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

Eigen techniques such as empirical orthogonal func1 tion (EOF) or coupled pattern (CP) / maximum covariance 2 analysis have been frequently used for detecting patterns 3 in multivariate climatological data sets. Recently, statisti4 cal methods originating from the theory of complex net5 works have been employed for the very same purpose of 6 spatio-temporal analysis. This climate network (CN) anal7 ysis is usually based on the same set of similarity matrices 8 as is used in classical EOF or CP analysis, e.g., the corre9 lation matrix of a single climatological field or the cross10 correlation matrix between two distinct climatological fields. 11 In this study, formal relationships as well as conceptual dif12 ferences between both eigen and network approaches are de13 rived and illustrated using global precipitation, evaporation 14 and surface air temperature data sets. These results allow 15 us to pinpoint that CN analysis can complement classical 16 eigen techniques and provides additional information on the 17 Jonathan F. Donges · Norbert Marwan · Jürgen Kurths Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany E-mail: [email protected] Jonathan F. Donges Stockholm Resilience Center, Stockholm University, Kräftriket 2B, 114 19 Stockholm, Sweden Irina Petrova Max-Planck-Institute for Meteorology, KlimaCampus, 20146 Hamburg, Germany Alexander Loew Department of Geography, University of Munich (LMU), Luisenstr. 37, 80333 Munich, Germany Jürgen Kurths Department of Physics, Humboldt University, Newtonstr. 15, 12489 Berlin, Germany Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB243UE, United Kingdom Department of Control Theory, Nizhny Novgorod State University, 603950 Nizhny Novgorod, Russia higher-order structure of statistical interrelationships in cli18 matological data. Hence, CNs are a valuable supplement to 19 the statistical toolbox of the climatologist, particularly for 20 making sense out of very large data sets such as those gen21 erated by satellite observations and climate model intercom22 parison exercises. 23