## 2 Materials and Methods
All \(p\)CO\({}_{2}\) data are temperature corrected in real time, with a measurement range of 0-10,000 uatm and 3% full scale accuracy. Both the C-Sense and YSI sensors equilibrated for 15 min and recorded for approximately 20 min during each sample, with the C-Sense collecting data every 30 s and the YSI every 5 s. Relevant atmospheric parameters, including hourly solar radiation, atmospheric temperature, and wind speed, were collected from the Louisiana State University Agricultural Center Ben Hur Research Station in Baton Rouge, LA (30\({}^{\circ}\)21\({}^{\prime}\)52\({}^{\prime\prime}\) N, 91\({}^{\circ}\)10\({}^{\prime}\)02\({}^{\prime\prime}\) W), located approximately 7 km southeast from the river sampling site. Solar radiation at Ben Hur Station is measured at the 400-1100 nm waveband interval using a LI200R-L pyranometer (Campbell Scientific, Logan, UT, USA). Hourly river discharge records of the Mississippi River at Baton Rouge were downloaded from the U.S. Geological Survey's gauging station, #07374000. These data built a foundation of ambient conditions for our \(p\)CO\({}_{2}\) and CO\({}_{2}\) outgassing analyses. The flux of CO\({}_{2}\), or outgassing, between surface water and atmosphere (\(F\)CO\({}_{2}\) in mmol CO\({}_{2}\) m\({}^{-2}\) h\({}^{-1}\)) was calculated utilizing the following equation developed by [PERSON] and [PERSON] [36]:  
\[F\mathrm{CO}_{2}=\mathrm{K}_{\mathrm{T}}\mathrm{K}_{\mathrm{H}}(\mathrm{\varphi CO }_{\mathrm{2 water}}-\mathrm{\varphi CO}_{\mathrm{2 air}}), \tag{1}\]  
where K\({}_{\mathrm{T}}\) is the gas transfer velocity (m d\({}^{-1}\)), K\({}_{\mathrm{H}}\) is a solubility constant (mol L\({}^{-1}\) atm\({}^{-1}\)), \(p\)CO\({}_{\mathrm{2 water}}\) is the partial pressure of dissolved CO\({}_{2}\) in the water column (uatm), and \(p\)CO\({}_{\mathrm{2 air}}\) is the partial pressure of atmospheric CO\({}_{2}\) (uatm), which was fixed as 400 uatm [37] for the study period. It is well understood that atmospheric CO\({}_{2}\) can demonstrate diel variation on terrestrial land, yet the pattern of this variation can vary between and even within land-uses [38; 39]. The nearest FLUXNET eddy covariance tower with atmospheric CO\({}_{2}\) data is located several hundred kilometers from the study site and does not have data available for the study period. While using a fixed value does not account for any potential diel variation in atmospheric CO\({}_{2}\), applying diel variation found in an environment very different and far from the study area to our study area would introduce great uncertainty to the outgassing analysis. Additionally, a fixed atmospheric value is a widely-used method that reduces these assumptions and increases the ability to reproduce similar studies in the future, though the limitations of a fixed value should not be overlooked when considering the conclusions of this study. We selected a K\({}_{\mathrm{T}}\) value of 4.3 m d\({}^{-1}\), which is a rate lower than the global average of 5.7 m d\({}^{-1}\)[3]; however, this has been reported as being more representative of large low-land rivers [3; 40]. The solubility constant (K\({}_{\mathrm{H}}\)) was calculated using the following equation by [PERSON] [41]:  
\[\mathrm{InK}_{\mathrm{H}}=\mathrm{A}_{1}+\mathrm{A}_{2}(\frac{100}{\mathrm{T}}) +\mathrm{A}_{3}\mathrm{In}(\frac{100}{\mathrm{T}})+\mathrm{S}[\mathrm{B}_{1}+ \mathrm{B}_{2}(\frac{\mathrm{T}}{100})+\mathrm{B}_{3}(\frac{\mathrm{T}}{100}) ^{2}] \tag{2}\]  
where A\({}_{1}\) = \(-\)58.0931, A\({}_{2}\) = 90.5069, A\({}_{3}\) = 22.2940, B\({}_{1}\) = 0.027766, B\({}_{2}\) = \(-\)0.025888, B3 = 0.0050578, T is the absolute temperature of water in Kelvin, and S is the salinity. The study area is classified as a freshwater system; therefore, an S of 0 was used for calculating K\({}_{\mathrm{H}}\). Daily CO\({}_{2}\) outgassing (mmol m\({}^{-2}\) d\({}^{-1}\)) was calculated for each 24-h period using two difference methods. The first extrapolated the hourly flux rate at the 15:00 CST sample over the entire 24-h period.