A Methodology for Estimating External Doses to Individuals and Populations Exposed to Radioactive Fallout from Nuclear Detonations

Abstract

A methodology of assessment of the doses from external irradiation resulting from the ground deposition of radioactive debris (fallout) from a nuclear detonation is proposed in this paper. The input data used to apply this methodology for a particular location are the outdoor exposure rate at any time after deposition of fallout and the time-of-arrival of fallout, as indicated and discussed in a companion paper titled “A Method for Estimating the Deposition Density of Fallout on the Ground and on Vegetation from a Low-yield Low-altitude Nuclear Detonation.” Example doses are estimated for several age categories and for all radiosensitive organs and tissues identified in the most recent ICRP publications. Doses are calculated for the first year after the detonation, when more than 90% of the external dose is delivered for populations close to the detonation site over a time period of 70 y, which is intended to represent the lifetime dose. Modeled doses in their simplest form assume no environmental remediation, though modifications can be introduced. Two types of dose assessment are considered: (1) initial, for a rapid but only approximate dose estimation soon after the nuclear detonation; and (2) improved, for a later, more accurate, dose assessment following the analysis of post-detonation measurements of radiation exposure and fallout deposition and the access of information on the lifestyle of the exposed population.

INTRODUCTION AND SCOPE OF THE STUDY

The purpose of this paper is to present a methodology that can be used to estimate the doses from external irradiation resulting from exposure to radioactive fallout from a nuclear detonation. The methods presented here are part of a proposed comprehensive schema for dose assessments for exposures to radioactive fallout from nuclear detonations (Simon et al. 2022). With the notable exception of the internal dose to the thyroid, the dose from external irradiation is usually the most important contributor to the total dose for most organs and tissues (US DHHS 2005; Simon et al. 2020).

Two types of dose assessment are described: (1) initial, used to make a rapid evaluation of the external dose within hours or days after the detonation based on default values for the parameters involved in the calculations; and (2) improved, made months or even years after the detonation, when better site- and time-specific data for critical parameters become available. The main population groups that are considered here are those residing within a few hundred kilometers of the detonation site. This paper is meant to be read and applied in conjunction with a companion paper (Beck et al. 2022) in which the ground-deposition density and other basic data related to the characteristics of the fallout and of the resulting exposure are presented and discussed.

While the method presented here, in particular the improved assessment strategy, is primarily envisioned for estimation of doses that might be received from a future contamination event, i.e., for a prospective dose assessment, as shown here, the initial assessment strategy is closely similar to those used previously in retrospective studies of doses for health risk determinations. Hence, with suitable consideration of the data available to conduct the dose assessment, either retrospective or prospective applications can be undertaken. Moreover, depending on the degree to which the data describe individual or population-average attributes (e.g., age, sex, ethnicity, lifestyle), the method can be applied for dose assessments either at the individual level or at the average level of a population group (such as that which might be defined by age and location).

Absorbed doses in this method can be estimated for all radiosensitive organs and tissues of the body, as specified in ICRP Publication 103 (ICRP 2007) and listed in Table D3 in Appendix D, as well as for all ICRP age groups: in utero, newborn, 1–2 y, 3–7 y, 8–12 y, 13–17 y, and adults. The first-year dose is a good approximation of the lifetime external dose because it will be shown in this paper that, under most conditions, at least 90% of the external dose from fallout deposition is delivered during the first year after the nuclear detonation. Only the first-year dose will be considered in the initial assessment method, but both the first-year dose and the lifetime dose will be discussed in the improved assessment method. The effective dose⁸ will also be calculated, or referred to, when appropriate.

The main source of external irradiation that is considered in the two dose assessments is that from gamma rays emitted from radionuclides deposited on the ground. Secondary sources of external irradiation are discussed in Appendices. These include (1) the dose due to descending fallout during the passage of the radioactive cloud, which is shown to be very small in comparison to the dose from radionuclides deposited on the ground (Appendix A), and (2) the dose from beta rays, which can be substantial for the skin and the lens of the eye but is unimportant for all other radiosensitive organs and tissues of the body (Appendix B). It is important to note that the dose arising from the prompt gamma rays and neutrons emitted during the nuclear detonation is outside the scope of this method, primarily because it is not associated with fallout (radioactive debris). Moreover, only persons within a few thousand meters of the detonation site would be affected by prompt gamma ray and neutron exposure.

Other Appendices discuss the variation of the exposure rate with time after detonation (Appendix C); the conversion from exposure to organ dose (Appendix D); the gamma-ray exposure shielding factors while indoors and outdoors (Appendix E); and estimates of time spent indoors, outdoors, and in vehicles (Appendix F). Finally, an example of application of the method is presented in Appendix G.

METHODOLOGY FOR ASSESSMENT OF PHOTON DOSES

During the passage of a fallout debris cloud over a particular site, radioactive particles fall out of the cloud due primarily to sedimentation for particle sizes greater than 5 μm. For smaller particles, the deposition on the ground is due to turbulent diffusion in the absence of precipitation, but the most important mechanism is washout or rainout. All particles, of course, are eventually deposited on the earth’s surface. The resultant exposure rate at ground level, or more precisely at 1 m above ground level, initially begins to increase as a result of radioactive decay of the nuclides in the air (descending fallout), followed soon after by the combination of the radioactive decay of descending fallout and of nuclides already deposited on the ground. The exposure rate usually reaches a maximum while there is still descending fallout before decreasing to a value at the end of fallout EOF (end of cloud passage over the site) that is due only to activity on the ground (Fig. 1). The exposure rate decreases after it reaches its maximum primarily because the rapid radioactive decay of nuclides deposited on the ground more than offsets the additional fallout. In this paper, the fallout time-of-arrival (TOA) is defined as “the time that equalizes the two shaded areas A and B in Fig. 1 so the area under the approximate curve is the same as the area under the true curve” (Kennedy 1981). We recognize, however, that fallout times-of-arrival are often reported with a less rigorous definition (Appendix A), though all strategies used attempt to make an estimate of the same general phenomenon. Here, we formalize the definition of TOA to remove ambiguity on how it is best obtained for dose-assessment purposes. For the purpose of the dose-calculation strategy presented here, it is assumed that all fallout occurs instantaneously at TOA. For locations within a few hundred kilometers of the detonation site, the TOA values are not generally expected to exceed 48 h.

Fig. 1.

Conceptual drawing showing variation of the exposure-rate data vs. time as a means to define TOA at any location following a nuclear weapons detonation (based on Thompson et al. 1994).

Two general approaches have been used to estimate doses from external irradiation resulting from fallout from nuclear weapons tests: (1) using as a basis the deposition densities estimated, for example, according to the method as described in Beck et al. (2022), calculate the dose from external irradiation from each radionuclide under consideration and sum them up to obtain the total dose (US DHHS 2005; Drozdovitch et al. 2021); or (2) using the exposure rate, $\dot{X}$(12), and the time of arrival of fallout, TOA, determined as indicated in Beck et al. (2022), calculate the dose from external irradiation from a functional form of the time-dependent variation of the exposure rate (Anspaugh and Church 1985; Simon et al. 1995; Gordeev et al. 2006; Bouville et al. 2010, 2020). It is the latter approach that was selected for the purposes of this paper. In the calculations presented here, the influence of fractionation (modification of the relative activity of various fission and activation products in fallout relative to that produced in the detonation) was not taken into account, as it is shown in Appendix C that the exposure decay rate from external irradiation is relatively insensitive to the degree of fractionation and to the type of fissile material. SI units are used in this paper for all radiation quantities, with the exceptions of exposure and of exposure rate, for which traditional units, R for exposure and mR h⁻¹ for exposure rate, have been used because their SI units, C kg⁻¹ for exposure and C kg⁻¹ s⁻¹ for exposure rate, are virtually never used in the fallout literature. One R is equal to 2.58 x 10⁻⁴ C kg⁻¹ and 1 mR h⁻¹ is equal to 7.17 x 10⁻¹¹ C kg⁻¹ s⁻¹.

According to the selected method, the external photon dose (mGy) delivered from TOA to a given time TC at which the dose is calculated to an organ or tissue m of a representative individual I at location P is expressed as follows:

where $\stackrel{·}{D}\left(t,I,P,m\right)$ is the dose rate (mGy h⁻¹) at time t to an organ or tissue m and at location P, which in turn is expressed as:

where:

• $\dot{X}\left(t,P\right)$ is the reference exposure rate (mR h⁻¹) at 1 m above the soil surface at location P, calculated assuming that fallout is deposited uniformly over a plane area infinite in extent⁹ and that the activity was uniformly deposited over that area with an exponential variation with depth in the soil corresponding to a relaxation length of 0.16 g cm⁻² (Beck 1980; Beck et al. 2022). The measurements of the reference exposure rates are assumed to have been conducted in areas where the fallout activity is not likely to have been disturbed and is not likely to be disturbed in the foreseeable future. A detailed discussion of the measurement techniques and of the associated uncertainties can be found in NCRP (2007);

• LF(t, I) is the location factor applicable to the representative individual I at time t. The location factor, first introduced by Meckbach and Jacob (1988), is defined as the ratio of the exposure rate at the specific location where the representative individual I is assumed to be, either indoors or outdoors, and of the reference exposure rate; and

• K(I, m) is the conversion coefficient from exposure to dose (mGy mR⁻¹) to the organ or tissue m under consideration.

Each of these parameters is discussed in detail in the following section.

IMPLEMENTATION OF THE METHODOLOGY—INITIAL ASSESSMENT

Selection of the parameter values

In the initial assessment method, the only detonation-related data assumed to be available for the estimation of the photon dose received by a representative individual I residing at location P are the fallout time-of-arrival, TOA, and the exposure rate at H + 12 h, $\dot{X}($12), for all locations under consideration. These data are estimated on the basis of measurements carried out immediately after the detonation, as described in the companion paper (Beck et al. 2022).

Under those conditions, the parameters involved in the calculation of the dose rate (mGy h⁻¹) at time t and location P to an organ or tissue m of a representative individual I (eqn 2) are determined as follows:

• $\dot{X}\left(t,P\right)$ is the reference exposure rate (mR h⁻¹) at 1 m above the ground at location P. As indicated in Beck et al. (2022), it is derived from the measured or estimated $\dot{X}$(12, P) assuming a variation with time of the exposure rate after detonation that can be described by a sum of exponentials:¹⁰

Based on data from Hicks (1981, 1982), the values of a_i, unitless, and of L_i, in h⁻¹, were fitted by Henderson (1991) or Beck et al. (2022) for various degrees of fractionation and for any value up to 50 y of the time post-detonation, t, expressed in hours. As discussed in Beck et al. (2022), the values of a_i and of L_i vary slightly from test to test and fractionation according to the characteristics of the explosive device.¹¹ Weathering¹² also is an influencing factor that is discussed in Appendix C. The default values of a_i and of L_i selected in the initial assessment are presented in Table 1, which is reproduced from Beck et al. (2022). These values were determined for Tesla, a typical Pu-fueled nuclear weapon test that was detonated at the Nevada Test Site in 1955 (Henderson 1991; Beck et al. 2022); at all locations, the degree of fractionation, R/V, is assumed to be equal to 0.5, and weathering is not taken into account. Eqn (3) can be applied to any time, t, after detonation and to any location, P, where $\dot{X}$(12, P) is available, with the exception of areas within a few kilometers from the detonation site, where damage from the detonation predominates over irradiation from fallout. Also, eqn (3) can only be applied to sites that have remained undisturbed until time t after detonation.

Table 1.

Values of the parameters a_i and L_i used in the initial dose assessment to estimate the variation of the exposure rate with time in eqn (3) (Henderson 1991; Beck et al. 2022).

i	ai	Li (h–1)
1	1.033 × 102	X–1.838 × 100
2	3.206 × 101	X–6.369 × 10X–1
3	2.476 × 100	X–1.189 × 10X–1
4	3.476 × 10X–1	X–3.075 × 10X–2
5	1.332 × 10X–1	X–8.284 × 10X–3
6	2.851 × 10X–2	X–2.208 × 10X–3
7	3.302 × 10X–3	X–4.653 × 10X–4
8	9.055 × 10X–5	X–8.166 × 10X–5
9	3.692 × 10X–6	X–2.312 × 10X–5
10	1.003 × 10X–5	X–2.649 × 10X–6

• LF(t, I) is the location factor applicable to the representative individual I at time t. In the initial assessment, the default value for outdoor conditions is taken to be equal to 1, meaning that the exposure rate at the position of the representative individual was equal to the value estimated for location P, irrespective of the type of ground surface, e.g., bare soil, mowed lawn, grassland, paved area, etc. For indoor conditions (at home, at work, at school, or in any other building) and during transportation, the default value is assumed to be equal to 0.2 (UNSCEAR 1982).

• K(I, m) is the conversion coefficient from exposure to dose (mGy mR⁻¹) to the organ or tissue m under consideration. It varies according to the age of the representative individual and to the energy of the gamma rays emitted by the radionuclides deposited on the ground and the irradiation geometry. It is assumed in the calculations that the representative individual is standing upright. Based on a similar work related to the nuclear weapons tests conducted in the Marshall Islands (Bouville et al. 2010), the conversion coefficients from exposure to dose were taken to have the same value for any organ or tissue m of the body and to be independent of the irradiation geometry, but to vary with age. The values that were used in the Marshall Islands study were 6.6 × 10⁻³ mGy mR⁻¹ for adults, 7.9 × 10⁻³ mGy mR⁻¹ for children aged 3 through 14, and 8.6 × 10⁻³ mGy mR⁻¹ for children less than 3 years old (Bouville et al. 2010). For the purposes of this paper, these values were modified to correspond to the age groupings considered by the ICRP (1989). The K(I) values obtained for each ICRP age group are presented in Table 2; as indicated previously, they are assumed to apply to any organ or tissue m of the body.

Table 2.

Selected values of K(I) for each of seven age groups considered.

Age group, I	K(I), mGy mR–1
In utero	6.6 × 10X–3
0 – 12 mo	8.6 × 10X–3
1 – 2 y	8.6 × 10X–3
>2 – 7 y	7.9 × 10X–3
>7 – 12 y	7.9 × 10X–3
>12 – 17 y	7.3 × 10X–3
> 17 y	6.6 × 10X–3

The values of the dose rate, calculated using the default values indicated above, must be integrated from TOA to TC in order to obtain the external photon dose (mGy) delivered to an organ or tissue m of a representative individual I at location P. In the implementation of this method, eqn (2) is modified as follows:

where BF(t, I, P) = (LF_out(t, P) x FT_out(t, P)) + (LF_in(t, P) x FT_in(t, P)) is the behavioral factor of the representative individual I at time t and location P, in which

• LF_out(t, P) and LF_in(t, P) are the location factors for outdoors and indoors at time t and location P, respectively; and

• FT_out (t, P) and FT_in (t, P) are the fractions of time spent outdoors and indoors at time t and location P, respectively.

In the initial dose assessment, the simplifying assumption is made that the values of LF and FT do not change with time between TOA and TC and have the same value at all locations P and for all representative individuals I; as in UNSCEAR (1982), the values of LF_out and FT_out are taken to be 1 and 0.2, respectively, while those of LF_in and FT_in are taken to be 0.2 and 0.8, respectively, so that:

From eqns (3) through (5), eqn (1) can be simplified as:

where IF(TOA, TC) is the integral from TOA to TC of the exposure rate, normalized to an exposure rate of 1 mR h⁻¹ 12 h after the time of detonation (H + 12 h):

The values of IF(TOA, TC) obtained using the data presented in Table 1 are shown in Table 3 for a range of values of TOA, with TC = 1 year after detonation.

Table 3.

Calculated values of IF(TOA, TC) from eqn (7), i.e., the integrated exposure rate (normalized to 1 mR h⁻¹ at H + 12 h) from TOA to TC = 1 y (8,760 h).

TOA, h	IF(TOA, TC), mR per mR h−1 at H + 12 h
2	78.0
4	62.0
6	55.5
9	50.2
12	46.7
18	41.9
24	38.8
48	31.8

In summary, for the initial assessment:

• Hicks’ data (Hicks 1981) for Tesla, as fitted by Henderson (1991), are assumed to adequately represent the reference exposure rate at 1 m above ground level due to radionuclides produced by the detonation;

• Estimates of $\stackrel{·}{X}$(12) and of TOA are assumed to be available for all locations P of interest;

• Only the first year after detonation is considered in the calculation of the photon dose, i.e., TC = 1 y;

• Weathering is not taken into account; and

• During the entire year of exposure, the population stays at the same location and does not change its lifestyle in a way that would affect shielding.

Example of implementation of the initial dose assessment

In this example of implementation of the initial dose assessment, it is assumed that the value of $\stackrel{·}{X}$(12) at location P is 330 mR h⁻¹ and that the fallout time-of-arrival TOA at that location is 2 h after the detonation in order to be consistent with the data used in the example chosen in a companion paper (Beck et al. 2022).

Under these assumptions, the first-year absorbed dose from photons received by an adult I at location P is estimated from eqn (6) to be equal to 61 mGy, from IF = 78.0 mR per mR h⁻¹ at H + 12 h (Table 3), K(adult) = 6.6 10⁻³ mGy mR⁻¹, (Table 2), and BF = 0.36 from eqn (5).

The photon doses calculated for all age groups and for a range of TOA values are presented in Table 4. It is clear from Table 4 that, on the basis of the simplifying assumptions that were made for the initial assessment, the estimated first-year photon dose at a given location P depends only to a small extent on the age of the representative individual I, and the time-of-arrival of fallout (TOA is a more important parameter). This implies that $\stackrel{·}{X}$(12) and TOA are the more important factors involved in the estimation of the dose from external irradiation.

Table 4.

Estimated first-year photon doses from external irradiation (mGy) for all age groups and a range of TOA values, at a location where $\stackrel{·}{X}$(12) equals 330 mR h⁻¹.

	Age group
TOA (h)	In utero	0–12 mo	1–2 y	>2–7 y	>7–12 y	>12–17 y	>17 y
2	61	80	80	73	73	68	61
4	49	63	63	58	58	54	49
6	44	57	57	52	52	48	44
9	39	51	51	47	47	44	39
12	37	48	48	44	44	41	37
18	33	43	43	39	39	36	33
24	30	40	40	36	36	34	30
48	25	33	33	30	30	28	25

The step-by-step calculations needed to calculate the first-year dose are further described in Appendix G, both for the initial and the improved dose assessments, using the same input data as in Beck et al. (2022).

IMPLEMENTATION OF THE METHODOLOGY—IMPROVED ASSESSMENT

General principles

The main difference between the initial and the improved assessment methods is that information obtained on the characteristics of the detonation, of the environment, and of the lifestyle of the population are taken into consideration in the improved assessment. In other words, in the improved assessment:

• improved estimates of $\stackrel{·}{X}$(12), TOA, and R/V, if available, are used in the calculations;

• both the lifetime and the first-year doses are calculated;

• the influence of weathering is taken into consideration in the estimation of the first-year and lifetime dose; and

• the parameters defining the lifestyle and the characteristics of individuals in the exposed populations are taken into account.

For the purposes of this improved assessment, it is assumed that:

• the function describing the variation with time of the decay rate including weathering can be accurately described as a sum of 10 exponentials with values for a_i and L_i that are specific to the detonation; and

• the whereabouts of individuals in the exposed population are available at all locations of interest in a detailed manner (hour by hour) for the first 10 d after detonation and, in a less detailed manner (day by day), for the remainder of the first year after detonation, thereby allowing for a more precise estimate of shielded vs. unshielded dose during the period when the exposure rate decreases very rapidly with time.

The basic equation to be used to calculate the doses from external irradiation is the same for the initial and the improved assessment methods (eqn 1). For the improved assessment $\dot{\mathit{D}}\left(t,I,P,m\right)$, the absorbed dose rate at time t in an organ or tissue m of a representative individual I at location P, depends on the specific activity of the representative individual I at time t (e.g., outdoors, traveling in a car or in public transport, at home, or at work/school/other building). Furthermore, in the improved dose assessment, TC could have two values: TC1 = 1 y for the calculation of the first-year dose, and TC2 = 70 y for the calculation of the lifetime dose.

For the purpose of the improved calculations, discrete intervals of time are considered:

where $\overline{D}\left(t,I,P,m\right)$ is the mean value of $\stackrel{·}{D}\left(t,I,P,m\right)$ over ∆t, and is calculated as:

During each interval of time ∆t, the value of LF remains constant; it could, for example, be a period of sleep at night or of travel in a vehicle. The way in which the three components of the mean dose over Δt are calculated are considered in turn.

Estimation of the mean exposure rate, $\overline{X}\left(t,P\right)$, over Δt

For the first year after the detonation, the mean exposure rate over Δt (beginning at time t₁ and ending at time t₂ after TOA) would be calculated analytically, using the revised values of a_i and L_i that take weathering into account. As indicated in Appendix C, because weathering is primarily due to precipitation, the region around the detonation site would be classified into one of three climate types, cl, determined according to the distribution of mean annual rainfall in the U.S.: DRY, for arid areas (average annual precipitation <57 cm), WET (average annual precipitation >120 cm), and MODERATE (average annual precipitation 57–120 cm). For the following years, that is, from year 2 to 70, it would be adequate to use the arithmetic averages of the calculated exposure rates at t₁ and t₂. Detailed information on the method used to obtain the values of a_i(cl) and L_i(cl), which are presented in Table 5, is provided in Appendix C.

Table 5.

Selected values of a_i(cl) and L_i(cl) for the multi-exponential function used to represent the variation with time of the exposure rate for the three climate types.

i	DRY climate		MODERATE climate		WET climate
	ai(DRY)	Li(DRY)	ai(MOD)	Li(MOD)	ai(WET)	Li(WET)
1	1.02 × 102	X–1.86 × 100	1.12 × 102	X–2.24 × 100	9.90 × 101	X–1.79 × 100
2	2.90 × 100	X–6.29 × 100	4.07 × 101	X–8.04 × 10−1	6.70 × 100	X–9.69 × 10−1
3	3.10 × 101	X–6.29 × 10−1	5.40 × 100	X–3.77 × 10−1	2.64 × 101	X–5.94 × 10−1
4	2.44 × 100	X–1.11 × 10−1	2.02 × 100	X–9.81 × 10−2	2.30 × 100	X–1.06 × 10−1
5	3.08 × 10−1	X–2.43 × 10−2	2.95 × 10−1	X–2.26 × 10−2	3.56 × 10−1	X–2.83 × 10−2
6	9.93 × 10−2	X–6.83 × 10−3	8.31 × 10−2	X–6.36 × 10−3	7.96 × 10−2	X–6.55 × 10−3
7	2.05 × 10−2	X–1.97 × 10−3	1.37 × 10−2	X–1.86 × 10−3	1.10 × 10−2	X–1.76 × 10−3
8	2.40 × 10−3	X–4.53 × 10−4	1.66 × 10−3	X–4.60 × 10−4	1.12 × 10−3	X–4.37 × 10−4
9	5.57 × 10−5	X–7.74 × 10−5	4.20 × 10−5	X–8.48 × 10−5	2.44 × 10−5	X–7.85 × 10−5
10	4.71 × 10−6	X–3.39 × 10−6	3.63 × 10−6	X–3.61 × 10−6	2.57 × 10−6	X–3.53 × 10−6

As shown in Appendix C, it is not deemed necessary to take the degree of fractionation, R/V, into account because the variation of R/V in its typical range from 0.5 to 3 has only a small effect on the exposure; for example, the first-year exposure for TOA = 3 h would only be 10% smaller for R/V = 3 than for R/V = 0.5.

The values of the integral of the normalized exposure rate from TOA to one year differ only by about 10% between dry and wet climate conditions for TOA = 2 h and by about 30% for TOA = 48 h. Approximately the same differences are obtained for the integrals from TOA to 70 y. More complete results are presented in Appendix C.

Estimation of the location factor, LF(t, I ,P)

It is assumed here that the location factor is known relatively well at each location of interest and for each age group. The results of a literature survey on the outdoor and indoor location factors for rural and urban areas are presented in Appendix E. A template similar to that shown in Table 6 is suggested, in this case for the first day after TOA, taken in this example to be 0500 (5:00 am), for adults. Such tables would be prepared for each location of interest, each age group, and each of the first 10 d after detonation when the exposure rate decreases rapidly and there are substantial differences between the outdoor and indoor exposure rates. During the remainder of the year, as the exposure rate decreases more slowly, it would be adequate to have one table for a typical working/school day and another table for weekends or vacation. During the following years, average values, independent of time, could be used, as is done for the initial dose assessment, but there should be a set of values for each age group.

Table 6.

Examples of location factors for adults for the first day after TOA.

Δt (h)	t1 (hours after TOA)	t2 (hours after TOA)	Location	LF
2	0	2	Aa	0.1
1	2	3	Bb	0.25
4	3	7	Cc	0.2
1	7	8	Dd	0.5
4	8	12	C	0.2
1	12	13	B	0.25
1	13	14	D	0.5
10	14	24	A	0.1

^aA = Indoors at home.

^bB = In vehicle.

^cC = Indoors at work, school, or other locations.

^dD = Outdoors.

As indicated in a companion paper (Simon et al. 2022), the models discussed in the series of papers assume no countermeasures were implemented or remediation conducted that could prevent or reduce possible exposure. Therefore, the values selected for the location factor would not take into account the possibility of evacuation or relocation. However, as noted in Simon et al. (2022), the external dose models could be modified without great difficulty to account for evacuations or remediations.

Estimation of the conversion coefficient from exposure to dose, K(I, m)

For photon energies of about 0.5 MeV, typically emitted by the fission products during their radioactive decay (Beck et al. 2022), there is little variation in the conversion coefficients from exposure to dose with differences in body organ or tissue for a given geometry of irradiation, as illustrated in Appendix D. The variation from one geometry of irradiation to another, which is more substantial, is also discussed in Appendix D (ICRP 2010; NCRP 2018).

As shown in Appendix D, information is available on the conversion coefficients from exposure (or air kerma) to dose for adults and for all radiosensitive organs and tissues of the body, typical irradiation geometries, and a range of photon energies (ICRP 2010). This information was used to calculate the doses to all radiosensitive organs and tissues of the body for adults for average fallout energies of 0.5 and 0.6 MeV. As similar information is available in the Federal Guidance Report No. 15 (Bellamy et al. 2019), the results could be extended to all age groups that are considered.

The conversion coefficient for effective dose was estimated using a combination of rotational, ROT (two thirds of the time), and isotropic, ISO (one third of the time), geometries. The choice of 2/3 rotational and 1/3 isotropic is believed to be a reasonable approximation of the average exposure conditions and is consistent with the general shape of experimental data for fallout (e.g., Huddleston et al. 1965; Mather et al. 1962). An indirect reference for the selection of the geometries of irradiation is Beck et al. (2017), where such a combination of geometries was used to calculate the doses to active marrow and male breast from fallout for atomic veterans. Using average values for gamma-ray energies of 0.5 and 0.6 MeV presented in Table D1, the exposure-to-effective dose conversion coefficient for adults is calculated to be 6.7 × 10⁻³ mSv mR⁻¹, which is very close to the value of 6.6 × 10⁻³ mGy mR⁻¹ used in the initial dose assessment for any organ or tissue of the body. For reasons of consistency, the value of 6.6 × 10⁻³ mGy mR⁻¹ was used for the exposure-to-dose conversion coefficient for adults in both the initial and the improved dose assessments.

ESTIMATION OF THE UNCERTAINTIES

The purpose of this section is to evaluate the extent to which the improved assessment yields dose estimates that are more accurate and precise than those obtained by an initial assessment. The same endpoints as discussed previously were chosen for this evaluation: the organ or tissue dose estimates for a representative adult exposed either in a rural area or in an urban area. In order to facilitate the comparison of the two dose assessments and their uncertainties in the dose estimates, a slightly modified eqn (6), shown below as eqn (10), will be used for both the initial and for the improved dose assessment. As indicated later on, this results in a simplification of the improved dose assessment:

The uncertainties in each of the four parameters of eqn (10), which are all independent of each other, are discussed below. They are all assumed to be lognormally distributed. The deterministic values of all four parameters are assumed to be the geometric means of those lognormal distributions.

$\stackrel{·}{X(}$12, P)

The reference exposure rate, $\stackrel{·}{X}($12) in mR h⁻¹, is assumed in this example to be equal to 330 mR h⁻¹ for the rural and urban areas, P, that are considered, as well as for the initial and improved dose assessments. As indicated in Beck et al. (2022), the uncertainty in $\stackrel{·}{X}($12) depends on several factors, including the measurement error, the uncertainty in the decay correction from time of measurement to 12 h, and the amount and type of available data. The uncertainty in $\stackrel{·}{X}($12) for any site will depend not only on the decay rate but more importantly on whether the site had an actual exposure rate measured at some time or whether $\stackrel{·}{X}($12) is based on an interpolation from nearby sites. Assuming that the measurement error can range up to 25%, the overall uncertainty in $\stackrel{·}{X}($12) at a given site can be as much as 30–40% (1 Standard Deviation) for the initial assessment but is assumed to be somewhat more precise for the improved assessment, when many more radiation measurements are presumably available. In this exercise, the reference exposure rates were subjectively estimated to be distributed lognormally with a geometric standard deviation (GSD) of 1.4 for the initial assessment and of 1.3 for the improved assessment.

IF(TOA, TC)

In this exercise, the normalized reference exposure rate is integrated from TOA = 2 h until TC = 1 y, the time referenced to the time of the detonation. As shown in Fig. C1, the variation of the normalized reference exposure rate with time is very small among a variety of past nuclear detonations during the first year after detonation. Therefore, the uncertainty in the integral of the normalized reference exposure rate, expressed, in mR per mR h⁻¹, as:

Fig. C1.

Variation of the normalized exposure rates with time after detonation for seven nuclear weapons tests for a fractionation level, R/V, of 0.5 (Henderson 1991; Hicks 1981, 1984; Bouville et al. 2010).

over the first year after detonation is expected to be minor in comparison to the uncertainty associated to the value of $\stackrel{·}{X}$(12) if TOA is known exactly. The value of IF(TOA, TC) and of its uncertainty is independent of the type of location (urban or rural), because the reference site is considered to be a flat lawn at a reasonable distance from any construction and is expected to remain undisturbed until TC. The differences between the values of the integrated exposures at the reference site and at the sites where population groups are exposed are taken into account by means of the location factor, which is included in the calculation of BF. The main uncertainty in the value of IF(TOA, TC) is assumed to result from the uncertainty in TOA. Quinn (1990) estimated that, depending on the nuclear test and on the distance from the test site, TOA could vary from 15 min to several hours. Taking as an example an uncertainty of 30 min for TOA = 2 h, the uncertainty in the integral would be about 10%. If the uncertainty in TOA is 1 h for TOA = 5 h, the uncertainty in the integral is about 5%. The other sources of uncertainty, related mainly to conditions of vertical migration of the deposited activity that could differ from the reference conditions, are difficult to estimate but are deemed to be small. The overall uncertainty in the value of IF(TOA, TC) was subjectively estimated to be distributed lognormally with a GSD of 1.2 for the two dose-assessment methods (initial and improved) and the two locations of interest (rural and urban).

K(I)

The value of K(I) depends on the geometry of irradiation, the energy spectrum of the incident gamma rays, the tissue or organ that is considered, and the age of the representative person. Data on the variation of K(I) for selected organs of a representative adult, gamma energies of 0.5 and 0.6 MeV, and selected geometries of irradiation are presented in Table D1: they show that the gamma energy has very little influence on K(I) in comparison to the geometry of irradiation and, to a lesser extent, to the organ or tissue. The most uncertain parameter is the assumed geometry of irradiation, which is merely an approximation of the average conditions of exposure. However, this average condition of angular incidence is rarely encountered: the actual average angular incidence will vary significantly depending on the particular exposure scenario (e.g., the fraction of time spent indoors in various types of structures or outdoors in the vicinity of structures or trees). The actual average angular incidence for any individual is, thus, very difficult to estimate and somewhat uncertain. In the study of the external doses resulting from the tests that were conducted in the Republic of the Marshall Islands in the 1950s, the uncertainty in K(I) was evaluated to be uniform with a range from 0.9 to 1.1 around the central estimate (Bouville et al. 2010). For the purposes of this paper, the uncertainty in the selected value of K(I) for any organ or tissue of the body was subjectively estimated to be distributed lognormally around the selected estimate with a GSD of 1.1 for the two dose assessments and locations of interest, as well as for any age group.

BF

Initial assessment

The default value of 0.36 for the behavioral factor, BF, which is used in the initial assessment, was calculated using the assumptions that people spend 20% of the time outdoors, with a location factor of 1, and 80% indoors, with a location factor of 0.2. These values are reasonable estimates for worldwide averages, with the implicit assumption that the populations exposed are residents of rural areas. With respect to urban areas, the only change that was made consisted in lowering the outdoor location factor from 1 to 0.3, in accordance with the measured values presented in Table E3 for the first year after deposition. The uncertainties in the location factors and in the fractions of time spent outdoors and indoors are presented in Table 7 in terms of practical ranges for various sites throughout the world. The practical ranges in the parameter values are based on the information presented in Tables E1, E2, E3, and E4 for the location factors and in Tables F1, F2, and F3 for the fractions of time spent indoors, including in vehicles, and outdoors. The geometric means and the uncertainties (expressed as GSDs) attached to the values of the behavioral factor, BF, were derived from the information presented in Table 7 on the location factors and on the fractions of time spent outdoors and indoors. The values of BF were found to be 0.36 (GSD = 2.2) for the initial dose assessment for a rural population, and 0.22 (GSD = 2.7) for the initial dose assessment for an urban population.

Table 7.

Estimated geometric means and practical ranges (within parentheses) of the location factors, LF, and of the fractions of time, FT, spent indoors and outdoors.

	Initial assessment		Improved assessment
	Rural area	Urban area	Rural area	Urban area
LFout	1 (0.4 – 1.5)	0.3 (0.2 – 0.4)	0.6 (0.4 – 0.9)	0.3 (0.2 – 0.4)
LFin	0.2 (0.02 – 0.5)	0.2 (0.001 – 0.5)	0.1 (0.07 – 0.13)	0.03 (0.02 – 0.05)
FTout	0.2 (0.05 – 0.4)	0.2 (0.05 – 0.4)	0.07 (0.05 – 0.1)	0.07 (0.05 – 0.1)
FTin	0.8 (0.6 – 0.95)	0.8 (0.6 – 0.95)	0.93 (0.9 – 0.95)	0.93 (0.9 – 0.95)

Improved assessment

The means and practical ranges of the location and occupancy factors for the improved dose assessment were also taken from the data presented in Appendices E and F. However, in this case, the appropriate values would be for specified population groups residing in either rural or urban areas, for whom large numbers of measurements of location and occupancy factors would have been made. The selected values, presented in Table 7, are taken from the results of single studies conducted in relatively small areas, which are available in tables of Appendices E and F. As was done for the initial dose assessment, the means and the uncertainties attached to the values of the behavioral factor, BF, were derived from the information presented in Table 7 on the location factors and on the fractions of time spent outdoors and indoors. The values of BF in the improved dose assessment were found to be 0.14 (GSD = 1.3) for the population group residing in a rural area and 0.049 (GSD = 1.4) for the population group residing in an urban area. Both the means and the geometric standard deviations of BF are estimated in this exercise to be smaller for the improved dose assessment than for the initial dose assessment: the means of BF are smaller because of the smaller values assigned to the means of the indoor location factors and to the means of the outdoor occupancy factors; the geometric standard deviations of BF are smaller because they refer to specific population groups instead of a variety of population groups with different lifestyle and residential habits.

Overall uncertainty in D(I, P)

The geometric means and GSDs of the distributions obtained for the four quantities involved in the estimation of the doses from external irradiation for a representative adult are presented in Table 8. For the initial dose assessments, the uncertainties in the estimates of BF are much greater than those of the other quantities, whereas for the improved dose assessments, the uncertainties in BF are much smaller and about equal to the uncertainties in the reference exposure rates. Because the first-year doses D(I, P) are calculated as the products of four statistically-independent parameters with subjectively-assumed lognormal distributions, their distributions are also lognormal, with GSDs obtained as:

Table 8.

Estimated geometric means (GMs) and geometric standard deviations (GSDs), within parentheses, of the doses from external irradiation for a representative adult and of the parameters involved in the calculations.

	Initial assessment		Improved assessment
	Rural area	Urban area	Rural area	Urban area
$\stackrel{·}{X}\left(12\right)$	330 (1.4)	330 (1.4)	330 (1.3)	330 (1.3)
IF	78 (1.2)	78 (1.2)	78 (1.2)	78 (1.2)
K	6.6 × 10–3 (1.1)	6.6 × 10–3 (1.1)	6.6 × 10–3 (1.1)	6.6 × 10–3 (1.1)
BF	0.36 (2.2)	0.22 (2.7)	0.14 (1.3)	0.049 (1.4)
D	61 (2.4)	37 (2.9)	24 (1.5)	8.3 (1.6)

As expected, the uncertainties in the first-year doses are much greater for the initial assessments than for the improved assessments. The estimated mean doses obtained with the initial assessments are also substantially higher than those obtained in the improved assessments.

It is important to note that the overall uncertainties obtained in this exercise rely heavily on the parameters of the uncertainty distributions (i.e., geometric means and uncertainties) that are subjectively assigned to the individual parameters involved in the estimation of the behavioral factor, BF. In addition, the improved dose assessments in this example were simplified, as the variations with time after detonation of the location and occupancy factors were not taken into account. More correct calculations would have required the use of Monte Carlo procedures. However, it is likely that the main conclusions derived from this exercise (that is, lower mean doses and uncertainties for the improved dose assessments) would still hold.

DISCUSSION

Assuming that the values of $\stackrel{·}{X}$(12) and TOA are known for the locations of interest, the initial dose assessment can be quickly implemented within a few hours after the detonation. This initial dose assessment is expected to provide conservative estimates of the first-year doses from external irradiation that would be received by representative individuals, classified by age group (see discussion of uncertainty above). However, many simplifying assumptions are made in the initial assessment method, including that the behavior of the population that affects shielding does not vary substantially over the year, that people do not leave their location of residence at any time during the first year after the detonation, and that no remediation of the environment takes place.

An improved dose assessment could be conducted up to years after the detonation, at a time when better information is available on the characteristics of the detonation, on the environmental behavior of fallout deposited on the ground, and on the whereabouts of the exposed individuals or populations. This more rigorous methodology is proposed to estimate more precise first-year doses as well as the lifetime doses from external irradiation. It is assumed in its implementation that sufficient knowledge has been acquired on the location and occupancy factors of the exposed populations, usually obtained by personal interviews and environmental measurements. In the simplified example presented in the previous section, it is shown that the mean doses and uncertainties that are obtained in the improved dose assessment are substantially lower than those obtained in the initial assessment.

It is interesting to compare the methods described in this paper with those that were used in dose assessments related to the nuclear weapons tests that were carried out in the 1950s and 1960s:

• The external doses received by the populations that resided in the vicinity of the Nevada Test Site were derived from measured exposure rates, the use of a model describing the variation of the exposure rate as a function of time, an indoor location factor of 0.5, and an indoor occupancy factor of 0.5. This methodology, which was developed by the U.S. Department of Energy Test Manager’s Committee to Establish Fallout Doses (TMCEFD),¹³ is roughly the same as that described in the initial assessment. The method the TMCEFD used to describe the exposure rate as a function of time was

where b and c are constants needed to ensure continuity. Also, in some locations around the Nevada Test Site, film badges were distributed to a number of individuals and the external doses were directly derived from the film-badge measurements.

• In locations far away from the Nevada Test Site, neither film badges nor exposure rates were measured (Beck and Anspaugh 1991; Bouville and Beck 2000). For those locations, the radionuclide mixture in fallout was inferred from either the measurements of daily deposition densities of total beta activity or from calculated ¹³⁷Cs deposition densities from specific tests inferred from contemporary measurements of the total (NTS + global) ¹³⁷Cs and total ^239,240Pu in soils, using a technique developed by Beck and Krey (1983). The exposure rates were then calculated from the radionuclide mix calculated by Hicks (1981), assuming R/V = 0.5, and the conversion from exposure to dose was carried out using parameter values recommended by UNSCEAR (1982): indoor location factor of 0.2, outdoor location factor of 1, indoor occupancy factor of 0.8, and a value of K equal to 7 × 10⁻³ mGy mR⁻¹ (Beck and Krey 1983).

• An approach similar to the improved assessment was used by Henderson and Smale (1990) to estimate dose from external irradiation for individuals living near the Nevada Test Site: measured exposure rates and a model describing the variation of the exposure rate with time were used to characterize the outdoor exposure rate. Indoor location factors were estimated for living areas and bedrooms, as well as being in a car, and indoor occupancy factors included time-specific data for the seasons of the year and day of the week. All parameter values were assumed to be distributed either normally or lognormally. The model used to calculate the external dose was run in a stochastic mode, thus providing the probability distribution of the dose estimate.

• In the Utah leukemia case-control study, bone-marrow doses were estimated for 6,507 individuals (Simon et al. 1995). The method used was close to the initial assessment method in many respects (use of measured reference exposure rates and of a multi-exponential model to describe the variation of the exposure rate as a function of time; identical behavioral factor and exposure-to-bone-marrow dose conversion factor for all subjects). There were, however, components of the improved assessment, as the residential history of all subjects was used, and exposure-to-bone-marrow dose factors, specific to the age of each subject, were interpolated from literature values. The same methodology was used in the Utah thyroid case-control study to estimate the thyroid doses from external irradiation (Simon et al. 1990, Simon et al. 2006b).

• The approach used in the Marshall Islands study (Bouville et al. 2010) to estimate the doses from external irradiation in each inhabited island or atoll is similar to the initial assessment, the major difference being that reference exposure rates were not available for many tests and had to be derived from ¹³⁷Cs measurements. Other differences are that: (1) the R/V ratio varied according to the time of arrival of fallout at the island or atoll under consideration, and (2) the rate of decay of the exposure rate took weathering into account. The indoor and outdoor location factors were taken to be equal to one, and the value of K was the same for all organs and tissues of the body.

• In the Kazakhstan study of thyroid diseases (Land et al. 2008), individual thyroid doses from external irradiation were estimated for almost 3,000 subjects, including Russians and Kazakhs, using a methodology developed by a US/Russian team (Simon et al. 2006a). In a second paper, the uncertainties in the thyroid dose estimates were evaluated in detail by means of a two-dimensional Monte-Carlo method (Land et al. 2015). In this study, the approach used for the dose estimation was more like the improved than the initial assessment, as (1) the R/V ratio varied according to the time of arrival of fallout at the location under consideration, (2) the rate of decay of the exposure rate took weathering into account, (3) on the basis of measurements, the indoor location factors had different values for the Russian and Kazakh subjects, and (4) the outdoor occupancy factors were taken to be age-dependent, ranging under most conditions from 0.2 for a 5-y-old to 0.6 for a young adult, but having more specific, time-dependent, values during the first few hours following the fallout time of arrival.

It is clear that, for most past studies, the approach used to estimate the doses from external irradiation was much closer to the initial assessment than to the improved assessment.

SUMMARY

A methodology for assessment of the doses from external irradiation resulting from the ground deposition of radioactive material produced in a nuclear detonation is proposed in this paper. The input data used for this methodology are the exposure rates at 12 h after detonation, $\stackrel{·}{X}\mathrm{\text{(12)}}$, and the times-of-arrival of fallout, TOA, as indicated and discussed in a companion paper (Beck et al. 2022). As examples, doses are estimated for several age categories and for all radiosensitive organs and tissues identified in the most recent ICRP publications. Doses are initially calculated for the first year after the detonation, when more than 90% of the dose is delivered, and later, over a time period of 70 y, which represents the lifetime dose. Modeled doses, in their simplest form, assume no environmental remediation or decontamination though the methods allow for remediation to be accounted for. Two types of dose assessment are considered: (1) initial, for a rough estimation soon after the nuclear detonation, and (2) improved, for a more accurate assessment much later, following the analysis of measurements of radiation data and information on the lifestyle of the exposed population. In a simplified example, it is shown that the mean doses and uncertainties that are obtained in an improved dose assessment are substantially lower than those obtained in an initial assessment. A review of some of the most important past dose-reconstruction efforts related to fallout from nuclear weapons tests shows that the approach used to estimate doses from external irradiation was, in many cases, much closer to the initial dose assessment than to the improved assessment. The most important parameters in the estimation of the dose from external irradiation are the measured exposure rate at a reference location, the estimated time-of-arrival of fallout, and the indoor location factor, which takes into account the distance from the outdoor contamination and the degree of shielding against the gamma rays that is provided by the building materials.

APPENDIX A: RELATIVE IMPORTANCE OF CLOUD DOSE VS. DOSE FROM ACTIVITY DEPOSITED ON THE GROUND SURFACE AND DEFINITION OF THE FALLOUT TIME-OF-ARRIVAL (TOA)

Cloud dose versus dose from activity deposited on the ground

During the passage of a fallout debris cloud over a particular site, radioactive particles fall out of the cloud, due primarily to gravitation, and deposit on the ground. The resultant exposure rate at ground level, or more precisely at 1 m above ground level, initially begins to increase as a result of radioactive decay from the nuclides in the air (descending fallout), followed soon after by the combination of the radioactive decay of descending fallout and of nuclides already deposited on the ground. The exposure rate usually reaches a maximum while there is still descending fallout before decreasing to a value at the end of fallout [EOF (end of cloud passage over the site)] that is due only to activity on the ground (Fig. 1). The exposure rate decreases after it reaches its maximum, primarily because the rapid radioactive decay of nuclides deposited on the ground more than offsets the increase due to additional fallout.

Determining the fraction of the exposure rates due to airborne vs. deposited debris at any time during fallout, while possible using very sophisticated computer models, would be very complicated and very uncertain due to a lack of detailed information on the distribution of activity with particle size in the cloud, as well as on the shape of the debris cloud overhead and the non-uniform distribution of debris within the cloud. It is, however, very clear from Figure 1 that the integral of the exposure rate from the initial arrival of fallout to EOF, which includes all descending fallout, is much smaller than the integral of the exposure rate from EOF onward, the latter due only to the fallout activity deposited on the ground. Consequently, the cloud dose from airborne debris (so-called cloud dose) is much smaller than the dose from activity deposited on the ground.

Definition of the fallout time of arrival (TOA)

In this paper, even though fallout occurs over a substantial length of time, usually about two times the fallout time-of-arrival, TOA is taken to be instantaneous and is defined as in Kennedy (1981) as “…the time that equalizes the two shaded areas A and B in Figure 1 so the area under the approximate curve is the same as the area under the true curve.” It is important to note that the exposure rates vs. time calculated using Hicks’ data account only for deposited activity, not airborne (in-cloud) activity. Thus, strictly speaking, they are only applicable from EOF onward, during the time span termed “Residual decay” in Fig. 1. However, if Hicks’s data are applied from TOA onward instead of EOF onward as done in this paper, the calculated exposure rates are higher than the measured exposure rates from TOA to EOF, but the calculated integral of the exposure rate from TOA to EOF adequately represents the total exposure during the time interval from the initial time of increase in air concentration to EOF, which includes the contributions from activity in the cloud and activity deposited on the ground surface.

Within the framework of the ORERP project (Church et al. 1990), at least three other definitions of the time of arrival of fallout were considered (Thompson et al. 1994):

• “the time when a substantial part of the fallout reached the ground (used by the Weather Bureau in creating original fallout patterns);

• the time when a time-of-arrival detector recorded a value 2 mR h⁻¹ above background (such detectors were used during Operation Plumbbob in 1957); and

• the time of the maximum rate of fallout (used by the Weather Service Nuclear Support Office (WSNSO) of the National Oceanic and Atmospheric Administration in their reanalysis of fallout patterns).”

In practice, it is usually difficult to determine TOA accurately:

• for the initial dose assessment, it is likely that only a limited number of measurements of exposure rates will be available and that the main purpose of these measurements will be to delineate the contaminated areas. In that case, the value of TOA at a location under consideration could be crudely estimated as the quotient of the distance from the site of detonation to that location and of the wind speed, either averaged over the height of the fallout cloud or measured near ground level. The limitations of that crude method are described in detail by Beck et al. (2022);

• for the improved dose assessment, the experience from the tests conducted at the Nevada Test Site indicates that the best estimates of fallout arrival times were made from sequential measurements of exposure rate, that is, from a radioactivity analysis. However, in the absence of those measurements, the fallout arrival time at a given location also could be estimated from a meteorological analysis, based on the calculated trajectories of a range of particle sizes descending to the ground surface from all layers of the radioactive cloud (Quinn 1990). Results of the radioactivity analysis and of the meteorological analysis for test Harry, detonated at the Nevada Test Site on 19 May 1953, are presented in Table A1 (Quinn 1990), where it is shown that there is a relatively good agreement between the time of maximum rate of fallout (radioactivity analysis) and the fallout particle arrival time (meteorological analysis). The values of TOA determined as indicated in this paper, which would be intermediate between the times of the first activity and of the peak exposure rate, would also be in relatively good agreement between the time of maximum rate of fallout and the fallout particle arrival time. It is, however, worth mentioning that this comparison was made for times of arrival of fallout of a few hours. Assuming that the data presented in Table A1 are representative of typical low-altitude low-yield tests, a rule of thumb would be that TOA is about 20% greater than the initial fallout time-of-arrival and 20% lower than the peak exposure rate for TOAs of a few hours. In the implementation of the improved dose assessment, it is recommended to use the radioactivity analysis, but to supplement it with a meteorological analysis in order to improve the reliability of the results.

Table A1.

Estimated times, in hours counted from the time of the detonation, of first activity, peak exposure rate, and maximum rate of fallout from radioactivity analysis and meteorological analysis of fallout particle arrival times for test Harry (Quinn 1990).

	Radioactivity analysis			Meteorological analysis
Location	First activity, h	Peak exposure rate, h	Maximum rate of fallout, h	Fallout particle arrival time, h
Groom Mine, NV	1.0	1.3	1.2	1.2
Alamo, NV	2.0	3.4	2.4 – 2.6	2.1
Bunkerville, NV		2.5		2.3
Mesquite, NV	2.2	2.7	2.4 – 2.5	2.5
St. George, UT	3.7	4.7	3.7 – 4.5	3.6

No published information was found for comparisons involving longer times of arrival of fallout. However, agreement would likely be poorer because of a lower density of exposure-rate measurements (radioactivity analysis) and of greater uncertainties in the trajectories of the fallout particles at longer distances from the detonation site (meteorological analysis).

APPENDIX B: RELATIVE IMPORTANCE OF BETA DOSE TO SKIN AND LENS OF THE EYE

Beta kerma in air from deposited fallout, effect of weathering

The exposure rate free-in-air at early times after fallout deposition also includes a contribution from beta rays as well as gamma rays. However, the beta-ray contribution is only a few times that from gamma rays immediately after deposition and decreases rapidly due to weathering and the limited range of beta rays in soil.

Gibson et al. (1969) measured the beta/gamma exposure from global fallout emitters in air. The mean ratio was about 11 with a range of 3–17. Barss and Weitz (2006) estimated a similar ratio for the beta kerma at 1 m from an ideal plane source. However, both the Gibson et al. (1969) and Barss and Weitz (2006) ratios do not reflect the significant shielding effect due to ground roughness. Ground roughness reduces the actual initial exposure rate for gamma rays (compared to an ideal plane source) by 15–30% (Table B1), so one would expect a much larger decrease for beta rays.

Table B1.

Ground roughness correction to plane source exposure rate from gamma rays (NCRP 1999).

Ground roughness correction factor	Method	Assumption	Reference
0.70	Measurements	—	Burson and Profio (1977)
0.66	Calculations	3-mm depth	Jacob et al. (1987)
0.85	Calculations	Exponential profile, with a relaxation length of 1 mm	Beck (1980)

Experimental evidence from beta rays is presented in Table B2: beta/gamma kerma ratios shortly after fallout from the test Simon, detonated in April 1953, were measured by film badges exposed at 1 m above the ground (Rainey et al. 1954). As shown in Table B2, the beta/gamma ratio varied from about 2 to 5, which is to be compared with the value of 11 obtained for an ideal plane source.

Table B2.

Film badge beta/gamma measurements after test Simon (Rainey et al. 1954).

Location	Film badge dose, mGy	Beta/gamma ratio
1	830	2.9
2	340	4.9
3	83	3.1
4	19	2.1
5	9.2	4.0
6	8.3	2.3

Gibson et al. (1969) also estimated the weathering for beta emitters based on measurements over time from global fallout at Cambray in the United Kingdom (Fig. B1). As can be seen, even for a high energy beta emitter such as ⁹⁰Y, the weathering of beta emitters results in a much faster reduction in exposure rate than for gamma emissions.

Fig. B1.

Estimated corrections on the exposure rate for weathering effects at times after deposition (Gibson et al. 1969).

Beta dose to skin

Because of the short range of beta rays in tissue, only superficial organs and tissues, typically skin and lens of the eye, receive non-negligible doses from external beta irradiation.

The most common situation is exposure from fallout deposited on the ground. In the US EPA FGR15 report (Bellamy et al. 2019), estimated dose rates to skin are provided for more than 1,000 radionuclides and for several source terms, including: (1) plane source buried under 3 mm of soil to take ground roughness into account, reflecting conditions of irradiation soon after deposition of fallout; and (2) slabs of fallout of various depths, reflecting the influence of weathering long after fallout deposition. Table B3 presents estimated doses to skin for pure beta emitters of various energies (¹³⁷Cs, ⁸⁹Sr, ⁹⁰Sr, and ⁹⁰Y) and for a gamma-ray emitter representative of fallout (^137mBa). It seems clear that the relative decrease with time of the dose to skin is much greater for beta rays than for gamma rays and that the dose to skin due to beta rays is significant only for emitters where the maximum beta energy is over 1 MeV. It is important to note that, as shown in FGR15 (Bellamy et al. 2019), much of the exposure rate from beta-particle emitters distributed in the soil is from bremsstrahlung radiation rather than from the beta rays themselves. Therefore, only a few nuclides in fallout account for most of the dose to skin from beta rays from a source distributed with depth, including ¹⁰⁵Ru (0.4 MeV), ¹¹²Ag (1.4 MeV); ¹³⁹Ba (0.9 MeV), and ^92–95Y (1.2–1.7 MeV).

Table B3.

Estimated dose rates to skin, in Gy s⁻¹ per Bq m⁻² (Bellamy et al. 2019).

		Dose rate to skin (Gy s–1 per Bq m–2)
Nuclide	Energy βMax (MeV)	Plane source	1-cm slab	5-cm slab	15-cm slab
		Electron emitters
137Cs	0.512	3.0 × 10−16	1.5 × 10−17	5.2 × 10−18	2.4 × 10−18
90Sr	0.546	1.4 × 10−16	6.8 × 10−18	3.6 × 10−18	1.9 × 10−18
89Sr	1.491	6.7 × 10−15	3.9 × 10−16	8.8 × 10−17	3.3 × 10−17
90Y	2.284	1.1 × 10−14	1.0 × 10−15	2.2 × 10−16	8.0 × 10−17
		Gamma-ray emitter
137mBa	NA	1.4 × 10−15	4.6 × 10−16	2.6 × 10−16	1.3 × 10−16

The calculated dose rate from beta rays can be substantial for the skin (factor of 10 or so higher than the dose rate from gamma rays for outdoor occupancy immediately after deposition). It is, however, almost always unimportant for all other radiosensitive organs and tissues of the body. Consequently, when a tissue-weighting factor of 0.01 is applied to the skin dose, as recommended in ICRP (2007), the effective dose from beta rays is about 10 times smaller than the effective dose from gamma rays for outdoor occupancy and is in fact much smaller when the protection afforded by clothing, indoor occupancy, and the shielding effect due to ground roughness and weathering are taken into account.

Another scenario of exposure to beta rays is the deposition of fallout particles on body surfaces from descending fallout or resuspension of activity initially deposited on the ground. Results of example calculations (Apostoaei and Kocher 2010) indicate that, in the occurrence of such pathways of exposure, the beta-ray doses from dermal contamination can be a significant and sometimes dominant contributor to the total dose to skin from all exposure pathways. However, while the modeling approaches are straightforward, the necessary parameters are not well known (Apostoaei and Kocher 2010).

Beta dose to the lens of the eye

The beta-ray doses to the lens of the eye are estimated at a depth of 3 mm (300 mg cm⁻²) from the anterior surface of the eye where the lenticular tissue at risk for posterior subcapsular cataract development is located (DTRA 2010). The estimation of the dose does not take into account the attenuation effects of the eyelid or corrective lens, e.g., contacts or glasses. In the case of exposure to fallout deposited on the ground, the dose to the lens of the eye is, thus, somewhat smaller than the dose to skin. Another scenario of exposure includes the possible deposition of fallout on the eyelid. In that case, assuming that the contamination of the eyelid occurred at H + 12 h, the dose to the lens of the eye is approximately 3% of the dose to the eyelid (DTRA 2010).

Conclusion

The exposure rate in air from beta rays in deposited fallout is only a few times that from gamma rays at TOA for outdoor occupancy and decreases much more rapidly with time due to weathering. The corresponding beta doses to skin and to the lens of the eye, integrated over 1 y after detonation, are much smaller than those from gamma rays because of the protection afforded by indoor occupancy and clothing (or eyeglasses). Thus, the doses to the skin and to the lens of the eye from beta rays from deposited fallout can be considered negligible compared to the doses from gamma radiation. It is likely that dose to skin from beta rays in fallout is due mostly to nuclides deposited directly on the skin or clothing or inadvertently transferred to the skin or clothing.

APPENDIX C: DECAY RATES—JUSTIFICATION OF THE MULTI-EXPONENTIAL MODEL, RELATIVE CONTRIBUTIONS OF SPECIFIC RADIONUCLIDES TO THE EXPOSURE, INFLUENCE OF WEATHERING ON THE EXPOSURE, AND OF FALLOUT IN URBAN AREAS

Justification of the multi-exponential model

In the 1950s and 1960s, the variation of the exposure rate after a nuclear weapons test was usually estimated by means of a power function ${\stackrel{·}{X}}_p\left(t\right)=\stackrel{·}{X}\left(1\right)x{t}^{-1.2}$, where t is the time after detonation, expressed in hours (Quinn 1990), derived as an approximation from the rate of decay of beta particles (Way and Wigner 1948). However, the US Department of Energy-sponsored Off-Site Radiation Exposure Review Program (ORERP), conducted in the 1980s, found that when series of measured exposure-rate data were available at the same locations, the exposure rates [normalized to H + 12 and calculated with a multi-exponential function ${\stackrel{·}{X}}_e\left(t\right)=\stackrel{·}{X}\left(12\right)x\sum _{i=1}^{i=10}{a}_{i}x\mathrm{EXP}\left(L_{i}xt\right)]$ showed excellent agreement with the measurements, as shown in Fig. C1 (Henderson 1991; Quinn 1990). The versatility of the multi-exponential model is derived from the summation of exposure rates from a large number of radionuclides with different half-lives. In contrast, the t^−1.2 approximation, as discussed below, does not always reflect the correct exposure rate for some time intervals.

A comparison of the exposure rates calculated with the power function ${\stackrel{·}{X}}_p\left(t\right)$ and with the multi-exponential function ${\stackrel{·}{X}}_e\left(t\right)$ is presented in Fig. C2. For the purposes of this comparison, the test Tesla was used as an example. Assuming that a multi-exponential function provides a more realistic picture of the actual decay rate, the use of the t^−1.2 approximation appears to result in significant errors in the inferred exposure rate at H + 12 if the actual measurement was made either within the first 6 h after detonation or later than 1 d after detonation. The ordinate reflects the error that would result in the exposure rate at H + 12 if the measurement was made at the time indicated on the abscissa. The largest discrepancies between the two sets of values are obtained 1 h after detonation (ratio of 1.8 for R/V = 0.5) and about 5 d after detonation (ratio of 1.3 for R/V = 0.5 or 1). As shown in Figure C2, the degree of error varies slightly with the degree of fractionation. A similar exercise, carried out by Simon et al. (2006a) under different conditions, also shows substantial differences between exposure rates calculated with the power function and with the multi-exponential function. It is important to note that, if the construction of the nuclear device leads to substantially different exposure rates than those for the test Tesla, as was the case for the Trinity test (Beck et al. 2022), a good fit can still be obtained using the multi-exponential function by means of a judicious selection of the parameters a_i and L_i.

Fig. C2.

Ratio of the exposure rates calculated by means of a power function ${\stackrel{·}{X}}_p\left(t\right)$, denoted as “t^−1.2”, and of a multi-exponential function ${\stackrel{·}{X}}_e\left(t\right)$, denoted as “actual”. Both functions were normalized to an exposure rate of 1 mR h⁻¹ at H + 12 h. It is assumed in the calculations that no weathering took place.

The integrals of the exposure rates, calculated by means of the power function, ${\stackrel{·}{X}}_p$, and of the multi-exponential function, ${\stackrel{·}{X}}_e$, are shown in Figs. C3 and C4 for TOAs of 1 and 48 h, respectively. The first-year exposures differ by 23 and 10% for TOA values equal to 1 and 48 h, respectively. The 70-y exposures are somewhat closer: differences of 15 and 6% for TOAs of 1 and 48 hours, respectively.

Fig. C3.

Variation of the exposure with time, calculated with the power function, ${\stackrel{·}{X}}_p\left(t\right)$, and with the multi-exponential function, ${\stackrel{·}{X}}_e\left(t\right)$. The ground deposition is assumed to have occurred 1 hour after detonation. The data labelled X_p and X_e refer to the exposures calculated with the power and multi-exponential functions, respectively.

Fig. C4.

Variation of the exposure with time, calculated with the power function, ${\stackrel{·}{X}}_p\left(t\right)$and with the multi-exponential function, ${\stackrel{·}{X}}_e\left(t\right)$. The ground deposition is assumed to have occurred 48 hours after detonation. The data labelled X_p and X_e refer to the exposures calculated with the power and multi-exponential functions, respectively.

In summary, the use of the multi-exponential model for the decay of the complex mixture of radionuclides in fallout appears justified and superior to using a t^X–1.2 model because it is shown to closely simulate the measured variation of the exposure rate with time for most tests. Also, the multi-exponential model can be easily modified if the construction of the device leads to substantially different exposure rates, as was the case for the Trinity test, which resulted in a much higher production of ²³⁹Np than other tests (Beck et al. 2022). For that reason, the multi-exponential description of the exposure rate is recommended in the methods presented here.

Relative contributions of specific radionuclides to the exposure

Even though the calculation of exposure does not involve knowledge of the activities of specific radionuclides deposited on the ground, it is interesting to note how the more important contributors to the exposure rate change from a time interval after detonation to another, due in part to their radioactive half-lives. The criterion used for the selection of the radionuclides is that they contribute, in the time interval under consideration, more than 1% to the exposure from TOA to 70 y after deposition on the ground. Four values of TOA were considered (1, 3, 6, and 12 h), along with 6 time intervals of exposure (TOA to 1 d, 1 to 10 d, 10 d to 1 mo, 1 mo to 1 y, 1 to 70 y, and TOA to 70 y). The radionuclides that met the criterion are presented in Table C1 for a typical test, Tesla, and a degree of fractionation R/V equal to 0.5. The selected radionuclides are, where appropriate, listed as parent-progeny pairs (e.g., ¹³²Te-I) or as chains (e.g., the ¹³¹I chain, which consists of ¹³¹Sb, ^131mTe, ¹³¹Te, and ¹³¹I):

Table C1.

Radionuclides contributing more than 1 percent to the exposure from the time of arrival of fallout (TOA, taken to vary from 1 to 12 hours) to 70 years after detonation. The results, given for various time intervals of exposure, apply to a typical test and a degree of fractionation R/V of 0.5.

Time interval of exposure	Radionuclides contributing more than 1% to the exposure from TOA (1 h) to 70 years
TOA (1 h) – 1 d TOA (3 h) – 1 d TOA (6 h) – 1 d TOA (12 h) – 1 d	134Te-I (13%), 135I (6.0%), 133I chaina (4.2%), 142La (3.6%), 105Ru-Rh (3.3%), 97Zr-Nb (3.0%), 131I chainb (2.2%), 132Te-I (2.0%), 91Sr-Y (1.7%), 92Sr-Y (1.6%),104Tc (1.5%), 129Sb (1.5%), 130Sb (1.4%),93Y (1.1%) 135I (6.9%), 134Te-I (5.6%), 97Zr-Nb (3.7%), 105Ru-Rh (3.4%), 133I chaina (3.1%), 132Te-I (2.5%), 142La (2.2%), 91Sr-Y (2.0%), 92Sr-Y (1.6%), 129Sb (1.6%), 93Y (1.2%) 135I (5.8%), 97Zr-Nb (3.7%), 132Te-I (2.6%), 133I chaina (2.6%), 105Ru-Rh (2.4%), 91Sr-Y (1.8%), 93Y (1.1%), 129Sb (1.1%) 135I (3.0%), 97Zr-Nb (2.5%), 132Te-I (2.0%), 133I chaina (1.7%), 105Ru-Rh (1.2%), 91Sr-Y (1.1%)
1 d – 10 d	TOA = 1 h: 132Te-I (7.9%), 140Ba-La (3.2%), 133I chaina (2.1%), 97Zr-Nb (2.5%), 131I chainb (1.2%), 135I (1.0%). TOA = 12 h: 132Te-I (16%), 140Ba-La (6.3%), 133I chaina (4.1%), 97Zr-Nb (5.0%), 131I chainb (2.4%), 135I (2.0%), 91Sr-Y (1.4%), 105Ru-Rh (1.1%).
10 d – 1 mo	TOA = 1 h: 140Ba-La (4.5%), 132Te-I (1.7%). TOA = 12 h: 140Ba-La (8.9%), 132Te-I (3.5%), 103Ru-Rh (1.5%), 131I chainb (1.2%).
1 mo – 1 y	TOA = 1 h: 140Ba-La (2.9%), 95Zr-Nb (2.6%), 103Ru-Rh (1.9%). TOA = 12 h: 140Ba-La (5.8%), 95Zr-Nb (5.2%), 103Ru-Rh (3.8%), 91Sr-Y (1.7%).
1 y – 70 y	TOA = 1 h: 137Cs–Ba (2.0%). TOA = 12 h: 137Cs–Ba (4.1%).
TOA (1 h) – 70 y	134Te-I (13%), 132Te-I (12%), 140Ba-La (11%), 135I (7.0%), 133I chaina (6.3%), 97Zr-Nb (5.5%), 131I chainb (4.2%), 105Ru-Rh (3.9%), 95Zr-Nb (3.8%), 142La (3.6%), 91Sr-Y (3.5%), 103Ru-Rh (3.1%), 137Cs–Ba (2.1%), 92Sr-Y (1.7%), 104Tc (1.5%), 129Sb (1.5%), 93Y (1.5%), 130Sb (1.4%).
TOA (12 h)–70 y	132Te-I (21%), 140Ba-La (21%), 95Zr-Nb (7.6%), 97Zr-Nb (7.5%),103Ru-Rh (6.2%), 133I chaina (5.9%), 135I (5.1%), 91Sr-Y (4.8%), 131I chainb (4.3%), 137Cs–Ba (4.2%), 105Ru-Rh (2.3%), 106Ru (1.8%), 93Y (1.5%)

^aThe ¹³³I chain consists of ^133mTe, ¹³³Te, and ¹³³I.

^bThe ¹³¹I chain consists of ¹³¹Sb, ^131mTe, ¹³¹Te, and ¹³¹I.

• For the time interval of exposure from TOA = 1 h to 1 d, there are 14 radionuclides, including 6 pairs and 2 chains, that contribute more than 1% of a continuous exposure from 1 h to 70 y. These radionuclides have half-lives ranging from 18 min (¹⁰⁴Tc) to 3.2 d (¹³²Te), several of them with half-lives shorter than 1 h, including the ¹³⁴Te-I pair, which dominates the exposure in the time interval from TOA = 1 h to 1 d after detonation;

• When TOA increases from 1 to 12 h in the time interval of exposure from TOA = 1 h to 1 d, the radionuclides with short half-lives of less than a few hours gradually disappear from the selected list, as shown in Table C1. The radionuclide contributing most to the exposure from TOA to 1 d, with TOA = 3, 6, or 12 h, is ¹³⁵I, with a half-life of 6.6 h;

• In the following time interval of exposure, from 1 d to 10 d, the ¹³²Te-I pair, followed by the ¹⁴⁰Ba-La pair become the leading contributors to the exposure from TOA to 70 y;

• For the time intervals of exposure from 10 d to 1 mo and from 1 mo to 1 y, the ¹⁴⁰Ba-La pair contributes the most to the exposure from TOA to 70 y, while for times longer than one year, only ¹³⁷Cs-Ba contributes more than 1% to the continuous exposure from TOA to 70 y after detonation; and

• When the time interval of exposure is considered to be continuous from TOA to 70 y after detonation, the number of selected radionuclides is 18 when TOA is assumed to be 1 h after detonation with ¹³⁴Te-I as the leading contributor, and 13 for a TOA of 12 h, with ¹³²Te-I and ¹⁴⁰Ba-La as the leading contributors, as shown in Table C1. In both cases, the added exposures due to the selected radionuclides amount to about 80% of the total exposure, meaning that the more than about 150 other radionuclides also produced by the nuclear explosion contribute only about 20% to the total exposure.

It is important to note that the values presented in Table C1 for R/V = 0.5 could be substantially different for other values of R/V. For example, 12 h after the time of detonation (H + 12 h), the contributions of volatile radionuclides (e.g., ¹³¹I or ¹³⁷Cs) to the exposure rate would be about 2–3 times smaller at locations where R/V = 3 than at locations where R/V = 0.5, whereas the contributions of refractory radionuclides, such as ⁹⁵Zr would be 2–3 times greater. However, as noted previously, the value of the overall exposure rate is relatively insensitive to the degree of fractionation.

A similar exercise was carried out by Simon et al. (2020) for the Trinity test. The results are in good agreement, taking into account that the exposure from ²³⁹Np was much larger for Trinity than for Tesla and that some of the radionuclides with short half-lives were not taken into consideration in the Trinity exercise.

Influence of weathering on the exposure

Following deposition of radioactive material on the ground and other surfaces, the exposure rate above the surface declines not only because of radioactive decay but also because of natural weathering processes, due mainly to precipitation that results in downward migration of the radionuclides into the soil column.

The assumption made in the model used for the initial assessment is that the exposure rates apply to a large plane surface uniformly contaminated that remains undisturbed for 70 y and that the concentration in soil, C(z), decreases with depth z as:

where the relaxation length alpha is the depth where the concentration in soil is equal to the concentration at the ground surface divided by e. In the initial assessment, the relaxation length is taken to be 0.1 cm (Hicks 1981) to account for ground roughness and is assumed not to vary with time after deposition, implying that weathering is ignored. The model used in the improved assessment is the same as that used for the initial assessment, with the difference that alpha is taken to vary with time after deposition, in order to take natural weathering processes due primarily to rain under consideration.

Because the annual rainfall varies significantly from site to site, sets of estimates of weathering vs. time have been developed for three different climate types: DRY, for arid areas (average annual precipitation < 57 cm), WET (average annual precipitation > 120 cm), and MODERATE (average annual precipitation 57–120 cm):

• First, the time after deposition needed for the relaxation length to be reduced from Hicks’s default value (alpha = 0.1 cm) to 1 cm, 3 cm, and 10 cm was subjectively estimated for each type of climate. Based on Beck (1980), these relaxation lengths of 1 cm, 3 cm, and 10 cm correspond to average ratios of exposure rate to the initial distribution (alpha = 0.1 cm) of 0.66, 0.47, and 0.25, respectively. The results, shown in Table C2, indicate that the times needed to reach the exposure rates corresponding to the considered values of the relaxation length are substantially different for the three assumed climate types. The estimated times are generally consistent with observed depth profiles in the vicinity of nuclear test sites at various times after detonation (30 y for a relaxation length of 3–4 cm in the arid region around Semipalatinsk in Kazakhstan; 6 mo and 20 y for relaxation lengths of 3 cm and 4–5 cm, respectively, in the temperate climate of the Nevada Test Site; and 3 y for a relaxation length of 10 cm in the wet climate of the Marshall Islands);

• In a second step, the estimates of reduction in exposure rate at specific times for each climate type were then interpolated to obtain smooth curves representing the estimated reduction in exposure rate at intermediate times (Fig. C5); and

• The final step consisted in fitting the results to a 10-term multi-exponential function of the form: $\stackrel{·}{X}\left(t,\mathit{cl}\right)=\stackrel{·}{X(}12)x\sum _{i=1}^{i=10}{a}_i\left(\mathit{cl}\right)x\mathrm{EXP}\left(L_i\left(\mathit{cl}\right)xt\right)$, where cl is an index representing the climate type. The selected values for a_i(cl) and L_i(cl) are presented in Table 5 of the main text. The variations of the exposure rate and of the exposure for the three climate types are compared to the values that would be obtained in the absence of weathering in Figs. C6 and C7, respectively; in these examples, the fallout time-of-arrival is assumed to be 1 h after the time of detonation. The exposure rates are normalized to 1 mR h⁻¹ at H + 12 h.

Table C2.

Estimated times after ground deposition needed to obtain depth profiles with specific relaxation lengths for three climate types.

Relaxation length (cm)	Relative decrease in exposure rate	Time needed to reach the relaxation length for:
		DRY climate	MODERATE climate	WET climate
0.1	1	0	0	0
1	0.66	1 y	1 mo	10 d
3	0.47	7 y	1 y	3 mo
10	0.25	>50 y	35 y	3.5 y

The variation with time of the exposure rate after detonation, shown in Fig. C6 for TOA equal to 1 h, is very rapid and shows little sensitivity to weathering during the first year after deposition on the ground. Consequently, the values of the first-year exposure with or without weathering are similar, only differing by about 10% (Fig. C7). The lifetime exposure (that is, the exposure rate integrated over 70 y after the detonation) and the exposure to infinity are only slightly greater than the first-year exposure, and the effect of weathering is still small because the exposure rates after one year are mainly due to ¹³⁷Cs, which is by then fixed on the clay content of the soil and is practically not affected by weathering.

Fig. C6.

Estimated variation with time of the exposure rate (mR h⁻¹) for the three climate types and for a situation when no weathering is assumed to occur. The time-of-arrival of fallout is assumed to be 1 h after the detonation. The exposure rates are normalized to 1 mR h⁻¹ at H + 12 h.

Fig. C7.

Estimated variation with time of the exposure (mR) for the three climate types and for a situation when no weathering is assumed to occur. The time-of-arrival of fallout is assumed to be 1 h after the detonation. The exposure rates are normalized to 1 mR h⁻¹ at H + 12 h.

As TOA increases from 1 to 48 h, which is the range of TOA values that is considered in this study, the lifetime exposure decreases by a factor of up to 5 (Table C3). In comparison, the influence of the weathering is much less important. For any of the TOA values under consideration, the exposure during the first year after the detonation represents at least 90% of the lifetime exposure without considering any weathering. Similar results were obtained by Simon et al. (1995).

Table C3.

Variation of the exposure (mR) with increasing TOA (h) and influence of the weathering effect. The exposure rate at H + 12 is normalized at 1 mR h⁻¹ and the relative degree of fractionation is assumed to be 0.5.

		Exposure (mR) from TOA to:
	Condition	1 wk	1 mo	1 y	70 y	Infinity
TOA = 1 h	No weathering	81	93	101	105	106
TOA = 1 h	Dry climate	81	92	98	100	100
TOA = 1 h	Moderate	80	89	93	94	95
TOA = 1 h	Wet climate	78	85	89	90	90
TOA = 2 h	No weathering	59	71	79	82	83
TOA = 2 h	Dry climate	58	69	76	77	77
TOA = 2 h	Moderate	57	66	71	72	72
TOA = 2 h	Wet climate	55	62	66	67	67
TOA = 4 h	No weathering	43	55	63	66	67
TOA = 4 h	Dry climate	42	53	60	61	62
TOA = 4 h	Moderate	41	50	55	56	56
TOA = 4 h	Wet climate	39	47	50	51	51
TOA = 12 h	No weathering	27	39	48	51	52
TOA = 12 h	Dry climate	27	38	44	46	46
TOA = 12 h	Moderate	26	35	40	41	41
TOA = 12 h	Wet climate	24	31	35	36	36
TOA = 48 h	No weathering	12	24	32	36	37
TOA = 48 h	Dry climate	12	23	29	31	31
TOA = 48 h	Moderate	11	20	25	26	26
TOA = 48 h	Wet climate	9	17	21	21	22

Fallout in urban areas

The model described by eqn (C1), which is used for the initial and the improved dose assessments, provides an adequate basis for the estimation of the exposure rate over undisturbed soil, but it overestimates the exposure rate if it is applied to cultivated land. Also, large uncertainties arise if the model is used to estimate the exposures in urban areas where most of the population would likely be located. Significant overestimation of the exposure could occur depending on, among other factors, the levels of deposition on urban surfaces compared with soils having various levels of vegetative cover and whether radionuclides deposited on urban surfaces are more rapidly removed (or retained) in comparison with deposition on soils (Kelly 1987).

Radionuclides deposited on soil will migrate downward from the surface by natural processes or become more rapidly transferred down the soil column as a consequence of cultivation. The activity deposited on less permeable surfaces, which are commonly found in urban areas (roads, pavements, buildings, etc.) may become physically fixed or may be more rapidly removed by wash-off or weathering-type processes (Andersson et al. 2003; Kelly 1987; Yu et al. 2009). In addition, deliberate decontamination, which is not considered in this paper, will result in further reduction to the exposure rate (Thiessen et al. 2009a).

APPENDIX D: CONVERSION FROM EXPOSURE TO ORGAN DOSE, K(I, m)

The conversion from exposure to organ dose depends on several parameters, as described in detail in NCRP Report No. 158 (NCRP 2007). Table D1 illustrates that the conversion to organ dose from air kerma (ICRP 2010) varies slightly with organ for adults. It also depends on the energy of the incident photons (averaging about 0.5 MeV for fallout), but only slightly (as shown). More importantly, the conversion is very sensitive to the angular incidence of the radiation, as indicated in Table D1 for the two irradiation geometries that are considered (isotropic and rotational). The angular incidence (for a standing individual) would tend to be closer to rotational at early times when the fallout is near the surface of the ground and would tend to be more isotropic as the fallout ages and weathers.

The organ and effective dose rates from radionuclides deposited on the ground, with a soil cover of 0.3 cm to account for ground roughness, were calculated by Bellamy et al. (2019) for standing individuals of various ages. Results for effective dose rate, normalized to the adult dose rate, are presented in Table D2 for exposure to ¹³⁷Cs-^137mBa. With decreasing age, the effective dose rate increases, up by 35% for newborns.

Table D1.

Variation of the conversion coefficient from air kerma to dose for selected organs of a representative adult and gamma energies of 0.5 and 0.6 MeV. Effective doses are presented for comparison purposes.

Organ	Energy (MeV)	Dose/air kerma (ISOa)	Dose/air kerma (ROTb)	Dose/air kerma (FALLOUTc)	Organ/Effective (FALLOUTc)
RBM	0.5	0.652	0.784	0.74	0.96
	0.6	0.660	0.785	0.74	0.96
Thyroid	0.5	0.717	0.892	0.83	1.09
	0.6	0.719	0.888	0.83	1.08
Lung	0.5	0.680	0.785	0.75	0.98
	0.6	0.691	0.791	0.76	0.99
Effective	0.5	0.684	0.807	0.77
	0.6	0.692	0.810	0.77

^aISO = isotropic geometry of irradiation.

^bROT = rotational geometry of irradiation.

^cFALLOUT = combination of 1/3 isotropic and 2/3 rotational geometries of irradiation.

Table D2.

Variation of the effective dose rate, normalized to the dose rate to adults, as a function of age, for exposure to ¹³⁷Cs-^137mBa (Bellamy et al. 2019).

Newborn	1-y-old	5-y-old	10-y-old	15-y-old	Adult
1.35	1.24	1.16	1.11	1.02	1.00

Table D3.

Variation of the external dose rate, normalized to the effective dose rate, for all radiosensitive organs and tissues (ICRP 2007), for exposure to ¹³⁷Cs-^137mBa (Bellamy et al. 2019).

Organ or tissue	Adult	Newborn
Active marrow	1.00	0.98
Adrenals	0.90	0.93
Bone surface	1.17	1.11
Brain	1.02	0.94
Breast	1.07	1.03
Colon	0.96	0.97
Esophagus	0.92	0.97
Extrathoracic region	1.01	0.96
Gall bladder	0.80	0.93
Heart	0.92	0.96
Kidneys	0.92	1.02
Liver	0.94	1.03
Lung	1.01	0.96
Lymph	1.04	0.99
Muscle	1.04	0.99
Oral mucosa	1.01	0.95
Ovaries	0.91	0.92
Pancreas	0.80	0.88
Prostate	0.85	0.99
Salivary glands	1.05	0.93
Skin	3.59	2.93
Small intestine	0.92	0.95
Spleen	0.92	0.96
Stomach	0.91	0.93
Testes	0.98	1.03
Thymus	0.91	0.99
Thyroid	0.97	1.06
Urinary bladder	0.96	1.00
Uterus	0.88	1.01

The variation of the external dose according to organ or tissue is illustrated in Table D3 for all radiosensitive organs and tissues considered by ICRP (2007) and two age categories, namely newborn and adults. In that Table, the results are expressed in the form of ratios of organ or tissue to effective dose rate and are presented taking exposure to ¹³⁷Cs-^137mBa as an example (Bellamy et al. 2019). For most organs and tissues, the ratios are between 0.9 and 1.11, the exceptions being skin and pancreas, for both newborn and adults, and gall bladder, bone surface, and prostate for adults.

APPENDIX E: INDOOR AND OUTDOOR LOCATION FACTORS FOR GAMMA RAYS FROM FALLOUT

As indicated in eqn (2), the location factor, LF, is defined as the ratio of the exposure rate at the specific location where the representative individual I is assumed to be, either indoors or outdoors, and of the reference exposure rate at a height of 1 m above ground uniformly contaminated to an essentially infinite area. The depth profile used to calculate the reference exposure rate may vary from one publication to another and is sometimes not indicated: it could be (1) an infinitely thin plane at the air-ground interface or buried under 3 mm of soil, (2) a time-independent exponential depth profile, (3) a time-dependent calculated depth profile, or (4) a measured exposure rate in a flat undisturbed area in the proximity of the indoor location under consideration.

Review of indoor location factors

The indoor location factor is derived either from measurements or from calculations of gamma-ray attenuation by the building materials used in typical dwellings. Because of the attenuation of gamma rays by building materials and of the distance separating the indoor location from the outdoor contaminated area, the exposure rate indoors is smaller than the reference (outdoor) exposure rate. Estimates of typical indoor location factors that have been reported in the literature are presented in Table E1, which is based on information provided in NCRP Publication 129 (NCRP 1999). The values presented in Table E1 correspond to high-energy gamma rays (0.5–0.7 MeV) of fallout from nuclear weapons tests or from the Chernobyl accident. As indicated in NCRP (1999), the shielding offered by dwellings varies widely depending on the type of construction, the height above ground, and other factors. Studies from areas affected by fallout from nuclear weapons tests or with radioactive deposition from the Chernobyl accident generally indicate that even for lightly constructed housing, the exposure rate from the high-energy gamma emitters is reduced to about 0.4 of the reference (outdoor) value. For more massive buildings, such as apartment houses, the exposure rate indoors can be reduced to less than 0.01 of the reference exposure rate.

The Chernobyl accident provided the opportunity to carry out numerous studies of indoor location factors in urban areas. Some of the estimates are derived from measurements (e.g., Golikov et al. 2002), but most are based on models of dwellings found in semi-urban and urban areas, such as prefabricated houses, rows of terraced houses, blocks of apartments, etc. (Catsaros and Vassiliou 1987; Crick et al. 1987; Meckbach et al. 1988; Meckbach and Jacob 1988). More recently, national and international organizations have expanded research on the estimation of doses from external irradiation in urban areas arising from a nuclear radiation accident or a terrorism event involving nuclear devices and on the evaluation of possible countermeasures (Andersson et al. 2008; Nisbet and Watson 2015; Thiessen et al. 2009a and b). Although these studies are not designed for the assessment of location factors, they provide useful information on the estimation of doses from external irradiation as a function of the type of dwelling and of the energy of the gamma radiation.

In the estimation of the location factor, it is generally assumed that the indoor location is devoid of contamination. In fact, some of the fallout activity may penetrate into the buildings during the passage of the radioactive cloud through openings (Steinhäusler 1987) or by filtration (Roed and Cannell 1987; Christensen and Mustonen 1987), or after ground deposition by mechanical transport on footwear (Cannell et al. 1987), but the effect of the indoor contamination on the location factor is expected to be minimal (NCRP 1999).

Review of outdoor location factors

The outdoor location factors related to fallout from nuclear weapons tests have been usually taken to be equal to 1, even though the reference sites are preferably chosen (McArthur and Miller 1989) to be flat, open, grassy areas at least 40 feet across that are not close to buildings, or natural obstructions that could affect fallout deposition, and they are not higher or lower than the surrounding ground in order to minimize runoff or pooling of fallout. Also, the reference sites should have been undisturbed since the time of deposition in order to preserve the vertical profile of the deposited activity. This selection process implies that there could be a significant temporal and spatial variation of the exposure rate due to fallout, even in a limited area, and therefore, that there is a spatial and temporal variation in the outdoor location factor. It was also suspected that fallout in forest could be higher than on a grassy field by a factor of about 2, because the presence of trees may increase the importance of impaction (Krey et al. 1973); however, impaction is likely to be important only in areas relatively far away from the detonation site. In close-in areas, the aerosol particle sizes are greater than 50 μm, so that gravitational sedimentation is the dominant process involved in the ground deposition of fallout and there would be little difference in fallout deposition between a forest and a grassy field. Little attention has been paid to the estimation of the outdoor location factors in the assessment of doses related to fallout from nuclear weapons tests, although numerical values were available in the 1970s, for example in Burson and Profio (1977).

Following the Chernobyl accident, substantial research was carried out to characterize the outdoor location factors and its variation according to the type of surface and as a function of time after deposition, both in rural and in urban areas. In rural areas of Ukraine, measured outdoor location factors averaged over a period from 2 to 42 mo after the accident are about 0.5 (Likhtariov et al. 1996), as presented in Table E2, in good agreement with the results presented in Fig. C5 for activity deposited after a nuclear weapons test. In Bavaria, the outdoor location factors measured at various times over a period of 2 to 36 mo after the accident in rural and urban areas of Bavaria (Table E3) do not show a variation of time after deposition in rural areas but a substantial decline in urban areas (Likhtariov et al. 1996), implying that the weathering of radioactive material is faster in urban areas than in rural areas. Estimates of outdoor location factors in urban areas based on models simulating a range of environmental conditions (Table E4) indicate that, in vegetated areas, the outdoor location factor could range up to 1.5 shortly after dry deposition due to the presence of trees and be lower by a factor of about 2 a year after deposition, when the deciduous trees have lost their foliage; in case of wet deposition, the outdoor location factors are estimated to be smaller shortly after deposition and similar to the values calculated for dry deposition 1 y after the accident; in urban areas without vegetation, the estimated outdoor location factors are smaller than those calculated for vegetated areas for dry and wet deposition and for any time within 1 y after the accident (Meckbach and Jacob 1988).

Fig. C5.

Estimated reductions in the exposure rate, relative to the exposure rate obtained in the absence of weathering, as a function of time after ground deposition, for the three climate types.

Table E1.

Literature survey of estimated indoor location factors (based on NCRP 1999).

Type	Location factor	Method	Reference
Typical dwellings	0.05–0.2	Calculations (0.5 MeV)	Le Grand et al. 1987, 1990
Worst case	0.35	Calculations (0.5 MeV)	Le Grand et al. 1987, 1990
Cars, buses	0.02–0.3	Calculations	Catsaros and Vassiliou, 1987
Semi-detached house	0.07–0.15	Calculations	Jacob and Meckbach 1987
Prefabricated house	0.3–0.5	Calculations	Jacob and Meckbach 1987
Terraced house	0.02–0.05	Calculations	Jacob and Meckbach 1987
Multi-story house block	0.0007–0.005	Calculations	Jacob and Meckbach 1987 Jacob and Meckbach 1987
Wood frame house	0.23–0.43	Measurements	Burson and Profio 1977
Lightly constructed houses	0.4 (value recommended)	Measurements	Burson and Profio 1977
Heavily constructed houses	0.2 (value recommended)	Measurements	Burson and Profio 1977
Large concrete office building	0.001–0.07	Measurements	Burson and Profio 1977
Cars	0.2–0.5	Literature review	Burson and Profio 1977
Two-story house	0.25	Chernobyl measurements	Steinhäusler 1987
Wooden house	0.13 ± 0.06	Chernobyl measurements	Likhtariov et al. 1996
Brick house	0.07 ± 0.06	Chernobyl measurements	Likhtariov et al. 1996
Wooden houses (rural)	0.13 ± 0.05	Chernobyl measurements	Golikov et al. 2002
Brick houses (rural)	0.07 ± 0.04	Chernobyl measurements	Golikov et al. 2002
Multi-story houses (rural)	0.02 ± 0.02	Chernobyl measurements	Golikov et al. 2002
Residences	0.33 (0.02-0.6)	Literature review	Kennedy and Strenge 1993
Average value	0.2	Literature review	UNSCEAR 1982
Average value (range)	0.2 (0.001–0.5)	Literature review	NCRP 1993

Table E2.

Outdoor location factors for rural environments in Ukraine, derived from measurements of ¹³⁷Cs between 2 and 42 mo after the Chernobyl accident (Likhtariov et al. 1996).

Site	Location factor
Place of residence:
Yard	0.42 ± 0.18
Vegetable garden	0.42 ± 0.16
Fruit garden	0.57 ± 0.22
Place of education:
Kindergarten	0.42 ± 0.18
School	0.49 ± 0.16
Street	0.50 ± 0.26

Table E3.

Measured outdoor location factors in rural and in urban environments in Bavaria (Likhtariov et al. 1996).

	Time after deposition (mo)
Site	2	12	24	36
Rural environment:
Parks, grassland	0.85 ± 0.08	0.85 ± 0.08	0.85 ± 0.08	0.85 ± 0.08
Predominantly unpaved areas	0.70 ± 0.11	0.68 ± 0.14	0.72 ± 0.17	0.71 ± 0.17
Urban environment:
Predominantly unpaved areas	0.41 ± 0.06	0.36 ± 0.14	0.32 ± 0.15	0.28 ± 0.12
Paved areas	0.29 ± 0.12	0.16 ± 0.04	0.11 ± 0.04	0.09 ± 0.02

Table E4.

Calculated outdoor location factors for urban environments, shortly after deposition and one year after deposition, for vegetated and non-vegetated areas, and for a source energy of 0.66 MeV (Meckbach and Jacob 1988).

	Outdoor location factor
	Vegetated areas	Non-vegetated areas
Dry deposition
- Shortly after deposition	0.6 – 1.5	0.1
- One year after deposition	0.3 – 0.8	0.1
Wet deposition
- Shortly after deposition	0.5 – 0.7	0.3
- One year after deposition	0.3 – 0.7	0.1

APPENDIX F: ESTIMATES OF OCCUPANCY FACTORS (TIME SPENT INDOORS, OUTDOORS, AND IN VEHICLES)

Occupancy factors vary according to a large number of factors, including age, gender, ethnicity, climate, time of day, day of week, time of year, health status, economic status, type of work, and personal habits. Occupancy factors derived from dietary recalls or interviews for US and Russian populations are listed in Table F1, which also includes estimated global averages. On average, people spend most of their time indoors, and the time spent indoors at home is greater than the time spent indoors elsewhere by a factor of 2 to 3.

In the US, the US Environmental Protection Agency (EPA) has compiled information on the activity patterns of the population according to age, location, season, etc. (US EPA 2011). The variation of the occupancy factor according to age is presented in Table F2 for the US population. The fraction of time spent indoors at home decreases with increasing age, while the fraction of time spent away from home increases, so that the total fraction of time spent indoors decreases only slightly with age. The rest of the time is shared about equally between the time spent outdoors and the time spent in vehicles.

A comparison of the fraction of time spent in different locations according to sex is presented in Table F3 for adults aged 18 to 64 in the entire US population and for the population of California. On the whole, the differences in the indoor occupancy factors between the entire country and the state of California are small. It is, however, clear that women spend more time at home, and less time away from home, than men.

Table F1.

Estimates of occupancy factors.

Population	Indoors at home	Indoors elsewhere	Indoors (total)	Outdoors	In vehicle	Reference
	USA
USA (>11y old)			0.89	0.05	0.06	USEPA 2011
California (>11 y old)	0.62	0.25	0.87	0.06	0.07	Jenkins et al. 1992
USA (<12 y old)	0.61	0.19	0.80	0.15	0.05	Cohen Hubal et al. 2000
	Russia, rural
Indoor workers	0.49	0.26	0.75	0.25	X–	Golikov et al. 2002
Outdoor workers	0.47	0.16	0.63	0.37	X–	Golikov et al. 2002
Pensioners	0.68	0.0	0.68	0.32	X–	Golikov et al. 2002
Schoolchildren	0.58	0.16	0.74	0.26	X–	Golikov et al. 2002
Pre-school children	0.52	0.34	0.86	0.14	X–	Golikov et al. 2002
	World average
World			0.8	0.2			UNSCEAR 1982

Table F2.

Recommended mean age-dependent occupancy factors for the US population (based on US EPA 2011).

Age group, in years	Indoors (total)	Indoors at residence	Indoors elsewhere	Outdoors	In vehicle
Birth to <1	0.94	0.77	0.17	0.03	0.03a
1 to <2	0.94	0.74	0.20	0.03	0.03a
2 to <3	0.91	0.68	0.23	0.05	0.04a
3 to <6	0.89	0.66	0.23	0.07	0.04a
6 to <11	0.86	0.62	0.24	0.09	0.05a
11 to <16	0.87	0.62	0.25	0.07	0.06a
16 to <21	0.87	0.58	0.29	0.07	0.06a
18 to <65	0.80	0.66	0.14	0.09	0.11b
≥65	0.79	X–	X–	0.10	0.11b

^aIncludes time spent in activities that could not be assigned to indoor or outdoor locations.

^bAssumed to be equal to the “Time Outdoors away from Residence.”

Table F3.

Mean fractions of time spent indoors, including on travel, by adult men and women (aged 18 to 64) of California and of the entire US (based on US EPA 2011).

	California study (1987-1988)		National study (1985)
	Men	Women	Men	Women
At home	0.57	0.67	0.62	0.71
Away from home	0.34	0.26	0.31	0.23
Travel	0.09	0.07	0.07	0.06

APPENDIX G: EXAMPLE OF APPLICATION OF THE PROPOSED METHODS

The purpose of this Appendix is to describe how the proposed methods of estimation of the dose from external irradiation would be applied. In this example, the absorbed dose from external irradiation received during the year following detonation is calculated to the thyroid of a representative adult residing in a rural area. Both the initial and the improved dose assessments are considered. The input data selected in a companion paper (Beck et al. 2022) are also used in this Appendix.

It is recognized that the thyroid dose from internal irradiation may exceed, in many situations, the thyroid dose from external irradiation. In this paper, only the dose from external irradiation is considered; examples of application of the methodology to estimate the thyroid dose from internal irradiation can be found in a companion paper (Anspaugh et al. 2022).

Initial dose assessment

Input data

• Reference outdoor exposure rate, $\stackrel{·}{X}$(12, P), in mR h⁻¹, at H + 12 h after detonation at the location P of the representative adult, I; $\stackrel{·}{X}$(12, P), is taken to be 330 mR h⁻¹; and

• Time of arrival of fallout TOA, in hours, at the location of the representative adult; TOA is taken to be 2 h after detonation.

Equation used to calculate the dose

The equation used to calculate the dose from external irradiation, in mGy, is:

Calculation of IF(TOA, TC)

IF(TOA, TC) is the integral from TOA to TC (8,760 h = 1 y) of the outdoor exposure rate, normalized to an exposure rate of 1 mR h⁻¹ at H + 12 h, obtained as:

Using the default values of a_i and of L_i presented in Table 1, IF(TOA, TC) is equal to 78.0 mR per mR h⁻¹ 12 hours after the time of detonation (H + 12 h) (Table 3).

Estimation of K(I)

The conversion coefficient from exposure to dose, K(I), is estimated to be 6.6 × 10⁻³ mGy mR⁻¹ for adults (Table 2) and to have the same value for any organ or tissue m of the body, including the thyroid.

Calculation of BF

Assuming that the representative individual does not change location or habits between TOA and TC, the behavioral factor, BF, is calculated as:

where:

• LF_out and LF_in are the location factors for outdoors and indoors in rural areas, taken to be equal to 1 and 0.2, respectively; and

• FT_out and FT_in are the fractions of time spent outdoors and indoors in rural areas, taken to be equal to 0.2 and 0.8, respectively.

Therefore, BF = (1 × 0.2) + (0.2 × 0.8) = 0.36.

Estimated dose from external irradiation and uncertainty

D(I, P) = 330 (mR h⁻¹ at H + 12 h) × 78.0 (mR per mR h⁻¹ at H + 12 h) × 6.6 × 10⁻³ (mGy mR⁻¹) × 0.36 = 61 mGy.

As indicated in the main text, the probability distribution of the thyroid dose estimates is assumed to be lognormal. The overall uncertainty in the initial dose estimate is associated with a geometric standard deviation of 2.4.

Improved dose assessment

The main difference between the initial and the improved dose assessments is that information obtained on the characteristics of the detonation, the environment, and the lifestyle of individuals in the population are taken into consideration in the improved assessment. It is shown in the main text that the major improvement is related to the knowledge of the type of residence and of the whereabouts of the representative or identified individuals that are considered. In order to facilitate the comparison of the two dose assessments and of their uncertainties in the dose estimates, eqn (6), already used for the initial dose assessment, will also be used for the improved dose assessment. This results in a simplification of the improved dose assessment.

Input data

• Reference outdoor exposure rate, $\stackrel{·}{X}$(12, P), in mR h⁻¹, at H + 12 h after detonation at the location P of the representative adult, I; $\stackrel{·}{X}$(12, P), is taken to be 330 mR h⁻¹;

• Time of arrival of fallout, TOA, in hours, at the location of the representative adult; TOA is taken to be 2 hours after detonation;

• Information on the type of residence of the representative adult, resulting in an outdoor location factor, LF_out, of 0.6, and in an indoor location factor, LF_in, of 0.1; and

• Information on the whereabouts of the representative adult, resulting in an outdoor occupancy factor, FT_out, of 0.07, and in an indoor occupancy factor, FT_in, of 0.93.

Equation used to calculate the dose

The equation used to calculate the dose from external irradiation, in mGy, is:

Calculation of IF(TOA, TC)

Even though the calculation of the time integral of the normalized exposure rate takes into account the type of climate and the associated weathering, the value of IF(TOA, TC) over the first year after detonation is relatively insensitive to the type of climate, as the difference in the first-year integral between dry and wet climates is only about 10%. For the purposes of this exercise, the value of IF(TOA, TC) used for the initial dose assessment (78.0 mR per mR h⁻¹ at H + 12 h) is also used for the improved dose assessment.

Estimation of K(I)

The conversion coefficient from exposure to dose, K(I), is estimated to be 6.6 × 10⁻³ mGy mR⁻¹ for adults and to have approximately the same value for almost all organs or tissues m of the body, including the thyroid (Table D3).

Calculation of BF

Assuming that the representative individual does not change location or habits between TOA and TC, the behavioral factor, BF, is calculated as:

where:

• LF_out and LF_in are the location factors for outdoors and indoors in rural areas, taken to be equal to 0.6 and 0.1, respectively, in the improved dose assessment for populations in rural areas (Table 7). Those values are substantially lower than those that were selected for the initial dose assessment (1 and 0.2, respectively). In addition, no consideration is taken for time planned outside of the area, for example for vacation or business reasons, where the reference outdoor exposure rate could be different from 330 mR h⁻¹; and

• FT_out and FT_in are the fractions of time spent outdoors and indoors in rural areas, taken to be equal to 0.07 and 0.93, respectively, in the improved dose assessment for populations in rural areas (Table 7). Those values are substantially different from those that were selected for the initial dose assessment, that is, 0.2 and 0.8, respectively.

Therefore, BF = (0.6 × 0.07) + (0.1 × 0.93) = 0.14.

Estimated dose from external irradiation and uncertainty

D(I, P) = 330 (mR h⁻¹ at H + 12 h) × 78.0 (mR per mR h⁻¹ at H + 12 h) × 6.6 × 10⁻³ (mGy mR⁻¹) × 0.14 = 24 mGy.

As indicated in the main text, the probability distribution of the thyroid dose estimates is assumed to be lognormal. The overall uncertainty in the dose estimate is associated with a geometric standard deviation of 1.5.