## 2 Materials and Methods
### Carbon Dioxide Emission Model from Wetlands  
This study was performed by considering the significant effect of soil temperature, the groundwater table, and ecosystem respiration on CO\({}_{2}\) emissions at the watershed scale in the wetlands. The CO\({}_{2}\) emission model from peat decomposition was modified based on the interaction between the soil temperatures, groundwater table, and ecosystem respiration in CO\({}_{2}\) emission. The SWAT model permitted estimating these parameters in this research using the new SWAT model subroutine. The carbon cycle in the SWAT model included CO\({}_{2}\) emission, plant growth, litter decomposition (aerobic and anaerobic), and the below-ground carbon cycle (Figure 3). The balance of carbon in the wetlands, A, was calculated based on the following equation [37]:  
\[\mathrm{A}=\mathrm{P}_{\mathrm{G}}-(\mathrm{R}_{\mathrm{s}}+\mathrm{D}+\mathrm{W} +\mathrm{F}) \tag{1}\]  
where PG is CO\({}_{2}\) uptake (\(\mathrm{\mu mol\,CO_{2}\,m^{-2}\,day^{-1}}\)), R\({}_{\mathrm{s}}\) is respiration (\(\mathrm{\mu mol\,CO_{2}\,m^{-2}\,day^{-1}}\)), D is CO\({}_{2}\) from decomposition (\(\mathrm{\mu mol\,CO_{2}\,m^{-2}\,day^{-1}}\)), W is weathering, and F is carbon loss via fire. Carbon emission to the atmosphere is marked negative, whereas CO\({}_{2}\) uptake is  
Figure 3: Conceptual model of CO\({}_{2}\) emission processes in the Wetlands. Figure 2: Wetland distribution in the study’s river basin and Canada. marked positive. The following equation represents the relationship between NEE and net ecosystem production (NEP):  
\[\mathrm{NEE}=-\mathrm{NEP} \tag{2}\]  
\[\mathrm{NEP}=\mathrm{P_{G}}-\mathrm{R_{s}} \tag{3}\]  
\[\mathrm{NEP}=\mathrm{GPP-RECO} \tag{4}\]  
\[\mathrm{NEE}=\left((\mathrm{GP_{max}}\times\alpha*\mathrm{PFD})\times((\alpha \times\mathrm{PFD})+\mathrm{GP_{max}}))^{-1}\right)-\mathrm{RECO} \tag{5}\]  
where NEE is the net ecosystem exchange (\(\mathrm{\mu mol~{}CO_{2}-C~{}m^{-2}~{}day^{-1}}\)), NEP is the net ecosystem production (\(\mathrm{\mu mol~{}CO_{2}-C~{}m^{-2}~{}day^{-1}}\)), PPFD is photosynthetic photon flux (\(\mathrm{\mu mol~{}m^{-2}~{}day^{-1}}\)), and \(\alpha\) is the slope of the curve. Plant biomass (kg), GPP, and soil temperature (\(\mathrm{{}^{\circ}C}\)) are calculated by submodels of plant growth in the SWAT. RECO is the ecosystem respiration (\(\mathrm{\mu mol~{}CO_{2}~{}m^{-2}-C~{}day^{-1}}\)), which was calculated based on regressions between respiration rates and temperature using the Lloyd and Taylor equation [38]:  
\[\mathrm{RECO}=\mathrm{R_{ref}}^{\mathrm{E_{0}}[(\frac{1}{r_{\mathrm{ref}}- \mathrm{T_{0}}})-(\frac{1}{r_{\mathrm{sol}}-\mathrm{T_{0}}})]}+\mathrm{R_{i}} \tag{6}\]  
where \(\mathrm{E_{0}}\) is the activation energy (K), \(\mathrm{T_{0}}\) (227.13 K) is the constant parameter, \(\mathrm{T_{ref}}\) is the reference temperature (283.15), and \(\mathrm{Rh_{i}}\) is the heterotrophic respiration (\(\mathrm{\mu mol~{}CO_{2}~{}m^{-2}~{}day^{-1}}\)) [38]. In the SWAT model, the daily average soil temperature was estimated based on the surface and the center of each soil layer. Soil layer temperature is a function of average annual temperature, surface temperature, and the depth of soil. Soil temperature for each layer was calculated within the SWAT models. For each hydrologic response unit, the soil temperature (\(\mathrm{T_{soil}}\)) at the center of the soil layer (z) was calculated using the below equation [23]:  
\[\mathrm{T_{soil}}(\mathrm{z})=\gamma\mathrm{T\,\prime_{soil}}(\mathrm{z})+(1- \gamma)\times[\mathrm{d}(\mathrm{T_{Aair}}-\mathrm{T_{sur}})+\mathrm{T_{sur}}] \tag{7}\]  
where \(\mathrm{T_{soil}}\) is the soil temperature (\(\mathrm{{}^{\circ}C}\)), \(\gamma\) is the lag coefficient, \(T_{soil}\) is the soil temperature (\(\mathrm{{}^{\circ}C}\)) at the depth (z), d is the depth (m), f is the actor, \(T_{Aair}\) is the air temperature (\(\mathrm{{}^{\circ}C}\)) on the day, and \(T_{sur}\) is the soil surface temperature (\(\mathrm{{}^{\circ}C}\)). The lag coefficient (\(\gamma\)) is 0.8 for the SWAT.