IONIZING RADIATION:
SOURCES AND BIOLOGICALEFFECTS
United Nations Scientific Committee
on the Effects of Atomic Radiation
1982 Report to the General Assembly, with annexes

UNITED NATIONSNew York, 1982

NOTE
The report of the Committee without its annexes appears as Official Records of the General Assembly, Thirtyseventh Session, Supplement No. 45 (A/37/45).
The designations employed and the presentation of material in this publication do not imply the expression of
any opinion whatsoever on the part oft he Secretariat of the United Nations concerning the legal status of any country,
territory. city or area, or of its authorities, or concerning the delimitation of its frontiers or boundaries.

UNITED NATIONS PUBLICATION
Sales No. E.82.IX.806300P

Scientific Annexes

ANNEX A

Dose assessment models

CONTENTSParagraphs!NTRODUCTJON ....................... .

Paragraphs2.

Direct inhalation from thecloud ..................... .
Direct inhalation from resuspended material ............ .
Population distribution models

106-109110-113

V. TERRESTRIAL MODELS ........... .

114-138

1-9

3.
I. THE PURPOSE OF DOSE ASSESSl\1ENTS ........................... .
IndMdual-related assessments ..... .
Source-related assessments ........ .

10-13
10-12
13

II. DOSIMETRIC MODELS ............ .

14-56

A.
B.

A.

Indh'idual-related assessments ..... .

23-44

External irradiation ......... .
Internal irradiation ......... .

23-28

Source-related assessments ........ .

45-56

1.

2.
B.

4.

A.
B.

C.

29-44

VI. AQUATIC MODELS ................ .
A.

III. ENVIRONMENTAL MODELS ...... .
A.
B.

General ....................... .
Uncertainty of predictions frommodels ........................ .

57-78
57-69
70-78

External irradiation from depositedradionuclides ..........•....•.••.
Dietary transfer models and dose calculations .•............•.......•.
Models for transport under the
ground surface ...•...............

B.
C.
D.
E.

Isolated water bodies ............. .
Rivers ......................... .
Seas and oceans ................. .
Global models .................. .
Dose calculation ................ .
1.

2.
IV. ATMOSPHERICTRANSPORTMODELS .......................... .
A.
B.
C.

79-113Models for local and regional transport from a defined point of release ..
Global models .................. .
Dose calculation ................ .
1.
Direct irradiation from the

81-93
94-97
98-113cloud ..................... .

100-103

4.

VII. CONCLUSIONS ................... .

120-128
129-137
138
139-161140-141
142-145
146-150
151-155
156-161
158
159
160
161
162-171
Page

Introduction
As stated in the main text of the UNSCEAR 1977
report [Ul], the Committee reviews data on human
exposure to radiation for several purposes. One
purpose is to assess the levels of exposure to which
individuals are subjected, another is to assess the levelsof exposure to populations resulting from identified
sources of radiation, a third is to provide basic data.
1.

2.

3.

Direct consumption of water ..
Consumption of fish and otheraquatic flora and fauna ...... .
Consumption of agricultural
products .................. .
Other pathways ............ .

104-105

The relationship between the levels of exposure toReferences .............................. .

79

an individual and the probability of induction of ahealth effect which is presumed to result from theexposure is a matter of great complexity. There arecertain effects which occur above some threshold doseand for which the clinical severity is dependent on
dose. These effects have been called "non-stochastic"by the ICRP [12). For another class of effects there
seems to be no evidence of a threshold dose and no
relationship between dose and clinical severity, such as
cancer induction. These effects have been called"stochastic" by the ICRP [12]. At the present state of43knowledge a reasonable presumption is that increased
exposure to radiation carries an increased probabilityof subsequent "stochastic" health effects. Therefore, for
an individual, the level of exposure can give an
indication of the presumed probability of occurrence ofa stochastic health effect. Such indication may be foundbyconsulting
theappropriate
dose-response
relationship for the health effect being considered. This
will be true irrespective of the form of the dose-

response relationship, although the actual response will
depend on other factors including the dose rate. If therelationship is not a simple proportionality, then theoverall probability of occurrence of the health effectbeing considered will he determined by the total doseand cannot strictly be obtained by summing the probabilities corresponding to each component of the dose.
This is illustrated in Figure I which shows two assumed
dose-response relationships for the induction of a parti-

P,
1-

u

w
u..
u..

UJ

..._,
I

<(

w
I

c::

_,

P,-+------------,r

<(

::::)

u

~

<(

P3 - + - - - - - - - - - - r - + - - - - - r

c..
<(

u.

a
>-

...

::;

;ii

P, + - - - - - - - - , - - - - - , , ;

a

C:
c..

p' -+------L------+--------,!----,,--------o,

D,

DOSE
Figure I. Two assumed examples of dose-response relatlonshlps
for the Induction of a particular stochastic health effectcular health effect: one relationship shown by thestraight line A is simple proportionality, the -othershown by the curve 8 is curvilinear, both are without
threshold. Other curves might be postulated withdifferent relationships between dose and response: thetwo curves presented in Figure I are merely examples.
If an individual is exposed to two doses D1 and D2 suchthat D1 + D2 = D3 and the relationship is given by
curve 8, then PJ will not be equal to the sum of P1 andP2: however. if the relationship is given by curve A, P6
will be equal to the sum of P4 and Ps. Similarly forincremental doses, the incremental probability of ahealth effect corresponding to a small incremental dose
will, for the curvilinear case, depend on the previous
level of dose, whereas for the proportional case it isindependent of other doses.

3. For the situation in which doses are delivered inaddition to a reasonably constant pre-existing dose,such as that from natural radiation, and the additionaldoses are not large in comparison with the pre-existing
dose, it is reasonable to approximate the relevant
portion of the curvilinear response by a linear

44

relationship; although in this case the straight line may
not, when extrapolated, pass through the origin. If thisapproximation is made then small additional doses canbe treated independently of the pre-existing dose and ofeach other. This is the basis which underlies the use ofrisk factors to relate the incremental probability of ahealth effect to the incremental dose, which are
independent of the absolute level of dose. Clearly thisapproximation may not hold if both large and small
additional doses arc involved, as for example in thecase of an individual who has received a large dose for
medical purposes and is then exposed to smaller doses
from environmental sources.

4. Because the above procedure relies to some extent
on an approximation, the Committee presents its basic
data in terms of absorbed dose in organs or tissues
wherever possible. Other dosimetric quantities which
combine absorbed doses weighted in various ways havebeen developed by ICRP in the context of radiation
protection. Although the purposes of the Committee
are different, it is possible in many cases to use the
ICRP quantities rather than defining new, but simi-

Jar. quantities. To avoid confusion. therefore, the
ICRP quantities have been adopted by the Committee
for use in the appropriate circumstances. These otherdosirnetric quantities contain further assumptions; forexample, dose equivalent includes assumptions as to
the relative risk factors for different types of radiation.
and takes the risk factors as constants for a given
organ; effective dose equivalent introduces further
assumptions as to the relative risk factors for irradiation of different organs or tissues.
5. When assessing exposures to populations. although
in principle these may be expressed as the distributionof individual doses, it is necessary in practice to carryout some procedure such as totalling or averaging toconvey these exposures in a manageable way. If there
are not many individuals in the population who receive
very high doses from medical treatments, and the otherdoses are comparable with or less than the dose fromnatural radiation, then the conditions for the approximation referred to earlier hold and the collective dose
obtained by summing individual incremental doses
from any source can be related to the mathematically
expected number of health effects using the appropriate
constant risk factor. This relationship will holdirrespective of the distribution of individual doses;
indeed in many cases the procedure may be carried out
without knowledge of the individual dose distribution.

6. In a few cases in which individuals are being
considered it may be possible to estimate the levels of
exposure from direct measurements. This is normallythe situation for occupational exposure to external andto some forms of internal irradiation. In most othercases involving exposure to members of the public.
whether considered as individuals or collectively. it will
be necessary to estimate the levels of exposure
indirectly, using models to connect the known ormeasured quantity of activity released or in theenvironment with the level of exposure to humans. The
purpose of this Annex is to collect together and explain
the dosimetric and environmental transport models
used by the Committee in this report.
7. The models used have been separated into twogeneral categories: environmental transport models
which describe the movement of radioactive materials
through all sectors of the environment after theirrelease, and dosimetric models to calculate theabsorbed dose following an intake of radioactive
materials or exposure to external irradiation.
Dosimetric models for intakes obtain the absorbed dosefrom calculations of the residence of radionuclides inthe body after intake. In the later Annexes environmental transport models are used first to assess theradionuclide distributions which then form the input todosimetric models. In this Annex. however, since thequantities involved in the dosimetric models containmany basic ideas and definitions, the order is reversed.
The dosimetric models are presented in chapter II.
followed by the environmental models in chapters I 11
to VI.
8. A specialized model which does not fall into eitherof the above categories is used in Annex H (Occupational exposures). This is based on the observation thatthe distribution of annual occupational doses appears
to be log-normal in a number of cases. Dose distributions on which there are insufficient data for direct
calculations are then analysed using the assumptionthat the distribution is log-normal. Other specialized

models, often tailored to particular irradiation conditions. are used in Annex G (Medical exposures).
9. To introduce some consistency into the use ofsymbols and terms for defined quantities, theCommittee has used the SI system [P4], but additionallybased its terminology in this report on the recommendations of the International Commission on Radiation
Units and "Measurements [19] and of the International
Commission on Radiological Protection [12] whereappropriate. Standard terminology used in areas otherthan radiation dosimetry has been retained where
possible [113]. In some cases, however. it has beennecessary for consistency to use unfamiliar symbols.
For this reason the quantity name. quantity symbol,
unit name and unit symbol for most of the quantities
used in the physical Annexes are given in Tables 1 and
2 of this Annex. Table 1 gives the basic and derived
units for some of the quantities of interest in this report:
Table 2 gives derived units for some other quantities.
along with the quantity and unit symbols. Symbols arealso given in Table 2 for terms used as designators orindices. There are a few terms indicated by multiple
letter symbols that are included because they are
generally recognized acronyms. The symbols used inTable 2 are those selected for use by the Committee inthe physical Annexes (A to H) of this report; some may
be used for different purposes by other bodies. The
biological Annexes (I to L) did not lend themselves tosuch a consistent treatment as the physical ones, since
many references are made to nomenclature introduced
by different authors, which may be inconsistent witheach other. The terms "radioactivity", "activity" and"radioactive material" are often confused and interchanged although they are not synonymous. ''Radioactivity" is the phenomenon of spontaneous decay, while•·activity'' is the number of nuclear transitions per unit
time. Some of the confusion arises because the activityof a sample used to be a measure of the ''quantity" ofthat sample. It was then permissible to refer to the"release of activity", etc. However, with the present
definitions by the ICRU [19], this is no longer correct.
The Committee has therefore tried to avoid the use of"activity" as a synonym for "radioactive material";
some unintentional misuse may have been carried on
because of previous practices.

I.

THE PURPOSE OF DOSE ASSESSMENTSA.

INDIVIDUAL-RELATED ASSESSMENTS

10. The important quantities to assess when considering individuals are the absorbed doses associated with
exposure during a year or over a lifetime. The magnitudes of both these quantities may be used to assess theprobability of harmful consequences to the health ofindividuals exposed to radiation in a given year or overa lifetime.
11. Considerations of external irradiation are
relatively simple as the absorbed dose is delivered at thetime of the irradiation. Thus there is no problem of
protraction of dose beyond the period of exposure.
12. Internal irradiation following an intake ofradioactive materials whether by inhalation, ingestionor other means is, however, protracted to some extent
and the absorbed dose in the organs or tissues of any
individual after an intake will depend on conditions
particular to the individual such as metabolism. age andlife expectancy as well as on more general determinants

45

such as the half-life of the radionuclide. While it ispossibl~ to make estimates for particular individuals,
and t~1s may be done for medical purposes, theCommittee assesses the mean absorbed dose in eachorgan or tissue, usually taking representative values forthe various conditions, either for complete populations
or for particular subgroups in the population.

D.

SOURCE-RELATED ASSESSMENTS

13. The source-related assessments carried out by theCommittee estimate the total human irradiation
resulting from the source. practice or event. This total
human _irradiation is obtained by considering all the
population groups exposed to radiation in different
geographical locations and at different times. This is
generally obtained by integrating in an appropriate
fashion to cover the spatial and temporal distributionsof radiation or radionuclides from the source. The
parameters used in the calculations and the models are
generally applicable to representative characteristics oflarge population groups. Source-related assessments areused by the Committee for comparisons of sources interms of their presumed total health impact.

II.

DOSIMETRIC MODELS

14. For the reasons given in the Introduction(paragraph 7), dosimetric models are described before
environmental transport models, although in practical
calculations the order is reversed. Dosimetric models
are used by the Committee to assess the absorbed doses
and weighted absorbed doses resulting from exposure
to radiations of different types or from intakes ofradioactive materials. The models include those forpredicting the behaviour of radioactive materials in the
body after intake and those making an allowance forthe risk of induction of particular health effects after
exposure to radiation. In some cases the model is notdescribed explicitly but is part of the backgroundunderlying the choice of a particular quantity for use incharacterizing the impact of radiation exposure of man.
For the quantities used here to quantify the effect ofirradiation of people, it is assumed that there is proportionality between the absorbed dose to an individual
and the probability of occurrence of stochastic healtheffects. as discussed in the Introduction (paragraph 3).
Other possible assumptions are discussed in Annexes I.
J. K and L (Genetic effects of radiation. Non-stochastic
effects of irradiation. Radiation-induced life shortening, and Biological effects of radiation in combination with other physical. chemical and biologicalagents, respectively).

15. Thefundamental
quantitative
assumption
describing the interaction of radiation with matter isthat the relevant measure of the interaction is the meanenergy deposited per unit mass. This energy deposition
can result from all types of radiation and the quantity
used to measure it is the absorbed dose, D, defined by[I9J as D =:!

where dE is the mean energy imparted

by ionizing radiation to matter of mass dm.
16. It soon becomes apparent that the biologicaleffects do not depend solely on the energy deposition
per unit mass, or absorbed dose, but also on otherfactors, notably the type of radiation. The additional
factor needed to relate the observed effects to the46

absorbed dose is known as the relative biological effectiveness (RBE). This is the ratio of the absorbed dose of
the radiation being studied needed to produce a
specified biological effect to the absorbed dose of thereference radiation which produces the same number ofthe sam.e effect. This reference radiation is usuallypenetratmg x- or gamma-radiation. The RBE depends
on the radiation type, the energy and all the circumstances of radiation delivery, which should be quoted.
The RBE is thus obtained experimentally. If the doseresponse relationship is linear with no 1hreshold. theprobability of occurrence of a given biological effectafter exposure lo radiation may be obtained from theabsorbed dose multiplied by the RBE appropriate to
the circumstances of the irradiation. As the RBE is arelative number, any change in the observed number ofeffects of a given type produced by a given absorbed
dose of !he reference radiation will cause a change in
the R B,E for that effect for all other radiation types .. If
the dose-response relationship for either radiation is
non-linear. or if there is a threshold dose below which
effects do not occur. a single value of RBE cannot be
used as a weighting factor for biological response.
17. For many purposes there is a need for a welldefined quantitative relationship between the radiationdose and the presumed number of resultant biologicaleffects. The RBE is an experimentally determined
quantity, and the best estimate of it for any particularradiation will change from time to time as better data
are obtained. The amount of data on which RBE can be
determined is limited and no functional relationships
with dose are established. In radiological protection
proportionality between absorbed dose and effect has
been assumed for small values of absorbed dose anddose rates for all radiation types and energies. Given
this assumption, the ICRP has defined the quantity
dose equivalent, H, which is intended to indicate forradiation protection purposes the biological implications of the radiation exposure at the low levels ofabsorbed dose encountered. H is defined by H =DQN, where Q is the quality factor and N is the
product of all other modifying factors specified by the
ICRP. For the present the ICRP has assigned a value ofunity to N. The quality factor is defined as a function of
the collision stopping power for radiation at the pointof interest, increasing from 1 for collision stopping
powers of less than 3.5 keV µm-1 to 20 at collision
stopping powers exceeding 175 keV µm-1. When the
precise distribution of collision stopping powers
throughout the mass of interest is unknown or
unimportant because the values of dose equivalent aresmall, it is permissible for radiation protection purposes
to use approximate values of the quality factor related
to the various types of primary radiation. The ICRP has
recommended the following approximate values of Q
for both external and internal radiation:
x rays, gamma rays and electrons
Neutrons and protons of unknown
energya-particles and other multiply charged
particles of unknown energy

1
10

20

These values of Q and hence values of H are intended
only for use at levels of exposure within or near dose
equivalent limits as defined by the ICRP. The values
are independent of the effect. the organ or tissue
exposed or other variables. For the general purposes ofcomparison between sources and assessment of
individual dose equivalent levels, these approximate
values are appropriate for use by the Committee formost radiation types. However, since they may not beappropriate for other purposes, the Committee ispresenting its basic data in terms of absorbed dose. For
some special cases, such as the assessment of dose
equivalents from cosmic radiation. the Committee has
used other values of quality factors based on specificcalculations.
18. It is assumed in the dosimetric model that theprobability of occurrence of a stochastic effect in aparticular organ or tissue is proportional to the meandose equivalent in the organ or tissue. The constant ofproportionality differs for the various organs or tissuesof the body. If the dose equivalents are sensibly
uniform for all organs or tissues of the body, then asingle overall risk factor can be used to describe theprobability of induction of health effects for theindividual. Assessments and comparisons can then be
made solely on the basis of the dose equivalent to thewhole body. However, if different organs or tissues areirradiated to different dose equivalent levels, then afurther procedure is necessary to evaluate the overall
probability.

19. The ICRP has recommended a system whichallows for the different probabilities of mortality
associated with the same dose equivalent delivered todifferent organs or tissues and the probability of hereditary effects in the first two generations. Th~ system
uses the effective dose equivalent: Herr = T WT HT
where WT is a weighting factor representing the
proportion of the probability of stochastic effects
resulting from irradiation of organ or tissue T to theprobability when the whole body is irradiateduniformly and HT is the mean dose equivalent in organor tissue T.
20. The values of reference risk coefficients and corresponding weighting factors recommended by the ICRP
[I2] are shown in Table 3. They are averaged over age
and sex and are therefore considered by theCommission to be appropriate for protection ofindividuals of all ages and both sexes. The value forgonads includes an allowance for serious hereditaryeffects expressed in the first two generations (i.e .. thechildren and grandchildren of a pair of individuals).
Numerically equivalent reference risk coefficients perunit collective dose equivalent can also be used toassess the expected number of the same health effects inpopulations.
21. The effective dose equivalent therefore is anindicator of the probability of occurrence of a healtheffect, which is either death from somatic effects or the
induction of serious hereditary effects in the first twogenerations, assumed to result from any irradiation,
whether uniform or non-uniform, from both external
and internal sources. The effective dose equivalent does
not include hereditary effects in generations after the
first two, nor any allowance for non-fatal somaticeffects such as in most cases of thyroid or skin cancer:
to this extent it will underestimate the overall probability of induction of all health effects. Where appropriate, therefore. the dose equivalents in the tissues ofinterest can be used directly to give an indication of thelikely incidence of non-fatal tumours. The risk coefficients to be used to give the probability of induction of
non-fatal tumours, which exclude the probability of
induction of fatal tumours in the same organ or tissues,
are 0.15 10-2 Sv-1 for breast, and 10-2 Sv-t for boththyroid and skin [U9]. The figures for the latter are a
sufficient approximation whether the fatal tumours areincluded or not.

22. It is possible to define different sets of weighting
factors which include some or all of these additional
health effects or which deal separately with each healtheffect [CJ]. For the present the Committee has decided
to carry out comparisons in terms of the quantities
defined in this chapter.
A.

INDIVIDUAL-RELATED ASSESSMENTS
1.

External irradiation

23. The primary assessment of radiation exposure ofindividuals should be carried out in terms of absorbed
dose. Conceptually, the assessment of the distributionof absorbed doses in body tissues from external irradiation requires knowledge of the energy and angular
distribution of the nuence rate of each component of
the electromagnetic and charged particle radiation
field. These differential distributions can be obtainedby spectrometric measurements, but in general only
calculated values, for known source distributions, areavailable. In practice most assessments of absorbed
doses from external irradiation are based on simpler
measurements.
24. Most measurements describe the field in theabsence of an exposed person in "receptor-free" conditions. The absorbed dose rate in air Da is used todescribe environmental exposure situations resulting
from gamma-emitting nuclides, and it is unambiguously
specified if full secondary electron equilibrium exists inair. From the environmental quantity, the absorbed
dose in the human organ or tissue of interest can beassessed. This inv.olves a number of assumptions about
factors which affect the results of depth dose calculations and about the periods of time during which theperson is exposed to the various radiation fields. The
latter factor is discussed further in section Y.A.
25. When the receptor is located in the region ofinterest, the assessment of absorbed doses in tissues
based on absorbed dose in air involves knowledge ofthe following parameters: the mass energy absorption,
the depth transmission, the backscatter and the degreeof isotropy. The mass energy absorption factor is theratio of the mass energy absorption coefficients fortissue and for air. A value of 1.10 was used in Annex Aof the 1977 report [Ul] and is retained in this report.
The other factors are to some extent interrelated.
Backscattered radiation may increase the dose rate at
the surface, but the body will also act as a shield andreduce the dose rate to deeper tissues. The overall effectwill depend on the location of the tissue of interest. andthe energy and angular distribution of the radiation.
26. Except for the rare case where the radiation field
is monodirectional and the irradiated person is notmoving, the apparent depth of an organ or tissue isdetermined from the weighted average absorption
through the body that would be experienced by rays
entering from different directions. The difference
between monodirectional and isotropic fields will also
be expressed in terms of a difference in absorbed dose
rate at any depth for fields which produce the sameabsorbed dose rate in air under receptor-free conditions. The ratio of the absorbed dose rates cannot
exceed 2 for points near the surface of the body, and it
approaches 1 near the centre of the body. These
problems have been discussed in detail by Kramer [K3]and by Kramer and Drexler [K4. K5] who have applieda Monte-Carlo method 10 a mathematical represen-47tation of ICRP Reference Man [16] to calculate
conversion ratios for a range of tissues, photon energies
and irradiation geometries.
27. In Annex A of the 1977 report [Ul], theCommittee has adopted a value of 0.82, which includes
all the factors mentioned, for the ratio between theabsorbed dose rate in the body and the absorbed dose
rate in air outdoors [Ul, U2] based on the work oflknnctt [BI] and a value of 0.69 indoors based on
Spiers and Overton [SI]. A value of about 0.7 Sv Gy-1
has :1lso been derived as the quotient of effective dose
equivalent to absorbed dose in air [N1] based on calculations for clouds of gamma emitters of about t MeV[C 1, Pl ]. This is compatible with the values derived by
Kramer and Drexler [K4]. The values for individualorgans are more sensitive to energy and to the fieldcharacteristics: for example, the ratio of absorbed dosein gonads to absorbed dose in air is about 0.6 for asemi-infinite cloud [Cl, Pl], 0.7 for an isotropic field(01, 02, Sl] and 0.8 for a normal field [B1, Jt]. It now
appears that the most appropriate average value of thequotient of effective dose equivalent rate to absorbed
dose rate in air for males and females for use in thisreport is 0.7 Sv Gy-1 for environmental exposures togamma rays. For medical exposures, specificconversion factors are discussed in Annex G (Medical
exposures).
28. Another quantity which can be used to describe
receptor-free conditions is the absorbed dose index, D1.
This has been defined by ICRU [19] as the maximum
absorbed dose that can occur in a 30-cm diameter tissue
equivalent sphere located with its centre at the point ofinterest. This quantity is used, for example, to describe
irradiation due to cosmic radiation. It is assumed thatthe absorbed dose index represents, sufficiently well,
the absorbed dose in tissue at the location of interest.

2.

Internal irradiation

29. For internal irradiation, the mean absorbed dosesin the organs or tissues of interest of a given individual
may be estimated from one or more of the following:
(a)

(b)

(c)

Measurements of activity concentrations in theenvironment and in diet components, leading toestimates of the intake and, by use of appropriate
metabolic models, to estimates of the uptake andresidence time of the radionuclide in the organs or
tissues of interest;
Assessments of the activity concentrations in therelevant organs or tissues, by measurement of theradiation emitted from the body or of the activity
concentration in tissue sam pies;
Measurements of the activity concentrations in
excreta or exhaled air leading, by the use of
appropriate metabolic models, to estimates of theactivity concentration in the relevant organs or
tissues of the body.

30. The use of this information to calculate absorbed
doses in organs or tissues requires models to describe
the transfer of radionuclides between tissues and theireventual elimination from the body as a function oftime. It is also necessary, given the radionuclide distribution between the various tissues as a function of time,to have further models to calculate the dose rate in any
tissue of interest from the activity in any tissue,
including the tissue of interest. The general concept ofthe mean absorbed dose per unit of time integrated
48

activity is that used by MIRO [Ll, 82], by ICRP (14]and by ICRU [110].
31. The general equation for absorbed dose calculations from internally deposited radionuelides is
12

D (Yq) = LL I Ak(t) dt E; <l>; (Yq -Vk)(I)

k i 11

where D(V q) is the mean absorbed dose in a target
volume Yq; Ak(t) is the activity of the radionuclide
considered in source tissue, k, as a function of time. E;
is the mean energy emitted per unit of time integral ofactivity through ionizing particles of type, i; <l>;(Vq - Vk)
is the specific absorbed fraction, i.e., for the type ofradiation i, the energy imparted to a target volume Yq
from a source volume Vk divided by the energy emitted
by soUI;ce volume Vk and the mass of the target volume.
It should be noted that, for the general calculation. thebiological parameters are assumed to be independent ofage.
32. Usually approximations to obtain the activity inan organ or tissue as a function of time A(t) are made;the most common is a sum of exponential terms:
A (t) = LA (m) exp (- (i. + Ab [ml) t)(2)m

where A(m) is the value of the mth exponential
component at time t = O; i. is the physical decay
constant of the radionuclide; 4(m) is the biologicalelimination rate constant for the mth exponential
component.
33. The function A(t) is sometimes determined empirically from retention measurements; it can also bederived from compartment models in which the activity
contents of the compartments are described in terms ofrate constants for transfers between compartments andin terms of input functions. These methods are used forexample by ICRP in calculating the integrated activities
in body tissues following ingestion or inhalation ofmaterial [14, I 11].
34. For some radionuclides such as 3H or 14c which
are continuously produced naturally or which havebeen uniformly distributed in the environment after
release it is possible to use a simplified procedure basedon the assumption that the activity concentration of thenuclide in tissue is constant. Activity concentration intissue may also be assumed, under many circumstances,
to be equal to the activity concentration in an appropriate environmental material such as water. Under thesecircumstances the formulation given in equation (1) canbe replaced by a time independent expression using
constant quotients to relate the absorbed dose rate inany organ or tissue directly to the activity concentrationin that organ or tissue. This procedure is used for theseradionuclides in Annex B (Exposures to naturalradiation sources) and in Annex E (Exposures resulting
from nuclear explosions).
35. In general, the Committee has not found it
necessary to calculate directly the matrices of values ofA(t) and <I>i which are needed for assessment ofabsorbed doses in tissues. The absorbed dose rate in an
organ or tissue is related as shown above to the activity
concentrations in all organs or tissues in the body. Thisabsorbed dose rate may be integrated over various

times for various purposes. An integration time of 50
years has been used by ICRP (12) to derive thecommitted dose equivalent Hso. This is relevant in thecontrol of internal doses to workers as the annual dose
equivalent at the end of the period at work. taken to be
50 years. cannot exceed the maximum annual
committed dose equivalent. Detailed tabulations of thecommitted dose equivalent per unit activity intake of allradionuclides of interest to the Committee have been
published by ICRP [14, 111).
36. Jn calculating the dose equivalent from intakes bypopulations. the Committee requires an appropriate
average relationship. The relationships will be different
for infants, young children and adults because of differences in metabolism and dosimetry. Nonetheless, whendeveloping an appropriate average, it is necessary torecognize that most individuals in a population will be
adults or older children for whom adult values are avery close approximation. Since a population contains
individuals of all ages, the appropriate time over which
to integrate the dose equivalent following an intake isthe average remaining life expectancy which is justunder 50 years. In the same way. for continuing intakes
by an average individual with an anticipated lifetime of
70 to 80 years the appropriate integration time will
decrease from 70 to 80 years for intakes in infancy andearly childhood to a few years for intakes in the lastyears of life; again the appropriate average over a
lifetime is less than 50 years. The Committee therefore
considers it appropriate for populations in both situations to use the conveniently tabulated ICRP values ofcommitted dose equivalent per unit activity intake
based on a 50-year integration period. The dose equivalent commitment from intakes by a population canthen be obtained from the infinite time integral of therate of activity intake by an average individual in the
population multiplied by the committed dose equivalent per unit activity intake.
37. As indicated earlier, the Committee feels it isreasonable to use the dose equivalent for comparison
purposes, modifying the absorbed dose by the appropriate quality factor. For individuals the effective dose
equivalent is also regarded as a reasonable approximation, implying use of further modifying factors asneeded. These modifications will be made in somecases at a late stage in the calculations; in other cases it
is more orderly to carry the modifications out at an
early stage. In the latter cases it will be reasonable touse tabulations of effective dose equivalent per unit ofactivity intake such as those produced by ICRP [14) orby Adams [Al], together with such additional calculations as may be needed for specific purposes; similar
procedures have been carried out in Annex G (Medical
exposures).
38. There are special problems connected with thedosimetric models for certain radionuclides which aredealt with in detail in the appropriate Annexes. An
example is the dosimetry of radon and its daughters forthe activity concentrations of which a special quantity,
Cpot, has been defined as the potential alpha energy
concentration in air of any combination of the shortlived radon daughters. This particular quantity isdefined to allow for situations where the daughters are
not in equilibrium. It can of course be expressed inunits of J m-3, but use is still made of the empiricallydetermined unit, the working level, WL, which corresponds to a potential alpha energy concentration of 1.3
1Q5 MeV per litre of air. Further problems concerning
the dosimetry of radon and a discussion of the more

complex models of the lung which have been developed
mainly for use in the dosimetry of radon are covered in
Annex D (Exposures to radon and thoron and theirdecay products).
39. In previous reports of the Committee, forabsorbed dose rate assessments from maintained
activity concentrations in the body, calculations havebeen carried out using a similar procedure to that
underlying the formulation in equation (1 ). The detailsof these calculations, given in Annex B (Natural
sources of radiation) of the 1977 report [Ul], will not
be repeated here. It should be noted that certain of
the parameters used in the calculations and aspects ofthe models differed from those used by ICRP in themost recent reports on this subject [14, 111 ], although
the principles are the same. In its previous reports, theCommittee has estimated, on the basis of measurements, the average activity intakes of radionuclides andthe average activity concentrations of these radionuclides in tissue. On the other hand. lCRP (14} provides aseries of models which give the dose equivalent in tissue
per unit intake of activity of a radionuclide as afunction of the aerosol size and of the chemical formsof the radionuclide considered. Another part of theseries of models enables the dose equivalent rate intissue to be calculated per unit activity concentration intissue.
40. The major differences between the ICRP and theCommittee occurred in the calculation of dose equivalent in bone tissues. Both the Committee and ICRP
calculated dose equivalents in the same tissues, namely
red bone marrow and bone lining cells in a 10-µm layeron the surface. For the purposes of the calculations,radionuclides were considered to be either uniformly
distributed throughout each bone tissue or distributedon the bone surface. The difference between the calculational methods used by the Committee and ICRP
stemmed mainly from which components of bone wereconsidered to be source regions. A comparison of thetwo methods is outlined in Table 4 for a-emitters fromwhich it can be seen that the Committee generally
calculated in its 1977 report [Ul] the dose equivalent in
the target region from activity in trabecular bone andred bone marrow based on the treatment of Spiers[S14]. whereas ICRP ignored activity in red bonemarrow but included activity in cortical bone in thecalculation of dose in bone lining cells [14). A further
difference was that the coefficient used by theCommittee in assessing the dose equivalent from
activity in trabecular bone was in most cases a functionof energy. However, this only led to differences in thatcomponent of the calculation of a factor of from 0.5 to
2 for a-energies from 4 to 8 MeV. The differences
resulting from inclusion of the other source regions
depend on the radionuclide under consideration andthe relative distribution of activity between the bone
tissues.
41. In all cases the calculational methods used by theCommittee in 1977 gave higher estimates than ICRP ofdose equivalent in red bone marrow from a given
activity concentration of an a-emitter. This difference
was generally about a factor of 2, for example the ratioof the results of the Committee to ICRP dose equivalentcalculation for the nuclides in the 23KU and 232Th series
varied from 1.1 to 3. For bone lining cells the ICRP
method gives the average dose equivalent in cells on
trabecular and cortical bone. whereas the earlier
Committee method obtained the dose equivalent onlyin cells on trabecular bone surfaces, but included the49effect of red bone marrow as a source region. In thiscase either calculation may give the higher result,depending on the distribution of activity between thebone tissues. For example, the Committee model gave
close equivalents higher than ICRP by factors from 1.1
to 1.7 for the nuclides in the 232Th series and dose
equivalents lower than ICRP by factors of from 0.7 to
0.9 for the nuclides in the 238U series (with the
exception of HOTh for which the factor is 1.7).

42. In this report, the Committee has modified its
previous treatment to include the source regions used by
ICRP and the red bone marrow, as shown in Table 4.
The doses to the bone tissues are then calculatedusing the ICRP conversion factors. The only difference
arises from the calculation by the Committee of thecontribution due to the activity present in red bonemarrow; for most radionuclides, that contribution to
the total dose in bone tissues is very small.
43. Another aspect of the comparison between thetreatments used by the Committee and by ICRP occurs
when assessments of doses are based on estimates ofintake and transfer through the body of radionuclides,
rather than on measured activity concentrations intissues. In general, the Committee has based its assessments of doses from naturally-occurring radionuclides
and of doses arising from atmospheric weapons testing
on measurements of activity concentrations in tissues.
However, in assessing dose equivalents from radionuclides released from nuclear power establishments, this is
not usually possible. Thus calculations are based on
assessed intakes and make use of ICRP methods.
Further differences are introduced between these twosituations which can be traced to the additional
assumptions needed about the transfer of activity fromlung or through the gut wall and on its subsequent
distribution in tissues. These differences depend on theradionuclide under consideration and on its physicaland chemical form; they are thus specific to the circumstances considered.
44. The results of individual-related assessments may
be expressed as the risk to an average individual. Thisrisk is the probability of occurrence of a health effectand may be obtained using the appropriate reference
risk coefficients from Table 3 if the organ or tissue dose
equivalents are known. Otherwise the probability of
induction of a fatal tumour or an hereditary effect in
the first two generations is obtained by applying theoverall reference risk coefficient of 1.65 10-2 Sv-1 to theeffective dose equivalent.
B.

SOURCE-RELATED ASSESSMENTS

45. Although, as explained in paragraph 13, forsource-related assessments the emphasis is on the
expected number of radiation-induced effects rather
than on the probability of effects for each individual,
nonetheless the basic information will still be expressedin terms of average absorbed doses in the organs andtissues of the individuals making up the irradiatedpopulation. For reasons expressed in paragraph 17, theCommittee finds it reasonable to modify the absorbed
dose by means of the quality factor and thus to give theirradiation in terms of dose equivalent.
46. As discussed in the Introduction to this Annex(paragraph 2), there is considerable uncertainty in thedose-response relationship for radiation-induced
tumours. This matter has recently been reviewed in
50

detail [N4]. Although accepting the uncertainty, theCommittee nevertheless needs quantities which can beused to derive the number of radiation-induced healtheffects which may be expected from radiation sourcesthat give a wide range of doses in large mqnbers ofpeople. For intercomparisons it would be too
cumbersome to deal always with the distribution ofabsorbed doses or dose equivalents in the irradiatedpopulations. The Committee has therefore decided toexpress this summation in terms of collective quantities
which arc weighted sums of the absorbed doses in each
irradiated individual. Implicit in most uses of thesecollective quantities is the assumption that the doseresponse relationships are linear for additional doses
which are not large in comparison with pre-existing
doses for irradiation of any tissue with radiation of any
type.
47. Tile collective dose equivalent rate, S. is defined as
the integral of the product of the dose equivalent rate
resulting from the source and the number of individuals
in the exposed population receiving that dose equivalent. It is defined by S = f H N (H) dH where N (H) dH
is the number of individuals receiving a dose equivalent rate between H and H + dH. The integral
expression can often be approximated in practice by asummation over population subgroups receiving dose
equivalent rates that can be sensibly averaged.

48. The collective dose equivalent rate can be
integrated as a function of time. The integration may becontinued to infinity. The quantity resulting has beencalled the collective dose equivalent commitment fromthe source,
defined by: S~ = fo' St (t) dt. This isalways related to a specific source, k. It is also often
useful to present the pattern of accumulation of thecollective dose equivalent commitment with time. Thispattern may be presented graphically or by giving
stages in the integration. It is also possible to define atruncated or incomplete integral in which the
integration is terminated at time,-, The main purpose oftruncation is to derive the maximum future dose equivalent rate from a practice which is assumed to continue
for a time period ,-.

st

49. Average or per caput quantities can be defined by
dividing the collective quantity by the population size
such that

H (t) = s <t>

N (t)

(3)

where H (t) is the per caput dose equivalent rate and:"J(t) is the population size at time t. It may be moreconvenient under some circumstances to evaluate percaput quantities rather than collective quantities. The
dose equivalent commitment, He, is delined as theinfinite time integral of the per caput dose equivalentrate.
50. These average quant1t1es are sometimes used torefer to individuals in the per caput sense. Insofar asthese are not real individuals and the dose equivalents
are usually assessed on the basis of the effect of a particular source, it is considered that these are more
properly treated as source-related quantities. The
quantity related to a source, k, will be the dose equivalent commitment Ht There is however one instance inwhich information on individuals can be derived. Thisis because the annual dose equivalent to an average
individual in the future from one year of release of aradionuclide into the environment does not exceed thedose equivalent commitment resulting from that
release. Thus a calculation of the dose equivalentcommitment per unit practice enables at least a roughestimate to be made of the maximum future annual
average dose equivalent per unit practice.

51. Where the collective effective dose equivalent isused for populations, care must be taken that thecircumstances of the irradiation arc not such that theomission of certain portions of the total health effects
can lead to a substantially erroneous estimate of the
expected number of health effects. This can occur, forexample. if the irradiation were confined to specificorgans such as skin or thyroid and it is felt that the total
incidence of malignancies is relevant, even though the
majority will not prove fatal. As stated earlier, theeffective dose equivalent as defined by ICRP does nottake into account hereditary effects after the first twogenerations, nor does it include non-fatal somaticeffects. Although these omissions may not be sufficiently serious to affect the general level of probabilityof occurrence of a health effect for an individual. when
considering irradiation of populations in a sourcerelated manner, it seems to the Committee necessary togive further consideration to these effects. Clearly thevarious effects are not of equivalent importance;
attempts have been made to assess the relative importance of each type of health effect with respect to theothers [15]. However, the Committee has decided not toattempt such analyses now but to separate and compare
the somatic and hereditary health effects in populations. This requires the assignment of the appropriate
sets of weighting factors for the irradiation of particularorgans or tissues in a manner analogous to those usedin the definition of effective dose equivalent. The
Committee has chosen to follow the format of its earlier
definition of genetically significant dose equivalent forconsistency with earlier reports.
52. The genetically significant dose equivalent. GSD,
is defined as the per caput gonad dose equivalent
which. if given uniformly to the irradiated population,
would result in the same number of hereditary effects as
those from the actual distribution of dose equivalents inthe population. It is thus the gonad dose equivalent
distribution modified by those factors which affect theoutcome, namely the age and sex distribution of theirradiated population. The formal definition is

LL

H1,s N1.s Vs
1
GSD = - -'-=,----Ns vs

L

(4)

s

where N1,s is the number of people of age/sex class s,irradiated within dose equivalent band I to an average
gonad dose equivalent level of H1,s: v5 is the expected
number of children for an individual of age/sex class s;
N 5 is the number of people of age/sex class s.
53. From the above definition, the informationneeded to compute the GSD is the distribution of
gonad dose equivalent in the population as a functionof age and sex. This information. together with thechild expectancy as a function of age and sex which isreadily available in most countries, can be obtained byobservation or by statistical methods. It is therefore
practically possible in a large number of cases to carrythrough the computation of GSD based on the formal
definition. The total number of hereditary effects isthen obtained by multiplying the GSD by the
population size and the appropriate collective risk

coefficient. taken as 0.8 10-2 (man Sv)-1, to include
effects in all subsequent generations.

54. By analogy with the GSD. it is possible to define asomatically significant dose equivalent, SSD. This is the
per caput whole-body dose equivalent which, if given
uniformly to the irradiated population, would result inthe same number of fatal tumours as those from theactual distribution of dose equivalents in the tissues of
the irradiated population. The formal definition is

LLI: H1.s,T N1,s Ws,T-=------

SSD = -'1'---'sc...,,;·1,,..·

L LT Ns w,. T(5)swhere N1,s is the number of people of age/sex class s,
whose tissue. T. is irradiated within a dose equivalent
band I to an average tissue dose equivalent level of
H1.s,T; Ws,T is the number of fatal tumours per unit dose
equivalent for irradiation of tissue T in a subgroup ofage/sex class s; Ns is the number of people of age/sex
class s. Although the total number of fatal tumours
predicted will be the same for the SSD as for the actual
distribution of dose equivalent, the tissues in which they
are predicted and the type of tumour will not necessarily be the same.

55.

The information needed to compute the SSD
includes the distribution of dose equivalents in thetissues of the population as a function of age and sex,
which together with the incidence of fatal tumours forirradiation of a particular tissue at a particular age foreach sex, is in principle obtainable by observation or bystatistical methods. This incidence should include
allowance for the induction rate of tumours which mayvary with age and sex. together with a further allowancefor the expression of the effect which will also dependon age and sex, taking into account the latent period of
the effect. This information is not in general available
at present in the detail required for computation of
SSD based on the formal definition.

56. An approximation to SSD can be made using
weighting factors for the incidence of somatic effects
which are averaged over the age and sex distribution ofa normal population. This approximation is so close to
the definition of effective dose equivalent derived by
ICRP that it does not seem useful to derive a separate
set of weighting factors. The per caput effective dose
equivalent, although containing a genetic component,
may be taken as a reasonable approximation to theSSD, using the weighting factors in Table 3. The total
number of health effects (fatal tumours and genetic
effects in the first two generations) is then obtained bymultiplying by the population size and by the appropriate collective risk coefficient. taken as 1.65 10-2(man Sv)-1 (12].

III.

ENVIRONMENT AL MODELS
A.

GENERAL

57. If it is possible to measure the absorbed dose rate
in air from radionuclides in the air or deposited on the
ground at a sufficient number of places and O\'er asufficient time, then the absorbed doses to individuals
and populations from external radiation can beassessed without the need for environmental transfer
51

models to describe the manner in which the airborne
contamination or deposition resulted from the sourceof radionuclides. Similarly, if the activity concentrations in organs or tissues of the radionuclides
concerned can be measured in a sufficient number ofpeople, the absorbed doses from incorporated radionuclides can be assessed using only dosimetric models
and without the need for environmental transfer
models. In many situations, especially for naturallyoccurring radionuclides and for those produced from
nuclear explosions, such measurements have been
carried out in sufficient numbers, in different places
and over long enough periods of time to enable theCommittee to estimate doses directly from them.
58. Slightly less direct estimates of internal doses canbe made from measurements of activity concentrationsof radionuclides in the air or in foodstuffs. In this casethe additional inform<1tion required is of the intake
rates of the radionuclides from air or from the foodstuff
concerned and the appropriate dosimetric models to
calculate the absorbed doses in organs and tissues
following intake. These less direct methods are used forsome radionuclides from nuclear explosions, often to
supplement a more limited measurement programmeon people. They are also used in assessing absorbed
doses to critical groups of the population exposed as aresult of deliberate releases of radionuclides from
nuclear installations, for a limited number of radionuc·)ides. A difficulty in placing too much reliance on suchmeasurements is that there has to be a great deal of
preliminary effort to ensure that the foodstuff being
monitored is the only, or the major, route of intake ofthe radionuclide concerned. When dealing with amixed diet and a large number of radionuclides thisbecomes extremely laborious. For radionuclides which
are not evenly distributed in the environment, it is not afeasible method to establish the collective dose.

59. Sometimes direct measurements may not bepracticable. This may be due to technical difficulties inmeasuring the activity concentration of the radionuclide concerned in an appropriate medium, or to thedifficulty of obtaining samples, or to the number ofradionuclides and pathways being too large. Direct
measurements may also be impracticable because
predictions of dose rates are required, for example toderive collective dose commitments, whereas measurements have to be carried out after or during the deliveryof the dose. In these cases models are required in orderto derive doses and dose distributions from data on thequant1t1es of radionuclides released into theenvironment and the rates of release. The relationshipwill depend on other factors such as the conditions of
the release, the physicochemical form of the radionuclide, whether the release is into the atmosphere, awater body or the ground and the characteristics of thereceiving environment. In general, the environmental
models with which the Committee is concerned aresimplified mathematical representations of actual
transfer processes. Some of those processes are wellunderstood and can be described reasonably precisely
by mathematical models which are based upon detailed
measurements. The transfer of fallout radionuclides
such as 90Sr through food chains is an example. Other
processes may be only partially known and the timescales or other aspects may render the models very
difficult to check directly by measurement, as in thecase of the long-term stability of sorption of actinides
on soils or sediment particles. It is not the intention toreview all types of transfer models but to concentrateon those used by the Committee in this report.
52

60. The type of mo<:lel used depends on the information required, on the characteristics of the radionuclide concerned and on its mode of introduction into
the environment. Of particular importance is whether
the radionuclide can be considered as uniformly distributed and whether the activity concentration is approximately constant with time. If both these conditions are
satisfied, as they are for certain naturally-occurring
radionuclides. then the simplest form of environmental
model is adequate to assess the collective absorbed dose
rate in the world population. This model relates directly
the assumed activity concentration in body organs or
tissues with the measured activity concentration in asuitable environmental medium, such as the circulatingwaters of the hemisphere or the air of the troposphere.
It is often referred to as a "specific activity model". If
the activity concentrations in the environment result
from continuous production, as for natural tritium and
14C, ai,1 empirical relationship can be developed
between the production rate and the activity concentrations. Very simple models of this type are used in
Annex B (Exposures to natural radiation sources) for
assessment of collective absorbed dose rates fromnatural radionuclides and in Annex E (Exposuresresulting from nuclear explosions) for the same radionuclides which are widely distributed as a result of
production in the atmosphere by nuclear explosions.
The results of such models are compared with more
complex time varying environmental models forappropriate radionuclides in Annex F (Exposuresresulting from nuclear power production).
61. The information required by the Committee in thepast has varied but has generally been directed towards
assessment of the dose commitment, particularly in thetreatment of the doses from fallout of debris from
nuclear explosions in the atmosphere. The Committee
developed a procedure for dealing with these calculations which was based on the idea of time-independenttransfer coefficients [U2, U3]. These transfer coefficients have been defined in Annex A (Concepts andquantities in the assessment of human exposures) of the
1977 report [Ul] in terms of the quotients of the infinite
time integral of the appropriate quantity incompartment n of a sequence to the infinite time
integral of the appropriate quantity in the precedingcompartment m. For example:
Pmn = },, Cn (t) dt /_lCm (t) dt(6)

where Pmn is the transfer coefficient from compartmentm (diet) to compartment n (bone); Cm(t) and C 0 (t) are
the appropriate activity concentrations in diet andbone. respectively, at time t. The models weredeveloped in a form which was appropriate to theresults required and are used again in Annex E(Exposures resulting from nuclear explosions).
62. These transfer models are examples of the type ofmodel in which the chain of events is represented by aseries of compartments and the transfer processes occur
betweencompartments: these will be called"compartment models". In some cases the compartments have some physical attribute such as representing
a given volume of water but this is not an essential
requirement of the technique. Other examples of suchmodels are food chain models and some oceanic
models. Some compartment models are better suited to
predicting time-independent results although many give
dynamic results.

63. A simple example of a compartment model is one
which has been used to estimate the global dispersionof 85Kr introduced into the northern hemisphere [NI].
Two compartments are assumed. corresponding to thetropospheres of the northern and southern hemispheres.
Exchange takes place between the two compartmentswith a transfer coefficient in each direction of 0.5 a-1.
Input is into the northern hemisphere compartment
which is assumed to be instantaneously uniformly
mixed: the results arc expressed in terms of the activity
concentration in air as a function of time after the startof a continuous input. The transfer of material between
the compartments is described by a set of two equations
dXN

Ao, N

dt = v;; -

k

NS XN

+

k
0

SN Xs -

,

11.XN
(7)

where Ao,N is the rate of input of activity of the radionuclide into the northern hemisphere compartment; VN
is the volume of the northern hemisphere compartment;
XN and xs are the instantaneous activity concentrationsof the radionuclides in air at time t after the start of the
input; A is the physical decay constant: k:,,is is thetransfer coefficient from the northern to the southernhemisphere compartment; and ksN is the reverse
transfer coefficient between the two compartments.
64. The general solution of compartment models of
this type depends on the assumption that the transfer
rate of materials between compartments is proportional
to the inventory of material in the source compartment
and that the rate is governed by a transfer coefficient
specific to the two compartments being considered.
These relationships can be expressed by the sets ofequationsdAm,l!.,-d- = 2..., knm An tn - I

which apply for two or more compartments; where
Am.An are the instantaneous activities in compartments
m.n at time t; kmn is the transfer coefficient fromcompartment m to n; Am is an effective transfer coefficient out of the system from compartment m which isused to describe loss of material, e.g., by radioactive
decay or transfer to a stable sink; Ao,m is the rate of
input of activity into compartment m; and p is the total
number of compartments connected directly to m.
These equations can be solved analytically for simple
systems or numerically for larger systems.
65. Another type of model is that in which an attempt
is made to represent the physics of a real transfer
process. Examples of such models are diffusion andadvection models in the seas. sediment transfer models
in rivers, and trajectory models for airborne dispersion.
Although these models are often used to produce results
for an eventual equilibrium situation, many of them are
inherently capable of producing time-varying outputs.
66. In general the model used should be the simplest
type which will produce the required answer and isappropriate to the radionuclide, its mode of release andits environmental behaviour. For natural radionuclides
in equilibrium in the environment, where the answer
required is the collective absorbed dose rate, then thespecific activity model is adequate. For mixtures ofartificial radionuclides released to atmosphere andwater from nuclear installations, answers are requiredon maximum absorbed doses to individuals resulting
from the combination of all the radionuclides via all thepathways, together with collective absorbed dose rates
in different groups of the population and integration ofthese collective dose rates over both space and time. Inthat case quite complex models may be needed which
are capable of accepting time-varying inputs and giving
dose distributions as a function of space and time. It is
requirements such as this and the need to predict results
well into the future which have led to the recent development of more complex and comprehensive models.
67. In principle all models are based on experimental
observa"tions and should be subject to experimental
verification, if not of the model form at least of theparameter values. The conclusions of a workshop on
the evaluation of models [HI] are that complex models
may, because of the descriptive detail incorporated. be
accepted as being more realistic and thus more defensible than simpler models. However, without adequate
validation, there is no assurance that the predictions ofthese complex models are any closer to the realsituation than those produced by simpler ones.
68. Since the purpose of models is to provide asimulation of reality and the real environment may be
conveniently separated into sectors, the various types ofmodels appropriate to each sector of the environment
will be described together. In each case the models usedby the Committee are described. The sectors of theenvironment considered are the atmosphere, the land
and the waters. These are not isolated because, forexample, a discharge into the atmosphere will, formany radionuclides, lead to an eventual input to bothother sectors.
69. A problem in reviewing models is the large
number of computer programmes in use. A survey by
Hoffman et al. in 1977 [H2] identified 83 programmes
for the assessment of accidental or routine releases ofradionuclides to the environment from nuclear power
facilities. Most of the programmes appear to have beendeveloped in relative isolation and only in recent years
have there been compilations which attempt to take
into account all sectors of the environment. Examples
of such compilations are the United States Nuclear
Regulatory Commission guides [U4. US. U6] which arevery formal sets of general equations; the models usedin the Federal Republic of Germany [F1]; and thecomprehensive reports by Killough and McKay [Kl]and by the National Radiological Protection Board of
the United Kingdom in cooperation with the Commissariat a l'Energie Atomique of France [NI).
B.

UNCERTAINTY OF PREDICTIONS FROMMODELS

70. All models are based on knowledge of the realsystems being simulated and where possible use data
determined empirically. The reliance to be placed on
the predictions emerging from models depends on theknowledge of the system and the reliability of data
used. Both of these aspects are felt by the Committee tobe reasonably satisfactory for modelling of radionuclide behaviour. It is because these models for the53

transport of radionuclides in the environment aredeveloped more fully than those for other potential
contaminants that it is possible to try to determine theuncertainty in their predictions. In simple situations
direct verification of model predictions may bepossible. but in many cases this will only be practicablefor some portions of the model output and for some of
the radionuclides being studied. Under these circumstances two techniques are available to investigate thevariability of the results. These techniques consist ofchanging the form of model used and evaluating thedifferences in predicted results; or varying the input
data over a range and evaluating the resultant changes
in the prediction. The first technique can only be
employed for particular problems where alternative
ways of describing the situation can be found; it is notdescribed further here. The second technique can andshould be applied to all predictive models and has been
insufficiently utilized up to now. This can be used toestablish the inherent uncertainty in a prediction basedon the model using the empirically determined ranges
of input data and to identify those portions of the input
data for which variations have the largest effect on theprediction and which therefore should be studied
further if there is a need to reduce the overall uncertainty.

71. A particular method of carrying out sensitivity
analyses of this type has been developed as part of ageneral assessment of models [H8, H9, M3, S12]. This
technique can be applied to simple multiplicative chain
models such as those used by the United States Nuclear
Regulatory Commission [U4] and relies on the observation that the central part of the distribution ofobserved values for many environmental variables
follows a log-normal form. In this case the log-normal
statistics can be simply propagated through the model[S13]. The results of such studies cannot usually be
expressed in a simple form; in general they indicate theprobability that actual values will exceed the predictions based on a particular set of data [H9]. The mostcommon method. and the simplest, of carrying out
sensitivity analysis is to change the value of one input
variable while holding all others constant [HlO]. This
procedure will not, however, give a complete range ofvariation in the output from the entire model andrequires a very large number of individual calculations
for complex models. Methods have been suggested forcarrying out analyses in which several variables arechanged together; see for example the suggestions by
McKay and Bruckner [M4], which rely on some methodof sampling output while changing all input variables
simultaneously. The results from all such studies areuseful in assessing the overall reliability of the model
system predictions in comparison with direct observations.
72. In order to assess the collective dose equivalent
rate as a function of time after the initiating event it isnecessary to make a number of assumptions. Some ofthese assumptions are of parameters which are predictable with more or less precision depending on thepresent state of knowledge; an example is the long-term
behaviour of radionuclides in the environment. Other
assumptions are in principle unknowable and unpredictable as they depend on the presence and on the habitsof human populations in the future; examples of suchassumptions are population distributions and the uses
made of flora and fauna as foodstuffs. Accordingly. theuncertainty of predictive calculations of collective dose
equivalent rates in future populations will increase withthe length of the time over which the predictions are
made.
54

73. A further source of uncertainty is the relationshipbetween the calculated collective dose rate in the future
and the number and severity of health effects presumed
to result. It is unlikely that the state of medical
knowledge will remain constant and future populations
may well have the ability to prevent or at least cureradiation-induced tumours which now prove fatal. This
comment may also apply to radiation-induced hereditary effects. For these reasons predictions over tens,
hundreds or even thousands of years may be useful
guides as to the consequences of present actions but
predictions over hundreds of thousands or millions ofyears are of very little use, except possibly by sensitivity
analysis to indicate the range of potential consequences.
74. Although there has been no systematic effort toassess the accuracy of the models used by theCommittee. some aspects of certain models have beenstudiei For example, the atmospheric dispersion
model has been assessed by comparison with observed
ground level concentrations after releases from elevatedsources [C2]. The emphasis was on the accuracy of theprediction of mean values and it was concluded thattypically the ratio of the standard deviation of concentrations about the mean, for a given dispersion
category, to the overall mean lies in the range of 0.5 to
0.7. The larger ratio refers to conditions dominated byconvection and the smaller one to conditions
dominated by mechanical turbulence. It was concluded
that the most likely error in calculations of the overallmean would come from an incorrect choice of windspeed and stability conditions. Under these circumstances a simple measure of the likely spread in results
could be obtained by carrying out calculations for
adjacent categories.
75. The models used for assessment of contaminationfrom nuclear explosions are firmly based on observed
data and have largely been derived through successive
approximations to measurements obtained over a
period of decades. These models therefore can be
expected to give good predictions of the results of suchcontamination. There will sometimes be substantial
uncertainties in the models for aspects of the environmental transport, especially close to the source, but if
these local aspects make only a small contribution to
the collective dose commitment the overall prediction
will still be reliable. A similar comment applies toglobally dispersed radionuclides from nuclear powersuch as 85Kr.

76. The dietary transfer models described in chapter V
are more difficult to verify, are more variable in timeand space and have a more tenuous link with direct
measurements. Sensitivity analyses of these models arebeing carried out but are not yet available. Somecomparisons of portions of the model with observed
values have been reported, for example the comparisonof the predictions of the soil migration model withmeasurements of the migration of single deposits ofplutonium in various soils [N 1]. The results of thislimited comparison showed agreement within a factorof two.
77. The models used for aquatic dispersion are allvery much simplified even for restricted systems such as
rivers. The general tendency of physical processes inaquatic systems is towards the well mixed average
concentration. which is the same tendency as exhibitedby the models. The major departures are in theprocesses which tend to perturb this situation and parti-cularly affect the radionuclide transfer to man, such as
sorption onto sediments or bioconcentration.
78. There has been a tendency to accept the values
generated by complex modelling techniques uncriticallyand ascribe more accuracy to the predictions than isjustified. This is now being challenged and theCommittee recommends that wherever possible somesuitable technique should be used to assess the overall
uncertainty associated with predicted results from alltypes of models and that this uncertainty be reported
together with the prediction.

IV.

ATMOSPHERIC TRANSPORT MODELS

79. The transport of radioactive material released into
the atmosphere is controlled by the normal atmosphericmixing processes. If the material is in the form of large
particles which fall rapidly under gravity then most will
settle close to the production point: small particles will
move with the air masses, as will gases. The major
mixing and transport processes which arc incorporated
into mathematical models are diffusion and advection.
These large-scale mixing processes give rise to the
distribution in the atmosphere of naturally-occurringcosmogenic radionuclides and of radionuclides
released by atmospheric nuclear explosions. They aredescribed briefly in Annex E (Exposures resulting from
nuclear explosions).
80. For releases from positions near ground level
models have been developed using two main
approaches: trajectory tracing. in which discrete
releases arc followed along the wind direction; andstatistical models, in which the activity concentration in
the airborne plume containing the radionuclides
released is described as a function of distance in the
direction of the wind. While the trajectory models suchas those in which successive very short duration releases
are individually traced through a time-varying windvelocity field [H3. S3] are capable of treating complex
situations and even operating in real time, the mainconcern of the Committee is with the relatively
Jong-term average results of routine releases to theatmosphere. For these calculations the statisticalmodels are adequate. As the plume containing theradionuclides travels downwind, the population will be
exposed to direct radiation from the plume and tointake of radionuclides by inhalation. For radioactive
materials other than gases both wet and dry deposition
processes will result in radionuclides being depositedon the ground and on vegetation. These depositedradionuclides will cause external irradiation, enter foodand drinking water supplies and become resuspended
to cause a further airborne hazard. Comprehensivemodels need to take account of all these routes, which
are described in chapter V.

A.

MODELS FOR LOCAL AND REGIONAL
TRANSPORT FROM A DEFINED POINT OF
RELEASE

81. There are some circumstances in which it isnecessary to assess the local transport of radionuclides
released into the atmosphere from a defined point. Thisoccurs in particular when dealing with releases fromknown nuclear sites such as reactors or reprocessing
plants of which there are only a small number.

82. It is sometimes possible to derive an empirical
relationship between the average or integrated activity
concentration in air at particular locations and thedischarge rates or total discharges in a given time ofradionuclides. These relationships are sometimes
referred to as empirically determined dispersion coefficients and arc used for some well-characterized nuclear
sites. This procedure is used, for example. in deriving
doses to local populations around the Pickering reactor
in Canada. referred to in Annex F (Exposures resulting
from nuclear power production).
83. The dispersion of materials released into theatmosphere is controlled by atmospheric diffusion, aprocess that depends on the state of the atmosphericturbulence over any area and at the relevant time. It has
been found useful in practice to develop empirically
based turbulence classification schemes using easily
observed quantities for characterization such as cloud
cover, wind speed and insolation. The most widely usedsystems are based on the one proposed by Pasquill [P2,P3] in which seven weather categories, A to G, aredefined in order of increasing atmospheric stability, as
shown in Table 5. Category A represents the most
unstable conditions, B and C Jess unstable. D neutral, E
and F stable. and G very stable. Rainfall is only
considered possible in categories C and D. The resultsof the dispersion calculations described later in thissection are normally generated for a series of releaseheights, for each stability category and for the situations C + rain and D + rain. These results are then
combined in the appropriate frequencies observed at
the place of interest. Many other methods for determining the category or defining stability categories
have been proposed and are in use: these are reviewed.
for example, by Gifford [Gl] and by Hoffman [Hl].
84. The most useful and commonly used statisticalmodel is the Gaussian plume equation initially
proposed by Sutton [S4]. This is based on an analyticalsolution of the diffusion equation under the assumptions of constant wind speed and direction, no wind
shear, flat topography and Fickian diffusion. The basic
equation in a generalized form, taking into account thereflection from the ground. can be expressed as [Nl]:Xa (x, y, z) =[exp

- (z - h)

2cr 2
2

(-y2)

Ao _ exp - - ,2nay cr2 v

2

+ exp

2cry

- (z + h)2]
2cr 22(9)

for the activity concentration corresponding to a given
release rate; the integrated activity concentration froma release is obtained by substituting ia for Xa and Ao for
Ao in equation (9), where Xa(x,y,z) and ia(x,y.z) are theactivity concentration and the time integrated activity
concentration per unit volume of air at the point (x,y,z):
ay and O"z are the standard deviations of the plumehorizontally and vertically; Ao is the activity released: v
is the average wind velocity at 10 m above the ground:h is the effective height of release; x is the downwind
distance; and z is the height above the ground of thesampling position. The origin of the co-ordinate system
is at ground level beneath the discharge point. In thederivation of equation (9) it is assumed that diffusion in
the x-direction can be ignored compared with transport55

by the wind for releases lasting a finite time. The
standard deviations CTy and o, arc not defined by themathematical assumptions hut arc determined from theatmospheric stability category as runctions or the
downwind distance. There arc many ways or obtaining
these values, and Vogt [VI] has produced a useful set orcomparisons.
85. For prolonged releases there will be nuctuations
in wind direction which lead to a more uniform activity
concentration across the plume. In this situation the
cross-wind Gaussian shape of the activity concentration
distribution is replaced by a uniform distribution.
Taking the angle subtended by the sector at the point of
release as 3 the activity concentration is given byAo

Xa (x, z, S) = - - - -l'2n Oz 3xv[

exp- (z - h)
,

2crz

2

2

+ exp - (z +2 h) ]
2crz

(10)

and as before the integrated act1v1ty concentration is
obtained by substituting Xa for Xa and A0 for Ao inequation (10), where Xa(x,z,B) and Xa (x.zA)) are theactivity concentration and the time integrated activity
concentration per unit volume of air at the points (x,z)
across the sector of angular width 3. In many situations
only the ground level activity concentration is required;this is obtained by setting z = 0 in equation (10).
Equations (9) and (10) apply for a single stability
category.
86. The accuracy of calculations based on equations
similar to (9) and (10) has been assessed by Hoffman etal. [Hl), and it was pointed out that they are generally
based on measurements at distances less than a few tensof kilometres from the source so that extrapolations togreater distances must be made cautiously. In addition.
the calculations are based on assumptions such as
steady meteorological conditions and Oat terrain.
However, the calculated results are probably accurate
within a factor of ten for relatively simple situations.
Improvements to the basic formulation given inequations (9) and (10) can be made to achieve a closer
approximation to the complexities of actual terrain.
Many of these are discussed by the United States
Nuclear Regulatory Commission [U4. U5, U6]. by ajoint study of the National Radiological Protection
Board of the United Kingdom and the Commissariat a
I'Energie Atomique of France [Nl] and by a United
Kingdom working group [C2).
87. When material is discharged from an elevatedsource. the plume will eventually reach the ground.
Thereafter the plume is reflected so that the radionuclides in it are dispersed back up into the air. Where an
inversion or boundary layer exists, the dispersedradionuclides are trapped between that and the ground.
Renections will in this case occur both at the groundand at the boundary layer. In the absence of renections
the plume would spread in the vertical plane to a size
determined solely by a, at the distance of interest. The
effect of introducing reflections is that the airborne
activity concentration must be obtained by summationof contributions from many points over the unreflectedradionuclide distribution across the plume. These may
56

be repre~ented by a series of virtual sources and themean t11nc integrated activity concentraction is
obtained hy summation. In most cases this series
converges rapidly and can be summed to any desiredmathematical accuracy, although the results are subject
to the uncertainties inherent in this modelling
approach.
88. The act1v1ty concentrations derived fromequations (9) and (10) apply to the dispersion of radionuclidcs which are not removed from the plume as it
tr.ivels downwind. A number of processes may act toremove the airborne radionuclides, in particularradioactive decay and dry or wet deposition. The
equations given above need to be modified to take theseprocesses into account. This is most simply achieved bymodifying the initial source activity Ao to allow for
depletion. This is simple for radioactive decay, except
where the daughter radionuclide concentration is being
considered but more complex for the deposition
processes.
89. Radionuclides are removed from the plume byrain falling through it. Precipitation is intermittent andthe true interaction with rain is very complex. The
simplifying assumption made is either that there is norain or that it rains for the duration of the dispersion; inthe latter case the effects of rain are estimated by theuse of a washout coefficient. As washout removes any
particulate radionuclide equally throughout the entire
vertical extent of the plume, the removal rate at any
distance from the source depends only upon the radionuclide concerned and the total activity reaching that
distance and not upon the vertical distribution of theradionuclide in the cloud.
90. Radionuclides are also removed from the plumeby many other processes; these include impaction withthe underlying surface or obstacles such as vegetation
on it, absorption from the air by plants and chemical
reactions with surfaces. The rate at which radionuclides
are transferred from the plume to the ground orvegetation surface can be modelled using the concept ofa deposition velocity. The deposition velocity, Vd, isdefined as the quotient of the activity of the radionuclide deposited on the surface per unit area and unit
time to the concentration of activity in air per unit
volume above the surface. Removal by this process
therefore depends on the activity concentration in air
immediately above the surface. This idealized mathematical description is a poor representation of theactual. very complex processes and it cannot easily becorrelated with experiments in which the concentrationof activity in air has to be measured some distanceabove the surface and in which the activity depositedon the surface has to be averaged over a finite depth
during measurement even for a flat surface. The
description for complex surfaces such as vegetation iseven less satisfactory.
91. The calculation of activity concentrations in air by
the methods outlined above is moderately complex but
the complexity is necessary in a general methodology
for dealing with the many different radionuclides
emitted from installations such as nuclear reactors or
nuclear fuel reprocessing plants. In some circumstanceswhere only single gaseous radionuclides are involved
for average weather conditions and no account need betaken of the height of release, deposition. radioactive

decay or weather conditions it is possible to use a
simple approximation such as)-pXXa (x) = A f ( ~0(II)where Xa(X) is the time integrated activity concentrationor the radionuclide in air at a distance x from therelease point; x1 = 103 m, is a normalization distance;
A 0 is the source activity: f is a coerlicient with dimensions s m-3; and p is a numerical exponent. For mostweather categories and release heights this approx imation. taking fas 3 1()-6 s m-3 and pas 1.5, is within afactor of ten of the more rigorous plume calculation formoderate release heights and distances out to about 100
km. A comparison is shown in Figure II with the results.,.;

l- 10-•

E
A
B
0

E

"

~

.,w
:-5
~

.z
a:

10-,.

:,

a:

...z

w
0

.~
.>
t;
.
."
a:

z

w

u

z

G

,o-1

0

u
>

F

<(

0

w

<(

a:
w

10 ...

!,

10'

10 1

10'

10•

DISTANCE OO'MffllNO 1ml

Figure II. Ground level Integrated activity concentration per unit
release as a function of distance downwind for uniform horizontal
dispersion Into a sector of angular width n/6 for a 30 m height of
release In various weather categories [C2] compared with the simple
approximate dispersion model taking f .. 3 10-6 s m-3, x1 = 103 m,
and p = 1.5

of calculations of the on-axis integrated act1V1ty
concentrations for uniform horizontal dispersion into a
sector of angular width n/6 in each weather category
from an effective release height of 30 m [C2].
The stack height of 30 m is only chosen for illustration. The choice of height will have little effect oncollective dose estimates but will considerably affectestimates of the maximum individual doses close to thedischarge point. In comparisons with calculations of
average
integrated
activity
concentrationsfordispersion in all directions a value off = 3 I 0-7 s m-3 ismore appropriate: this value is used in the calculations
for Table 6 which compares the time integrated activity
concentrations in air predicted by the dispersion model
for various distances. with those predicted by simple
global models. A better approximation for continuous
release would be obtained by changing the exponent p
from 1.5 to 1.2 in equation (11); however a value of 1.5
is often used.

92. For many purposes the annual integrated activity
concentration in air is needed as a function of distancefrom the discharge point. The expression for this isgiven in polar coordinates by [Nl]ia (x, ~J) = N Ao _LX,, {P, x. S) f(3. P)

(12)

p

where Xu(x. 3) is the annual integrated activity concentration in air at a distance x in a sector in the direction 9; Xo(P.x,9) is the integrated concentration of theradionuclide per unit release in a dispersion category,
P: f(-9,P) is the fraction of time a particular stability
category, P, exists with the wind in the sector withdirection 3 and of width 2n/N; N is the number ofsectors in the windrose.

93. The atmospheric dispersion models described inthis section apply to the behaviour of the radioactive
57

plume immediately after release and as it travels
downwind. The model forms and parameters arc mostreliable for distances up to a few tens of kilometres
although they are commonly used for distances up to
100 km. There are as yet no suitable general models
which describe the behaviour of released radionuclidcs
in the atmosphere at distances from the release point of
thousands of kilometres. This is a distance at whichcalculations based on dispersion of plumes are likely to
be increasingly in error but where the activity concentrations may not have approximated to the levels givenby the global dispersion model discussed in the next
section. For many relatively short-lived radionuclides
or those with sufficiently large deposition velocities,
this is of little consequence as the activity in the plume
will be depleted to relatively very low percentages of
the initial activity by distances of the order of 1000 km.
For example. it has been shown that for long-lived
radionuclides with a deposition velocity of 5 10-3 m s- 1
at most 4% of the material remains in the plume after
3000 km in category D conditions assuming no rain
LNl], while under all other conditions whether or not
rain is assumed essentially none will remain at that
distance.
B.

97. If the simple two-compartment model described inchapter III (paragraph 63) is used with input into thenorthern hemisphere compartment and transfer coefficients of 0.5 a-I then H5Kr becomes uniformly dispersed
within a few years. This model is used in Annex F(Exposures resulting from nuclear power production)for 85Kr inputs from nuclear power production but inAnnex E (Exposures resulting from nuclear explosions)the simpler approximation of instantaneous uniform
dispersion is again used, as it was in Annex C(Radioactive contamination due to nuclear explosions)of the 1977 report [Ul]. The time integrals of theactivity concentrations in air from the two models perunit activity input are 1.0 10-10 and 1.2 10-10 Bq s
m-3/Bq from Annexes F (Exposures resulting from
nuclear power production) and E (Exposures resulting
from nuclear explosions), respectively.
C.

GLOBAL MODELS

94. The radionuclides released from ground level
point sources whose atmospheric dispersion need to beconsidered on a global basis are the noble gases withhalf-lives longer than a few days, of which 85Kr is themost important example, and long-lived radionuclides
with very low deposition velocities such as certain
organic forms of 129) . Other radionuclides which
remain in the environment such as 3H and 14C and thebulk of the 1291 reside principally in the aquatic andterrestrial compartments and the models for these aredescribed in the appropriate chapters. Radionuclides
introduced into the atmosphere by nuclear explosions
are widely distributed as a result of their mode of introduction and thus have also to be modelled on a global
basis.

95. As has been described in chapter III (paragraph57). for many purposes the Committee uses direct
measurements of activity concentrations to obtain
estimates of collective doses from globally distributed
radionuclides from natural sources or fallout from
nuclear explosions. For some nuclides such as 239Pu
insufficient direct measurements are available andtherefore estimates are based on observed ratios of theradionuclide concentration in air to that of otherradionuclides, especially to 90Sr. Nonetheless comparisons are made with more complex models of theatmosphere such as the 12-compartment model
developed by Bennett [810] and this model was useddirectly to estimate the activity concentrations of 241Am
in surface air.
96. Some radionuclides such as 85Kr will remain in
the atmosphere and for the present there seems noalternative, for the purpose of estimating doses from thedispersion of such materials, to extending the models
described out to distances of about a thousand
kilometres and then making an abrnpt transition to a
global model. That this results in few difficulties isapparent from Table 6 in which typical time integrals of
the activity concentrations in air at distances of I 0, 100
and 1000 km for uniform dispersion in all directions
from the dispersion models [C2] are compared with thepredictions of simple global mixing models. The uncer58

tainty in the prediction of collective dose commitments
is less than might be thought since the results in, forexample. Annex F (Exposures resulting from nuclear
power production), show that the local and regional
component contributes only about I 0% of the collective
dose commitment per unit discharge of 85Kr.

DOSE CALCULATION

98. Given the concentrations of radionuclides in air as
predicted by the various models, then a number ofpathways exist through which man can be exposed. The
major pathways are direct irradiation from the cloud ofradioactive material, direct inhalation from the cloud,inhalation of resuspended material, and ingestion via
terrestrial or aquatic food chains. The first three will beconsidered here, the last two are more conveniently
discussed in the chapters on the terrestrial and aquatic
environment in sections V.B and VI.D, respectively.
99. If the specific activity model referred to in section
III.A is used, then no direct account is taken of theactual pathways by which activity enters the body. It ismerely assumed that the activity concentration per unit
mass of the stable element in the relevant organs or
tissues are equal to the corresponding activity concentration in an environmental material, in this case air.
and the absorbed dose rates are obtained from these
activity concentrations.

1.

Direct irradiation from the cloud100. Several systems of equations and nuclear data
are available to perform these calculations. as forexample those used by the United States Nuclear
Regulatory Commission [U4] or by the National Radiological Protection Board and the Commissariat al'Energie Atomique [Nl]. Provided that care is used inselecting the data and avoiding inappropriate models,such as the semi-infinite cloud at short distances, only
slightly different results will be obtained from different
calculation systems.
101. When the radionuclide is uniformly distributedin the atmosphere or the photon energy is sufficiently
low that this is a reasonable approximation over thevolume of a plume, then the simplest calculational
method is the semi-infinite cloud model. This is basedon the radiation from the cloud being in electronic
equilibrium so that the energy absorbed by a given
volume element equals that emitted by the same

element. For a point located at ground level only half
the space contributes to the dose, so that the energy
absorbed is divided by two. The absorbed dose rate in
air is then given by(13)

where Da is the absorbed dose rate in air~ Xa is theaverage value of activity concentration of the radionuclide in the cloud; Pa is the mass density of air; F; isthe fraction of photons of initial energy E; emitted per
disintegration; and k is a conversion coefficient fromenergy deposition per unit mass and unit time toabsorbed dose rate, which although strictly not needed
if the energy is expressed in joules, is sometimes given
as Gy h-l(MeV kg-1 s--1)-1. A modified version of thismodel is used for beta irradiation of the skin.
102. If the distribution of the activity concentration in
the plume is sufficiently non-uniform to invalidate theabove approach, then a finite cloud model must be
used. This involves simulating the cloud by a number ofsmall volume sources and integrating over thesesources. The calculation proceeds by finding thephoton flux density, scattered and unscattered, for aparticular decay energy, summing over all the decayenergies for the radionuclide of interest and thencarrying out a conversion to absorbed dose. The basic
expression for the photon fluence due to the fraction F;of photons of energy E; emitted per disintegration is
[N1]

$;=

~

Xv F; Ben (E;, µ;x) exp (-µ;x) V
d
4nx 2

(14)

\"

where$; is the photon fluence; Xv is the concentrationof the atoms of each radionuclide in volume elementdV; µ; is the linear attenuation coefficient; x is the
distance from the volume element dV; B00 (E;,µ;x) is theenergy absorption build-up factor at a distance, x, for aradiation of initial energy, E;, having an attenuation
coefficient, µ;. The integration is carried out over all
space. The integral is evaluated numerically, the calculations in Annex F (Exposures resulting from nuclear
power production) being based on the computer codedeveloped by Jones [J3).
103. The conversion from absorbed dose in air to dose
equivalent in tissue has already been discussed ingeneral terms in section II.A.1. When the absorbed dosein air is the result of a calculation such as described inthis section, then there are sufficient data on the photon
energy spectrum to use more precise conversions. These
conversion coefficients have been derived for adults[Nl] from the work of Poston and Snyder [Pl] based ona semi-infinite cloud model and are given in Table 7.
Similar conversion coefficients for electrons emitted by
the radionuclides of interest have been derived
assuming an inert layer thickness on the surface of the
body of 70 µm and are given in Table 8. The imprecise
nature of the estimation of the dose in skin fromelectrons must be stressed. This imprecision arises fromtheoretical difficulties associated with the estimation ofelectron absorption in the epidermis and also frompractical considerations such as absorption by clothingor nearby objects [Nl].

2.

Direct inhalation from the cloudCalculation of doses from direct inhalation fromthe cloud only depend upon data concerning the
integrated activity concentration in air over the periodof exposure, the breathing rate and the committed
absorbed dose per unit activity inhaled. The first
depends on the circumstances (i.e., whether the
exposure is to an isolated plume or to an annual
average concentration) and is assessed as describedearlier in this chapter. The breathing rates chosen by
the Committee are normally taken to be similar to thosespecified by the ICRP [16]; for example. a mean adultbreathing rate B of 20 ml d-1 is taken in Annex F(Exposures resulting from nuclear power production).
The committed absorbed dose per unit activity inhaledis generally obtained from the tabulations given by
ICRP [14. 111].

104.

105. A 'very simple model is used in Annex C(Technologically modified exposures to naturalradiation) to estimate the contribution of the inhalation
pathways to the collective dose commitments resulting
from the atmospheric release of a given radionuclide.
The relationship between the activity Ao associated withthe release of the radionuclide concerned and thecollective dose commitment M~ in organ or tissue q is
given by the expression(15)

where AolvdS is the integrated activity concentration of
the radionuclide in ground level air, obtained simply as
the activity released divided by the area of thedeposition region S and by the deposition velocity vd;
SON is the population affected, which is the product of
the area of the deposition region S and of the
population density ON. The areal dependence isremoved by the product of the quantities A0 /vdS and
SON; B is the individual adult breathing rate: Dq/l;h isthe committed absorbed dose in organ or tissue q perunit activity inhaled.

3.

Direct inhalation from resuspended material

106. The resuspension of materials from surfaces
depends on many conditions such as the physicalcharacteristics of the surface, the age of the deposit. thestrength of the wind and other disturbances. For agiven radionuclide, the real relationship between theactivity concentration in air per unit volume and theactivity per unit surface area is extremely complex andmany models of varying degree of complexity havebeen proposed. The simplest of them is the model
implicit in the use of the ··resuspension factor" which isdefined as the quotient of the resuspended activity
concentration in air per unit volume to the activity perunit area in the surface layer. If this factor is taken as aconstant, it implies a time-independent relationshipbetween those two quantities irrespective of the otherparameters referred to earlier or that the model is only
valid at one specific time; it further implies that theconcentration of activity in air results only from theactivity on the surface in the immediate neighbourhood. The problems involved in using this model
have been reviewed by Linsley [L2].

59107. As the deposited material weathers, it becomes
more closely associated with the soil and the activity
concentration profile gradually extends down into thesoil. Only the top layers of soil are available to beresuspended and the net effect is that the activity
concentration in air from resuspension falls off withtime following a given deposition event. Suchbehaviour can be represented mathematically by atime-dependent resuspension factor, which then has tobe defined in terms of the instantaneous values of therelevant quantities. This approach has been used withsome success [A2, U7] in models which assume different
initial resuspension factors in the range from 104 to
1o--6 m-1, but all converge to a value of the order of 10-S
to 10-9 m-t for times longer than about 20 years after
deposition. Healy [H4] has suggested that the activity
concentration in air declines at a slower rate and to alesser extent than the previously cited models would
imply, but this suggestion appears to be based on very
conservative interpretations of the observed results.
Comparison of models with observations is complicated by inconsistency of those reporting data inassessing the depth of soil over which the contamination is averaged and which is assumed to be available
for resuspension.

culate content of the air and the specific a~tivity of thesurface soil, the concentration of activity per unit mass
or volume of air can be derived [A2, U8]. The main
problem with this model is the assumption that thecontaminant and the soil are resuspended equally. Thisis almost certainly untrue for fresh deposits and evenfor aged deposits requires empirical correction factors[U8]. However, for material which is uniformly mixed
in the surface soil, such as long-lived naturallyoccurring radionuclides, these problems do not arise,
therefore the model is used in Annex B (Exposures tonatural radiation sources) for natural radionuclides
such as uranium. The particulate content of air is taken
as 50 µg m-3; this is a representative global value forground level air and corresponds to a resuspension
factor of about 3 10-9 m-t. There may, however, besome enrichment of the activity concentration ofcertain radionuclides in resuspended material; thisshould be taken into account if it is found to occur.
Subsequent calculations of doses are carried out as insection IV.C.2 for direct inhalation from the cloud.

108. The Committee has decided that the mostappropriate model at present is a time-dependent
resuspension factor and has applied this in Annex F(Exposures resulting from nuclear power production).
The value of the resuspension factor immediately after
deposition is uncertain and will depend on the precise
conditions of the land surface, whether it is desert or
pasture, wet or dry, etc.; a value intermediate in thereported range of 10-s m-1 is adopted. This initialresuspension factor is assumed to decline exponentiallyover about 2 years to a value typical of an aged depositof 10-9 m-1. Direct observations of the time dependenceof resuspension factors are limited to about a 20-year
period after deposition and therefore any estimates ofthe subsequent behaviour must be tentative.
Nonetheless it seems likely that there will be somefurther decline in availability and a second exponential
decrease with a half-life of about 100 years is assumed.
The resuspension model is therefore given by110. To calculate the distribution of individual doses
from radionuclides dispersed in the air it is necessary toknow or to assume the population density as a functionof position or distance from the source. If the distribution of individual doses is not needed, and only thecollective dose is required without any indication of its
distribution among the exposed population then it may
be calculated directly from the total deposition,
assuming some fraction of it is inhaled or ingested by
the total exposed population. The simplest assumption
which can be made of the population distribution isthat it is uniform and a population density of 100 km-2
has been taken for some purposes in Annex C (Technologically modified exposures to natural radiation).

K(t) = K1 exp [- 0,1 + 11.2 + 11.) tf ++ K2 exp [- (11.2 + 11.) t](16)

where K(t) is the resuspension factor defined as thequotient of the activity concentration in air to theactivity concentration in the top 1 cm of soil at time t;
Kt and K2 are the initial and intermediate values of theresuspension factors taken as 1o-s and 10-9 m-t. respectively; J..1 and 1i.2 are the decay constants for the initialand longer term decline in the resuspension factor; A is
the physical decay constant of the radionuclide ofinterest. The values taken for 11.1 and 11.2 are 1.46 10-7 s-t(4.6 a-1) and 2.2 10-10 s-1 (0.007 a-1), respectively. Morecomplex models have been developed which take into
account such factors as the size of the contaminatedarea, the surface roughness and the wind speed [ HS,H6]. At present, however, they can only be applied if
there is site-specific information while no generally
applicable model taking account of such factors is yet
available.

109.

Another simple approach to the modelling ofresuspension is to assume that particulates in air andsurface soil contain the same proportion of the contaminant. Then, given a knowledge of the average parti60

4.

Population distribution models

111. Population distribution weighting has also beenused to modify the physical distribution of radionuclides in calculating dose commitments from fallout.
This procedure was described by the Committee [U2]and consists of weighting the integrated deposit of aradionuclide in a latitude band by the percentage of theworld population in that latitude band. The population
distribution is given in Table 9 and is used in Annex E(Exposures resulting from nuclear explosions). The
resultant has been referred to as the populationweighted deposition of the radionuclide.
112. For calculations of local and regional doses.
particularly if they are to yield the numbers of people
receiving doses within given ranges as well as thecollective dose, the population distributions may need
to be fairly detailed as are those taken in Annex F(Exposures resulting from nuclear power production)around some model sites. Two examples are shown in
Table 10 for the distribution around a model reactorsite and a model uranium mining and milling site. The
total population out to 2000 km is in each case about
2.5 108 but the average population density up to 100 km
is only 3 km-2 for the mining site compared with 300
km-2 for the reactor site. The average population
density out to 2000 km is 20 km-2 for both sites.
Another example of this type of data generation is theplacing of the population distribution of the countriesof the European Community into a computer
programme on an approximate 10 km square grid,using census data [N 1).

113. To calculate collective dose commitments it isnecessary to specify the population distribution andmagnitude as a function of time. In most cases it is
implicitly assumed that the distribution and magnitude
at the start of the exposure continues indefinitely. In
Annex E (Exposures resulting from nuclear explosions)and Annex F (Exposures resulting from nuclear power
production) that assumption is used for relatively shortJived radionuclides such as 3H and 137Cs. For current
inputs of activity a world population of 4 109 is taken,
but for inputs in the 1960s the value at that time of
3.2 109 was taken. For long-lived radionuclides such as
14C and 1291 it is assumed that the world population
increases to a value of 1010 and then remains constant.

V.

TERRESTRIALMODELS

114. The simplest methods for calculation ofcollective doses from deposited material are based
directly on empirical relationships between measurements of activity concentrations in human organs or
tissues and in environmental materials such as soil orfoodstuffs. These have been discussed in chapter I II
and will be covered in more detail in section V.B. They
are appropriate either for individual doses where
specific data are available or for collective doses whenbroad average values are required and there is anadequate coverage of measurements. This procedure isused in Annex B (Exposures to natural radiation
sources) for doses from naturally-occurring radionuclides. In many cases, however, the development ofmodels based on the measurements can give more
confidence to extrapolations to other situations and to
predictions. In cases where direct measurements are notavailable then models may be the only means ofassessing the doses to people.
115. As described in chapter III, the Committee
developed models for the transfer of material throughfood chains in order to assess the doses resulting fromradioactive fallout from nuclear explosions after
deposition. The formalism developed by the Committee
relates the infinite time integrals of appropriatequantities in successive compartments of theenvironment; this differs from that used in othermodels although the concepts are similar. Models of
this type have been developed to assess doses fromdirect consumption of vegetables and intake via
animals and animal products and are used in Annex E(Exposures resulting from nuclear explosions). Terrestrial transfer models are of two general types, timeindependent models applicable to chronic conditions ofradioactive release and dynamic models applicable totime-varying behaviour after accidents or isolated
releases. This distinction is the same as that made by
ICRP between the concentration factor and systems
analysis models [17]. Often, dynamic models can beextended to long times when they should approximate
to time-independent models.
i16. The most widespread contamination of thesurface of the ground arises as a result of deposition of
airborne radionuclides. The models required are similar
whether the source is fallout from nuclear explosions ordischarge from nuclear installations. There are many
pathways by which deposited radionuclides can cause
irradiation of man but not alJ of them are of importance for all radionuclides. The simplest mechanism isdirect irradiation from the deposits on the ground but
even this will be affected by the movement of deposited
activity down from the surface soil into deeper layers.

Radionuclides can also enter food chains by contamination of the surfaces of human food crops, throughroot uptake or indirectly through contamination ofanimal food crops. All these routes must be considered.
117. If the rates of movement of radionuclides and theintegration periods over which results are required aresuch that the situation can be regarded for practical
purposes as in quasi-equilibrium. i.e., such that the time
variations can be ignored without introducing significant errors, then the models for assessing the concentrations of radionuclides in each compartment can betime-independent. Most models of this type use empirically derived transfer coefficients to calculate theradionuclide concentrations in selected compartments
along each pathway. Several of these models in use fortransfers of radionuclides through the environment [S5]are developed from the initial models incorporated in
the computer programme HERMES [F2], but in generalthey are simple models incorporating only a few
compartments and in some cases only a few pathways.
For example, the programme FOOD [83], which wasdeveloped for irrigation and its extension to include
direct deposition which is the basis of the model for
calculating nuclide concentrations in vegetation in the
United States Nuclear Regulatory Commission Guide[U4] takes account only of direct foliar retention androot uptake.
118. The result given by each of these models is theequilibrium concentration of radionuclides per unit
mass or volume in an end compartment, for example
vegetation, for a continuous rate of deposition ofactivity onto the ground surface. The results may
therefore be expressed as the ratio between the concentrations of activity in one compartment of theenvironment and the next compartment when thesehave reached equilibrium. This procedure is therefore
formally identical to the use of transfer coefficients by
the Committee in the context of fallout, where the ratiois that of the time integrals of activity.
119. Dynamic models also present the transfer
pathways as a series of interconnected compartments,
but the activity in each compartment is allowed to be afunction of time and the transfers between compartments are represented as rates. A typical example ofsuch a model is the programme TERMOD [B4] which isshown in diagrammatic form in Figure III. Models of
RADIONUCLIDE DEPOSITION

Above wrl,,ce

Soil rnrface

food r:rop

food crop

btlow theSubsurf1ce
soil p,:iol forthl' food crop

INPUT TO MAN

TT

I

Figure Ill. Compartments In the TERMOD computer
programme f84J

61

this type can deal with pathways in parallel as well as inseries, can allow for interconnections between different
pathways and can take account of feedback routes suchas the movement of activity from surfaces of pasturegrass into the soil and back into the grass via root
uptake. AJthough models of this type have many advantages and provide a more accurate qualitativedescription of the real situation, being particularly
useful in assessing the consequences of accidental
releases of activity, they require a very large amount ofdata as input values without giving necessarily morereliable answers than simpler techniques. They have
however been used in Annex F (Exposures resulting
from nuclear power production) for the assessment ofdoses from releases of activity to the environment.
A.

EXTERNAL IRRADIATION FROMDEPOSITED RADIONUCLIDES

120.
The most direct method for ascertaining theabsorbed dose rate in air above a surface incorporating
radionuclides, or on which radionuclides have been
deposited, is by measurement. This is the normal
method when estimating exposures to naturallyoccurring radionuclides and has been the techniqueused for fallout radionuclides. Local and countrywide
surveys for this purpose are described in Annex B(Exposures to natural radiation sources) and Annex E(Exposures resulting from nuclear explosions).
However, in many situations direct measurements ofdose rates from deposited radionuclides cannot bemade because of the relatively much higher dose ratefrom natural radionuclides; absorbed dose rates mustthen be calculated from a knowledge of the activity anddistribution of the radionuclide in and on the ground.
121. The simplest way to calculate the dose rate in air
above a contaminated surface is to assume that this is
an infinite plane source with the activity uniformly
distributed on the surface. This method is appropriate
for deposits with a short effective half-life on the soil
surface, which includes most fallout radionuclides, andwas used in Annex C (Radioactive contamination due
to nuclear explosions) of the previous report of theCommittee for all such nuclides except mes [Ul].
Standard formulae are available for such calculations.
In the case of 137Cs from fallout the distribution withdepth in the soil was assumed to be exponential with amean depth of 3 cm. The same methods are used in
Annex E (Exposures resulting from nuclear explosions).
122. When considering the naturally-occurring
primordial radionuclides, the distribution in the soil
may be taken to be uniform with depth. This distribution is also appropriate for ploughed land since in thiscalculation it makes little difference how deep thecontamination is, provided it is assumed to be uniform
to at least 30 cm [B5]. Standard methods are again
available [Nl) and are used where appropriate inAnnex F (Exposures resulting from nuclear power
production).
123. Intermediate between these extremes is thesituation where the radionuclide has penetrated theground but not to such an extent that it can beconsidered uniformly distributed. In this situation
models are required to predict the concentration profile
which may vary with time and to calculate the resultant
dose rate. A simple model of this type which does notinclude variation with time is the assumption of an
62

exponential distribution with depth of mes fromfallout. A more complex time-varying model [NI] isused in Annex F (Exposures resulting from nuclear
power production) in which the soil is divided into
compartments, with depths of0-1 cm, 1-5 cm, 5-15 cm,
and 15-30 cm. Each compartment is well mixed,
deposition is assumed to be into the top compartment
and activity is lost from the system out of the bottom
compartment. Transfers downwards are by simple
transfer coefficients and do not vary with time but may
be different for different chemical elements.
124. The absorbed dose rates in the human organs or
tissues of interest can be assessed from the absorbed
dose rates in air, taking into account the mass energy
absorption in the body tissues, the depth transmission,
the backscatter and the degree of isotropy (see thediscussion in paragraphs 23 to 27). In Annex A(Concepts and quantities in the assessment of human
exposures) of the 1977 report [Ul], the Committee
adopted a value of 0.82, which includes all the factors
mentioned, for the ratio between the absorbed dose ratein the body and the absorbed dose rate in air outdoors.
based on the work of Bennett [81] and a value of 0.69
indoors based on Spiers and Overton [Sl]. It now
appears (paragraph 27) that the most appropriate
average value of the quotient of effective dose equivalent rate to absorbed dose rate in air for males andfemales for use in this report is 0.7 Sv Gy-1 for environmental exposures (outdoors and indoors) for gamma
rays of moderate energy. For medical exposures
specific conversion factors are discussed in Annex G(Medical exposures).
125. Most studies of the shielding afforded bybuildings were carried out in the context of determining
the likely effects of nuclear explosions or reactor
accidents. The transmission factor for an externalsource of radiation is defined as the ratio of the photon
absorbed dose rate in air inside the building to thephoton absorbed dose rate in air outside. The mostextensive recent survey is that provided by Burson andProfio (86] which is summarized in Table 11 together
with some additional data on brick houses in the
United Kingdom [S6]. The absorbed dose rate indoors
may be increased by 10-20% if the roof and walls arecontaminated with deposited activity but deposition
which has penetrated inside the house is unlikely to add
more than an extra 5% [Ml].
126. The data given in Table 11 show that the transmission factors for buildings vary considerably. The
highest transmission factor is 0.3 for a brick house
relative to deposited activity (although wooden houses
would be expected to have even higher values), whereas
office and multi-storey buildings give considerably
more shielding with transmission factors below 0.01. In
trying to estimate a world-wide average the Committee
assumes that about 80% of all buildings are masonrywith the rest wooden; and that most time is spent inhomes rather than in office buildings. If transmission
factors for office buildings, masonry homes andwooden homes are taken as 0.05, 0.2 and 0.4, respectively, then assuming half the population to be workers
in offices and that 25% of their time is spent at work,
the average transmission factor is 0.22. Changing thepercentage of time spent at work to 10% or 50% changes
this average factor to 0.23 or 0.19, respectively. Jt
therefore seems reasonable to retain the previous
average value of 0.2 for the transmission factor ofbuildings with respect to activities of depositedradioactive materials.

127. A further important consideration is the amountof time spent outdoors compared with that withinbuildings. This will obviously vary greatly for different
areas of the world, being as low as 10% in the United
Kingdom and the United States [S7, Rl] but probably
much greater in warmer or less urbanized countries.
The Committee has previously taken, as a world-wide
average, that 20% of time is spent outdoors and there
seems no reliable data on which to base any change tothis estimate. Combining the transmission andoccupancy factors, the overall conversion factor toapply to the calculated or measured absorbed dose rates
in air from deposited radioactivity would now be
strictly 0.25. This factor includes allowance forconversion to absorbed dose in tissue as discussed in
section I I.A. I (paragraph 27), and for the proportion oftime spent outdoors or indoors in various buildings.
Changing the percentage of time spent outdoors to 10%
or 30% changes this overall conversion factor to 0.20 or
0.31, respectively; for consistency, the Committee has
decided to continue to use the overall factor of 0.3
adopted in Annex A (Concepts and quantities in theassessment of human exposures) of the 1977 report
[U1].

128.

In Annex C (Technologically modified exposures
to natural radiation) account is also taken of thecontribution to the dose rate indoors from naturalradionuclides in the building materials themselves. Avery simple model is used assuming the indoor space isa cavity in an infinite mass of the building material, sothat the dose rate is proportional to the gamma-ray
emission constants of the radionuclides of interest. The
value obtained is only an index allowing comparison
between building materials and not an estimate of thedoses that would be received in houses constructed withthose building materials. In many cases, adequate
indoor measurements are available for assessment of
actual doses.

B.

nuclear explosions) of the 1977 report [Ul] and in
earlier reports [U2, U3]. The same models are used in
Annex E (Exposures resulting from nuclear explosions). As described in the introduction to chapter III,the results of transfer models are expressed as therelationships between appropriate time-integrated
quantities in two compartments of the environment.
131. This formulation is used in Annex E (Exposuresresulting from nuclear explosions) with regard to themost important radionuclides in fallout which enter
dietary food chains. The transfer coefficients ofconcern for this aspect of the modelling are from
deposition to human diet and from human diet totissue, denoted as P23 and P34, respectively. The transfer
coefficient from deposition to diet is given by
00i

C (t) dt
P23 = _o_ _ __

(17)

00

I o et> dt

0where C(t) is the act1v1ty concentration of theconsidered radionuclide in the diet at time t and O(t) isthe deposition density rate. For values of C(t) and U(t)assessed on a yearly basis, the integrations can be
replaced by summation
00

I CCi)i= I

P23 = -

(18)

--00

L O(i) .

i = I

In the case of 90Sr and 137Cs, the following model isused to relate the activity concentrations in food groups
or in the total diet to the annual deposition densities:

DIETARY TRANSFER MODELS AND DOSECALCULATIONS

129. Probably the simplest model is that which has
become known as the specific activity model. This does
not attempt to describe the environmental transfer
behaviour of the radionuclide under study. It is basedon the assumption that activity is dispersed so as toresult in a uniform concentration in a defined receptor
medium. In this situation the radionuclide will bepresent in the environment at a particular specificactivity with respect to some stable analogue. The
concentration of the radionuclide in body tissues isthen assumed to bear the same relationship to theconcentration of the stable analogue in the body. Given
the knowledge of the mass of the stable analogue, thenthe activity of the radionuclide in the body can befound. This method is used for example in Annex B(Exposures to natural radiation sources) and in Annex
E (Exposures resulting from nuclear explosions) toassess doses from tritium and carbon-14.
130. As described in the introduction to chapter V,
models of several types can be used to describe thetransfer of deposited radionuclides through vegetable
and animal food chains to man. For the situation inwhich the integration periods over which results arc
required are relatively long, as when dealing with thelong-term contamination from nuclear explosions,models have been developed by the Committee andused in Annex C (Radioactive contamination due to

C (i) = b 1 0 (i) + b2 0 (i -

+ b3

I) +

co

L

e-µm

O (i - m)

(19)

m - I

There are contributions to activity concentrations indiet from the annual deposition density in the year
considered O(i), in the previous year O(i-1) and for all
preceding years, expressed by the summation, with an
exponential term describing the combined physicaldecay of the radionuclide considered and any decreasein availability to plants in soil. The values of b1, b2, b3,
and As can be derived from measured data by regression
analysis. The combination of equations (18) and (19)leads to(20)

where n = 1 year, a constant in this case. A similar
treatment is applied in calculating the transfer from dietto tissue (coefficient P3 4) for 90Sr. In some cases, acombined transfer coefficient P24 is used to directly
relate the time-integrated concentration in human tissue
to the integrated deposition density; this is theprocedure used for deposited mes.
63132. In the previous reports of the Committee theresults have been expressed in terms of the quotient of
the activity of 90Sr per unit mass of calcium in diet or inbone. This treatment is retained in Annex E (Exposuresresulting from nuclear explosions) but data are also
given on the concentrations of calcium per unit mass inrelevant materials where available. Standard values of
the concentrations of calcium per unit mass are usedwith measurements of the activity concentration of 90Sr
in foodstuffs of various kinds and standard values of
the intakes of these foodstuffs to calculate the intake of
90Sr.
133. The most useful time-dependent models havecompartments to represent the various environmental
materials, vegetables, animals and animal products.
The transfer between compartments is assumed to obey
first order kinetics, so that the system forms a set of
coupled first order differential equations as describedin the introduction to chapter III and in more detail by
ICRP [17]. The compartment models used in Annex F(Exposures resulting from nuclear power production)
are of this general form. The models are howevercomposed of alternative subsets of compartments ofvarying degrees of complexity, depending on theradionuclide under consideration and to some extent
on the availability of data. The general layout of thecompartments is shown in Figure IV, which includes

RADIONUCLIDE DEPOSITION

Soil

Bone

INPUT TO MAN

Figure V. Alternative sub-sets of compartments forthe "Animal" compartment shown In Figure IV

The depth is taken as 30 cm in Annex C (Technologically modified exposures to natural radiation) and in
Annex F (Exposures resulting from nuclear power
production). For undisturbed land such as permanentpasture the model used in Annex F uses a set of four
compartments representing soil depths of 0-1 cm,
1-5 cm, 5-15 cm and 15-30 cm. Transfers from the firstto second and second to third compartments is one way
downwards, transfers between the third and fourthcompartments are in both directions and loss is represented by transfer out of the fourth compartment.

INPUT TO MAN

Figure IV. The major compartments In the terrestrial foodchain models used In Annex F (Exposures resulting from
nuclear power production)

135. Transfer of radionuclides to food plant crops ismodelled in Annex F (Exposures resulting from nuclear
power production) by part of the general system illustrated in Figure IV; the portion of interest for thispathway is shown in- Figure VI. The initial input of
Deposition---~
more processes than Figure III, and more feedback
loops. In further refinements, even these compartments
can be divided into sub-compartments, if desired. For
example, the single soil (mixed) compartment in Figure
IV can be replaced by a four-layer compartment suchas that described in [N1] and the "Animal"
compartment can be replaced by either of the twoalternative subsets shown in Figure V. The various
adaptations of the general model used for specifictransfer routes are considered in the following
paragraphs. More details may be found in [N1].

Periodic
removal of plantsfrom land due tocropping[XTERNAL
PLANT
Trans location

Resuspens ior,
processes--- ---~HITERNAL
PLANT

Root
uptakeSOIL

134. Two models are used for the migration of radionuclides through soil. For soil which has been well mixedby ploughing or cultivation, a model consisting of asingle compartment extending to a defined depth isused; loss, including radioactive decay, is represented
by a single transfer coefficient out of the compartment.

64

Remova 1

Figure VI. Schematic representation of the model tor transferof radlonuclldes to plants [N1]

radionuclides into the system is by deposition into thecompartments representing surface soil and theexternal surfaces or the plant. Subsequent interactions
within the system represent translocations between theexternal and internal parts or the plant and between theinternal parts of the plant and the soil. Allowance isalso made for direct transfers between the external
plant surfaces and the soil, although it is assumed thatwhen plants arc harvested some form or washing orouter husk shedding removes 90% or the remaining
surface contamination. This model is used for green
vegetables, grain and root crops with the appropriate
sets of transfer coefficients, some of which depend on
the element being considered.
136. The intake of radionuclides by grazing animals is
modelled in Annex F (Exposures resulting from nuclear
power production) in a similar fashion to that shown in
Figure VI for soil but incorporates the more complex
soil model and several routes of transfer to the animal.
The model is shown in Figure VII. Provision is made
Depositioo--·•---------Deposition

PASTURESURF/ICE

Resuspens ion

ANIMAL

Figure VII. Schematic representation of theprlnclpal mechanisms for the transfer of radlonuclldes to grazing animals [N1]

not only for consumption by the animal of plants but
also for some direct uptake of soil from the uppercompartment, either by eating it or by inhaling
resuspended soil particles. For all radionuclides otherthan the transuranium elements the simpler representation of the "Animal" compartment shown in Figure V
is used; for transuranium elements the more complex
representation is used. These models are used torepresent cows and sheep with the appropriate sets ortransfer coefficients [Nl], some of which are elementdependent. The models are used to derive matrices ofresults for contamination by particular radionuclides.
The results are expressed as the time integrals of theactivity in unit mass of the foodstuff over different
periods of time following deposition of the radionuclide on land at unit activity per unit area; theseresults are used in Annex F (Exposures resulting from
nuclear power production).
137. The doses to particular individuals fromingestion or contaminated foodstuffs cannot generally
be correlated with the local level or environmental
contamination because most foodstuffs are transported
some distance between harvesting and consumption.
The local contamination will only predominate for rareindividuals who subsist almost entirely on local
products. In the more general case and in order toassess collective doses it is sufficient to know thequantity or food or each type derived from an area or
known contamination, the fraction or the food ingestedby the population and the delay between harvesting (oranimal slaughter) and consumption. The time integralof the collective dose rate in tissue is obtained as the
product of the collective intake or activity or the radionuclide and or the committed dose per unit intake ofactivity.

C.

MODELS FOR TRANSPORT UNDER THE
GROUND SURFACE

138. All the models so far reviewed in this chapter are
confined to describing the behaviour of activity on thesurface or the ground or in the layer of soil down to adepth of a few tens of centimetres. There is, however, abranch of modelling which is becoming of more interest
with the various propositions to dispose of large
quantities of radioactive wastes by burial in the ground[S8]. This branch is the modelling of radionuclidetransport from the buried waste repository back to thesurface or to portions or the terrestrial environment
directly available to man, e.g., potable water supplies.
The main transport route considered in studies of thistype is transport in association with a flow of groundwater [B7, H7, K2]. The major processes taking placewhen nuclides are transported in this way areadvection, dispersion, sorption and radioactive decay;
it appears from studies that axial convection anddispersion in the direction or flow predominate andtherefore unidirectional paths have so far been
generally assumed through the soil or rock column
between the repository and the output point. Equations
describing these processes can be solved .analytically or
numerically and a number or solutions have been
derived for various boundary conditions [B7, H7, L3].
The output of the transport calculation is used as input
for terrestrial or aquatic models of varying degrees ofcomplexity in order to calculate doses to man. The
Committee has decided for the present report not toassess this aspect in detail, but to rely for the time being
on other reviews such as that carried out as part of theInternational Fuel Cycle Evaluation [112].

VI.

AQUATIC MODELS

139. The primary hydrodynamic mechanisms ofradionuclide transport in aquatic systems are advection
and diffusion/dispersion. Interactions with suspended
matter and sediments are important physico-chemical
processes and under some circumstances interaction
with biota may provide a transport mechanism. There
are perhaps more models of more different types
available for modelling hydrologic transport than for
any other sector or the environment. For example, in
the report by Hoffman et al. [H2] which contained arevie~ or hydrologic models, 24 models were identified
of which 11 included provision for calculating radionuclide concentration. The majority of these models
have been developed for some specific place such as aparticular river system or estuary. In the following
sections the calculations or activity concentration foreach sector of the aquatic environment will beconsidered together with the pathways by which man
utilizes this water. The sectors or the aquatic
environment are linked together so that radionuclides
which enter a lake or river may eventually reach theseas and oceans.
65

A.

ISOLATED WATER BODIES

140. The simplest type of aquatic model considers thereceiving water body as a single volume and assumes
that the radionuclides are uniformly diluted in thisvolume. Allowance is normally made for some renewalof water in the receiving body and for removal
processes such as sorption onto sediments andradioactive decay. The model previously used by theCommittee in Annex D (Radioactive contamination
due to nuclear power production) of the 1977 report[U I] is of this type. The change in activity concentration
with time in such a water body is given by

where ).'.w is the activity concentration per unit volume
in the water body at time. t; A0 is the rate of input ofactivity; V is the volume of water: At- is the fractional
rate of renewal of water; As is the fractional rate ofremoval of activity by sorption onto sediments;).. is thephysical decay constant.

141. Removal of activity onto sediments is assessed in
Annex F (Exposures resulting from nuclear power
production) with a particle scavenging model [Nl]. This
uses the equilibrium distribution coefficient between
suspended sediment and water to calculate the activity
concentration in the suspended sediment: the removal
is then determined by the rate of settling of particulatematerial onto the bottom. The fractional rate of loss ofactivity by sorption onto sediments is therefore given
by(22)

where Kd is the sediment to water distribution coefficient, defined as the quotient of the radionuclide
concentration per unit mass in sediments to the radionuclide concentration per unit volume in the water; z is
the average water depth in the water body; ms is therate of sedimentation expressed as mass per unit area
and time; Psed is the concentration of suspended
sediment load in mass per unit volume of the water
body. This type of model is appropriate for isolated
water bodies such as lakes but can also be used as areasonable approximation for relatively isolated andinternally well mixed portions of larger water bodies[Nl]. It is used in Annex F (Exposures resulting from
nuclear power production) to describe the local
behaviour of activity discharged to coastal waters.

B.

RIVERS

142. Models of river systems either are extensions of
the single compartment model described in theprevious section or attempt to represent the physicalmixing processes. Many examples of the latter type arebased on solutions of diffusion/advection equations
which include velocity and diffusion in the downstream
direction, together with the rates of input of activity at
the discharge point, and of loss of activity byradioactive decay and processes such as sorption on thebottom sediments. Most practically developed models
do not incorporate all these processes, although they
may treat one or more in a thorough fashion. For
66

example, in the United States Nuclear Regulatory
Commission treatment of non-tidal rivers [U6], which isof this general form, the diffusion has been considered
in two dimensions to give horizontal and downstream
concentrations (assuming vertical mixing) after
Yotsukura [YI, Y2] for meandering irregularly shapedriver cross sections, but there is no treatment of
sediment interactions.

143. The other major class of models divides the river
into a system of interconnected compartments linked
by transfer coefficients. Two of the most thoroughmodels of complete river systems are of this type: thestudy of the Mississippi basin by Martin et al. [M2] andthe study by Bayer of the Rhine-Meuse system [B9]. The
model used by Bayer is a set of compartments, eachcorresponding to the single compartment represented
by equation (21), and leads once again to the solutionof a set of first order differential equations similar to
those described in chapter I I I. Bayer chose to consider
only equilibrium conditions and to ignore bulk
transport of bed sediment by comparison withtransport via suspended matter: under these conditions
the solution is readily obtained analytically for single
radionuclides. In the computer programme RVRDOS
used by Martin et al. [M2], however, the emphasis is on
the provision for daughter products and specificarrangements are made for impoundments (e.g., dams)
at various positions downstream. Diffusion is notconsidered, nor is sedimentation. In effect. the onlychanges in concentration are due to additional inputsof activity, dilution from additional tributary water
inputs and the effects of radioactive decay, including
build-up of daughters. Impoundments are treated as
uniformly mixed volumes at the end of each stretch ofwater.

144. A model which includes treatment of sedimentinteractions, not merely as a method for removal ofactivity, but with provision for transport of contaminated sediment downstream, has been developed by the
National Radiological Protection Board jointly with
the Commissariat a l'Energie Atomique [Nl], based on
the work of Schaeffer [Sll]. This model assumes arectangular river cross-section, ignores the effect ofdiffusion and thus simplifies the calculation to a systemof linked first order differential equations. Solutions ofthese for an equilibrium situation show an exponentially declining activity concentration in the water
downstream of the input point, but predict peaks in theactivity concentrations in the bed sediments at positions
downstream which are dependent on the bed sedimentand suspended sediment velocities. This model has
been used where appropriate in Annex F (Exposuresresulting from nuclear power production). The model isbased on the observation [Sl 1] that the long-term
average activity concentration in a transversely wellmixed river decreases exponentially with distance fromthe discharge point. The activity concentration X.w in thewater (including suspended sediments) at a distance, x,
is therefore given by

Ao

Xw (x) "" V exp (- k x)

(23)

where Vis the volume flow rate of the river: and k is acoefficient dependent on the river and the radionuclide.
For a given nuclide the value of k depends on the half-life, the river velocity and the rate of sorption onto
sediments and is given bycurr~nt ~ecreases. approximately inversely in proportion with the distance from a point source.

k = A+ As

148. Despite the existence of these rather welldeveloped models many practical calculations ofdispersion in coastal seas or in oceans use very simple
models, although these may be based on more complex
background calculations. For instance, in an example
of a plume calculation used by the IAEA [18] for
deriving
the definition andrecommendations
concerning high-level radioactive wastes unsuitable fordumping at sea, it is assumed that the width of theplume is about one-tenth of its length and that theactivity concentration from a continuous release isinversely proportional to the current; this is inagreement with the results of the more rigorous
treatment referred to above.

(24)

V

where v is t~e river v~locity; A is the physical decay
constant_; A.s 1s the fractional rate of removal of activity
onto sediments. The measured values of the sediment towater distribution coefficient, Kd, defined in section
VJ.A. are taken to be indicative of the fractional rate ofremoval. Elements with Kd values greater than to m3
kg-_1 are taken to have strong interaction and A.s is
assigned the value 2 10-5 s-1; elements with Kd values
between 1 and 10 m3 kg-1 are medium with a A.s value of
4 1 Q-6 s-1; elements with lower Kd values are assigned azero value of A,s. All these values apply for a river
velocity of 2 m s-1.

145. Models of .this type are designed to apply only to
long-term cond1t1ons averaged over at least a year· noattempt is made to model seasonal changes such as
spring lloods or droughts. The outputs from the model
are the concentrations of activity in the water and in thesuspended sediments as a function of distance from theactivity discharge point, together with the amount ofactivity on the river bed sediments as a function of
distance and time. The routes of exposure of man are'reviewed in section VI.E.
C.

SEAS AND OCEANS

146. In some situations where the activity concentration of a radionuclide has been measured, as forsome naturally-occurring radionuclides there is nor~qu)re~ent for a model of the processes'leading to thed1.stnbut1?n· I~ oth:r cases, especially when dealing
with rad1onuchdes introduced at a defined location
rather tha~ as a widely distributed source, the activity
concentration may vary so much with space and timethat complex models are required to assess either
individual or collective doses.
147. Although the basic mixing processes in the seas
a1_1d oceans. are still advection and diffusion, a majordifference 10 modelling activity distribution is introduce? by ~h.e s.cale of th: water bodies [N3]. The
physical m1xmg processes m the seas have been thesubject of extensive study for many years and theemphasis among most oceanographers has been on
producing models to describe dispersion and dilution
processes. Many of these are of a diffusion typealthough some include an advective term and may evenal~ow f~r shear effects. i~troduced by the change in'Ymd-dnven mean veloc1ties with depth. In many situat10ns, the seas tend to be vertically stratified and incoastal seas the depth is small in comparison to thehorizontal extent, so these can often be assumed to bewell-mixed vertically; in these cases one- or two-dimensional treatments of dispersion are usually sufficient.
The starting point for many of these calculations is thesolution of the radially symmetrical horizontal
diffusion equation for a substance introduced instantaneously at a point in an infinite sea. Solutions to thisra_dial diffu~ion equation [N3] may then be combined~Ith advect1ve terms obtained by empirical observat10ns of current llows or theoretical treatments such as
those of Gifford [G3]. In practice, it may be reasonable
for mathematical convenience to ignore diffusion in the
direction of mean flow. The result of calculations of
this type is that the activity concentration at the centre
of a plume of radionuclides in the direction of the149. The simple single compartment model describedin section VI .A is also applicable to relatively isolated
and well mixed seas or ocean basins, especially if only
integrated activity concentrations are required. Thismodel is used in Annex F (Exposures resulting from
nuclear power production) for some preliminary
estimates of activity concentrations from coastal
discharges into appropriate receiving bodies such asbays or local sea regions.
150. The same treatment can be extended to deal withmore compl~x situations by adding compartments torepresent adJacent water bodies. This leads once again~o a system of differential equations of the form given
in chapter III. An example of such a set of interlinked
compartments is that developed to model the coastal
se~s around North-Western Europe [Nl]. The geographical components are illustrated in Figure VIII whilethe volumes of the water bodies and volumetricexchange rates are presented in Figure IX. Removal to

ARCTIC OCEANNORTH EASTATLANTIC OCEAN

FigureVIII. Compartments Into which North-Western
European waters can be divided [N1]67

radioactive material discharged eventually ·resides in
the aquatic compartments of the environment,
irrespective of whether the radioactive material isdischarged to atmosphere or to a water body. The
normal treatment of these radionuclides is either bydirect measurement of activity concentrations or bycompartment models of an appropriate degree ofcomplexity.

Arc t le Oct an

North-Ea51
Atlcn11c.

"'

Othrr Oceans

1.0 •to'KEy,-.---~

Volum• e-xchon91 rate. km 1 a- 1

Figure IX. Compartments and their volumes and theexchange rates between compartments of theNorth-Western European regional model [N1]sediments· requires the specification of z, ms- and Psed
(see section VI.B.) for each water.body. This model isused in Annex F (Exposures resulting from nuclear
power production), where the values are given.
D.

GLOBAL MODELS

151. For certain long-lived radionuclides other than
noble gases and some naturally-occurring rad.ionu~li_d~s
the majoritf of the activity assocfa"tecf . with the

AIRBORNE
ANO LIOUIO-...;,---i
DISCHARGE

152. For radionuclides which are produced naturally
such as 3H and 14C, it is possible to derive an empirical
relationship between measurements of activity concentrations and estimates of production rates. The activity
concentration per unit mass of hydrogen in humantissues from natural tritium has been estimated byassuming it is the same as that in continental surface
waters• before nuclear explosions began. This is thenused to relate the annual average absorbed dose in the
body to the annual production rate of natural tritium.
In the case of 14C the activity concentration of natural
origin is taken to be that measured in biologicalsamples such as wood from the time before nuclear
explosions began. Using the concentration of carbon in
the body ·given by ICRP [16], the annual averageabsorbed dose in the body is related to the natural
production rate, deduced from an estimate of thenatural inventory. These procedures are used in Annex
B (Exposures to natural radiation sources) to assess
absorbed doses from natural production. In Annex E(Exposures resulting from nuclear explosions) the dose
commitments resulting from the production of 3H. and
14C in atmospheric nuclear explosions are based on theabove relationships and on the quotients of the activity
inputs from nuclear explosions to the annual rates of
input from natural production~ These procedures arecompared in Annex F (Exposures resulting from
nuclear power production) with the slightly morerefined models described in the following paragraphs.

153. A compartment model can be used to assess theactivity concentration of tritium, which is rapidly taken
up in the circulating waters. The model is shown in
Fig~re X and is made up of four compartments representing the circulating anddeep waters of the northern
and the southern hemispheres, respectively.

0.1

Ciculating
hemisphera

0.0014Circulatingwater
southernwaternorthern

0.05

hemisphere

0.1

0.1

0.00140.005
Deep O<:San

Deep oaan
northernhemispheresouthernhemisphere

0.005

Figure X. The model used for global circulation of tritium.
(Fractional exchange rates are given In units of e-1) (N1]154. A similar but rather more detailed model can beused for carbon-14, based on the extensive work on the68

carbon cycle. It is shown in Figure XI and is used in
Annex F (Exposures resulting from nuclear power

0.5

Atmotphereand landAtmosphereand landsou1hcrn

northernhemls1,here
Hunws
northernhemispherehemisphere

0.5

Humus
southefn

0.1

hemisphere

0.1

0.1

0.1

Surface ocean 1 - - - 4 - - ~ Surface ocean
LIQUIDs,outhern
DISCHARGE -----'.>----1 northernhemiiphern
hem\!aphcre

0.05
0.00140.1'0.1

0.0014'0.005
Deep ocean

Deep ocean

southernhemisphere

northernhemisphere

0.005

Figure XI. The model used for global clrculotlon of cerbon-14. (Frectlonel exchange rates
ere given In units of a-1) [N1]production) although this model does not incorporate
uptake into deep ocean sediments. A model of this typewas used in earlier reports of the Committee.
155. For nuclides as long-lived as 1291, although, inprinciple, a model similar to that used for tritium may
be applied, the activity concentrations in all compartments become equal over a time scale so short incomparison with the half-life that it is sufficient toassume uniform dispersion in all circulating waters
after any local behaviour has been allowed for.

E.

DOSE CALCULATION

156. The output from all of the models used is theactivity concentration in the water and if appropriate in
the suspended and bed sediments. There are a verylarge number of pathways by which man can be
exposed, many of which are common to fresh and sea
water, although a few such as irrigation and direct use
as drinking water are only appropriate for fresh water.
These pathways may need to be studied separately indetail to obtain individual doses. especially for a
mixture of radionuclides. If only collective doses are
required then it may suffice to know the quantity ofactivity transferred via a particular pathway and thefraction taken in by man, or even the total quantity ofactivity transferred to man via all pathways.
157. For some radionuclides such as tritium and 14C,
for which a relationship has been established bymeasurement between the natural activity concentrations in surface waters and the activity concentrationsin the organs or tissues of the body then the dose
estimates can be derived from these relationships.

radionuclide concerned. In some circumstances where
desalinated sea water may be used as drinking water,
the calculation is the same although the effective decontamination by the desalination process may be muchgreater than that produced by freshwater treatment.
This is rarely a major pathway compared with ingestionof marine foodstuffs.
2.

Consumption of fish and other aquatic flora andfauna

159. The act1v1ty concentrations in fish and otheraquatic fauna and flora are frequently derived on theassumption that they are in equilibrium with the water.
The ratio of the activity concentration per unit mass infish and other organisms to the corresponding activity
concentration in water is, under this assumption, aconstant. The edible fractions vary for the different
fresh water and marine flora and fauna. The individual
or collective dose calculation then requires only
knowledge of the mass consumed by the individual orby the population and the dose per unit activity intake
via ingestion for the radionuclide concerned.
3.

Consumption of agricultural products.
160. The most important route by which activity canreach man from irrigation is by spray irrigation of cultivated crops. The form of model used to assess this is thesame as that used for any other deposition process andhas been described in chapter V. The only difference isthat the fraction deposited on the external surface ofvegetation is taken as 0.05 rather than 0.2 for deposition
from the atmosphere [Dl, D2].
4.

1.

Other pathways

Direct consumption of water158. The simplest pathway to man for fresh water isdirect ingestion. It is necessary in principle to allow for
any decontamination by water treatment processes
before supply although for freshwater the effect is small
and no decontamination is included in Annex F(Exposures resulting from nuclear power production).
The dose calculation then merely requires anassumption of the volume consumed together with thedose per unit activity intake via ingestion for the161. Most other pathways are relatively unimportantin terms of collective doses, although they may be
important for individuals. An example is direct external
irradiation from contaminated sediments along theshoreline in which a knowledge of occupancy times is
crucial together with an assessment of the dose rate. A
related pathway is inhalation of airborne activity either
from contaminated sediment particles which have been
resuspended from coastal sediments or those whichhave been directly transferred to the atmosphere from69

the sea surface [PS]. Direct exposure to activity in waterfrom swimming, boating, etc., can in principle beestimated in the same way.

VII.

CONCLUSIONS

162. The main purposes of the Committee are toassess and compare natural and man-made sources ofradiation by estimating the resulting individual andcollective doses. Some of these sources are globallydispersed, as arc most naturally-occurring radionuclides. Others are initially highly localized, such asdischarges from nuclear installations. Some sources
such as x-ray machines give only external radiation andlead to no contamination of the environment, others
lead to widespread distribution of radionuclides in any
or all sectors of the environment, air, ground and water.
Exposure may be to external radiation, incorporated
radionuclides or a combination of both.
163. Dosimetric quantities used to describe exposureof individuals or populations to radiation werereviewed. The most basic quantity is the absorbed dosein any organ or tissue. As the evaluations of risk madeby the Committee are based on the assumption of
proportionality between the absorbed dose and theprobability of induction of stochastic health effects,
results are where possible first reported in terms ofabsorbed dose. The dose equivalent is needed to
combine the consequences of different radiation types
and the effective dose equivalent to take account of thedifferent relative stochastic risks of irradiation ofdifferent body organs or tissues. These quantities areappropriate to describe the irradiation of individuals
and for any individual the effective dose equivalent canbe used to estimate the probability of induction of astochastic health effect, defined as cancers which provefatal and serious hereditary effects in the first twogenerations.
164. When dealing with populations analogous
collective quantities are generally defined as related tothe sources of exposure, but some additional quantities
are also needed for particular reasons. Although forindividuals it may be appropriate to produce an overall
probability of a health effect, for populations it may beappropriate to separate hereditary effects from somaticeffects and for some organs or tissues the cancers which
do not pro~e fatal may also be identified separately.
~he. Committee has. therefore retained the geneticallys1gmficant dose equivalent and discussed the possible~se of another .similar quantity, the somatically significant dose eqmvalent, for the purpose of broad intercomparisons.

165. The dosimetric models needed to assess doses inorgans or tissues from measurements of absorbed dose
rates in air are described, as are those needed to assess
doses in organs or tissues from intakes of activity orfrom activity concentrations in the same or otherorgans or tissues. These are based on measurements ofthe movement of radionuclides in the body, the rate ofelimination from particular organs or tissues and fromthe body, the characteristics of the organ or tissue andof the radiations emitted by each radionuclide.
166. In assessing doses from any source, the first
recourse is to direct measurements. These may be eitherof the external dose rate, as in most estimates ofoccupational exposures, external doses from fallout or
doses from medical x rays; or of the activity conce_ntrations in human organs or tissues, as for many exposures
to naturally produced incorporated radionuclides.
70

167. Slightly less direct estimates can be made frommeasurements or activity concentrations of radionuclides in air or in foodstuffs which are consumed bypeople. In this case some additional information isrequired on the intake rates of the radionuclides fromair or from the foodstuff concerned before using theappropriate dosimetric models. These less direct
methods are used for many environmentally dispersedradionuclides, particularly to assess exposures toindividuals irradiated as a result or discharges from
nuclear installations and to assess doses from someradionuclides resulting from nuclear explosions.

168. When direct measurements arc not possible orpracticable, either because of technical difficulties inmeasuring the activity concentration of the radionuclide concerned in an appropriate medium, because
the number of radionuclides or media are too large or
becaUS\! predictions or extrapolations are required, thensome form of model has to be used to describe theenvironmental transfer processes.
169. In general the simplest type of model should be
used which will produce the required answer and isappropriate to the radionuclide concerned, its mode of
introduction and its environmental behaviour. For
naturalradionuclides
inequilibrium
intheenvironment, simple empirical relationships between
measured activity concentrations are adequate. This
treatment, or slight elaborations of it, may also be used
for the same or analogous radionuclides widelydispersed in the environment and which may be taken
for practical purposes to be in equilibrium; theseinclude some fallout radionuclides and globallydispersed radionuclide releases from nuclear installations. For other individual radionuclides such as 90Sr
produced in fallout it may be necessary to model theirtransfer through the environment in a time-varying
fashion often using simple compartment models.
170. For mixtures of artificial radionuclides released
to atmosphere and water from nuclear installations at
rates which vary considerably over time and for which
both individual and collective dose estimates are
required, then quite complex models may be needed.
These should be capable of accepting time-varying
inputs and of giving maximum individual doses, dose
distributions as a function of space and time, andcollective doses. Models of this type are describedwhich are used mainly for assessing the consequencesof releases from the nuclear power industry.
171. When models are used to describe a given
situation, it is important to carry out comparisons
between calculated and observed results where possible
and to refine the models on the basis of such comparisons. This has in general been done for the models
used by the Committee. In some circumstancespredictive models cannot be directly verified by thatmethod. For such models, techniques such as sensitivity
analysis are being developed to assess the variability ofpredictions and their dependence on the model form
and available data. The Committee wishes to encourage
wider comparisons or different forms of models for thesame sectors of the environment as well as analyses ofthe effects of uncertainties in the data bases. These
comparisons will improve confidence in the general
results from such models. Similar analyses could also
be more widely applied to dosimetry models. Models
which have been developed to describe the movementof radionuclides through the environment can also be
used in an appropriate fashion for stable elements.

~ - e__lUnits of the SI sys tern and other basic, derived and experimental
units used in this report
Quantity

SymbolLength
Mass

m

Time

t

Electric current
Electric charge
Thermodynamic temperature
Energy

I
Q

E

Power
Volumep
VAmount of substancena/Unit name

Unit syr.;bolmetrekilogram
tonne
secondminute
hour
day
year
amperecoulomb
kelvinjoule
electron volt a/watt
cubic metre
1itre'
r.iole

m

kg
t
s

min
h
d

a
A
C
K

J

eV

u3
m

1
r.iol

1 eV = 1.60219 10- 19 J (ap~roximately}.

Ta b1 e2

Quantities, units and symbols

Quantity

Sy11.bol

Unit

SI restricted unit
Name
s·l
A
ActivityA
Anteriors·lAAdministered activity
0
µm
AMAD
Activity Median Aerodynamic
Diameter
m3 5-1
B
Breathing rate
Energy absorption build-up factor
Ben(E,µx)
at a distance, x, for a radiationof energy, E, having an attenuat'ion
coefficient,µ, in the materialof interest
Bone lining cells designator
BLC
s-1 kg-1
Activity concentration per unitCmass
J m- 3 b/
Potential a-energy concentration
Cpot
J s m- 1
Potential a-energy exposure't'potCortical bone designatorCBµmCount Medi an Aerodynamic Diameter C~lAD
J kg-1D
Absorbed dose
D
Class of inhaled substance
J kg-1IT
Per caput (arithmetic mean)
absorbed dose
J kg-1
Absorbed dose index
J kg-1
Mean absorbed dose in tissue, TJ kg-1
Absorbed dose COlll11itment
J kg-1
Absorbed dose convnitment
from a source, kMean energy of particles of typeJ
per nuclear transformation of
the parent nuclide
J
Potential a-energy
Equilibrium factor {radon or
thoron)Fraction of photons of initialenergy, E, emitted per
disintegration
Fraction of air admitted
Fraction of foodstuff, g, consumed

Symbol a/becquerelBqbecquerel

Bq

gray

Gy

gray

Gy

gray
gray
gray
gray

Gy
Gy
Gy
Gy

71

Table 2 (continued)

Quantity

SymbolSI restricted unit
Name

Symbol a/

J kg-1s ievert

Sv

J kg -1

sieverts ievert

Sv
Sv

kg-I

sieve rtsieverts ievert
sieve rtsievertsieve rtsievert

Sv
Sv
Sv
Sv
Sv
Sv
Sv

J kg-1

sievertSv

becquerelbecquerelBq
Bq

becquerel

Bq

J kg-1

gray

Gy

H

J kg-IM'

J kg-1man gray ::/man grayman Gyman Gyman grayman GyEquilibrium factor of nth daughter Fn
Fraction of free daughters compared Ffd
with all such daughters
Fraction of free daughters compared F' fd
with all such daughters as if
they were in equilibrium wi tilradon or thoron
Emanating power
Genetically significant dose
equivalent
H
Dose equivalentIT
Per caput (arithmetic mean)dose equivalent
Co11111itted dose equivalent
Effective dose equivalent
Dose equivalent index
Dose equivalent in tissue, T
Uniform whole-body dose equivalent
Dose equivalent corrmitment
Effective dose equivalentcommitment
Dose equivalent corrmitment
from a source, kIntake of radionuclide
Intake of radionuclide
by ingestion
Intake of radionuclide
by inhalation

72

Unit

Kerma

K

Sediment/water distribution
coefficient
Sorption equilibrium constantLinear energy transfer
Collision stopping power
La tera 1
Collective absorbed dose
Incomplete collective absorbed
dose corrmitment to time,,from a source, kCollective absorbed dose fromabsorbed doses in the range
0 to D
Collective absorbed dose ratio
Modifying factor (in definitionof dose equivalent)
Integral number (population,
windrose sectors, etc.)
Posterior
Atmospheric stability category
designator
Transfer coefficient fromcompartment m to compartment n
Probability of a value, xQuality factor (in definitionof dose equivalent)
Exhalation rate
Exhalation coefficient
Relative biological effectivenessRed bone marrow designator
Collective dose equivalent
Surface areaKd

J kg-1
J kg-1
J kg-1
J kg-1

J kg-1

J kg-IJ kg-1
J

LAT

k

MR
N
N

P
P
Pl!Yl
P(x)
Q
Bq m- 2 s-l
Bq m- 3 s -l

R
Rv
RBE
RM

s

J kg-1s

m2

man sievert

man Sv

Table 2 (continued)

Quantity

SymbolCollective effective dose
equivalentBeam area
Filter area
Collective dose equivalentcommitment from a source, kCollective effective dose
equivalent colll!litment
from a source, ks•kIncomplete collective dose equivalent commitment to time,,,from a source, k
SSD
Somatically significant dose
equivalentT
Tissue or organ designator
Half-life (physical)\12
Half-life (effective)
Teff
TB
Trabecular bone designatoru
Activity surface densityw
Class of inhaled substanceX
Exposure
X
Nunt>er per unit volume
Number of condensation nuclei
per unit volume in air
Number of radon atoms per unit
volume in airyClass of inhaled substanceAtomic numberz
Air designatoradParticle diameterg
Foodstuff designatorhHeightParticle type designatorjRadionuclide designator
Source designatorkCompartment designatorm
Mass per unit area
Compartment designator
IntegernMean number of particles of typeni
per nuclear transfonnation of
the parent nuclide
Target designatorq
Radial distancer
Range of a particle of energy, Er(E)Age/sex class designatorsSurface densitysChild expectancy weighting factor v
Velocityv
Deposition velocity
vd
Water designatorw
Weighting factor for organ or
wT
tissue, T (in definition ofeffective dose equivalent)
Horizontal axisx
Horizontal axis
Y
Vertical axisz
Depth
Air kenna-rate constantSI restricted unit
Unit

Name
J kg-1

Symbol~/man sievert

man Sv

J kg-1man sievert

man Sv

J kg-1man sievert

man Sv

J kg-1man sievert

man Svs ievert

Sv

m2
m2

s
s

µm
m

m

m

73

Table 2 (continued)

Quantity

SymbolSI restricted unit

Unit

flame
Dispersion coefficient
Turbulent diffusion coefficient
Washout coefficient (including
rainout)
Product
Sum
Particle fluence
Specific absorbed fraction
Energy f1 uenceaRadiation typeRadiation type6
yRadiation typey
Life span of red cells£
Energy impartedaAngular directionl(Resuspension factor
Physical decay constantAttachment rate (of free radon
daughter atoms to aerosol
particles)
Biological elimination
rate constant
Deposition rate of radonAddaughter atoms on indoor surfaces
Physical decay constantof radionuclide, j
Effective elimination rate constant Am
out of compartment, mAv
Ventilation rate (fractionalchange in volume per unit time)
Linear attenuation coefficientuMean, median or mode of a log
unormal distribution
Energy absorption coefficientAir flow rate
Densityropulation density
Density of rockStandard deviation
Geometric standard deviation
Standard deviation with respect
to parameter, xTime of duration (of a practice)T
Mean residence timeT
Mean lifetime
TParticle fluence rate
(I)
Activity concentration per unit
X
volumeTime integrated activity
X
concentration per unit volume
Energy fluence rate

Symbol ~/

s
J

-1

m
3

m s -1kg m-3m-2

kg m- 3

a
s
s

-2

m

s

-1

s-1 m-3

a/ Symbol for the special name of the SI unit restricted to specified quantities,
Some of the referenced data are given in terms of working levels. The
working level (WL) is a potential a-energy concentration of 1.3 10 5 MeV per
litre of air.
c/ The term "man" is not a physical unit but is retained to reinforce understanding of the collective quantities.
d/ Some of the referenced data are giv~ij in t~pns of rontgen (R). The required
conversion factor is: 1 R = 2.58 ID C kg •

TS/

74

Table3

Weighting factors recommended by the ICRP
for calculation of effective dose e9uivalentand the reference risk coefficients on whtch the are based

Reference
Weightingrisk
coefficient
factora/1/2" Sv-l

TissueGonadsBreastRed bone marrow
Lungs
Thyroid
Bone surfaces
Remainder b/

0.40
0.25
0.20
0.20
0.05
0.05
0.50

0.25
0.15
0.12
0.12
0.03
0.03
0.30

a/ The average probability per unit dose
equivalent over both sexes and all ages
of induction of a fatal tumour or ahereditary effect in the first twogenerations.
b/ A weighting factor, wT, of 0.06 applies
to each of the five remaining organs or
tissues receiving the highest dose
equivalents; exposure of all other organs
or tissues can be neglected. (When thegastro-intestinal tract is irradiated, thestomach, small intestine, upper large
intestine and lower large intestine aretreated as four separate organs).

Table

4

Comparison of the source regions included by UNSCEAR and ICRP,n the calcuiat,on of dose e u,valent 1n bone-l1n1n cells
or re one marrow rom a em tters ,n one
Source region a/ b/

Type ofradionuclide
distribution

Target volume

UHSCEARICRPUIISCEAR(this report)

TB+CB
TB+CB

TB(E)+RM+CB
TM(E)+RM+CB
TB-.RM
TB(E)+RII( 1977 report)

9one lining cells
Red bone marrow

SurfaceVolumeSurfaceVolumeTB(E)+RM
TB(E)+RM
TB+RM
TB(E)+RM

TB

TB

a/ The notation (E) indicates that the coefficient in the equation
relating dose equivalent rate to activity concentration and energy
is itself a function of energy.
b/ TB - Trabecular bone; RM - Red bone marrow; CB - Cortical bone.
Ta b 1e

5

The Pasgui 11 stabi 1ity categories[J:i2, 153]
Night

Surface windspeed
(m s- 1)

StrongModerate

Slight

< 2
2 - 3
3 - 5

A - B
B

A a/

A - B
B

5 - 6
> 6

C
C

B- C
C- D
D

B
C
C
D
D

a/

lnsolation~

1/2 cloud£.I" 3/8 cloud
G

E
D
D
IJ

F
E

D
D

Weather categories are arranged in order of increasing atmosphericstability, A being the most unstable and G the most stable condition;category Dis used for any sky conditions during the hour precedingor following night as well as for overcast conditions, day or night,
regardless of windspeed.
Night is from 1 h before sunset to 1 h after dawn.

75

modelHodel

Time integral of activity
concentration per unit release(Bq s m- 3 /Bq)

Distance(km)-9Dispersion mode 1 IC2)

10
100
1000
Approximate dispersion 7
10model w!th f = 3 10- s m- 3 , 100
x1 = 10 m, and p = 1. 5
Uniform global dispersion
model for krypton-85

3 10_ 10 to
2 10 11 tol 10to32l-8

1 10_10
3 10
10-10

Table

7

Conversion coefficients from absorbed dose in air
to dose equivalent in t1ssue
as a function of the 1n1t1al photon energy
I P1.

Nl l

PhotonenergyAbsorbed dose Quotient of effective dose equivalent or dosein air per unit equivalent in the specified organ or tissue
to absorbed dose in air
photon f1 uence(Sv Gy-l)(MeV){l0- 16 Gy m2)

Effective

GonadsThyroid

Skin

7.5
3.1
1. 7
0.7
0.3
0.3

0.002
0.014
0.054
0.23
0.57
0.63
0.77
0.80
0.72
0.71
0.80
0.78
0.97
0.97

0.004
0.014
0.07
0.22
0.43
0.46
0.53
0.73
0.57
0.57
0.70
0.65
0.71
0.71

0.00040.0002
0.033
0.27
0.60
0. 71
0.97
0. 76
0.63
0.55
0.84
0. 76
1.6
1.6

0.19
0.35
0.44
0.58
0.76
0.80
0.90
0.95
0.91
0.98
0.91
1.0
0.95
0.95

-2
1.0 10_2
1.5 10_2
2 .0 10_2
3.0 10_2
5.0 10_2
6. 5 10 _1 2_/
1.0 10_ 1
2.0 10_1
5.0 10
1.0
1.5
2.0
4.0
10.0
a/

0.4

0.9
2.3
4.6
6.2
7.5
12
23

a/ These energies were not considered by Poston and Snyder [P1: but areincluded to facilitate interpolation.

76

1 a b I e

8raa{ation emitted

Nuclide

3H
14c

41 Ar
51cr
54Mn
59Fe
58co
60co
83mKr
85mKr
85Kr
87Kr
88Kr
89Kr
86Rb
88Rb
89Rb
89Sr
90sr
90y
9ly
95zr
95Nb
99Mo
99 Tc
99",-c
103Ru
106Ru c/lO~h124 5b
125Sb
125~e
127~e
127Te
129mTe129Tea/Absorbed dose rate~_/ perunit activity concentration[I0- 7 Gy a-I (Bq m- 3)]
In airIn skin

0.25
2.1
16
0.002
0.008
5.0
0.01
4.3
1. 0
9.7
8.9
43
13
39
22
62
30
19
7.3
30
21
5.2
2.2
14
3.9
0.61
3.1
45
1.4
14
5.1
3.9
3.1
9.2
9.6
19

0
0.22
7.6
0.001
0.004
1.8
0.005
1.4
0
4.4

3.9
21
5.8
19
11
31
14
9.3
3.0
15
9.8
1.9
0.26
6.7
1.1
0.18
0. 72
22
0
6.5
1. 5
l.O

0.6
4.0
4.1
9.0

Nuclide131mTe
132Te
1290
1311
132 r
1331
1341
1351
13lrnxe
133rnxe
133Xe
l 35f11xe
135xe
137Xe
138xe
134cs
13Scs
136cs
137cs sJ
138Cs
140Ba
.140La
14lce
144ce
144Pr
147Pm
154Eu
155Eu
239Np
238Pu
239Pu
240Pu
241Pu
242Pu
241Am
242cm
244cm

Absorbed dose rat~/ perunit activity concentration(I0- 7 Gy a-l (Bq m- 3)]
In airIn skin

6.0
4.3
2.8
8.2
18
15
22
15
5.4
7.4
5.9
3.7
13
56
23
6.9
2.8
5.3
9.6
39
12
19
7.3
4.2
40
3.0
9.9
2.6

2.5
0.87
0.19
3.4
8.8
7.2
10
6.9
2.0
3.2
1.6
1.8
6.0
28
11
2.9
0.54
1.8
4.2
19
5.0
9.3
2.8
1.2
19
0.63
4.3
0.26
3.9
0.001
0.09
0.001
0.000004
0.008
0.003
0.0000001
0

11

0.27
0.28
0.25
0.28
0.06
0.89
0.24
0.20

Multiply by an 1.0 to convert to dose equivalent rate in skin.

'fj/ Assuming an inert layer thickness of 70 µm.

""f./ Including the short-1 ived decay prc:ducts.

77

TableLa ti tudc band
(degrees)

0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
80-90

9

Population distribution(per cent)llorthern
hemisphere

Southernhemisphere

6.3
11.0
32.7
20.4
15.5
13.7
0.4

54.0
16.7

14 .9
13.0
0.9
0.5

0

0
0

0

0

Ta b l e

10

Population distribution around model release locations
Population distribution aroundmodel release locations
Distance (km)

0-1
1-2

2-5
5-10
10-20
20-50
50-1000-100100-200
200-500
500-1000
1000-2000
100-2000Model reactor
site

Model uranium
m1n1ng andmilling site

I. 3 10;
3.0 104
2.6 104
9. 0 105
4. 3 106
2 .8 106
6.1 106(9.5 10 }9 .4 10 4i
2 .0 lOi
7.0 108
1.4 lOi
1. 7 10(2.5 10 8 )2 .5 108

Table

11

Effects of shielding by buildings on the ratio
of indoor and outdoor ehoton absorbed dose rates 1n air
under egu1l1br1um conditions~86. S6)

Structure or location

Brick house
Small multi-storey building c/
Basement
Ground floor or first floor
Large multi-storey building c/
Basement
Upper fl oars
a/

_t:/

c/

78

Transmission
Transmission
factor forfactor for
immersion in adeposited
uniform cloud 2._/ activity~/
0.6

0.05 - 0.3
0.01
0.05
0.005
0.01

The ratio of the photon absorbed dose rate inside thebuilding to the photon absorbed dose rate in an infinite
unifonn cloud of activity.
The ratio of the photon absorbed dose rate inside thebuilding to the photon absor~ed dose rate 1 m above
an infinite smooth plane wit~ activity unifonnly distributed on the surface.
Away from doors and windows.

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