# Linking Remotely Sensed Carbon and Water Use Efficiencies with In Situ Soil Properties
## 4 Discussion  
Overall, our approach is robust and applicable to our study sites given the significant relationships of soil chemical and physical properties with CUE and WUE. The recursive partitioning that CART is built upon can model WUE and CUE from soil physical and chemical properties by providing a simplified, but yet powerful perspective on the drivers of WUE and CUE. The CART models showed higher predictability for CUE than for WUE likely due to the uncertainties in MODIS ET or other environmental controls on WUE (e.g., vapor pressure deficit). Our results did not reject our hypothesis that CUE depends on the land cover type with grasslands and forest being the most important predictors of CUE\({}_{30}\) and CUE\({}_{250}\), respectively. Conversely, our results rejected the hypothesis that WUE is dependent on land cover type. The CART WUE and CUE results revealed indirectly the correlations of soil \(\delta^{13}\)C and OM with soil depth. In general, OM was higher and soil \(\delta^{13}\)C values were lower in the topsoil layers and OM becomes lower and \(\delta^{13}\)C values increase with an increase in soil depth [71], which was also the case for our study sites (Figure S6). Although CART WUE and CART CUE\({}_{\text{SIF}}\) models did not show that soil depth was an important predictor of WUE and CUE\({}_{\text{SIF}}\), they did reveal an indirect indication of the soil depth-related properties in regulating WUE and CUE as evident in Figures 4, 5 and 8. Therefore, our results failed to reject our hypothesis that WUE and CUE are independent of soil depth-related properties. Our analysis revealed the importance of soil extractable Ca and Mg in regulating CUE and WUE and calls for more data collections and synthesis to better understand the potential role that these soil properties play in moderating the effects of climate change on CUE and WUE. Our methodology demonstrated the ability of remotely sensed data to capture the observed relationships of CUE, WUE, NDVI, and EVI with soil and provides a platform for future exploration of the soil-vegetation interactions using satellite vegetation data and in situ soil data. The regression tree trained using MODIS data relied on soil \(\delta^{13}\)C and soil order to predict WUE (Figure 4). Soil \(\delta^{13}\)C values showed a positive correlation with WUE (Figure S4A) similar to the observed positive correlations between Leaf \(\delta^{13}\)C and intrinsic WUE [72; 73]. This relationship can be attributed to the close relationship between SOC and \(\delta^{13}\)C values [71; 74] and the role that SOC plays in controlling soil water availability. Regression tree analysis showed that soil order Alfisol was important for predicting WUE. This could be driven by our three sites with soil order Ultisol that on average had higher WUE than the other sites. In general, the three forest sites with soil order Ultisol had lower soil extractable Ca and K than the other sites. An increase in the uptake of soil extractable Ca and K can enhance WUE by decreasing ET [37]. We hypothesized that higher WUE in these three sites is due to an increase in the uptake of soil extractable Ca and K. We plan to measure leaf nutrient concentration data from our study sites to test this hypothesis in future studies. Soil OM was the only statistically significant predictor of WUE\({}_{\text{SIF}}\) (Figure 5). Additionally, OM showed a negative correlation with WUE and can indicate structural water in clay minerals and/or SOC and can affect soil water holding capacity. This is because an increase in soil OM is critical for forming soil aggregate that can increase the soil-plant available water and the latter controls the ET rates [75]. These findings indicate that an increase in OM could lead to a decrease in WUE. The regression trees trained using Landsat and MODIS data were very similar, with both relying on land cover and soil extractable Ca to predict CUE.