How complex climate networks complement eigen techniques for the statistical analysis of climatological data

Abstract

Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP)/maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using global precipitation, evaporation and surface air temperature data sets. These results allow us to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises

Pairwise network information and nonlinear correlations

“…These techniques are widespread since they provide greatly simplified descriptions of complex systems, and allow for the analysis of what might otherwise be intractable problems [4]. In particular, functional networks have been widely applied in fields such as neuroscience [4,5], genetics [6], and cell physiology [7], as well as in climate research [1,8].…”

“…Pairwise measures of dependence such as crosscorrelations (as measured by the Pearson correlation coefficient or covariance matrix) and mutual information are widely used to characterize the interactions within complex systems. They are a key ingredient to techniques such as principal component analysis, empirical orthogonal functions, and functional networks (networks inferred from dynamical time series) [1][2][3]. These techniques are widespread since they provide greatly simplified descriptions of complex systems, and allow for the analysis of what might otherwise be intractable problems [4].…”

“…This has not been done in the vast majority of applications in the past. Due to the computational efficiency, our proposed methodology should allow to revisit this question, especially in areas where functional networks have already been widely applied such as in climate research [1,8,9,50].…”

Unified functional network and nonlinear time series analysis for complex systems science: Thepyunicornpackage

“…20 It has been already successfully used in a wide variety of applications, ranging from the complex structure of teleconnections in the climate system, 15,18,49 including backbones and bottlenecks, 19,89 to dynamics and predictability of the El Niño-Southern Oscillation (ENSO). 66,92,93 Climate networks (class climate.ClimateNetwork) represent strong statistical interrelationships between time series and are typically reconstructed by thresholding the matrix of a statistical similarity measure S (Fig.…”

“…11 In the last several years, two strands of research have taken advantage of the synergies obtained by combining complex network theory and nonlinear time series analysis. On the one hand, the analysis of functional networks put forward in neuroscience [12][13][14] and climatology [15][16][17][18][19][20] as well as other application areas, such as economics and finance, 21 applies methods from linear and nonlinear time series analysis to construct networks of statistical interrelationships among a set of time series and, subsequently, studies the resulting functional networks by means of methods from a)…”