Abstract
In this paper, we investigate both the dominant modes of variability and the large-scale regimes associated with tropical convection that can be recovered from infrared brightness temperature data using data mining and machine learning approaches. A hierarchy of spatiotemporal patterns at different timescales (annual, interannual, intraseasonal, and diurnal) is extracted using a nonlinear dimension reduction method, namely, nonlinear Laplacian spectral analysis (NLSA). The method separates very clearly the boreal winter and boreal summer intraseasonal oscillations as distinct families of modes. The predictability of the Madden-Julian oscillation (MJO) is then quantified using a cluster-based information-theoretic framework adapted for cyclostationary variables. Data clustering is performed in the space of the NLSA temporal patterns and the results show a strong influence of ENSO in the early MJO season.
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References
Aubry N, Lian WY, Titi ES (1993) Preserving symmetries in the proper orthogonal decomposition. SIAM J Sci Comput 14:483–505
Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15:1373–1396
Berry T, Cressman R, Greguric Ferencek Z, Sauer T (2013) Time-scale separation from diffusion-mapped delay coordinates. SIAM J Appl Dyn Syst 12:618–649
Bishop CM (2006) Pattern recognition and machine learning. In: Information science and statistics. Springer, New York
Broomhead DS, King GP (1986) Extracting qualitative dynamics from experimental data. Physica D 20(2–3):217–236
Coifman RR, Lafon S (2006) Diffusion maps. Appl Comput Harmon Anal 21:5–30
Dhillon IS, Guan Y, Kulis B (2004) Kernel k-means, spectral clustering and normalized cuts. In: Proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining, KDD’04, Seattle, pp 551–556
Duda RO, Hart PE, Stork DG (2000) Pattern classification, 2nd edn. Wiley-Interscience, New York
Ghil M et al (2002) Advanced spectral methods for climatic time series. Rev Geophys 40:1-1–1-41
Giannakis D (2015) Dynamics-adapted cone kernels. SIAM J Appl Dyn Syst 14(2):556–608
Giannakis D, Majda AJ (2012a) Limits of predictability in the North Pacific sector of a comprehensive climate model. Geophys Res Lett 39:24602
Giannakis D, Majda AJ (2012b) Quantifying the predictive skill in long-range forecasting. Part I: Coarse-grained predictions in a simple ocean model. J Clim 25:1793–1813
Giannakis D, Majda AJ (2013) Nonlinear Laplacian spectral analysis: capturing intermittent and low-frequency spatiotemporal patterns in high-dimensional data. Stat Anal Data Min 6(3):180–194
Giannakis D, Majda AJ (2014) Data-driven methods for dynamical systems: quantifying predictability and extracting spatiotemporal patterns. In: Melnik R (ed) Mathematical and computational modeling: with applications in engineering and the natural and social sciences. Wiley, Hoboken, p 288
Giannakis D, Majda AJ, Horenko I (2012) Information theory, model error, and predictive skill of stochastic models for complex nonlinear systems. Physica D 241:1735–1752
Ham J, Lee DD, Mika S, Schölkopf B (2004) A kernel view of the dimensionality reduction of manifolds. In: Proceedings of the twenty-first international conference on machine learning, ICML’04, Banff. ACM, pp 369–376
Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 27:417–441
Kikuchi K, Wang B, Kajikawa Y (2012) Bimodal representation of the tropical intraseasonal oscillation. Clim Dyn 38:1989–2000
MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth berkeley symposium on mathematical statistics and probability, vol 1. University of California Press, Berkeley, CA, pp 281–297
Madden RA, Julian PR (1972) Description of global-scale circulation cells in the tropics with a 40–50 day period. J Atmos Sci 29(6):1109–1123
Sauer T, Yorke JA, Casdagli M (1991) Embedology. J Stat Phys 65(3–4):579–616
Schölkopf B, Smola A, Müller K (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10:1299–1319
Székely E, Giannakis D, Majda AJ (2014) Extraction and predictability of coherent intraseasonal signals in infrared brightness temperature data. Clim Dyn. doi:10.1007/s00382-015-2658-2
Takens F (1981) Detecting strange attractors in turbulence. In: Dynamical systems and turbulence, Warwick 1980, vol 898. Springer, Berlin/New York, pp 366–381
Tung Ww, Giannakis D, Majda AJ (2014) Symmetric and antisymmetric signals in MJO deep convection. Part I: basic modes in infrared brightness temperature. J Atmos Sci 71:3302–3326
Wheeler MC, Hendon HH (2004) An all-season real-time multivariate MJO index: development of an index for monitoring and prediction. Mon Weather Rev 132(8):1917–1932
Yanai M, Chen B, Tung Ww (2000) The Madden-Julian oscillation observed during the TOGA COARE IOP: global view. J Atmos Sci 57(15):2374–2396
Zhang C, Dong M (2004) Seasonality in the Madden-Julian oscillation. J Clim 17:3169–3180
Acknowledgements
The research of Andrew Majda and Dimitrios Giannakis is partially supported by ONR MURI grant 25-74200-F7112. Eniko Székely is supported as a postdoctoral fellow through this grant. The authors wish to thank Wen-wen Tung for stimulating discussions.
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Székely, E., Giannakis, D., Majda, A.J. (2015). Kernel and Information-Theoretic Methods for the Extraction and Predictability of Organized Tropical Convection. In: Lakshmanan, V., Gilleland, E., McGovern, A., Tingley, M. (eds) Machine Learning and Data Mining Approaches to Climate Science. Springer, Cham. https://doi.org/10.1007/978-3-319-17220-0_14
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DOI: https://doi.org/10.1007/978-3-319-17220-0_14
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