## 2 Materials and Methods
### Prediction Models and Accuracy Assessment  
Models were calibrated using three approaches (Figure 2). In the first, only S2 bands (a) were used for model calibration to compare the performance of PLS regression, RF, and the DNN. Based on the results of approach 1, only the two algorithms with the best prediction performance in cross-validation were retained for use in the following two approaches. In the second approach, S2-indices (a + b), S1-indices (a + c), and S1-soil moisture (a + d) were used separately during calibration to assess their individual effects and then used together (a + e). In the third approach, the Lab-indices were added incrementally in the order of decreasing correlation with SOC content (NBR2, NDVI, ARVI2, Maccioni, and TSAVI) to assess their effects on model accuracy. To group all available Sentinel-2 data with bare soil, we constructed a table with 512 rows, which corresponded to \"point \(\times\) date\" individuals for the 58 sampling points that had bare soil (range: 1-18 dates). We then randomly split the data into calibration (70%) and validation (30%) datasets. To test the robustness of our approaches, we performed three iterations of each.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ab.** & **Index** & **Equation for Sentinel-2 Indices** & **Equation for Laboratory Spectral Indices** & **Ref.** \\ \hline \multicolumn{5}{c}{Vegegetation indices} \\ \hline AFRI21 & Aerosol free vegetation & \(\frac{88A-0.5\times R12}{8A+0.5\times R12}\) & \(\frac{R_{96A}-0.5\times R_{2202}}{R_{96A}+0.5\times R_{2202}}\) & [79] \\ ARVI2 & Atmospherically resistant vegetation index2 & \(-0.18\ +\ 1.17\ \times\ \left(\frac{88}{8}-\frac{84}{8}\right)\) & \(-0.18\ +\ 1.17\ \times\ \left(\frac{R_{92}-R_{942}}{R_{92}+R_{942}}\right)\) & [80] \\ GVMI & Globus vegetation & \(\frac{(88\ +0.1)\ -\ (122\ +0.02)}{(18\ +0.1)\ +\ (R12\ +0.02)}\) & \(\frac{(R_{920}+0.1)\ +\ (R_{920}+0.02)}{(R_{920}+0.1)\ +\ (R_{920}+0.02)}\) & [81] \\ Maccioni & Maccioni vegetation index & \(\frac{R_{92}-R_{92}}{R_{92}+R_{942}}\) & \(\frac{R_{920}-R_{942}}{R_{942}+R_{942}}\) & [82] \\ NBR & Normalized burn ratio & \(\frac{88\ -R12}{8B+B12}\) & \(\frac{R_{920}-R_{920}}{R_{920}+R_{920}}\) & [83] \\ NBR2 & Normalized burned & \(\frac{811\ -R12}{811\ +R12}\) & \(\frac{R_{920}-R_{920}}{R_{914}+R_{920}}\) & [84; 85] \\ NBR2 & Ratio 2 & \(\frac{811\ -R12}{811\ +R12}\) & \(\frac{R_{920}-R_{920}}{R_{914}+R_{920}}\) & [70] \\ NDVI & Normalized difference & \(\frac{88\ -B4}{88\ +B4}\) & \(\frac{R_{920}-R_{942}}{R_{920}+R_{942}}\) & [70] \\ SIVSI & Shortwave infrared water & \(\frac{88A-B11}{8A+B11}\) & \(\frac{R_{920}-R_{914}}{R_{920}+R_{942}}\) & [86] \\ stress index & Soil-adjusted vegetation index & \(\frac{1.22\ \times(88\ -1.22\times 84\ -0.03)}{122\ \times 88\ +B4\ -122\ \times 0.03 +0.08\times\ (1+122^{2})}\) & [87] \\ \hline \multicolumn{5}{c}{Solid indices} \\ \hline BI & Brightness index & \(\sqrt{\frac{82^{2}+82^{3}+82^{4}}{3}}\) & \(\sqrt{\frac{82^{2}+82^{6}+82^{6}}{3}+R_{95}^{2}}\) & [88; 89] \\ BSI & Bare soil index & \(\frac{(812\ -B4)\ -\ (88\ -B2)}{(812\ -B4)\ +\ (188\ -B2)}\) & \(\frac{(R_{920}-R_{965})\ -\ (R_{920}-R_{920})}{(R_{920}-R_{965})+(R_{920}-R_{920})}\) & [90] \\ \hline \multicolumn{5}{c}{Water indices} \\ \hline NDMI & Normalized difference & \(\frac{88\ -B11}{88\ +B11}\) & \(\frac{R_{920}-R_{914}}{R_{920}+R_{914}}\) & [91] \\ \hline \multicolumn{5}{c}{Ab.breviation, Ref.: Reference.} \\ \hline \hline \end{tabular}
\end{table}
Table 2: Equations of the Sentinel-2 spectral indices selected based on multiple factor analysis and equations of the corresponding laboratory spectral indices. Subscripts in the latter equations indicate the central wavelengths of the Sentinel-2 bands.