# Estimating Tetrachloroethene Sorption Coefficients Based on Soil Properties in Organic-Poor Soils
## 3 Results and Discussion
### Statistical Data Analysis
Additionally, low Pearson's correlations were observed between Al content and clay/silt particles (Al/Clay = 0.225; Al/Silt = 0.0173), as well as between Si content and sand particles (Si/Sand = \(-0.136\)), indicating no significant relationship between these elemental compositions and particle size distributions. Since SSA data were only available for 21 samples, PCA was conducted separately on two datasets to ensure a thorough analysis: (i) the first set comprising 34 soil samples with 7 variables (six soil properties and \(K_{\text{d}}\) values), and (ii) a second set consisting of 21 soil samples with 9 variables, including SSA and porosity. Further details are provided in Text S5. The optimal number of PCs was determined by eigenvalues of the correlation matrix. In the first PCA analysis, PC1 and PC2 explained 63.77 % of the variance (PC1 38.83%; PC2 24.95%), both with eigenvalues higher than 1.7 (Table S2). Figure 2 presents a biplot combining loading and score plots, illustrating the contribution of original variables to the main components. Proximity between variables in the biplot indicates strong correlations. The PCA results revealed a strong positive correlation between \(K_{\text{d}}\) and OC, as well as moderate positive correlations between \(K_{\text{d}}\) and both clay and silt content. A negative correlation between \(K_{\text{d}}\) and sand content was indicated by an angle close to 180\({}^{\circ}\) between their vectors. Si and Al content showed minimal relevance in the PCA model. These findings suggest that OC, clay, and silt content are primary factors governing PCE sorption in the studied soils, while sand content negatively influences sorption, aligning with results  
Figure 1: **Summary of Pearson’s correlation coefficients and corresponding \(p\)-values. ** The heatmap displays the Pearson’s correlation coefficients for all studied parameters, with positive correlations shown in red and negative correlations in blue. The coefficients range from \(-1\) to \(1\), where \(-1\) indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 signifies no linear relationship between the variables. from previous studies [45; 51; 52; 53]. In the second PCA analysis, which included SSA and porosity, PC1 and PC2 explained 56.38% of the variance (PC1: 36.84%; PC2: 19.54%), both with eigenvalues higher than 1.7 (Table S3). The results highlighted the contributions of SSA and porosity to PCE sorption in soils. The corresponding biplot is displayed in Figure S1. AHC was utilized to group samples based on their soil properties and measured \(K_{\text{d}}\) values resulting in a dendrogram (Figure S2) with three distinct clusters (green, red, and blue). The green cluster, containing 14 samples, is the most cohesive, while the red and blue clusters contain 6 and 14 samples, respectively. Most mergers occur at low dissimilarity levels (below 5000), but the three clusters remain distinct until around 6400 units, indicating strong between-cluster differences. Combined with PCA, these analyses revealed a relationship between soil particle size distribution and \(K_{\text{d}}\). The samples in this study were categorized into 10 classes according to the international soil texture classification standard. The soil texture triangle in Figure 3A depicts the relative proportions of sand, silt, and clay particles in the samples. Each soil texture class exhibits unique characteristics, such as water retention, permeability, and pore volume. Figure 3: Soil texture triangles: (**A**) the relative composition of tested soil samples, (**B**) three soil texture classes identified through AHC analysis. Figure 2: Biplot of PC1 and PC2 axes (63.77% variance explained): points represent 34 soil samples, vectors represent seven variables (reps. \(K_{\text{d}}\) and six soil properties).