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Quantification of relations between measured variables of interest bystatistical measures of dependence is a common step in analysis of climatedata. The term "connectivity" is used in the network context including thestudy of complex coupled dynamical systems. The choice of dependence measure iskey for the results of the subsequent analysis and interpretation. The use oflinear Pearson's correlation coefficient is widespread and convenient. On theother side, as the climate is widely acknowledged to be a nonlinear system,nonlinear connectivity quantification methods, such as those based oninformation-theoretical concepts, are increasingly used for this purpose.  In this paper we outline an approach that enables well informed choice ofconnectivity method for a given type of data, improving the subsequentinterpretation of the results. The presented multi-step approach includesstatistical testing, quantification of the specific non-linear contribution tothe interaction information, localization of nodes with strongest nonlinearcontribution and assessment of the role of specific temporal patterns,including signal nonstationarities. In detail we study the consequences of thechoice of a general nonlinear connectivity measure, namely mutual information,focusing on its relevance and potential alterations in the discovereddependence structure.  We document the method by applying it on monthly mean temperature data fromthe NCEP/NCAR reanalysis dataset as well as the ERA dataset. We have been ableto identify main sources of observed non-linearity in inter-node couplings.Detailed analysis suggested an important role of several sources ofnonstationarity within the climate data. The quantitative role of genuinenonlinear coupling at this scale has proven to be almost negligible, providingquantitative support for the use of linear methods for this type of data.

Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity