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 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.

Parsimonious modeling with information filtering networks

“…Once the sparse precision matrix has been estimated, a number of efficient tools-mostly based on research in sparse numerical linear algebra-can be used to sample from the distribution, calculate conditional probabilities, calculate conditional statistics, and forecast [2,3]. GMRFs are of great importance in many applications spanning computer vision [4], sparse sensing [5], finance [6][7][8][9][10][11], gene expression [12][13][14]; biological neural networks [15], climate networks [16,17]; geostatistics and spatial statistics [18][19][20]. Almost universally, applications require modeling a large number of variables with a relatively small number of observations, and therefore the issue of the statistical significance of the model parameters is very important.…”

A study of links between the Arctic and the midlatitude jet stream using Granger and Pearl causality

“…Here, instead of performing multiple dynamical model simulations to act as interventions, we focus solely on an observational-type analysis, using model output that already exists in place of actual observations. Several different frameworks for observational analysis have been applied to climate science to provide graphical representations of likely cause-effect relationships (Bahadori & Liu, 2011;Chen, Liu, Liu, & Carbonell, 2010;Chu, Danks, & Glymour, 2005;Ebert-Uphoff & Deng, 2012;Ebert-Uphoff & Deng, 2015;McGraw & Barnes, 2018;Runge, 2014;Runge, Heitzig, Petoukhov, & Kurths, 2012;Wang, Banerjee, Hsieh, Ravikumar, & Dhillon, 2013;Zerenner, Friederichs, Lehnertz, & Hense, 2014). However, of highest relevance to the application considered here are causality studies related to the Arctic, primarily the works by Strong, Magnusdottir, and Stern (2009), Matthewman and Magnusdottir (2011), and Kretschmer, Coumou, Donges, and Runge (2016.…”

Evaluating lossy data compression on climate simulation data within a large ensemble

“…Then conditional independence tests (e.g., testing for vanishing partial correlations) are used to disprove causal connections, resulting in a remaining "interaction map" of causal connections (that may or may not be given direction through additional techniques). Such tools were initially applied in the fields of social sciences and economics, but have more recently been applied successfully to climate science data (e.g., Chu et al, 2005;Ebert-Uphoff and Deng, 2012a, b;Zerenner et al, 2014). For example, for atmospheric data, one could imagine using causal discovery methods to understand large-scale atmospheric processes in terms of information flow around the earth.…”