A. Timmermann wishes to acknowledge the support of the EU project SINTEX ENV4-CT98-0714. H. U. Voss acknowledges support from the Max Planck society. We are very grateful to Prof. Jürgen Kurths for his scientific support and many fruitful discussions.
Achatz, U., , and G. Schmitz, 1997: On the closure problem in the reduction of complex atmospheric models by PIPs and EOFs: A comparison for the case of a two-layer model with zonally symmetric forcing. J. Atmos. Sci., 54 , 2452–2474.
——, and Branstator, G., 1999: A two-layer model with empirical linear corrections and reduced order for studies of internal climate variability. J. Atmos. Sci., 56 , 3140–3160.
Barnett, T. P., , M. Latif, , N. Graham, , M. Flügel, , S. Pazan, , and W. White, 1993: ENSO and ENSO-related predictability. Part I: Prediction of equatorial Pacific sea surface temperature with a hybrid coupled ocean–atmosphere model. J. Climate, 6 , 1545–1566.
Battisti, D. S., , and A. C. Hirst, 1989: Interannual variability in the tropical atmosphere–ocean system: Influence of the basic state, ocean geometry and nonlinearity. J. Atmos. Sci., 46 , 1687–1712.
Blanke, B., , J. D. Neelin, , and D. Gutzler, 1997: Estimating the effect of stochastic wind stress forcing on ENSO irregularity. J. Climate, 10 , 1473–1486.
Breiman, L., , and J. H. Friedman, . 1985: Estimating optimal transformations for multiple regression and correlation. J. Amer. Stat. Assoc., 80 , 580–598.
Brown, R., 1993: Orthogonal polynomials as prediction functions in arbitrary phase space dimensions. Phys. Rev. E, 47 , 3962–3969.
Buizza, R., , M. Miller, , and T. N. Palmer, 1999: Stochastic representation of model uncertainties in the ECMWF Ensemble Prediction System. Quart. J. Roy. Meteor. Soc., 125 , 2887–2908.
Cane, M. A., , M. Münnich, , and S. E. Zebiak, 1990: A study of self-excited oscillations of the tropical ocean–atmosphere system. Part I: Linear analysis. J. Atmos. Sci., 47 , 1562–1577.
Eckert, C., , and M. Latif, 1997: Predictability of a stochastically forced hybrid coupled model of El Niño. J. Climate, 10 , 1488–1504.
Flügel, M., , and P. Chang, 1996: Impact of dynamical and stochastic processes on the predictability of ENSO. Geophys. Res. Lett., 23 , 2089–2092.
Hasselmann, K., 1988: PIPs and POPs: The reduction of complex dynamical systems using Principal Interaction and Oscillation Patterns. J. Geophys. Res., 93 , 11 015–11 021.
Johnson, S. D., , D. S. Battisti, , and E. S. Sarachik, 2000: Empirically derived Markov models and prediction of tropical Pacific sea surface temperature anomalies. J. Climate, 13 , 3–17.
——,. 1997: Optimal Galerkin approximations of partial differential equations using principal interaction patterns. Phys. Rev. E, 55 , 5365–5375.
Larimore, W. E., , and J. Baillieul, 1990: Identification and filtering of nonlinear systems using canonical variate analysis. Proc. 26th IEEE Conf. on Decision and Control, Honolulu, HI, IEEE,. 596–604.
Lorenz, E. N., 1956: Empirical orthogonal functions and statistical weather prediction. MIT Department of Meteorology Science Rep. 1, 49 pp.
Monahan, A., 2000: Nonlinear principal component analysis by neural networks: Theory and application to the Lorenz system. J. Climate, 13 , 821–835.
Münnich, M., , M. A. Cane, , and S. E. Zebiak, 1991: A study of self-excited oscillations of the tropical ocean–atmosphere system. Part II: Nonlinear cases. J. Atmos. Sci., 48 , 1238–1248.
Neelin, J. D., , D. S. Battisti, , A. C. Hirst, , F. F. Jin, , Y. Wakata, , T. Yamagata, , and S. E. Zebiak, 1998: ENSO theory. J. Geophys. Res., 103 . (C7) 14 261–14 290.
North, G. R., , T. L. Bell, , R. F. Cahalan, , and F. J. Moeng, 1982: Sampling errors in the estimation of empirical orthogonal functions. Mon. Wea. Rev., 110 , 699–706.
——, and Magorian, T., 1993: Prediction of Niño 3 sea surface temperatures using linear inverse modeling. J. Climate, 6 , 1067–1076.
Roeckner, E., , J. M. Oberhuber, , A. Bacher, , M. Christoph, , and I. Kirchner, 1996: ENSO variability and atmospheric response in a global atmosphere–ocean GCM. Climate Dyn., 12 , 737–754.
Sethuraman, J., 1990: The asymptotic distribution of the Rényi maximal correlation. Commun. Stat., Theory Methods, 19 , 4291–4298.
——, Latif, M., , A. Bacher, , J. Oberhuber, , and E. Roeckner, 1999: Increased El Niño frequency in a climate model forced by future greenhouse warming. Nature, 398 , 694–696.
Trenberth, K. E., , and T. J. Hoar, 1996: The 1990–1995 El Niño–Southern Oscillation event: Longest on record. Geophys. Res. Lett., 23 , 57–60.
Tziperman, E., , L. Stone, , M. A. Cane, , and H. Jarosh, 1994: El Niño chaos: Overlapping of resonances between the seasonal cycle and the Pacific ocean–atmosphere oscillator. Science, 264 , 72–74.
——, Cane, M. A., , S. E. Zebiak, , Y. Xue, , and B. Blumenthal, 1998: Locking of El Niño's peak time to the end of the calendar year in the delayed oscillator picture of ENSO. J. Climate, 11 , 2191–2199.
Voss, H. U., 2000: Analysing nonlinear dynamical systems with nonparametric regression. Nonlinear Dynamics and Statistics, A. Mees, Ed., Birkhäuser, in press.
——, and Kurths, J., 1997: Reconstruction of nonlinear time delay models from data by the use of optimal transformations. Phys. Lett. A, 234 , 336–344.
——, Schwache, A., , J. Kurths, , and F. Mitschke, 1999: Equations of motion from chaotic data: A driven optical fiber ring resonator. Phys. Lett. A, 256 , 47–54.
Xue, Y., , M. A. Cane, , S. E. Zebiak, , and M. B. Blumenthal, 1994: On the prediction of ENSO: A study with a low-order Markov model. Tellus, 46A , 512–528.
Zwiers, F. W., , and H. von Storch, 1990: Regime-dependent autoregressive time series modeling of the Southern Oscillation. . J. Climate, 3 , 1347–1363.