Comparison of ²¹⁰Pb Age Models of Peat Cores Derived from the Arkhangelsk Region

Abstract

Dating young peatlands using the ²¹⁰Pb dating procedure is a challenging task. The traditional ²¹⁰Pb 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 ¹³⁷Cs, 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 ¹³⁷Cs and ²¹⁰Pb is associated with physical characteristics, like the peat ash and the bulk density of the bog. Comparison between the natural activity of ²¹⁰Pb in the peat and the radioactivity of ¹³⁷Cs 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 ¹³⁷Cs activity specific to the reference layer, allowing the error. The core dating of ²¹⁰Pb showed an age of 1963 for a depth of 17–19 cm, which was in agreement with the reference horizon ¹³⁷Cs 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 ²¹⁰Pb 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 ²¹⁰Pb 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

In the northern regions of European Russia, the main biocenoses are represented by ombrotrophic bogs, which are mainly fed by aerosols, dust, and atmospheric precipitation [1]. Researchers have noted that peatlands are an archive of atmospheric pollutants, including radioactive elements. The investigation of radionuclides offers insightful knowledge required to understand previous environmental events and climatic changes [2]. In tandem with palaeoenvironmental and palaeoclimatic records, peatlands provide information about the anthropogenic pressures associated with the deposition of a variety of air contaminants [3]. The latter variable contains valuable information on the changes in climatic conditions in the region and incoming contamination, which can be obtained via absolute dating, such as dating with excess ²¹⁰Pb [4,5]. Natural ²¹⁰Pb radionuclide, which is continuously generated in the atmosphere via the radioactive decay of ²²²Rn, which is a component of the ²³⁸U chain, is commonly used as an autonomous geochronometer to perform ¹³⁷Cs 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 ²¹⁰Pb activity with the depth of the core, giving a rather precise and complete time line for the peat. [7].

Accurate dating requires the proper selection of dating models, with refinement and subsequent validation using independent radioisotopes, e.g., ¹³⁷Cs.

The rationale is that the maximum levels of man-made radionuclides in natural sediments correspond to specific radioactivity episodes in the past, especially the signing of the 1963 Partial Test Ban Treaty, which provides an appropriate time point for this study. In the present study, the authors used dating models, such as CA (constant activity model), CF/CS (constant sedimentation model), PF (periodic flow model), and CF (constant flow model) via the Monte Carlo simulation method and IP-CRS (initial penetration-constant rate of supply model). Their features were briefly outlined to allow researchers to choose the most correct model.

Since the start of the nuclear century on Earth, bogs have begun to contain man-made radioactivity and other isotopes released into the atmosphere via nuclear tests and radiation emergencies [8]. Studying radionuclides from atmospheric fallout in peats is an essential way of studying peat chronology, peat deposit formation, the productivity of peatlands over time, etc. [9]. The arrival rate of ²¹⁰Pb 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.

Recent studies have observed variations in the exponential decrease in ²¹⁰Pb 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 ²¹⁰Pb 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 ²¹⁰Pb along the core layer.

When selecting the most suitable age model for a peat core, the following core characteristics were investigated (in addition to the ²¹⁰Pb activity study): We considered anthropogenic ¹³⁷Cs and natural ²¹⁰Pb 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

The studied peatland forms part of the Ilasskiye bog massif and is located in Northwestern Russia (Primorsky District, Arkhangelsk Region, Russia), near the town of Novodvinsk (64°18′55.3″ N, 40°41′15.6″ E). A peat core was extracted from the site on 12 August 2020. The total depth of the profile was 49 cm, and it was cut into 2-centimeter fragments. ²¹⁰Pb and ¹³7Cs were used to perform isotope studies throughout the core depth, establishing a rectangular sampling surface area of 1050.9 cm² 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.

The study area is represented by lake–glacial plains. Glacial deposits underlying the peatlands are made up of sand, clay, gravel, and sandy loam. The climate represents a transition from a temperate maritime climate to a subarctic climate. The average precipitation is 600–700 mm per year. The winter season is longer than 180 days. The depth of snow cover is up to 60 cm. The frost-free period is 90–100 days [11].

The studied profile was sampled in an oligotrophic bog without trees. Vegetation cover was dominated by following mosses of the genus Sphagnum: Sphagnum majus, Sphagnum cuspidatum, Sphagnum balticum, and Sphagnum medium. Grasses and shrubs present included Eriophorum vaginatum, Scheuchzeria palustris, and Andromeda polifolia.

The thickness of the studied peat core was 2.19 m. The peat was similar in botanic structure, there was an admixture of cotton, and we noted that its content increased towards the lower horizon. The degree of decomposition (R) assessed in the ground was 5–20% and increased with vertical position. The subsurface material was a light-textured moraine [12]. The water table was in the range of 0–5 cm during the investigation. In situ, the Eh of the peat deposit was measured on a depth-graded scale, and a core was then taken.

Next, 49 cm of the undisturbed peat core was removed using a PVC pipe. After being transported to the institute, this core was cut into sections of 2 cm, excluding the upper 0–3 cm zone.

The determination of the physicochemical characteristics of the peat was performed at the Swamp Ecosystems Laboratory of the Institute of Environmental Problems of the North of the N. Laverov Federal Centre for Integrated Arctic Research (FECIAR UrB RAS). The radiochemical analysis of radionuclides was performed in the Laboratory of Environmental Radiology of the Institute of Geodynamics and Geology of FECIAR UrB RAS. The samples were air-dried at ambient temperature and crushed to a 0.5–2-mm fraction via grinding in a rotary mill and sieving using a mesh. The resulting peat samples were analysed to determine the following physical characteristics: ash content, and bulk density. To determine the specific activity of ¹³⁷Cs and ²¹⁰Pb, 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

We analysed the plant material as in [13,14]. The determination was carried out via 5 repetitions for each studied layer.

2.2.2. Determining the Ash Content of Peat

A 2-gram sample of peat was weighed on an analytical scale acquired from Bel Engineering Srl, Monza, Italy (model DA-224C), with an error limit of ±0.5 mg according to the device data sheet. The quartz crucible was calcined to a constant mass via ignition in a muffle furnace at 900 °C. The sample was then placed in the crucible and successively subjected to calcination at temperatures of 525 °C and 900 °C to reach a constant weight, which was recorded on the analytical scale. The estimate of calcination losses (COI, %), was carried out according to the formula used in GOST 27784-88 [1,15], and the index moisture content of the sample (%) was determined according to the formula used in GOST 28268-89 [16].

2.2.3. Determining the Bulk Density of Peat

The bulk density of turf was obtained using the gravity method for air-dried samples with a fraction size of 0.5–2 mm. The estimate was determined by counting the volume of the samples with a measuring cylinder and determining their weight on technical balances in 5 parallel duplicates for every layer [15,17].

2.2.4. Determining ¹³⁷Cs and ²¹⁰Pb Isotopes

Radionuclide ¹³⁷Cs 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 (⁶⁰Co) line was 1.75 keV, and the relative efficiency was 22.4%.

Detector calibration using energies and the assessment of registration efficiency were carried out using the standard solutions of the following radionuclides: ²⁴¹Am, ¹⁰⁹Cd, ⁸⁸Y, ¹³⁷Cs, and ¹⁵²Eu. The specific activity of ¹³⁷Cs was measured from the gamma line 661.66, with a quantum yield of 89.90% for ^137mBa radionuclide. The minimum measured radioactivity of ¹³⁷Cs at exposure t = 18,000 s for geometry of a flat container of a 0.1-L volume measure was 0.1 Bq [18].

To determine ²¹⁰Pb, a peat sample was treated according to the methodology used in [19]. The obtained counting sample with radionuclides ²¹⁰Po and ²¹⁰Pb 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; ²¹⁰Bi and ²¹⁰Bi) decayed. The range of measured specific activity according to this method extended from 10 to 2·10³ 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

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 ²¹⁰Pb 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 ²¹⁰Pb_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 ²¹⁰Pb and the ¹³⁷Cs 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 ¹³⁷Cs-specific radioactivity in the control horizon, taking errors into account. The total activity concentration of ²¹⁰Pb (²¹⁰Pb_tot) as a function of core profile depth z_i is shown in the graph in Figure 2a and

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	zi, cm	mi, g	210Pbtot, Bk·kg−1		137Cs, 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

. The supported fraction (²¹⁰Pb_sup) was calculated as the average level (±standard deviation (SD), 1σ) of activity for the lowest levels at which the level of ²¹⁰Pb_tot reached a steady state, as shown graphically by the red line in Figure 2a.

Deducting the ²¹⁰Pb_sup activity of the ²¹⁰Pb_tot at the level behind the level, we calculated the unsupported fraction (²¹⁰Pb_uns), which was used to perform the next stages of dating and is indicated in Figure 2b. The independent marker ¹³⁷Cs 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

The index of ash content for the studied sample is present in the interval of 1.10–5.77%, which allows it to be attributed to the low ash type, as can be seen in Figure 3. In the vertical distribution, the maximum content of ash is found in the 20-cm layer, which may be related to the influx of the mineral fraction from the upper layers (due to leaching of minerals from the surrounding rocks) or the anthropogenic dusting of the atmosphere during the development of peat deposits. Below a depth of 21 cm, they tend to heterogeneously decline with depth, which is related to the type of atmosphere feeding of peat.

According to the obtained results, the bulk density gradually increases with depth and is found in between 0.075 and 0.109 g·cm⁻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

The radioactivity of ¹³⁷Cs 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 ¹³⁷Cs 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.

We also note that the high ¹³⁷Cs 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 ¹³⁷Cs distribution for the first few centimeters of the peat core is typical of upland bogs [23].

The maximum ¹³⁷Cs 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 ¹³⁷Cs in the highlands is the lack of the appropriate mineral particulates required for ¹³⁷Cs adsorption [8].

In this case, relative to the maximum level of ¹³⁷Cs at the top of the core, we watched a similar activity at depths ranging from 17 to 21 cm.

A close match between the behaviours of caesium radioactivity and ash content based on depth is shown in Figure 2 and Figure 3 and likely related to the processes of caesium deposition within the atmosphere, as ¹³⁷Cs and ash are introduced into the peat via air deposition.

As can be seen in the graph of the ¹³⁷Cs 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.

²¹⁰Pb activity in the sampled peat core fluctuates between 21.9 and 330.6 Bq·kg⁻¹. The peak ²¹⁰Pb activity is shown in Figure 2 and occurs in the 3–5 cm horizon. Below the 35–37 cm horizon, the activity of ²¹⁰Pb 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 ²¹⁰Pb in these layers is supported by the decay of ²²⁶Ra.

The migration of ²¹⁰Pb through the peat core only seems to occur in colloidal form. The migration of ¹³⁷Cs through the profile only takes place in ionic form [24].

3.3. Chronology ²¹⁰Pb and Rate of Peat Accumulation

The concentrations and range of values were first calculated for the studied peat core, as all dating models use an excess of ²¹⁰Pb_ex [25].

Here, we describe the process of calculating sectional concentrations and activities:

–

Sample code.

–

Concentration ²¹⁰Pb (C_i, Bq·kg⁻¹).

–

Uncertainty (u(²¹⁰Pb))—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 ²²⁶Ra (Bq·kg⁻¹)—we calculated the arithmetic mean and standard deviation for the three lowest sites (43–49 cm), which, in our case, were ²²⁶Ra = 26.2 ± 0.1 Bq·kg⁻¹.

Using the 95% confidence interval, its upper limit, i.e., the mean SD, was 26.2 Bq·kg⁻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(²²⁶Ra), Bq·kg⁻¹) corresponded to the calculated standard deviation.

–

Excess ²¹⁰Pbex (C_i, Bq·kg⁻¹) was computed as follows: ²¹⁰Pbex = ²¹⁰Pb − ²²⁶Ra, 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 ²¹⁰Pbex (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 = $A_i=10C_i\left(\frac{\Delta m_i}{S}\right)$.

–

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

This constant activity model has a second traditional name, according to a number of authors, namely the constant initial concentration model (the CIC) [4,5,26,27,28]; we included these authors’ views [21] in the title of the model. In the CA model (calculated values are presented in

Table 2. The CA model calculation data for the studied peat profile.

z(i), cm	ln(Ci)	t(i), Year	u(t(i)), Year	Year (A.D.)	ur(l)	ur(C0)	ur(Ci)	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

), it is necessary to know the initial concentration of ²¹⁰Pb_ex, which is C₀ = C_i(t = 0). We determined C₀ 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 (R₂ = 0.72). Both at this point and later on in the text, the R-squared value was denoted as R₂. The intercept was 5.52 ± 0.17, giving C₀ = 250.3 ± 1.1 Bq·kg⁻¹.

We determined C₀ 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 (R₂ = 0.72). The intersection was 5.52 ± 0.17, meaning that C₀ = 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)): $u\left(t_i\right)=\frac{1}{\lambda }\sqrt{{\left(u\left(\lambda \right)t_i\right)}^2+{\left(\frac{u\left(C_0\right)}{C_0}\right)}^2+{\left(\frac{u\left(C_i\right)}{C_i}\right)}^2}$.

Since C₀ 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: $t\left(43\right)=t_{43}+\frac{t_{43}-t_{42}}{2}$.

We also used the following equations at his stage of the study:

–

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 (Δt₁; 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)): $\mathrm{u}\left(\mathrm{r}\right)=\mathrm{r}\frac{\mathrm{u}\left(\Delta \mathrm{t}\right)}{\Delta \mathrm{t}}$.

We note that the uncertainties in the accumulation rate u(s) and u(r) are significant [21].

3.3.2. Application of the CF/CS Model

The values used in the constant flux/constant sedimentation model were the cut depth (z_i), the average mass depth (m_i, g·cm⁻²), and the logarithm ²¹⁰Pb_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 $u\left(r\right)=r\sqrt{{\left(\frac{u\left(\lambda \right)}{\lambda }\right)}^2+{\left(\frac{u\left(b\right)}{b}\right)}^2}$.

Our linear equation (R = 0.88) gives b = −5.129 ± 0.613, meaning that r = 0.006 ± 0.001 g·cm⁻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 $u\left(s\right)=s\sqrt{{\left(\frac{u\left(\lambda \right)}{\lambda }\right)}^2+{\left(\frac{u\left(b\right)}{b}\right)}^2}$.

The linear regression (R = 0.91) gives b = −0.222 ± 0.023, meaning that s = 0.140 ± 0.015 cm/year. As can be seen in Figure 5 and

Table 3. The CF/CS model calculation data for the studied peat profile.

z(i), cm	m(i), g cm−2	ln(Ci)
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

, while the correlation coefficient is good, a simple regression line does not show the variations in the parameters in the profile, suggesting that the graph should be broken down into linear segments. Figure 5 shows one mass accumulation rate of the profile (Figure 5a) and three mass accumulation rates of individual line segments (Figure 5b). Figure 5b shows for the CF/CS model, activity values below 37 cm have been omitted, as at this level, they reach a value of ²¹⁰Pb_sup. The fitting of a simple regression to the natural logarithm plot of the activity concentration of ²¹⁰Pb_uns ln (²¹⁰Pb_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.

As a result, we identified three linear segments in the peat record. The linear regression was fitted three times, resulting in different groups of fitted parameters. These are represented as “1, 2, 3” in Figure 5b. All points have been involved in the operations. Figure 5 presents the alternative interpretation by breaking the graph into three regression lines.

3.3.3. Application of the PF Model

The values used in periodic flux (notation in the text PF) model were as follows:

–

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].

The results for the studied peat core are presented in

Table 4. The PF model calculation data for the studied peat profile.

z(i), cm	zi, cm	ΔAi, Bq·m−2	u(ΔAi)	A(i), Bq·m−2	u(A(i))	t(i), Year	u(t(i)), Year	Year (A.D.)	Δt	u(Δt)	r(i), kg m3	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

. The mass accumulation rate r(i) in this model could lead to different values, as MAR showed large variations in its values and the flux value changed. The suitability of the model should be checked. In our study, the ²¹⁰Pb 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 ¹³⁷Cs 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 constant flux model (the CF model) is known as the CRS model (CRS) [4,5,25,26] (note that we are sticking to these authors’ views [21] in the title of the model).

In a Monte Carlo simulation, it is assumed that repetition of the experiment will produce a frequency distribution of results. Assuming that the final distribution is Gaussian, we can express the uncertainty in terms of the mean and its standard deviation.

The values used in constant flux model were defined as follows:

–

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

As there is no layer 41 ²¹⁰Pb_ex below, the calculation starts with A(41) = 0 Bq·m⁻².

For upper layer, A(39) = ΔA₃₉. In addition, u(A(39)) = u(ΔA₃₉). 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 ²¹⁰Pbex, 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].

The value SAR (s_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.

The values of MAR (r_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 model calculation data for the studied peat profile.

z(i), cm	ΔAi, Bk·m−2	u, ΔAi	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))	ρi, g·cm−3	u(ρi)	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

, 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 ¹³⁷Cs reference horizon, considering the error.

The CF/CS and CF models, in combination with the Monte Carlo method, were used to calculate the linear accumulation rate s and the mass accumulation rate r in the sampled peat core, as illustrated in Figure 7. The s values for CF ranged between 0.09 ± 0.02 and 1.3 ± 0.05 cm·year⁻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.

The mean index of r via CF was 3.615 ± 0.005 g·cm⁻² year, while the constant r via CF/CS was at 0.006 ± 0.001 g·cm⁻²·year⁻¹.

In general, as we note in Figure 7b,c the rate of peat accumulation throughout the depth of the peat core is unstable. However, as can be seen in Figure 7a, the density of the peat is constant throughout the profile. The s values are of the same order. The mass accumulation rates do not agree, and we have noted above the unstable rate of peat accumulation.

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

To perform ²¹⁰Pb 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 ²¹⁰Pb (²¹⁰Pb_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. IP-CRS modelling and dating results for the ISNO core.

Layer, cm	Depth, cm	Bulk Density, g·cm−3	210Pb Original, Bk·kg−1	210Pb Corrected		D, cm−3·Year−1	w, cm·Year−1	ri, Year−1	fi	Dates from Original 210Pb, Model CRS, Years	Dates from Corrected 210Pb, 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

).

The IP-CRS model is a modification of the CRS model. The key point regarding the IP-CRS model is that the amount of ²¹⁰Pb_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).

The vertical migration of ²¹⁰Pb_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, ²¹⁰Pb_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 ²¹⁰Pb 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 ²¹⁰Pb_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 ²¹⁰Pb_xs accumulated.

The lower boundary of the zone was determined by the greatest depth in which ²¹⁰Pb activity was detected [20].

B.

Solving a system of integro-differential equations

We solved the system n equations in the peat section, followed the bounding conditions and continuity constraints between the layers to find the penetration rates (r_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).

The time evolution of the average volumetric activity of ²¹⁰Pb_xs (Ci, Bq/cm³) 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].

The solutions to the equations were as follows:

From 0 to z_k:

$$C_i\left(z\right)=A_i{e}^{\theta +\left(i\right)z}+B_i{e}^{\theta -\left(i\right)z}$$

(1)

where i = 1, 2,…, k.

From z_k to ∞:

$$C_i\left(z\right)=A_i{e}^{\theta +\left(i\right)z}+B_i{e}^{\theta -\left(i\right)z}$$

(2)

where i = k + 1, k + 2, …., n.

C.

Determine the quantity of ²¹⁰Pb_xs removed from each layer of the washout area

The quantity of ²¹⁰Pb_xs (Bq·m⁻²) transported from each horizon of the upper section was estimated using the following equation:

$${\mathrm{R}}_{\mathrm{i}}={{\displaystyle \int }}_0^{{\mathrm{T}}_{\mathrm{i}}}{\mathrm{r}}_{\mathrm{i}}{\mathrm{A}}_{\mathrm{i}}\left(\mathrm{t}\right)\mathrm{dt}=\frac{{\mathrm{r}}_{\mathrm{i}}\mathsf{\Phi }}{\mathsf{\lambda }+{\mathrm{r}}_{\mathrm{i}}}\left[{\mathrm{T}}_{\mathrm{i}}+\frac{1}{\mathsf{\lambda }+{\mathrm{r}}_{\mathrm{i}}}\left({\mathrm{e}}^{-\left(\mathsf{\lambda }+{\mathrm{r}}_{\mathrm{i}}\right){\mathrm{T}}_{\mathrm{i}}}-1\right)\right]$$

(3)

where T_i—the date when this layer started to form.

D.

Determining the total amount of ²¹⁰Pb_xs

The total amount of ²¹⁰Pb_xs transferred downward was assessed by adding up the sums of ²¹⁰Pb_xs obtained in C.

E.

Determining the additional ²¹⁰Pb_xs for each layer

The quantity of additional ²¹⁰Pb_xs integrated into each layer was determined by multiplying the overall extracted ²¹⁰Pb_xs by the corresponding fractional amplification f_i.

F.

Determination of corrected ²¹⁰Pb_xs volumetric activities

In this stage, we, firstly, added the volumetric activities of ²¹⁰Pb_xs obtained from layer C to the appropriate layers of the wash zone; secondly, we subtracted the volumetric activities of ²¹⁰Pb_xs determined in E from the appropriate layers of the lower zone.

G.

Applying the CRS model to the corrected profile

The modified ²¹⁰Pb_xs activity profile was fitted to the CRS model using the Monte Carlo method [20,22].

Figure 8 and Table 6 display the resulting values determined by dating the studied peat sample. According to the CF model calculation data, the horizon of 17–19 cm corresponds to the year 1963. The peak of ¹³⁷Cs 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 ¹³⁷Cs in peat soils mean that it does not always indicate radiation episodes on the horizon [8].

In our study, the physicochemical characteristics of the peat core were able to leach out some of the ¹³⁷Cs, 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.

Figure 9 shows the calculated values of the linear accumulation rate s and the mass accumulation rate r in the peat profile used in this study.

The s values ranged between 0.073 ± 0.05 and 0.635 ± 0.05 cm·year⁻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.

The linear accumulation rate s uniformly decreased with depth and exhibited a distinct peak at 19–21 cm, which was possibly coincident with the altered climatic conditions for peat in 1964. The pattern of the mass accumulation rate r was complex, with several peaks at 19–21 cm dating from 1964 and probably associated with the changing climatic conditions for the peat. We noted that the regular has a decreasing r with depth as the peat deposit compacts with depth.

Based on the ²¹⁰Pb dating IP-CRS model, we estimated an atmospheric flux of ²¹⁰Pb 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 ²¹⁰Pb 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

The research carried out allows us to draw the following conclusions.

The peat profile investigated is typical of the species composition and physical characteristics of the peatlands of the subarctic region of European Russia. The core of the peat has not been subjected to economic impacts and reclamation works. It was found that the 20-centimeter horizon is characterised by significant fluctuations in the ash content and bulk density, which can be associated with a range of factors, such as the leaching of the mineral part from the higher layers and anthropogenic dusting of the atmosphere during peat accumulation.

For the vertical distribution of ¹³⁷Cs, 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 ¹³⁷Cs intake transport with atmospheric deposition. The concentration of ²¹⁰Pb displays the common exponential decline of activity with depth.

A comparison between different dating models revealed that those years closest to the given 1963 benchmark were provided by the CF/CS, CF, and IP-CRS models. The IP-CRS model was favoured because the values demonstrated that the 17–19 cm layer in the peat profile corresponded to an age of 1963.

The chronological reference point was the signing of the Partial Test Ban Treaty in 1963. It should be noted that the maximum radioactivity of ¹³⁷Cs and the peak of the ash content fall on the 19–21-cm horizon. In this case, downwards biological migration of ¹³⁷Cs on the core occurs. However, the results confirm the accuracy and adequacy of our chosen peat core dating model.

We also estimated the atmospheric flux of ²¹⁰Pb 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 ²¹⁰Pb. This outcome aligns with prior research conducted by the authors into peatlands located in the subarctic region of European Russia.

The results of this study add new details to the information regarding the processes of radionuclide migration from atmospheric deposition applied to the peatlands in the subarctic region of European Russia.