Cross-Scale Interactions and Information Transfer

Abstract

An information-theoretic approach for detecting interactions and information transfer between two systems is extended to interactions between dynamical phenomena evolving on different time scales of a complex, multiscale process. The approach is demonstrated in the detection of an information transfer from larger to smaller time scales in a model multifractal process and applied in a study of cross-scale interactions in atmospheric dynamics. Applying a form of the conditional mutual information and a statistical test based on the Fourier transform and multifractal surrogate data to about a century long records of daily mean surface air temperature from various European locations, an information transfer from larger to smaller time scales has been observed as the influence of the phase of slow oscillatory phenomena with the periods around 6-11 years on the amplitudes of the variability characterized by the smaller temporal scales from a few months to 4-5 years. These directed cross-scale interactions have a non-negligible effect on interannual air temperature variability in a large area of Europe.

Spatial and temporal scales of atmospheric dynamics

“…When we include with these the higher-frequency cycles apparent in climate dynamics, such as the annual cycle, their harmonics, diurnal cycle and so on, we come to the conclusion that many distinct behaviours in climate dynamics can be described in frequency-domain. Or put differently, they exhibit oscillatory or quasi-oscillatory behaviour, the maxima and minima are recurring with some approximate period and the dynamics of the climate as a whole can be thought of as a collection (or a network) of these coupled phenomena, from which arises complex multi-scale behaviour we can measure by the means of temperature, pressure and other atmospheric observables [Paluš, 2014a]. The immediate connection one usually makes with the word "Fourier" is that of a spectrum.…”

“…Typically, the bias is larger in the direction from slower to a faster system (considering typical periods, in this case, the frequencies ω 1 and ω 2 ), or from a system with simpler dynamics to a system with more complex dynamics (e.g. a periodic system seemingly drives a chaotic system) [Paluš, 2014a]. The noise level can also bias the estimates of CMI.…”

“…For a numerical experiment in the aforementioned setting, let us follow Paluš [2014a], section 3. For the first experiment, 65 536 samples of Gaussian white noise were generated.…”

“…(c) z-score (colour-coded for z > 2) and (d) significance levels (colour-coded if p < 0.05). For the second numerical experiment, Paluš [2014a] has chosen a dyadic tree of wavelet coefficients, which is constructed using random multipliers with a log-normal distribution [Paluš, 2008]. Same sample size as before is generated from this multifractal process and similar methodology is applied to infer the cross-scale interactions in this sample.…”

“…scales 8 and 16, or 16 and 32, etc are coupled). Other question would be whether these cross-scale interactions are symmetrical or directed, and Paluš [2014a] answered the question by computing the conditional mutual information in form I(φ 1 (t); φ 2 (t + τ) | φ 2 (t), φ 2 (t − η), φ 2 (t − 2η)) to estimate the directed phase-phase coupling. Again, the true cross-scale directed interactions are visible only after estimating the empirical distribution using 1000 FT surrogate data realisations.…”