## 2 Material and Methods
### Environmental Covariates
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline \multicolumn{2}{p{142.3 pt}}{**Soil Properties (s), Parent Material (p)**} \\ \hline CF\({}_{\ldots}\) & coarse fragments [\%] \\ \(S\%\)\({}_{\ldots}\), \(S\%\)\({}_{\ldots}\), \(C\%\)\({}_{\ldots}\) & proportions of particle-size classes (sand, silt, clay) \\ \(Dg\%\)\({}_{\ldots}\) & geometric mean particle size \\ \(z_{\text{CaCO}_{3}}\) & depth of calcareous horizon depth of groundwater \\ \(z_{\text{GW}}\) & **Climate (c)** \\ \hline \(\textit{CWB}_{\text{sum}}\), \(\textit{CWB}_{\text{win}}\) & climatic water balance (seasonal) annual mean temperature \\ \(T_{\text{a}}\) & annual mean temperature \\ \(n_{\text{d}>0\,\text{C}}\) & frost-free days \\ \(\Delta_{T}\) & annual range of temperature (as surrogate for continentality) \\ \(P_{\text{a}}\), \(P_{\text{win}}\), \(P_{\text{sum}}\) & precipitation (annual, seasonal) \\ \hline \hline \end{tabular}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline \multicolumn{2}{p{142.3 pt}}{**Organisms, Vegetation, Land Use (o)**} \\ \hline \(P_{\text{de deciduous}}\), \(P_{\text{Ppine}}\), \(P_{\text{beech}}\), \(P_{\text{oak}}\) & proportions of tree species \\ \hline \multicolumn{2}{p{142.3 pt}}{**Topography (r)**} \\ \hline \hline \multicolumn{2}{p{142.3 pt}}{**terrain attributes derived from the digital elevation model (DEM) (see Table 2)**} \\ \hline \hline \multicolumn{2}{p{142.3 pt}}{**Age (a)**} \\ \hline \hline \multicolumn{2}{p{142.3 pt}}{series\({}_{\ldots}\)} & geochemical series (age of deposit) \\ \(t_{\text{stand}}\), & forest stand age \\ \hline \hline \multicolumn{2}{p{142.3 pt}}{**Spatial Position (n)**} \\ \hline \(\textit{WA}_{200}\), \(\textit{WA}_{500}\), \(\textit{WA}_{1000}\), \(\textit{I}_{\text{edge}}\) & proportion of surrounding forest area (within search radii of 200, 500, 1000 m) \\ \(\textit{I}_{\text{edge}}\) & distance to nearest forest edge \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Environmental covariates for the regionalisation of SOC arranged by the associated SCORPAN factors. In addition to the consideration of space by the use of geostatistics, we also computed simple distance-based indices. The created indices should serve as proxies for edge effects, like micro-climate and atmospheric deposition. Since the probability of land-use changes in the past increases with closeness to the forest edge, the indices may also act as proxies for former stand history (beyond the time horizon of forest inventory data). During the development of the model, we tried to circumnavigate the positional errors contained in the different sources of spatial data. Thus, whenever the NFSI contained the same information, as in the case of soil texture or tree species composition, we favoured the inventory data as a source for derivation of environmental covariates. Field estimates from the NFSI of terrain features, slope, exposition, and curvature were also used to verify the spatial positioning of sample locations within the DEM. Following [PERSON] and [PERSON] (2018), we also iteratively inspected alternative residual values at DEM cells surrounding the measured coordinates. Thereby, we attempted to obtain a further mitigation of uncertainties resulting from locational errors of the DEM and sample points. The assumed range of spatial uncertainty and, thus, the respective domain for virtually shifting the sample points within the DEM were constrained to the \(3\times 3\) altitude submatrix in both cases.