## 2 Material and Methods
### Regression Analysis of Total Solum SOC  
The amount of SOC within the soil column was assumed to be equal to the sum of SOC stored in the six NFSI depth layers (organic layer plus mineral soil 0-90 cm). Altogether, 424 profiles could be used within the analysis. The total amount of SOC stored within the soil column SOC\({}_{\text{Solum}}\) (kg m\({}^{-2}\)) was modelled using multiple linear regression equations in the usual form of Equation (2). Predicted values, the constant, regression coefficients, covariates, and the number of explanatory variables are denoted by \(\hat{Y}\)\(b_{0}\), \(b_{j}\), \(X_{j}\), and \(J\), respectively:  
\[\hat{Y}=b_{0}+\sum_{j=1}^{J}b_{j}X_{j}. \tag{2}\]  
Distributions of column stocks were inspected by histogram analysis. The functional relationships to predictor variables were examined using scatter plots. In cases showing evidence of non-linear relationships, appropriate intrinsically linear functions were tested. Residual values were examined for heteroscedasticity and autocorrelation in scatter plots and were additionally tested with the Durbin-Watson statistic for the latter. As a measure for the multicollinearity, the tolerance value \(T_{j}\) was computed. Low tolerances indicate increasing magnitudes of multicollinearity. A tolerance value of 1 denotes perfectly uncorrelated predictors. Thresholds for entry and removal of covariates into/from the regression equations within the stepwise selection process were set to probabilities of F of 0.1 and 0.15, respectively [69]. We chose stepwise linear regression analysis over the more elaborate statistical techniques that are currently used in digital soil mapping. The intended advantages by sticking to this well-established approach were the integrated variable selection during model development and the direct interpretability of covariate effects: Using multiple linear regression, the influence of each predictor on the SOC can be seen from the regression coefficients \(b_{j}\). Positive coefficients indicate that SOC increases with increasing covariate values. Absolute values of standardised regression coefficients \(\hat{b}_{j}\) were used as an indicator for relative variable importance within the regression models. Throughout the iterative model development, we permanently examined the plausibility of the predictors that were entered. Covariates that failed to comply with the expected effects associated with the respective soil forming factors were continuously eliminated. This was especially the case if the sign of the estimated regression coefficients was not in accordance with the a priori assumed causal relationships. We also examined the stability of the direction of effects within the lower and upper confidence interval bounds, \(b_{j}-t_{95}s_{b_{j}}\) and \(b_{j}+t_{95}s_{b_{j}}\). Model performance was assessed by means of scatter plots and statistical indices. For the latter, the common measures--coefficient of determination \(r^{2}\), adjusted coefficient of determination \(r^{2}_{\text{adj}}\), norm of residuals \(s_{e}\), and F-statistic \(F_{\text{emp}}\)--were calculated. In addition to the classical model performance measures computed on the calibration sample, we used cross-validation to estimate the effects of random fluctuations due to the limited calibration sample size [70]. For this purpose, we employed repeated tenfold cross-validation [71]. For each model one hundred runs of tenfold cross-validation were performed, resulting in one thousand model fits. Based on the one hundred validation data sets that were obtained, the coefficient of determination \(r^{2}_{\text{cv}}\) and the root mean square error \(\text{RMSE}_{\text{cv}}\) were recalculated. We also computed the least squares analysis of slope \(b_{1\text{cv}}\) and the concordance correlation coefficient of Lin [72] (CCC\({}_{\text{cv}}\)). Both statistics are common indicators in assay and instrument validations. All computations were performed using IBM SPSS Statistics 19 (IBM(r)).