## 3 Results
### Prediction of Light Use Efficiency  
The model which included crop type produced a higher \(R^{2}\) and lower mean of squared residuals (Table 4), indicating that crop type is an important predictor of LUE. This was reflected in the variable importance results (Figure 4). However, the OOB predictions for \(\mathrm{LUE_{max}}\) from random forest models did not explain much variation in \(\mathrm{LUE_{max}}\) in situ (Table 4). Additionally, Figure 5 shows that the stress scalars in the CASA Equation (2) do not sufficiently downscale the fixed \(\mathrm{LUE_{max}}\) values to match \(\mathrm{LUE_{in\,situ}}\), especially for maize. The negative mean error indicates that \(\mathrm{LUE_{CASA}}\) is an overestimate of \(\mathrm{LUE_{in\,situ}}\), \(L\tilde{U}E_{\mathrm{RF}}\) from Model 1 (Table 4) shows a much closer distribution to that of \(\mathrm{LUE_{in\,situ}}\). For this reason, only Models 1 and 2, which give \(L\tilde{U}E_{\mathrm{RF}}\), not \(\mathrm{LUE_{max}}\), were chosen for further evaluation.  
Figure 3: Figures showing (**a**) in situ Gross Primary Productivity (GPP) and (**b**) light use efficiency (LUE) aggregated by crop type and over crop seasons by day after sowing. Colours denote codes for the FLUXNET flux tower sites shown in Table 1. Plotted lines were fitted with a local polynomial regression and ribbons show the 95% confidence interval.  
Crop type was the most important predictor in Model 1 (Figure 5), reflecting variation in \(\text{LUE}_{\text{in situ}}\) between crops shown in Figure 2. Thereafter, the agroclimatic variables--day length, DAS, and temperature--were relatively important predictors. Vegetation indices  
Figure 4: In situ light use efficiency (\(\text{LUE}_{\text{in situ}}\)) values compared with LUE reduced below its potential by stress scalars as per Equation (2) (\(\text{LUE}_{\text{CASA}}\)) and LUE predicted from a random forest model with satellite-derived and agroclimatic predictors (\(L\tilde{U}E_{\text{RF}}\)) in Table 3. Median is shown with a horizontal line, and the fixed maximum light use efficiency (\(\text{LUE}_{\text{max}}\)) for C3 and C4 crops are shown with points.  
Figure 5: Variable importance plot for the random forest regression model using all predictors shown in Table 3, expressed as percentage increase in mean square error.  
were of similar importance. Satellite bands were scattered amongst other predictors in terms of importance, and relative humidity was relatively unimportant.  
Partial dependence plots (Figure 6) from random forest Model 1 show that LAI values less than approximately 2 reduced \(L\hat{U}E_{\text{RF}}\). Higher SAVI and NDVI were associated with greater \(L\hat{U}E_{\text{RF}}\), while GCVI between approximately \(-0.5\) and \(1\) reduced predicted values. Partial dependence on DAS reflected temporal patterns in GPP and LUE shown in Figure 3. Greater day length was associated with higher \(L\hat{U}E_{\text{RF}}\), as was average temperature, although values greater than approximately 25 \({}^{\circ}\)C reduced predictions.  
Figure 6: Partial dependence of light use efficiency predictions on (**a**) vegetation index and (**b**) agroclimatic predictors in the random forest regression model fit with all variables in Table 3 as predictors.