Statistical Prediction of ENSO from Subsurface Sea Temperature Using a Nonlinear Dimensionality Reduction

Carlos H. R. Lima Department of Earth and Environmental Engineering, Columbia University, New York, New York

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Upmanu Lall Department of Earth and Environmental Engineering, Columbia University, New York, New York

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Tony Jebara Computer Science Department, Columbia University, New York, New York

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Anthony G. Barnston International Research Institute for Climate and Society, The Earth Institute of Columbia University, Lamont Campus, Palisades, New York

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Abstract

Numerous statistical and dynamical models have been developed in recent years to forecast ENSO events. However, for most of these models predictability for lead times over 10 months is limited. It has been hypothesized that the tropical Pacific thermocline structure may have critical information to permit longer lead ENSO forecasts. Models that use subsurface sea temperature information have already been known to produce better long lead forecasts. Here, a two-stage statistical ENSO forecasting model is developed and demonstrated using the spatially distributed depth of the 20°C isotherm (D20) as a proxy for the thermocline. In the first stage, a nonlinear dimension reduction method [maximum variance unfolding (MVU)] is used to decompose the D20 data into canonical modes. The leading spatial patterns as well as lagged values of Niño-3 are then used as predictors in a set of linear regression models to predict the Niño-3 index at lead times of up to 24 months. Cross-validated forecasts using this methodology are shown to have higher skill than those that use a dimension reduction of the same thermocline data using principal component analysis (PCA). The first three modes of the D20 data as revealed by MVU account for 89% of the variance of the data, as compared to only 48% of the variance if PCA is used. The spatial patterns of the MVU modes partition the data field in a different way than the PC modes, even though some similarities exist as to the main regions that are active. These patterns and their temporal structure are discussed here, with a view to understanding the possible source of the longer-range predictability of ENSO using the MVU modes. The skill of the PCA- and the MVU-based forecasts of Niño-3 varies depending on the starting month of the forecast for short lead times (5–10 months). However, for the lead times longer than 1 yr, the MVU-based forecast skill is not seasonally variable, while the PCA-based models do not provide significant skill at these lead times irrespective of the starting month of the forecast. Similar conclusions are obtained for forecast models for the Niño-3.4 and Niño-1.2 indices. The differences between the MVU- and PCA-based models are most marked for the Niño-1.2 long lead forecasts.

Corresponding author address: Carlos H. R. Lima, 918 Mudd, 500 W 120th St., New York, NY 10027. Email: chr2107@columbia.edu

Abstract

Numerous statistical and dynamical models have been developed in recent years to forecast ENSO events. However, for most of these models predictability for lead times over 10 months is limited. It has been hypothesized that the tropical Pacific thermocline structure may have critical information to permit longer lead ENSO forecasts. Models that use subsurface sea temperature information have already been known to produce better long lead forecasts. Here, a two-stage statistical ENSO forecasting model is developed and demonstrated using the spatially distributed depth of the 20°C isotherm (D20) as a proxy for the thermocline. In the first stage, a nonlinear dimension reduction method [maximum variance unfolding (MVU)] is used to decompose the D20 data into canonical modes. The leading spatial patterns as well as lagged values of Niño-3 are then used as predictors in a set of linear regression models to predict the Niño-3 index at lead times of up to 24 months. Cross-validated forecasts using this methodology are shown to have higher skill than those that use a dimension reduction of the same thermocline data using principal component analysis (PCA). The first three modes of the D20 data as revealed by MVU account for 89% of the variance of the data, as compared to only 48% of the variance if PCA is used. The spatial patterns of the MVU modes partition the data field in a different way than the PC modes, even though some similarities exist as to the main regions that are active. These patterns and their temporal structure are discussed here, with a view to understanding the possible source of the longer-range predictability of ENSO using the MVU modes. The skill of the PCA- and the MVU-based forecasts of Niño-3 varies depending on the starting month of the forecast for short lead times (5–10 months). However, for the lead times longer than 1 yr, the MVU-based forecast skill is not seasonally variable, while the PCA-based models do not provide significant skill at these lead times irrespective of the starting month of the forecast. Similar conclusions are obtained for forecast models for the Niño-3.4 and Niño-1.2 indices. The differences between the MVU- and PCA-based models are most marked for the Niño-1.2 long lead forecasts.

Corresponding author address: Carlos H. R. Lima, 918 Mudd, 500 W 120th St., New York, NY 10027. Email: chr2107@columbia.edu

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  • Balmaseda, M. A., M. K. Davey, and D. L. T. Anderson, 1995: Decadal and seasonal dependence of ENSO prediction skill. J. Climate, 8 , 27052715.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., M. Chelliah, and S. B. Goldenberg, 1997: Documentation of a highly ENSO-related SST region in the equatorial Pacific. Atmos.–Ocean, 35 , 367383.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., M. H. Glantz, and Y. He, 1999: Predictive skill of statistical and dynamical climate models in SST forecasts during the 1997–98 El Niño episode and the 1998 La Niña onset. Bull. Amer. Meteor. Soc., 80 , 217243.

    • Search Google Scholar
    • Export Citation
  • Behringer, D. W., M. Ji, and A. Leetmaa, 1998: An improved coupled model for ENSO prediction and implications for ocean initialization. Part I: The ocean data assimilation system. Mon. Wea. Rev., 126 , 10131021.

    • Search Google Scholar
    • Export Citation
  • Belkin, M., and P. Niyogi, 2003: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput., 15 , 13731396.

    • Search Google Scholar
    • Export Citation
  • Borchers, D., 1999: CSDP, a C library for semidefinite programming. Optim. Methods Software, 11 , 613623.

  • Chavez, F. P., J. Ryan, S. E. Lluch-Cota, and M. Ñiquen C, 2003: From anchovies to sardines and back: Multidecadal change in the Pacific Ocean. Science, 299 , 217221.

    • Search Google Scholar
    • Export Citation
  • Chen, D., M. A. Cane, A. Kaplan, S. E. Zebiak, and D. Huang, 2004: Predictability of El Niño over the past 148 years. Nature, 428 , 733736.

    • Search Google Scholar
    • Export Citation
  • Clarke, A. J., and S. Van Gorder, 2003: Improving El Niño prediction using a space-time integration of Indo-Pacific winds and equatorial Pacific upper ocean heat content. Geophys. Res. Lett., 30 , 1399. doi:10.1029/2002GL016673.

    • Search Google Scholar
    • Export Citation
  • Diebold, F. X., and R. Mariano, 1995: Comparing predictive accuracy. J. Bus. Econ. Stat., 13 , 253265.

  • Drosdowsky, W., 2006: Statistical prediction of ENSO (Niño 3) using sub-surface temperature data. Geophys. Res. Lett., 33 , L03710. doi:10.1029/2005GL024866.

    • Search Google Scholar
    • Export Citation
  • Glantz, M. H., 2001: Currents of Change: Impacts of El Niño and La Niña on Climate and Society. Cambridge University Press, 252 pp.

  • Goddard, L., S. J. Mason, S. E. Zebiak, C. F. Ropelewski, R. Basher, and M. A. Cane, 2001: Current approaches to seasonal-to-interannual climate predictions. Int. J. Climatol., 21 , 11111152. doi:10.1002/joc.636.

    • Search Google Scholar
    • Export Citation
  • Hasegawa, T., T. Horii, and K. Hanawa, 2006: Two different features of discharge of equatorial upper ocean heat content related to El Niño events. Geophys. Res. Lett., 33 , L02609. doi:10.1029/2005GL024832.

    • Search Google Scholar
    • Export Citation
  • Hastie, T., R. Tibshirani, and J. Friedman, 2001: The Elements of Statistical Learning. Springer, 533 pp.

  • Ji, M., and T. M. Smith, 1995: Ocean model response to temperature data assimilation and varying surface wind stress: Intercomparisons and implications for climate forecast. Mon. Wea. Rev., 123 , 18111821.

    • Search Google Scholar
    • Export Citation
  • Ji, M., A. Leetmaa, and J. Derber, 1995: An ocean analysis system for seasonal to interannual climate studies. Mon. Wea. Rev., 123 , 460481.

    • Search Google Scholar
    • Export Citation
  • Jin, F-F., 1997: An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model. J. Atmos. Sci., 54 , 811829.

  • 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 , 1856718589.

    • Search Google Scholar
    • Export Citation
  • Livezey, R. E., and W. Y. Chen, 1983: Statistical field significance and its determination by Monte Carlo techniques. Mon. Wea. Rev., 111 , 4659.

    • Search Google Scholar
    • Export Citation
  • Mason, S. J., and L. Goddard, 2001: Probabilistic precipitation anomalies associated with ENSO. Bull. Amer. Meteor. Soc., 82 , 619638.

    • Search Google Scholar
    • Export Citation
  • McPhaden, M. J., 2003: Tropical Pacific Ocean heat content variations and ENSO persistence barriers. Geophys. Res. Lett., 30 , 1480. doi:10.1029/2003GL016872.

    • Search Google Scholar
    • Export Citation
  • McPhaden, M. J., and D. Zhang, 2004: Pacific Ocean circulation rebounds. Geophys. Res. Lett., 31 , L18301. doi:10.1029/2004GL020727.

  • Meinen, C., and M. J. McPhaden, 2000: Observations of warm water volume changes in the equatorial Pacific and their relationship to El Niño and La Niña. J. Climate, 13 , 35513559.

    • Search Google Scholar
    • Export Citation
  • Michaelsen, J., 1987: Cross-validation in statistical climate forecast models. J. Climate Appl. Meteor., 26 , 15891600.

  • Peterson, W. T., and F. B. Schwing, 2003: A new climate regime in northeast Pacific ecosystems. Geophys. Res. Lett., 30 , 1896. doi:10.1029/2003GL017528.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., and T. M. Smith, 1994: Improved global sea surface temperature analyses using optimum interpolation. J. Climate, 7 , 929948.

    • Search Google Scholar
    • Export Citation
  • Ropelewski, C., and M. Halpert, 1987: Global and regional scale precipitation patterns associated with the El Niño/Southern Oscillation. Mon. Wea. Rev., 115 , 16061626.

    • Search Google Scholar
    • Export Citation
  • Ropelewski, C., and M. Halpert, 1989: Precipitation patterns associated with the high index phase of the Southern Oscillation. J. Climate, 2 , 268284.

    • Search Google Scholar
    • Export Citation
  • Roweis, S. R., and L. K. Saul, 2000: Nonlinear dimensionality reduction by locally linear embedding. Science, 290 , 23232326.

  • Ruiz, J. E., I. Cordery, and A. Sharma, 2005: Integrating ocean subsurface temperatures in statistical ENSO forecasts. J. Climate, 18 , 35713586.

    • Search Google Scholar
    • Export Citation
  • Schölkopf, B., A. Smola, and K. Müller, 1998: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput., 10 , 12991319.

    • Search Google Scholar
    • Export Citation
  • Shaw, B., and T. Jebara, 2007: Minimum volume embedding. Proc. 11th Int. Conf. on Artificial Intelligence and Statistics, San Juan, Puerto Rico, Society for Artificial Intelligence and Statistics, 460–467.

    • Search Google Scholar
    • Export Citation
  • Smith, T., A. G. Barnston, M. Ji, and M. Chelliah, 1995: The impact of Pacific Ocean subsurface data on operational prediction of tropical Pacific SST at the NCEP. Wea. Forecasting, 10 , 708714.

    • Search Google Scholar
    • Export Citation
  • Tenenbaum, J., 1998: Mapping a manifold of perceptual observations. Advances in Neural Information Processing Systems, Vol. 10, M. Jordan, M. Kearns, and S. Solla, Eds., MIT Press, 682–688.

    • Search Google Scholar
    • Export Citation
  • Webster, P. J., and S. Yang, 1992: Monsoon and ENSO: Selectively interactive systems. Quart. J. Roy. Meteor. Soc., 118 , 825877.

  • Weinberger, K. Q., and L. Saul, 2006: Unsupervised learning of image manifolds by semidefinite programming. Int. J. Comput. Vision, 70 , 7790.

    • Search Google Scholar
    • Export Citation
  • Weinberger, K. Q., F. Sha, and L. K. Saul, 2004: Learning a kernel matrix for nonlinear dimensionality reduction. Proc. 21st Conf. on Machine Learning, Banff, AB, Canada, ACM, 839–846.

    • Search Google Scholar
    • Export Citation
  • Wyrtki, K., 1975: Fluctuations of the dynamic topography in the Pacific Ocean. J. Phys. Oceanogr., 5 , 450459.

  • Xue, Y., A. Leetmaa, and M. Ji, 2000: ENSO prediction with Markov models: The impact of sea level. J. Climate, 13 , 849871.

  • Zebiak, S. E., and M. A. Cane, 1987: A model El Niño–Southern Oscillation. Mon. Wea. Rev., 115 , 22622278.

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