Links matrix Every monthly phenomenon paired with every other, with false discovery control

Data. 24 monthly series of the observatory, from January 1979 (start of the satellite era) or their first month; monthly means of the daily and hourly series; monthly number of M ≥ 6 earthquakes from the USGS catalogue; incomplete months left out.

Preprocessing. Gaps of up to three months interpolated; CO₂ and CH₄ taken as 12-month growth; anomaly to the mean of each calendar month (seasonal cycle removed); centred 121-month running mean subtracted (trends and variations longer than 10 years removed); series standardised.

Statistic. For each pair, Pearson correlation at every lag from −12 to +12 months, over the longest common period without gaps (at least 180 months); the largest in absolute value is kept.

Significance. 2,999 phase-randomised surrogates of the first series (Ebisuzaki, 1997): they keep its spectrum, hence its autocorrelation, and the same search for the best lag is repeated; p = (1 + number of surrogates at least as correlated) / 3,000. This accounts both for the persistence of the series and for the choice of the lag.

Multiple tests. 276 pairs tested: at 5 %, a dozen would come out by chance. The Benjamini–Hochberg (1995) false discovery rate, recommended for such screenings (Wilks, 2016), limits the share of false links among those kept to 5 % on average (q ≤ 0.05).

Without ENSO. Each series is regressed by least squares on Niño 3.4 lagged by 0 to 6 months, then the matrix is recomputed on the residuals. A simple linear method; Compo and Sardeshmukh (2010) propose a fuller dynamical version.

Computed by the Python pipeline of the observatory (numpy, data-pipeline/py/obspipe/links.py), with a fixed seed: the result is reproducible.