Fig. 1

Example applications of causal inference methods in Earth system sciences. a Tropical climate example of dependencies between monthly surface pressure anomalies in the West Pacific (WPAC, regions depicted as shaded boxes below nodes), as well as surface air temperature anomalies in the Central Pacific (CPAC) and East Pacific (EPAC). Correlation analysis and standard bivariate Granger causality (GC) result in a completely connected graph while a multivariate causal method (PCMCI)^23,24 better identifies the Walker circulation: Anomalous warm surface air in the East Pacific is carried westward by trade winds across the Central Pacific. Then the moist air rises towards the upper troposphere over the West Pacific and the circulation is closed by the cool and dry air sinking eastward across the entire tropical Pacific. PCMCI systematically identifies common drivers and indirect links among time-lagged variables, in this particular example based on partial correlation tests. Details on data in ref. ⁵³. b Application of a similar method to Arctic climate²⁵: Barents and Kara sea ice concentrations (BK-SIC) are detected to be important drivers of mid-latitude circulation, influencing winter Arctic Oscillation (AO) via tropospheric mechanisms and through processes involving vertical wave activity fluxes (v-flux) and the stratospheric Polar vortex (PoV). Details on methodology and data in ref. ²⁵. ^©American Meteorological Society. Used with permission. c Application from ecology (details in ref. ¹¹): dependencies between sea surface temperatures (SST), and California landings of Pacific sardine (Sardinos sagax) and northern anchovy (Engraulis mordax). Granger causality analysis only detects a spurious link, while convergent cross mapping (CCM) shows that sardine and anchovy abundances are both affected by SSTs