## 2 Materials and Methods
### Data Compilation and Processing

Table 1: Proxies for the environmental factors used in the tree-based modeling of soil organic matter. We obtained the digital elevation model (DEM) data (90 m resolution) (Table 2), which represented a continuous topographic elevation surface, from the National Spatial Data Infrastructure (NSDI) portal [32]. We used the DEM data to derive slope, aspect, roughness, topographic position index, terrain ruggedness index, and flow direction. Hill shade was computed from slope and aspect [35], assuming sun elevation and direction (azimuth) angles of 45\({}^{\circ}\) and 0\({}^{\circ}\), respectively. Lastly, we estimated the upslope contributing area and topographic wetness index according to [PERSON] et al. [36]. We used a global estimate of annual net primary production in TIFF format from 2019 to 2021 to represent vegetation from the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard NASA's Terra and Aqua satellites [34]. The spatial resolution of the data is 0.1\({}^{\circ}\) (approximately 11 km). To \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Units** & **Mean** & **Median** & **s.d.** & **Min.** & **Max.** \\ \hline Organic matter & g kg\({}^{-1}\) & 24.2 & 21.9 & 11.1 & 0.6 & 74.0 \\ Available phosphate & mg kg\({}^{-1}\) & 303.7 & 199.4 & 281.5 & 0.8 & 3589.7 \\ Available silicate & mg kg\({}^{-1}\) & 191.8 & 175.9 & 153.9 & 0.1 & 1896.0 \\ Exchangeable magnesium & cmol\({}^{-1}\) kg\({}^{-1}\) & 1.82 & 1.60 & 1.08 & 0.04 & 14.56 \\ Exchangeable potassium & cmol\({}^{-1}\) kg\({}^{-1}\) & 0.74 & 0.52 & 0.68 & 0.01 & 8.31 \\ Exchangeable calcium & cmol\({}^{-1}\) kg\({}^{-1}\) & 6.43 & 6.03 & 3.08 & 0.11 & 31.90 \\ pH (1:5 H\({}_{2}\)O) & 6.30 & 6.30 & 0.68 & 4.00 & 9.50 \\ Electric conductivity & dS m\({}^{-1}\) & 0.81 & 0.56 & 1.03 & 0.01 & 20.00 \\ Elevation & m & 71.38 & 35.89 & 81.40 & 0.25 & 671.00 \\ Mean annual temperature & \({}^{\circ}\)C & 12.97 & 13.26 & 1.028 & 6.12 & 16.02 \\ Maximum annual & \({}^{\circ}\)C & 18.55 & 18.57 & 0.78 & 11.22 & 20.40 \\ temperature & \({}^{\circ}\)C & 8.17 & 8.68 & 1.46 & 2.01 & 13.19 \\ Mean annual & mm & 1358.28 & 1269.33 & 215.95 & 934.89 & 2636.66 \\ precipitation & MJ m\({}^{-2}\) & 13.70 & 13.71 & 0.53 & 10.62 & 15.78 \\ Relative humidity & \% & 71.20 & 72.43 & 2.98 & 59.61 & 76.81 \\ Wind speed & m s\({}^{-1}\) & 1.84 & 1.93 & 0.41 & 0.19 & 5.46 \\ Net primary productivity & g C m\({}^{-2}\) y\({}^{-1}\) & 184.86 & 188.00 & 10.41 & 138.00 & 255.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics of numeric data (\(n=9584\)). Figure 1: Spatial distribution of the field data (\(n=9584\)). Points are field-wide averages of organic matter (OM; g kg\({}^{-1}\)) for the period of 2020 to early 2023.  
represent the current climate, we used mean annual air temperature, maximum/minimum air temperature, mean annual precipitation, solar irradiation, relative humidity, and wind speed data based on the Modified Korean-Parameter-elevation Regressions on Independent Slopes Model (MK-PRISM, version 1.2). All data were available from 2000 to 2019, except for solar irradiation (2014-2019) [33]. The MK-PRISM data were in netCDF format. All climatic variables were averaged annually and then over the entire period, whereas the sum of precipitation values was calculated and averaged over the same period. According to the land cover data from EGIS [37], agricultural land subclasses include the following: (1) fields (including rearranged fields), (2) rice paddies, (3) facility cultivation, (4) orchards, and (5) pastures and nurseries. Based on the survey of arable land in 2021 [38], the total field area was 766,000 ha. We first compiled valid soil chemical data and the coordinates of the fields (\(n=310\),716). We then extracted the values of the climate, terrain, and soil map variables with the coordinates of the samples. We removed outliers from the complete dataset based on [PERSON]'s distance (\(n=9584\)) and scaled the data for modeling. All data were compiled and processed in R (version 4.3.1) [39].