## 2 Material and Methods
### Statistical Analyses  
We used the Principle Component Analyses (PCA) to analyze relationships between the individual organic and inorganic pollutants. Here the dimension of the original dataset is reduced by transforming it to a new set of variables, that are linear functions of those in the original dataset [45]. These so-called principal components possibly can be interpreted in terms of the different sources of the soil contamination. The statistical analyses were performed with SPSS 25 (Statistical Package for Social Science, IBM(r)). The number of principle components to be extracted was determined using the Kaiser criterion [46; 47], which is the one most widely used since it does not require visual inspection of eigenvalue plots and is easily computerized [48; 49]. A varimax rotation [46; 50] was performed to facilitate interpretation of the result. The component values were calculated using regression.  
We used geostatistical methods to obtain estimates of historical atmospheric deposition rates of calcium. Isotropic variogram analysis and ordinary point kriging were employed to convey available legacy data, that was measured within a former ecological monitoring network (OWK = ecological forest condition control), to the current NFSI plots. All geostatistics were conducted according to Webster and Oliver [51]. Computations were performed using SPSS's matrix programs and nonlinear parameter estimations routines [52].  
Furthermore, standard statistical methods such as nonparametric test statistics (Mann-Whitney U test), correlation analysis and multiple linear regression analysis and the LOESS method [53] implemented in SPSS for determining and visualizing regression curves were carried out. The correlation matrices presented in this paper refer to the Spearman correlation coefficient. Multiple linear regression analyzes were carried out using the stepwise method, which is a combination of both the forward selection and backward elimination method [54]. Residual values were examined for heteroscedasticity and autocorrelation in scatter plots and were additionally tested with the Durbin-Watson statistic for the latter. We also calculated the F-statistic (\(F\)). The following levels of significance were used: * significant (\(p<0.05\)) and ** highly significant (\(p<0.01\)).  
Distributions of soil data were examined by histogram analyses with regard to the occurrence of outliers. In the regression analyses in Section 3.1 peat soils were excluded from the sample, and 4 plots with extremely high element concentrations, in order to prevent individual outliers from leading to statistical bias and faking high coefficients of determination. For the excluded plots with extreme values of the pollutant concentration, local causes of the contamination could be determined in all cases; e.g., non-local (contaminated) soil material for road construction or garbage deposits in the immediate vicinity of the soil samples taken. The regression relationships described in Section 3.1 are therefore valid for the following ranges of the parameters related to the mineral topsoil (0-5 cm, 5-10 cm):  
As \(<5.34\) mg/kg  
Cd \(<0.31\) mg/kg  
Cr \(<8.63\) mg/kg  
Cu \(<7.70\) mg/kg  
Ni \(<5.14\) mg/kg  
Pb \(<39.23\) mg/kg  
Zn \(<35.47\) mg/kg  
pH(KCl) \(<6.0\)  
Organic carbon content (C\({}_{\text{org}}\)) \(<15\%\)  
Clay content \(<10\%\)  
Cation exchange capacity (CEC\({}_{\text{eff}}\)) \(<120\) mmol\({}_{c}\)/kg