## 2 Materials and Methods  
### Data Compilation and Processing  
We compiled environmental variables representing soil, terrain, climate, and vegetation to describe diverse field conditions in South Korea. We categorized explanatory variables into five groups: (1) soil chemical properties, (2) a soil map, (3) terrain, (4) vegetation, and (5) climate (Table 1). The National Institute of Agricultural Sciences (NAS) provides data on the soil chemical properties (0-0.15 m depth) of the agricultural fields (Figure 1, Table 2) [30]. Four to ten soil subsamples were collected from each field using a random zig-zag method and mixed to make one composite sample. The samples were analyzed for organic matter (g kg\({}^{-1}\)), pH (1:5 H\({}_{2}\)O), available P\({}_{2}\)O\({}_{5}\) (mg kg\({}^{-1}\)), available SiO\({}_{2}\) (mg kg\({}^{-1}\)), exchangeable magnesium (cmol\({}^{+}\) kg\({}^{-1}\)), exchangeable potassium (cmol\({}^{+}\) kg\({}^{-1}\)), exchangeable calcium (cmol\({}^{+}\) kg\({}^{-1}\)), and electric conductivity (dS m\({}^{-1}\)) [30]. The soil chemical data are updated annually across fields to recommend a crop management plan and fertilizer application rates. The dataset is open-source and contains field-specific data for the last three years (2020-early 2023), which is accessible from the administrative division. Thus, we compiled all data within each division organized by location and sampling date. The Rural Development Administration (RDA) provides thematic soil maps of 30 physical properties at a 125 m resolution (1:25,000 scale) [31]; we selected topsoil (0-20 cm) texture, drainage class, erosion grade, soil order, soil structure, and parent material in this study. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Variable (Abbreviation)** & **Unit** & **Resolution** & **Source** \\ \hline \multirow{8}{*}{Soll} & Organic matter (OM) & g kg\({}^{-1}\) & Field & \\  & Available phosphate (AP) & mg kg\({}^{-1}\) & Field & \\  & Available silicate (AS) & mg kg\({}^{-1}\) & Field & \\  & Exchangeable magnesium (Mg) & cmol\({}^{+}\) kg\({}^{-1}\) & Field & \\  & Exchangeable potassium (K) & cmol\({}^{+}\) kg\({}^{-1}\) & Field & \\  & Exchangeable calcium (Ca) & cmol\({}^{+}\) kg\({}^{-1}\) & Field & \\  & pH (1:5 H\({}_{2}\)O) & & Field & \\  & Electric conductivity (EC) & dS m\({}^{-1}\) & Field & \\ \hline \multirow{8}{*}{Soil map} & Topsoil texture (TT) & class & 250 m & \\  & Drainage (DC) & class & 250 m & \\  & Soil order (OR) & group & 250 m & \\  & Soil structure (SS) & class & 250 m & \\  & Parent material (PM) & type & 250 m & \\  & Erosion (EC) & grade & 250 m & \\ \hline \multirow{8}{*}{Terrain} & Elevation (DEM) & m & 90 m & \\  & Slope \({}^{1}\) & radians & 90 m & \\  & Aspect \({}^{1}\) & radians & 90 m & \\  & Flow direction (flowdir) \({}^{1}\) & m & 90 m & \\  & Roughness \({}^{1}\) & m & 90 m & \\  & Hill shade (hill) \({}^{2}\) & & 90 m & \\  & Topographic position index (TPI) \({}^{1}\) & & 90 m & \\  & Terrain ruggedness index (TRI) \({}^{1}\) & & 90 m & \\  & Upslope contributing area (a) \({}^{1}\) & & 90 m & \\  & Topographic wetness index (TWI) \({}^{1}\) & & 90 m & \\ \hline \multirow{8}{*}{Climate} & Mean annual temperature (TA) & \({}^{\circ}\)C & 1 km & \\  & Maximum annual temperature (TAMAX) & \({}^{\circ}\)C & 1 km & \\  & Minimum annual & \({}^{\circ}\)C & 1 km & \\  & temperature (TAMIN) & \({}^{\circ}\)C & 1 km & \\  & Mean annual precipitation (RN) & mm & 1 km & \\  & Solar irradiation (SI) & MJ m\({}^{-2}\) & 1 km & \\  & Relative humidity (RHM) & \% & 1 km & \\  & Wind speed (WS) & m s\({}^{-1}\) & 1 km & \\ \hline \multicolumn{2}{c}{Vegetation} & Net primary productivity (NPP) & g C m\({}^{-2}\) y\({}^{-1}\) & 11 km & [34] \\ \hline \hline \end{tabular} \({}^{1}\) Estimated based on DEM data. \({}^{2}\) Computed from slope and aspect values, assuming sun elevation and direction (azimuth) angles of 45\({}^{\circ}\) and 0\({}^{\circ}\), respectively.  
\end{table}