## 3 Results
### Depth Gradients  
In the first step, relative depth gradients of the individual inventory plots are grouped into depth gradient types by clustering. Throughout the stagewise proceeding of the clustering process, the number of clusters decreases, starting with the number of observations (424), until all sites and clusters are unified (Figure 6). While the the number of clusters decreases, the ESS based on squared Euclidean distances increases. After discarding the initial partition of 424 clusters and the final one-cluster solution, 422 possible cluster solutions remain. A first approximation of the optimal number of clusters with the elbow method suggests a solution with five clusters, since the most distinct increase in the ESS appears after the solutions with four clusters. Regarding the standardised ESS values obtained by clustering the relative depth gradients of SOC, the stopping rule of Mojena [78] indicates an optimal solution in the range of 5 to 8 clusters. Finally, taking into account practical considerations on handy cluster sizes that facilitate interpretation and prediction of the resulting depth gradient types, we selected the solution with five clusters for the subsequent analyses. Figure 5: Scatter diagrams of residuals retained from regression analysis \(e_{\text{Reg}}\) against residuals estimated by ordinary kriging \(\delta_{\text{Krig}}\) and measured SOC stocks versus predictions improved by kriging estimates of residuals obtained during leave-one-out cross-validation. The five relative depth gradient types obtained and the sites assigned to the respective clusters are shown in Figure 7. The most distinct differences between the five clusters can be seen for the forest floor and top soil layers. This is also indicated by the t-statistics. In these depth increments, the t-statistics attain the highest absolute values. In contrast, close to the bottom of the soil column, the derived depth gradient types seem very similar, which is also expressed by small t-values in these depth increments. The cluster C\({}_{5}\) stands out as having the highest proportions of SOC stored in the organic layer of any cluster. Consequently, C\({}_{5}\) is also characterised by the smallest SOC portions inside the mineral soil with t-statistics that are invariably negative. An opposite depth gradient is typified by cluster C\({}_{3}\), which contains the lowest proportions of SOC inside the organic layer. It also shows the highest t-values for any mineral soil layer below 10 cm depth. Cluster C\({}_{4}\) is in close accordance with C\({}_{3}\) concerning the forest floor, whereas the mineral soil SOC is closely bunched in the upper parts of the profile. The clusters C\({}_{1}\) and C\({}_{2}\) can be seen as intermediate types between C\({}_{3}\) and C\({}_{5}\) in which increasing proportions of SOC are stored in the forest floor layer. It does not seem far fetched to bring the derived depth gradients in line with soil types and humus forms. Actually, the clusters C\({}_{3}\) and C\({}_{4}\) often coincide with the humus forms of mull and mull-like moder, respectively. The humus forms of more humus and mor-humus-like moder appear most frequently within the clusters C\({}_{2}\) and C\({}_{5}\). Soil types were merely in rough accordance with the derived depth gradient types. Lessives tend to occur preferentially in cluster C\({}_{4}\). Additionally, the frequencies of aerosols and podzols are increased in the clusters associated with mor humus forms C\({}_{2}\) and C\({}_{5}\). The loose relationship between clusters and soil types may be a consequence of the fact that vertical distribution of SOC is not a diagnostic criterion for many soil types. On the other hand, the observed differences between soil types and humus forms indicate that the vertical distribution of SOC throughout the soil profile is often altered by current land-use and stand history. The plotted depth gradients (Figure 7) show a reasonable homogeneity.