Metabolic scaling of stream dissolved oxygen across the U.S. Atlantic Coast

We investigated the hypothesis of emergent 'biogeochemical' similitude (parametric reduction) and scaling of dissolved oxygen (DO) in coastal streams across the U.S. Atlantic Coast by employing dimensional analysis methodology from fluid mechanics and hydraulic engineering. Two mechanistically meaningful dimensionless numbers were discovered as the stream 'metabolic' number and the fraction of 'DO saturation' number. The 'metabolic' number represented the synergistic control on stream DO from various climatic, hydrologic, biochemical, and ecological drivers (e.g., water temperature, atmospheric pressure, stream width and depth, total phosphorus, pH, and salinity). A graphical exploration of the 'metabolic' versus the 'DO saturation' numbers led to collapse of data during 1998-2015 from diverse coastal streams into an emergent process diagram, indicating three metabolism regimes (high, transitional, and low). The high and low metabolism regimes were, respectively, characterized by the most and least favorable environmental conditions for stream DO depletion-through reduced dissolution and reaeration, as well as increased organic decomposition, respiration, and nitrification. The emergent process diagram led to a generalized power law scaling relationship of the 'DO saturation' number as a function of the 'metabolic' number (exponent ~ 1/3; Nash-Sutcliffe Efficiency, NSE = 0.83-0.85). The metabolic scaling law was leveraged to develop a generalized empirical model to successfully predict DO in diverse streams across the U.S. Atlantic Coast (NSE = 0.83). The emergent process diagram, metabolic scaling law, and prediction model of DO would help understand and manage water quality and ecosystem health of coastal streams in the U.S. and elsewhere.