# Comparison of \({}^{210}\)Pb Age Models of Peat Cores Derived from the Arkhangelsk Region
## 2 Material and Methods
### Study of Physical and Radioactive Characteristics of Peat Samples
#### 2.2.5 The Dating Procedure  
In this study, we applied the CA, CF/CS, PF, and CF models using Monte Carlo simulations and IP-CRS dating models. The IP-CRS \({}^{210}\)Pb dating model (the initial penetration-constant rate of supply) is a modification of the CRS model. The main change in this model is that the amount of \({}^{210}\)Pb\({}_{\text{ss}}\) that has been transported in the peat volume can be estimated. The dating method and its validity are described in more detail in [20]. For the models listed above, we followed the recommended calculation procedure [21]. We use the aforementioned calculation procedure [22], taking special care to consider the dependent variables when evaluating the errors. To perform the dating, we followed the supplementary approximation method described in [10] for this data set. For the aforementioneddating model, we followed the work of the authors of [20]. A comparison between \({}^{210}\)Pb and the \({}^{137}\)Cs activity associated with the 1963 global deposition at 19-21 cm depth showed that the CF/CS, CF and IP-CRS models (1965, 1962 and 1964, respectively) provide the closest ages to this reference point. Among these three variants, the IP-CRS was preferred because it provided a rather good correlation with \({}^{137}\)Cs-specific radioactivity in the control horizon, taking errors into account. The total activity concentration of \({}^{210}\)Pb (\({}^{210}\)Pb\({}_{\text{tot}}\)) as a function of core profile depth z\({}_{i}\) is shown in the graph in Figure 2a and Table 1. The supported fraction (\({}^{210}\)Pb\({}_{\text{sup}}\)) was calculated as the average level (\(\pm\)standard deviation (SD), 1\(\sigma\)) of activity for the lowest levels at which the level of \({}^{210}\)Pb\({}_{\text{tot}}\) reached a steady state, as shown graphically by the red line in Figure 2a. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Sample Code**} & \multirow{2}{*}{\(z_{i}\)**, \(\mathbf{cm}\)**} & \multirow{2}{*}{\(m_{i}\)**, \(\mathbf{g}\)**} & \multicolumn{2}{c}{\({}^{210}\)Pb\({}_{\text{tot}}\), \(\mathbf{Bk}\)-\(\mathbf{kg}^{-1}\)} & \multicolumn{2}{c}{\({}^{137}\)Cs, \(\mathbf{Bk}\)-\(\mathbf{kg}^{-1}\)} \\ \cline{4-6}  & & & \multicolumn{2}{c}{\(\mathbf{x}\pm\Delta\)} & \multicolumn{2}{c}{\(\mathbf{x}\pm\Delta\)} \\ \hline ISNO-1 0.3 & 1.5 & 141.18 & 310.7 & 34.1 & 38.8 & 4.6 \\ ISNO-1 3-5 & 4.0 & 72.40 & 211.1 & 50.6 & 45.6 & 9.1 \\ ISNO-1 5.7 & 6.0 & 106.03 & 168.4 & 21.9 & 31.2 & 4.1 \\ ISNO-1 7.9 & 8.0 & 81.19 & 155.3 & 35.7 & 15.5 & 4.3 \\ ISNO-1 9-11 & 10.0 & 124.67 & 168.5 & 21.9 & 16.4 & 2.3 \\ ISNO-1 11-13 & 12.0 & 83.95 & 158.0 & 20.5 & 19.8 & 3.0 \\ ISNO-1 13-15 & 14.0 & 99.77 & 155.0 & 26.3 & 19.8 & 3.5 \\ ISNO-1 15-17 & 16.0 & 108.92 & 131.0 & 20.9 & 27.5 & 3.8 \\ ISNO-1 17-19 & 18.0 & 99.31 & 180.8 & 20.3 & 43.4 & 7.4 \\ ISNO-1 19-21 & 20.0 & 96.26 & 243.9 & 73.1 & 45.5 & 6.8 \\ ISNO-1 21-23 & 22.0 & 90.26 & 72.7 & 28.8 & 37.8 & 6.4 \\ ISNO-1 23-25 & 24.0 & 78.44 & 77.9 & 38.9 & 21.1 & 4.4 \\ ISNO-1 25-27 & 26.0 & 68.70 & 44.4 & 26.2 & 13.3 & 4.0 \\ ISNO-1 27-29 & 28.0 & 72.24 & 34.3 & 13.7 & 9.9 & 2.2 \\ ISNO-1 29-31 & 30.0 & 96.57 & 26.5 & 15.9 & 4.6 & 2.3 \\ ISNO-1 31-33 & 32.0 & 85.96 & 28.8 & 11.5 & 4.9 & 3.4 \\ ISNO-1 33-35 & 34.0 & 82.87 & 26.5 & 15.9 & 4.3 & 1.3 \\ ISNO-1 35-37 & 36.0 & 78.64 & 26.3 & 10.5 & 4.3 & 1.7 \\ ISNO-1 37-39 & 38.0 & 75.98 & 26.4 & 10.5 & 3.9 & 1.6 \\ ISNO-1 39-41 & 40.0 & 92.25 & 26.5 & 10.6 & 3.2 & 1.6 \\ ISNO-1 41-43 & 42.0 & 72.76 & 26.3 & 10.5 & 3.3 & 1.6 \\ ISNO-1 43-45 & 44.0 & 50.42 & 26.2 & 10.4 & 5.1 & 2.0 \\ ISNO-1 45-47 & 46.0 & 55.68 & 26.2 & 10.5 & 3.9 & 1.5 \\ ISNO-1 47-49 & 48.0 & 40.39 & 26.3 & 10.5 & 3.7 & 2.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial data for the studied peat profile of the Primorsky district in Arkhangelsk region, Northwestern Russia (\(\pm\)standard error of the mean, 1\(\sigma\)).