## 4 Discussion
### Displacement of the Rectangular Hyperbolic Model and Temperature Factors  
The photosynthetic response to light, as represented by the light-response-curve models, is influenced by factors such as vapour pressure deficit and temperature. Cold temperatures limit photosynthesis; during winter, the GPP fluxes can switch from PAR to temperature-driven. This phenomenon is well-known in boreal areas where, despite the high photosynthetic potential, GPP fluxes are not significant even during spring [29]. Hence, the determined cold season is often assumed to be negligible when there is a combination of light and temperature limitations [30]. The effect of the cold temperatures is visible in the light curves presented in Section 3.2; instead of reaching no uptake of CO\({}_{2}\) when no PAR is available, the temperature limitation induces a displacement, and 0 GPP is already reached with PAR ranging from 200 to 400 \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\). Higher light intensities are needed to jumpstart photosynthesis; consequently, the RH can often overestimate GPP [10]. The effect of high temperatures on GPP fluxes is similar, as it can also limit photosynthetic capacity. However, the reasons behind this can be different, and apart from the decrease in electron transport and Rubisco activity, the stomatal closing also induces a reduction in GPP [19]. High temperatures can be accompanied by an elevated vapour pressure deficit when humidity is inadequate; this combination induces stomatal closing to prevent water loss and limits the assimilation of CO\({}_{2}\)[31]. While there is a displacement at the start of the photosynthetic light curve response due to low-temperature limitations, high temperatures induce a constant decrease in GPP, lowering the curve, especially near the saturation point. At canopy scale during short-term low water content--induced by high temperatures--the canopy conductance and GPP are strongly coupled and the lowest the conductance, the highest the decrease in GPP in a continuous pattern [32]. Adding temperature to the photosynthetic light curves is a widespread technique generally used to adapt the models to the stressful conditions of elevated temperatures and reduce the overestimations of the classical approaches [33; 34], though in our case, it has been applied to account for both hot and cold limitations. Generally, the temperature factors employed to correct classical GPP models include hourly, thirty minutes or daily temperatures, and estimated optimal and tolerated temperatures. In our study, it was assumed that there is a legacy effect of the previous hours' temperature and the plants under frozen conditions before sunrise will not react the same way to the immediate temperature oscillations as those under non-frozen conditions or hot conditions will not affect the same way if they are punctual (30 min measurements) than if they are constantly high (1.5 h average). Hence, the temperature factors have been calculated based on the 3 h and 1.5 h averages, as described in the Methodology section. The simplest displacement of the RH model adding an intercept (TRH) has shown the most remarkable improvement of the RH estimates during winter, estimating the limitations of cold temperatures at the CL site. In the case of the CR site, the adjustments enhance the performance of the models at the end of the year, while at the start of the year, both adjustments seem to increase the model's error (TRH, TRH_exp). During June and July, when overheating is most frequent, both temperature models performed similarly, with less than a 1% difference in statistical performance. Both models improved upon the RH model by reducing GPP based on temperature constraints. It is uncertain why the performance of the models worsens at the start of the year, though, during this period, the relationship between GPP and PAR seems to be exponential and not a rectangular hyperbola.