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Title: A Gaussian graphical model approach to climate networks

Abstract

Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and stronglymore » locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.« less

Authors:
 [1]; ;  [1];  [2]
  1. Meteorological Institute, University of Bonn, Auf dem Hügel 20, 53121 Bonn (Germany)
  2. Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn (Germany)
Publication Date:
OSTI Identifier:
22250977
Resource Type:
Journal Article
Journal Name:
Chaos (Woodbury, N. Y.)
Additional Journal Information:
Journal Volume: 24; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLIMATES; CORRELATIONS; EARTH PLANET; GRIDS; HARMONICS; LENGTH; SPACE

Citation Formats

Zerenner, Tanja, Friederichs, Petra, Hense, Andreas, Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn, Lehnertz, Klaus, Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn. A Gaussian graphical model approach to climate networks. United States: N. p., 2014. Web. doi:10.1063/1.4870402.
Zerenner, Tanja, Friederichs, Petra, Hense, Andreas, Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn, Lehnertz, Klaus, Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, & Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn. A Gaussian graphical model approach to climate networks. United States. https://doi.org/10.1063/1.4870402
Zerenner, Tanja, Friederichs, Petra, Hense, Andreas, Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn, Lehnertz, Klaus, Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn. 2014. "A Gaussian graphical model approach to climate networks". United States. https://doi.org/10.1063/1.4870402.
@article{osti_22250977,
title = {A Gaussian graphical model approach to climate networks},
author = {Zerenner, Tanja and Friederichs, Petra and Hense, Andreas and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn and Lehnertz, Klaus and Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn},
abstractNote = {Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.},
doi = {10.1063/1.4870402},
url = {https://www.osti.gov/biblio/22250977}, journal = {Chaos (Woodbury, N. Y.)},
issn = {1054-1500},
number = 2,
volume = 24,
place = {United States},
year = {Sun Jun 15 00:00:00 EDT 2014},
month = {Sun Jun 15 00:00:00 EDT 2014}
}