Lagged Coupled Climate Networks for Identifying Recurrent Circulation Patterns Behind Extreme Rainfall in Europe

Extreme precipitation over Europe is often linked to large-scale atmospheric circulation anomalies, yet it remains unclear which dynamical features recur systematically across many independent events, and how their influence evolves with time and altitude. In particular, the extent to which coherent, large-scale dynamical structures act as precursors to extreme rainfall has not been quantified so far beyond traditional composite-based approaches.

Here, we introduce a lagged coupled climate-network framework to investigate the interdependency between extreme precipitation events and atmospheric circulation from a functional climate network perspective. Extreme precipitation events are identified from ERA5 precipitation data by applying a local percentile threshold to daily precipitation sums and represented as binary event series, while two-dimensional fields of additional variables in different atmospheric layers—including geopotential height, relative vorticity, and temperature at multiple pressure levels—are treated as continuous variables. Using point-biserial correlation as statistical association measure between these different types of time series, we construct lagged event–field coupled networks that explicitly distinguish positive and negative statistical associations. Network connectivity is quantified through the cross-degree, which measures how many grid points of surface extreme events are significantly linked to a given atmospheric grid point (and vice versa), thereby emphasizing the recurrence and spatial relevance of circulation features rather than their correlation strength alone.

Our analysis reveals a coherent temporal evolution and vertical structure of circulation coupling to hydrometeorological extremes at the surface. At negative lags, cross-degree patterns are dominated by mid- to upper-tropospheric geopotential height and vorticity anomalies, indicating the recurrent presence of large-scale dynamical features prior to extreme precipitation events. With increasing lag, the coupling progressively shifts toward lower tropospheric levels, suggesting a transition from large-scale circulation influences before the events to near-surface circulation imprints afterward. Spatially, regions of enhanced cross-degree exhibit a systematic west-to-east displacement with changing lag, extending from the western North Atlantic and Greenland sector toward continental Europe. This spatial progression is consistent with downstream evolution along the North Atlantic–European circulation corridor. A pronounced and recurrent signal over the British Isles emerges across multiple variables, highlighting this region as a dynamically relevant area in the large-scale circulation context of European precipitation extremes.

By explicitly quantifying where, when, and at which vertical levels circulation anomalies of the same type recur across many extreme events, our coupled network approach provides a complementary perspective to conventional correlation and composite analyses. Our results demonstrate the potential of coupled functional climate networks to identify robust, recurring circulation patterns associated with extreme precipitation, offering new insights into precursor dynamics, vertical coupling, and large-scale organization of midlatitude extremes without assuming a specific underlying mechanism.