## Materials and Methods
### Forward Modeling of Gross Primary Productivity  
In the following we use [PERSON]'s LUE concept [4; 5] to calculate GPP. We postulate that the fraction of absorbed light (\(f_{\mathrm{APAR}}\)) and the efficiency of the photosynthetic apparatus (LUE) can be determined from the remotely sensed parameters NDVI, F\({}_{760\text{-}\text{yield}}\), and the PRI:  
1. [label=()]
2. \(\mathrm{GPP_{A}}\) describes the classical approach where LUE is considered to remain constant over the course of the day. Thus LUE is parameterized as an optimized but constant value for each diurnal course. We measured \(f_{\mathrm{APAR}}\) and PAR directly using the spectroradiometer on the ground. \[\mathrm{GPP_{A}}=\mathrm{LUE_{const}}\cdot f_{\mathrm{APAR}}\cdot\mathrm{ PAR}\;[\mathrm{\mu mol\cdot m^{-2}\cdot s^{-1}}]\] (10)
3. It has been described in the literature that the NDVI of the observed surface can be used as proxy for \(f_{\mathrm{APAR}}\) in the canopy [39]. Consequently, approach \(\mathrm{GPP_{B}}\) was formulated by using NDVI as a proxy for \(f_{\mathrm{APAR}}\) in \(\mathrm{GPP_{A}}\), aiming to estimate GPP solely from spectroscopic measurements, while using a constant LUE as for \(\mathrm{GPP_{A}}\). The \(\mathrm{LUE_{const}}\) is the daytime mean (07-16 UTC) of the LUE measured with the EC method. The parameters m and k were obtained from the slope and axis interception of the linear fit between \(f_{\mathrm{APAR}}\) and NDVI. The parameters of the linear fit can be found in Table S1 in the supplemental materials. \[\mathrm{GPP_{B}}=\mathrm{LUE_{const}}\cdot(\mathrm{m\cdot NDVI}+\mathrm{k} )\cdot\mathrm{PAR}\;[\mathrm{\mu mol\cdot m^{-2}\cdot s^{-1}}]\] (11) As we will show later (see Section 3.5), approaches \(\mathrm{GPP_{A}}\) and \(\mathrm{GPP_{B}}\) performed equally well for all five observation days. Therefore, NDVI scaling for \(f_{\mathrm{APAR}}\) as in \(\mathrm{GPP_{B}}\) was also used in the remaining approaches. For those three approaches LUE is also parameterized linearly using the variables F\({}_{760\text{-}\text{yield}}\) and PRI. \(\mathrm{GPC_{C}}\) describes the approach where LUE is considered to be parameterized linearly using the F\({}_{760\text{-}\text{yield}}\). Parameters a and b (Equations (12)-(14)) represent the slope and the axis interception of the linear fit between LUE measured with the EC method and each remote sensed parameter. The parameters of the linear fits can be found in Tables S2-S4 in the supplemental materials.  
\[\mathrm{GPP_{C}}=(\mathrm{a_{1}}\cdot F_{760-yield}+\mathrm{b_{1}})\ \cdot(\mathrm{m}\cdot\mathrm{NDVI}+\mathrm{k})\cdot\mathrm{PAR}\ [\mathrm{\upmu mol\cdot m^{-2}\cdot s^{-1}}] \tag{12}\]
2. Another approach, where LUE is considered to be parameterized linearly to PRI, could be written as follows: \[\mathrm{GPP_{D}}=(\mathrm{a_{2}}\cdot PRI+\mathrm{b_{2}})\cdot(\mathrm{m} \cdot\mathrm{NDVI}+\mathrm{k})\cdot\mathrm{PAR}\ [\mathrm{\upmu mol\cdot m^{-2}\cdot s^{-1}}]\] (13)
3. To include both the non-photochemical energy dissipation (NPQ) and the efficiency of photochemical energy separation in the LUE concept, a linear relation to the product of both parameters, \(PRI\) and \(F_{760}\)-yield, is used: \[\mathrm{GPP_{E}}=\left(\mathrm{a_{3}}\cdot\left(F_{760-yield}\cdot PRI\right) +\mathrm{b_{3}}\right)\cdot(\mathrm{m}\cdot\mathrm{NDVI}+\mathrm{k})\cdot \mathrm{PAR}\ [\mathrm{\upmu mol\cdot m^{-2}\cdot s^{-1}}]\] (14)