Community structure and dynamics in climate networks Anastasios A. Tsonis • Geli Wang • Kyle L. Swanson • Francisco A. Rodrigues • Luciano da Fontura Costa Received: 15 March 2010 / Accepted: 18 June 2010 / Published online: 6 July 2010 Ó Springer-Verlag 2010 Abstract We consider climate networks constructed from observed and model simulated fields of three climate variables and investigate their community structure. We find that for all fields the number of effective communities is rather small (four to five). We are able to trace the origin of these communities to certain dynamical properties of climate. Our results suggest that the complete complexity of the climate system condenses beyond the ‘weather’ time scales into a small number of low-dimensional interacting components and provide clues as to the nature of the cli- mate subsystems underlying these components. Keywords Networks  Teleconnection patterns  Climate variability 1 Introduction Climate exhibits variability over a wide range of space and time scales, from ‘weather’ at small spatio-temporal scales to ‘climate’ at large scales. However, it remains an open question whether a single dynamical system dictates the complete range of variability, or whether the high-dimensional (complicated) small-scale variability collapses at larger scales into a small number of nonlinear low-dimensional systems whose interplay adequately describes variability on these larger scales. The latter viewpoint is strongly suggested by nonlinear time series analysis of numerous records in the last 25 years. Although the procedures underlying such an analysis are rather demanding and not always applied properly, convincing evidence has emerged that variability over inter-annual, decadal, and longer time scales is characterized by small correlation dimensions (Tsonis 1992; Tsonis 2001). An interpretation of small dimensionalities in climate is that they represent the dynamics of subsystems, e.g. El Nin ˜o, which appear at specific space and time scales (Tsonis and Elsner 1989; Lorenz 1991). Up to now, however, the relevant climate subsystems and the variables defining their state space have not been adequately identified, making extensions to physics and dynamics impossible. Here we employ a newly developed approach, which not only confirms that indeed the number of subsystems is small but also identifies the geographical basis and physical mecha- nisms underlying these subsystems. A network is defined by a set of nodes and their links, where any pair of nodes is connected according to some rule. The topology of the network can reveal important and novel features of the system it represents (Albert and Barabasi 2002; Strogatz 2001; da F. Costa et al. 2007). One such feature is communities (Newman and Girvan 2004). Communities represent groups of densely connected nodes with only a few connections between groups. It has been conjectured that each community represents a subsystem, which operates relatively independent of the other com- munities (Arenas et al. 2006). Thus, identification of these communities can offer useful insights about dynamics. In addition, communities can be associated to network A. A. Tsonis (&)  K. L. Swanson Department of Mathematical Sciences, Atmospheric Sciences Group, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA e-mail: aatsonis@uwm.edu G. Wang LAGEO, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China F. A. Rodrigues  L. d. F. Costa Institute of Physics at Sao Carlos, University of Sao Paulo, P.O. Box 369, Sao Carlos, SP 13560-970, Brazil 123 Clim Dyn (2011) 37:933–940 DOI 10.1007/s00382-010-0874-3