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APPENDIX D
THE SUBSISTENCE-FARMER CRITICAL GROUP
In Chapter 2 we recommenct that the form ofthe stanciard be a limit
to the risk to the average individual in a future critical group. This
appendix summarizes the steps that could be involves] in assessing
compliance with such a standard! for a particular exposure scenario that
defines the critical group as inclucling a subsistence farmer exposed to a
maximum concentrator of raclionuclicles in ground water.
The risk involved here is the risk of ill health from a radiation
dose. Risk entails probabilities as well as consequences. A risk analysis
must entail the development of probabilistic distributions of doses to fixture
individuals for various times in the future and the development of
probabilistic distributions of consequences (health effects) from those
dosed.
There are various means of constructing risk measures from such
probabilistic distributions to be comparer! with a risk limit. The risk
measure recommended in Chapter 2 is the expected value of the
consequences, determined by integrating the probabilistic distribution of
consequences over the entire range of estimated consequences.
The conceptual approach to analyzing risks to future individuals
from a geologic repository will be illustrateci here for undisturbed
performance (e.g., not including human intrusion, meteoric impact, etc.~.
Radionuclicles can be released via air or water pathways. The steps in
calculating risks for the water pathways are summarizer! here. Similar
steps are involves! in calculating risk to fixture individuals via air pathways.
For this illustration, radionuclides in waste solids are calculated to
eventually dissolve in water and undergo hydrogeologic transport to the
saturated zone and subsequently transport via an aquifer to the biosphere.
A plume of contaminated ground water will spread! out underground,
downstream from Yucca Mountain, to places where it might be susceptible
to human use. Calculating the space- and time-dependent probabilistic
A probabilistic distribution of a variable can be thought of as the probability per
unit increment of that variable as a function of that variable.
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154
YUCCA MOUNTAIN STANDARDS
distributions of concentrations of radionuclides in the ground-water plume
is the purpose of geosphere performance analysis.
Calculation of Geosphere Performance
As clescribed in Chapter 3, there are many different possible
mechanisms ant! pathways for the dissolution-transport processes. For
example, dissolved radionuclides might be transported to the lower aquifer
by slow processes that provide time for local sorptive equilibrium with the
rock. In other locations, radionuclides might be transported via fast
pathways resulting from episodic local saturation, with little time for
diffusion into the surrounding rock matrix.
The analysis must begin with what might be, in principle, a time-
dependent statistical distribution of such scenarios of release and transport.
Enough scenarios must be identified that will reasonably sample the events
that can contribute to important releases of radionuclides. The probability
of each ofthese geosphere scenarios must be estimated so that the resulting
analysis can reasonably approximate the statistical distribution of
consequences that would be expected.
For each geosphere scenario there are large uncertainties in the
parameters used in the equations for release ant} transport. For full
probabilistic analysis, a state-of-knowledge distribution for each parameter
must be developed. Using the equations of transport, these probabilistic
distributions of input quantities can be projected into a probabilistic
distribution of ground-water concentration, which will vary with position
ant! time. Although many useful calculations are made with analytic
techniques (NRC, 1983), detailed results require discretizing input
quantities, followed by event-tree transport calculations of a large number
of combinations of input quantities (EPRI, 1994) or by Monte CarIo/Latin
Hypercube sampling of a smaller number of data combinations, as used by
the WIPP anti Yucca Mountain Projects (Wilson et al., ~ 994~.
Semianalytical adjoins techniques that help create probabilistic
distributions from the discretized results are also available. Any of these
numerical techniques can yield useful probabilistic distributions, if done
properly. The choice is better left to the analyst, who must consider
limitations of time, budget, and computer power. Estimates of errors

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APPENDIX D -THE SUBSISTENCE-FARMER CRITICAL GROUP 155
introduced by sampling techniques shouIc! be incluclec] when such
techniques are used to reduce the number of discrete calculations.
These space- and time-dependent probabilistic distributions of
concentrations in ground water, with emphasis on ground water beyond the
repository footprint, are the input quantities needed for calculating
radiation doses, consequences, and risks for the biosphere scenarios.
Similar approaches are followed for calculating the space and time
dependent concentrations of raciionuclides released to the atmosphere.
Many analysts employ system software that feeds geosphere results
(Erectly into biosphere calculations, bypassing the display of probabilistic
distributions of concentrations in ground water.
Calculation of Biosphere Performance
For the biosphere scenario involving the subsistence-farmer critical
group, ground water is assumed to be withdrawn at the location of
temporal-maximum concentration of radionuciides. The time of that
maximum concentration specifies the time at which the doses,
consequences, and risk are being calculated at that location. In the era of
temporal-maximum concentration, the concentrations at a given location
vary little over a human lifetime, so the ground-water concentration can be
assumed constant in calculating lifetime closes and risks for that critical
group. The critical assumption in this model, then, is that a subsistence
farmer extracts water from the location of maximum concentration of
radionuclides in the aquifer, provided that no natural geologic feature
precludes drilling for water at that location.
The subsistence farmer is assumed to use the extracted
contaminated water to grow his food and for all his potable water.
Conservatively, the farmer is to receive no food from other sources. A
pumped well to extract ground water can perturb the local flow of ground
water, so that concentrations of contaminants in the extracted water can be
less than in the unperturbed ground water. The extent of concentration
reduction depends on the extraction rate (Charles and Smith, 19911. A
reasonable extraction rate can be calculated assuming that the subsistence
farmer or even the entire critical group uses a single well for extracting
ground water.

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YUCCA MOUNTAIN STANDARDS
If the subsistence farmer's water is obtained from commercial
pumping of the underground aquifer at the point of maximum local
contaminations, the effect of commercial rates of water extraction on the
withdrawn concentration can be included in the analysis. Obviously, for
commercial water withdrawal, it is the withcirawal location rather than the
location of the subsistence farmer that is important.
The vertical variation of concentration in grounc! water at a given
surface position can be obtained from the geosphere analysis. If methods
of predicting the vertical location of the point of water withdrawal within
the aquifer are clefensible for the long-term future, then the effect of
withdrawing at locations other than that of the vertical maximum
concentration can be included. Otherwise, arbitrary assumptions of well
depth would diminish confidence in the resulting calculated risk.
The largest radiation exposure to fixture humans from contaminants
in grounc! water is predicted to result from internal radiation from ingested
or inhaler! radionuclides. For the water pathways, eating food
contaminated by irrigation or by other use of contaminated ground water
for growing food is expected to be the source of largest dose, greater than
closes from drinking water (NRC, 1983~. Therefore, realistic prediction of
closes and risks to future humans requires knowlecige of their diets and
amounts of fooci and water consumed. Such information for the distant
future is unknowable. Therefore, as is clone in all other biosphere
scenarios, we must assume that future humans have the same diets as
ourselves (including foot] and water consumption). This amounts to the
unavoidable policy decision that geologic clisposal is to protect future
humans whose diets are the same as ours or whose diets would! not lead to
greater radiation closes from using contaminated water than would the filets
of people today.
All biosphere scenarios must also rely on tiara for the uptake of
radionuclides from contaminated water into food. Here, one can rely on
scientific data for the typical soil conditions and for the kinds of foods
assumed for this analysis. For a given food chain and for drinking, the
amount of radioactivity ingested in a given time, or over a human lifetime,
2 There is a current proposal for commercial withdrawal of ground water Tom the
aquifer near Yucca Mountain. This water could be distributed to local
communities as well as others that might exist or be developed farther from
Yucca Mountain.

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APPENDIX D - THE SUBSISTENCE-FARMER CRITICAL GRO UP I 5 7
is proportional to the concentration of radionuclicles in the extracted ground
water.3
The ingredients of the biosphere approach describer} here,
beginning with specified concentrations in extracted ground water, are
iclentical with those of the widely used GENI computer code cleveloped by
Napier et al. (19881. The GENT code is used by the WIPP Project in
predicting closes to future inclividuals who utilize contaminates! water for
drinking and for growing foot] ant} who receive no food from outside
sources. It is an example of what could be used or updater} for calculating
subsistence-farmer doses.
The GEN! code includes intake-close parameters recommender} by
ICRP and other agencies. Therefore, employing GENI or a similar code
to predict radiation doses to future humans who inadvertently use
contaminated water requires the adclitional assumption that future humans
have the same dose-response to ingested radioactivity as clo present
humans. All biosphere scenarios adopt this assumption. Of course, it is
expected that the intake-dose parameters will be updated when new
information is available.
Given the probabilistic distribution of concentration of
radionuclides in extracted grounc} water at a given future time and location,
the human-uptake-response mociel, such as GENI, can predict the statistical
distribution of radiation doses to the subsistence farmer. Because the
grounci-water concentrations vary little over a human lifetime, it is
necessary only to sum the close commitments for a human who uses that
contaminated water over his/her lifetime. The result is a probabilistic
distribution of lifetime dose commitments, easily converted to lifetime
average annual close commitments.
The probabilistic distribution of lifetime dose commitments can be
converted into a distribution of consequences by multiplying each value of
dose commitment by the appropriate dose-risk parameters, obtainable from
ICRP and others. If the constant dose-risk parameter of the linear
hypothesis is used, the probabilistic distribution of consequences will differ
from that of doses by only a constant multiplier. Here, by adopting dose
3 This assumes uptake factors, i.e., distribution coefficients for a given
radiochemical species in a given plant or other organism immersed in
contaminated water, that are independent of radionuclide concentration.

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YUCCA MOUNTAIN STANDARDS
risk parameters developed for present humans, we are assuming that fixture
humans will have the same present risk when exposed to a given radiation
dose. All biosphere scenarios adopt this assumption. Of course, it is
expected that the close-risk parameters will be updater] when new
information is available.
Each value ofthe consequence is then multiplied by the probability
distribution function for that consequence, and this integrand is then
integrated over all consequences. The result is the calculated risk to the
subsistence farmer from ground-water pathways, expressed either as the
lifetime risk or as the lifetime average annual risk. To this risk from the
ground-water pathways are to be added other calculated risks for the
subsistence farmer, who is the individual at maximum risk within the
critical group.
To obtain the risk to the average member of the critical group, for
compliance determination, it can be arbitrarily assumed for simplicity that
there is a uniform distribution of inclividual risk within that group.4
Because {CRP's homogeneity criterion specifies that the critical group
should have no more than a tenfold variation in inclividual dose, and
because large departures from the linear dose-response theory are not
expected for this calculation, the expected value of the risk to the average
individual will be about ore-half that ofthe maximally exposed subsistence
farmer.S
The expected value of risk to the average individual within the
subsistence-farmer critical group is to be compared with the risk limit that
is to be selected for compliance. The regulator can specify how far below
4 Adopting any distribution, uniform or otherwise, for the risks within a critical
group projected to exist in the distant future, cat 100,000 years and beyond, is
arbitrary, because the habits, location, etc. of that future group of people are
not knowable to us. Whether one postulates some distribution, as is done here,
or calculates a distribution based on the assumed relevance of the current site-
specific population, adopting any such distribution for the future is arbitrary.
5 Because of the large uncertainties in the calculated doses and risks to any of
these individuals, the uncertainty of uniformity of risk within the group cannot
introduce an important uncertainty in the result. An uncertainty of 2 or 3 in the
calculated dose is not expected to be important.

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APPENDIX D -THE SUBSISTENCE-FARMER CRITICAL GROUP 159
or above the specified risk limit the calculated risk must be for compliance
clecision.6
6 UK's NRPB specifies the calculation of a 95°/0 confidence interval for the
expected or central value of risk. The upper value of this confidence interval is
what is compared with a regulatory limit [Barraclough et al., 19921.

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