# Linking Remotely Sensed Carbon and Water Use Efficiencies with In Situ Soil Properties
## 3 Results
### Soil Variables Versus CUE and WUE
Since the difference between the original CART and \(\text{CART}_{\text{nSH}}\) for \(\text{CUE}_{250}\) was almost identical, we decided to use the model that included all the soil variables (Table 3). The pruned CART model for \(\text{CUE}_{\text{SIF}}\) showed that soil \(\delta^{13}\)C was the first split showing a positive relationship with \(\text{CUE}_{\text{SIF}}\), that the second split was soil silt content with lower \(\text{CUE}_{\text{SIF}}\) at lower soil silt content, and that the third split was soil extractable Mg that a positive relation with \(\text{CUE}_{\text{SIF}}\) (Figure 8A); the model had r\({}^{2}\) of 0.45 and MAE of 0.1 (Table 3). The variable importance plots for the CART models are shown in the Supplementary Figures S1-S5. As expected, soil order and soil \(\delta^{13}\)C were the most important predictors of WUE (Figure S1), while OM was the most powerful predictor of \(\text{WUE}_{\text{SIF}}\) (Figure S2). Land cover was the most important predictor of \(\text{CUE}_{30}\) and \(\text{CUE}_{250}\) (Figures S3 and S4). Soil \(\delta^{13}\)C was the most important predictor of \(\text{CUE}_{\text{SIF}}\) (Figure S5). It is important to note that all other soil variables had some amount of predictive capacity for both WUE and CUE (Figures S1-S5). Figure 6: Pruned regression tree for (**A**) Landsat-based CUE predicted as a function of two significant variables. The number in boxes 1 and 3 represent the mean CUE of the node, the \(n\) value represents the terminal node size, soil variables names under the boxes represent the splitting criterion, and the numbers in boxes 2, 6, and 7 represent the mean estimated CUE. Note that the position of “yes” and “no” at each split represents the decision split at each node. (**B**) Boxplots showing the distribution of CUE in each terminal node in the regression tree. The model has \(r^{2}\) of 0.64 and MAE of 0.04 for CUE. Figure 7: Pruned regression tree for (**A**) MODIS CUE predicted as a function of two significant variables The number in boxes 1 and 3 represent the mean CUE of the node, \(n\) value represents the terminal node size, soil variables names under the boxes represent the splitting criterion, and the numbers in boxes 2, 6, and 7 represent the mean estimated CUE. Note that the position of “yes” and “no” at each split represents the decision split at each node. (**B**) Boxplots showing the distribution of CUE in each terminal branch in the regression tree. The model has \(r^{2}\) of 0.78 and MAE of 0.06. Impacts of Different Productivity Measures and Spatial Resolution on the Relationship Satellite-Derived CUE and, WUE Withsoil Properties  
We applied the CART for MODIS WUE and WUE\({}_{\text{SIF}}\) to investigate the impacts of different productivity measures (based on the MODIS light use efficiency model vs. GPP based on OCO-2 SIF) on the CART results. There were no common variables detected between CART-MODIS and CART-SIF (Figures 4 and 5). We compared GEOSIF GPP and MODIS GPP and found a low correlation (r\({}^{2}\) = 0.19) between these two products (Figure S7). In general, GOSIF GPP values were much higher than MODIS GPP which was reported to underestimate site measured GPP, particularly for cropland [40; 70]. Besides, we applied CART for Landsat CUE, MODIS CUE, and SIF-based CUE to investigate the impact of spatial resolution on the results of CART. The land cover type and soil extractable Ca were the common variables between MODIS CUE and Landsat CUE (Figures 7A and 8A) highlighting the importance of these soil variables for predicting CUE. No common soil variables were detected among CUE\({}_{\text{SIF}}\), CUE\({}_{30}\), and CUE\({}_{250}\) (Figures 6-8). This could be due to different algorithms used to estimate MODIS and Landsat GPP compared to the GPP derived from SIF and the different spatial resolutions of these data products (Table 4).