## 2 Materials and Methods
### Environmental Covariates  
The spatial distribution of SOC is influenced by multiple environmental factors, among which topography and climate are the key drivers shaping its spatial patterns [32]. Topographic heterogeneity leads to the spatial redistribution of water and heat, thereby altering local conditions such as moisture, temperature, and solar radiation. These changes contribute to the formation of microclimatic systems with spatial variation and affect the type and distribution of vegetation [33]. As a major source of SOC accumulation, vegetation plays a critical role in shaping the spatial pattern of SOC. In turn, the accumulation of SOC further influences the content of SOM [34]. Climate change also plays a critical role in regulating the distribution of SOM. Increased precipitation raises soil moisture content, alleviates drought stress, and enhances plant root uptake of water and nutrients, thereby promoting vegetation growth [35]. As plant biomass increases, the input of root exudates and aboveground litter also rises, which in turn enhances the soil's capacity to accumulate SOC [36]. Meanwhile, rising temperatures stimulate microbial metabolic activity and enzymatic expression, accelerating the decomposition rate of SOM [37]. When warming and increased precipitation occur simultaneously, higher soil moisture may partially mitigate drought stress induced by elevated temperatures and support continued plant growth. However, temperature-induced microbial decomposition processes may dominate SOM turnover, intensifying SOM loss and weakening the soil carbon sink function [38]. Topography and climate jointly regulate the dynamic balance among water and heat conditions, organic matter input from vegetation, and microbial decomposition, playing a key role in shaping the spatial heterogeneity of SOM [39]. Based on this mechanistic understanding, this study incorporates topographic and bioclimatic factors as environmental covariates to comprehensively characterize the influence of terrain and climate on SOM distribution and to enhance the model's predictive performance and spatial generalization in complex landscapes. Topographic factors were derived from the Shuttle Radar Topography Mission 1 (SRTM1) digital elevation model (DEM) provided by the United States Geological Survey, with a spatial resolution of 30 m (data source: [[https://earthexplorer.usgs.gov](https://earthexplorer.usgs.gov)]([https://earthexplorer.usgs.gov](https://earthexplorer.usgs.gov))). Using the Terrain Analysis module in SAGA GIS with default parameter settings [40], 16 terrain-derived variables were calculated using the DEM. Together with the original elevation, a total of 17 topographic covariates were constructed. Detailed information is provided in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indices** & **Description** & **Spatial Resolution** \\ \hline Aspect & The angle between the projection of the downslope direction & 30 m \\ (Asp) & (i.e., surface normal) on the horizontal plane and true north. & 30 m \\ Analytical Hillshading Index & Terrain shadow distribution calculated based on solar & 30 m \\ (AHI) & azimuth and elevation at a specific time. & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of topographic covariates. Bioclimatic factors were selected from the Worldclim global climate database [41], from which 19 variables, representing long-term average climate conditions for the period 1970 to 2000, were extracted. The original spatial resolution was 1000 m. To ensure spatial consistency with the topographic factors, all climate variables were resampled to a resolution of 30 m using bilinear interpolation. Detailed information is provided in Table 2.