## 3 Results
### Relationships with Environmental Factors  
Figures 6 and 7 illustrate relationships between environmental factors and productivity metrics, with the color of the data points representing months (winter months in purple and summer months red). Temperatures T\({}_{\text{can}}\), T\({}_{\text{air}}\), and LST display similar trends with SIF\({}_{\text{i}}\) and SIF\({}_{\text{d}}\), despite a larger range of T\({}_{\text{can}}\) and T\({}_{\text{air}}\) values attributed to higher values versus LST (Figure 6a,b,d,e,j,k). SIF\({}_{\text{i}}\) and SIF\({}_{\text{d}}\) vs. T\({}_{\text{can}}\), T\({}_{\text{air}}\), and LST trends are flat in the winter months, and then they climb in spring and reach the maximum values, followed by a distinct decrease at the hottest temperatures (Figure 6a,b,d,e,j,k). SIF\({}_{\text{i}}\) and SIF\({}_{\text{d}}\) vs. VPD trends show clustering in the winter months and summer peak earlier than that for temperatures, followed by slowly decreasing trends at the highest VPD (Figure 6g,h). SIF\({}_{\text{y}}\)-environmental variable trends share some general features with those of SIF\({}_{\text{i}}\) and SIF\({}_{\text{d}}\)-environmental variable trends; however, SIF\({}_{\text{y}}\) outliers affect the trends (Figure 6c,f,i,l). In all cases, the relationships are not linear in nature, but there is a great deal of scatter among the SIF metrics and environmental variables (Figure 6). Trends among VIs and environmental variables (Figure 7) indicate that GPP reaches a maximum before the hottest months and then decreases at high T\({}_{\text{can}}\), T\({}_{\text{air}}\), and LST (Figure 7a,d,j). NDVI and EVI tend to saturate at high T\({}_{\text{can}}\) and T\({}_{\text{air}}\), although NDVI values cluster more tightly at the highest T\({}_{\text{can}}\) and T\({}_{\text{air}}\) than EVI values (Figure 7a-f,j-l). Driven by an outlier, NDVI and EVI-LST trends appear to reach their maximum values before the hottest months and then decrease at the highest LST value, without which these trends would also cluster and saturate similar to NDVI, EVI-T\({}_{\text{can}}\), and T\({}_{\text{air}}\) (Figure 7a,d,j). The relative importance of environmental variables in predicting productivity metrics was conducted in two ways. First, the analysis was conducted only with the environmental variables T\({}_{\text{can}}\), T\({}_{\text{air}}\), VPD, and LST, and then again with the four environmental variables plus the intermediate variables fPAR and LAI. The results presented here include the group of environmental variables plus the intermediate variables because the variance of productivity explained with only environmental variables was 34.9-70.89%, while adding the intermediate variables improved the variance to 43.2-84.1%. The variance explained by the environmental variables plus intermediate variables in this study is as follows: SIF\({}_{\text{i}}\) 83.56%, SIF\({}_{\text{d}}\) 83.75%, SIF\({}_{\text{y}}\) 43.22%, GPP 81.02%, NDVI 84.06%, and EVI 83.73%. All metrics of productivity were similarly well explained by these predictors, except SIF\({}_{\text{y}}\), which was \begin{table}
\begin{tabular}{c c c c c c} \hline
**Value** & **SIF\({}_{\text{i}}\)** & **SIF\({}_{\text{d}}\)** & **SIF\({}_{\text{y}}\)** & **GPP** & **NDVI** & **EVI** \\ \hline SIF\({}_{\text{d}}\) & 1.00 *** & & & & \\ \hline SIF\({}_{\text{y}}\) & 0.67 *** & 0.65 *** & & & \\ \hline GPP & 0.85 *** & 0.86 *** & 0.43 ** & & \\ \hline NDVI & 0.84 *** & 0.84 *** & 0.46 ** & 0.84 *** & \\ \hline EVI & 0.89 *** & 0.89 *** & 0.48 ** & 0.88 *** & 0.96 *** & \\ \hline LAI & 0.76 *** & 0.76 *** & 0.42 ** & 0.80 *** & 0.87 *** & 0.85 *** \\ \hline fPAR & 0.82 *** & 0.82 *** & 0.42 ** & 0.84 *** & 0.82 *** & 0.88 *** \\ \hline \end{tabular}
\end{table} 
Table 2: Correlations among SIF\({}_{\text{i}}\), SIF\({}_{\text{d}}\), SIF\({}_{\text{y}}\), GPP, NDVI, EVI, LAI, and fPAR (Pearson, \(r\)-values. *** indicates \(p\)-value \(<\) 0.001; *** indicates \(p\)-value \(<\) 0.01).