## 3 Results
### Performance of the PRI-Based LUE Model and SIF-Based Linear Model for GPP Estimation
Figure 3: Linear regressions of half-hourly (**a**) single-angle observed PRI (\(\mathrm{PRI_{s}}\)) and light use efficiency based on eddy covariance (EC) measurement (\(\mathrm{LUE_{EC}}\)), (**b**) canopy PRI (\(\mathrm{PRI_{can}}\)) and \(\mathrm{LUE_{EC}}\), and (**c**) their diurnal variation on DOY 204 (23 July, 2018). Effects of Different Environmental Variables on the Abilities of the PRI-Based and SIF-Based Models in Tracking Diurnal Variations of GPP  
Figure 5 illustrates the seasonal variations of the environmental variables, \(\mathrm{GPP_{EC}}\) and \(\mathrm{LUE_{EC}}\). PAR and Q exhibited the largest day-to-day variations and high Q usually occurred with high PAR (Figure 5a). The day-to-day variation of RH appeared opposite those of PAR, while the several abrupt changes of SWC depended on irrigation and precipitation (Figure 5b). Both \(\mathrm{T_{a}}\) and \(\mathrm{T_{s}}\) remained around 30 \({}^{\circ}\)C during DOY 180-220, and then slowly decreased to around 22 \({}^{\circ}\)C at the end of the growing season (Figure 5c). The day-to-day fluctuation of \(\mathrm{T_{a}}\) was larger than that of \(\mathrm{T_{s}}\) (Figure 5c). The maize canopy showed pronounced seasonal variations in \(\mathrm{GPP_{EC}}\) and \(\mathrm{LUE_{EC}}\) (Figure 5d). The onset of \(\mathrm{GPP_{EC}}\) occurred on DOY 167, several days after emergence. \(\mathrm{GPP_{EC}}\) increased with maize development and reached its peak of 60 \(\mathrm{\SIUnitSymbolMicro mol\,CO_{2}\,m^{-2}\cdot s^{-1}}\) on around DOY 215. During the early reproductive stage, \(\mathrm{GPP_{EC}}\) had high and stable values, sometimes dropped to low values due to low PAR. \(\mathrm{GPP_{EC}}\) decreased with leaf senescence at the end of the growing season. \(\mathrm{LUE_{EC}}\) increased from the start of the growing season, reaching the maximum on around DOY 190, and remaining until the early reproductive stage, and then decreasing. Figure 4: Coefficients of determination between \(\mathrm{LUE_{PRI}}\)\(\times\)APAR and \(\mathrm{GPP_{EC}}\) (\(\mathrm{R^{2}_{PRI}}\)), \(\mathrm{SIF_{can}}\) and \(\mathrm{GPP_{EC}}\) (\(\mathrm{R^{2}_{SIF}}\)) on individual days and distribution of their relative frequency over the 2018 growing season of the maize field. (**a**) and (**b**) represented the \(\mathrm{R^{2}_{PRI}}\) and its relative frequency respectively, while (**c**) and (**d**) represented the \(\mathrm{R^{2}_{SIF}}\) and its relative frequency respectively. Figure 5: Seasonal variations of the daily mean (**a**) photosynthetically active radiation (PAR) and sky condition (Q), (**b**) relative humidity (RH), and soil water content (SWC), (**c**) air temperature (\(\mathrm{T_{a}}\)) and soil temperature (\(\mathrm{T_{s}}\)), and (**d**) \(\mathrm{GPP_{EC}}\) and \(\mathrm{LUE_{EC}}\). Daily means were calculated from half-hourly values from 6:00 to 18:00 in the day. Small dot indicates half-hourly \(\mathrm{GPP_{EC}}\). To avoid the interactions between environmental variables, a random forest regression analysis was used to assess the effects of environmental variables on R\({}^{2}\)\({}_{\text{PRI}}\) and R\({}^{2}\)\({}_{\text{SIF}}\). Among the environmental variables, the most important one affecting R\({}^{2}\)\({}_{\text{PRI}}\) was RH, with the percentages increase in mean square error (\(\%\)IncMSE) of 25.6\(\%\). T\({}_{\text{s}}\) (\(\%\)IncMSE = 22.0\(\%\)) was the second most important environmental variable affecting R\({}^{2}\)\({}_{\text{PRI}}\) followed by SWC (\(\%\)IncMSE = 13.9\(\%\)). PAR and Q were the least important variables (Figure 6a). Obvious differences were found between R\({}^{2}\)\({}_{\text{SIF}}\) and those of R\({}^{2}\)\({}_{\text{PRI}}\). PAR appeared to be the most important driver for R\({}^{2}\)\({}_{\text{SIF}}\) (\(\%\)IncMSE = 22.3\(\%\)). Q was of secondary importance to R\({}^{2}\)\({}_{\text{SIF}}\) (\(\%\)IncMSE = 11.5\(\%\)) (Figure 6b).