Identifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Earth's climate to volcanic eruptions, extreme events or geoengineering. Here a data-driven approach is introduced based on a dimension reduction, causal reconstruction, and novel network measures based on causal effect theory that go beyond standard complex network tools by distinguishing direct from indirect pathways. Applied to a data set of atmospheric dynamics, the method identifies several strongly uplifting regions acting as major gateways of perturbations spreading in the atmosphere. Additionally, the method provides a stricter statistical approach to pathways of atmospheric teleconnections, yielding insights into the Pacific-Indian Ocean interaction relevant for monsoonal dynamics. Also for neuroscience or power grids, the novel causal interaction perspective provides a complementary approach to simulations or experiments for understanding the functioning of complex spatio-temporal systems with potential applications in increasing their resilience to shocks or extreme events.

Computer Science Institute Charles University Malostranské náměstí 2 25 Prague 1 18000 Czech Republic

Department of Atmospheric Physics Charles University 5 Holešovičkách 2 Prague 8 18000 Czech Republic

Department of Control Theory Nizhny Novgorod State University Gagarin Avenue 23 Nizhny Novgorod 606950 Russia

Department of Nonlinear Dynamics and Complex Systems Institute of Computer Science Academy of Sciences of the Czech Republic Pod vodárenskou věží 2 Prague 8 18207 Czech Republic

Department of Physics Humboldt University Newtonstrasse 15 Berlin 12489 Germany

Institute for Complex Systems and Mathematical Biology University of Aberdeen Aberdeen AB24 3UE UK

Institute of Applied Physics of the Russian Academy of Sciences Ul Ulyanova 46 603950 Nizhny Novgorod Russia

Potsdam Institute for Climate Impact Research PO Box 60 12 03 Potsdam 14412 Germany

Stockholm Resilience Centre Stockholm University Kräftriket 2B Stockholm 11419 Sweden

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