# Upscaling Northern Peatland CO2 Fluxes Using Satellite Remote Sensing Data
## 2 Materials and Methods
### Empirical Regression Models for GPP, ER, and NEE  
The GPP model structure was based on previous work by [PERSON] et al. (2010), where EVI, LST, and photosynthetic photon flux density (PPFD) were used as regression model inputs. In this study, we investigated how satellite-derived EVI2, LST, and W\({}_{\text{s}}\) along with site-measured environmental variables (T\({}_{\text{air}}\), PPFD, water table depth (WTD) and annual precipitation) were related with GPP time-series data. Based on the goodness-of-fit of the regressions, EVI2, W\({}_{\text{s}}\), and daytime LST were chosen as input variables into the GPP model. The derived linear regression model for estimating GPP at all the sites simultaneously can be described as:  
\[\text{GPP}=a\times\text{EVI2}\times\text{W}_{\text{s}}\times\text{ LST}. \tag{4}\]  
Because of the abovementioned scaling of EVI2 and NDWI, it was possible to force the regression line through the origin, which is a physically reasonable way to estimate GPP. Equation (4) can be regarded as an empirical variation of the LUE model, where the parameter \(a\), W\({}_{\text{s}}\), and LST jointly function as a proxy for PAR and the light use efficiency coefficient. Since photosynthesis does not take place in cold temperatures, only data when LST was above 0 \({}^{\circ}\)C were used to determine the model parameter a.  
Ecosystem respiration (ER) was also modelled using an empirical model. Three existing models were tested: [PERSON] (1994) (Equation (5)), [PERSON] et al. (1995) (Equation (6)), and [PERSON] et al. (2006) (Equation (7)), who added the dependence on GPP to [PERSON] and [PERSON]'s model:  
\[\text{ER}=R_{ref}e^{E_{0}(\frac{1}{r_{ref}-t_{0}}-\frac{1}{r+2\times 315-t_{0}})}, \tag{5}\]  
\[\text{lnER}=a+bT+cT^{2}, \tag{6}\]  
\[\text{ER}=a\times\text{GPP}+R_{ref}\times e^{E_{0}(\frac{1}{r_{ref}-t_{0}}- \frac{1}{r+2\times 315-t_{0}})}, \tag{7}\]  
where \(T_{ref}\)= reference temperature (set to 10 \({}^{\circ}\)C); \(T\) = daytime LST; \(T_{0}\) = -46.02 \({}^{\circ}\)C (value taken from [PERSON] and [PERSON] (1994)); GPP = modelled GPP; and \(R_{ref}\), \(E_{0}\), \(a\), \(b\), and \(c\) are parameters to be estimated. To model ER, we started by testing the three models (Equations (5)-(7)) at each of the sites separately, for all available years, in order to find the best model (see results in Table S3). We also tested multiplying each model by an EVI2 scalar (formulated in the same way as W\({}_{\text{s}}\)) or the W\({}_{\text{s}}\) scalar (Table S3). The [PERSON] et al. (2006) model (Equation (7)) provided the best fit. Including vegetation productivity in the ER model improved the fit, because it helped better capture the magnitude and timing of the peak growing season ER. We tested modelling ER separately during the growing and dormant seasons, but it yielded no or only minor improvements in the goodness-of-fit. Since Equation (7) is sensitive to possible errors in the modelled GPP as an input, EVI2 was used as a proxy for modelled GPP to reduce the uncertainties in the modelled ER (Equation (8)). Equation (8) was the ER model used in the rest of the analysis:  
\[\text{ER}=a\times\text{EVI2}+R_{ref}\times e^{E_{0}(\frac{1}{r_{ref}-t_{0}}- \frac{1}{r+2\times 315-t_{0}})}. \tag{8}\]  
We compared two methods for modelling NEE, where NEE = ER - GPP. We followed the sign convention that NEE is negative when the ecosystem is a carbon sink (GPP > ER) and NEE is positive when the ecosystem is a carbon source (ER > GPP). NEE was estimated 1) by subtracting the modelled GPP (Equation (4)) from the modelled ER (Equations (2) and (8)) by fitting a non-linear regression model that included the GPP and ER components (Equation (9)) to the EC NEE measurements:  
\[\text{NEE}=b_{1}\times\text{EVI2}+R_{ref}\times e^{E_{0}(\frac{1}{r_{ref}-t_{0} }-\frac{1}{1+2\times 315-t_{0}})}-b_{2}\times\text{EVI2}\times\text{W}_{\text{s}} \times\text{ LST}. \tag{9}\]  
In addition to these two NEE models, we also tested a third, purely empirical, NEE model based on multiple linear regression.