Editorial Type:
Article
Article Type:
Research Article

A Hierarchy of Data-Based ENSO Models

D. Kondrashov Department of Atmospheric and Oceanic Sciences, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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S. Kravtsov Department of Atmospheric and Oceanic Sciences, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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A. W. Robertson Department of Atmospheric and Oceanic Sciences, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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M. Ghil Department of Atmospheric and Oceanic Sciences, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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Print Publication:
01 Nov 2005
DOI:
https://doi.org/10.1175/JCLI3567.1
Page(s):
4425–4444
Restricted access

Abstract

Global sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset’s statistics. These inverse models assume that the system’s variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset’s leading empirical orthogonal functions. Multiple linear regression has been widely used to obtain inverse stochastic models; it is generalized here in two ways. First, the dynamics is allowed to be nonlinear by using polynomial regression. Second, a multilevel extension of classic regression allows the additive noise to be correlated in time; to do so, the residual stochastic forcing at a given level is modeled as a function of variables at this level and the preceding ones. The number of variables, as well as the order of nonlinearity, is determined by optimizing model performance.

The two-level linear and quadratic models have a better El Niño–Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models’ simulated Niño-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Niño and negative La Niña events. The benefits of the quadratic model are less clear in terms of its overall, cross-validated hindcast skill; this model outperforms, however, the linear one in predicting the magnitude of extreme SST anomalies.

Seasonal ENSO dependence is captured by incorporating additive, as well as multiplicative forcing with a 12-month period into the first level of each model. The quasi-quadrennial ENSO oscillatory mode is robustly simulated by all models. The “spring barrier” of ENSO forecast skill is explained by Floquet and singular vector analysis, which show that the leading ENSO mode becomes strongly damped in summer, while nonnormal optimum growth has a strong peak in December.

* Current affiliation: International Research Institute for Climate Prediction, Palisades, New York

+ Permanent affiliation: Départment Terre–Atmosphère–Océan and Laboratoire de Météorologie Dynamique du CNRS/IPSL, École Normale Supérieure, Paris, France

Corresponding author address: Dr. Dmitri Kondrashov, Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, 405 Hilgard Ave., Los Angeles, CA 90095-1565. Email: dkondras@atmos.ucla.edu

Abstract

Global sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset’s statistics. These inverse models assume that the system’s variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset’s leading empirical orthogonal functions. Multiple linear regression has been widely used to obtain inverse stochastic models; it is generalized here in two ways. First, the dynamics is allowed to be nonlinear by using polynomial regression. Second, a multilevel extension of classic regression allows the additive noise to be correlated in time; to do so, the residual stochastic forcing at a given level is modeled as a function of variables at this level and the preceding ones. The number of variables, as well as the order of nonlinearity, is determined by optimizing model performance.

The two-level linear and quadratic models have a better El Niño–Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models’ simulated Niño-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Niño and negative La Niña events. The benefits of the quadratic model are less clear in terms of its overall, cross-validated hindcast skill; this model outperforms, however, the linear one in predicting the magnitude of extreme SST anomalies.

Seasonal ENSO dependence is captured by incorporating additive, as well as multiplicative forcing with a 12-month period into the first level of each model. The quasi-quadrennial ENSO oscillatory mode is robustly simulated by all models. The “spring barrier” of ENSO forecast skill is explained by Floquet and singular vector analysis, which show that the leading ENSO mode becomes strongly damped in summer, while nonnormal optimum growth has a strong peak in December.

* Current affiliation: International Research Institute for Climate Prediction, Palisades, New York

+ Permanent affiliation: Départment Terre–Atmosphère–Océan and Laboratoire de Météorologie Dynamique du CNRS/IPSL, École Normale Supérieure, Paris, France

Corresponding author address: Dr. Dmitri Kondrashov, Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, 405 Hilgard Ave., Los Angeles, CA 90095-1565. Email: dkondras@atmos.ucla.edu

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  • Alexander, M. A., I. Bladé, M. Newman, J. R. Lanzante, N-C. Lau, and J. D. Scott, 2002: The atmospheric bridge: The influence of ENSO teleconnections on air–sea interaction over the global oceans. J. Climate, 15 , 2205–2231.

    • Search Google Scholar
    • Export Citation

  • Allen, M. R., and L. A. Smith, 1996: Monte Carlo SSA: Detecting irregular oscillations in the presence of colored noise. J. Climate, 9 , 3373–3404.

    • Search Google Scholar
    • Export Citation

  • Balmaseda, M. A., M. K. Davey, and D. T. Anderson, 1995: Decadal and seasonal dependence of ENSO prediction skill. J. Climate, 8 , 2705–2715.

    • Search Google Scholar
    • Export Citation

  • Barnston, A. G., and Coauthors, 1994: Long-lead seasonal forecasts—Where do we stand? Bull. Amer. Meteor. Soc., 75 , 2097–2114.

  • Barnston, A. G., M. H. Glantz, and Y. He, 1999: Predictive skill of statistical and dynamical climate models in forecasts of SST during the 1998–97 El Niño episode and the 1998 La Niña onset. Bull. Amer. Meteor. Soc., 80 , 217–244.

    • Search Google Scholar
    • Export Citation

  • Blumenthal, M. B., 1991: Predictability of a coupled atmosphere–ocean model. J. Climate, 4 , 766–784.

  • Burgers, G., and D. B. Stephenson, 1999: The “normality” of El Niño. Geophys. Res. Lett., 26 , 1027–1030.

  • Chao, Y., M. Ghil, and J. C. McWilliams, 2000: Pacific interdecadal variability in this century’s sea surface temperatures. Geophys. Res. Lett., 27 , 2261–2264.

    • Search Google Scholar
    • Export Citation

  • Dettinger, M. D., M. Ghil, C. M. Strong, W. Weibel, and P. Yiou, 1995: Software expedites singular-spectrum analysis of noisy time series. Eos, Trans. Amer. Geophys. Union, 76 , 12–21.

    • Search Google Scholar
    • Export Citation

  • Flugel, M., and P. Chang, 1998: Does the predictability of ENSO depend on the seasonal cycle? J. Atmos. Sci., 55 , 3230–3243.

  • Fraedrich, K., 1986: Estimating the dimension of weather and climate attractors. J. Atmos. Sci., 43 , 419–432.

  • Ghil, M., and K. C. Mo, 1991: Intraseasonal oscillations in the global atmosphere. Part I: Northern Hemisphere and tropics. J. Atmos. Sci., 48 , 752–779.

    • Search Google Scholar
    • Export Citation

  • Ghil, M., and N. Jiang, 1998: Recent forecast skill for the El Niño/Southern Oscillation. Geophys. Res. Lett., 25 , 171–174.

  • Ghil, M., and A. W. Robertson, 2000: Solving problems with GCMs: General circulation models and their role in the climate modeling hierarchy. General Circulation Model Development: Past, Present and Future, D. Randall, Ed., Academic Press, 285–325.

    • Search Google Scholar
    • Export Citation

  • Ghil, M., and Coauthors, 2002: Advanced spectral methods for climatic time series. Rev. Geophys., 40 .1003, doi:10.1029/2000RG000092.

  • Goddard, L., and D. G. DeWitt, 2005: Seeking progress in El Niño prediction. U.S. CLIVAR, Vol. 3, No. 1, U.S. CLIVAR Office, 1–5.

  • Grieger, B., and M. Latif, 1994: Reconstruction of the El Niño attractor with neural networks. Climate Dyn., 10 , 267–276.

  • Hannachi, A., D. B. Stephenson, and K. R. Sperber, 2003: Probability-based methods for quanfifying nonlinearity in the ENSO. Climate Dyn., 20 , 241–256.

    • Search Google Scholar
    • Export Citation

  • Hartman, P., 1982: Ordinary Differential Equations. Birkhaeuser, 612 pp.

  • Hoerling, M. P., A. Kumar, and M. Zhong, 1997: El Niño, La Niña, and the nonlinearity of their teleconnections. J. Climate, 10 , 1769–1786.

    • Search Google Scholar
    • Export Citation

  • Höskuldsson, A., 1996: Prediction Methods in Science and Technology. Thor Publishing.

  • Hsieh, W. W., and B. Tang, 1998: Applying neural network models to prediction and data analysis in meteorology and oceanography. Bull. Amer. Meteor. Soc., 79 , 1855–1870.

    • Search Google Scholar
    • Export Citation

  • Iooss, G., and D. D. Joseph, 1980: Elementary Stability and Bifurcation Theory. Springer-Verlag, 286 pp.

  • Jiang, N., J. D. Neelin, and M. Ghil, 1995: Quasi-quadrennial and quasi-biennial variability in the equatorial Pacific. Climate Dyn., 12 , 101–112.

    • Search Google Scholar
    • Export Citation

  • Jin, F-F., 1997a: A theory of interdecadal climate variability of the North Pacific ocean–atmosphere system. Climate Dyn., 10 , 1821–1835.

    • Search Google Scholar
    • Export Citation

  • Jin, F-F., 1997b: An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model. J. Atmos. Sci., 54 , 811–829.

  • Jin, F-F., 1997c: An equatorial ocean recharge paradigm for ENSO. Part II: A stripped-down coupled model. J. Atmos. Sci., 54 , 830–847.

    • Search Google Scholar
    • Export Citation

  • Jin, F-F., J. D. Neelin, and M. Ghil, 1994: El Niño on the Devil’s Staircase: Annual subharmonic steps to chaos. Science, 264 , 70–72.

    • Search Google Scholar
    • Export Citation

  • Jin, F-F., J. D. Neelin, and M. Ghil, 1996: El Niño/Southern Oscillation and the annual cycle: Subharmonic frequency-locking and aperiodicity. Physica D, 98 , 442–465.

    • Search Google Scholar
    • Export Citation

  • Johnson, S. D., D. S. Battisti, and E. S. Sarachik, 2000a: Empirically derived Markov models and prediction of tropical Pacific sea surface temperature anomalies. J. Climate, 13 , 3–17.

    • Search Google Scholar
    • Export Citation

  • Johnson, S. D., D. S. Battisti, and E. S. Sarachik, 2000b: Seasonality in an empirically derived Markov model of tropical Pacific sea surface temperature anomalies. J. Climate, 13 , 3327–3335.

    • Search Google Scholar
    • Export Citation

  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 341 pp.

  • Kaplan, A., M. Cane, Y. Kushnir, A. Clement, M. Blumenthal, and B. Rajagopalan, 1998: Analyses of global sea-surface temperature 1856–1991. J. Geophys. Res., 103 , 18567–18589.

    • Search Google Scholar
    • Export Citation

  • Keppenne, C. L., and M. Ghil, 1992: Adaptive filtering and prediction of the Southern Oscillation index. J. Geophys. Res., 97 , 20449–20454.

    • Search Google Scholar
    • Export Citation

  • Kiehl, J. T., and Coauthors, 2003: Community Climate System Model science plan. National Center for Atmospheric Research.

  • Kondrashov, D., K. Ide, and M. Ghil, 2004: Weather regimes and preferred transition paths in a three-level quasigeostrophic model. J. Atmos. Sci., 61 , 568–587.

    • Search Google Scholar
    • Export Citation

  • Kravtsov, S., D. Kondrashov, and M. Ghil, 2005: Multilevel regression modeling of nonlinear processes: Derivation and applications to climate variability. J. Climate, 18 , 4404–4424.

    • Search Google Scholar
    • Export Citation

  • Landsea, C. W., and J. A. Knaff, 2000: How much “skill” was there in forecasting the very strong 1997–98 El Niño? Bull. Amer. Meteor. Soc., 81 , 2107–2120.

    • Search Google Scholar
    • Export Citation

  • Latif, M., and Coauthors, 1998: A review of the predictability and prediction of ENSO. J. Geophys. Res., 103 , C7,. 14375–14393.

  • Lau, N-C., and M. J. Nath, 2001: Impact of ENSO on SST variability in the North Pacific and North Atlantic: Seasonal dependence and role of extratropical sea–air coupling. J. Climate, 14 , 2846–2866.

    • Search Google Scholar
    • Export Citation

  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20 , 130–141.

  • Mardia, K. V., 1980: Tests of univariate and multivariate normality. Handbook of Statistics, Vol. 1, P. R. Krishnaiah, Ed., North-Holland, 279–320.

    • Search Google Scholar
    • Export Citation

  • Marshall, J., and F. Molteni, 1993: Toward a dynamical understanding of atmospheric weather regimes. J. Atmos. Sci., 50 , 1792–1818.

  • Mason, S. J., and G. M. Mimmack, 2001: Comparison of some statistical methods of probabilistic forecasting of ENSO. J. Climate, 15 , 8–29.

    • Search Google Scholar
    • Export Citation

  • McCullagh, P., and J. A. Nelder, 1989: Generalized Linear Models. Chapman and Hall, 511 pp.

  • McPhaden, M. J., 2004: Evolution of the 2002–03 El Niño. Bull. Amer. Meteor. Soc., 85 , 677–695.

  • Meyer, Y., 1992: Wavelets and Operators. Cambridge University Press, 223 pp.

  • Moron, V., R. Vautard, and M. Ghil, 1998: Trends, interdecadal and interannual oscillations in global sea-surface temperatures. Climate Dyn., 14 , 545–569.

    • Search Google Scholar
    • Export Citation

  • Neelin, J. D., M. Latif, and F-F. Jin, 1994: Dynamics of coupled ocean–atmosphere models: The tropical problem. Annu. Rev. Fluid Mech., 26 , 617–659.

    • Search Google Scholar
    • Export Citation

  • Neelin, J. D., D. S. Battisti, A. C. Hirst, F-F. Jin, Y. Wakata, T. Yamagata, and S. Zebiak, 1998: ENSO theory. J. Geophys. Res., 103 , C7,. 14261–14290.

    • Search Google Scholar
    • Export Citation

  • Penland, C., 1989: Random forcing and forecasting using principal oscillation pattern analysis. Mon. Wea. Rev., 117 , 2165–2185.

  • Penland, C., 1996: A stochastic model of Indo-Pacific sea-surface temperature anomalies. Physica D, 98 , 534–558.

  • Penland, C., and M. Ghil, 1993: Forecasting Northern Hemisphere 700-mb geopotential height anomalies using empirical normal modes. Mon. Wea. Rev., 121 , 2355–2372.

    • Search Google Scholar
    • Export Citation

  • Penland, C., and P. D. Sardeshmukh, 1995: The optimal growth of tropical sea-surface temperature anomalies. J. Climate, 8 , 1999–2024.

  • Penland, C., and L. Matrosova, 1998: Prediction of tropical Atlantic sea-surface temperatures using linear inverse modeling. J. Climate, 11 , 483–496.

    • Search Google Scholar
    • Export Citation

  • Penland, C., and L. Matrosova, 2001: Expected and actual errors of linear inverse model forecasts. Mon. Wea. Rev., 129 , 1740–1745.

  • Philander, S. G. H., 1990: El Niño, La Niña, and the Southern Oscillation. Academic Press, 286 pp.

  • Preisendorfer, R. W., 1998: Principal Component Analysis in Meteorology and Oceanography. Elsevier, 425 pp.

  • Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1994: Numerical Recipes. 2d ed. Cambridge University Press, 994 pp.

    • Search Google Scholar
    • Export Citation

  • Rasmusson, E. M., X. Wang, and C. F. Ropelewski, 1990: The biennial component of ENSO variability. J. Mar. Syst., 1 , 71–96.

  • Sardeshmukh, P. D., G. P. Compo, and C. Penland, 2000: Changes of probability associated with El Niño. J. Climate, 13 , 4268–4286.

  • Strang, G., 1989: Wavelets and dilation equations: A brief introduction. SIAM Rev., 31 , 614–627.

  • Strong, C. M., F-F. Jin, and M. Ghil, 1995: Intraseasonal oscillations in a barotropic model with annual cycle, and their predictability. J. Atmos. Sci., 52 , 2627–2642.

    • Search Google Scholar
    • Export Citation

  • Tang, B. Y., W. W. Hsieh, A. H. Monahan, and F. T. Tangang, 2000: Skill comparisons between neural networks and canonical correlation analysis in predicting the equatorial Pacific sea surface temperatures. J. Climate, 13 , 287–293.

    • Search Google Scholar
    • Export Citation

  • Tangang, F. T., B. Tang, A. H. Monahan, and W. W. Hsieh, 1998: Forecasting ENSO events: A neural network–extended EOF approach. J. Climate, 11 , 29–41.

    • Search Google Scholar
    • Export Citation

  • Thompson, C. J., and D. S. Battisti, 2000: A linear stochastic dynamical model of ENSO. Part I: Model development. J. Climate, 13 , 2818–2883.

    • Search Google Scholar
    • Export Citation

  • Thompson, C. J., and D. S. Battisti, 2001: A linear stochastic dynamical model of ENSO. Part II: Analysis. J. Climate, 14 , 445–466.

  • Timmermann, A., H. U. Voss, and R. Pasmanter, 2001: Empirical dynamical system modeling of ENSO using nonlinear inverse techniques. J. Phys. Oceanogr., 31 , 1579–1598.

    • Search Google Scholar
    • Export Citation

  • Trenberth, K., and J. W. Hurrel, 1994: Decadal atmosphere–ocean variations in the Pacific. Climate Dyn., 9 , 303–319.

  • Tziperman, E., L. Stone, M. 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.

    • Search Google Scholar
    • Export Citation

  • Vautard, R., and M. Ghil, 1989: Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D, 35 , 395–424.

    • Search Google Scholar
    • Export Citation

  • Vautard, R., P. Yiou, and M. Ghil, 1992: Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Physica D, 58 , 95–126.

    • Search Google Scholar
    • Export Citation

  • Von Mises, R., 1964: Mathematical Theory of Probability and Statistics. Academic Press, 694 pp.

  • Wang, B., and Y. Wang, 1996: Temporal structure of the Southern Oscillation as revealed by waveform and wavelet analysis. J. Climate, 9 , 1586–1598.

    • Search Google Scholar
    • Export Citation

  • Weiss, J. P., and J. B. Weiss, 1999: Quantifying persistence in ENSO. J. Atmos. Sci., 56 , 2737–2760.

  • Wetherill, G. B., 1986: Regression Analysis with Applications. Chapman and Hall, 311 pp.

  • Winkler, C. R., M. Newman, and P. D. Sardeshmukh, 2001: A linear model of wintertime low-frequency variability. Part I: Formulation and forecast skill. J. Climate, 14 , 4474–4494.

    • Search Google Scholar
    • Export Citation

  • Wold, S., A. Ruhe, H. Wold, and W. J. Dunn III, 1984: The collinearity problem in linear regression: The Partial Least Square approach to generalized inverses. SIAM J. Sci. Stat. Comput., 5 , 735–743.

    • Search Google Scholar
    • Export Citation

  • Xue, Y., A. Leetma, and M. Ji, 2000: ENSO prediction with Markov models: The impact of sea level. J. Climate, 13 , 849–871.

  • Yiou, P., D. Sornette, and M. Ghil, 2000: Data-adaptive wavelets and multi-scale SSA. Physica D, 142 , 254–290.

  • Zebiak, S. E., and M. A. Cane, 1987: A model El-Niño–Southern Oscillation. Mon. Wea. Rev., 115 , 2262–2278.

  • Zhang, X., J. Sheng, and A. Shabbar, 1998: Modes of interannual and interdecadal variability of Pacific SST. J. Climate, 11 , 2556–2569.

    • Search Google Scholar
    • Export Citation
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