Knowledge about relations between changes of air pressure, temperature or other meteorological variables in different locations on the Earth is a key to understand what impacts global change. A new mathematical and computational method uncovers causal relations, gateways and mediators that help to comprehend input and spreading of perturbations in complex spatiotemporal systems such as the climate and assessing the effect of geoengineering interventions or global impact of local weather extremes. The method can also be used for uncovering paths for information dissemination in financial markets or for tracing information transmission in the human brain.