Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks where individual nodes represent different shares on a spherical surface, and describe a strategy for correcting for this effect. Moreover, we illustrate the application of the mentioned edge directionality properties to different examples of real-world spatial networks in spherical geometry (with or without the geometric correction depending on each specific case), including functional climate networks, transportation and trade networks. In climate networks, our approach highlights relevant patterns like large-scale circulation cells, the El Niño-Southern Oscillation and the Atlantic Niño. In an air transportation network, we are able to characterize distinct air transportation zones, while we confirm the important role of the European Union for the global economy by identifying convergent edge directionality patterns in the world trade network.
The Earth’s climate is a complex system characterized by multi-scale nonlinear interrelationships between different subsystems like atmosphere and ocean. Among others, the mutual interdependence between sea surface temperatures (SST) and precipitation (PCP) has important implications for ecosystems and societies in vast parts of the globe but is still far from being completely understood. In this context, the globally most relevant coupled ocean–atmosphere phenomenon is the El Niño–Southern Oscillation (ENSO), which strongly affects large-scale SST variability as well as PCP patterns all around the globe. Although significant achievements have been made to foster our understanding of ENSO’s global teleconnections and climate impacts, there are many processes associated with ocean–atmosphere interactions in the tropics and extratropics, as well as remote effects of SST changes on PCP patterns that have not yet been unveiled or fully understood. In this work, we employ coupled climate network analysis for characterizing dominating global co-variability patterns between SST and PCP at monthly timescales. Our analysis uncovers characteristic seasonal patterns associated with both local and remote statistical linkages and demonstrates their dependence on the type of the current ENSO phase (El Niño, La Niña or neutral phase). Thereby, our results allow identifying local interactions as well as teleconnections between SST variations and global precipitation patterns.
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