## 4 Discussion  
\(L\hat{U}E_{\rm RF}\) from a machine learning model produced more accurate estimates of \(G\dot{P}P\) than G\(\rm{P}_{\rm CASA}\) estimated with a fixed \(\rm{LUE}_{\rm max}\) and stress scalars, as shown in Figure 8. This was because CASA gave grossly overestimated GPP estimates (Figure 7) due to overestimation of \(\rm{LUE}_{\rm max}\) and insufficient downscaling from the stress scalars (Figure 4). These findings are consistent with [PERSON] et al. [25] who, using some of the flux tower sites in Table 1, found that CASA overestimated GPP by a RMSE of approximately 6 \(\rm{gC/m^{2}/day}\), while the  
Figure 8: Predicted Gross Primary Productivity (\(G\dot{P}P\)) with predicted light use efficiency (\(L\hat{U}E_{\rm RF}\)) values from the model with (**a**) all predictor variables in Table 3 against G\(\rm{P}_{\rm in\,situ}\) from flux tower sites in Table 1, and (**b**) without crop type as a predictor. Root mean square error (RMSE) and mean error (ME) between observed and predicted observations are shown and the standard error on out-of-bag prediction is denoted by error bars. MODIS MOD17 GPP product underestimated cropland GPP by a RMSE of approximately 12 gC/m\({}^{2}\)/day. This means that using crop-specific \(\mathrm{LUE_{max}}\) values in CASA is likely to produce more accurate estimates of GPP than continental GPP products over cropland, and that accuracy can be further improved by varying LUE using a predictive model. Furthermore, prediction of \(L\Omega E_{\mathrm{RF}}\) on a combination of agroclimatic and vegetation index predictors for calculation of \(G\widehat{\varPhi}P\) gave more accurate estimates than other approaches applied to these flux tower sites. [PERSON] and [PERSON] [28; 69] produced RMSEs of 2.75 and 2.9 gC/m\({}^{2}\)/day, respectively, by focusing on GCVI and NDVI as predictors. RMSEs between 1 and 2 gC/m\({}^{2}\)/day were achieved by incorporating other indices such as the LAI and Wide Dynamic Range Vegetation Index (WDRVI) [27; 45]. Our estimation of RMSEs < 1 gC/m\({}^{2}\)/day (Figure 8), across similar ranges of \(\mathrm{GPP_{in\,situ}}\), for the same flux tower sites demonstrates the enhanced accuracy attributable to the machine learning approach encompassing within-season variation. Our findings demonstrate that varying LUE dynamically over a cropping season will produce more accurate estimates of remotely sensed GPP. Figure 3 shows that \(\mathrm{LUE_{in\,situ}}\) varies within seasons, and variables related to seasonality, namely DAS and day length, have been highlighted as important by the random forest model (Figure 5). This is also supported by the partial dependence patterns of the random forest model on DAS, NDVI, and day length (Figures 5 and 6), which reflects patterns identified in Figure 3. Neither the \(\mathrm{LUE_{max}}\) or stress scalars in CASA account for within-season variation in LUE. We suggest that this source of variation should be a primary component of productivity estimation methods for cropland. Furthermore, Figure 4 shows that stress scalars did not sufficiently reduce \(\mathrm{LUE_{max}}\) to reflect \(\mathrm{LUE_{in\,situ}}\), especially for maize. This may be because temperature, vapor, and soil moisture stress did not explain much variation in \(\mathrm{LUE_{in\,situ}}\), though setting \(\mathrm{LUE_{max}}\) too high also contributed. A weak relationship between the stress scalars and \(\mathrm{LUE_{in\,situ}}\) may also explain the poor predictive ability of Model 3 with \(\mathrm{LUE_{max}}\) as the response (Table 4). This corresponds to [PERSON] et al. [8] who found greater NPP estimate accuracy with CASA when stress scalars were omitted for irrigated and temperature-resistant crops. They attributed this to the stress scalars being inappropriate indicators of variation in LUE for some croplands where stress may be overcome by either genotypic (temperature stress-resistant cultivars) or agronomic (irrigation) management. Additionally, components of CASA have been criticised for their weak relationship to LUE.