a, c, e, Plots of link distances (red and blue circles), power-law fits for the range 100–2,500 km (dashed black lines) and KDEs of the distribution of all possible great-circle distances (solid black lines) for τmax = 3 days (a), τmax = 10 days (b) and τmax = 30 days (c). The vertical line at d = 2,500 km marks the regime shift from regional weather systems to large-scale teleconnections. We note that the distribution of significant link distances below 2,500 km (red circles) decays slightly faster for τmax = 3 days than for τmax = 10 days or τmax = 30 days, implying that 3 days are not sufficient to capture the entire global-scale teleconnection pattern. b, d, f, Link bundles attached to SCA are shown for τmax = 3 days (b), τmax = 10 days (d) and τmax = 30 days (f), after correcting for the multiple-comparison bias. Links shorter (longer) than 2,500 km are shown in red (blue). A spherical Gaussian KDE of the regional link density, in combination with a null model of randomly distributed links, is used to determine link bundles; links that are not part of significant bundles are omitted (Methods section ‘Significance of spatial patterns’). Significant link bundles are shown by blue contours in units of standard deviations above the mean. The mean and the standard deviation are inferred from the null model of the regional link density. The black contour lines delineate areas in which the regional link density is higher than the 99.9th percentile of the null-model distribution.