## 3 Results
### Performance of the Temperature Factors  
The improvement in the performance of the rectangular hyperbolic approach, due to the addition of the temperature effect, solved the problem observed during measurements of the displaced light curve when temperatures are too low. For example, this displacement can be observed in CL_3 and CR_2 during the first campaigns modelled (25 February and 31  
Figure 5: Hydromteeorological conditions for CR and CL sites in the Rzecin peatland during 2020–2021. Conditions are presented in a weekly timestep for the averaged water table depth (WTD) and cumulative precipitation (**a**) and in daily timesteps for air temperature (**b**). Dashed lines indicate dates of CO\({}_{2}\) chamber campaigns (from 1 to 5 in 2020 and from 6 to 16 in 2021).  
March of 2021, merged as 14 March), with air temperatures ranging from 6.5 \({}^{\circ}\)C to 20.2 \({}^{\circ}\)C in February and from 9.5 \({}^{\circ}\)C to 26.8 \({}^{\circ}\)C in March during measurements after the nighttime frost when the peatland surface was frozen (the minimum air temperature on 25 February and 31 March 2021 was \(-\)3.7 \({}^{\circ}\)C and \(-\)2.7 \({}^{\circ}\)C, respectively). In Figure 6, it can be observed that the RH model in CL_3 and CR_2 fails to predict the low GPP values measured early in the morning under low PAR (\(\sim\)340 \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\) and \(\sim\)500 \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\)) and low air temperatures (11.2 \({}^{\circ}\)C and 15.2 \({}^{\circ}\)C). Conversely, the adapted models displace the curve to fit these values, reaching 0 GPP with PAR < 300 \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\) due to the constraint in photosynthesis produced by low temperatures and vegetation not yet recovered after the frozen night periods.  
Generally, adding temperature to the rectangular hyperbola increased the model's accuracy, decreasing the average BIAS from 77% to 92% of the time and RMSE from 54% to 77% (Figure 7). The thresholds of optimal temperatures for GPP were calculated for each plot's best performance based on the average optimal temperature reported for the peatland area studied. Despite this adjustment for each particular case instead of a generalization of the thresholds, the vegetation coverage differences and distinct WTD regimes between CL and CR sites generate different performances between plots and sites. Furthermore, the  
Figure 6: The light response curve of photosynthesis with the Michaelis–Menten rectangular hyperbolic approach (RH) and the modified RH with temperature factors (TRH, TRH_exp) for the first campaigns of the year (25 February and 31 March) in CL_3 (**a**) and CR_2 (**b**) plots.  
seasonal distribution of the effectiveness of the temperature factors also oscillates between plots (Supplementary Tables S3-S7).  
In the case of CL_1 and CR_2 plots, the statistics show how adding temperatures does not improve the RH model during the start and end of the growing season (April-May, October), while it only occurs for the start of the season (April-May) in CL_3 (Supplementary Tables S3-S7). At the same time, CL_2 displays no improvement of RH with temperature during the early middle of the season (June). The temperature addition to the model did not increase the performance during the late-mid-season for CR_1 and CR_2, and CR_3 showed the weakest performance. The results in the CR site can be due to the higher coverage of _Splagnum_ spp.; mosses can desicate during hot months, reducing their GPP and the changes in the shape of the light-response curve.