# Heavy Metals in Post-Exploitation Reservoirs--The Bagry Lake Case Study (Poland)
## 5 Relationships between Metals in Supernatant and Sediments  
The relationships between metals in the supernatant and the sediment can be very complex. Formation of similar compounds, adsorption or absorption on suspensions and in the sediments result in numerous interactions that have an effect on metals concentrations in water. Cluster analysis enables description of relationships and interaction between various features or factors. Only positive values \(w\) (Equation (2)) were used in the cluster analysis,  
Figure 17: (**a–f**). Fit of the model (1) describing the relations between metals in the sediments. although non-positive values were also present in the cluster transformation tables. Clustering was performed by beam analysis. This way it was possible to find common features, treated as tendencies of quantitative changes, to explain certain links (relationships), e.g., whether a higher concentration of one metal in the supernatant is accompanied by a higher concentration of another one in the sediment or whether a higher metal concentration in the sediment is associated with its higher concentrations in the mineral or the volatile fraction in the sediment, etc. Since the cluster analysis took into account only positive tangential distances, the resulting clusters refer to the increase or decrease of both values of the features, i.e., concentrations in supernatant, sediment or shares of different fractions in the sediment. The dendrogram of links between features and sequences of clusters is shown in Figure 18. The distances between features and clusters in Figure 19 correspond to the distances shown in Figure 18. The definitions of clusters are presented in Table 4.  
Figure 18: Dendrogram of the following features: presence of metals in the supernatant, in the sediment, mass of mineral and volatile fractions and mass fractions of particles larger or smaller than 0.06 mm. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{1}{c}{**Clusters (Definitions):**} & \multicolumn{1}{c}{**Distances between Clusters w**} & \multicolumn{1}{c}{**Distances**} & \multicolumn{1}{c}{**Cluster**} \\ \hline Cu supernatant + Pb supernatant = A & 0.312 & 1.025 & A \\ \hline Volatile fraction + mass fraction \textless{} 0.06 mm = B & 0.362 & 1.189 & B \\ \hline Mineral fraction + mass fraction \textgreater{} 0.06 mm = C & 0.362 & 1.189 & C \\ \hline Fe sediments + Mn sediments = D & 0.680 & 2.235 & D \\ \hline Fe supernatant + Mn supernatant = E & 0.757 & 2.489 & E \\ \hline E + A = F & 0.758 & 2.492 & F \\ \hline F + Cd supernatant =G & 0.787 & 2.588 & G \\ \hline Pb sediment +B = H & 0.866 & 2.846 & H \\ \hline D + Zn sediment = I & 0.880 & 2.895 & I \\ \hline I + H = J & 0.900 & 2.960 & J \\ \hline J + Cu sediment = K & 1.230 & 4.044 & K \\ \hline K + Cd sediment = L & 1.599 & 5.259 & L \\ \hline G + L = M & 3.109 & 10.224 & M \\ \hline M + Ca sediment = N & 3.566 & 11.728 & N \\ \hline N + Zn supernatant = O & 3.570 & 11.742 & O \\ \hline O + C = P & 30.407 & 100.000 & P \\ \hline \hline \end{tabular} Three lower-level clusters can be distinguished in the dendrogram (Figure 18):  
* Clusters for metals in the sediment;
* Clusters for metals in the supernatant without zinc;  
\end{table} 
Table 4: Definitions of clusters and distances in-between. Figure 19: Distances between features and clusters. Cluster for the sediment mineral fraction and the fraction of particles \(\geq\) 0.06 mm. A characteristic feature of the clusters are two sets of links for metals in sediments and in the supernatant, without zinc (Figure 18). The link between these clusters exists but is quite distant (\(w\) = 3.109), which means that the relations between the metals in the sediment and the supernatant are relatively weak. This may be due to a strong adsorption or absorption of metals in the sediments and/or their poor dissolution (whether they occur alone or in metal alloys).