# Multi-Year Monitoring of Ecosystem Metabolism in Two Branches of a Cold-Water Stream
## Materials and Methods
### Ecosystem Metabolism  
Elements of ecosystem metabolism were determined using the single station method [53], which relies on measuring the daily changes in dissolved oxygen levels. Gross primary production (GPP) was assessed as the increase in oxygen in the stream due to photosynthesis. Ecosystem respiration (ER) was assessed as the decrease in oxygen in the stream due to respiration and assumes that respiration is constant during the day and night. Both GPP and ER were corrected for oxygen loss or gain from the atmosphere, termed reaeration. Finally, net ecosystem production (NEP) was calculated as the amount of production that exceeds GPP. The relationship between these measures of ecosystem metabolism is described in Equations (1) and (2):  
\[\frac{dC}{dt}=GPP-ER+k(C_{s}-C)+GWA \tag{1}\]  
\[NEP=GPP-ER \tag{2}\]  
where \(C\) = concentration of oxygen, \(Cs\) = concentration of oxygen at saturation, \(k\) = reaeration coefficient, and \(GWA\) = oxygen accrual from groundwater. The Bayesian single-station estimation model (BASE--version 2.3) was used to estimate \(k\), GPP, and ER [54]. This model is available as an R-package ([[https://github.com/dgiling/BASEmetab](https://github.com/dgiling/BASEmetab)]([https://github.com/dgiling/BASEmetab](https://github.com/dgiling/BASEmetab)), accessed on 19 July 2018). To ensure valid estimates of ecosystem metabolism, the convergence of the Markov chain Monte Carlo method used in the model, the posterior prediction fit, the R\({}^{2}\) for the model, the effective number of parameters, and the visual fit of the model were all assessed. In 2019, oxygen data were not available from August 3 to August 12 due to issues with the probe, so values of ecosystem metabolism could not be modeled for those dates. Mixed-model ANOVAs were used to test whether there were significant differences between locations and years (as independent nominal variables) for GPP, ER, and NEP, with day of the year as the random variable. The metabolism data were not normally distributed and, thus, were natural log (ln)-transformed. For analysis of ln(NEP), since NEP is often negative, constant (43--the minimum NEP measured) was added to each value to ensure that all values were positive.  
ANCOVAs were performed to examine the influence of water temperature, light input (PAR), or discharge (covariables) and location (independent variable) and their interaction on ln-transformed ecosystem metabolism parameters dependent variables (GPP, ER, and NEP). ANCOVAs are a blend of ANOVA and linear regression. They test for the difference in the mean of a dependent variable for various levels of an independent variable, while controlling for the effects of a continuous variable (the covariable). For discharge, separate analyses were conducted for the North and South Branches, since discharge data were available for all three years for the South Branch but only for 2017 a July 13-November 8 in 2019 when data were available.  
All statistical analyses were conducted with JMP\({}^{\circledR}\) Pro version 14.2 (SAS Institute, Cary, NC, USA).