Coordinate invariance in stochastic dynamical systems

Tellus, Series A: Dynamic Meteorology and Oceanography

Volumn 55, Issue 3, 2003, Pages 208-218

  Weiss, Jeffrey B ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC DYNAMICS; MODELING; NUMERICAL METHOD; STOCHASTICITY;

EID: 0038445228     PISSN: 02806495     EISSN: None     Source Type: Journal    
DOI: 10.1034/j.1600-0870.2003.00014.x     Document Type: Article

References (25)

1. DelSole, T. and Farrell, B. F. 1996. The quasi-linear equilibration of a thermally maintained stochastically excited jet in a quasigeostrophic model. J. Atmos. Sci. 53, 1781-1797.
2. DelSole, T. and Hou, A. Y. 1999. Empirical stochastic models for the dominant climate statistics of a general circulation model. J. Atmos. Sci. 56, 3436-3456.
3. Epstein, E. 1969. Stochastic dynamic prediction. Tellus 21, 739-759.
4. Farrell, B. F. and Ioannou, P. J. 1993. Stochastic dynamics of baroclinic waves. J. Atmos. Sci. 50, 4044-4057.
5. Farrell, B. F. and Ioannou, P. J. 1994. A theory for the statistical equilibrium energy spectrum and heat flux produced by transient baroclinic waves. J. Atmos. Sci. 51, 2685-2698.
6. Farrell, B. F. and Ioannou, P. J. 1996a. Generalized instability theory. Part I: Autonomous operators. J. Atmos. Sci. 53, 2025-2040.
7. Farrell, B. F. and Ioannou, P. J. 1996b. Generalized instability theory. Part II: Nonautonomous operators. J. Atmos. Sci. 53, 2041-2053.
8. Farrell, B. F. and Ioannou, P. J. 2000. Perturbation dynamics in atmospheric chemistry. J. Geophys. Res. 105, 9303-9320.
9. Gardiner, C. 1983. Handbook of stochastic methods. Springer-Verlag, Berlin, 442 pp.
10. Horn, R. A. and Johnson, C. R. 1985. Matrix analysis. Cambridge University Press, Cambridge, 561 pp.
11. Ioannou, P. J. 1995. Nonnormality increases variance. J. Atmos. Sci. 52, 1155-1158.
12. Leith, C. 1974. Theoretical skill of monte carlo forecasts. Mon. Wea. Rev. 102, 409-418.
13. Lu, A. and Wachspress, E. L. 1991. Solution of Lyapunov equations by alternating direction implicit iteration. Comput. Math. Appl. 21, 43-58.
14. Liitkepohl, H. 1996. Handbook of matrices. John Wiley, New York, 304 pp.
15. Moore, A. M. 1999. Wind-induced variability of ocean gyres. Dyn. Atmos. Oceans 29, 335-364.
16. Moore, A. M. and Farrell, B. F. 1993. Rapid perturbation growth on spatially and temporally varying oceanic flows determined using an adjoint method: Application to the Gulf Stream. J. Phys. Oceanogr. 23, 1682-1702.
17. Moore, A. M. and Kleeman, R. 1996. The dynamics of error growth and predictability in a coupled model of ENSO. Q. J. R. Meteorol. Soc. 122, 1405-1446.
18. Newman, M., Sardeshmukh, P. D. and Penland, C. 1997. Stochastic forcing of the wintertime extratropical flow. J. Atmos. Sci. 54, 435-455.
19. Penland, C. and Magorian, T. 1993. Prediction of Nin̄o 3 sea surface temperature using linear inverse modeling. J. Climate 6, 1067-1076.
20. Penland, C. and Sardeshmukh, P. D. 1995. The optimal growth of tropical sea surface temperature anomalies. J. Climate 8, 1999-2024.
21. Risken, H. 1984. The Fokker-Planck equation: Methods of solution and applications. Springer-Verlag, Berlin, 454 pp.
22. van Kampen, N. 1992. Stochastic processes in physics and chemistry. North-Holland, Amsterdam, 465 pp.
23. Weickmann, K. M., Robinson, W. A. and Penland, C. 2000. Stochastic and oscillatory forcing of global atmospheric angular momentum. J. Geophys. Res. 105, 15543-15557.
24. Whitaker, J. S. and Sardeshmukh, P. D. 1998. A linear theory of extratropical synoptic eddy statistics. J. Atmos. Sci. 55, 237-258.
25. Zhang, Y. and Held, I. M. 1999. A linear stochastic model of a GCM's midlatitude storm tracks. J. Atmos. Sci. 56, 3416-3435.