METHODS

The used calculation approach assumes that the concentration of ¹⁴C in the annual ring of a tree corresponds to the average annual concentration in the ambient air. The sampling site is expected to have the highest concentration of ¹⁴C in the air and, as a result, the highest effective dose.

The ¹⁴C air concentration A _V (Bq/m³) was calculated using following formula:

(1) $${A_V} = \Delta pMC\cdot S\cdot{C_{st}},$$

where ΔpMC – difference between measured and background ¹⁴C concentration (Table 1);

Table 1 Concentrations of ¹⁴C in tree rings and ¹²C in air.

S – coefficient between pMC and Bq/kg C. 100 pMC = 226 Bq/kg C;

C _st – stable carbon concentration in air. The concentration of stable carbon was determined using carbon dioxide levels in atmosphere (NASA 2023). The carbon dioxide concentration varied from 332 ppm in 1976 to 414 ppm in 2020. The values of C _st used in calculations are presented in Table 1.

The estimate of the annual ¹⁴С discharge Q (Bq/a) was calculated by formula:

(2) $$Q = 3.15\cdot{10^7}{A_V}/{G_{n,j}},$$

where 3.15·10⁷ – the conversion factor, s/a;

G _n,j – the annual average meteorological dilution factor in the surface layer of the atmosphere at a distance x from the i-th source in the wind direction of the n-th point, s/m³ (Figure 1). For sampling site, the values were calculated for each year, where it possible, by analyzing the meteorological data (Table 2).

Table 2 Dilution factor values for each year.

The IAEA approach for estimating annual effective doses from ¹⁴C releases assumes that all the food consists only of local products and, as a result, there is an equilibrium in the ¹⁴С concentration in food, human tissue, and atmospheric air. Then the estimate of the expected annual dose of internal exposure D (Sv/a) from ¹⁴С contained in the atmospheric air in the form of carbon dioxide ¹⁴СО₂ can be obtained by the following formula (IAEA 2001):

(3) $$D = {A_V}G/{C_{st}},$$

where G – is the effective dose rate factor that relates the annual dose rate (Sv/a) to the concentration of ¹⁴C per gram of carbon in people (Bq/g). The dose rate factor recommended for screening is 5.6·10^–5 Sv/a per Bq/g (IAEA 2001).

Since ingestion is the primary mode of expose, and the share of consumption of local products does not always exceed the share of imported, it is reasonable to assume that there may not be an equilibrium of ¹⁴C. In this case, the expected annual dose of ¹⁴C exposure can be calculated using the formula (Kryshev et al. Reference Kryshev, Kryshev, Vasyanovich, Ekidin, Kapustin and Murashova2020):

(4) $$D = {\varepsilon _{ing}}U{A_V} + {\varepsilon _{food}}\mathop \sum \limits_i {\alpha _i}{R_i}{A_{food,i}},$$

where ε _ing = 6.5·10⁻¹² Sv/Bq – dose conversion factor for an adult when inhaling ¹⁴C in the form of CO₂ (ICRP 2012);

U = 8.1·10³ m³/a – respiratory rate of an adult (Pleil et al. Reference Pleil, Ariel Geer Wallace, Davis and Matty2021);

ε _food = 5.8·10⁻¹⁰ Sv/Bq – dose conversion factor for dietary intake of ¹⁴C for an adult (IAEA 2014);

α _i – the share of local products in the diet of the population (Table 3);

Table 3 Parameters of products consumption in Kursk region.

^a Rostekhnadzor (2021).

^b IAEA (2012).

R _i – annual consumption of the product by the population, kg (Table 3);

A _food,i – ¹⁴C concentration in the local food product, Bq/kg.

The ¹⁴C concentration in the food product, based on the balance of ¹⁴C between atmospheric air and local plant or animal products, was calculated by the formula:

(5) $${A_{food,\,i}} = {A_V}{f_{p,i}}/{C_{st}},$$

where f _p,i – the share of stable carbon in plant or animal product, kg C/kg product (Table 3).