## 3 Results
### Results of Spectroradiometric and Eddy Covariance Measurements on the Ground
For sugar beet, PRI and LUEEC are positive correlated (Figure 6(B3,B4)), however, the correlation on DOY 253 is only weak and not significant (see Table S3 in the supplementary materials). For winter wheat the relationship between PRI and LUEEC is not clear. Figure 6(B1,B2) does not show any obvious correlation on both measurement days. However, statistical analyses revealed a slight negative correlation on DOY 176 only (Table S3 supplementary materials). Figure 5: Diurnal behavior of gas exchange parameters derived at saturating light intensities, measured at leaf level for winter wheat (DOY 127, 176) and sugar beet (DOY 183, 253). Circles represent values for winter wheat and triangles values for sugar beet. Top row (**A1–A4**): Maximum net photosynthetic CO2 uptake rate (Amax); Bottom row (**B1–B4**): Maximum stomatal resistance (\(rs_{\text{max}}\)). Vertical error bars indicate uncertainties of the fitting used to determine Amax and \(rs_{\text{max}}\). Horizontal error bars indicate the time intervals of measurements. Vertical dashed lines indicate solar noon. See also Figure S2 in supplementary materials for additional measurements at three other days that show a similar diurnal behavior of Amax. Modeling GPP Using Spectroradiometric Measurements of Sun-Induced Fluorescence and PRI as Dynamic Input Parameters  
Diurnal courses of GPP were calculated according to Equations (10)-(14): using constant values of LUE or by replacing them with F\({}_{760}\) and PRI, and using NDVI as a proxy for \(f_{\text{APAR}}\). The use of constant LUE values (modeling approaches A and B) did not allow accurate modeling of the asymmetric diurnal course of measured GPP\({}_{\text{EC}}\), which exhibited maximum values of carbon assimilation that do not coincide with highest PAR values at solar noon (Figure 7). Incorporating instantaneous F\({}_{760\text{-yield}}\) and PRI measurements, however, allowed a substantially improved modeling of GPP diurnals; even the asymmetric GPP\({}_{\text{EC}}\) behavior of sugar beet across the day could be partly reproduced (Figure 7(A3,A4)). Figure 6: Light-use efficiency derived from eddy covariance (EC) observations (LUE\({}_{\text{EC}}\)) in relation to sun-induced fluorescence yield (F\({}_{760\text{-yield}}\)) and photochemical reflectance index (PRI) obtained from ground-based spectroscopy for winter wheat (DOY 127, 176) and sugar beet (DOY 183, 253). Top row (**A1**–**A4**): relationship between light use efficiency (LUE\({}_{\text{EC}}\)) and sun-induced fluorescence yield (F\({}_{760\text{-yield}}\)). Bottom row (**B1**–**B4**): relationship between light use efficiency (LUE\({}_{\text{EC}}\)) and photochemical reflectance index (PRI). The color code indicates the observation time (UTC). Gray lines represent a linear model fitted to the sugar beet data, the goodness of fit is indicated with the correlation coefficient (r). All parameters of the linear model and results of the cross validation are given in Tables S2 and S3 in the supplementary materials. Figure 7: Diurnal behavior of gross primary productivity (GPP) derived from the eddy covariance (EC) method (GPP\({}_{\text{EC}}\)) and GPP calculated using two different approaches (GPP\({}_{\text{B}}\) and GPP\({}_{\text{E}}\)) for winter wheat (DOY 127, 176) and for sugar beet (DOY 183, 253). Other model runs (GPP\({}_{\text{A}}\), GPP\({}_{\text{C}}\) and GPP\({}_{\text{D}}\)) are also available and results of the improvement are presented in Figure 8.  
We statistically compared the modeling results with the measured \(\mathrm{GPP_{EC}}\) to quantify the improvement for each model per species, by calculating averages of the coefficient of determination (\(r^{2}\)) and the root mean square error (RMSE), considering all days (Figure 8, Table 1). No significant difference between \(\mathrm{GPP_{A}}\) and \(\mathrm{GPP_{B}}\) was observed for either species, neither in terms of \(r^{2}\) nor in terms of RMSE. This supports the assumption that NDVI can be taken as proxy for \(f_{\mathrm{APAR}}\) in both canopies.