24.02.2010
Synchronized Motions and Detached Events, from Global Climate to the River Basin Scale

A Time Series Study

The study to be outlined aims at contributing to conceptual understanding of climate variability and change, and it goes beyond a specific model-borne, qualitative view on global climate dynamics in tracing its consequences, via Central European climate and weather regimes, down to the river basin of the Middle Elbe. The presentation offers a geometrical interpretation first of
boreal spring-to-autumn intraseasonal climate dynamics and its interannual consequences, draws conclusions then about needs on the techniques of data analysis, offers a preliminary methodological solution, gives a sketch of conceptually relevant results of a terminal, independent synthesis stage following the analyses, and finally discusses a suite of potential applications.

Reasoning about dynamics in the back of climate variability and change may have recourse to well-known competing, partially contradictory, conceptions like
(quasi-) cyclostationarity, stochastic resonance, or "chaos". This reflects the fact that the system's "dynamical status" is unknown and the same has to be stated, unfortunately, for its advanced General Circulation Models (GCMs). Using a small tropospheric GCM, in contrast, attractor studies until the mid-1990s have confirmed Lorenz' conception of structurally conditioned climate variability owing to existence of different seasonal attractors (more correctly: attractor sets) of the summer and winter circulation, respectively. A full route to chaos has been identified here for the boreal summer where the model's seasonal cycle topologically a driven limit cycle) blows up into a torus segment of varying order across the season. Of special interest is the fact that this geometrical phase space object is borne in the atmospheric water cycle, notably in the active-break cycle of the planetary monsoon system. The latter is dynamically represented as a free intraseasonal oscillator, visible in the global system's integrals of motion, with changing recurrence properties and frequency as the season advances. Given the qualitatively correct simulation of tropical/subtropical precipitation fields by this GCM (a task which is notoriously difficult), its hints at substantial
low-dimensional contributions to present-day climate dynamics and variability should be taken seriously, not only in a conceptual sense. A potentially high-dimensional system that obviously behaves low-dimensionally in part necessarily organizes internal synchronizations, other than loose internal coupling in the case of (quasi-)equilibrium dynamics.

Speaking in terms of signal analysis, loose coupling relates to "sparse"
representation of time series, whereas synchronized motions call for "dense" representations. A strictly univariate, sparse climate time series analysis thus serves a null hypothesis here, in a sense, of mutual independence at large. To the extent that the subsequent multivariate synthesis unveils synchronized
motions ('more dense' structures in signal space), however, this null hypothesis is rejected step by step, that is, it becomes more and more improbable as a relevant conception for the data at hand. Sparse time series representations may be found using Singular-system Analysis (SSA), Independent Component Analysis (ICA), Empirical Mode Decomposition (EMD), or the Matching Pursuit (MP) approach to quote just the most advanced, adaptive techniques known today.

Non-adaptive methods like Wavelet or Fourier Transforms (WT, FT) do not generate sparse data structures in general. MP is the method of choice here, furnished with a redundant 'dictionary' of waveforms to be matched to the time series, which comprises the dictionaries of WT and FT but goes far beyond in allowing for frequency modulation (FM) and superresolution. To justify this choice, an intercomparison of some of these methods using a couple of test time series with known internal structure will be presented.