Climatic observables are often correlated across long spatial distances, and extreme events, such as heatwaves or floods, are typically assumed to be related to such teleconnections1,2. Revealing atmospheric teleconnection patterns and understanding their underlying mechanisms is of great importance for weather forecasting in general and extreme-event prediction in particular3,4, especially considering that the characteristics of extreme events have been suggested to change under ongoing anthropogenic climate change5,6,7,8. Here we reveal the global coupling pattern of extreme-rainfall events by applying complex-network methodology to high-resolution satellite data and introducing a technique that corrects for multiple-comparison bias in functional networks. We find that the distance distribution of significant connections (P < 0.005) around the globe decays according to a power law up to distances of about 2,500 kilometres. For longer distances, the probability of significant connections is much higher than expected from the scaling of the power law. We attribute the shorter, power-law-distributed connections to regional weather systems. The longer, super-power-law-distributed connections form a global rainfall teleconnection pattern that is probably controlled by upper-level Rossby waves. We show that extreme-rainfall events in the monsoon systems of south-central Asia, east Asia and Africa are significantly synchronized. Moreover, we uncover concise links between south-central Asia and the European and North American extratropics, as well as the Southern Hemisphere extratropics. Analysis of the atmospheric conditions that lead to these teleconnections confirms Rossby waves as the physical mechanism underlying these global teleconnection patterns and emphasizes their crucial role in dynamical tropical–extratropical couplings. Our results provide insights into the function of Rossby waves in creating stable, global-scale dependencies of extreme-rainfall events, and into the potential predictability of associated natural hazards.
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This study was conducted within the scope of IRTG 1740/TRP 2015/50122-0, funded by the German Science Foundation (DFG)/FAPESP. N.B. acknowledges further funding by the Alexander von Humboldt Foundation, the German Federal Ministry for Education and Research and DFG (reference BO 4455/1-1). B.G. is funded by the DFG project IUCLiD (project number DFG MA4759/8) and has received additional partial funding from the European Union’s Horizon 2020 Research and Innovation programme under the Marie Skłodowska-Curie grant agreement number 691037 (project QUEST) and MWFK Brandenburg.
Nature thanks M. Barreiro, A. Gozolchiani and the other anonymous reviewer(s) for their contribution to the peer review of this work.
The authors declare no competing interests.
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Extended data figures and tables
Extended Data Fig. 1 Means and standard deviations of the null-model distribution for the regional link density.
a, Mean of the null-model distribution for the regional link density, obtained by randomly redistributing the links as described in the Methods section ‘Significance of spatial patterns’. b, Standard deviation of the same null-model distribution as in a. The white contour lines indicate regions in which the regional link density of the observations is higher than the 99.9th percentile of the null model. Hatched areas indicate regions with fewer than three events in total, which are excluded from the analysis.
Plot of link distances (red and blue circles) restricted to links attached to SCA (red circles), the power-law fit for the range 100–2,500 km (dashed black line) and the KDE of the distribution of all possible great-circle distances (solid black line). The distance distribution of links that remain after correcting for the multiple-comparison bias (blue circles; see Methods section ‘Significance of spatial patterns’) resembles the original distribution closely.
Extended Data Fig. 3 Extended atmospheric conditions for the teleconnection pattern between Europe and SCA.
a–h, Composite anomalies of precipitable water (PRWT; a), TRMM rainfall (b), geopotential height (GPH; c, e, g) and streamfunction (PSI; d, f, h) at high (c, d), middle (e, f) and low (g, h) atmospheric levels. The anomalies are centred at day 3 after the maximum ERE occurrence in Europe, with significant subsequent counterparts in SCA. The two regions are indicated by magenta boxes.
Extended Data Fig. 4 Dependence of ERE occurrence in SCA on the phase of the MJO and the time of the season.
a, Frequency of EREs in SCA over the eight phases of the MJO (blue) and corresponding distribution for all days during the JJA season over these phases (red). We note that EREs in SCA occur predominantly during phases 1 and 2. b, Frequency of EREs in Europe with synchronous subsequent counterparts in SCA over the months of June, July, August and September.
Extended Data Fig. 5 Distance distributions of extreme-event synchronizations in the tropics and extratropics.
a, Link distance distributions for the December–January–February season are shown for the following cases: considering only links within the tropics (green squares), links within the tropics and to the extratropics of both hemispheres (magenta diamonds), links connecting the tropics and the extratropics of both hemispheres (cyan stars), links within the Northern Hemisphere (NH; upward red triangles) and links within the Southern Hemisphere (SH; downward blue triangles). b, Same as a, but for the JJA season. The distance distributions for all links taken together (as in Fig. 2) are indicated by black circles in both panels. We note that the super-power-law part of the distribution (that is, the part of the distribution for distances longer than 2,500 km) is substantially suppressed if the analysis is restricted to the global tropics (green squares), whereas it remains strong if links to the extratropics are included (magenta diamonds). In particular, the super-power-law part is much more pronounced if only the links connecting the tropics with the extratropics are considered, compared with the distribution of all links (black circles). We also note that the distributions are very similar for both seasons.
Extended Data Fig. 6 Comparison of the global distance distribution and teleconnection patterns in SCA for different event thresholds.
a, Fraction of links longer than 2,500 km (blue) and median of the link-distance distribution (orange) for different event percentile thresholds. Both quantities remain similar over the range of thresholds, with slight increases towards the strongest events. b, d, f, h, The corresponding distance distributions are shown for the 80th (b), 85th (d), 90th (f) and 95th (h) percentiles for comparison. c, e, g, i, Significant link bundles attached to SCA are also shown for events above the 80th (c), 85th (e), 90th (g) and 95th (i) percentiles. 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 line delineates areas in which the regional link density is higher than the 99.9th percentile of the null-model distribution.
Extended Data Fig. 7 Distance distribution and teleconnection pattern in SCA for different extreme-event thresholds.
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 EREs above the 94th (a), 95th (c) and 96th (e) percentile. The vertical line at d = 2,500 km marks the regime shift from regional weather systems to large-scale teleconnections. We note that the power-law exponent remains very similar over this range, indicating that the 1/d decay of the distance distribution is robust. b, d, f, Link bundles attached to SCA are shown for EREs above the 94th (P94; b), 95th (P95; d) and 96th (P96; f) percentile, 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.
Extended Data Fig. 8 Distance distribution of extreme-event synchronizations and teleconnection pattern in SCA for different values of τmax.
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.
Extended Data Fig. 9 Atmospheric conditions for the teleconnection pattern between Europe and SCA for different cutoff values of the low-pass filter.
a, Lead–lag correlations (solid black line) of timeseries obtained from spatially averaging the daily numbers of EREs in boxes in Europe (EUR; 42° N to 50° N, 3° E to 15° E) and SCA. The timeseries are low-pass-filtered (LP) at a cutoff period of 8 days (Methods section ‘Identification of specific times with high synchronization’). b, Composite anomalies of TRMM rainfall for days with high numbers of EREs in Europe that are followed by associated EREs in SCA. c, Same as b, but 3 days later. d, Composite anomalies of the meridional wind component v at 250 hPa for the same time steps as in b. e, Same as d, but 3 days later. f–j, Same as a–e, but for a cutoff of 12 days.
Extended Data Fig. 10 Distance distribution of extreme-event synchronizations based on the GPCP instead of the TRMM dataset.
Plot of link distances (red and blue circles), power-law fit for the range 100 km–2,500 km (dashed black line) and KDE of the distribution of all possible great-circle distances (solid black line) for EREs above the 95th percentile, derived from the GPCP instead of the TRMM dataset. The vertical line at d = 2,500 km marks the regime shift from regional weather systems to large-scale teleconnections. We note that in contrast to the TRMM data, the GPCP data extend to latitudes λ beyond 50°. The spatial distance that corresponds to a resolution of 1° scales with (111 km) × cos(λ), and therefore the distance distribution includes distances below 100 km. The part of the distribution that is relevant for comparison with that obtained from the TRMM data (Fig. 2) is for distances above 100 km. For smaller distances, a bias exists owing to the very small distances between grid cells near the poles.
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Boers, N., Goswami, B., Rheinwalt, A. et al. Complex networks reveal global pattern of extreme-rainfall teleconnections. Nature 566, 373–377 (2019). https://doi.org/10.1038/s41586-018-0872-x
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