## Appendix A  
### Model Description  
#### a.1.1 Primary Productivity  
The simulation of daily canopy GPP is based on the P-model v1.0 [50], by multiplying with the stand's LAI. \[GPP=\varphi_{0}(T)I_{abs}REWm^{\prime}Mc \tag{1}\]  
where \(\varphi_{0}\) is the temperature-dependent (T) intrinsic quantum yield efficiency, I\({}_{\text{abs}}\) is the PAR absorbed by the canopy, REW is the soil relative extractable water by the plants (see Equation (18)), m\({}^{\prime}\) is the CO\({}_{2}\) limitation factor for light-limited assimilation and Mc is the molar mass of carbon (g mol\({}^{-1}\)). The temperature-dependent intrinsic quantum yield of photosynthesis is calculated from:  
\[\varphi_{0}(T_{mean})=c_{L}\Big{(}0.352+0.022T_{mean}-0.00034T_{mean}{}^{2 }\Big{)} \tag{2}\]  
where c\({}_{\text{L}}\) = 0.08718; it is a parameter determining the quantum efficiency of photosynthesis from leaf light absorptance [50]. The fraction of PAR that is absorbed by the canopy is given by:  
\[I_{abs}=PPFD(1-\exp(-0.51 LAI)) \tag{11}\]  
where PPFD is the sum of the PAR of the day. The CO\({}_{2}\) limitation factor for light-limited assimilation is given by:  
\[m^{\prime}=m\sqrt{1-(c^{*}/m)^{2/3}} \tag{12}\]  
with  
\[m=\frac{C_{a}-\Gamma_{T}^{*}}{C_{a}+2\Gamma_{T}^{*}+3\Gamma_{T}^{*}\sqrt{\frac {1.6\eta^{*}D}{\beta\left(K+\Gamma_{T}^{*}\right)}}} \tag{13}\]  
c* is equal to 0.41 [98], C\(\alpha\) is the ambient CO\({}_{2}\) concentration (Pa), D is the vapor pressure deficit, \(\eta^{*}\) is the change in the viscosity of the water relative to its value at 25 \({}^{\circ}\)C (water viscosity at T\({}^{\circ}\)C/water viscosity at 25\({}^{\circ}\)C) and \(\beta\) is the unit cost ratio, taken as 146.0 [50]. For D, K and \(\Gamma_{T}^{*}\), see Equations (10), (11) and (12), respectively. Water vapor pressure deficit D (Pa) is calculated by the difference of the pressure of water vapor in saturated air (esat) and the actual vapor pressure (eact) as  
\[D=e_{sat}-e_{act} \tag{14}\]  
with  
\[e_{sat}=611\exp(17.27T/(T+237.3)) \tag{15}\]  
Note that, if temperature data are not instant, but daily, \(e_{sat}\) is more desirable to calculate as the mean of \(e_{sat\_min}\) and \(e_{sat\_max}\) using the daily T\({}_{\rm min}\) and T\({}_{\rm max}\), respectively, and that T is in \({}^{\circ}\)C.  
\[e_{act}=\frac{e_{sat\_min}\frac{RH_{max}}{100}+e_{sat\_max}\frac{RH_{min}}{100}}{2} \tag{16}\]  
K is the Michaelis-Menten coefficient for photosynthesis (Pa) given by:  
\[K(T_{K},p)=K_{c}(T_{K})(1+(pO_{2}/K_{o}(T_{K}))) \tag{17}\]  
with \(K_{c}(T_{K})\) and \(K_{o}(T_{K})\) being the Michaelis-Menten constants for carboxylation and oxygenation reactions, respectively (Pa):  
\[K_{c}(T_{K})=K_{c}*\exp(\Delta H_{K_{c}}*(T_{K}-298.15)/(298.15*R*T_{K})) \tag{18}\]  
\[\varphi_{0}(T_{mean})=c_{L}\Big{(}0.352+0.022T_{mean}-0.00034T_{mean}{}^{2 }\Big{)} \tag{2}\]0  
where \(K_{c}\) = 39.97 (Pa), \(K_{o}\) = 27480 (KPa), \(\Delta H_{K_{c}}\) = 79430 (J mol\({}^{-1}\)), \(\Delta H_{K_{o}}\) = 36380 (J mol\({}^{-1}\)) and \(T_{K}\) is the leaf temperature in \({}^{\circ}\)K. R is the universal gas constant (8.3145 J mol\({}^{-1}\) K\({}^{-1}\)). pO\({}_{2}\) is the partial pressure of oxygen in the atmosphere, corrected for elevation differences (z), with the assumption of a constant mixing ratio:  
\[\varphi_{0}(T_{mean})=c_{L}\Big{(}0.352+0.022T_{mean}-0.00034T_{mean}{}^{2 }\Big{)} \tag{2}\]1  
with p\({}_{0}\) the atmospheric pressure at sea level (Pa), L the mean adiabatic lapse rate (0.0065 \({}^{\circ}\)K m\({}^{-1}\)), z is the elevation (m), g the gravitational constant (9.80665 m s\({}^{-2}\)) and M\({}_{\alpha}\) is the molecular weight for dry air (0.028963 kg mol\({}^{-1}\)). The photorespiratory compensation point is calculated from:  
\[\varphi_{0}(T_{mean})=c_{L}\Big{(}0.352+0.022T_{mean}-0.00034T_{mean}{}^{2 }\Big{)} \tag{2}\]2  
with \(\Delta H_{\Gamma_{*}}\) being the activation energy (23,400 Pa) and \(\Gamma^{*}\) being the photorespiratory compensation point at 25 \({}^{\circ}\)C (4.332 Pa).