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...as been recently suggested that data-driven detection of climate causality networks could be used for deriving hypotheses about causal relationships between prominent modes of atmospheric variability =-=[12,13]-=-. The family of causality methods include linear approaches such as Granger causality analysis [14], as well as more general nonlinear methods. A prominent representative of nonlinear causality assess...

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...s apart and a significance value of α = 0.001 for the conditional independence tests (Fisher Z-tests), the PC algorithm yielded the temporal model shown in Fig. 4. Fig. 5 is a summary graph with the strongest connections from Fig. 4. The numbers next to the arrows indicate the delay in days from potential cause to effect (they are multiples of 3, because we used D = 3). There are a few arrows hidden behind other blocks in Fig. 4. Namely, each compound index, WPO, EPO, PNA and NAO, actually affects itself strongly for 3-6 days, as shown in the self-loops in Fig. 5. For more interpretation, see [20]. Application 2 - Graphs of information flow: One of the most complex applications of causal discovery in climate science is to track the pathways of physical interaction around the globe. In order to do that we define a grid around the globe and evaluate an atmospheric field (such as temperature or geopotential height) at all grid points, which provides time series data at all grid points. Our approach is to then use the temporal version of PC stable to identify the strongest pathways of interactions around the globe based on the time series data [21]. Gaussian graphical models present an alt...

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...ional and geographically distributed climate data with complex dependence structures. Network-based graphical models have been used to discover causality among different modes of climate variability (=-=Ebert-Uphoff and Deng, 2012-=-; Runge et al., 2009). Applications of methods in nonlinear data sciences, from complex networks (Steinhaeuser et al., 2011a) to multifractals (García-Marín et al., 2013; Muzy et al., 2006) and dynami...