## 2 Materials and Methods
### The Calculation of Pollution Indices  
The threshold values established based on the Geochemical Atlas of Romania were used to compute pollution indices. Among the simple indices calculated for each trace element, the Geoaccumulation Index (\(I_{geo}\)) [22] is a widely employed, readily interpretable, and precisely scaled metric [21]. It is defined as  
\[I_{geo}=\log_{2}\left(\frac{C_{n}}{1.5\cdot B_{n}}\right) \tag{3}\]  
where \(C_{n}\) is the measured concentration of the investigated element, \(B_{n}\) is the geochemical background, and the constant 1.5 has the role of reducing the variations of lithology. Seven classes were defined (Table 2) for the Geoaccumulation Index [93]:  
Figure 4: Box-plots for trace elements: (**a**) As, (**b**) Cd, (**c**) Cr, (**d**) Cu, (**e**) Hg, (**f**) Ni, (**g**) Pb, and (**h**) Zn from the Danube data set. The mean is represented by the cyan-colored “\(\square\)” symbol, “\(\times\)” represents the 99% and 1% percentiles, “-” represents the maximum and minimum values from the data set, and the magenta-colored circles represent outliers. From the category of complex indices, which take into account all analyzed trace elements, the Nemerow Pollution Index (\(PI_{Nemerow}\)), developed for the Environmental Protection Agency (EPA) of the United States in [94], was selected due to its wide use in a multitude of regions across the globe [95; 96; 97; 98; 99]. This index features a precise scale focused on the most contaminated element and is designed to evaluate the overall quality of the sediment/soil. The Pollution Index \(PI\) has a relatively straightforward calculation based on the ratio between the concentration of a specific element and a reference value, which is typically the geochemical background or a threshold concentration:  
\[PI=\frac{C_{n}}{B_{n}} \tag{4}\]  
\[PI_{Nemerow}=\sqrt{\frac{\left(\left(\frac{\left(\frac{\left(\frac{\mu_{i}^{ \text{T}}PI}{n}\right)^{2}}\right)+PI_{max}{}^{2}}\right.\right.}{2}} \tag{5}\]  
The quality classes based on \(PI_{Nemerow}\) values are listed in Table 3 [100; 101]:  
Another index that was employed in this study was the Potential Ecological Risk (\(RI\)), which was introduced in [8] and can be calculated using the following formula:  
\[RI=\sum_{i=1}^{n}E_{r}^{i} \tag{6}\]  
\[E_{r}^{i}=T_{r}^{i}.PI \tag{7}\]  
where \(n\) is the number of trace elements, \(E_{r}^{i}\) is the index of ecological risk factor [21; 23; 36], \(PI\) is the simple Pollution Index (2), and \(T_{r}^{i}\) is the toxicity response coefficient of a trace element. These toxicity responses are [23; 36] Cr = 2; Zn = 1; Ni = Cu = Pb = 5; As = 10; Cd = 30; and Hg = 40. The ecological risk is classified into four categories (Table 4). The \(PI\) was calculated using the regional geochemical background values, as indicated in Table 1. Studies conducted in other regions cannot use the pre-industrial values observed in Scandinavian lakes as a basis for comparison. Research conducted in [102] employed regional \begin{table}
\begin{tabular}{c c c} \hline
**Class** & **Description** & \(I_{geo}\) \\ \hline
0 & unpolluted & \(I_{geo}\leq 0\) \\
1 & slightly polluted & \(0<I_{geo}\leq 1\) \\
2 & moderately polluted & \(1<I_{geo}\leq 2\) \\
3 & moderately to strongly polluted & \(2<I_{geo}\leq 3\) \\
4 & strongly polluted & \(3<I_{geo}\leq 4\) \\
5 & strongly to extremely polluted & \(4<I_{geo}\leq 5\) \\
6 & extremely polluted & \(I_{geo}>5\) \\ \hline \end{tabular}
\end{table} 
Table 2: Soil/sediment quality classes according to \(I_{geo}\) values. \begin{table}
\begin{tabular}{c c c} \hline
**Class** & **Description** & \(PI_{Nemerow}\) \\ \hline
1 & safety domain/clean & \(PI_{Nemerow}\leq 0.7\) \\
2 & precaution domain/warning & \(0.7<PI_{Nemerow}\leq 1\) \\
3 & slightly polluted & \(1<PI_{Nemerow}\leq 2\) \\
4 & moderately polluted & \(2<PI_{Nemerow}\leq 3\) \\
5 & seriously polluted & \(3<PI_{Nemerow}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Soil/sediment quality classes according to \(PI_{Nemerow}\) values.