## 3 Results
### Mapping of Relative Depth Gradient Types  
The selection of an optimum-sized classification tree for the prediction of relative depth gradients is shown in Figure 8. The starting point of the selection process is the initially grown much-too-large tree with 18 terminal nodes \(|\widetilde{T}_{k}|\) and the 10 respective auxiliary trees grown on subsamples for cross-validation. Subsequently, the weakest subbranches are incrementally pruned off by minimal cost-complexity pruning with respect to the complexity parameter \(\alpha_{k}\). This results in a sequence of 18 subtrees (and 180 auxiliary subtrees) with decreasing complexity, finally ending at the root node (\(|\widetilde{T}_{k}|\) = 1). Since \(\alpha\) is used as a penalty for complexity in the pruning procedure, the complexity parameter \(\alpha_{k}\) consequently increases at every stage. As one might expect, the resubstitution estimates for the risks \(R(T_{k})\), which directly express the diversity within the terminal nodes, monotonically increase with each pruning stage. In contrast, the misclassification rate of the auxiliary trees is highest when sequential pruning is started. Hence, after a phase of decreasing cross-validation estimates \(R^{cv}(T_{k})\) and reaching of the minimum 0.689 at \(k\) = 15, \(R^{cv}(T_{k})\) increases again and equals \(R(T_{k})\) at the end, when all subbranches of the auxiliary tree are pruned off and just the root nodes remain. In addition to using \(R^{cv}(T_{k})\) as an honest estimate of the misclassification rate, [PERSON] et al. (2018) introduced the 1 \(SE\) rule, additionally invoking the standard error \(SE\), to guide the user towards a more stable tree selection. Using the 1 \(SE\) rule, the subtree of the smallest complexity within the range of \(\pm SE\) around the minimum value of \(R^{cv}(T_{k})\) should be selected. Keeping close to this rule, the tree \(T_{16}\), which contains just three terminal nodes \(|\widetilde{T}_{k}|\), should be selected. It is obvious that a classification tree pruned back to three terminal nodes is not able to predict five clusters. Therefore, we used a less rigid interpretation of this rule and selected tree \(T_{14}\)  
Figure 7: Equal-area quadratic smoothing splines fitted to the relative depth gradients of SOC percentage. The black solid line depicts the mean value of all sites assigned to the respective clusters. Additional f- and t-statistics assess the homogeneity within each cluster and the distinctness between the clusters, respectively. This is exactly the smallest tree within the range of \(\pm SE\) around the minimum of \(R^{cv}(T_{k})\) that makes it feasible to predict any distinguished depth gradient type. The obtained classification tree \(T_{14}\) is shown in Figure 9. In addition to the splitting rules determined, the frequencies of the clusters contained in each node are also given. The frequencies shown for the root node thus equal the number of clusters inside the total sample. A quite distinct split between clusters associated with thick organic layers, C\({}_{2}\) and C\({}_{5}\) and the clusters with high fractions of SOC contained in mineral soil, C\({}_{3}\) and C\({}_{4}\), can thus be achieved by the proportions of deciduous trees within the forest stand. Actually, in sum just nine sites of the types C\({}_{2}\) and C\({}_{5}\) remained within the right subbranch (\(p_{\text{deciduous}}>92\%\)). The clear recognition of depth gradient types associated with mor-humus-like humus forms by the proportions of deciduous trees is in line with the well-known preference of coniferous stands for developing thicker organic layers. The next and final split on the right is the SOC stored in the soil column, and it separates cluster C\({}_{3}\) from cluster C\({}_{4}\). This separation reflects the usually less distinct gradients of SOC across the mineral soil layers in soils rich in organic matter, like gleysols, or soils containing colluvic material.