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.

An information-theoretic approach for studying synchronization phenomena in experimental bivariate time series is presented. “Coarse-grained” information rates are introduced and their ability to indicate generalized synchronization as well as to establish a “direction of information flow” between coupled systems, i.e., to discern the driving from the driven (response) system, is demonstrated using numerically generated time series from unidirectionally coupled chaotic systems. The method introduced is then applied in a case study of electroencephalogram recordings of an epileptic patient. Synchronization events leading to seizures have been found on two levels of organization of brain tissues and “directions of information flow” among brain areas have been identified. This allows localization of the primary epileptogenic areas, also confirmed by magnetic resonance imaging and pasitron emission tomography scans.

We discuss some problems encountered in inference of directionality of coupling, or, in the case of two interacting systems, in inference of causality from bivariate time series. We identify factors and influences that can lead to either decreased test sensitivity or false detections and propose ways to cope with them in order to perform tests with high sensitivity and a low rate of false positive results.

A directionality index based on conditional mutual information is proposed for application to the instantaneous phases of weakly coupled oscillators. Its abilities to distinguish unidirectional from bidirectional coupling, as well as to reveal and quantify asymmetry in bidirectional coupling, are demonstrated using numerical examples of quasiperiodic, chaotic, and noisy oscillators, as well as real human cardiorespiratory data.