Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 4 pp 131-194 | Cite as

# Synchronous Motions Across the Instrumental Climate Record

## Abstract

The Earth’s climate system bears a rich variety of feedback mechanisms that may give rise to complex, evolving modal structures under internal and external control. Various types of synchronization may be identified in the system’s motion when looking at representative time series of the instrumental period through the glasses of an advanced technique of sparse data approximation, the Matching Pursuit (MP) approach. To disentangle the emerging network of oscillatory modes to the degree that climate dynamics turns out to be separable, a large dictionary of “Gaussian logons,” i.e. frequency modulated (FM) Gabor atoms, is applied. Though the extracted modes make up linear decompositions, this flexible analyzing signal matches highly nonlinear waveforms. Univariate analyses over the period 1870–1997 are presented of a set of customary time series in annual resolution, comprising global and regional climate, central European synoptic systems, German precipitation, and runoff of the Elbe river near Dresden. All the evidence from this first-generation MP-FM study, obtained in subsequent multivariate syntheses, points to dynamically excited regimes of an organized yet complex climate system under permanent change—perhaps a (pre)chaotic one at centennial timescales, suggesting a “chaos control” perspective on global climate dynamics and change. Findings and conclusions include, among others, internal structure of reconstructed insolation, the episodic nature of global warming as reflected in multidecadal temperature modes, their swarm of “interdomain” companions across the whole system that unveils an unknown regime character of interannual climate dynamics, and the apparent onset early in the 1990s of the present thermal stagnation.

## Notes

### Acknowledgements

Thanks are due to Fred Hattermann of the Potsdam Institute for Climate Impact Research (PIK) who provided the Elbe runoff data. Generally, the success of the study hinges on the quality of data, and the author hopes to have expressed his respect to this community in spending substantial effort and using advanced techniques in order to make the best of the data. MP-FM is an own product, but its coding has much profited from the detailed MP description given in [73]. Further sources which helped in own software developments over the years have been acknowledged in [21]. Last but not least, however, graphics solutions as provided by the freely available GrADS [33] and Xvgr packages [99] are explicitly referred to here with due gratitude.

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