A Coupled O2-CO2 Model for Joint Estimation of Stream Metabolism, O-C Stoichiometry, and Inorganic Carbon Fluxes

We determine where stream carbon dioxide (${\text{CO}}_2$) comes from by developing a model for the joint estimation of stream metabolism, oxygen-carbon (O-C) stoichiometry, and fluxes of dissolved inorganic carbon (DIC), based on observations of stream oxygen ($O_2$) and ${\text{CO}}_2$ concentrations. The model is based on a stream reach mass balance of $O_2$, DIC, and total alkalinity, and it accounts for the carbonate system and the contribution of lateral flow. $O_2$ and $\text{DIC}$ mass balances are coupled through stoichiometric coefficients for photosynthesis and combined autotrophic and heterotrophic respiration. Under the assumption of constant alkalinity and circumneutral pH, the model simplifies and includes 8 parameters, which are estimated through a Bayesian hierarchical framework. The model accurately reproduced time series of $O_2$ and ${\text{CO}}_2$ from three diverse sites across size and carbonate chemistry gradients. Results allow partitioning of the stream DIC budget, and thus the source of stream ${\text{CO}}_2$ outgassing, into internal (in-stream net ecosystem production) and external (lateral input of terrestrial DIC and atmospheric input) contributions. We observed that the estimated stoichiometric coefficients were typically different from 1—contrary to typical assumptions—leading to divergent estimates of stream ${\text{CO}}_2$ sources depending on the measurement (i.e., $O_2$ vs. C). Parameter posterior distributions revealed the source of parameter uncertainty and the equifinality of some processes in reproducing stream ${\text{CO}}_2$ dynamics, suggesting targeted variables to further investigate in order to better constrain stream C balance. The proposed model is a useful tool for incorporating the rapidly growing stream ${\text{CO}}_2$ data sets into our understanding of terrestrial-aquatic C linkages.