## 4 Discussion  
In this study, we examined two different types of optical remote sensing variables (PRI, SIF) to track the physiological status of plants for monitoring carbon assimilation in a cornfield. We made  
Figure 6: Results of the k-fold cross-validation (\(K\) value set to 10) performed on the GPP model presented in Figure 5. The cross-validated r\({}^{2}\) (r\({}^{2}_{\rm cv}=0.79\)) and RMSE (RMSE\({}_{\rm ev}=0.188\) mg CO\({}_{2}\)/m\({}^{2}\)/s) confirms the robustness of the GPP model using PRI and SIF (red). Figure 7: Cross-validation of the GPP model presented in Figure 5 using a systematic partitioning approach: (**a**) data acquired in 2008 were used as training data to develop the model; and (**b**) data from 2010 to 2012 were used as validation data. The results confirm the consistency of the GPP model applied over four growing seasons. observations over different environmental and crop conditions in four growing seasons, which included different corn cultivars in each year. We documented inter-annual and diurnal variations in the optical indices as well as GPP values (Figure 1), which were influenced by weather conditions. Precipitation in this rain-fed field increased GPP values. But unseasonably high temperatures, observed in the middle of the 2011 season and in 2012 during the vegetative stage, created strongly expressed canopy stress which reduced productivity and GPP. Diurnal GPP cycles showed higher mid-day production when the vegetation was exposed to abundant solar radiation. However, both the SIF and PRI responses indicated that plants experienced physiological stress during mid-day, also induced by high solar radiation and temperatures. Higher SIF and lower PRI values expressed higher stress conditions during mid-day, while lower SIF/higher PRI values described stress abatement during early morning and late afternoon (Figure 2c,d). This diurnal trend was captured in the tower-based LUE, which exhibited the opposite diurnal dynamics to GPP (Figure 2a,b). A similar pattern to diurnal trends was seen in the seasonal trends of GPP, PRI, and SIF (Figure 3). Certain growth variables (e.g., LAI, phenological stage) affected the observed values for GPP, PRI and SIF. In 2008, NDVI value remained fairly consistent across the field season. On the contrary, both PRI and SIF displayed seasonal changes in concert with GPP that year, similar to the results for a sorghum field [75]. This shows that the PRI and SIF provide information that is more related to photosynthetic function than might be inferred from the NDVI. Several previous studies investigated similar topics and evaluated the performance of PRI and SIF for carbon monitoring. [PERSON] _et al_. [73] examined SIF (far-red) retrievals at 760 nm for fAPAR estimates, combined with either SIF yield or PRI, to model LUE in a rice field during two growing seasons; this method significantly improved estimates and reduced uncertainty in mid-day GPP (r\({}^{2}\) = 0.91, RMSE = 3.40 \(\upmu\)mol CO\({}_{2}\)/m\({}^{2}\)/s). [PERSON] _et al_. [74] examined various formulations that coupled a suite of spectral vegetation indices, including the PRI, to estimate mid-day and daily GPP in a subalpine grassland. [PERSON] _et al_. [26] utilized SIF retrievals at 760 nm and PRI to improve LUE estimates for describing the diurnal GPP course in a comfield. [PERSON] _et al_. [79] reported that the PRI and SIF retrievals at the 760 nm showed a similar seasonal trend to that of GPP measured at the same time of spectral observations (r\({}^{2}\) between 0.75 and 0.84; \(p<0.01\)). The study reported a GPP model (r\({}^{2}\) = 0.67, RMSE = 5.77 \(\upmu\)mol CO\({}_{2}\)/m\({}^{2}\)/s) using LUE estimates based on the SIF (far-red) yield at 760 nm, while the PRI-based LUE exhibited weaker performance (r\({}^{2}\) = 0.26, RMSE = 9.25 \(\upmu\)mol CO\({}_{2}\)/m\({}^{2}\)/s) for GPP estimates. These field studies demonstrate that variable results across vegetation types and conditions can be obtained in using SIF and/or PRI to estimate LUE or GPP.