359
Views
20
CrossRef citations to date
0
Altmetric
Original Articles

Coordinate invariance in stochastic dynamical systems

Pages 208-218 | Received 27 May 2002, Accepted 07 Nov 2002, Published online: 15 Dec 2016

References

  • DelSole, T. and Farrell, B. F. 1996. The quasi-linear equili-bration of a thermally maintained stochastically excited jet in a quasigeostrophic model. J. Atmos. Sci. 53, 1781–1797.
  • 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.
  • Epstein, E. 1969. Stochastic dynamic prediction. Tellus 21, 739–759.
  • Farrell, B. F. andIoannou, P. J. 1993. Stochastic dynamics of baroclinic waves. J. Atmos. Sci. 50, 50–4057.
  • 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.
  • Farrell, B. F. and Ioannou, P. J. 1996a. Generalized instability theory. Part I: Autonomous operators. J. Atmos. Sci. 53, 2025–2040.
  • Farrell, B. E and Ioannou, P. J. 1996b. Generalized instability theory. PartNonautonomous operators. J. Atmos. Sci. 53, 53–2053.
  • Farrell, B. F. and Ioannou, P. J. 2000. Perturbation dynamics in atmospheric chemistry. J. Geophys. Res. 105, 105–9320.
  • Gardiner, C. 1983. Handbook of stochastic methods. Springer-Verlag, Berlin, 442 pp.
  • Horn, R. A. and Johnson, C. R. 1985. Matrix analysis. Cambridge University Press, Cambridge, 561 pp.
  • Ioannou, P. J. 1995. Nonnormality increases variance. J. Atmos. Sci. 52, 1155–1158.
  • Leith, C. 1974. Theoretical skill of monte carlo forecasts. Mon. Wea. Rev. 102,409–418.
  • Lu, A. and Wachspress, E. L. 1991. Solution of Lyapunov equations by alternating direction implicit iteration. Com-put. Math. AppL 21,43–58.
  • Liitkepohl, H. 1996. Handbook of matrices. John Wiley, New York, 304 pp.
  • Moore, A. M. 1999. Wind-induced variability of ocean gyres. Dyn. Atmos. Oceans 29, 335–364.
  • 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.
  • 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.
  • Newman, M., Sardeshmulch, P. D. and Penland, C. 1997. Stochastic forcing of the wintertime extratropical flow. J. Atmos. Sci. 54, 435–455.
  • Penland, C. and Magorian, T. 1993. Prediction of Nino 3 sea surface temperaturs using linear inverse modeling. J. Climate 6, 1067–1076.
  • Penland, C. and Sardeshmulch, P. D. 1995. The optimal growth of tropical sea surface temperature anomalies. J. Climate 8, 1999–2024.
  • Risken, H. 1984. The Fokker-Planck equation: Methods of solution and applications. Springer-Verlag, Berlin, 454 pp.
  • van Kampen, N. 1992. Stochastic processes in physics and chemistry. North-Holland, Amsterdam, 465 pp.
  • 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.
  • Whitaker, J. S. andSardeshmulch, P. D. 1998. A linear theory of extratropical synoptic eddy statistics. J. Atmos. Sci. 55, 55–258.
  • Zhang, Y. andHeld, I. M. 1999. A linear stochastic model of a GCM’s midlatitude storm tracks. J. Atmos. Sci. 56, 56–3435.