Articles | Volume 22, issue 1
Nonlin. Processes Geophys., 22, 87–108, 2015
Nonlin. Processes Geophys., 22, 87–108, 2015

Research article 03 Feb 2015

Research article | 03 Feb 2015

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

C. A. L. Pires1 and R. A. P. Perdigão2 C. A. L. Pires and R. A. P. Perdigão
  • 1Instituto Dom Luiz (IDL), Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisbon, Portugal
  • 2Institute of Hydraulic Engineering and Water Resources Management, Vienna University of Technology, Vienna, Austria

Abstract. 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.

Short summary
Non-Gaussian joint PDFs and Shannon negentropies allow for nonlinear correlations and synergetic interaction information among random variables. Third-order cross-cumulants (triadic correlations -- TCs) under pair-wise (total or partial) independence are maximized on projections and orthogonal rotations of the full PDF. Fourier analysis allows decomposing TCs as wave resonant triads working as non-Gaussian sources of dynamical predictability. An illustration is given in a minimal fluid model.