## 2 Material and Methods
### Environmental Covariates  
Since the preliminary considerations strongly suggested that SOC is controlled by a wide range of influences, we tried to obtain environmental covariates that address all seven SCORPAN factors appropriately. A short overview of the compiled variables is given in Tables 1 and 2. Covarates related to parent material and soil properties were primarily derived from forest site mapping data ([PERSON], 2017; [PERSON], 2017) and by means of digital soil mapping techniques ([PERSON], 2017; [PERSON], 2017). In addition to widely used particle size fractions, we additionally computed the geometric mean particle size \(D_{\text{g}}\%_{...}\) for numerical characterisation of the soil texture. \(D_{\text{g}}\%_{...}\) was originally proposed by [PERSON] et al. (2017) to improve the reflection of SOC variation due to texture. For estimates of the depth of groundwater, we additionally considered water-table maps based on monitoring wells ([PERSON], 2017). Climatic factors were directly taken from the detailed compilation by [PERSON] et al. (2018). The selection of indicators to be considered was guided by assumptions on dominant processes influencing the storage of SOC inside the study area. Thus, \(CWB_{\text{win}}\) (climatic water balance during winter) and \(P_{\text{win}}\) (winter precipitation) were chosen as proxies for vertical translocation, whereas \(\textit{CWB}_{\text{sum}}\) (climatic water balance in the summer half-year), \(P_{\text{sum}}\) (summer precipitation), and \(T_{\text{a}}\) (annual mean temperature) were used to indicate climatic effects on soil biological activity. Additionally, we calculated the annual rage of temperature \(\Delta_{T}\) as a surrogate for continentality and the number of frost-free days. The latter was originally introduced by [PERSON] [48] and then revisited by [PERSON] [23] as Ramann's Weathering Factor, expressing the length of the 'chemical weathering season'. The proportions of tree species were derived from forest inventory data (Datenspeicher Wald') to obtain forest-specific indicators on land-use effects. The usage of forest inventory data allowed us to calculate the respective percentages from ratios of a single-species basal area to the total basal area of the forest stands. In the rare case of missing data, CORINE landcover classes [49] were used instead (applies to mapping only). The role of topography on SOC was examined with several terrain attributes derived from a digital elevation model (DEM). As the cell size of the underlying DEM was 25 m, the terrain attributes derived form the environmental covariates with the highest spatial resolution in our study. Seeing that the covariates derived from DEM might be able to improve the prediction of SOC at the smallest spatial scales and the general availability of DEM data, we made exhaustive use of them. Nevertheless, the selection of indices from the vast number of existing terrain attributes was once again strictly constrained with respect to the theory of topography as a soil forming factor. The computed terrain attributes are tabulated in Table 2.  
The time factor on SOC was considered from a geologic and a forest management perspective. For this, we computed the mean stand age as a basal-area-weighted average on the basis of forest inventory data. To cope with the problem of soil formation time, we used the geochemical series gathered by forest site mapping as a rough estimate.