## 3 Results
### Mapping of Relative Depth Gradient Types
In particular, the concordance between \(s_{e}\) and \(\text{RMSE}_{\text{cv}}\) is promising for an estimation of the prediction errors that is not overly optimistic. Larger discrepancies between the calibration and cross-validation estimates are limited to the depth layers at 0-5 and 60-90 cm. As indicated by the doubled standard deviations, the results of the repeated runs of cross-validation are also less stable within these depth layers. Since \(\text{CCC}_{\text{cv}}\), which comprises an additional assessment of slope, is a much stricter model performance indicator than \(r\) is, the squared values of \(\text{CCC}_{\text{cv}}\) are again distinctly lower than \(r_{\text{cv}}^{2}\). The application of the derived models for mapping SOC stored in the forest soils of Brandenburg is shown in Figure 12. As examples, the geographic distributions of SOC within the six NFSI depth layers used for model development are shown. Nevertheless, whenever required, the usage of the relative depth gradient types enables the user to predict any depth layer of interest. Figure 11: Scatter diagrams of measured versus predicted values of volumetric SOC at National Forest Soil Inventory (NFSI) depth layers of the mineral soil (0–5, 5–10, 10–30, 30–60, and 60–90 cm) and SOC stocks of the organic layer. Figure 12: Cartograms displaying the spatial distribution of SOC within the NFSI depth layers obtained by regionalisation using relative depth gradients for a 100 m grid of the forested area of Brandenburg. The cartograms are based on estimates derived for a grid resolution of 100 m. To prevent the estimates from drifting beyond physical bounds, the range of values of the predictor variables was constrained. Cut-offs were set with respect to the limits that are present in the NFSI data used for model development. This became necessary because, in case of the grid, which contains one million individual grid cells, the sample size was drastically enlarged compared to the NFSI sample. Associated with this is a broadened range of values for the environmental covariates, resulting in extreme combinations of predictors in single grid cells. Similarly, according to the soil types that were present in the training sample, histosols, which were not within the scope of the conducted analysis, were excluded from mapping. To obtain a proper visualisation of the spatial distribution for the majority of sites, the colour map legends of the final cartograms were made to span between the 5 th und 95 th percentiles. The cartograms for every depth layer drawn show a high spatial variation. Especially at small spatial scales, a high heterogeneity can be observed. As can be seen within the example landscape extract under the magnifying glass, even at the smallest distances, changes of SOC equivalent to the total range of values appear. In particular, the SOC contents of the three upper mineral soil layers attain magnitudes that may significantly contribute to soil water storage and nutrient status. The SOC contents also vary in a range wide enough to substantially alter the soil's physical and chemical properties, which underlines the practical importance of regionalisation. Pursuant to the classification given by Arbeitsgruppe Boden (2018), the equivalent soil organic matter contents within the 0-5 cm layer range from medium (h3) to very high (h5) values. Even within the 10-30 cm layer, the h2 class still occurs frequently. The SOC contents of the two subsoil layers are generally very low (h1), and are thus usually only of minor importance for ecological site characteristics. On the other hand, only small quantities of hydrophobic compounds are required to form water-repellent particle coatings (2018). In particular, under acidic conditions, the SOC within the subsoil layers may still contribute to prolongation of preferential flow paths. However, in terms of carbon sequestration, the amounts of SOC actually stored within these thick subsoil layers are essential reservoirs (see below).