LARCalc, a tool to estimate sex- and age-specific lifetime attributable risk in populations after nuclear power plant fallout

Abstract

A tool called LARCalc, for calculating the radiological consequences of accidental large scale nuclear power plant releases based on estimates of ¹³⁷Cs ground deposition, is presented. LARCalc is based on a previously developed models that has been further developed and packaged into an easy-to-use decision support tool for training of decision makers. The software visualises the radiological impact of accidental nuclear power plant releases and the effects of various protective measures. It is thus intended as a rapid alternative for planning protective measures in emergency preparedness management. The tool predicts projected cumulative effective dose, projected lifetime attributable cancer risk, and residual dose for some default accidental release scenarios. Furthermore, it can predict the residual dose and avertable cumulative lifetime attributable risk (LAR) resulting from various protective measures such as evacuation and decontamination. It can also be used to predict the avertable collective dose and the increase in cancer incidence within the specified population. This study presents the theoretical models and updates to the previous models, and examples of different nuclear fallout scenarios and subsequent protective actions to illustrate the potential use of LARCalc.

Introduction

The consequences of a nuclear power plant (NPP) accident, resulting in the release of radionuclides to the environment, will largely depend on the protective measures implemented soon after the accident. According to international recommendations, such actions should be planned in advance¹. Comprehensive decision support systems are available today (e.g. ARGOS² and JRODOS³), intended for the assessment of environmental and radiological consequences for various scenarios involving atmospheric dispersion of fission products from nuclear facilities. It is challenging to estimate the individual radiation doses from radioactive fallout due to the numerous factors that influence the distribution of doses. These factors include the actual NPP fallout scenario (radionuclides, activities, and variation over time), the atmospheric dispersion of the radioactive material, the areal distribution of deposition and whether fallout occurs by wet or dry deposition, the type of land use and ecosystems in the area, local and regional food production, human behaviour patterns, residence times in different environments etc.⁴.

An important component of nuclear fallout in the case of an atmospheric release in which fission products and fuel particles escape filtration systems is the fission product ¹³⁷Cs, as the deposition density, A_dep (kBq m^-2), dictates the long-term habitability in the affected area. It may be difficult to measure the actual ¹³⁷Cs deposition following an accidental release from a NPP by uncollimated in situ gamma spectrometry, even using modern-day digital amplification to mitigate pulse pile-up in high-dose-rate environments⁵. However, it may still be feasible to determine the ground deposition at a relatively early stage after the accident, for example, by means of unmanned or conventional airborne gamma spectrometry⁶. Regardless of the radiometric techniques used, emergency preparedness strategies in most countries will be focused on the ability to estimate and report values of A_dep of ¹³⁷Cs. The authors of this paper have previously developed models that aggregate external and internal exposure pathways from fallout to humans from radioactive fallout^7,8,9,10, enabling the estimation of the long-term radiation dose from initial measurements of the ground deposition of the gamma-emitting fission product ¹³⁷Cs.

In the previous models (see Eq. 1 and 2), the radiation dose was determined for a NPP fallout scenario representing the Chernobyl accident’s fallout in Sweden (e.g. IAEA¹¹ and UNSCEAR¹²). This was done by relating the initially measured ambient equivalent dose rate from all gamma-emitting radionuclides in the fallout to the measured initial ground deposition of ¹³⁷Cs in terms of a proportionality factor, d_Cs¹³. The weathering process and gradual ground penetration of the radionuclides was taken into account by applying element-specific ecological half-times to obtain the predicted variation of the ambient equivalent dose rate over time. Furthermore, in the wake of the ICRP publication 144¹⁴, in which nuclide-specific conversion factors between ground deposition and the corresponding dose rate contribution are presented in terms of effective dose rate, air kerma and ambient dose equivalent rate, the previous models have been further developed and coded as a MATLAB app. This app, and the underpinning models, are referred to as the tool LARCalc.

This paper presents the extended features implemented in LARCalc, including the management of a variety of radionuclides associated with nuclear power generation and with nuclear detonations fallout, using the gamma emitter ¹³⁷Cs as a key nuclide. This enables the modelling of the risk to the public for various fallout scenarios. These can be matched to a larger number of potential nuclide vectors than in the previous models, which were based on specific releases from Chernobyl and Fukushima fallout. Furthermore, we exemplify some typical risk assessments and the impact of various protective measures, and combinations thereof, in terms of the averted cumulative attributable risk and residual dose, and the way in which LARCalc can visualise the effects of these parameters for specific age and sex cohorts. Note that LARCalc mainly is intended to be used as a tool for training of decision makers. The tool can also be used to plan for protective actions before an NPP accident. LARCalc is therefore not intended to be used for real-time decision support in connection to an on-going accidental release.

Model and scenarios

Description of the previous basic models

Provided the relation between the initial nuclide-specific ground deposition (kBq m^-2) and the release of ¹³⁷Cs has been established, the ground deposition of ¹³⁷Cs can be used as a proxy for both the long-term external exposure of local inhabitants and the internal exposure due to potential long-term transfer of radiocaesium to the population if no protective measures were implemented¹³. Figure 1 illustrates a general model with multiple underlying sub-models for the prediction of the cumulative effective dose (CED) and lifetime attributable risk (LAR) from a given NPP fallout scenario using ¹³⁷Cs as a key nuclide. This general model combines the results from different sub-models that are designed to estimate radiation dose and risk from specific pathways of exposure, such as groundshine (exposure of radiation from nuclides on or in soil), ingestion of contaminated foodstuffs, inhalation and cloudshine (exposure of radiation from nuclides in the plume). By integrating these sub-models, the comprehensive model provides a completer and more accurate estimate of the total radiation dose and risk received by a population or individual. This general model aggregates the long-term internal and external exposure of a population to NPP fallout, based on quantities that can be determined in the early phase of the accident. The general model thus includes empirical relationships between local and regional ground deposition and time-integrated internal doses that have previously been established under various conditions regarding climate zone and food restrictions^8,15,16,17. The sub-models included in the LARCalc tool also include settings to express the exposure as age-dependent organ-absorbed doses, and can convert these into LAR, as defined by the EPA¹⁸. The LAR represents the estimated radiation-induced lifetime risk of suffering from cancer in a certain organ at some point in life. The models implemented in LARCalc are a further development of the one presented in detail by Rääf et al.⁹.

Figure 1

A general model for the prediction of long-term radiological consequences of atmospheric nuclear power plant fallout, including the exposure pathways external groundshine and internal committed dose by ingestion of contaminated locally produced foodstuff.

In the previous version of the model, two parameters were defined to describe the relationship between the local ground deposition density of ¹³⁷Cs, A_{dep,Cs-137,loc} (kBq m^-2), and the corresponding external dose rate from all gamma-emitting fission products, namely the initial ambient dose equivalent rate at fallout (t = 0), d_Cs (mSv y^-1/(kBq m^-2)), and the variation of the external dose rate over time, r(t). The latter, r(t), was observed to follow a four-component exponential decay function in terms of half-times⁷. However, r(t) is normalized to the initial external dose rate at t = 0, so it needs to be combined with d_Cs to describe how the external dose rate per unit initial ¹³⁷Cs ground deposition changes over time, in other words r(0) = 1 (unitless).

In addition to the external exposure pathway following large-scale NPP fallout, various transfer pathways will cause contamination of locally and regionally produced foodstuff, such as dairy products, meat, vegetables, freshwater fish, mushrooms, berries, wild game, etc. In previous studies on the whole-body burden of radiocaesium in different population cohorts after nuclear weapons fallout and Chernobyl fallout in 1986, it has been shown that the average internal contamination of radiocaesium in a population can be predicted by the regional average deposition of ¹³⁷Cs, A_{dep,Cs-137,reg} (kBq m^-2), combined with time-integrated aggregate transfer factors, sometimes also referred to as radioecological sensitivity^17,19,20. These transfer pathways can be represented by the convolution of transfer pathways P₂₃ and P₃₄ in Fig. 1. Once the average ¹³⁷Cs body concentration has been established, transient equilibrium in the intake and excretion of radiocaesium can be assumed after one year. The committed effective dose (accounting for the biokinetic fate of radiocaesium when ingested) can then be related to the corresponding organ-absorbed dose rate and effective dose rate²¹.

In our previous model⁹, the general expression for the CED (mSv) from combined external and internal exposure arising from the initial ground deposition of nuclear fallout containing ¹³⁷Cs with accompanying short-lived fission products and ¹³⁴Cs, was given by the following expression:

(1)

where t_acc (y) is the time considered for integration of the dose rate after the initial fallout at t = 0. In Table 1 is given a further explanation of the other parameters. Note that the first term on the right-hand side of Eq. (1) refers to the external dose contribution from the local ground deposition, A_{dep,Cs-137,loc} (kBq m^-2), and the second term refers to the internal dose contribution from radioecological transfer of regional deposition of ¹³⁷Cs (represented by the quantity A_{dep,Cs-137,reg} (kBq m^-2)).

Table 1 Parameters used in the previous models for calculation of the CED, and CUMLAR resulting from fallout from a nuclear power plant. Note that some of the parameters are still used in the updated models (see Sect. "Updates and extended features of LARCalc").

The corresponding expression for a specific organ-absorbed dose, ${D}_{org,sex}$, as a function of ¹³⁷Cs deposition was given by:

(2)

The cumulative lifetime attributable risk, CUMLAR, of radiation-induced cancer in a specific organ resulting from the external and internal exposure pathways is given by:

(3)

where ${\dot{D}}_{org,sex}$ is the organ-specific absorbed dose rate (i.e. the time-derivate of Eq. (2)) and LAR_org,sex is the organ- and sex-specific risk coefficient of cancer induction per unit absorbed dose, as given by EPA¹⁸. The remaining parameters for the given equations are given in Table 1. The equations for the empirical transfer functions between ground deposition and whole-body concentration of ¹³⁷Cs and ¹³⁴Cs, T_ag,max,Cs(t), are explained in Isaksson et al.⁸. These expressions have been used to estimate representative values of CED and D_org,sex for various Swedish populations^22,23,24.

The quantity LAR_org,sex(age) is expressed as the probability of cancer arising from low-dose and low LET exposure, incurred at a certain age of the exposed person, during the person’s remaining life expectancy. Values of LAR_org,sex can be obtained from the EPA¹⁸ for 15 organ-specific cancers (12 for male and 14 for female) and for 5-year age classes from newborn to 80 y old. Interpolation using a piecewise cubic hermite interpolating polynomial (PCHIP)³⁰ was used to obtain a continuous expression from the age- and sex-specific values tabulated by the EPA¹⁸ (see Fig. 2).

Figure 2

Illustration of the age- and sex-dependent lifetime attributable risk per unit absorbed organ dose for the sum of all 15 cancer types specified by the EPA, excluding non-fatal skin cancer (adopted from the EPA¹⁸).

Description of protective measures

When comparing the potential impact of accidental fallout from a NPP and the outcome of protective measures in terms of CED and CUMLAR for representative individuals in a population, three quantities are of special importance in order to comply with the ICRP’s recommendations^31,32. The first is the projected radiological consequences in terms of effective dose if no protective measures are implemented (Eq. 1) and the second is the time integration of LAR (Eq. 3). When integrated between 0 and 70 y, the quantities CED(t_acc = 70 y) and CUMLAR(t_acc = 70 y) can thus be referred to as the projected unmitigated CED and CUMLAR , respectively. The residual dose, CED_res, is the amount of remaining cumulative effective dose to a representative individual in a population after a given set of protective measure has been in use. Thus, CED_res excludes the cumulative effective dose averted by those protective measures.

The main protective measures used to reduce external dose from groundshine, are: (i) sheltering, (ii) evacuation and (iii) clean-up, or a combination of these. Regarding internal exposure, initial indoor sheltering reduces the dose resulting from inhalation of airborne radionuclides, but the most influential protective measure will be food restrictions. As well as providing the residual dose, we have included the computation of the so-called avertable cumulative lifetime attributable risk, CUMLAR_av, in LARCalc. This quantity, which was mainly used in the previous system for radiological protection³³, enables a direct comparison how a given protective measure relates to the averted detriment and it can be related to the efficiency of the measure. The quantities S_indoor, S_evac, S_aliment and S_decont are coarse parameters describing the average dose-reducing effects of protective measures for external and/or internal exposure. All these quantities reduce the total dose rate by a factor in the range 0 to 1, (see e.g. Equations 1, 2 and 11). All the protective measures used in the model are described in the equations below (Eq. 4 to Eq. 8).

The shielding effect of staying indoors (sheltering) is described in Eq. (4) by the so-called damping factor, f_u, and the previously mentioned factor f_shield. The factor f_u describes the damping of the internal dose rate from inhalation by staying indoors, whereas f_shield describes both the shielding from external dose rate resulting from groundshine, as well as the external dose rate resulting from the passing plume (cloudshine). Default values of f_u = 0.5³⁴ and f_shield = 0.4^26,35 are used in LARCalc. The overall damping effect of sheltering is given by S_indoor (Eq. 4a) and for inhalation by S_indoor,inh (Eq. 4b):

(4a)

(4b)

where f_out is the fraction of time spent outdoors, as described in Eq. (5), and can vary between 0 to 1.

(5)

The effect of evacuation on the effective dose rate (Eq. 1) and the organ-absorbed dose rate (Eq. 2) as a function of time is given by S_evac (Eq. 6). During evacuation (${t}_{ret,start}\le t\le {t}_{ret,stop}$) this will be equal to 0 and otherwise 1. Evacuation affects both internal and external pathways.

(6)

The dose-averting effect of food restrictions on internal radiation dose is described by Eq. (7). Calculated as the effectivity of restrictions, f_aliment may be in the interval 1 to 0, where 0 implies 100% effective restrictions, and 1 is the level of food restrictions assumed by the Swedish authorities after the Chernobyl fallout in 1986³⁶. This factor only affects the pathways for the ingestion of radiocaesium and radioiodine.

(7)

The effect of decontamination on external radiation dose is described by the factor S_decont given in Eq. (8) and is dependent on the effectivity of clean-up in terms of relative instantaneous dose reduction, f_decont. A default value of f_decont = 0.5 is set as default in this study, reflecting an average value of clean-up efficiency, giving a value of S_decont = 0.5. When f_decont = 0.9, representing a highly efficient clean-up measure, the value of S_decont will be 0.1 after clean-up at t = t_decont,done. Default values are based on previous experience from Japan and Eastern Europe³⁷. Linear interpolation is performed between the start (t = t_decont,start) and end (t = t_decont,end) of decontamination.

(8)

Updates and extended features of LARCalc

Introducing nuclide vectors

The NPP fallout scenario in connection with a release to the atmosphere can involve a number of volatile radionuclides, depending on the efficiency of the consequence mitigation systems of the NPP. In addition to ¹³⁴Cs and ¹³⁷Cs, radionuclides such as ¹³¹I, ¹³²I, and ¹³²Te can also be released. The initial activity ratio of a fallout radionuclide in relation to that of ¹³⁷Cs is given by the following expression (Eq. 9).

(9)

Table 2 lists nuclide vectors representative of four nuclear fallout scenario, normalized to the initial fallout of ¹³⁷Cs. In the updated LARCalc, nuclide vector can be adjusted to a specific fallout scenario involving ¹³⁷Cs and accompanying radionuclides.

Table 2 Initial nuclide vectors for three NPP fallout events and one fictious NPP release, normalized to the initial fallout of ¹³⁷Cs (A_dep,i/A_dep,Cs-137).

Element-specific ecological half-time, Eco(t)

In this updated model the ecological element-specific half-time is defined as a separate entity that can be modified by the operator for each element. The ecological half-time is a quantity that describes the aggregated effect on external dose rate 1 m above ground, resulting from various ecological and weathering processes, such as depth migration into soil⁴¹. In the LARCalc tool, Eco_i(t) is thus defined as a damping factor that takes into account the gradual decrease in the external dose rate to air 1 m above ground, and is expressed as a bi-exponential function in the form given in Eq. (10):

(10)

Such a biexponential ecological damping was found for caesium nuclides by Gale et al.⁴², with a short-term component (i = Cs) of c_short,Cs = 0.63 (which was somewhat lower than the median value of about 0.78 found from observations by Kinase et al. for urban areas⁴³), and with T_eco,Cs,short = 0.6 y. Jönsson et al.⁷ performed polynomial regression, r(t), to estimate the contribution of radiocaesium to the total ambient dose rate equivalent (H*(10)) in the areas of Sweden that were most affected by the Chernobyl fallout after 1986. The r(t) was normalised to the H*(10) measured on the first day of the plume's arrival. They found a long-term component with an effective half-time of 5.5 y, corresponding to T_eco,Cs,long = 6.7 y. No significant short-term component for the radiocaesium contribution could be extracted from the reported data, and Jönsson et al. therefore suggested that a value of c_short,Cs = 0 provides a better fit to the environmental conditions in those parts of Sweden (for a detailed list of locations, see Jönsson et al.⁷).

Based on the second component in the equation for r(t) given by Jönsson et al.⁷, it can be deduced that the decrease with an effective half-time of 6.8 d is mainly attributed to ¹³¹I, which would roughly correspond to an ecological half-time of 0.125 y. Due to the relatively short half-life of ¹³¹I it is suggested a short-term component of c_short,I = 1 combined with T_eco,I,short = 0.125 y will adequately describe the ecological damping of the short-lived radioiodine nuclides.

Bremsstrahlung generation in soil and air from radiostrontium (including daughter nuclides) will contribute to the external dose, the effective dose rate for ⁹⁰Sr/⁹⁰Y being as high as 0.068 (mSv y^-1)/(kBq m^-2) for deposition on a plane surface¹⁴. However, this will decline rapidly as radiostrontium penetrates the surface and lower soil layers (< 0.001 (mSv y⁻¹)/(kBq m^-2) at a penetration mass depth of 0.5 g cm^-1). According to Sahoo et al.⁴⁴, radiostrontium typically migrates 1 cm y^-1, and we therefore suggest values of T_eco,Sr,short of 0.15 y, and c_short,Sr = 1 for dry deposition, leading to an almost zero contribution to the external dose after reaching a mass depth of 0.5 g cm⁻¹, assuming a soil density of 1.5 g cm^-3. Due to the lack of comprehensive data on ecological half-times in terms of external dose rate from ground deposition for radionuclides of other elements than Cs, Sr and I, we suggest default ecological half-times of T_eco,i,short = 0.6 y (with a c_short,I = 0.63) and T_eco,i,long = 22.7 y, for all other radionuclides, which are the same as the values for Cs reported by Gale et al.⁴². Users of the LARCalc tool can however use specific values for the long-term and short-term ecological half-times of the various elements represented by the NPP fallout scenario radionuclide vector based on the data available. The suggested default values in the absence of any local or region-specific values are 6.7 y for radiocaesium, with options of using e.g. 3.2 y (representing the lower extreme value reported from Japan⁴⁵), or 15 y, representing values observed in Russia⁴⁶. Table 3 lists suggested values of the parameters T_eco,i,short, T_eco,i,long and c_short,i.

Table 3 Element-specific ecological half-times parameters of the contribution to the external dose rate 1 m above ground from fallout in terms of a double exponential decay function (Eq. 9) for the elements represented in the nuclide vectors in Table 2. N/A = Not applicable.

Inclusion of the ICRP nuclide-and organ-specific dose coefficients

In this study, the model used in LARCalc has been adapted to include the recently published nuclide-specific dose coefficients for a given fission product, relating the ground deposition, A_dep, to the corresponding dose rate (effective, organ, air kerma and ambient dose equivalent rate 1 m above ground) by the ICRP¹⁴, to enable a broader range of hypothetical NPP release scenarios. The initial external dose rate during the first few days following a single fallout event will depend on the initial ground penetration depth of the nuclide $i$ in the fallout. Hence, the user must define the initial penetration (or relaxation) mass depth, $\beta$ (g cm^-2) of the fallout. Dry deposition is associated with a shallower depth distribution in soil, whereas the wet deposition of NPP nuclides may lead to initial ground penetration of several cm²⁶. In the LARCalc model, the user can choose between dry or wet initial deposition by setting $\beta$ equal to 0.0 or 1.0 g cm^-2. If dry deposition is selected, an initial penetration depth, $\beta$ = 0.0 g cm^-2 will be the default value assigned to all nuclides included in the nuclide vector. If wet deposition is chosen, the default ground penetration depth is set to $\beta$ = 1.0 g cm^-2, at which LARCalc then retrieves the corresponding dose coefficient from the ICRP tabulated data¹⁴. This penetration depth can be considered representative of wet deposition following the Chernobyl fallout in Sweden²⁶.

Petoussi-Henss et al.⁴⁸ and the ICRP¹⁴ have presented age-dependent organ dose rate and effective dose rate coefficients for the uniform surface deposition of a gamma emitter for the estimation of external dose rate in environmental irradiation geometries such as a radioactive fallout. Rääf et al.⁹ used polynomials of organ dose as a function of age as correction factors to account for the higher organ dose rate to children than in adults for a specific surface deposition. The ICRP¹⁴ now provides age-dependent coefficients of effective dose (e_i) and organ-specific equivalent dose (d_i), which have been incorporated into the groundshine model. A library consisting of the dose conversion coefficients for newborns, 1-year-, 5-year-, 10-year-, 15-year-olds and adults (≥ 20 y) is defined in LARCalc, and the dose conversion factors for an individual of a specific age, e_i(age) and d_i(age) are then obtained by PCHIP of the tabulated data in the library. The updated external organ dose rate equation (Eq. 2) is thus as shown in Eq. (11).

(11)

Updated internal organ-absorbed dose rate coefficients

The age dependence of the internal dose contribution from long-term intake of radiocaesium has been accounted for by adopting the same mathematical relationship between average body dose and body weight for a homogeneous distribution of radiocaesium body burden, as reported by Leggett et al.⁴⁹, and later adopted by Falk et al.²⁷. Isaksson et al.²¹ have recently published computed sex- and nuclide-specific organ dose coefficients for radiocaesium isotopes distributed in the human body when exposed to protracted intakes of radiocaesium. Organ-specific absorbed dose rate coefficients δ_{org,Cs-137,sex} and δ_{org,Cs-134,sex} were taken from Table 4 in Isaksson et al.²¹, but are here expressed in units of mGy y^-1 instead. These parameters replace e_Cs and k_Organ,int,Cs in the previous model (see Eq. 2). The dose rate coefficients have thus been updated based on models described by the ICRP³⁰. The calculated effective dose rate coefficients are given in Table 4.

Table 4 Effective dose rate coefficients calculated from sex- and nuclide-specific organ dose coefficients for radiocaesium isotopes from Isaksson et al.²¹.

The coefficients δ_{org,Cs-137,sex} and δ_{org,Cs-134,sex} are implemented in LARCalc in the aggregate transfer functions between ground deposition and internal organ-specific absorbed dose resulting from the intake of contaminated foodstuff (corresponding to the transfer parameter P₂₅ defined by UNSCAR¹⁵) according to Eqs. (12) and (13). Note that the time integral of P₂₅ is given by the product of ${\int }_{0}^{{t}_{acc}}{P}_{24} \cdot {P}_{45}\cdot dt$, and that P₂₄ corresponds likewise to P₂₃ and P₃₄ in Fig. 1.

(12)

(13)

The explanations of remaining parameters are given in Table 1.

Although radiocaesium is the dominant contributor to long-term internal dose from accidental NPP fallout, initial transfer of radioiodine to humans via contaminated fresh milk can be substantial if no iodine prophylaxis is distributed to local residents¹¹, or if dairy cows continue to graze (as happened in Belarus after the Chernobyl fallout in 1986). Furthermore, if fallout from nuclear weapons or fallout in areas close to a damaged NPP is considered, radiostrontium may be present in high concentrations and contribute significantly to the internal dose many decades after the fallout, as was the case after the global fallout from nuclear weapons testing in the 1950s and 60s¹⁵. In contrast to radiocaesium, both radioiodine and radiostrontium exhibit high organ-specific uptake in humans; iodine being highly accumulated in the thyroid and strontium, a calcium analogue, being mainly retained in bone tissue¹⁵.

The yearly fallout and measured ⁹⁰Sr activities in human bone in Denmark⁵¹ were used to numerically obtain time-dependent aggregated transfer factors for radiostrontium. For a detailed description of the derivation of the transfer functions for radiostrontium, the reader is referred to Sundström¹⁰.

(14)

S_Build-up(t) is a linear function that takes into account the build-up of radiostrontium in the body in the first 3 months from the start of the fallout. T_ag,Sr is the age-dependent aggregated transfer factor between the ground deposition and ⁹⁰Sr activity in human bone, normalized to the mass of calcium ((Bq g(Ca)^-1)/(kBq m^-2)). c_Sr,short and c_Sr,long are the short- and long-term weighting factors for the transfer parameter. T_eco,Sr,short and T_eco,Sr,long are the age-dependent ecological half-times in years for short- and long-term transfer, respectively. Age-specific values for the parameters of aggregated transfer factors and ecological half-time for strontium are given in Table 5. The coefficient δ_{MIRD,org,Sr-90+Y-90} (mGy y^-1) is the sum of the absorbed organ-specific dose rates per unit activity in bone for ⁹⁰Sr and ⁹⁰Y, taken from MIRD pamphlet no. 11⁵². m_Ca,sex(age(t)) is a PCHIP fit to the age- and sex-dependent whole-body mass of calcium in kg⁵³. A more comprehensive description of the derivations of the parameters in Eq. (14) can be found in Sundström¹⁰. Note that no protective measures have yet been included in Eq. (14). This work is still in progress, and is intended to be published separately.

Table 5 Age-specific parameters for the bi-exponential aggregated transfer factor and ecological half-time given in Eq. (16). Values are taken from Sundström¹⁰.

In scenarios with NPP releases of radiostrontium, the more short-lived strontium isotope ⁸⁹Sr may also accompany ⁹⁰Sr/⁹⁰Y. To be consistent with the approach used in the model for LARCalc, a similar absorbed dose rate coefficient, δ_{MIRD,org,Sr-89}, to that used for the sum of ⁹⁰Sr and ⁹⁰Y must be defined for ⁸⁹Sr. Since this nuclide is not listed by Snyder et al.⁵², the absorbed dose coefficient δ_{MIRD,org,Sr-89} was interpolated between δ_{MIRD,org,Sr-90} and δ_{MIRD,org,Y-90} with regard to the maximum emitted beta energy, E_β,max. Coefficients for the effective dose rate (ε_MIRD) were calculated for radiostrontium, following the same procedure as for radiocaesium (Eqs. 12, 13), excluding all organs except the skeleton and bone marrow. The values of δ_MIRD,org,Sr for the skeleton and red bone marrow, and ε_MIRD are listed in Table 6. Corresponding coefficients for the other organs are assumed to be negligible compared with the skeleton and red bone marrow and are therefore excluded.

Table 6 Organ-specific absorbed dose rate coefficients, δ_MIRD,org,Sr, for an adult subjected to chronic intake of radiostrontium-contaminated foodstuff. Values are taken and/or adopted from Snyder et al. ⁵².

Additional exposure pathways: Internal dose from inhalation during plume passage and external dose from cloudshine

Although the model behind LARCalc was originally intended for long-term predictions of unmitigated and remediated exposures from NPP fallout, the need for coarse estimates of the magnitude of inhalation doses during plume passage, related to a certain ground deposition was identified. An additional algorithm has therefore been added so that LARCalc can provide a conservative estimate of the inhalation dose, in which the average near-ground concentration in the passing plume, C_i,ave (Bq m^-3), is related to the local ground deposition of a given radionuclide, A_dep,i,loc (Bq m^-2) by the equation:

(15)

where v_d (m s⁻¹) is the dry deposition velocity⁵⁴. For wet deposition the velocity is assumed to be infinite (due to washout) and thus giving a C_i,ave(t) = 0 Bq m⁻³. This gives rise to two extremes: a conservative plume in the case of dry deposition, and an attenuated plume in the case of wet deposition. Assuming an age-dependent inhalation rate, INH(age) (m³ s⁻¹)⁵⁵, and using nuclide-, age- and organ specific-dose coefficients taken from the ICRP⁵⁶, the conservative estimate of the time-integrated dose rate from inhalation, Ḋ_inh (mSv) is given by Eq. (16).

(16)

The dose coefficients, d_inh,i, relating unit intake with the committed equivalent or effective dose (Sv Bq⁻¹), depend on aerosol or particle size, and whether the radionuclide is inhaled as a gas, vapour or organic molecule. This is important for iodine, as the inhalation of gaseous iodine (I₂(g) or organic iodine, CH₃I) results in more than double the organ dose to the thyroid compared to the inhalation of iodine bound to aerosols⁵⁶. A detailed description of the way in which the dose contribution from inhalation of airborne radionuclides from the release plume is estimated in relation to the remaining ground deposition is given by Sundström¹⁰. The inhalation absorbed dose rate will hence be nuclide-, age- and organ-specific as well as being specific in terms of aerosol size in the form of activity median aerodynamic diameter (µm), AMAD, and absorption type fast (F), moderate (M) or slow (S). For a more comprehensive description see the ICRP⁵⁶.

The algorithm for cloudshine dose uses the same average time-integrated near-ground air concentration (Eq. 15) in combination with the air submersion nuclide-, sex-, age- and organ-specific dose coefficient, d_cloud,i, from the ICRP¹⁴. The dose rate from cloudshine, $\dot{D}$_cloud,org (mGy y^-1) is given by Eq. (17).

(17)

Additional exposure pathways: Internal dose from ingested iodine-131 from consumed milk

A rapid transfer of radioiodine through cow’s milk was observed in many places after the Chernobyl NPP accident, both in the area surrounding the damaged plant⁵⁷, and also further away from Chernobyl⁵⁸, resulting in high doses to the thyroid in the population. An algorithm to estimate the absorbed dose rate (mGy/y) due to the consumption of milk containing ¹³¹I is given in Eq. (18).

(18)

where TF_milk,grass is the transfer factor from grass to milk (in this case 0.274 Bq L⁻¹/Bq m⁻²), f_inter is the interception factor (0.1), k_delay is a factor correcting for the decay between milking and consumption (in this case 3.5 days, giving a factor of 0.739), T_eff,grass is the effective half-time of ¹³¹I in the pasture, in this study assumed to be 3.5 days as reported by Håkansson et al.⁵⁸, a(age(t)) is the age-dependent dairy milk consumption rate. The latter was determined using PCHIP of age-dependent annual intake data of 50 kg y⁻¹ for 1-year-olds, 100 kg y⁻¹ for 12-years-ols and 150 kg y⁻¹ for 20-year-old and older (values taken from Rääf et al.²³ and references therein). d_ing is the age- and organ-dependent dose coefficient for ingested ¹³¹I, taken from the ICRP⁵⁹. For a more detailed description of the model, see Sundström¹⁰.

Final expression of CED and CUMLAR for updated LARCalc

The final expressions for the CED and the CUMLAR as a function of local and regional average deposition density, A_{dep,Cs-137,loc} and A_{dep,Cs-137,reg}, respectively, for the combined internal and external pathways considered in the current version of LARCalc are given in Eqs. 19 and 20:

(19)

(20)

Thus, for a given NPP fallout scenario including the assumed local or regional average ground deposition of ¹³⁷Cs, LARCalc predicts the anticipated unmitigated dose accumulated over a specified time period (e.g. 70 years). The corresponding residual dose, CED_res, and averted cumulative lifetime attributable risk, CUMLAR_av, can be found for a given set of protective measures using the S-factors for the different protective measures, S_evac, S_shield, S_aliment and S_decont. The CED_res can then be compared with reference levels suggested by the ICRP for existing radiation exposures³⁰, e.g. 20 mSv annual effective dose for returning evacuees, or 100 mSv residual dose for returning evacuees.

For planning purposes, the emergency preparedness coordinator of the NPP, as well as the relevant national authorities, may need to address the following questions:

• For a certain average local deposition of ¹³⁷Cs, accompanied by other fission products resulting from a certain fallout scenario, for how long must the residents in the affected area be evacuated to ensure that the residual dose of 100 mSv or returning dose rate of 20 mSv y^-1 is not exceeded?

• At which ground deposition, A_dep,Cs-137, should restrictions on foodstuffs be implemented, for how long time and to which extent?

• What is the averted risk of developing radiation-induced cancer for different age and sex cohorts, especially on more sensitive sub-cohorts, in terms of CUMLAR_av?

• Given that decontamination of evacuated zones can be important when encouraging evacuees to return to an evacuated area, what additional gain in terms of CUMLAR_av, can be achieved by decontamination measures? How does this gain depend on the time frame and dose reduction efficiency for different age and sex cohorts?

Table 7 presents an overview of the mathematical expressions for CED_res (mSv), and CUMLAR_av (%), for some typical combinations of protective measures to decrease radiation exposure after NPP fallout. If the individuals are evacuated before the plume reaches their habitat, S_decont = 0 for t < t_evac, where t_evac is the time of resettlement in the area. For t > t_evac, the value of S_decont is selected by the operator, between 0 to 1, and represents the average external dose rate reduction resulting from decontamination measures implemented in the residential area.

Table 7 Examples of protective measures listed by extent and time duration and the quantities describing the outcome of protective measures, CED_res and CUMLAR_av, based on sheltering, evacuation, decontamination, and extensive food restrictions.

Results and examples

To illustrate the use of LARCalc, we here present some different examples of how the tool can be applied. The general set-up for the calculations of the CED and CUMLAR in these examples were mainly based on a fictious Swedish NPP fallout scenario (see Table 2).

Default values for all following accident fallout scenarios and subsequent protective actions were: no protective measures, t_acc = 80 y (life expectancy), A_dep,loc = A_dep,reg = 1 MBq m^-2 of ¹³⁷Cs, f_sheild = 0.4, f_out = 0.2, f_snow = 1, T_eco,Cs,long = 6.7 y, T_ag,max,Cs = 6.7 Bq kg^-1/(kBq m^-2), inhalation absorption type “medium” with 24 h plume passage, including all pathways. Any deviations from these values will be mentioned in the title of the table or figure in the following sections. Figures 3 and 4 are based on a ¹³⁷Cs ground deposition of 1000 kBq m^-2 both locally and regionally, assuming dry deposition, for an adult male aged 30 at the time of fallout, to an age of 80 y. In this case, no protective measures were included, corresponding to the first example in Sect. 3.1 below.

Figure 3

CED for an adult male (30-years-old at accident) after exposure fictious Swedish NPP fallout scenario (Swedish NPP in Table 2), assuming dry deposition (0 g cm^-2). Calculated in LARCalc.

Figure 4

Effective dose rate for an adult male (30-years-old at accident) after exposure fictious Swedish NPP fallout scenario (Swedish NPP in Table 2), assuming dry deposition (0 g cm^-2)as calculated by LARCalc. Note that both x- and y-axis are in log-scale.

Results of CED _res and CUMLAR _av for the different NPP fallout scenarios and protective action scenarios

CED _res and CUMLAR _av for residents in protective action scenario (1) in Table 7

Table 8 gives the results obtained from LARCalc and the underpinning model when computing the CED_res as a function of sheltering time, t_shelt, for three different NPP fallout scenarios (Chernobyl 1, Fukushima and Swedish NPP, specified in Table 2), for dry and wet deposition. The calculations are based on Scenario (1) in Table 7. For 3-days´ sheltering, the typical residual doses will range from 106 to 230 mSv per MBq m^-2, depending on the fallout scenario and whether the deposition of the fallout is dry or wet.

Table 8 CED_res (mSv) to a 30-year-old male for three NPP fallout scenarios (listed in Table 2) using protective action scenario (1) in Table 7. Values are presented for dry- (0 g cm⁻²) and wet deposition (1 g cm^-2), and for various sheltering times. Note t_shelt = 0 d gives the effects of no sheltering.

The residual cumulative lifetime attributable risk, CUMLAR_res, and the CUMLAR_av for a newborn female and a 30-year-old male, and the corresponding CED_res for dry deposition of radionuclides for the three NPP fallout scenarios are given in Table 9. The CUMLAR_av due to sheltering will depend heavily on age, and the averted risk for a newborn female is ten times higher than for adult male. Note that CUMLAR_av and CUMLAR_res both are given in the unit percental points, or total risk of developing cancer.

Table 9 CUMLAR_av (%), CUMLAR_res (%) and CED_res (mSv) for a newborn female and a 30-year-old male for three NPP fallout scenarios (Table 2) using protective action scenario (1) in Table 7. Values are given for dry deposition, and for various sheltering times.

CED _res and CUMLAR _av for residents in protective action scenario (2) in Table 7

CED_res after sheltering and evacuation for one year before resettlement for three different NPP fallout scenarios, for three different ecological half-times of radiocaesium, T_eco,Cs,long, assuming dry deposition, is given in Table 10. The calculations are based on the mitigated accident Scenario (2) in Table 7. CUMLAR_av is given for various resettlement times, t_ret, in Table 11. It can be seen that a one-year evacuation will give the highest CED_res for nuclide vectors with high ¹³⁴Cs/¹³⁷Cs-ratios, like Swedish NPP (Table 2).

Table 10 CED_res (mSv) for a 30-year-old male for three NPP fallout scenarios using protective action scenario (2) in Table 7. Values are presented for different values of T_eco,Cs,long(y) and for different evacuation times, 3 days’ sheltering, assuming dry deposition.

Table 11 CUMLAR_av (%), CUMLAR_res (%) and CED_res (mSv) for a newborn female and a 30-year-old male for three NPP fallout scenarios (in Table 2) using protective action scenario (2) in Table 7. Values are given for T_eco,Cs,long = 6.7 y, dry deposition, 3 days’ sheltering, and for different evacuation times, t_ret.

In Table 11, the high impact of age on the averted risk by this protective measure can be seen, where, regardless of the fallout scenario, the CUMLAR_av for a newborn female can be more than a factor 10 higher compared with a male adult.

CED _res and CUMLAR _av for residents in protective action scenario (3) in Table 7

CED_res for three NPP fallout scenarios, decontamination with 50% efficiency, for four different ecological half-times for radiocaesium, T_eco,Cs,long, assuming wet deposition, is given for various resettlement times in Table 12. The calculations are based on the mitigated accident Scenario (3) in Table 7. It can be seen that CED_res can vary by up to a factor of 2 for short resettlement times between a very short and very long T_eco,Cs,long, and that the relative difference increases for longer resettlement times.

Table 12 CED_res (mSv) as a function of resettlement time, t_ret, and long-term ecological half-time of caesium, T_eco,Cs,long, assuming protective action scenario (3) in Table 7 with 50% decontamination after evacuation. Residual dose computed for c_short,i = 0 (conservative assumption for all nuclides), 3 days’ sheltering, and assuming wet deposition.

Table 13 gives CUMLAR_av for various relocation times, using protective action scenario (3) in Table 7, The consistently higher averted risk for newborn female compared to adult (average of 30-year-old old male and female) (almost a factor 7) can be clearly seen for short resettlement times, although this difference decreases somewhat with increasing t_res. The higher ¹³⁴Cs/¹³⁷Cs ratio for fallout event Fukushima and Swedish NPP results in a substantially higher benefit of evacuation, in terms of averted risk, especially for newborn female.

Table 13 CUMLAR_av (%) of total cancer (excluding non-fatal skin cancers) from external ground exposure for newborn female and 30-year-old adult for various resettlement time, using T_eco,Cs,long = 6.7 y, c_short,Cs = 0, with 3 days’ sheltering, and assuming wet deposition.

External dose from groundshine: Initial local deposition density vs. reference level of 100 mSv

LARCalc can be used to calculate which A_{dep,Cs-137,loc} values are compatible with evacuation when considering various protective measures. This A_{dep,Cs-137,loc} value can then be used as an initial operational intervention level for e.g. evacuation. Table 14 gives the corresponding initial deposition density values for ¹³⁷Cs that will give rise to an external dose contribution from groundshine exceeding 100 mSv for a certain resettlement time, t_ret.

Table 14 Initial local deposition density of ¹³⁷Cs (kBq/m²), A_{dep,Cs-137.loc}, at which a certain resettlement time will ensure compliance with the reference value CED_res = 100 mSv from external dose, calculated for three fallout scenarios and for four values of T_eco,Cs,long.

CED _res and CUMLAR _av for residents in protective action scenario (3) and (4) in Table 7

CED_res resulting from fictitious fallout from a Swedish NPP, assuming wet deposition, decontamination with 50% efficiency for three different ecological half-times, T_eco,Cs,long, are given in Table 15 . The calculations are based on the mitigated accident Scenario (4) in Table 7. From Table 15 it can be seen how the residual dose increases with an increasing T_eco,Cs,long. Assuming a similar decontamination efficiency to that in Japan after the Fukushima accident, the residual dose would have been much higher if T_eco,Cs,long had been similar to that found in the Russian rural settings after the Chernobyl accident (around 15 y)^46,60.

Table 15 CED_res (mSv) for decontamination efficiencies, S_decont of 50% and 90%, and for three different values of T_eco,Cs,long (Table 3), with 3 days’ sheltering. NPP fallout scenario: Fictious Swedish NPP fallout scenario (Table 2), assuming wet deposition and extensive food restrictions, S_aliment = 0.

The CUMLAR_av for Scenario (3) in Table 7 for the fictious Swedish NPP fallout scenario (Table 2) is illustrated in pie charts for a 30-year-old male, a newborn female, and a female born 10 years after the accident in Fig. 5. In this scenario, a value of T_eco,Cs,long = 6.7 y, and a decontamination efficiency of either 50% or 90% were used. It can be seen that in relative terms, evacuation will have a proportionally higher protective effect on newborn female than male adult.

Figure 5

Pie charts showing the CUMLAR_av for two different evacuation times, for an adult male, a newborn female and female born 10 years after the accident. The fallout scenario was Swedish NPP (Table 2), with T_eco,Cs,long = 6.7 y, assuming 3 days’ sheltering, decontamination with 50% efficiency performed after evacuation. Note that Evac_av, Decont_av, Indoor_av and Food_av are given as percent of the total averted risk, and that averted risk, CUMLAR_av, are given as percental points.

CED _res and CUMLAR _av for residents in protective action scenario (5) in Table 7

Values of CED_res for three NPP fallout scenarios (Table 2) and various resettlement times, combined with different durations of food restrictions are given in Table 16. Lifting food restrictions 10 y after the accident can result in up to twice as high a CED_res to the resettled population, compared with when lifted after 30 years. Another observation is that extensive food restrictions (S_aliment = 0) will generally lead to less reduction in the radiation detriment than decontamination for future generations of newborns in the affected area.

Table 16 CED_res (mSv) for various food restriction times, and resettlement times for typical urban populations, for three different fallout scenarios (Table 2) assuming extensive food restrictions (S_aliment = 0), 3 days’ sheltering, and assuming wet deposition. Decontamination with 50% efficiency performed after evacuation.

The CUMLAR_av from a fictitious Swedish NPP release event in relation to the protective measures implemented (according to Scenario (5) in Table 7) is illustrated as pie charts for a 30-year-old male, a newborn female, and a female born 10 years after the accident in Fig. 6.

Figure 6

Pie charts showing the averted risk, CUMLAR_av, for two different evacuation times, for an adult male, a newborn girl and a female born 10 years after the accident. The fallout scenario was Swedish NPP (Table 2). Results are given for 3 days’ sheltering, 20 years of food restrictions (S_aliment = 0) and decontamination with 50% efficiency performed after evacuation. CED_res, CUMLAR_res and CUMLAR_av are included. Note that Evac_av, Decont_av, Indoor_av and Food_av are presented in terms of their relative contribution to the total averted risk, CUMLAR_av, whereas CUMLAR_av and CUMLAR_res are given as percental points of lifetime cancer risk.

Inclusion of ¹³¹I in milk, aggregate transfer of ⁹⁰Sr/⁹⁰Y and ⁸⁹Sr, and initial inhalation dose in LARCalc

To illustrate the impact of the added exposure pathways in LARCalc including the dose from plume inhalation, their contributions to the unmitigated CED (mSv) are given in Table 17. Here the residual doses, CED_res (mSv), are presented for a 30-year-old male for three different NPP fallout scenarios using protective action scenario (1) in Table 7 when including 1 MBq m² of ⁹⁰Sr/⁹⁰Y ground deposition. Values are presented for dry deposition, with the default values: f_shield = 0.4, f_out = 0.2, f_snow = 1, inhalation absorption type “Medium” and a 24-h plume. The corresponding values for the unmitigated CUMLAR_res are given in Table 18.

Table 17 CED (mSv) without any protective measures for dry deposition from different NPP fallout scenarios (Table 2) and including 1 MBq m^-2 90Sr, for a 30-year-old male at the time of the accident and a 1-year-old female.

Table 18 CUMLAR_res (%) without any protective measures for dry deposition from different fallout scenarios (Table 2) including 1 MBq m^-2 90Sr, for both an adult male (30 years at accident) and a 1-year-old female.

It can be seen in Tables 17 and 18 that groundshine will dominate the radiation risk to all age cohorts, and that the increasing ¹³⁴Cs/¹³⁷Cs ratio between the nuclide vectors (Table 2) is reflected in an absolute increase in CUMLAR_res for a given deposition density of A_{dep,Cs-137,reg}. It can also be seen that the relative contributions from Sr transfer will be more significant for adults than children, as the build-up of Sr is related to the total mass of calcium in the bones¹⁰. Furthermore, iodine transfer in milk will have a higher impact on CUMLAR_res in children.

Validation with other models and observations

The strontium transfer described in Eq. (16) was compared with the monthly fallout of ⁹⁰Sr in New York during the years 1950 to 2000 given in The Integrated Global Fallout Database (IGFD)⁶¹, in order to estimate the activity concentration in bones for adults. As the data in the IGFD are monthly averages, the average activity concentration was calculated for each year, and compared with the data published by UNSCEAR⁶². The results are given in Fig. 7. The average absolute error between the model and the UNSCEAR data is 0.024 Bq/kg(Ca) while the LARCalc average relative error is a factor 2.12 times larger the UNSCEAR data, for the period 1955 to 1970 (seen in Fig. 7b).

Figure 7

(a) Estimate using the strontium model with the IGFD fallout data⁶¹ as input, averaged over each year, and measured bone activity concentration⁶². (b) Absolute and relative error between the modelled estimate and UNSCEAR data⁶².

A comparison with the European COSYMA model for the transfer of fission products to man, presented by Andersson et al.⁶³, shows a factor 2–3 agreement with the present LARCalc model, as can be seen in Table 19.

Table 19 Long-term dose contribution to adults (mSv/(MBq m^-2)) (integrated to age 80 years, average for male and female, 30 years old at accident) assuming wet deposition occurring at the beginning of the growth season. Calculations made with the European COSYMA model reported by Andersson et al.⁶³ and LARCalc.

LARCalc predicted a 4.6 times higher external dose from ¹³⁷Cs than COSYMA. This discrepancy may be due to the use of coefficients from the ICRP¹⁴ in LARCalc, which were not available at the time of the study by Andersson et al.⁶³. Using the coefficients given by the ICRP¹⁴ to calculate the dose for constant outdoor exposure (i.e. excluding all types of shielding) to ¹³⁷Cs, only taking into account for the physical- and ecological half-time of 6.7 y and assuming wet deposition, gives a CED of 84.5 mSv.

Results from LARCalc have been compared with observations made in Russia, in a study by Isaksson et al.⁸. It was found that the Russian data on the aggregate transfer of radiocaesium from the 1990s were between the T_ag,max,Cs(t) values obtained for hunters and urban residents in Sweden using LARCalc. A more detailed comparison between the T_ag,max,Cs values for radiocaesium in the Nordic countries has been performed by Hjellström et al.¹⁹.

Sensitivity and uncertainty analysis

An uncertainty analysis was performed in the present study in which each parameter was sampled from a probability distribution (see Table 20). Parameters included in the underlying models but not listed in Table 20 were assumed to have no uncertainty, and thus had fixed values in this analysis. Results for the CED to an adult male (aged 30 y at the time of the fallout) and up to the age of 80 y, are presented in Fig. 8, following the Chernobyl fallout in Sweden (Chernobyl 1 in Table 2), normalized to A_{dep,Cs-137,reg} and A_{dep,Cs-137,loc} = 1 MBq/m^{2 137}Cs. The nuclide vector were edited to A_dep,Sr-90 = 1 (resulting in 1 MBq/m² of ⁹⁰Sr) to include the strontium model, thus the doses are comparable to those in Tables 18 and 19. The simulation was performed with 50,000 samples, and yielded a median CED of 225.8 mSv with a 5^th percentile of 118.8 mSv and a 95^th percentile of 429.5 mSv (note that the mean of the doses will be overestimated due to the distributions, as there is a greater probability of a higher value for both lognormal and uniform distributions). The values given in Table 20 were based on uncertainties considered to be appropriate for each parameter (uncertainties briefly described in Isaksson et al.⁸).

Table 20 Parameter probability distributions used in uncertainty and sensitivity analysis. Empty cells indicate parameters that are not applicable for the respective type of distribution.

Figure 8

Histogram of the CED for an adult male (30 years-old at accident, until age of 80) living in an area affected by fallout containing a nuclide vector according to the Chernobyl 1 (Table 2) without any protective measures. The parameters used in the computations are based on the uncertainties given in Table 20.

Two sensitivity analyses were performed on the LARCalc tool. In the first, each parameter was randomized 5000 times and sampled from the distributions given in Table 20. In the second, each parameter was varied ± 10% from the default value. Both analyses were performed on CED, including all pathways, without any protective measures, for an adult male (aged 30 years at the time of the accident) up to the age of 80 years. Figure 9 shows the absolute change in CED for 5^th and 95^th percentiles from the sample distribution of each parameter in the first analysis, while Fig. 10 shows absolute change in CED when each parameter was varied. It should be noted that A_dep,i and c_short,i affect all nuclides in the nuclide vector except ¹³⁷Cs.

Figure 9

Results of the first sensitivity analysis of the total CED for adult male (30 years) up to the age of 80 y. The 5^th (blue) and 95^th percentiles (yellow) of the 5,000 samples are shown for each parameter. (a): results for the 14 most dominant parameters. (b): results for the 14 least dominant parameters.

Figure 10

Results of the second sensitivity analysis of the total CED for adult male (30 years) up to the age of 80 y. The results for a 10% decrease (blue) and a 10% increase (yellow) in each parameter. (a): results for the 14 most dominant parameters. (b): results for the 14 least dominant parameters.

The results of the sensitivity analyses show that the parameters that directly affect the fallout, such as A_{dep,Cs-137,loc}, A_{dep,Cs-137,reg} and A_dep,i, and the shielding effect of remaining indoors, f_shield, have considerable impact on CED. On the other hand, parameters that have a short-term effect, such as T_eco,i,short and c_short,i, and the body weight (in this analysis, for a male), w_male, have a smaller effect on the CED.

Future work with Larcalc

At the same time as this work was being carried out, the ICRP was updating the dose coefficients for members of the public (ingestion and inhalation of nuclides). Our plan is to include these dose coefficients in an updated version of LARCalc. We also intend to include our own future work on e.g. nuclear weapons fallout and accident releases from the European Spallation Source (ESS) to make LARCalc a more complete tool for estimating doses and risks from different pathways of radiation exposure. There are also plans on making the tool more available as a python program or as an online-based web calculation tool.

Conclusions

The LARCalc easy-to-use tool is based on models for the prediction of radiation exposures and the associated LAR resulting from an atmospheric release of radionuclides from NPP. LARCalc is intended to be used as a training tool for decision makers and can facilitate visualization of how different protective actions can affect the dose and lifetime cancer risk to populations in the event of an NPP emission. In its current version, it is designed to relate the CED and CUMLAR_res to the initial local and regional average ground deposition of ¹³⁷Cs. The tool is based on previously published models^8,9,10. This paper presents a number of extended features, including the implementation of dose conversion factors presented by the ICRP¹⁴ to obtain relationships between equivalent doses for various organs and ground deposition of a gamma-emitting radionuclides at various depths, as well as inhalation doses and the contribution to the internal dose from radionuclides such as ¹³¹I and ⁹⁰Sr/⁹⁰Y.

Furthermore, various doses can now be computed for a wider range of NPP fallout scenarios and their associated nuclide vectors. The user can customize the event after a specific fallout scenario by editing the nuclide vector and ¹³⁷Cs deposition.

This paper has also provided examples of ways in which LARCalc can be used to estimate the projected cumulative effective dose (CED), the residual dose (CED_res), and the cumulative averted lifetime attributable risk (CUMLAR_av) for various combinations of protective measures. The target audience for LARCalc comprises decision-makers involved in emergency preparedness planning at authorities.

The LARCalc tool has been developed for Swedish conditions. For use in other countries, it is recommended that the parameter T_ag,max,Cs and its related time parameters (presented in Table 1) be adapted to better match locally or regionally recorded body burdens of radiocaesium. The sheltering factor and occupancy factor may also need to be adjusted in other countries.