Movies illustrating the nonlinear perspective of climate variability from neural network methods


Neural network (NN) methods have been used to nonlinearly generalize many classical statistical methods, such as regression, principal component analysis, canonical correlation analysis, etc. The nonlinear NN techniques allow the extraction of high fidelity signals from climate data, as illustrated by the movies here.

Click image to see this GIF movie comparing the first mode from the nonlinear principal component analysis (NLPCA) and that from the principal component analysis (PCA) of the tropical Pacific sea surface temperature (SST) anomalies. As the nonlinear principal component (NLPC) or the principal component (PC) swings from one extreme to the other, the climate system goes from extreme La Niña to extreme El Niño. (The movie loops continuously, but pauses for a few seconds at the extreme La Niña and El Niño states). The PCA first mode shows La Niña to be anti-symmetrical to El Niño (but with a weaker magnitude), i.e. the PCA mode is a standing wave. The NLPCA was used to extract the nonlinear relation among the 7 leading PCs. The first NLPCA mode shows the La Niña cool SST anomalies to be located further west, and the El Niño warm SST anomalies to be more intense and located further east than those in the first PCA mode. The NLPCA solution agrees much better with the observations. (For details, see Hsieh, 2007) (preprint). [This movie is also available in AVI format].
[Movie produced by Laure Gaillard]

Click image to see this animated GIF movie comparing the nonlinear and linear projection (i.e. regression) of the El Niño-Southern Oscillation (ENSO) index to the 500 mb geopotential height (Z500) anomaly of the Northern Hemisphere winter, i.e. the movie shows the anomalies in the Z500 field associated with changes in the ENSO index as it swings from one extreme (La Niña, corresponding to cold conditions in the tropical Pacific) to the other extreme (El Niño, warm conditions). The linear projection gives a standing wave response in the Z500 anomaly field as the ENSO index varies, while in the nonlinear projection, the response is not spatially fixed. The presence of substantial response over the Euro-Atlantic region, in the form of a positive "North Atlantic Oscillation" (NAO) pattern (during both extreme La Niña and El Niño) in the nonlinear projection is missing in the linear projection. This shows that there is a nonlinear excitation of the positive NAO pattern by ENSO. (For more details on nonlinear atmospheric teleconnections, see Hsieh et al. 2006). [This movie is also available in AVI format].
[Movie produced by Clément Suavet]

Click image to see this GIF movie comparing the first mode from the nonlinear canonical correlation analysis (NLCCA) and that from the canonical correlation analysis (CCA) of the tropical Pacific sea level pressure (SLP) and sea surface temperature (SST) anomalies. Both methods try to find the strongest correlated patterns between the SLP and the SST anomaly fields. In the movie, the SLP anomalies are shown in the left column and the SST anomalies in the right column, with the NLCCA mode on top of the CCA mode. As the canonical variates u and v swing from one extreme to the other, the climate system goes from extreme La Niña to extreme El Niño. The CCA first mode shows La Niña to be anti-symmetrical to El Niño (but with a weaker magnitude). The NLCCA first mode shows both the SLP and SST anomalies to be located further west during La Niña, and the SLP and SST anomalies to be concentrated further east during El Niño than those in the first CCA mode. (For details, see Hsieh 2001b, or Hsieh, 2004). [This movie is also available in AVI format].
[Movie produced by Clément Suavet]

References:

Hsieh, W.W., 2001. Nonlinear canonical correlation analysis of the tropical Pacific climate variability using a neural network approach. J. Climate, 14: 2528-2539. (reprint in PDF)

Hsieh, W.W., 2004. Nonlinear multivariate and time series analysis by neural network methods. Reviews of Geophysics, 42, RG1003, doi:10.1029/2002RG000112. (reprint in PDF)

Hsieh, W.W., 2007. Nonlinear principal component analysis of noisy data. Neural Networks, 20: 434-443. DOI: 10.1016/j.neunet.2007.04.018 Neural Networks, 20: 434-443. DOI: 10.1016/j.neunet.2007.04.018) (preprint in PDF)

Hsieh, W.W., A. Wu and A. Shabbar, 2006. Nonlinear atmospheric teleconnections. Geophys. Res. Lett. 33, L07714, doi:10.1029/2005GL025471. (preprint in PDF) (Videos).

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