Fig. 3: Regions and links inference with δ-MAPS and PCMCI.

a Region map extracted from HadISST dataset with δ-MAPS algorithm. Thirty regions are identified and associated to a signal (cumulative Sea Surface Temperature anomalies). b Corresponding weight map: each region is colored as function of its weight (sum of covariances with all other regions divided by total sum of covariance). The region with biggest weight lies in the central east Pacific Ocean, and is referred to as the El Nino Southern Oscillation(\({ENSO}\) region. c SST anomalies in ENSO region in HadISST. d Nine regions which serve as nodes for the causal network, labeled with their names: the \({ENSO}\) region, the Indian Ocean (\({IO}\)) region, the Indo-Pacific Warm Pool (\({IPWP}\)) region, the region in South Pacific (\({SP}\)) Ocean, the regions in the Western Tropical Pacific Ocean in the north and south hemisphere (\({{WP}}_{n}\) and \({{WP}}_{s}\)), the regions in the Tropical Atlantic Ocean in the north and south hemisphere (\({{TA}}_{n}\) and \({{TA}}_{s}\)) and the region in north of the Tropical Pacific (\({{TP}}_{n}\)). Regions are colored as function of their Average Causal Effect (\({ACE}\)) value in the reference HadISST dataset. The \({ENSO}\) region has the largest \({ACE}\) (e) Causal network reconstructed from nine regions with PCMCI algorithm, and its reference causal effects inferred in HadISST dataset with a lag of one month. Only causal paths at lag one month are displayed here. Link are labeled with the value of the lag \(\tau\) in months and the value of the path coefficient \(\varPhi\) which is equal to causal effect for direct causal path. Red and blue link respectively indicate positive and negative causal effects (sign of the path coefficient \(\varPhi\)). Nodes are colored as function of the \({ACE}\) displayed on (d).