## 4 Discussion
Our study addressed a similar topic: to investigate the potential use of PRI and SIF to estimate GPP, and to reduce uncertainties in the GPP and LUE estimates (Figure 5, Table 4). The models investigated and presented in our current study were composed solely of remotely-sensed observations. Unlike many previous studies, no micrometeorological variables (e.g., PAR or air temperature) were needed to achieve acceptable performance. The format of the models was determined after reviewing previous studies [73, 74, 26]. The models we utilized are similar to the Type 1 model in [PERSON] _et al_. [74], or the E3 model examined in [PERSON] _et al_. [73]. This confirms the potential for this type of GPP modeling approach, which has the advantage of simplifying the input data type requirements. Although most previous studies have focused on retrievals using the O\({}_{2}\)-A band to obtain SIF (far-red), we included SIF retrievals at the O\({}_{2}\)-B band feature to obtain SIF (red), which provided the strongest relationship to GPP, possibly due to its important role in photosystem II (PSII) processes [53, 89]. Furthermore, we undertook the challenge to model the diurnal variation of GPP during four growing seasons, which presented a complex task since both plant physiological conditions and GPP were changing significantly within any day, as well as across the four growing seasons due to varying climate conditions (Figure 1). The results (Tables 3 and 4) showed the challenge of modeling diurnal variations of LUE and GPP at this site for multiple growing seasons when using only PRI or SIF. Better correlations between PRI, SIF, LUE and GPP were found when using daily average values to study seasonal variations. For instance, for the 2008 growing season, when using daily average values, better performance was observed for the PRI:LUE model (r\({}^{2}\) = 0.76), the SIF (red) yield:LUE model (r\({}^{2}\) = 0.71), and the SIF (red):GPP model (r\({}^{2}\) = 0.61). However, the performance changed when we made the attempt to model diurnal variations across multiple growing seasons. In general, the GPP models examined in this study performed better than the LUE models. Multiple studies have demonstrated the potential of using the PRI to track LUE and photosynthetic activities for various vegetation types (e.g., [17, 18, 21, 22, 29, 50, 51]). The PRI:LUE model we developed with our dataset performed adequately (r\({}^{2}\) = 0.54) and overall results were comparable to previously published results [50]. Nevertheless, one can easily observe year-to-year variations among the four growing seasons, since many factors affect the PRI values as well as the PRI:LUE relationship, e.g., canopy structure, LAI, soil background, and pigment content [42, 45, 48, 50, 51, 85]. No significant correlations were observed between SIF and either LUE or GPP for this dataset, but adding SIF to a simple PRI-based model improved its capability to track the variation in LUE by as much as 16% (Table 3). These findings suggest a future approach to significantly improve the performance of current LUE models, by combining these two optical signals. NPQ and chlorophyll fluorescence emission are considered as direct indicators of photosynthetic activities and physiological stress when plants are under sub-optimal environmental conditions [28, 53, 59, 80, 90, 91, 92, 93] such as low water availability [81, 93, 94, 95], unfavorable temperatures [96, 97], nutrients [98, 99, 100], and salinity [102, 103]. Consequently, many studies have utilized the spectral indices, PRI and SIF retrievals, as indicators of stress and down-regulation of LUE and GPP [29, 50, 51, 65, 82, 92, 104, 105, 106, 107]. Our results lend support to those reported from previous studies that demonstrated that PRI and SIF retrievals were correlated to two important protective mechanisms (NPQ and chlorophyll fluorescence emissions), discarding excess absorbed solar radiation that could not be used in photosynthesis [3, 29, 54].