predictability

Chaos

Volumn 19, Issue 4, 2009, Pages

  Deremble, Bruno ^a   D'Andrea, Fabio ^a   Ghil, Michael ^a,b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ATMOSPHERE; COMPUTER SIMULATION; NONLINEAR SYSTEM; WEATHER;

ALGORITHMS; ATMOSPHERE; COMPUTER SIMULATION; NONLINEAR DYNAMICS; WEATHER;

EID: 74349091649     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3230497     Document Type: Article

References (86)

1. Aurell, E., Boffetta, G., Crisanti, A., Paladin, G., and Vulpiani, A., " Predictability in the large: an extension of the concept of Lyapunov exponent.," J. Phys. A 0305-4470 30, 1-26 (1997). 10.1088/0305-4470/30/1/ 003 (Pubitemid 127011902)
2. Barreira, L., in Proceedings of the XIVth International Congress on Mathematical Physics (World Scientific, Singapore, 2006), pp. 415-422.
3. Benzi, R., P. Malguzzi, A. Speranza, and A. Sutera, " The statistical properties of the general atmospheric circulation: Observational evidence and a minimal theory of bimodality.," Quart. J. Roy. Meteor. Soc. 112, 661674 (1986). 0022-4928 10.1002/qj.49711247306
4. Bowman, K. P., "Manifold geometry and mixing in observed atmospheric flows", 1999 (unpublished);
5. see also Bowman, K. P., Pan, L. L., Campos, T., and Gao, R., " Observations of fine-scale transport structure in the upper troposphere from the High-Performance Instrumented Airborne Platform for Environmental Research.," J. Geophys. Res. 112, D18111, doi:10.1029/2007JD008685 (2007). 10.1029/2007JD008685 (Pubitemid 350142577)
6. Buizza, R. and Palmer, T., " The singular vector structure of the atmospheric general circulation.," J. Atmos. Sci. 0022-4928 52, 1434-1456 (1993). 10.1175/1520-0469(1995)052<1434:TSVSOT>2.0.CO;2
7. Branstator, G., " Analysis of general circulation model sea-surface temperature anomaly simulations using a linear model. Part II: Eigenanalysis.," J. Atmos. Sci. 0022-4928 42, 2242-2254 (1985). 10.1175/1520-0469(1985)042<2242:AOGCMS>2.0.CO;2 (Pubitemid 16461737)
8. Cai, M., Kalnay, E., and Toth, Z., " Bred Vectors of the Zebiak-Cane model and their potential application to ENSO predictions.," J. Clim. 0894-8755 16, 40-56 (2003). 10.1175/1520-0442(2003)016<0040:BVOTZC>2.0. CO;2
9. Charney, J. G. and Devore, J. G., " Multiple flow equilibria in the atmosphere and blocking.," J. Atmos. Sci. 0022-4928 36, 1205-1216 (1979). 10.1175/1520-0469(1979)036<1205:MFEITA>2.0.CO;2
10. Charney, J. G. and Eliassen, A., " A numerical method for predicting the perturbations of the middle latitude westerlies.," Tellus 0040-2826 1, 38-54 (1949).
11. Charney, J. G. and Straus, D. M., " Form-drag instability, multiple equilibria and propagating planetary waves in Baroclinic, orographically forced, planetary wave systems.," J. Atmos. Sci. 0022-4928 37, 1157-1176 (1980). 10.1175/1520-0469(1980)037<1157:FDIMEA>2.0.CO;2
12. Corti, S. and Palmer, T. N., " Sensitivity analysis of atmospheric low-frequency variability.," Q. J. R. Meteorol. Soc. 0035-9009 123, 2425-2447 (1997). 10.1002/qj.49712354413
13. Crommelin, D. T., " Homoclinic dynamics: A scenario for atmospheric ultralow-frequency variability.," J. Atmos. Sci. 0022-4928 59, 1533-1549 (2002). 10.1175/1520-0469(2002)059<1533:HDASFA>2.0.CO;2
14. Crommelin, D. T., Opsteegh, J. D., and Verhulst, F., " A mechanism for atmospheric regime behavior.," J. Atmos. Sci. 0022-4928 61, 1406-1419 (2004). 10.1175/1520-0469(2004)061<1406:AMFARB>2.0.CO;2
15. D'Andrea, F., " Extratropical low-frequency variability as a low-dimensional problem. Part II: Stationarity and stability of large-scale equilibria.," Q. J. R. Meteorol. Soc. 0035-9009 128, 1059-1073 (2001). 10.1256/003590002320373201
16. D'Andrea, F. and Vautard, R., " Extratropical low-frequency variability as a low-dimensional problem. Part I: A simplified model.," Q. J. R. Meteorol. Soc. 0035-9009 127, 1357-1374 (2001). 10.1002/qj.49712757413
17. Deloncle, A., Berk, R., D'Andrea, F., and Ghil, M., " Weather regime prediction using statistical learning.," J. Atmos. Sci. 0022-4928 64, 1619-1635 (2007). 10.1175/JAS3918.1 (Pubitemid 46882312)
18. DeSwart, H., " Analysis of a six-component atmospheric spectral model: chaos, predictability and vacillation.," Physica D 0167-2789 36, 222-234 (1989). 10.1016/0167-2789(89)90082-1
19. DeSwart, H. E., and J. Grasman, " Effect of stochastic perturbations on a spectral model of atmospheric circulation.," Technical Report, 1985.
20. Dijkstra, H. A. and Ghil, M., " Low-frequency variability of the large-scale ocean circulation: A dynamical systems approach.," Rev. Geophys. 8755-1209 43, RG3002, doi:10.1029/2002RG000122 (2005). 10.1029/2002RG000122
21. Doedel, E., A. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Sandstede, and X. Wang, AUTO97: Continuation and bifurcation software for ordinary differential equations, 1997.
22. Evans, E., Kalnay, E., " The Lorenz model is predictable.," Bull. Am. Meteorol. Soc. 0003-0007 85, 520-524 (2004). 10.1175/BAMS-85-4-520
23. Ghil, M., " Hilbert problems for the geosciences in the 21st century.," Nonlinear Processes Geophys. 1023-5809 8, 211-222 (2001).
24. Ghil, M. and Childress, S., Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics (Springer-Verlag, New York, 1987).
25. Ghil, M. and Robertson, A., " Waves vs. particles in the atmosphere's phase space: A pathway to long-range forecasting?," Proc. Natl. Acad. Sci. U.S.A. 0027-8424 99, 2493-2500 (2002). 10.1073/pnas.012580899 (Pubitemid 34165057)
26. Ghil, M. and Robertson, A. W., "," in General Circulation Model Development: Past, Present and Future (Academic, New York, 2000), Chap., pp. 285-325.
27. Goldhirsch, I., Sulem, P. -L., and Orszag, S. A., " Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method.," Physica D 0167-2789 27, 311-337 (1987). 10.1016/0167-2789(87) 90034-0
28. Grassberger, P. and Procaccia, I., " Characterization of strange attractors.," Phys. Rev. Lett. 0031-9007 50, 346-349 (1983). 10.1103/PhysRevLett.50.346
29. Gyarmati, G., Szunyogh, I., and Patil, D. J., " Local predictability in a simple model of atmospheric balance.," Nonlinear Processes Geophys. 1023-5809 10, 183-196 (2003).
30. Haller, G., " Finding finite-time invariant manifolds in two-dimensional velocity fields.," Chaos 1054-1500 10, 99-108 (2000). 10.1063/1.166479
31. Hannachi, A. and Legras, B., " Simulated annealing and weather regimes classification.," Tellus, Ser. A 0280-6495 47, 955-973 (1995). 10.1034/j.1600-0870.1995.00203.x
32. Hide, R. and Mason, P. J., " Sloping convection in a rotating fluid.," Adv. Phys. 0001-8732 24, 47-100 (1975). 10.1080/00018737500101371
33. Holloway, G. and Eert, J., " Intransitive multiple equilibria in eddy-active barotropic flows.," J. Atmos. Sci. 0022-4928 44, 2001-2005 (1987). 10.1175/1520-0469(1987)044<2001:IMEIEA>2.0.CO;2
34. Houtekamer, P. L., Lefaivre, L., Derome, J., Ritchie, H., and Mitchell, H. L., " A system simulation approach to ensemble prediction.," Mon. Weather Rev. 0027-0644 124, 1225-1242 (1996). 10.1175/1520-0493(1996) 124<1225:ASSATE>2.0.CO;2
35. Jiang, S., Jin, F. -F., and Ghil, M., " Multiple equilibria, periodic, and aperiodic solutions in a wind-driven, double-gyre, shallow-water model.," J. Phys. Oceanogr. 1520-0485 25, 764-786 (1995). 10.1175/1520-0485(1995)025<0764:MEPAAS>2.0.CO;2
36. Jin, F. -F. and Ghil, M., " Intraseasonal oscillations in the extratropics: Hopf bifurcation and topographic instabilities.," J. Atmos. Sci. 0022-4928 47, 3007-3022 (1990). 10.1175/1520-0469(1990)047<3007: IOITEH>2.0.CO;2
37. Joseph, B. and Legras, B., " Relation between kinematic boundaries, stirring, and barriers for the Antarctic polar vortex.," J. Atmos. Sci. 0022-4928 59, 1198-1212 (2002). 10.1175/1520-0469(2002)059<1198:RBKBSA>2. 0.CO;2
38. Kimoto, M. and Ghil, M., " Multiple flow regimes in the Northern Hemisphere winter. Part 1: Methodology and hemispheric regimes.," J. Atmos. Sci. 0022-4928 50, 2625-2643 (1993). 10.1175/1520-0469(1993)050<2625: MFRITN>2.0.CO;2 (Pubitemid 24402587)
39. Kondrashov, D., Ghil, M., Chen, J., and Berk, R., " Predicting weather regime transitions in Northern Hemisphere data sets.," Clim. Dyn. 0930-7575 29, 535-551 (2007). 10.1007/s00382-007-0293-2 (Pubitemid 47262098)
40. Kondrashov, D., Kravtsov, S., and Ghil, M., " Empirical mode reduction in a model of extratropical low-frequency variability.," J. Atmos. Sci. 0022-4928 63, 1859-1877 (2006). 10.1175/JAS3719.1 (Pubitemid 44184030)
41. Landau, L. D. and Lifshitz, E. M., Mechanics, Course of Theoretical Physics, 2nd ed. (Pergamon, Oxford, 1969).
42. Legras, B. and Ghil, M., " Persistent anomalies, blocking and variations in atmospheric predictability.," J. Atmos. Sci. 0022-4928 42, 433-471 (1985). 10.1175/1520-0469(1985)042<0433:PABAVI>2.0.CO;2
43. Legras, B. and Vautard, R., Predictability Seminar Proceedings (European Center for Medium-Range Weather Forecasts, Reading, UK, 1995), pp. 141-156.
44. Lorenz, E. N., " Empirical orthogonal functions and statistical weather prediction, Scientific Report 1, Statistical Forecasting Project.," MIT, Cambridge, Mass. (Defense Doc. Center No. 110268), 49 pp., 1956.
45. Lorenz, E. N., " Deterministic nonperiodic flow.," J. Atmos. Sci. 0022-4928 20, 130-141 (1963). 10.1175/1520-0469(1963)020<0130:DNF>2. 0.CO;2
46. Lorenz, E. N., " The mechanics of vacillation.," J. Atmos. Sci. 0022-4928 20, 448-465 (1963). 10.1175/1520-0469(1963)020<0448:TMOV>2.0. CO;2
47. Lorenz, E. N., " Atmospheric predictability as revealed by naturally occurring analogues.," J. Atmos. Sci. 0022-4928 26, 636-646 (1969). 10.1175/1520-0469(1969)26<636:APARBN>2.0.CO;2
48. Lorenz, E. N., " On the existence of a slow manifold.," J. Atmos. Sci. 0022-4928 43, 1547-1557 (1986). 10.1175/1520-0469(1986)043<1547: OTEOAS>2.0.CO;2
49. Lorenz, E. N., " Regimes in simple systems.," J. Atmos. Sci. 0022-4928 63, 2056-2073 (2006). 10.1175/JAS3727.1 (Pubitemid 44288594)
50. Lott, F., Robertson, A. W., and Ghil, M., " Mountain torques and Northern Hemisphere low-frequency variability: Part I: Hemispheric aspects.," J. Atmos. Sci. 0022-4928 61, 1259-1271 (2004). 10.1175/1520-0469(2004)061<1259:MTANHL>2.0.CO;2 (Pubitemid 38861514)
51. Lott, F., Robertson, A. W., and Ghil, M., " Mountain torques and Northern Hemisphere low-frequency variability. Part II: regional aspects.," J. Atmos. Sci. 0022-4928 61, 1272-1283 (2004). 10.1175/1520-0469(2004) 061<1272:MTANHL>2.0.CO;2 (Pubitemid 38861515)
52. Lynch, P., in Large-Scale Atmosphere-Ocean Dynamics (Cambridge University Press, Cambridge, 2002), pp. 64-108.
53. Madden, R. A. and Julian, P. R., " Detection of a 40-50 day oscillation in the zonal wind in the Tropical Pacific.," J. Atmos. Sci. 0022-4928 28, 702-708 (1971). 10.1175/1520-0469(1971)028<0702:DOADOI>2.0. CO;2
54. Madden, R. A. and Julian, P. R., " Description of global-scale circulation cells in the tropics with a 40-50 day period.," J. Atmos. Sci. 0022-4928 29, 1109-1123 (1972). 10.1175/1520-0469(1972)029<1109:DOGSCC>2. 0.CO;2
55. Majda, A. J., Franzke, C. L., Fischer, A., and Crommelin, D. T., " Distinct metastable atmospheric regimes despite nearly gaussian statistics: A paradigm model.," Proc. Natl. Acad. Sci. U.S.A. 0027-8424 103, 8309-8314 (2006). 10.1073/pnas.0602641103 (Pubitemid 43838451)
56. Marcus, S. L., Ghil, M., and Dickey, J. O., " The extratropical 40-day oscillation in the UCLA general circulation model. Part I: atmospheric angular momentum.," J. Atmos. Sci. 0022-4928 51, 1431-1446 (1994). 10.1175/1520-0469(1994)051<1431:TEDOIT>2.0.CO;2
57. Marcus, S. L., Ghil, M., and Dickey, J. O., " The extratropical 40-day oscillation in the UCLA general circulation model. Part II: Spatial structure.," J. Atmos. Sci. 0022-4928 53, 1993-2014 (1996). 10.1175/1520-0469(1996)053<1993:TEDOIT>2.0.CO;2
58. Michelangeli, P. A., Vautard, R., and Legras, B., " Weather regimes: recurrence and quasistationarity.," J. Atmos. Sci. 0022-4928 52, 1237-1256 (1995). 10.1175/1520-0469(1995)052<1237:WRRAQS>2.0.CO;2
59. Mo, K. and Ghil, M., " Cluster analysis of multiple planetary flow regimes.," J. Geophys. Res. 0148-0227 93, 10927-10952, doi:10.1029/ JD093iD09p10927 (1988). 10.1029/JD093iD09p10927
60. Molteni, F., " Weather regimes and multiple equilibria.," in Encyclopedia of Atmospheric Sciences (Academic, New York, 2003), pp. 2577-2586.
61. Molteni, F., Buizza, R., Palmer, T. N., and Petroliagis, T., " The ECMWF ensemble prediction system: methodology and validation.," Q. J. R. Meteorol. Soc. 0035-9009 122, 73-119 (1996). 10.1002/qj.49712252905
62. Namias, J., " The index cycle and its role in the general circulation.," J. Atmos. Sci. 0022-4928 7, 130-139 (1950). 10.1175/1520-0469(1950)007<0130:TICAIR>2.0.CO;2
63. Oseledec, V. I., " A multiplicative ergodic theorem. Characteristic Lyapunov exponents of dynamical systems.," Trudy Moskow Mat. Obshch. 0134-8663 19, 179-210 (1968).
64. Pea, M. and Kalnay, E., " Separating fast and slow modes in a coupled system.," Nonlinear Processes Geophys. 1023-5809 11, 319-327 (2004).
65. Pfeffer, R. L. and Chiang, Y., " Two kinds of vacillation in rotating laboratory experiments.," Mon. Weather Rev. 0027-0644 95, 75-82 (1967). 10.1175/1520-0493(1967)095<0075:TKOVIR>2.3.CO;2
66. Philander, S., El Nio, la Nia and the Southern Oscillation (Academic, San Diego, 1989).
67. Quon, C. and Ghil, M., " Multiple equilibria in thermosolutal convection due to salt-flux boundary conditions.," J. Fluid Mech. 0022-1120 245, 449-484 (1992). 10.1017/S0022112092000545
68. Quon, C. and Ghil, M., " Multiple equilibria and stable oscillations in thermosolutal convection at small aspect ratio.," J. Fluid Mech. 0022-1120 291, 33-56 (1995). 10.1017/S0022112095002618
69. Reinhold, B. B. and Pierrehumbert, R. T., " Dynamics of weather regimes: quasi-stationary waves and blocking.," J. Atmos. Sci. 0022-4928 110, 1105-1145 (1982).
70. Rossby, C. G., " Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action.," J. Mar. Res 2, 38-55 (1939).
71. Sardeshmukh, P. D., Compo, G. P., and Penland, C., " Changes of probability associated with El Nio.," J. Clim. 0894-8755 13, 4268-4286 (2000). 10.1175/1520-0442(2000)013<4268:COPAWE>2.0.CO;2
72. Schneider, S. H. and Dickinson, R. E., " Climate modeling.," Rev. Geophys. Space Phys. 0034-6853 12, 447-493, doi:10.1029/RG012i003p00447 (1974). 10.1029/RG012i003p00447
73. Simonnet, E., Ghil, M., Ide, K., Temam, R., and Wang, S., " Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part I: Steady-state solution.," J. Phys. Oceanogr. 1520-0485 33, 712-728 (2003). 10.1175/1520-0485(2003)33<712:LVISMO>2.0.CO;2 (Pubitemid 37190153)
74. Simonnet, E., Ghil, M., Ide, K., Temam, R., and Wang, S., " Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part I: Time dependant solution.," J. Phys. Oceanogr. 1520-0485 33, 729-752 (2003). 10.1175/1520-0485(2003)33<729:LVISMO>2.0. CO;2 (Pubitemid 37190154)
75. Smyth, P., Ide, K., and Ghil, M., " Multiple regimes in Northern Hemisphere height fields via mixture model clustering.," J. Atmos. Sci. 0022-4928 56, 729-752 (1999). 10.1175/1520-0469(1999)056<3704:MRINHH>2.0. CO;2
76. Stephenson, D., Hannachi, A., and O'Neill, A., " On the existence of multiple climate regimes.," Q. J. R. Meteorol. Soc. 0035-9009 130, 583-605 (2004). 10.1256/qj.02.146
77. Sura, P., Newman, M., Penland, C., and Sardeshmukh, P., " Multiplicative noise and non-qaussianity: A paradigm for atmospheric regimes?," J. Atmos. Sci. 0022-4928 62, 1391-1409 (2005). 10.1175/JAS3408.1 (Pubitemid 40815606)
78. Tian, Y., Weeks, E. R., Ide, K., Urbach, J. S., Baroud, C. N., Ghil, M., and Swinney, H. L., " Experimental and numerical studies of an eastward jet over topography.," J. Fluid Mech. 0022-1120 438, 129-157 (2001). 10.1017/S0022112001004372 (Pubitemid 32653253)
79. Toth, Z. and Kalnay, E., " Ensemble forecasting at NMC: The generation of perturbations.," Bull. Am. Meteorol. Soc. 0003-0007 74, 2317-2330 (1993). 10.1175/1520-0477(1993)074<2317:EFANTG>2.0.CO;2
80. Toth, Z. and Kalnay, E., " Ensemble forecasting at NCEP and the breeding method.," Mon. Weather Rev. 0027-0644 125, 3297-3319 (1997). 10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2
81. Trevisan, A., " Statistical properties of predictability from atmospheric analogs and the existence of multiple flow regimes.," J. Atmos. Sci. 0022-4928 52, 3577-3592 (1995). 10.1175/1520-0469(1995)052<3577: SPOPFA>2.0.CO;2
82. Vautard, R. and Legras, B., " Invariant manifolds, quasi-geostrophy and initialization.," J. Atmos. Sci. 0022-4928 43, 565-584 (1986). 10.1175/1520-0469(1986)043<0565:IMQGAI>2.0.CO;2
83. Weeks, E. R., Tian, Y., Urbach, J. S., Ide, H. L., Swinney, K., and Ghil, M., " Transitions between blocked and zonal flows in a rotating annulus with topography.," Science 0036-8075 278, 1598-1601 (1997). 10.1126/science.278.5343.1598 (Pubitemid 27516272)
84. Xue, Y., Cane, M. A., Zebiak, S. E., and Palmer, T. N., " Predictability of a coupled model of ENSO using singular vector analysis. Part II: Optimal growth and forecast skill.," Mon. Weather Rev. 0027-0644 125, 2057-2073 (1997). 10.1175/1520-0493(1997)125<2057:POACMO>2.0.CO;2 (Pubitemid 127579479)
85. Yoden, S., " Bifurcation properties of a quasi-geostrophic barotropic, low-order model with topography.," J. Meteorol. Soc. Jpn. 0026-1165 63, 535-546 (1985).
86. Zebiak, S. E. and Cane, M. A., " A model El Nio southern oscillation.," Mon. Weather Rev. 0027-0644 115, 2262-2278 (1987). 10.1175/1520-0493(1987)115<2262:AMENO>2.0.CO;2