Understanding the Hydrological Interconnections: A Network and Relationship Matrix Approach

Water within the terrestrial environment is fundamentally interconnected. A single unit of precipitation follows multiple pathways: infiltrating soils, being taken up by vegetation, evaporating, undergoing freeze-thaw cycles, percolating into groundwater, flowing as surface and subsurface runoff, and being withdrawn or artificially recharged by human activities. However, quantitative understanding of the magnitudes of these flux fractions, as well as their temporal, regional, and global-scale variability, remains limited.To address this gap, we develop a standard relationship matrix framework to represent flux exchanges—such as rainfall, evapotranspiration, and runoff—within the terrestrial water cycle. This framework incorporates two derived matrices termed “contribution” and “delivery”, which together characterize transfer rates and efficiencies among key subsystems: the atmosphere, oceans, pedosphere, and anthroposphere. These matrices help identify principal “donor” and “receiver” compartments within the terrestrial water system, revealing the dominate pathway of both blue and green water. Furthermore, we re-examine the terrestrial water cycle from a network-based perspective. By constructing water-cycle networks at global and regional scales—treating subsystems as nodes and fluxes as links—we apply a suite of network analysis methods to quantify key structural features. Metrics such as node strength, closeness, betweenness, and clustering are used to identify critical nodes, pivotal flux pathways, and structurally dominant subnetworks, thereby revealing the central subsystems and major flux routes in the water cycle.Through these approaches, we systematically identify primary water flux pathways across regions with differing climate and land-use types, analyze their temporal dynamics, and thereby elucidate the principal factors shaping regional and global terrestrial water cycle patterns. Notably, the partitioning of surface streamflow to groundwater differs across regions, contributing to distinct terrestrial water network configurations. The influence of groundwater dynamics warrants further consideration in future studies.