# Linking Remotely Sensed Carbon and Water Use Efficiencies with In Situ Soil Properties
## 4 Discussion
Land cover was the most important predictor for CUE highlighting the difference between forest and grassland ecosystems, which was similar to the observed pattern in MODIS-derived CUE [33; 55]. The importance of soil extractable Ca for predicting CUE highlighted the close interactions between plant N uptake, soil N pools, and soil extractable Ca [76; 77], and an increase in soil extractable Ca increases GPP and eventually decreased CUE. The CUE increased with a decrease in soil extractable Mg because of the role that Ca plays in regulating physiological responses related to plant stress and growth [37; 78]. For instance, the deficiency in soil Ca was related to an increase in root biomass and a decrease in respiration [78], whichcan lead to an increase in NPP and potentially CUE. The importance of the soil \(\delta^{13}\)C as a predictor of the \(\text{CUE}_{\text{SIF}}\) has not been reported before mainly because of limited site CUE data. As more soil \(\delta^{13}\)C data becomes available, more in-depth studies can potentially further probe into the linkages between soil \(\delta^{13}\)C values and vegetation WUE and CUE. The CART \(\text{CUE}_{\text{SIF}}\) model showed a positive relationship between \(\text{CUE}_{\text{SIF}}\) and soil extractable Mg. Soil Mg is involved in various processes that affect photosynthesis and plant growth, such as chlorophyll a and b production and root and shoot biomass [37; 79; 80]. A recent meta-analysis study found that an increase in soil extractable Mg leads to an increase in NPP and biomass [81], which can eventually increase CUE as predicted by our CART results. The regression tree analysis revealed relationships of soil chemical and physical properties with WUE and CUE. The CART analysis allowed us to: unravel the interactions among various soil properties and their and combined effects on WUE and CUE; and to identify soil variables that are most important for predicting WUE or CUE. Our approach provided an understanding of the interrelationships within the datasets (e.g., soil depth) more easily than using, for example, simple or multiple regression analysis. It should be noted that the results shown in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 did not mean that these variables were the only soil variables important for predicting WUE and CUE, but rather that the CART method found these variables to be able to minimize the variability in WUE and CUE between all the tree nodes. Figures S1-S5 show the ranking of the importance of soil variables in predicting WUE and CUE. Thus, all the other soil variables (Figures S1-S5) had certain predictive power for WUE and CUE suggesting the need for more comprehensive soil-vegetation analysis to better untangle the complex soil-vegetation processes that underlie WUE and CUE. All soil chemical and physical variables included in this study have direct or indirect effects on vegetation processes, including plant growth, WUE, GPP, and ET [37; 79; 80; 82]. Soil extractable Zn and C:N ratio were the only soil variables that did not show any predictive power for either WUE or CUE. (Figures S1-S5). Soil \(\delta^{15}\)N values appeared once as a variable that had predictive power for WUE (Figure S1). Thus, for our study sites, these soil variables were not important in minimizing the errors in CUE or WUE between the CART tree nodes. We collected soil samples from two soil orders to minimize the effects of soil order on soil chemical properties. We expect that our soil chemical and physical data to have little variability as they were collected from the center of Landsat 30 m pixels with a homogenous land cover type. This is less likely to be the case for the coarse-resolution MODIS (250 m) and GOSIF GPP (0.05\({}^{\circ}\)) data, as individual grid cells could contain multiple land cover types. With time, vegetation type and land use could alter soil properties and result in different soil chemical concentrations, leading to heterogeneous soil properties in a pixel with multiple land cover types.