## 2 Methodology
### Parametrisation and Models' Implementation  
The RH model was selected as the base photosynthetic light response curve used in this study. Within the rectangular hyperbolas, the selected variations include the original formulation, which follows the enzyme kinetic curve of [PERSON] (Equation (1)), along with two modified rectangular hyperbolic models that incorporate the average temperature from the previous hours (Equations (2) and (3)). These models were used for comparison. The classical hyperbolic light response model (Equation (1)) estimates GPP (called here \(GPP_{RH}\)) in \(\upmu\)mol\({}^{-1}\) m\({}^{-2}\) s\({}^{-1}\) based on the measured photon flux density of _PAR_ (\(\upmu\)mol\({}^{-1}\) m\({}^{-2}\) s\({}^{-1}\)), maximum rate of carbon fixation at infinitive _PAR_ (\(GP_{max}\); \(\upmu\)mol\({}^{-1}\) m\({}^{-2}\) s\({}^{-1}\)), and the light-use efficiency (\(\alpha\), mol CO\({}_{2}\) mol\({}^{-1}\) photons). \[GPP_{RH}=\frac{GP_{max}\cdot\alpha\cdot PAR}{GP_{max}+\alpha\cdot PAR} \tag{1}\]  
Due to the observed shift in the light response curve during winter and early spring--associated with near-freezing temperatures typical for frost events--and during extremely hot summer days, modifications of RH modelling approach were implemented to better capture the effects of stressed conditions on GPP. The temperature factors are calculated based on the previous hours' air temperature average, and the length of the moving average is altered depending on the time of the day (Figure 2). Before 11:00, the average temperature is calculated over three hours to account for the possible effect of night frost periods. Conversely, after 11:00, the span is reduced to 1.5 h to detect the possible heat stress in summer. The first temperature-adjusted model, TRH, applies a linear factor that only shifts to the left of the RH curve when the temperature is displaced from the optima (\(T_{opt}\); defined by [PERSON] et al. [19] in this case) for photosynthetic activity. Temperatures below 0 \({}^{\circ}\)C are considered limiting for plants with highly reduced active photosynthesis. Consequently, when the average temperature is below zero, the maximum displacement of the first temperature factor (\(T_{f1}\)) is applied: \(GPP=GPP_{RH}-2\). In the same way, when the temperature average is above 45 \({}^{\circ}\)C, the \(T_{f1}\) factor is set to saturate (\(T_{f1}\) = 2) and again \(GPP\) = \(GPP_{RH}-2\). In order to have the same displacement penalizing too-cold and too-warm temperatures, the \(T_{f1}\) calculation is split in two: (i) it decreases from 0 to \(-2\) from \(T_{f1}\) = optimum temperature \(-\)\(x_{2}\)\({}^{\circ}\)C until \(T_{f1}\) = 0 \({}^{\circ}\)C; (ii) it increases from 0 to 2 from \(T_{f1}\) = optimum temperature \(+\)\(x_{1}\)\({}^{\circ}\)C until \(T_{f1}\) = 45 \({}^{\circ}\)C; and lastly to obtain the new \(GPP_{T1}\), the computed factors are subtracted from the RH result (Equation (2)). \[ \begin{split} GPP_{Tf1}=T_{f1}+\frac{GP_{max}+PAR}{GP_{max}+x+PAR} \left\{T_{f1}>(T_{opt}+x_{1}),\;T_{f1}=2,\frac{(T_{opt}+x_{1})-T_{opt}}{45-(T _{opt}+x_{1})}\;(T_{opt}-9.5)<T_{f1}\right.\\ <(T_{opt}+x_{1})\;,\;T_{f1}=0\;T_{f1}<(T_{opt}-x_{2}),\;T_{f1}=2,\frac{T_{opt}-(T_{opt}-x_{2})}{(T_{opt}-x_{2})}\end{split}  \tag{2}\]  
The second model adjusting temperature uses the temperature factor (\(T_{f2}\)) to decrease the light-use efficiency (\(\alpha\)) value exponentially when the temperature is displaced from the optima, assuming that the effect of too-high or too-low temperature results in reducing the efficiency of photosynthetic activity (Equation (3)). In this case, the penalization for conditions below 0 \({}^{\circ}\)C is set to reduce a maximum of 85% of the GPP expected at the same \(PAR\) with an optimum temperature. At the same time, when the temperature average is above 45 \({}^{\circ}\)C, the \(T_{f2}\) is fixed to a rate reducing \(\sim\)70% of the GPP expected at the same \(PAR\) with an optimum temperature (both reduction percentages established based on empirical results).