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\begin{document}

\title{A Process-based Stream Network Model for Predicting CO\textsubscript{2}
Concentrations and Fluxes}



\author[1]{Brian Saccardi}%
\author[1]{Matthew Winnick}%
\affil[1]{University of Massachusetts Amherst}%


\vspace{-1em}



  
  \date{June 13, 2024}


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\begin{abstract}
Inland waters are recognized as a significant source of
CO\textsubscript{2} to the atmosphere; however, the global magnitude of
this flux remains uncertain. In particular, CO\textsubscript{2}
concentrations and fluxes in stream systems are extremely variable at
scales of 10's to 100's of meters, complicating monitoring and
prediction efforts. Thus, models of pCO\textsubscript{2} that capture
these scales of spatial variability are necessary for the accurate
prediction and monitoring of stream CO\textsubscript{2} fluxes. Despite
a strong conceptual framework for the hydrologic processes that control
stream CO\textsubscript{2}, predictive models to date have been
empirical, based on Strahler stream order and regressions between
observed pCO\textsubscript{2} and landscape variables. We hypothesize
that models incorporating well-described hydrologic processes may lead
to new insights into the magnitude of various CO\textsubscript{2}
sources and improve predictions. Here, we develop and apply a
process-based stream network model of CO\textsubscript{2} based on
NHDplus flowlines and driven by groundwater inputs, hyporheic exchange,
water-column metabolism, advective transport, and atmospheric exchange.
Model output is compared with 151 measurements of pCO\textsubscript{2}
(424 - 9718 ppm) collected in August, 2019 across the upper East River
watershed in Gothic, CO, a mountainous, high-elevation headwaters system
within the Colorado River basin. We find that modeled
pCO\textsubscript{2} captures observed spatial patterns and predicts
measured values with a RMSE of \textasciitilde{}250 ppm and
R\textsuperscript{2} of 0.47 (p\textless{}10\textsuperscript{-15}).
Additionally, our process-based model performs significantly better than
a multiple linear regression model between observations and a geomorphic
variables (r\textsuperscript{2}=0.35,
p\textless{}10\textsuperscript{-7}). Estimates from an optimized stream
network model give additional insight into CO\textsubscript{2} sources,
suggesting that groundwater accounts for 70-80\% of evasion fluxes,
hyporheic processes for 20-30\%, and water-column metabolism for
\textasciitilde{}1\% across the East River watershed. The ability of our
model to predict pCO\textsubscript{2} at the spatial scales of
variability may provide an important next step in estimating global
CO\textsubscript{2} fluxes, and future research will test the predictive
power of process-based models at regional and global scales.%
\end{abstract}%



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