# Linking Remotely Sensed Carbon and Water Use Efficiencies with In Situ Soil Properties
## 2 Materials and Methods
### Soil Physical and Chemical Analysis  
Continuous soil cores were extracted using a hammer-percussion coring device and the soil horizons were described [58]. The cores were cut in half in the laboratory and an interval-sampling approach was used, where soil samples were extracted from the core every \(8\pm 2\) cm, to ensure that each horizon was sampled at least once. The soil physical and chemical properties were measured on samples collected to a depth of 60 cm. Particle size, oven-dry bulk density, gravimetric water content, pH, and loss on ignition (LOI) were measured for the 19 sites at Murray State University using previously established methods [59] with modifications [60]. LOI describes the variance in soil organic matter content (SOM) and is herein referred to as OM%. Soil samples were sent to the University  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Site ID** & **Latitude** & **Longitude** & **Land Cover** \\ \hline ARB & 36.60N & 88.33W & Grassland \\ \hline NFM & 36.63N & 88.33W & Grassland \\ \hline FFG & 37.75N & 86.62W & Grassland \\ \hline HLF & 37.88N & 84.46W & Grassland \\ \hline HLP & 38.13N & 86.71W & Grassland \\ \hline SPF & 38.13N & 84.50W & Grassland \\ \hline BCF & 36.60N & 88.23W & Grassland \\ \hline HBS & 36.76N & 88.12W & Deciduous Forest \\ \hline CR & 36.93N & 88.46W & Deciduous Forest \\ \hline HEA & 37.41N & 88.19W & Deciduous Forest \\ \hline FFF & 37.75N & 86.63W & Deciduous Forest \\ \hline RFS & 37.47N & 83.17W & Deciduous Forest \\ \hline MMF & 36.69N & 88.15W & Deciduous Forest \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
Figure 1: Location of the 19 study sites and their land over types in our study region, (Kentucky, USA).  
of Kentucky Soils Characterization Lab and extractable P, C, Ca, Mg, Zn, and Fe were measured using the Mehlich-3 extraction method [61; 62].  
We performed soil stable isotopes analysis because they are indicators of soil C and N dynamics in an ecosystem and can be used to determine the sources of SOM and soil C turnover rates [63; 64]. Soil samples were sent to the Stable Isotope Ecosystem Lab of the University of California, Merced (SIELO) for isotope analysis and elemental content of organic C and N. Splits of the soil sample (<2 mm size fraction) were prepared for stable isotope and elemental composition analysis with an initial homogenization step where samples were powdered using mortar and pestle for three to five minutes. One portion of this powdered subsample was placed in centrifuge vials and treated with 1N HCl to remove any inorganic C (calcite), which confounds the organic C signal for isotopic and elemental compositional analysis. After acidification, these subsamples were triple-rinsed in deionized water, then dried overnight at 50 \({}^{\circ}\)C. The other split was weighed without acid treatment to preserve \(\delta^{15}\)N values. All powdered samples were weighed to 20-40 mg (based on organic C and N content) into 5 \(\times\) 9 tin capsules for stable isotope (\({}^{13}\)C/\({}^{12}\)C and \({}^{15}\)N/\({}^{14}\)N) and organic elemental (C and N) analysis. The SIELO analyses content and isotopes of C and N with an Elemental Analyzer (Costech 4010) coupled to a Thermo Scientific Delta V Plus isotope ratio mass spectrometer via conflo IV. Reference materials for elemental and isotopic composition were run with all samples and included at least \(n\) = 3 of each Costech acetanilide, Peach Leaf (NIST 1547), and USGS 40. Reproducibility for these reference materials was <0.3% for both \(\delta^{13}\)C and \(\delta^{15}\)N values as well as <3% for C and N content (Table 2). Stable isotope compositions are reported with VPDB and AIR as references for \(\delta^{13}\)C and \(\delta^{15}\)N values, respectively, and in per mille (%). All C:N ratios are reported as weight percent.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline
\begin{tabular}{c} **\(\delta^{\text{ID}}\)**