Lyapunov exponents of a simple stochastic model of the thermally and wind-driven ocean circulation

Dynamics of Atmospheres and Oceans - Tập 35 - Trang 363-388 - 2002
Adam Hugh Monahan1
1Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany

Tài liệu tham khảo

Arnold, L., 1998. Random Dynamical Systems. Springer, Berlin, 586 pp. Arnold, L., Imkeller, P., Sri Namachchivaya, N., 2001. The asymptotic stability of weakly perturbed two dimensional Hamiltonian systems. In: Proceedings of the 18th Biennial Conference on Mechanical Vibration and Noise, ASME Design Engineering Technical Conferences, Pittsburg, PA, USA, 9–12 September 2001. Barsugli, 1998, The basic effects of atmosphere-ocean thermal coupling on midlatitude variability, J. Atmos. Sci., 55, 477, 10.1175/1520-0469(1998)055<0477:TBEOAO>2.0.CO;2 Balusara, 1990, Noise effects in a nonlinear dynamic system The rf superconducting quantum interference device, Phys. Rev., 42, 4614, 10.1103/PhysRevA.42.4614 Boffetta, 2002, Predictability: a way to characterize complexity, Phys. Rep., 356, 367, 10.1016/S0370-1573(01)00025-4 Delworth, 2000, Multidecadal thermohaline circulation variability driven by atmospheric surface flux forcing, J. Clim., 13, 1481, 10.1175/1520-0442(2000)013<1481:MTCVDB>2.0.CO;2 Farrell, 1996, Generalized stability theory. Part I. Autonomous operators, J. Atmos. Sci., 53, 2025, 10.1175/1520-0469(1996)053<2025:GSTPIA>2.0.CO;2 Farrell, 1996, Generalized stability theory. Part II. Nonautonomous operators, J. Atmos. Sci., 53, 2041, 10.1175/1520-0469(1996)053<2041:GSTPIN>2.0.CO;2 Farrell, 1999, Perturbation growth and structure in time-dependent flows, J. Atmos. Sci., 56, 3622, 10.1175/1520-0469(1999)056<3622:PGASIT>2.0.CO;2 Gardiner, C.W., 1997. Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences. Springer, Berlin, 442 pp. Griffies, 1995, A linear thermohaline oscillator driven by stochastic atmospheric forcing, J. Clim., 8, 2440, 10.1175/1520-0442(1995)008<2440:ALTODB>2.0.CO;2 Hasselmann, 1976, Stochastic climate models, Tellus, 28, 473, 10.3402/tellusa.v28i6.11316 Kloeden, P.E., Platen, E., 1992. Numerical Solution of Stochastic Differential Equations. Springer, Berlin, 632 pp. Lin, 2000, Influence of a stochastic moist convective parameterisation on tropical climate variability, Geophys. Res. Lett., 27, 3691, 10.1029/2000GL011964 Maas, 1994, A simple model for the three-dimensional, thermally and wind-driven ocean circulation, Tellus, 46A, 671, 10.3402/tellusa.v46i5.15651 Monahan, A.H., 2002. Stabilisation of climate regimes by noise in a simple model of the thermohaline circulation. J. Phys. Oceanogr. 32, 2072–2085. Monahan, A.H., Timmermann, A., Lohmann, G., 2002. Comments on Noise-induced transitions in a simplified model of the thermohaline circulation. J. Phys. Oceanogr. 32, 2072–2085. Moore, 1999, Wind-induced variability of ocean gyres, Dyn. Atmos. Ocean, 29, 335, 10.1016/S0377-0265(99)00010-X Ott, E., 1993. Chaos in Dynamical Systems. Cambridge University Press, Cambridge, 385 pp. Paladin, 1994, Predictability in spatially extended systems, J. Phys. A, 27, 4911, 10.1088/0305-4470/27/14/018 Palmer, T.N., 1995. In: ECMWF Seminar Proceedings on Predictability of the Atmosphere and Oceans: From Days to Decades. Predictability, European Centre for Medium-Range Weather Forecasts, Reading, UK, 4–8 September 1995. Palmer, 2001, A nonlinear dynamical perspective on model error: a proposal for nonlocal stochastic-dynamic parameterisation in weather and climate prediction models, QJ Roy Meteo. Soc., 127, 279 Penland, C., 2001. A stochastic approach to nonlinear dynamics: a review. Bull. Am. Met. Soc., submitted for publication. Penland, 2000, Identification of dynamical regimes in an intermediate coupled ocean-atmospheric model, J. Clim., 13, 2105, 10.1175/1520-0442(2000)013<2105:IODRIA>2.0.CO;2 Schimansky-Geier, 1993, Positive Lyapunov exponents in the Kramers oscillator, J. Stat. Phys., 70, 141, 10.1007/BF01053959 Timmermann, 1998, Northern Hemispheric interdecadal variability: a coupled air-sea mode, J. Clim., 11, 1906, 10.1175/1520-0442-11.8.1906 van der Schrier, G., 2000. Aspects of the thermohaline circulation in a simple model. Ph.D. Thesis, KNMI, The Netherlands. van der Schrier, 1998, Chaos in a simple model of the three-dimensional, salt-dominated ocean circulation, Clim. Dynamics, 14, 489, 10.1007/s003820050236