#
Comparison of ^{210}Pb Age Models of Peat Cores Derived from the Arkhangelsk Region

^{*}

## Abstract

**:**

^{210}Pb dating procedure is a challenging task. The traditional

^{210}Pb age models assume an exponential decline in radioactivity in line with depth in the peat profile. Lead exhibits considerable migratory capacity in Arctic peatlands; hence, to perform precise peat dating, existing models should be enhanced to remove the effects of migration. Independent isotope chronometers, such as

^{137}Cs, can verify this. The Monte Carlo method and IP-CRS were utilised, together with several CA, CF/CS, PF, and CF models, to analyse the peat core samples acquired in the Arkhangelsk region. Data analysis revealed that the height partitioning of

^{137}Cs and

^{210}Pb is associated with physical characteristics, like the peat ash and the bulk density of the bog. Comparison between the natural activity of

^{210}Pb in the peat and the radioactivity of

^{137}Cs measured at depths of 19–21 cm in relation to the global fallout in 1963 indicated that the CF/CS, CF, and IP-CRS models (1965, 1962 and 1964, respectively) gave the closest age to the reference point given. IP-CRS was found to be the preferred model of these three options, as it gave a rather closer correlation with the

^{137}Cs activity specific to the reference layer, allowing the error. The core dating of

^{210}Pb showed an age of 1963 for a depth of 17–19 cm, which was in agreement with the reference horizon

^{137}Cs and ash content, thus validating the accuracy and sufficiency of the selected model turf profile chronology. The maximum content of man-made radioisotopes in the peatlands corresponded to the formulation of the Partial Test Ban Treaty of 1963. The rates of accumulation of peat and atmospheric flux of

^{210}Pb are in good agreement with the values available for the bogs of Northern Europe and those previously estimated by the authors in the subarctic region of European Russia. Although the problems of the complex migration-related distribution of

^{210}Pb in the peat layer were considered, the dating methods used were effective in our study and can be adapted in following studies to perform the age determination of different peat deposits.

## 1. Introduction

^{210}Pb [4,5]. Natural

^{210}Pb radionuclide, which is continuously generated in the atmosphere via the radioactive decay of

^{222}Rn, which is a component of the

^{238}U chain, is commonly used as an autonomous geochronometer to perform

^{137}Cs dating in studies of peat deposit accumulation to verify man-made radionuclide data [6]. It is important to note that dating performed via this method is a challenging problem due to the planned migration capacity of Pb in modern peatlands, as standard dating models assume an exponential decline in

^{210}Pb activity with the depth of the core, giving a rather precise and complete time line for the peat. [7].

^{137}Cs.

^{210}Pb on top of the peat layer is relatively constant, and its migration capacity along the peat profile is highly confined because of its chemical properties; thus, it is very useful when estimating the range of physical characteristics of the peatlands that influence the transport of radioisotopes.

^{210}Pb activity along the peat profile, which may result in serious errors in the dating and estimation of the peat accumulation rate [10]. A reason for the increased rate of

^{210}Pb migration could be variations in the physical and chemical characteristics of the peatland, depending on the environmental conditions. In the subarctic regions of Europe, larger seasonal temperature fluctuations, groundwater tables (hydrological conditions), redox and acid-base regimes, and the development of frozen events may be more important than they are in southern regions, along with variations in the vertical concentration of

^{210}Pb along the core layer.

^{210}Pb activity study): We considered anthropogenic

^{137}Cs and natural

^{210}Pb to be radionuclides derived from atmospheric fallout. We also studied ash concentration and bulk density as the physical characteristics of the turf.

## 2. Material and Methods

#### 2.1. Study Area and Sample Collection

^{210}Pb and

^{13}7Cs were used to perform isotope studies throughout the core depth, establishing a rectangular sampling surface area of 1050.9 cm

^{2}for which radionuclide deposition was assessed. The position of the area used to take samples and a photograph of the sample location are illustrated in Figure 1.

^{137}Cs and

^{210}Pb, samples were also ground and filtered to a fraction of 0.1 mm. Peat samples without sample preparation were used to determine the contents of botanical species.

#### 2.2. Study of Physical and Radioactive Characteristics of Peat Samples

#### 2.2.1. Determining the Plant Material

#### 2.2.2. Determining the Ash Content of Peat

#### 2.2.3. Determining the Bulk Density of Peat

#### 2.2.4. Determining ^{137}Cs and ^{210}Pb Isotopes

^{137}Cs was detected via a CANBERRA Packard low background gamma spectrometer (USA) with coaxial semiconductor detector GX2018 using the Ge(Li) crystal and Genie-2000 program (Version 3.1). The resolution of the gamma spectrometer at the 1.33 MeV (

^{60}Co) line was 1.75 keV, and the relative efficiency was 22.4%.

^{241}Am,

^{109}Cd,

^{88}Y,

^{137}Cs, and

^{152}Eu. The specific activity of

^{137}Cs was measured from the gamma line 661.66, with a quantum yield of 89.90% for

^{137m}Ba radionuclide. The minimum measured radioactivity of

^{137}Cs at exposure t = 18,000 s for geometry of a flat container of a 0.1-L volume measure was 0.1 Bq [18].

^{210}Pb, a peat sample was treated according to the methodology used in [19]. The obtained counting sample with radionuclides

^{210}Po and

^{210}Pb was measured 10 h after its receipt via the alpha-beta radiometer “Abelia”. During this period, the daughter alpha and beta radionuclides (

^{212,214,216,218}Po;

^{210}Bi and

^{210}Bi) decayed. The range of measured specific activity according to this method extended from 10 to 2·10

^{3}Bq·kg

^{−1}. Measurement uncertainty (p = 0.95) was estimated at each specific measurement and did not exceed 30% [19]. We noted that the average actual value for the studied sample was 10%.

#### 2.2.5. The Dating Procedure

^{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

_{xs}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 aforementioned dating 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

_{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

_{sup}) was calculated as the average level (±standard deviation (SD), 1σ) of activity for the lowest levels at which the level of

^{210}Pb

_{tot}reached a steady state, as shown graphically by the red line in Figure 2a.

^{210}Pb

_{sup}activity of the

^{210}Pb

_{tot}at the level behind the level, we calculated the unsupported fraction (

^{210}Pb

_{uns}), which was used to perform the next stages of dating and is indicated in Figure 2b. The independent marker

^{137}Cs was used to check the chronology. Figure 2c shows the peaks of man-made radioisotopes in native sediments associated with specific dates in past radioactive contamination; in particular, 1963, i.e., the year in which the Partial Test Ban Treaty was agreed, provided a suitable indicator point for this study.

## 3. Results and Discussion

#### 3.1. Physico-Chemical Parameters of Peat

^{−3}which is typical for undisturbed high-moor peatlands. The natural moisture content lies between 15 and 24 g·y

^{−1}and declines at an increased depth of occurrence, which is in part caused by the gradually increasing compaction of the porous peat structure as it moves from the surface to the subsurface.

#### 3.2. Vertical Distribution of the Peat Profile of Radionuclides

^{137}Cs in the ISNO-1 peat profile is between 3.2 and 45.6 Bq·kg

^{−1}, as shown in Table 1. According to the graph shown in Figure 4, for the vertical distribution, there are two distinct peaks of

^{137}Cs activity. The activity of 45.5 Bq·kg

^{−1}is located at 19–21 cm, and the activity of 45.6 Bq·kg

^{−1}is located at 3–5 cm.

^{137}Cs reading of 43.4 Bq·kg

^{−1}is located at a depth of 17–19 cm. The downward migration of the radionuclide through the core can be assumed. In general, the highest

^{137}Cs distribution for the first few centimeters of the peat core is typical of upland bogs [23].

^{137}Cs activity here is in part linked to the chemistry of Cs and K, which are both active in terms of moving through the peat layer through plants. The additional explanation for the great mobility of

^{137}Cs in the highlands is the lack of the appropriate mineral particulates required for

^{137}Cs adsorption [8].

^{137}Cs at the top of the core, we watched a similar activity at depths ranging from 17 to 21 cm.

^{137}Cs and ash are introduced into the peat via air deposition.

^{137}Cs distribution, the peak of caesium absorption by vegetation is 11 cm for the investigated core, as lower down, i.e., between 19 and 21 cm, we see a peak of activity exceeding the maximum limit, which was potentially caused by global deposition.

^{210}Pb activity in the sampled peat core fluctuates between 21.9 and 330.6 Bq·kg

^{−1}. The peak

^{210}Pb activity is shown in Figure 2 and occurs in the 3–5 cm horizon. Below the 35–37 cm horizon, the activity of

^{210}Pb ceases to change and is ~26 Bq·kg

^{−1}in all lower horizons, as there is no excess of atmospheric lead below, and the measured activity of

^{210}Pb in these layers is supported by the decay of

^{226}Ra.

^{210}Pb through the peat core only seems to occur in colloidal form. The migration of

^{137}Cs through the profile only takes place in ionic form [24].

#### 3.3. Chronology ^{210}Pb and Rate of Peat Accumulation

^{210}Pb

_{ex}[25].

- –
- Sample code.
- –
- Concentration
^{210}Pb (C_{i}, Bq·kg^{−1}). - –
- Uncertainty (u(
^{210}Pb))—Its calculation is specific to the analytical method used. The sources of uncertainty are as follows: the number of samples, efficiency or indicator activity, and sample weight. - –
- Contents
^{226}Ra (Bq·kg^{−1})—we calculated the arithmetic mean and standard deviation for the three lowest sites (43–49 cm), which, in our case, were^{226}Ra = 26.2 ± 0.1 Bq·kg^{−1}.

^{−1}. This value is less than the value for the lower part of the section, which was 26.3 Bq·kg

^{−1}for the 41–43 cm core layer. The key values used in this process were as follows:

- –
- Uncertainty (u(
^{226}Ra), Bq·kg^{−1}) corresponded to the calculated standard deviation. - –
- Excess
^{210}Pbex (C_{i}, Bq·kg^{−1}) was computed as follows:^{210}Pbex =^{210}Pb −^{226}Ra, except for the areas used to calculate 226Ra, where 210Pbex was missing. - –
- Uncertainty (u (C
_{i}), Bq·kg^{−1}) was computed as follows: $u\left({C}_{i}\right)=\sqrt{{u}^{2}\left(P{b}^{210}\right)+{u}^{2}\left(R{a}^{226}\right)}.$ - –
- Reserve
^{210}Pbex (A_{i}, Bq·m^{−2}) was computed as follows: multiplying C_{i}by the air-dried mass $\left(\frac{\Delta {m}_{i}}{S}\right)$. We used a factor of 10 to obtain kg·m^{−2}, and A_{i}= ${A}_{i}=10{C}_{i}\left(\frac{\Delta {m}_{i}}{S}\right)$. - –
- Uncertainty (u (A
_{i}), Bq·m^{−2}) was defined as follows: $u\left({A}_{i}\right)=\sqrt{{\left(\frac{u\left({C}_{i}\right)}{{C}_{i}}\right)}^{2}+{\left(\frac{u\frac{\Delta {m}_{i}}{S}}{\frac{\Delta {m}_{i}}{S}}\right)}^{2}}$ [21].

#### 3.3.1. Application of the CA Model

^{210}Pb

_{ex}, which is C

_{0}= C

_{i}(t = 0). We determined C

_{0}based on the intersection of the linear regression between ln C

_{i}and m

_{i}for the first 6 layers, and the correlation relationship was good (R

_{2}= 0.72). Both at this point and later on in the text, the R-squared value was denoted as R

_{2}. The intercept was 5.52 ± 0.17, giving C

_{0}= 250.3 ± 1.1 Bq·kg

^{−1}.

_{0}based on the intersection of the linear regression between ln C

_{i}and m

_{i}for the first 6 layers, and the correlation relationship was good (R

_{2}= 0.72). The intersection was 5.52 ± 0.17, meaning that C

_{0}= 250.3 ± 1.0 Bq·kg

^{−1}. The following values were also determined:

- –
- Age (t
_{i}; years): ${t}_{i}=\frac{1}{\lambda}\mathit{ln}\left(\frac{{C}_{0}}{{C}_{i}}\right)$. - –
- Uncertainty (u(t
_{i})): $u\left({t}_{i}\right)=\frac{1}{\lambda}\sqrt{{\left(u\left(\lambda \right){t}_{i}\right)}^{2}+{\left(\frac{u\left({C}_{0}\right)}{{C}_{0}}\right)}^{2}+{\left(\frac{u\left({C}_{i}\right)}{{C}_{i}}\right)}^{2}}$.

_{0}is generated via the selection process, we assume that the uncertainties are independent. Subtracting the CA age from the sampling date yields the calendar year (Ti). The problem with this approach that the age of deep layers is rejuvenated. For the studied ISNO-1 core, the 5–7 cm layer is dated to 4.96 years, which is older than the layer deeper than 7–9 cm, which is 4.86 years. This outcome is in conflict with the assumption of an unbroken peat core, meaning that this chronology is not applicable to this core. In response, we used the following calculations:

- –
- In order to compute the accumulation rate, it is necessary to obtain the age of the layers. The age 0 is assigned to layer 0 (t = 0), and the average age of each of the layers is computed as follows: $t\left(1\right)=\frac{{t}_{1+}{t}_{2}}{2}$.
- –
- The calculation used to determine the age of the last horizon should be carried out as follows: $t\left(43\right)={t}_{43}+\frac{{t}_{43}-{t}_{42}}{2}$.

- –
- Uncertainty (u(t(i))) was computed as follows (one section): $u\left(t\left(1\right)\right)=\frac{1}{2}\sqrt{{u}^{2}\left({t}_{1}\right)+{u}^{2}\left({t}_{2}\right)}$.
- –
- Section formation time (Δt
_{1}; years) was defined as the difference between two successive layers: $\Delta {t}_{1}={t}_{2}-{t}_{1}$. - –
- Uncertainty (u(Δt)) was computed as follows (one section): $u\left(\Delta t\right)=\sqrt{{u}^{2}\left({t}_{1}\right)+{u}^{2}\left({t}_{2}\right)}$.
- –
- Mean sediment accumulation rate (s
_{i}, cm·year^{−1}) was the relationship between the transect width and formation time. For Section 1, we used the following equation: ${s}_{1}=\frac{{z}_{2}-{z}_{1}}{\Delta {t}_{1}}$. - –
- Uncertainty (u(s)): $u\left(s\right)=s\frac{u\left(\Delta t\right)}{\Delta t}$.
- –
- Mean mass accumulation rate (ri, g·cm
^{−2}·year^{−1}): ${r}_{1}=\frac{{m}_{2}-{m}_{1}}{\Delta {t}_{1}}$. - –
- Uncertainty (u(r)): $\mathrm{u}\left(\mathrm{r}\right)=\mathrm{r}\frac{\mathrm{u}\left(\Delta \mathrm{t}\right)}{\Delta \mathrm{t}}$.

#### 3.3.2. Application of the CF/CS Model

_{i}), the average mass depth (m

_{i}, g·cm

^{−2}), and the logarithm

^{210}Pb

_{ex}(ln C

_{i}). We executed the expression as y = a + bx, where y = ln C

_{i}and x = m

_{i}. The equation $\mathit{ln}{C}_{i}=\mathit{ln}{C}_{0}-\frac{\lambda}{r}{m}_{i}$ shows that $r=-\frac{\lambda}{b}$, with uncertainty defined as $u\left(r\right)=r\sqrt{{\left(\frac{u\left(\lambda \right)}{\lambda}\right)}^{2}+{\left(\frac{u\left(b\right)}{b}\right)}^{2}}$.

^{−2}·year

^{−1}At this point and later in the text, the mass accumulation rate (r, g·cm

^{−2}·year

^{−1}was denoted as MAR, and the sediment accumulation rate (s, cm·g

^{−1}) was denoted as SAR. Also, SAR could be estimated via a linear equation using the cut depth (z

_{i}) instead of the depth of mass (m

_{i}). Then, $=-\frac{\lambda}{b}$, and its uncertainty was defined as $u\left(s\right)=s\sqrt{{\left(\frac{u\left(\lambda \right)}{\lambda}\right)}^{2}+{\left(\frac{u\left(b\right)}{b}\right)}^{2}}$.

^{210}Pb

_{sup}. The fitting of a simple regression to the natural logarithm plot of the activity concentration of

^{210}Pb

_{uns}ln (

^{210}Pb

_{uns}) as a function of the depth mass m

_{i}is shown in Figure 5a. Even if the value of determination (COD) for the whole data set was quite significant, i.e., 0.78, as can be seen from Figure 5, we characterized our model as being of good quality (COD = 0.8). One trend line cannot explain all of the variability in the core.

#### 3.3.3. Application of the PF Model

- –
- The time of formation of the profile (∆t
_{i}, year) was calculated using the following equation: $\Delta {\mathrm{t}}_{1}=\mathrm{t}\left(2\right)-\mathrm{t}\left(1\right)$. - –
- Uncertainty (u(Δt1)) was defined as follows: $u\left(\Delta {t}_{1}\right)=\sqrt{{u}^{2}\left(t\left(1\right)\right)+{u}^{2}\left(t\left(2\right)\right)}$.
- –
- MAR (ri) was calculated using the equation $r\left(i\right)=\frac{\lambda A\left(i\right)}{C\left(i\right)}$, and the uncertainty was determined as follows: $u\left(r\left(i\right)\right)=r\left(i\right)\sqrt{{\left(\frac{u\left(A\left(i\right)\right)}{A\left(i\right)}\right)}^{2}+{\left(\frac{u\left(\Delta t\left(i\right)\right)}{\Delta t\left(i\right)}\right)}^{2}+{\left(\frac{u\left(C\left(i\right)\right)}{C\left(i\right)}\right)}^{2}}$ [21].

^{210}Pb dating model used for the ISNO-1 core for the 19–21-cm layer shows an age of 1965. This finding has better agreement with the activity of

^{137}Cs in the indicator layer than the above models, but this agreement is not sufficient.

#### 3.3.4. Application of the CF Model Alone and via Monte Carlo Simulation

- –
- The accumulated
^{210}Pbex deposits under horizon (i) (Bq·m^{−2}) were computed as follows: $A\left(i\right)={\displaystyle \sum}_{j=i+1}^{j=\infty}\Delta {A}_{i}$.

^{210}Pb

_{ex}below, the calculation starts with A(41) = 0 Bq·m

^{−2}.

_{39}. In addition, u(A(39)) = u(ΔA

_{39}). For layer 37, A(37) = A(39) + ΔA

_{37,}and this pattern continued towards the top. If certain intervals were not analysed, the value of the mass concentration (C

_{i}) (and Δm

_{i}if its corresponding value is unknown) were estimated via interpolation from neighbouring intervals, and ΔA

_{i}was computed for the missing section. Relevant values were defined as follows:

- –
- Uncertainty u(A(37)): $u\left(A\left(37\right)\right)=\sqrt{u{\left(\left(A\left(39\right)\right)\right)}^{2}+{\left(u\left(\Delta {A}_{37}\right)\right)}^{2}}$. This pattern continued towards the top.
- –
- A(0) = 1682 ± 117 Bq·m
^{−2}—reserve^{210}Pbex, on the basis of which we determined its flux to the sediment surface to be 52 ± 4 Bq·m^{−2}·year^{−1}. - –
- The age of CF was determined via the expression$t\left(i\right)=\frac{1}{\lambda}\mathit{ln}\frac{A\left(0\right)}{A\left(i\right)}$. The extension of uncertainty was performed with care (see [29]).
- –
- The expression for the uncertainty of age was defined as follows:$$u\left(t\left(i\right)\right)=\frac{1}{\lambda}\sqrt{{\left(u\left(\lambda \right)t\left(i\right)\right)}^{2}+{\left(\frac{u\left(A\left(0\right)\right)}{A\left(0\right)}\right)}^{2}+\left(1-\frac{2A\left(i\right)}{A\left(0\right)}\right){\left(\frac{u\left(A\left(i\right)\right)}{A\left(i\right)}\right)}^{2}}$$
- –
- To calculate the calendar year T(i), we subtracted the age of the CF from the sampling date.
- –
- MAR (r(i), kg·m
^{−2}·year^{−1}) was determined via the formula $r\left(i\right)=\frac{\lambda A\left(i\right)}{C\left(i\right)}$, and its uncertainty was $u\left(r\left(i\right)\right)=r\left(i\right)\sqrt{{\left(\frac{u\left(\lambda \right)}{\lambda}\right)}^{2}+{\left(\frac{u\left(A\left(i\right)\right)}{A\left(i\right)}\right)}^{2}+{\left(\frac{u\left(C\left(i\right)\right)}{C\left(i\right)}\right)}^{2}}$. MAR was shown in Figure 6. - –
- SAR (s(i), cm·year
^{−1}) was computed using the bulk density of dry sediment ρ, as $s\left(i\right)=\left(\frac{r\left(i\right)}{\rho \left(i\right)}\right)\times 100$. SAR is shown in Figure 6. - –
- Uncertainty u(s(i)): $u\left(s\left(i\right)\right)=s\left(i\right)\sqrt{{\left(\frac{u\left(r\left(i\right)\right)}{r\left(i\right)}\right)}^{2}+{\left(\frac{u\left(\rho \left(i\right)\right)}{\rho \left(i\right)}\right)}^{2}}$ [21].

_{i}) for the upper core layers 0–9 cm varied little, and the value range was 0.44 to 0.53 cm·year

^{−1}, as can be seen in Table 2; from 9 to 33 cm, we observed a relatively uniform and gradual decrease in the mean sediment accumulation rate to 0.03 cm·year

^{−1}. We also noted the increased s

_{i}values for the 35–39-cm interval.

_{i}) for all core layers were almost constant and fluctuated very slightly from to 0 and 0.01 to 0.02 g·cm

^{−2}·year

^{−1}. In Table 5, the CF dating model used in the ISNO-1 core for the 19–21-cm layer shows an age of 1965. The Monte Carlo method was employed to provide a refined age of 1962, which slightly improved the agreement with the

^{137}Cs reference horizon, considering the error.

^{−1}, with an average of 0.48 ± 0.08 cm·year

^{−1}. This finding agrees with constant s estimate of 0.14 ± 0.01 cm·year

^{−1}obtained through the CF/CS method. A similar situation occurred in the case of r, which ranged between 0.43 ± 0.01 and 7.2 ± 0.02 g·cm

^{−2}·year

^{−1}.

^{−2}year, while the constant r via CF/CS was at 0.006 ± 0.001 g·cm

^{−2}·year

^{−1}.

^{210}Pb dating, the air flux of

^{210}Pb could be estimated. Based on the CF and CF models, in combination with the Monte Carlo simulation, the flux of

^{210}Pb was 52 ± 4 Bq/m

^{−2}·year

^{−1}and 69.13 ± 10 Bq/m

^{−2}·year

^{−1}, which agrees well with the literal data [10].

#### 3.3.5. Application of the IP-CRS Model

^{210}Pb dating, we also used the initial penetration-constant rate of supply (IP-CRS) model, the calculation of which we performed by following the procedure described in detail by the authors of [20]. To describe the content of

^{210}Pb (

^{210}Pb

_{xs}) in the studied sample, we partitioned the peat column into n layers represented by the z (cm) distance from top to bottom. Each layer extended from depth z

_{i}

_{−1}to depth z

_{i}(see Table 6).

^{210}Pb

_{xs}that has been transported in the peat volume can be estimated. The dating method and its validity are described in more detail in [20]. To calculate the IP-CRS chronology (calculated values are presented in Table 3), we carried out the following process:

- A.
- Limiting the depth of the section of the peat section subject to leaching (z
_{k}).

^{210}Pb

_{xs}in the peat profile was determined by fundamentally dividing it into two distinct zones. The first zone was the washout zone, which extended from the core surface to a depth of z

_{k}, which, in our case, was 20 cm. In this zone,

^{210}Pb

_{xs}migrated downwards, which was modelled using various penetration rates r

_{i}for each horizon. The next leaching zone consisted of living mosses and was different for different wetland types. It was characterised by high water migration, which caused the downward transport of

^{210}Pb as part of the infiltrated sediments. Thus, the washing (accumulation) zone was a cumulative area from z

_{k}to ∞ (for the studied profile from 20 to 33 cm), in which

^{210}Pb

_{xs}from the overlying core horizons are were transferred to peat horizons. Here, the mosses comprising the peat had a higher density. Since the hydraulic conductivity decreased here, a layer was eventually formed, in which the deposited

^{210}Pb

_{xs}accumulated.

^{210}Pb activity was detected [20].

- B.
- Solving a system of integro-differential equations

_{i}), and considered the fractional amplification factors (f

_{i}). The model was realised using MATLAB software (https://www.mathworks.com/products/matlab/getting-started.html, accessed on 14 August 2023).

^{210}Pb

_{xs}(Ci, Bq/cm

^{3}) in the solid form of every interval was described using Equations (1) and (2), the detailed derivation of which was given in the Supplementary Materials section in [20].

_{k}:

_{k}to ∞:

- C.
- Determine the quantity of
^{210}Pb_{xs}removed from each layer of the washout area

^{210}Pb

_{xs}(Bq·m

^{−2}) transported from each horizon of the upper section was estimated using the following equation:

_{i}—the date when this layer started to form.

- D.
- Determining the total amount of
^{210}Pb_{xs}

^{210}Pb

_{xs}transferred downward was assessed by adding up the sums of

^{210}Pb

_{xs}obtained in C.

- E.
- Determining the additional
^{210}Pb_{xs}for each layer

^{210}Pb

_{xs}integrated into each layer was determined by multiplying the overall extracted

^{210}Pb

_{xs}by the corresponding fractional amplification f

_{i}.

- F.
- Determination of corrected
^{210}Pb_{xs}volumetric activities

^{210}Pb

_{xs}obtained from layer C to the appropriate layers of the wash zone; secondly, we subtracted the volumetric activities of

^{210}Pb

_{xs}determined in E from the appropriate layers of the lower zone.

- G.
- Applying the CRS model to the corrected profile

^{210}Pb

_{xs}activity profile was fitted to the CRS model using the Monte Carlo method [20,22].

^{137}Cs activity coincides with the horizon of 19–21 cm, which also corresponds to the peak of the ash index. Generally, the peaks of man-made radionuclides in the peat soils are associated with large-scale radiation episodes, like the Partial Test Ban Treaty of 1963 and the Chernobyl accident, and provide a starting point for research work. The high migration and bioavailability of

^{137}Cs in peat soils mean that it does not always indicate radiation episodes on the horizon [8].

^{137}Cs, which had entered the top of the peatland during the global deposition in 1963, to a depth of 19–21 cm. The data collected confirm the validity and sufficiency of our selected peat core age model.

^{−1}and had a mean value of 0.28 ± 0.08 cm·year

^{−1}, which are slightly lower than the earlier reported values for the subarctic region of European Russia [1] and lower than the values given in [10], where the latter value was 0.38 ± 0.07 cm·year

^{−1}. The accumulation rate of the peat mass r ranged between 0.0019 ± 0.001 and 0.0199 ± 0.001 g·cm

^{−2}·year

^{−1}. The mean rate was 0.0117 ± 0.001 g·cm

^{−2}·year

^{−1}.

^{210}Pb dating IP-CRS model, we estimated an atmospheric flux of

^{210}Pb of 58.98 ± 2.94 Bq·m

^{−2}·year

^{−1}, which agrees well with data sourced from peatlands in Northern Europe: for Southern Finland, the

^{210}Pb flux was 50–80 Bq·m

^{−2}·year

^{−1}[30]; for Central Sweden, the value was 78 Bq·m

^{−2}·year

^{−1}[31]; and based on our previously obtained data, the value was 80–91 Bq·m

^{−2}·year

^{−1}for subarctic European Russia [1].

## 4. Conclusions

^{137}Cs, there are two separate activity maxima at the very top of the profile and a depth of 19–21 cm, which can be explained based on the peculiarities of the

^{137}Cs intake transport with atmospheric deposition. The concentration of

^{210}Pb displays the common exponential decline of activity with depth.

^{137}Cs and the peak of the ash content fall on the 19–21-cm horizon. In this case, downwards biological migration of

^{137}Cs on the core occurs. However, the results confirm the accuracy and adequacy of our chosen peat core dating model.

^{210}Pb using various dating models, such as CF, CF with Monte Carlo simulation, and IP-CRS. The model deemed to be most accurate yielded an atmospheric flux of 58.98 ± 2.94 Bq·m

^{−2}·year

^{−1}for

^{210}Pb. This outcome aligns with prior research conducted by the authors into peatlands located in the subarctic region of European Russia.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The location of the wetlands in which the studied sample was taken (Arkhangelsk region) A red cross on map indicates the location where the studied sample was taken.

**Figure 2.**Plots of total

^{210}Pb activity (

**a**), unsupported

^{210}Pb activity (

**b**), and total

^{137}Cs activity (

**c**) based on the depth z

_{i}for the peat profile derived from Northwestern Russia.

**Figure 4.**Changes in the vertical distribution of

^{137}Cs and

^{210}Pb radioisotopes in the studied peat profile.

**Figure 5.**Graphs showing the one (

**a**) and three-fold approximations (

**b**) performed using the linear regression method for the data set ln (

^{210}Pb

_{uns}) depending on the mass depth m

_{i}.

**Figure 6.**Deposit accumulation rates based on the CF model: mass accumulation rate (g·cm

^{−2}·year

^{−1}) (

**a**); sediment accumulation rate (cm·year

^{−1}) (

**b**).

**Figure 7.**Graphs of a density ρ (

**a**), linear accumulation rate s (

**b**), and mass accumulation rate r (

**c**) versus z

_{i}.

**Figure 8.**The

^{210}Pb chronology results for the ISNO peat profile based on the IP-CRS model via the supplementary application of the Monte Carlo method. The red dots on the graph mark the year’s corresponding to a particular depth of peat core, the red line marks the depth range for the core dating from 1963.

**Figure 9.**The linear accumulation rate (s) and the mass accumulation rate (r) as a function of the depth of the peat core. The blue and red colours on the graph indicate the negative and positive error for the indicated values respectively.

**Table 1.**Initial data for the studied peat profile of the Primorsky district in Arkhangelsk region, Northwestern Russia (±standard error of the mean, 1σ).

Sample Code | z_{i}, cm | m_{i}, g | ^{210}Pb_{tot}, Bk·kg^{−1} | ^{137}Cs, Bk·kg^{−1} | ||
---|---|---|---|---|---|---|

x ± Δ | x ± Δ | |||||

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 |

z(i), cm | ln(C_{i}) | t(i), Year | u(t(i)), Year | Year (A.D.) | ur(l) | ur(C_{0}) | ur(C_{i}) | t(i) (Year) | u(t(i)), Year | Δt (Year) | u(Δt) | s (cm·Year ^{−1}) | u(s) | r (g cm ^{−2} Year^{−1}) | u(r) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0.00 | 0.00 | ||||||||||||||

1.5 | 5.65 | −4.1 | 3.8 | 2025 | −0.0007 | 0.005 | 0.12 | 2.81 | 4.79 | 1.07 | 1.82 | 0.05 | 0.08 | ||

2.81 | 4.79 | ||||||||||||||

4.0 | 5.22 | 9.7 | 8.8 | 2011 | 0.0016 | 0.005 | 0.27 | 11.12 | 6.95 | 0.18 | 0.11 | 0.01 | 0.00 | ||

13.93 | 5.04 | ||||||||||||||

6.0 | 4.96 | 18.1 | 4.9 | 2002 | 0.0031 | 0.005 | 0.15 | 5.76 | 7.15 | 0.35 | 0.43 | 0.02 | 0.02 | ||

19.70 | 5.08 | ||||||||||||||

8.0 | 4.86 | 21.2 | 8.9 | 1999 | 0.0036 | 0.005 | 0.28 | −0.01 | 7.18 | −177.38 | 112,976.25 | −6.85 | 4364.19 | ||

19.68 | 5.08 | ||||||||||||||

10.0 | 4.96 | 18.1 | 4.9 | 2002 | 0.0031 | 0.005 | 0.15 | −0.33 | 6.17 | −6.02 | 112.03 | −0.36 | 6.65 | ||

19.35 | 3.51 | ||||||||||||||

12.0 | 4.88 | 20.6 | 5.0 | 2000 | 0.0035 | 0.005 | 0.16 | 1.60 | 5.41 | 1.25 | 4.24 | 0.05 | 0.17 | ||

20.95 | 4.12 | ||||||||||||||

14.0 | 4.86 | 21.3 | 6.6 | 1999 | 0.0036 | 0.005 | 0.20 | 3.68 | 6.16 | 0.54 | 0.91 | 0.03 | 0.04 | ||

24.63 | 4.58 | ||||||||||||||

16.0 | 4.65 | 27.9 | 6.4 | 1993 | 0.0047 | 0.005 | 0.20 | −2.93 | 5.97 | −0.68 | 1.39 | −0.04 | 0.07 | ||

21.70 | 3.83 | ||||||||||||||

18.0 | 5.04 | 15.5 | 4.2 | 2005 | 0.0026 | 0.005 | 0.13 | −11.73 | 6.94 | −0.17 | 0.10 | −0.01 | 0.00 | ||

9.97 | 5.78 | ||||||||||||||

20.0 | 5.38 | 4.5 | 10.8 | 2016 | 0.0008 | 0.005 | 0.34 | 19.27 | 12.70 | 0.10 | 0.07 | 0.00 | 0.00 | ||

29.25 | 11.31 | ||||||||||||||

22.0 | 3.84 | 54.0 | 19.9 | 1967 | 0.0091 | 0.005 | 0.62 | 23.06 | 19.30 | 0.09 | 0.07 | 0.00 | 0.00 | ||

52.31 | 15.64 | ||||||||||||||

24.0 | 3.94 | 50.6 | 24.1 | 1970 | 0.0085 | 0.005 | 0.75 | 15.06 | 30.42 | 0.13 | 0.27 | 0.00 | 0.01 | ||

67.37 | 26.09 | ||||||||||||||

26.0 | 2.90 | 84.1 | 46.3 | 1936 | 0.0142 | 0.005 | 1.44 | 29.78 | 44.24 | 0.07 | 0.10 | 0.00 | 0.00 | ||

97.15 | 35.73 | ||||||||||||||

28.0 | 2.09 | 110.2 | 54.5 | 1910 | 0.0185 | 0.005 | 1.70 | 67.69 | 957.18 | 0.03 | 0.42 | 0.00 | 0.01 | ||

164.84 | 956.51 | ||||||||||||||

30.0 | −1.32 | 219.5 | 1912.3 | 1801 | 0.0369 | 0.005 | 59.63 | 18.36 | 1354.35 | 0.11 | 8.03 | 0.01 | 0.37 | ||

183.20 | 958.82 | ||||||||||||||

32.0 | 0.94 | 146.9 | 143.7 | 1874 | 0.0247 | 0.005 | 4.48 | 0.00 | 1355.98 | 0.00 | 0.00 | 0.00 | 0.00 | ||

183.20 | 958.82 | ||||||||||||||

34.0 | −1.32 | 219.5 | 1912.3 | 1801 | 0.0369 | 0.005 | 59.63 | 58.54 | 2865.72 | 0.03 | 1.67 | 0.00 | 0.07 | ||

241.74 | 2700.56 | ||||||||||||||

36.0 | −2.71 | 264.0 | 5051.3 | 1757 | 0.0444 | 0.005 | 157.50 | 7.54 | 3833.08 | 0.27 | 134.96 | 0.01 | 5.05 | ||

249.28 | 2720.20 | ||||||||||||||

38.0 | −1.79 | 234.6 | 2020.5 | 1786 | 0.0395 | 0.005 | 63.00 | −22.23 | 2970.92 | −0.09 | 12.02 | 0.00 | 0.43 | ||

227.05 | 1194.54 | ||||||||||||||

40.0 | −1.32 | 219.5 | 1274.8 | 1801 | 0.0369 | 0.005 | 39.75 | 14.69 | 2865.67 | 0.14 | 26.55 | 0.01 | 1.17 | ||

241.74 | 2604.83 | ||||||||||||||

42.0 | −2.71 | 264.0 | 5051.3 | 1757 | 0.0444 | 0.005 | 157.50 | 44.46 | 3628.22 | 0.04 | 0.00 | 0.00 | 0.13 | ||

286.20 | 2525.64 |

z(i), cm | m(i), g cm^{−2} | ln(C_{i}) |
---|---|---|

1.50 | 0.07 | 5.65 |

4.00 | 0.17 | 5.22 |

6.00 | 0.25 | 4.96 |

8.00 | 0.34 | 4.86 |

10.00 | 0.44 | 4.96 |

12.00 | 0.54 | 4.88 |

14.00 | 0.63 | 4.86 |

16.00 | 0.73 | 4.65 |

18.00 | 0.83 | 5.04 |

20.00 | 0.92 | 5.38 |

22.00 | 1.01 | 3.84 |

24.00 | 1.09 | 3.94 |

26.00 | 1.16 | 2.90 |

28.00 | 1.22 | 2.09 |

30.00 | 1.31 | −1.32 |

32.00 | 1.39 | 0.94 |

34.00 | 1.47 | −1.32 |

36.00 | 1.55 | −2.71 |

38.00 | 1.62 | −1.79 |

40.00 | 1.70 | −1.32 |

42.00 | 1.78 | −2.71 |

z(i), cm | z_{i},cm | ΔA_{i},Bq·m ^{−2} | u(ΔA_{i}) | A(i), Bq·m ^{−2} | u(A(i)) | t(i), Year | u(t(i)), Year | Year (A.D.) | Δt | u(Δt) | r(i), kg m ^{3} | u(r(i)) | ρ(i), g m ^{−3} | u(ρ(i)) | s(i), cm Year ^{−1} | u(s(i)) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1680 | 115 | 0.0 | 0.0 | 2021 | |||||||||||

1.50 | 382 | 46 | 8.28 | 1.06 | 0.02 | 0.00 | 0.04 | 0.00 | 0.36 | 0.07 | ||||||

3 | 1298 | 106 | 8.3 | 1.1 | 2012 | |||||||||||

4.00 | 127 | 35 | 3.31 | 1.74 | 0.02 | 0.01 | 0.03 | 0.00 | 0.60 | 0.36 | ||||||

5 | 1170 | 100 | 11.6 | 1.4 | 2009 | |||||||||||

6.00 | 143 | 22 | 4.19 | 2.17 | 0.02 | 0.01 | 0.05 | 0.00 | 0.48 | 0.26 | ||||||

7 | 1027 | 98 | 15.8 | 1.7 | 2005 | |||||||||||

8.00 | 100 | 28 | 3.28 | 2.57 | 0.02 | 0.02 | 0.04 | 0.00 | 0.61 | 0.51 | ||||||

9 | 927 | 94 | 19.1 | 1.9 | 2002 | |||||||||||

10.00 | 169 | 26 | 6.45 | 3.17 | 0.02 | 0.01 | 0.06 | 0.00 | 0.31 | 0.16 | ||||||

11 | 758 | 90 | 25.5 | 2.5 | 1995 | |||||||||||

12.00 | 105 | 16 | 4.79 | 3.92 | 0.02 | 0.01 | 0.04 | 0.00 | 0.42 | 0.35 | ||||||

13 | 653 | 88 | 30.3 | 3.0 | 1990 | |||||||||||

14.00 | 103 | 21 | 5.50 | 4.76 | 0.01 | 0.01 | 0.04 | 0.00 | 0.36 | 0.33 | ||||||

15 | 550 | 86 | 35.8 | 3.7 | 1985 | |||||||||||

16.00 | 109 | 22 | 7.05 | 5.98 | 0.01 | 0.01 | 0.05 | 0.00 | 0.28 | 0,25 | ||||||

17 | 442 | 83 | 42.8 | 4.7 | 1978 | |||||||||||

18.00 | 146 | 19 | 12.88 | 8.78 | 0.01 | 0.01 | 0.05 | 0.00 | 0.16 | 0.11 | ||||||

19 | 296 | 81 | 55.7 | 7.4 | 1965 | |||||||||||

20.00 | 199 | 67 | 36.01 | 16.19 | 0.00 | 0.00 | 0.05 | 0.00 | 0.06 | 0,03 | ||||||

21 | 96 | 45 | 91.7 | 14.4 | 1929 | |||||||||||

22.00 | 40 | 25 | 17.20 | 25.48 | 0.00 | 0.01 | 0.04 | 0.00 | 0.12 | 0.19 | ||||||

23 | 56 | 38 | 108.9 | 21.0 | 1912 | |||||||||||

24.00 | 39 | 29 | 37.13 | 48.67 | 0.00 | 0.00 | 0.04 | 0.00 | 0.05 | 0.09 | ||||||

25 | 18 | 24 | 146.1 | 43.9 | 1875 | |||||||||||

26.00 | 12 | 17 | 35.77 | 105.54 | 0.00 | 0.01 | 0.03 | 0.00 | 0.06 | 0.20 | ||||||

27 | 6 | 17 | 181.8 | 96.0 | 1839 | |||||||||||

28.00 | 6 | 9 | 101.43 | 1914.38 | 0.00 | 0.01 | 0.03 | 0.00 | 0.02 | 0.38 | ||||||

29 | 0 | 15 | 283.3 | 1912.0 | 1737 | |||||||||||

30.00 | 0 | 15 | ||||||||||||||

31 | 0 | 0 |

z(i), cm | ΔA_{i}, Bk·m^{−2} | u, ΔA_{i} | A(i), Bk·m^{−2} | u(A(i)) | t(i), Year | u(t(i)), Year | Year (A.D.) | r(i), g·cm^{−2}·Year^{−1} | u(r(i)) | ρ_{i}, g·cm^{−3} | u(ρ_{i}) | ρ(i), g·cm^{−3} | u(ρ(i)) | s(i), cm·Year^{−1} | u(s(i)) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1682 | 117 | 0 | 0 | 2021 | 0.02 | 0 | 0.04 | 0 | 0.48 | 0.01 | ||||

382 | 46 | 0.04 | 0 | ||||||||||||

3 | 1300 | 108 | 8.3 | 1.1 | 2012 | 0.02 | 0 | 0.04 | 0 | 0.44 | 0.02 | ||||

127 | 35 | 0.03 | 0 | ||||||||||||

5 | 1173 | 102 | 11.6 | 1.4 | 2009 | 0.02 | 0 | 0.04 | 0 | 0.53 | 0.01 | ||||

143 | 22 | 0.05 | 0 | ||||||||||||

7 | 1029 | 100 | 15.8 | 1.7 | 2005 | 0.02 | 0 | 0.04 | 0 | 0.53 | 0.02 | ||||

100 | 28 | 0.04 | 0 | ||||||||||||

9 | 930 | 96 | 19.0 | 2.0 | 2002 | 0.02 | 0 | 0.05 | 0 | 0.44 | 0.01 | ||||

169 | 26 | 0.06 | 0 | ||||||||||||

11 | 761 | 92 | 25.4 | 2.5 | 1995 | 0.02 | 0 | 0.05 | 0 | 0.35 | 0.01 | ||||

105 | 16 | 0.04 | 0 | ||||||||||||

13 | 656 | 91 | 30.2 | 3.1 | 1990 | 0.02 | 0 | 0.04 | 0 | 0.36 | 0.02 | ||||

103 | 21 | 0,05 | 0 | ||||||||||||

15 | 553 | 88 | 35.7 | 3.8 | 1985 | 0.01 | 0 | 0.05 | 0 | 0.30 | 0.02 | ||||

109 | 22 | 0.05 | 0 | ||||||||||||

17 | 444 | 86 | 42.7 | 4.8 | 1978 | 0.01 | 0 | 0.05 | 0 | 0.22 | 0.03 | ||||

146 | 19 | 0.05 | 0 | ||||||||||||

19 | 298 | 84 | 55.5 | 7.6 | 1965 | 0 | 0 | 0.05 | 0 | 0.11 | 0.03 | ||||

199 | 67 | 0.05 | 0 | ||||||||||||

21 | 99 | 50 | 90.9 | 15.4 | 1930 | 0 | 0 | 0.04 | 0 | 0.05 | 0.02 | ||||

40 | 25 | 0.04 | 0 | ||||||||||||

23 | 59 | 43 | 107.5 | 22.9 | 1913 | 0 | 0 | 0.04 | 0 | 0.09 | 0.02 | ||||

39 | 29 | 0.04 | 0 | ||||||||||||

25 | 20 | 32 | 141.5 | 50.4 | 1879 | 0 | 0 | 0.04 | 0 | 0.05 | 0.02 | ||||

12 | 17 | 0.03 | 0 | ||||||||||||

27 | 9 | 27 | 169.6 | 103.0 | 1851 | 0 | 0.01 | 0.03 | 0 | 0.06 | 0.02 | ||||

6 | 9 | 0.03 | 0 | ||||||||||||

29 | 3 | 26 | 203.4 | 279.0 | 1817 | 0 | 0.02 | 0.04 | 0 | 0.06 | 0.02 | ||||

0 | 15 | 0.05 | 0 | ||||||||||||

31 | 3 | 21 | 206.2 | 250.7 | 1814 | 0.01 | 0.06 | 0.04 | 0 | 0.14 | 0.02 | ||||

2 | 9 | 0.04 | 0 | ||||||||||||

33 | 1 | 19 | 253.8 | 993.8 | 1767 | 0 | 0.04 | 0.04 | 0 | 0.03 | 0.02 | ||||

0 | 13 | 0.04 | 0 | ||||||||||||

35 | 0 | 14 | 267.3 | 1137.6 | 1753 | 0.01 | 0.51 | 0.04 | 0 | 0.20 | 0.02 | ||||

0 | 8 | 0.04 | 0 | ||||||||||||

37 | 0.35 | 12 | 271.5 | 1086.0 | 1749 | 0.01 | 0.68 | 0.04 | 0 | 0.26 | 0.03 | ||||

0 | 8 | 0.04 | 0 | ||||||||||||

39 | 0.23 | 9 | 284.8 | 1274.7 | 1736 | 0 | 0.18 | 0.04 | 0 | 0.08 | 0.02 | ||||

0 | 9 | 0.04 | 0 | ||||||||||||

41 | 0 | 0 |

Layer, cm | Depth, cm | Bulk Density, g·cm^{−3} | ^{210}PbOriginal, Bk·kg ^{−1} | ^{210}Pb Corrected | D, cm^{−3}·Year^{−1} | w, cm·Year^{−1} | r_{i}, Year^{−1} | f_{i} | Dates from Original ^{210}Pb, Model CRS, Years | Dates from Corrected ^{210}Pb, Model IP-CRS, Years | |
---|---|---|---|---|---|---|---|---|---|---|---|

Bk·m^{−2} | Bk·kg^{−1} | ||||||||||

0–3 | 3 | 0.0448 | 310.75 ± 34.18 | 411.0 ± 45.12 | 305.6 ± 33.60 | 0.100 | 0.288 | 0.100 | 2021 | 2021 | |

3–5 | 2 | 0.0345 | 211.16 ± 50.68 | 228.0 ± 54.72 | 330.6 ± 79.34 | 2014 | 2012 | ||||

5–7 | 2 | 0.0505 | 168.39 ± 21.89 | 190.0 ± 24.70 | 188.1 ± 24.45 | 0.100 | 2011 | 2006 | |||

7–9 | 2 | 0.0387 | 155.35 ± 35.73 | 158.0 ± 36.34 | 204.3 ± 46.98 | 2008 | 2000 | ||||

9–11 | 2 | 0.0594 | 168.49 ± 21.90 | 132.0 ± 15.84 | 111.1 ± 13.33 | 0.100 | 2005 | 1994 | |||

11–13 | 2 | 0.0400 | 158.02 ± 20.54 | 110.0 ± 14.30 | 137.5 ± 17.87 | 2000 | 1988 | ||||

13–15 | 2 | 0.0475 | 155.02 ± 26.35 | 92.0 ± 26.35 | 96.8 ± 22.26 | 0.100 | 1996 | 1982 | |||

15–17 | 2 | 0.0519 | 131.06 ± 20.97 | 76.0 ± 20.96 | 73.2 ± 11.71 | 0.100 | 1991 | 1976 | |||

17–19 | 2 | 0.0473 | 180.80 ± 20.32 | 64.0 ± 11.23 | 67.6 ± 11.49 | 0.100 | 1986 | 1970 | |||

19–21 | 2 | 0.0458 | 243.93 ± 73.18 | 54.0 ± 21.6 | 58.9 ± 17.67 | 0.100 | 1978 | 1964 | |||

21–23 | 2 | 0.0430 | 72.20 ± 28.88 | 44.0 ± 17.6 | 51.1 ± 20.44 | 0.173 | 1962 | 1958 | |||

23–25 | 2 | 0.0374 | 77.89 ± 38.94 | 38.0 ± 19.0 | 50.8 ± 25.40 | 0.162 | 1956 | 1951 | |||

25–27 | 2 | 0.0327 | 44.42 ± 26.65 | 30.0 ± 18.0 | 45.8 ± 27.48 | 0.081 | 1949 | 1945 | |||

27–29 | 2 | 0.0344 | 34.34 ± 13.74 | 26.0 ± 10.4 | 37.7 ± 15.08 | 0.066 | 1945 | 1938 | |||

29–31 | 2 | 0.0460 | 26.54 ± 15.92 | 11.0 ± 6.6 | 23.9 ± 14.34 | 0.068 | 1941 | 1932 | |||

31–33 | 2 | 0.0409 | 28.80 ± 11.52 | 18.0 ± 10.8 | 21.9 ± 13.14 | 0.065 | 1937 | 1924 |

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## Share and Cite

**MDPI and ACS Style**

Yakovlev, E.; Kudryavtseva, A.; Orlov, A.
Comparison of ^{210}Pb Age Models of Peat Cores Derived from the Arkhangelsk Region. *Appl. Sci.* **2023**, *13*, 10486.
https://doi.org/10.3390/app131810486

**AMA Style**

Yakovlev E, Kudryavtseva A, Orlov A.
Comparison of ^{210}Pb Age Models of Peat Cores Derived from the Arkhangelsk Region. *Applied Sciences*. 2023; 13(18):10486.
https://doi.org/10.3390/app131810486

**Chicago/Turabian Style**

Yakovlev, Evgeny, Alina Kudryavtseva, and Aleksandr Orlov.
2023. "Comparison of ^{210}Pb Age Models of Peat Cores Derived from the Arkhangelsk Region" *Applied Sciences* 13, no. 18: 10486.
https://doi.org/10.3390/app131810486