# Linking Remotely Sensed Carbon and Water Use Efficiencies with In Situ Soil Properties
## 2 Materials and Methods
### Statistical Analysis  
To identify and rank the soil chemical and physical properties that are significant in predicting CUE and WUE, we used the classification and regression trees (CART) method (the rpart package in R). The advantage of the regression tree is that it uses recursive partitioning to split the data into nodes or branches. This allows the training data to be split into groups that behave independently without the need for data stratification before analysis. For soil data analysis, whereas soil variables are the results of interdependent soil processes, the CART model is very helpful because it reveals variable interactions [67; 68]. Thus, CART can help address the interdependence between soil data with depth and CUE and WUE. The predictors used to estimate WUE and CUE were land cover type, soil order, soil horizon, soil depth, layer thickness, bulk density, silt, sand, clay, OM, EC, pH-CaCl2, pH-H2O (1:1 H\({}_{\rm 2}\)O), soil organic carbon (SOC), total C, total N, C:N ratio, \(\delta^{\rm 13}\)C, \(\delta^{\rm 15}\)N, and extractable soil P, K, Ca, Mg, Zn, and Fe. Prediction errors were estimated by randomly dividing the data to 70% training (\(n=80\) for WUE and WUE\({}_{\rm SIF}\); \(n=72\) for \({\rm CUE}_{\rm 30}\), \(n=63\) for \({\rm CUE}_{\rm 250}\), and \(n=76\) for \({\rm CUE}_{\rm SIF}\)) and 30% testing samples (\(n=35\) for WUE and WUE\({}_{\rm SIF}\); \(n=31\) for \({\rm CUE}_{\rm 30}\), \(n=28\) for \({\rm CUE}_{\rm 250}\), and \(n=33\) for \({\rm CUE}_{\rm SIF}\)). The differences in the sampling sizes for the CUE data were related to the availability of satellite data for ourstudy sites. We built the regression tree using the training sample and then pruned the tree to minimize overfitting by selecting the number of splits in the CART that is associated with a minimized cross-validated error estimate. The CART results were used to identify the soil chemical and physical variables that were important predictors for CUE and WUE. Then, the mean absolute error (MAE) was calculated by using the testing sample with the pruned CART model. We applied the CART for the 30 m and 250 m CUE and WUE to investigate the impact of spatial resolution on the results of CART. Additionally, CART was developed for CUESTF and WUESTF. Finally, we analyzed the CART results based on GPP derived from MODIS and SIF data to detect any difference in soil chemical and physical variables identified as important predictors for CUE and WUE. The reason for such comparison is that GOSIF GPP is directly estimated from SIF that is a direct measure of energy emitted by plants during photosynthesis, while MODIS GPP and NPP are based on the light use efficiency model and process-based model, respectively. Thus, they represent two different approaches to estimate CUE and WUE. To test for the effects of land cover type, soil order, soil horizon, and soil depth, we performed four additional CART analyses.: (1) excluding only land cover from the CART model (CART\({}_{\text{nLC}}\)); (2) excluding only soil order from the CART model (CART\({}_{\text{nSO}}\)); (3) excluding only soil horizon from the CART model (CART\({}_{\text{nSH}}\)); and (4) excluding only soil depth from the CART model (CART\({}_{\text{nSD}}\)). This was performed for each of the WUE and CUE data and the model with the highest r\({}^{2}\) and lowest MAE was selected as the best model.  
Soil physical and chemical properties were compared to satellite CUE and WUE. To achieve this, we summed the 8-day MODIS GPP and ET and 16-day Landsat GPP to produce annual GPP for the study sites. Both MODIS and Landsat-based NPP are directly available as annual products. Then, we used the annual data to calculate WUE and CUE at the annual timescale.