• Belkin, M., and P. Niyogi, 2003: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput., 15, 13731396, doi:10.1162/089976603321780317.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berry, T., and T. Sauer, 2016: Local kernels and the geometric structure of data. Appl. Comput. Harmonic Anal., 40, 439469, doi:10.1016/j.acha.2015.03.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berry, T., R. Cressman, Z. Greguric Ferencek, and T. Sauer, 2013: Time-scale separation from diffusion-mapped delay coordinates. SIAM J. Appl. Dyn. Syst., 12, 618649, doi:10.1137/12088183X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Broomhead, D. S., and G. P. King, 1986: Extracting qualitative dynamics from experimental data. Physica D, 20, 217236, doi:10.1016/0167-2789(86)90031-X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Budisić, M., R. Mohr, and I. Mezić, 2012: Applied Koopmanism. Chaos, 22, 047510, doi:10.1063/1.4772195.

  • Chen, N., and A. J. Majda, 2015a: Predicting the cloud patterns for the boreal summer intraseasonal oscillation through a low-order stochastic model. Math. Climate Wea. Forecasting, 1, 120, doi:10.1515/mcwf-2015-0001.

    • Search Google Scholar
    • Export Citation
  • Chen, N., and A. J. Majda, 2015b: Predicting the real-time multivariate Madden–Jullian oscillation index through a low-order nonlinear stochastic model. Mon. Wea. Rev., 143, 21482169, doi:10.1175/MWR-D-14-00378.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, N., A. J. Majda, and D. Giannakis, 2014: Predicting the cloud patterns of the Madden–Julian oscillation through a low-order nonlinear stochastic model. Geophys. Res. Lett., 41, 56125619, doi:10.1002/2014GL060876.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, T.-C., and J. C. Alpert, 1990: Systematic errors in the annual and intraseasonal variations of the planetary-scale divergent circulation in NMC medium-range forecasts. Mon. Wea. Rev., 118, 26072623, doi:10.1175/1520-0493(1990)118<2607:SEITAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Coifman, R. R., and S. Lafon, 2006: Diffusion maps. Appl. Comput. Harmonic Anal., 21, 530, doi:10.1016/j.acha.2006.04.006.

  • Comeau, D., Z. Zhao, D. Giannakis, and A. J. Majda, 2017: Data-driven prediction strategies for low-frequency patterns of North Pacific climate variability. Climate Dyn., doi:10.1007/s00382-016-3177-5, in press.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deser, C., A. Phillips, and V. Bourdette, 2012: Uncertainty in climate change projections: The role of internal variability. Climate Dyn., 38, 527546, doi:10.1007/s00382-010-0977-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fernández, A., N. Rabin, D. Fishelov, and J. R. Dorronsoro, 2014: Auto-adaptive Laplacian pyramids for high-dimensional data analysis. arXiv.org, 11 pp. [Available online at https://arxiv.org/abs/1311.6594.]

  • Giannakis, D., 2015: Dynamics-adapted cone kernels. SIAM J. Appl. Dyn. Syst., 14, 556608, doi:10.1137/140954544.

  • Giannakis, D., 2016: Data-driven spectral decomposition and forecasting of ergodic dynamical systems. arXiv.org, 55 pp. [Available online at https://arxiv.org/abs/1507.02338.]

  • Giannakis, D., and A. J. Majda, 2011: Time series reconstruction via machine learning: Revealing decadal variability and intermittency in the North Pacific sector of a coupled climate model. Proc. Conf. on Intelligent Data Understanding 2011, Mountain View, CA, NASA, 107–117.

  • Giannakis, D., and A. J. Majda, 2012: Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability. Proc. Natl. Acad. Sci. USA, 109, 22222227, doi:10.1073/pnas.1118984109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giannakis, D., and A. J. Majda, 2013: Nonlinear Laplacian spectral analysis: Capturing intermittent and low-frequency spatiotemporal patterns in high-dimensional data. Stat. Anal. Data Min., 6, 180194, doi:10.1002/sam.11171.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giannakis, D., and A. J. Majda, 2014: Data-driven methods for dynamical systems: Quantifying predictability and extracting spatiotemporal patterns. Mathematical and Computational Modeling: With Applications in Engineering and the Natural and Social Sciences, Engineering, and the Arts, R. Melnik, Ed., Wiley, 135–191, doi:10.1002/9781118853887.ch7.

    • Crossref
    • Export Citation
  • Giannakis, D., W.-w. Tung, and A. J. Majda, 2012: Hierarchical structure of the Madden–Julian oscillation in infrared brightness temperature revealed through nonlinear Laplacian spectral analysis. 2012 Conference on Intelligent Data Understanding (CIDU 2012), K. Das, N. V. Chawla, and A. N. Srivastava, Eds., IEEE, 55–62, doi:10.1109/CIDU.2012.6382201.

    • Crossref
    • Export Citation
  • Goswami, B. N., 2011: South Asian monsoon. Intraseasonal Variability in the Atmosphere–Ocean Climate System, W. K. M. Lau and D. E. Waliser, Eds., Springer, 19–61.

    • Crossref
    • Export Citation
  • Hendon, H. H., B. Liebmann, M. Newman, J. D. Glick, and J. Schemm, 2000: Medium-range forecast errors associated with active episodes of the Madden–Julian oscillation. Mon. Wea. Rev., 128, 6986, doi:10.1175/1520-0493(2000)128<0069:MRFEAW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hodges, K., D. Chappell, G. Robinson, and G. Yang, 2000: An improved algorithm for generating global window brightness temperatures from multiple satellite infrared imagery. J. Atmos. Oceanic Technol., 17, 12961312, doi:10.1175/1520-0426(2000)017<1296:AIAFGG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, C., D. Waliser, J.-K. Schemm, and W. Lau, 2000: Prediction skill of the Madden and Julian oscillation in dynamical extended range forecasts. Climate Dyn., 16, 273289, doi:10.1007/s003820050327.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kikuchi, K., B. Wang, and Y. Kajikawa, 2012: Bimodal representation of the tropical intraseasonal oscillation. Climate Dyn., 38, 19892000, doi:10.1007/s00382-011-1159-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., J. Dias, K. H. Straub, M. C. Wheeler, S. N. Tulich, K. Kikuchi, K. M. Weickmann, and M. J. Ventrice, 2014: A comparison of OLR and circulation-based indices for tracking the MJO. Mon. Wea. Rev., 142, 16971715, doi:10.1175/MWR-D-13-00301.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kondrashov, D., M. D. Chekroun, A. W. Robertson, and M. Ghil, 2013: Low-order stochastic model and “past-noise forecasting” of the Madden–Julian oscillation. Geophys. Res. Lett., 40, 53055310, doi:10.1002/grl.50991.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kousky, V. E., and M. T. Kayano, 1993: Real-time monitoring of intraseasonal oscillations. Proc. 18th Annual Climate Diagnostics Workshop, Boulder, CO, NOAA, 1–5.

  • Lau, K., and F. Chang, 1992: Tropical intraseasonal oscillation and its prediction by the NMC operational model. J. Climate, 5, 13651378, doi:10.1175/1520-0442(1992)005<1365:TIOAIP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, J.-Y., B. Wang, M. C. Wheeler, X. Fu, D. E. Waliser, and I.-S. Kang, 2013: Real-time multivariate indices for the boreal summer intraseasonal oscillation over the Asian summer monsoon region. Climate Dyn., 40, 493509, doi:10.1007/s00382-012-1544-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1969: Atmospheric predictability as revealed by naturally occurring analogues. J. Atmos. Sci., 26, 636646, doi:10.1175/1520-0469(1969)26<636:APARBN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1972: Description of global-scale circulation cells in the tropics with a 40–50 day period. J. Atmos. Sci., 29, 11091123, doi:10.1175/1520-0469(1972)029<1109:DOGSCC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mezić, I., 2005: Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dyn., 41, 309325, doi:10.1007/s11071-005-2824-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miyakawa, T., and et al. , 2014: Madden–Julian oscillation prediction skill of a new-generation global model demonstrated using a supercomputer. Nat. Commun., 5, 3769, doi:10.1038/ncomms4769.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mo, K. C., 2001: Adaptive filtering and prediction of intraseasonal oscillations. Mon. Wea. Rev., 129, 802817, doi:10.1175/1520-0493(2001)129<0802:AFAPOI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neena, J. M., J. Y. Lee, D. Waliser, B. Wang, and X. Jiang, 2014: Predictability of the Madden–Julian oscillation in the Intraseasonal Variability Hindcast Experiment (ISVHE). J. Climate, 27, 45314543, doi:10.1175/JCLI-D-13-00624.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Packard, N. H., and et al. , 1980: Geometry from a time series. Phys. Rev. Lett., 45, 712716, doi:10.1103/PhysRevLett.45.712.

  • Rabin, N., and R. R. Coifman, 2012: Heterogeneous datasets representation and learning using diffusion maps and Laplacian pyramids. Proceedings of the 2012 SIAM International Conference on Data Mining, J. Ghosh et al., Eds., Proceedings, Society for Industrial and Applied Mathematics, 189–199, doi:10.1137/1.9781611972825.17.

    • Crossref
    • Export Citation
  • Sauer, T., J. A. Yorke, and M. Casdagli, 1991: Embedology. J. Stat. Phys., 65, 579616, doi:10.1007/BF01053745.

  • Slingo, J., and et al. , 1996: Intraseasonal oscillations in 15 atmospheric general circulation models: Results from an AMIP diagnostic subproject. Climate Dyn., 12, 325357, doi:10.1007/BF00231106.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Subramanian, A., M. Jochum, A. J. Miller, R. Neale, H. Seo, D. Waliser, and R. Murtugudde, 2014: The MJO and global warming: A study in CCSM4. Climate Dyn., 42, 20192031, doi:10.1007/s00382-013-1846-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Székely, E., D. Giannakis, and A. J. Majda, 2016a: Extraction and predictability of coherent intraseasonal signals in infrared brightness temperature data. Climate Dyn., 46, 14731502, doi:10.1007/s00382-015-2658-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Székely, E., D. Giannakis, and A. J. Majda, 2016b: Initiation and termination of intraseasonal oscillations in nonlinear Laplacian spectral analysis indices. Math. Climate Wea. Forecasting, 2, 125, doi:10.1515/mcwf-2016-0001.

    • Search Google Scholar
    • Export Citation
  • Takens, F., 1981: Detecting strange attractors in turbulence. Dynamical Systems and Turbulence, D. Rand and L.-S. Young, Ed., Lecture Notes in Mathematics, Vol. 898, Springer, 366–381, doi:10.1007/bfb0091924.

    • Crossref
    • Export Citation
  • Tung, W.-w., D. Giannakis, and A. J. Majda, 2014: Symmetric and antisymmetric signals in the Madden–Julian Oscillation. Part I: Basic modes in infrared brightness temperature. J. Atmos. Sci., 71, 33023326, doi:10.1175/JAS-D-13-0122.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vitart, F., 2014: Evolution of ECMWF sub-seasonal forecast skill scores. Quart. J. Roy. Meteor. Soc., 140, 18891899, doi:10.1002/qj.2256.

  • von Storch, H., and X. Jinsong, 1990: Principal oscillation pattern analysis of the 30- to 60-day oscillation in the tropical troposphere. Part I: Definition of an index and its prediction. Climate Dyn., 4, 175190, doi:10.1007/BF00209520.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waliser, D. E., 2011: Predictability and forecasting. Intraseasonal Variability in the Atmosphere–Ocean Climate System, 2nd ed. W. K. M. Lau and D. E. Waliser, Eds., Springer, 433–468, doi:10.1007/978-3-642-13914-7_12.

    • Crossref
    • Export Citation
  • Waliser, D. E., C. Jones, J.-K. E. Schemm, and N. E. Graham, 1999: A statistical extended-range tropical forecast model based on the slow evolution of the Madden–Julian oscillation. J. Climate, 12, 19181939, doi:10.1175/1520-0442(1999)012<1918:ASERTF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, B., F. Huang, Z. Wu, J. Yang, X. Fu, and K. Kikuchi, 2009: Multi-scale climate variability of the South China Sea monsoon: A review. Dyn. Atmos. Oceans, 47, 1537, doi:10.1016/j.dynatmoce.2008.09.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Webster, P. J., and R. Lucas, 1992: TOGA COARE: The Coupled Ocean–Atmosphere Response Experiment. Bull. Amer. Meteor. Soc., 73, 13771416, doi:10.1175/1520-0477(1992)073<1377:TCTCOR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wheeler, M. C., and H. H. Hendon, 2004: An all-season real-time multivariate MJO index: Development of an index for monitoring and prediction. Mon. Wea. Rev., 132, 19171932, doi:10.1175/1520-0493(2004)132<1917:AARMMI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xavier, P. K., and B. N. Goswami, 2007: An analog method for real-time forecasting of summer monsoon subseasonal variability. Mon. Wea. Rev., 135, 41494160, doi:10.1175/2007MWR1854.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xiang, B., M. Zhao, X. Jiang, S. J. Lin, T. Li, X. Fu, and G. Vecchi, 2015: The 3–4-week MJO prediction skill in a GFDL coupled model. J. Climate, 28, 53515364, doi:10.1175/JCLI-D-15-0102.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yanai, M., B. Chen, and W.-w. Tung, 2000: The Madden–Julian oscillation observed during the TOGA COARE IOP: Global view. J. Atmos. Sci., 57, 23742396, doi:10.1175/1520-0469(2000)057<2374:TMJOOD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, C., 2005: Madden–Julian oscillation. Rev. Geophys., 43, RG2003, doi:10.1029/2004RG000158.

  • Zhang, C., J. Gottschalck, E. D. Maloney, M. W. Moncrieff, F. Vitart, D. E. Waliser, B. Wang, and M. C. Wheeler, 2013: Cracking the MJO nut. Geophys. Res. Lett., 40, 12231230, doi:10.1002/grl.50244.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, Z., and D. Giannakis, 2016: Analog forecasting with dynamics-adapted kernels. Nonlinearity, 29, 28882939, doi:10.1088/0951-7715/29/9/2888.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 65 65 9
PDF Downloads 51 51 5

Kernel Analog Forecasting of Tropical Intraseasonal Oscillations

View More View Less
  • 1 Courant Institute of Mathematical Sciences, New York University, New York, New York
© Get Permissions
Restricted access

Abstract

This paper presents the results of forecasting the Madden–Julian oscillation (MJO) and boreal summer intraseasonal oscillation (BSISO) through the use of satellite-obtained global brightness temperature data with a recently developed nonparametric empirical method. This new method, referred to as kernel analog forecasting, adopts specific indices extracted using the technique of nonlinear Laplacian spectral analysis as baseline definitions of the intraseasonal oscillations of interest, which are then extended into forecasts through an iterated weighted averaging scheme that exploits the predictability inherent to those indices. The pattern correlation of the forecasts produced in this manner remains above 0.6 for 50 days for both the MJO and BSISO when 23 yr of training data are used and 37 days for the MJO when 9 yr of data are used.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Current affiliation: Department of Electrical and Computer Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois.

Corresponding author e-mail: Romeo Alexander, romeo@cims.nyu.edu

Abstract

This paper presents the results of forecasting the Madden–Julian oscillation (MJO) and boreal summer intraseasonal oscillation (BSISO) through the use of satellite-obtained global brightness temperature data with a recently developed nonparametric empirical method. This new method, referred to as kernel analog forecasting, adopts specific indices extracted using the technique of nonlinear Laplacian spectral analysis as baseline definitions of the intraseasonal oscillations of interest, which are then extended into forecasts through an iterated weighted averaging scheme that exploits the predictability inherent to those indices. The pattern correlation of the forecasts produced in this manner remains above 0.6 for 50 days for both the MJO and BSISO when 23 yr of training data are used and 37 days for the MJO when 9 yr of data are used.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Current affiliation: Department of Electrical and Computer Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois.

Corresponding author e-mail: Romeo Alexander, romeo@cims.nyu.edu
Save