## 2 Materials and Methods
### Denitrification Estimates  
Hourly triplicate dissolved gas samples were collected for dinitrogen (N\({}_{2}\)) and argon (Ar) [53; 54]. Using a polyvinyl chloride sampler, exetainer vials were overfilled 3x, preserved with zinc chloride (ZnCl\({}_{2}\)), capped, and stored until analysis. We measured dissolved N\({}_{2}\):Ar in dissolved gas samples with a Membrane Inlet Mass Spectrometer (MIMS) (Bay Instruments, Easton, MD, USA) [49; 55]. Sample N\({}_{2}\):Ar for each sample was converted to N\({}_{2}\)-N concentrations based on the following equation [56]:  
\[\left[DG\right]_{sample}=\left(\frac{DG}{Ar_{sample}}\times Ar_{ expected}\right)\left(\frac{\left[DG\right]/\left[Ar\right]_{expected}}{DG/Ar_{ standard}}\right) \tag{3}\]  
where \(DG/Ar_{sample}\) is the measured dissolved gas sample signal and \(DG/Ar_{standard}\) is the measured dissolved gas signal for well-mixed, deionized water open to the atmosphere at the same temperature as the sample. The terms \(\left[Ar\right]_{expected}\) and \(\left[DG\right]/\left[Ar\right]_{expected}\) are the theoretical saturated concentration and ratio, respectively, calculated for each field sample using gas solubility tables [57]. Diel patterns of dissolved gas data indicated the strong patterns in O\({}_{2}\) concentrations throughout the 24 h period which corresponded with diel N\({}_{2}\) patterns [43]. We developed and applied a correction factor to eliminate instrument specific O\({}_{2}\) interference with N\({}_{2}\):Ar measurements which may have contributed to below equilibrium N\({}_{2}\):Ar ratios observed during daytime hours [43; 58].  
N\({}_{2}\):Ar values were then used to model daily fluxes in a Bayesian framework [50; 53]. Specifically, we used a single-station approach which allows for the possibility of N\({}_{2}\) consumption to estimate posterior distributions for denitrification and \(K\) using the following model [49]:  
\[N_{2(t)}=\frac{\left(\frac{N_{\text{moment}}}{z}\times\frac{PPFD_{t}}{PPFD_{ total}}\right)+\frac{DN}{z}\Delta t+K_{t}\Delta t\left(\frac{N_{2\text{,equil}(t)}+N_{2\text{,equil}(t-1)}-N_{2(t-1)}}{2} \right)}{\left(1+\frac{K_{t}\Delta t}{2}\right)} \tag{4}\]  
where \(N_{2(t)}\) is the dissolved \(N_{2}\) at time t (g m\({}^{-3}\)); DN is the denitrification rate (g m\({}^{-2}\) d\({}^{-1}\)), z is depth of water (m), \(N_{2\text{,equil}(t)}\) is the equilibrium concentration of \(N_{2}\) at time t (g m\({}^{-3}\));and K\({}_{t}\) is the gas exchange rate (d\({}^{-1}\)) for N\({}_{2}\) at time t calculated from K\({}_{600}\). K\({}_{600}\) is utilized to normalize the model daily estimates of K from the metabolism model (Equation (2)) as K\({}_{600}\) is comparable across temperatures and gases [59]. \(N_{consume}\) is the N\({}_{2}\) consumption rate (g m\({}^{-2}\) d\({}^{-1}\)) from ebullition or fixation. For any parcel of water, the fraction of light it accumulates is photosynthetic photon flux density (_PPFD\({}_{t}\)_, umol m\({}^{-2}\) s\({}^{-1}\)) at time t divided by the daily total of PPFD (_PPFD\({}_{total}\)_, umol m\({}^{-2}\) s\({}^{-1}\) d\({}^{-1}\)). DN was transformed from a daily rate to an average hourly rate of daily DN flux in mg m\({}^{-2}\) h\({}^{-1}\). We acknowledge the application of the single station model may violate minimum reach assumptions [60] and thus the rates should be used with caution; however, the relative magnitude of denitrification and uptake as well as qualitative differences in rates across the vegetation and hydraulic residence times may still be informative to land managers because any effects from the upstream water source would be equal across the treatments.