According to Eq. ( 1), the flux of CO 2 across the air–water interface ( F) is directly proportional to the concentration gradient between the top and the bottom of the water boundary layer through a gas exchange velocity ( k). Where F is the CO 2 flux ( µmol s −1 m −2), k the gas exchange velocity (m s −1), C e is the concentration in the water ( µmol m −3), and C 0 is the concentration in the water as if it was in equilibrium with the atmosphere ( µmol m −3). The gas flux across atmosphere–water interfaces ( F) is commonly evaluated with Fick’s first law of diffusion ( Wanninkhof et al., 2009): Therefore, accurately quantifying air–water CO 2 exchange in small headwater catchments is of paramount importance for global and regional assessments of CO 2 emissions ( Rawitch et al., 2019). In particular, first-order streams are characterized by relatively high per-area CO 2 evasion fluxes and cover a significant proportion of the global stream surface ( Raymond et al., 2013 Schelker et al., 2016). Most running waters are supersaturated in CO 2 and are believed to be responsible for a globally large biogeochemical flux to the atmosphere occurring across air–water boundaries ( Horgby et al., 2019 Hall and Ulseth, 2020). Growing concerns about greenhouse gas emissions have increased the scientific interest in quantifying the role of inland waters in the global carbon cycle ( Battin et al., 2009 Raymond et al., 2013 Hotchkiss et al., 2015 Marx et al., 2017). These findings have important implications for improving estimates of greenhouse gas emissions and reaeration rates in running waters. Furthermore, the study demonstrates the value of analytical and numerical tools in the identification of accurate estimations for gas exchange velocities. Our study suggests that a flexible foil design and the anchored deployment might be useful techniques to enhance the robustness and the accuracy of CO 2 measurements in low-order streams. Interestingly, for the standard chamber the uncertainty was larger ( + 20 %) as compared to the flexible foil chamber. For the anchored mode, the standard deviations of k 600 were between 1.6 and 8.2 m d −1, whereas significantly higher values were obtained in drifting mode. Overall, uncertainty in k 600 was moderate to high, with enhanced uncertainty in high-energy set-ups. The uncertainty in the estimate of gas exchange velocities was then estimated using a generalized likelihood uncertainty estimation (GLUE) procedure. Moreover, acoustic Doppler velocimeter measurements indicated a limited increase in the turbulence induced by the flexible foil chamber on the flow field (22 % increase in ε, leading to a theoretical 5 % increase in k 600). The flexible foil chamber gave consistent k 600 patterns in response to changes in the slope and/or the flow rate. Estimates of gas exchange velocities were in line with the existing literature ( 4 < k 600 < 32 m 2 s −3), with a general increase in k 600 for larger turbulent kinetic energy dissipation rates. The runs were performed using various combinations of discharge and channel slope, leading to variable turbulent kinetic energy dissipation rates ( 1.5 × 10 - 3 < ε < 1 × 10 - 1 m 2 s −3). During the experiment, 100 runs were performed using two different chamber designs (namely, a standard chamber and a flexible foil chamber with an external floating system and a flexible sealing) and two different deployment modes (drifting and anchored). Here, these issues were addressed by analysing the results of a flume experiment carried out in the Summer of 2019 in the Lunzer:::Rinnen – Experimental Facility (Austria). Moreover, as of now the uncertainty of k 600 estimates from chamber data has not been evaluated. Whereas craft-made floating chambers supplied by internal CO 2 sensors represent a promising technique to estimate CO 2 fluxes from rivers, the existing literature lacks rigorous comparisons among differently designed chambers and deployment techniques.
However, quantifying CO 2 fluxes across air–water boundaries remains challenging due to practical difficulties in the estimation of reach-scale standardized gas exchange velocities ( k 600) and water equilibrium concentrations.
Carbon dioxide ( CO 2) emissions from running waters represent a key component of the global carbon cycle.