The backbone of the climate network

We propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system, relying on the nonlinear mutual information of time series analysis and betweenness centrality of the complex network theory. We show that this approach reveals a rich internal structure in complex climate networks constructed from reanalysis and model surface air temperature data. Our novel method uncovers peculiar wave-like structures of high-energy flow, that we relate to global surface ocean currents. This points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long-term mean (140 years for the model run and 60 years for reanalysis data). We find that these results cannot be obtained using classical linear methods of multivariate data analysis, and have ensured their robustness by intensive significance testing. Copyright c © EPLA, 2009 Introduction. – In the last decade, the complex network paradigm has proven to be a fruitful tool for the investigation of complex systems in various areas of science, e.g., the internet and world wide web in computer science, food webs, gene expression and neural networks in biology, and citation networks in social science [1]. The intricate interplay between the structure and dynamics of real networks has received considerable attention [2]. Particularly, synchronization arising by the transfer of dynamical information in complex network topologies has been studied intensively [3]. The application of complex network theory to climate science is a young field, where only few studies have been reported recently [4–8]. The vertices of a climate network are identified with the spatial grid points of an underlying global climate data set. Edges are added between pairs of vertices depending on the degree of statistical interdependence between the corresponding pairs of anomaly time series taken from the climate data set. Climate networks enable novel insights into the topology and dynamics of the climate system over many spatial scales ranging from local properties as the number of first neighbors of a vertex v (the degree centrality kv) to global network measures such as the clustering coefficient or the average path length. The local degree centrality and related measures have been used (a)E-mail: [email protected] to identify supernodes (regions of high degree centrality) and to associate them to known dynamical interrelations in the atmosphere, called teleconnection patterns, most notably the North Atlantic Oscillation (NAO) [4]. On the global scale, climate networks were found to possess “small-world” properties due to long-range connections (edges linking geographically very distant vertices), that stabilize the climate system and enhance the energy and information transfer within it [4]. By studying the prevalence of long-range connections in El Niño and La Niña climate networks [5] and the time dependence of the number of stable edges [6], it has been shown very recently, that the El Niño-Southern Oscillation (ENSO) has a strong impact on the stability of the climate system. Until now, researchers have used the linear crosscorrelation function of pairs of anomaly time series to quantify the degree of statistical interdependence between different spatial regions. But the highly nonlinear processes at work in the climate system call for the application of nonlinear methods to obtain more reliable results. Here we also use mutual information [9] to construct climate networks allowing to capture linear and nonlinear relationships between time series [8]. Furthermore we use a measure of vertex centrality, betweenness (BC), that is defined locally but takes into account global topological information. Combining these two techniques, we uncover peculiar wave-like structures in the BC fields