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. One critical challenge of studying Earth's hydroclimate system, in the face of global environmental changes, is to predict whether the system approaches a critical threshold. Here, we identified the critical transitions of hydrological processes, including precipitation and potential evapotranspiration, by analyzing their early-warning signals and system-based network structures. The statistical early-warning signals are manifest in increasing trends of autocorrelation and variance in the hydrologic system ranging from regional to global scales, prior to climate shifts in the 1970s and 1990s, in agreement with observations. We further extended the conventional statistics-based measures of early-warning signals to system-based network analysis in urban areas across the contiguous United States. The topology of an urban precipitation network features hub-periphery (clustering) and modular organization, with strong intra-regional connectivity and inter-regional gateways (teleconnection). We found that several network parameters (mean correlation coefficient, density, and clustering coefficient) gradually increased prior to the critical transition in the 1990s, signifying the enhanced synchronization among urban precipitation patterns. These topological parameters can not only serve as novel system-based early-warning signals for critical transitions in hydrological processes but also shed new light on structure–dynamic interactions in the complex hydrological system.

Critical transitions in the hydrological system: early-warning signals and network analysis