# Linking Remotely Sensed Carbon and Water Use Efficiencies with In Situ Soil Properties
## 3 Results
### Soil Variables Versus CUE and WUE  
The pruned CART model for MODIS WUE showed that soil \(\delta^{13}\)C was the primary splitting node indicating the role of SOC in regulating WUE since soil \(\delta^{13}\)C is a facet of soil carbon content. MODIS WUE decreased with greater soil \(\delta^{13}\)C values (less negative) and increased with lower soil \(\delta^{13}\)C values (Figure 4A). The second split was soil order Alfisol that decreased MODIS WUE (Figure 4A), indicating lower WUE in Alfisol soils. Soil OM was the only split for WUE\({}_{\text{SIF}}\), showing a negative relationship between soil OM and WUE\({}_{\text{SIF}}\) (Figure 5A). Table 3 shows the r\({}^{2}\) and MAE values for each of the CART models developed to address the impacts of land cover, soil order, soil horizon, and soil depth. The model with the best model was the one with land cover excluded (CART\({}_{\text{nLC}}\)) from the analysis for MODIS WUE with r\({}^{2}\) of 0.39 and MAE of 0.17 gC/KgH\({}_{2}\)O (Table 3). The WUE\({}_{\text{SIF}}\) models showed the highest MAE when all the soil variables were included (Table 3), and thus we selected the model with land cover excluded (CART\({}_{\text{nLC}}\)) (r\({}^{2}\) = 0.19, MAE = 0.64 gC/KgH\({}_{2}\)O) (Table 3). We found that MODIS WUE outperformed WUE\({}_{\text{SIF}}\) likely because MODIS had finer spatial resolution (250 m) than the GOSIF GPP (0.05\({}^{\circ}\)). Figure 2: Soil texture pyramid for the study sites showing the dominance of silty clay (SIC) and silty clay loam (SICL) soils. Data represents soil texture for every soil depth sampled for each site. C = clay, SC = sandy clay, SCL = sandy clay loam, SL = sandy loam, LS = loamy sand, S = sand, L = loam, CL = clay loam, SIL = silt loam, and SI = silt. Figure 3: Variability of soil chemical properties with soil depth for the study sites: (**A**) total soil carbon (%); (**B**) \(\delta^{15}\)N; (**C**) extractable phosphorus (P); (**D**) extractable potassium (K). Figure 4: Pruned regression tree for (**A**) MODIS-based WUE predicted as a function of two significant variables. The number in boxes 1 and 2 represent the mean \(\text{CUE}_{\text{SIF}}\) of the node, \(n\) values represent the terminal node size, soil variables names under the boxes represent the splitting criterion, and the numbers in boxes 3–5 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 WUE in each terminal node in the regression tree. The model has \(\text{r}^{2}\) of 0.39 and a MAE of 0.175 gC/\(\text{KgH}_{2}\)O for WUE. Figure 5: Pruned regression tree for (**A**) WUE\({}_{\text{SIF}}\) predicted as a function of one significant variable. The number in box 1 represents the mean \(\text{WUE}_{\text{SIF}}\) 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 and 3 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 WUE in each terminal branch in the regression tree. The model has \(\text{r}^{2}\) of 0.19 and MAE of 0.64 gC/\(\text{KgH}_{2}\)O for WUE. The pruned CART model for \(\text{CUE}_{30}\) showed that land cover was the first split, grassland being the main land cover type in the first split (Figure 6A). The second split was soil extractable Ca that showed a negative relationship with \(\text{CUE}_{30}\), with \(\text{CUE}_{30}\) increasing at lower Ca values (Figure 6A), and the CART model had r\({}^{2}\) of 0.64 and MAE of 0.04 (Table 3). Land cover was the first split and the most important predictor for \(\text{CUE}_{250}\), but with the forest as the land cover predictor rather than a grassland as in \(\text{CUE}_{30}\) (Figure 7A). \(\text{CUE}_{250}\) decreased with forest with higher soil extractable Ca (Figure 7A), and the model had r\({}^{2}\) of 0.78 and MAE of 0.06 (Table 3).