## 3 Results  
### Estimating ANHP from iAPAR  
We observed a strong and positive relationship between iAPAR and ANHP. On average, for each unit of added iAPAR, ANHP increased by 9.39 kg/ha (\(\chi^{2}\) = 64.31, df = 1, \(p\) < 0.001; Table 1; Figure 5). As predicted, the effect of iAPAR on ANHP varied significantly by ecosite (\(\chi^{2}\) = 28.5, df = 2, \(p\) < 0.001; Figure 5). The interaction coefficient between iAPAR:Sandy Plains ecosite was 3.92 \(\pm\) 0.96, indicating an increase in the amount of ANHP produced per unit of iAPAR, relative to the reference ecosite (Loamy Plains) (\":\" denotes interaction) (Figure 6). Similarly, the interaction coefficient for iAPAR:Salt Flats ecosite was 5.71 \(\pm\) 1.2, signifying an even greater increase in ANHP produced per unit of iAPAR compared to the Loamy Plains ecosite (Figure 6). The effect of iAPAR on ANHP did not vary based on grazing management treatments (\(\chi^{2}\) = 0.69, df = 2, \(p\) = 0.71), and the effect of grazing management on the iAPAR-ANHP relationship did not vary by ecosite (three-way interaction \(\chi^{2}\) = 7.49, df = 4, \(p\) = 0.11). Figure 5: Ground-collected Above Ground Net Herbaceous Production (ANHP) values to satellite-based iAPAR values. The analysis involved assessing the slopes of the linear relationships after allowing random intercepts to vary by year and plot ID (**top** panels). We also visualize a more realistic prediction scenario where only fixed effects are considered when predicting ANHP (**bottom** panels). Points represent the ground-collected data, with colors and shapes denoting different grazing managements. Lines depict linear relationships between predicted ANHP and iAPAR values. Lines sharing letters did not have significantly different slopes (Tukey HSD; \(p<0.05\)). \begin{table}
\begin{tabular}{c c}  & **Dependent Variable:** \\ \hline \multicolumn{2}{c}{**ANHP (SE) (kg/ha –1)**} \\ \hline iAPAR & 9.39 *** (1.17) \\ Grazing management: Ungrazed & \(-11.96\) (92.45) \\ Grazing management: Pulse-grazed & \(55.44\) (78.54) \\ Ecosite Sandy Plains & \(-28.11\) (77.39) \\ Ecosite Salt Flats & \(94.16\) (110.03) \\ \hline \end{tabular}
\end{table} 
Table 1: Estimated coefficients, standard errors, and significance levels for the fixed effects obtained from the empirical linear mixed model. The reference level for the ecosite was Loamy Plains, and for grazing management, the reference level was season-long grazing. Figure 6: Coefficients with 95% confidence intervals for a linear mixed model predicting ANHP based on iAPAR, ecosite, grazing management treatment, and interactions of these factors. Large circles denote mean coefficients, and lines display 95% confidence intervals. Interaction terms included denoted by “:”. To examine whether more intensive grazing may influence the relationship between ANHP and iAPAR, we separately fit a model predicting ANHP from iAPAR and grazing management treatments for a subset of the data for which we also had a higher stocking rate grazing management treatment, referred to as'season-long heavy' (2019-2022, Loamy Plains ecosite plots only) (Figure 7). For this subset of data, neither grazing management (\(\chi^{2}=1.1\), df = 3, \(p=0.76\)) nor the interaction between iAPAR and grazing management (\(\chi^{2}=2.23\), df = 3, \(p=0.52\)) significantly influenced ANHP.