Non-Gaussian interaction information: estimation, optimization and diagnostic application of triadic wave resonance

• Published in: Nonlinear processes in geophysics Vol. 22; no. 1; pp. 87 - 108
• Main Authors: Pires, C. A. L., Perdigão, R. A. P.
• Format: Journal Article
• Language: English
• Published: Gottingen Copernicus GmbH 01-01-2015; Copernicus Publications
• Subjects: Correlation analysis; Fluid mechanics; Geophysics; Optimization techniques; Oscillators; Principal components analysis; Probability distribution
• ISSN: 1607-7946; 1023-5809; 1607-7946
• DOI: 10.5194/npg-22-87-2015

Non-Gaussian multivariate probability distributions, derived from climate and geofluid statistics, allow for nonlinear correlations between linearly uncorrelated components, due to joint Shannon negentropies. Triadic statistical dependence under pair-wise (total or partial) independence is thus possible. Synergy or interaction information among triads is estimated. We formulate an optimization method of triads in the space of orthogonal rotations of normalized principal components, relying on the maximization of third-order cross-cumulants. Its application to a minimal one-dimensional, periodic, advective model leads to enhanced triads that occur between oscillating components of circular or locally confined wave trains satisfying the triadic wave resonance condition.