## 3 Results
### Mapping Total Solum SOC
The distinctly most important predictor in the submodel for soils with near-surface groundwater was, of course, the depth of groundwater \(z_{\text{GW}}\) itself. The standardised coefficient obtained for the terrain parameter \(A_{\text{C}}\) must be seen in terms of the groundwater regime rather than terrain effects. Although the number and importance of included variables are quite different, predictors related to nearly every SCORPAN factor are incorporated into the regression equations. The only exception to this is the space factor, indicating that edge effects and stand history are of minor importance. The \(p\)-values \(p_{j}\) derived from the t-statistic are small for the majority of the regression coefficients. Increased \(p\)-values occur only for coefficients in the submodel for sites with near-surface groundwater. However, even in these cases, the sign and, thus, the direction of effects do not shift within the lower and upper confidence interval bounds, \(b_{j}-t_{95}s_{b_{j}}\) and \(b_{j}+t_{95}s_{b_{j}}\). All in all, the results of the t-statistic suggest statistically reliable regression equations. The model performance measures are given in Figure 2. As expected, the \(p\)-values derived from the F-distribution signal high significance. The number of explanatory variables \(J\) entered into both equations is distinctly below the threshold of \(10\)\(N//\) that was recommended by [PERSON] et al. (2018) to prevent overfitting. Particularly in terms of absolute errors, the norm of residuals \(s_{e}\) confirms that the performance of the groundwater submodel is slightly poorer. The increased differences in this domain can also be seen clearly from the scatter plot of the measured and predicted values (Figure 2). These differences between both submodels mainly result from the high variability of SOC in the group of soils with near-surface groundwater. Thus, the coefficients of determination, \(r^{2}\) and \(r_{\text{adj}}^{2}\), are quite similar in both models. The scatter plot shows no extreme outliers or systematic deviations. Merely by viewing the data of both models at once, some heteroscedasticity appears. Within the single models, though, the observed overall heteroscedasticity has no effect on the estimation of confidence intervals ([PERSON] et al., 2017). Figure 2: Measured SOC stocks versus values predicted by regressions models for terrestrial soils and soils with near-surface groundwater. Model performance measures for the regressions models: number of observations \(N\), number of explanatory variables \(J\), coefficient of determination \(r^{2}\), adjusted coefficient of determination \(r_{\text{adj}}^{2}\), norm of residuals \(s_{e}\), standard deviations of observed SOC stocks \(s_{\text{soc}}\), F-statistic \(F_{\text{emp}}\), and \(p\)-value \(p\). The assessment of random fluctuations due to the limited size of the calibration sample is shown in Figure 3. The cross-validation estimates of \(r_{\text{cv}}^{2}\) derived for the terrestrial soil models are in good agreement with the values obtained from the calibration sample. In the case of models for hydromorphic conditions, the agreement between the calibration sample and cross-validation estimates of \(r_{\text{cv}}^{2}\) is slightly poorer. In comparison to the cross-validation results for the group of terrestrial sites, the fluctuations of \(r_{\text{cv}}^{2}\) across the repetitions are distinctly higher for the hydromorphic sites. Quite similar relations can be discovered by inspecting \(s_{e}\) and \(\text{RMSE}_{\text{cv}}\). The cross-validation estimates \(\text{RMSE}_{\text{cv}}\) are almost as small as the respective calibration sample estimates \(s_{e}\). The fluctuation of \(\text{RMSE}_{\text{cv}}\) across validation runs is nearly negligible. Again, the situation is different for the cross-validation estimates derived for hydromorphic sites, showing slightly increased values that vary substantially over the performed repetitions.