A Dimensionless Framework for the Partitioning of Fluvial Inorganic Carbon

Rivers are pivotal in the global carbon cycle, transporting terrestrial carbon to the ocean while emitting significant amount of (Formula presented.) to the atmosphere. However, the partitioning of fluvial inorganic carbon (IC) between downstream transport and atmospheric evasion remains uncertain due to intricate hydrodynamic and biogeochemical processes. Inspired by Budyko's hydrological work, this study introduces a dimensionless framework to identify critical factors in fluvial IC partitioning: the IC fraction in equilibrium with the atmosphere and the ratio of advection to evasion timescales. River catchment analyses and modeling reveal that the equilibrium ratio determines the fraction of IC stably transported downstream. The hydrodynamic-driven timescale ratio determines the fate of out-of-equilibrium IC, with low-order streams favoring atmospheric evasion and higher-order streams promoting downstream transport. This framework provides a simple yet robust approach to predicting river carbon dynamics, with implications for land-to-ocean transport, fluvial emissions, and climate mitigation strategies such as enhanced weathering.