Uncertainty and the “Sharpness” of the Performance Assessment Tool
for Repository Performance Assessments Over

Increasingly Longer Time Periods

September 26, 2008

I	Introduction

 	Performance assessment is the primary tool for making dose projections
for the Yucca Mountain disposal system.  An important consideration in
using performance assessment (PA) analyses to evaluate the projected
performance of a geologic disposal system is the role of uncertainties
in framing the analyses and interpreting the results.  This is
particularly true for deep geologic disposal, because these assessments
cover extraordinary time frames (many tens to hundreds of thousands of
years) compared to other regulatory efforts.  Performance assessment is
the only tool available to make these long term dose projections, and
the limitations of the tool should be understood if meaningful
interpretations of the results are to be made.  Understanding the
uncertainties in the performance assessment tool is also important for
framing performance standards for any disposal system in question.

Many comments on the EPA 2005 proposed standards for Yucca Mountain
addressed the connection between uncertainties in making dose
projections, the rationales for selecting a peak dose limit and other
aspects of the rulemaking for the Yucca Mountain standards.  The intent
of this document is to examine available information and present
analyses that will provide some insight on how various kinds of
uncertainty, discussed further below, affect the level of confidence
that can be placed on performance assessment results as reasonable
projections of expected performance.  The particular emphasis in this
paper is the question of the effects of various uncertainties over time
(tens to hundreds of thousands of years) in terms of the “sharpness”
of the PA tool, as the term is used here, and its ability to
meaningfully distinguish between alternative descriptions of disposal
system performance and the associated dose projection histories.  

This document is intended to support our Yucca Mountain standard setting
effort by: (1) examining how various uncertainties in performance
assessments over the geologic stability period influence dose
projections and, (2) developing an understanding of these uncertainties
and how they contribute to formulating the standard.  This paper will
present information we have gathered and analyses we have performed to
understand the “sharpness” of the performance assessment tool in
making long-term dose projections for the disposal system and, address
some of the concerns articulated in the comments we received on the
proposed standards, as well as to respond to the issues raised. The
analyses we have performed have led us to the conclusion that any peak
dose limit choice in the low hundreds of mrem/yr. will constrain the
disposal system to keep releases minimal for many tens to hundreds of
thousands of years.  The choice of a peak dose limit of 100 mrem/yr in
the final standards, the low end of the range mentioned above, is a
challenging limit in that it constrains the disposal system to limit
doses to very low levels for long periods of time in order to meet the
peak dose limit within the geologic stability period.  We also discuss
the spatial and temporal uncertainties in the important processes and
parameters responsible for the timing and magnitude of the peak dose,
i.e., the “driver” parameters, and illustrate through our analyses
that these uncertainties generally increase over time for the Yucca
Mountain disposal system, in contrast to the thesis proposed in some
comments on the proposed standards.  

The terms precision and accuracy are commonly used to describe
measurements and calculations, rather than the term “sharpness”. 
For performance assessments, precision can be thought of as how close
multiple calculations agree, while accuracy refers to how well the
results simulate actual performance.  The accuracy of performance
assessment calculations is not possible to verify because of the long
time periods simulated, and is a matter of professional judgment about
how well the conceptual model developed for the assessments is believed
to simulate the disposal system’s expected characteristics and
operation.  For the purpose of the discussions here, the term
“sharpness” will be used as a more general term which combines both
the concepts of precision and accuracy, but focuses on the ability of
performance assessments to distinguish between alternative
conceptualizations of the disposal system.  For developing a standard
and making regulatory decisions against an established standard, the
ability of performance assessments to meaningfully distinguish between
alternative descriptions of disposal system performance is an important
question, when these alternative descriptions result in different dose
histories or entail differing degrees of confidence that the
conceptualizations are truly the best representations of the system.
Performance assessment is a tool for making analyses that provide
important input to decision making.  This question of “sharpness” in
the analytical tool is also important in making compliance decisions
against a fixed numerical standard.  If the “uncertainty” band
(discussed more extensively below) around a set of analyses is large and
overlaps the standard, it may be difficult to confidently determine if
the disposal system performs well enough to demonstrate compliance with
the standard.  How well the tool can distinguish between alternatives,
in light of the uncertainties inherent in making assessments, is a
fundamental question bearing on the use of the tool in formulating a
standard and subsequent regulatory decision making.  Some conclusions
about the “sharpness” of the PA tool, and its application to
standard setting and regulatory decisions, are also presented based upon
these analyses.

The reader is assumed to have some familiarity with the process of
performance assessment as applied to deep geologic disposal, i.e., to
have a basic understanding of how performance assessment models are
constructed and exercised.  Extensive descriptions and discussions of
performance assessment as applied to projecting dose histories for the
Yucca Mountain disposal system are presented in other documents (DOE
1998, CRWMS M&O, 2000, BSC, 2001a, DOE 2002) that can be consulted for
background information on the PA technology, as well as a more in depth
study of the subject as applied to the Yucca Mountain repository site
and repository design.  It should also be noted that the use of the term
“peak dose” in this document refers to the maximum dose delivered to
the RMEI when the engineered barriers have degraded.  For most of the
past disposal system assessments performed by DOE for the Yucca Mountain
site, this peak dose occurs within the period of geologic stability (1
million years). From a regulatory standpoint, the peak dose is regarded
as the highest dose calculated during the course of the compliance
period.  For some more recent performance assessments published by DOE,
the peak dose, as used in the discussions in this document (the maximum
dose produced by the degraded engineered barrier) occurs beyond the end
of the geologic stability period, and the regulatory usage of the term
should be kept in mind when considering discussion of peak dose in
reference to those cases.

II	Types of Uncertainty

For the purposes of this paper, uncertainties of two types will be
discussed and examined.  These two categories are not distinctly
separate in that some uncertainties concerning the characterization of
the processes expected to be operative in the disposal system, and the
modeling of the total system performance, can be considered to have
elements of both categories.  A definitive treatment of all the
uncertainties involved in site characterization and numerical techniques
for performance modeling is beyond the scope of this paper.  The two
categories to be discussed here are aleatoric and epistemic
uncertainties.  In practice, the treatment of uncertainties in a
specific application may combine these two types of uncertainty,
sometimes in ways that may make it difficult to separate effects due to
randomness and those due to less than a definitive understanding of the
system under consideration.

Aleatoric uncertainties, within the context of this paper, refer to
uncertainties arising from randomness – more specifically the
uncertainty resulting from the randomized selection of parameter values
from the distributions of parameter values included in a particular
performance assessment model being exercised.  These uncertainties could
be more simply described as “data” uncertainties.  However, the term
aleatoric will be used to avoid confusion with calculational errors such
as rounding errors, numerical convergence errors, etc., that are
inevitably present in complex numerical calculations, and sampling
frequency and spatial variations and analytical errors that are inherent
in doing laboratory analyses or field tests to generate data from which
the parameter distributions are eventually developed.  Aleatoric
uncertainty in a particular conceptual model being used in a performance
assessment can be reduced by increasing the number of calculations done.
 In practice for large complex numerical models, a compromise is struck
between the number of calculations done and the reduction in this type
of uncertainty.

Epistemic uncertainties in contrast refer to uncertainties resulting
from the less than complete understanding of how the complex interactive
processes involved in geologic disposal will operate quantitatively over
the performance period.  More simply put, epistemic uncertainties refer
to how well we know the system being modeled and how confident we can be
in its mathematical representation.  Here again, a simpler term such as
“model” uncertainties can be used, but the generalized term has
differing connotations, some of which include aspects of the aleatoric
uncertainties mentioned above.  We will use the more formal term to
avoid potential confusion, as defined above, remembering that it refers
to uncertainties in knowledge of the processes involved in disposal
system performance and the consequent possible variations in the
conceptualizations of the system for modeling.  Epistemic uncertainties
can be reduced by more extensive efforts to study the processes
anticipated to operate, but at some point these efforts can reach a
point of diminishing returns, i.e., the remaining uncertainty cannot be
removed, or argued to be sufficiently understood that no additional
effort is warranted to meet the objectives of the task – demonstrating
acceptable performance of the disposal system.  

Often, optimization exercises are done with performance assessment codes
to examine the comparative effects of either improving the data base for
various components of the disposal system or design changes in the
engineered components.  For example, if engineering design changes
produce a more dramatic effect on projected dose histories than that
produced by additional extensive characterizations of the ground-water
flow system in the natural barrier, the disposal system designers may
elect to change the design elements rather than expend additional
resources for field studies.  Uncertainties involved in these
optimization studies factor into the design choices and also into the
question of carrying the design and performance projections into a
regulatory compliance decision process.  Chapter 3 of the EPA economic
impact assessment for the 2001 Yucca Mountain standards (EPA, 2001),
discusses the use of performance assessments in the evolution of the
Yucca Mountain repository engineered barrier design.  

  In summary, it is not possible to know everything definitively, nor is
it absolutely necessary, to adequately execute the goal of establishing
acceptable confidence in the assessment of disposal system performance,
i.e., deciding “how much is enough” and when do we decide the task
is finished.  This goal involves both the applicant as well as the
regulator.  Each must determine when enough information has been
gathered and analyses performed to make confident representations of the
disposal system performance.  While these concerns are not directly
relevant to the standard setting effort before EPA, understanding the
uncertainties in making long-term dose projections for the Yucca
Mountain disposal system is important in formulating a standard that can
be clearly and convincingly implemented in a licensing process.  This
paper will address the aspects of uncertainty in site performance and
how they impact our standard setting effort.

Making the decision about “how much is enough” for regulatory
decisions is the purview of the Nuclear Regulatory Commission and
exercised within the licensing process.  For our standard setting task,
an understanding of the uncertainties and how they play into the
performance assessments provides a necessary insight for the Agency, so
that a standard can be crafted that will be a reasonable test of the
disposal system’s performance, and one that can be clearly implemented
in a licensing process.  Without an understanding of the uncertainties
in projecting dose histories over the exceptionally long time periods
involved, we could easily formulate the standards in ways that would not
allow them to be implemented clearly.  For example, if a requirement in
the standards were stated in terms of either/or measures for compliance
(i.e., satisfy one measure or the other for the requirement depending on
which is more restrictive), but the uncertainties were such that the
tool (performance assessments) used to examine the two alternative
measures could not distinguish between them meaningfully, the standard
requirement would not be implementable in a meaningful way.

III	NAS Perspectives on Uncertainties Over the Post-Closure Performance
Period

 	The Energy Policy Act of 1992 (EnPA) directed the Agency to develop a
standard for public health and safety specifically for the Yucca
Mountain candidate repository site.  The EnPA also directed that the
Agency to contract with the National Academy of Sciences (NAS) to
prepare advice on the technical bases for the Yucca Mountain standards
and directed that the standards be “based upon and consistent” with
the NAS recommendations.  The National Academy of Sciences report (NAS
1995), providing recommendations on standards for the Yucca Mountain
site, discusses uncertainties in terms of spatial and temporal
uncertainties (NAS, pgs. 70-81).  

The Committee believed that spatial uncertainties would always be
present in the disposal system, and that these uncertainties could be
addressed adequately by studies of the present conditions at the site,
and the assumption that the site is “geologically stable”.  An
example of these types of uncertainties would include those in
characterizing the ground-water flow system in and around the repository
from localized hydrologic testing in the field, i.e., going from
measurements at discrete places to developing flow models for areas of
many square kilometers in heterogeneous rock masses.  This particular
uncertainty is inherent in any hydrologic field characterization effort,
and would be present whether the effort is being done today or at some
point far into the future.  As a practical matter, characterization
studies must always come to a point where a professional judgment is
made about “how much is enough” in terms of field and laboratory
testing to adequately characterize the site for the task at hand. 
Inherent in that decision is a level of uncertainty about the natural
variations in the site captured by the characterization activities.  We
agree with the NAS characterization of spatial uncertainties in that
sense.  However, there is also a time element in these uncertainties
concerning spatial characterization, as discussed in more detail below,
for processes that are important in determining the timing and magnitude
of the peak dose.  A geologically stable site should not be considered
immutable over time frames of hundreds of thousands of years, in terms
of its physical characteristics.  While the NAS characterized the Yucca
Mountain setting as being geologically stable for period a “on the
order of a million years” (NAS Report pp. 2, 9, 68-69), this should
not be understood as meaning no changes in its characteristics are
possible.  Stability simply means that the processes currently active in
and around the site are anticipated to continue at their current rate
for the foreseeable future (“on the order of a million years”) and
are believed to be boundable by site characterization studies.  The
continued operation of these processes may, over long time periods,
alter conditions around the site that could affect performance to some
degree.  Such changes are also anticipated to be incorporated into the
development of parameter value distributions derived from field studies
and used in performance assessment models.  These parameter
distributions are, in fact, called probability distribution functions,
connoting that a probability estimate based on measurements and other
considerations is incorporated into the parameter value variations
within the distributions.  Therefore, some degree of uncertainty is
inherent in these parameter value distributions because the actual
cumulative extent of slow changes to the site’s characteristics over
these extended time periods cannot be predicted with certainty.  This
uncertainty is epistemic in nature since it concerns the limitations of
how well we can know and simulate the details of the disposal system. 
We cannot be completely sure that site conditions measured today will be
exactly the same if they were measured hundreds of thousands of years in
the future (i.e., the uncertainty in field measurements).  Out of
necessity, field studies sample only a limited portion of the
three-dimensional volume of the natural barrier, and therefore, there is
a degree of randomness in the sampling locations, although they are
selected on the basis of professional judgment with the intent of
generating representative parameter values.  These are the sampling
uncertainties mentioned above in the definition of aleatoric
uncertainties in that there is a degree of randomness involved in
selecting locations for field measurements.

 The uncertainties in using field information in developing hydrologic
models of the ground-water flow field can also be considered epistemic
in nature since these measurements may be such that alternate conceptual
models of the flow processes could be consistent with the available
field evidence, or alternative conceptualizations of the disposal system
might require alternative parameter characterizations.  

In terms of temporal uncertainties, the NAS committee expected that in
general uncertainties would increase over time (NAS Report Chapter 3). 
The committee reasoned that some sources of uncertainty may well
decrease, making the task of projecting total system performance easier
because of their removal.  The example used was the eventual failure of
the waste package containment (well within the stability period), which
would remove uncertainties in modeling radionuclide releases from the
engineered barrier in the repository when that performance is
complicated by the complex coupled effects of the thermal period as the
repository heats up and then cools down as a function of the decay of
short half-life radionuclides.  When all the packages have failed, all
the packages could be assumed to be contacted by ground water and
releasing radionuclides for transport.  There would be little need to
incorporate progressive failures of the packages in the very long-term
dose projections, with all the attendant uncertainties in deriving such
model inputs (e.g., differing corrosion rates and mechanisms operative
under the various thermal states in the repository, coupled thermal,
mechanical and chemical processes during the thermal pulse early in the
repository’s post-closure history). 

 	As one would intuitively suspect, failure of the waste packages is a
major “driver” of disposal system performance, and the predicted
performance of the metal waste package components to corrosive failure
will have a dominating effect on the magnitude and timing of the peak
dose, as illustrated by modeling results presented here.  Modeling the
progressive failure of waste packages, and the engineered barrier system
in general over time, is additionally complicated by the thermal pulse
during the early portion of the post-closure period, where higher
temperatures are present from the decay of short half-life fission
products in the wastes.  Modeling the disposal system after the thermal
pulse has passed is easier in some respects since the complex coupled
interactions driven by temperature excursion would not be part of the
model.  However, although the modeling problem could be considered
simpler in some respects after the thermal pulse, the thermal pulse has
the potential to change physical and chemical conditions in and around
the underground facility.  These changes have the potential to
significantly alter the behavior of the system (SC&A, 2005, Chapter 11).
 For example, the thermal pulse may cause significant movement of pore
waters in the host rock in response to the heat, causing possible
precipitation of minerals in fractures around the emplacement drifts
which could then affect the movement of pore waters back into the drifts
after the thermal pulse ends and then their outward movement into the
natural barrier after interacting with the waste packages and the
materials in the emplacement drifts.  These changes can affect the flow
rates and amounts of ground water that could enter and leave the
emplacement drifts and contact the waste packages, which in turn can
affect release rates.  Modeling the post-thermal pulse behavior of the
repository after complete waste package failure has occurred would
appear to be a simpler problem.  However the difficultly of predicting
the characteristics of the disposal system around the repository from
the effects of the thermal pulse and waste package failure adds
additional areas of speculative assumptions that must be addressed in
the modeling.  The actual uncertainties and their effects are not as
simple as they might appear from a limited look at the disposal system. 
Additional discussion on some of these issues will be presented below in
Section V).  Lengthier discussion of the uncertainties involved in
modeling the engineered and natural barriers for the disposal system are
discussed in another document supporting the rulemaking (SC&A, 2005).

IV	 Aleatoric Uncertainties in Yucca Mountain Performance Assessments

Numerous performance assessments for the Yucca Mountain disposal system
have been performed and reported in the literature.  The process of
performing the assessments with a complex performance model is called
Total System Performance Assessment (TSPA).  For these assessments, the
simulation model is exercised repeatedly.  Each calculation, or
“realization”, represents a possible “future” charting the dose
received by the defined receptor (the Reasonably Maximally Exposed
Individual, the RMEI) over the time frame of the modeling exercise.  For
the case at hand, this would be a 1 million year geologic period over
which the peak dose is to be calculated for regulatory compliance.  This
section of the paper will examine the nature of this types of
uncertainty in performance assessments and implications for regulatory
decision making and standard setting.

The models used to simulate disposal system performance are complex and
contain many hundreds of variable parameters.  For each realization, a
set of parameter values is chosen from the distribution of possible
values (the probability density functions - pdfs) developed through the
site characterization activities and incorporated into the performance
model.  Consequently the possible combinations of values for all the
parameters that can be chosen for the “realizations” can number into
the many millions.  From practical considerations, only a much smaller
number of realizations are calculated, typically numbering in the
hundreds, since the calculations are lengthy and time consuming. 
Statistically based sampling techniques are used to select values with
the intention of generating a “representative” group of
realizations.  Once completed, a dose versus time curve of each
realization (a dose history for a particular set of parameter values) is
prepared.  These diagrams are often called “horse hair” plots.  A
performance measure is calculated, such as the mean or median of the
dose estimates at each time step, using the data from many realizations,
and plotted along the time line.  The calculations are repeated with new
sets of realizations and plotted the same way until a “stable”
measure is observed (i.e., a relatively unchanging result is obtained
– as defined by the analyst, e.g., no more than 10% variation in the
calculated performance measure of interest, for example the mean of
results at each time step for the individual realizations ).  While the
performance measure chosen (such as the mean, i.e., the average) may
become stable across many sets of realizations, there is variation
within each set of realizations.  For example, one set of realizations
may contain high and low end doses that another set may not, but the
mean value may be the same as another set of realizations that does not
have counterbalancing high and low end numbers.  While mathematically
equivalent in terms of the mean value, these different sets of
realizations may represent physically different conceptualizations of
the disposal system performance, with differing uncertainties attached
and consequent levels of confidence that they are  more or less
realistic or defensible representations of the disposal system’s
performance (i.e., the confidence we may have in one conceptualization
versus another may differ significantly although mathematically they are
indistinguishable).

Since each set of realizations is only a small fraction of all the
possible combinations of parameter values and the PA calculations are
repeated until a measure of stability is observed, in this context the
aleatoric uncertainty refers to how well any separate set of
realizations can be distinguished from another set.  This question
becomes important when considering alternative conceptualizations of the
disposal system performance as mentioned above.  If alternative
conceptualizations cannot be statistically distinguished from each
other, the regulatory compliance decision is made more difficult in that
the confidence that we understand the system performance is lessened. 
Although different conceptualizations may not be statistically
separable, there may be significant differences in the confidence that
can be placed in one conceptualization versus another, as truly
representing the likely performance as well as identifying uncertainties
that might significantly affect performance projections.  Distinguishing
between alternative sets of realizations is also an issue when comparing
sets of realizations from the same calculational model and comparing the
results against a fixed numerical standard, such as a mean dose limit. 
For example, if a given performance assessment yields a mean peak dose
estimate of 85 mrem/yr. but the aleatoric uncertainty for that
assessment is ± 10 mrem/yr., (at a fixed level of statistical
confidence, e.g.., 95% typically) another dose distribution (a different
set of realizations) calculated with the same model and showing a mean
peak dose of 91 mrem/yr. would be considered statistically
indistinguishable from the first at that confidence limit.  If the means
of these two distributions are well below the regulatory standard, there
is little concern in that both conceptual alternatives meet the
standard.  If the means of the two distributions straddle the regulatory
limit the compliance decision is more complicated in that some decision
must be made about the relative confidence of one conceptualization over
another.  For a case like this, additional model development and
assessments make resolve the difficulty.  

To examine the nature of aleatoric uncertainties in some Yucca  Mountain
performance projections, two sets of model results were examined from
two different models for disposal system performance.  The first is
taken from the Department of Energy (DOE) Final Environmental Impact
Statement (FEIS) for the Yucca Mountain site (DOE, 2002), and the second
model is the DOE Peak Dose Model (PDM)  (EPA-HQ-OAR-2005-0083-0352).  We
obtained data from DOE for the performance assessment results presented
in the FEIS.  Those data are included in the Yucca Mountain docket entry
containing this document.  The DOE Peak Dose Model was developed to
examine uncertainties in the peak dose calculations for the repository,
and was submitted by the DOE as part of its comment package on the EPA
proposed standards for Yucca Mountain, as referenced above.  The results
of the analyses we performed to examine aleatoric uncertainties in these
two models is discussed more fully in Appendix A.

The analyses examined the arithmetic means for different numbers of
realizations produced by both of the models.  The FEIS data set was for
300 realizations of the large site model, a TSPA performance model used
for the FEIS analyses.  The DOE PDM was exercised to produce a set of
300 realizations and a larger set of 1000 realizations from which the
arithmetic mean and other calculations were done.  Table 1 shows the
result of these calculations (discussed more fully in Appendix 1).  The
two sample Student t-test was used to determine bounds of uncertainty
around the estimated mean for each set of realizations).  Results of
these statistical analyses can be interpreted as follows.  For the DOE
PDM set of 1,000 realizations (n=1000 in Table 1), the upper and lower
bounds indicate that, at the 95% confidence level, the mean of another
equivalent set of realizations, e.g., if another set of 1000
realizations with the DOE PDM were calculated, the second set of
realizations would not be interpreted as significantly different than
the mean of the first set unless the mean of the second set fell outside
the bounds shown in the Table 1.  This result illustrates the level of
aleatoric uncertainty (that due only to the random sampling of the
parameter distributions in the model) in any given set of realizations. 
This uncertainty is present in any set of realizations produced, but
will vary in magnitude depending on the number of realizations in the
sample set and the distribution of the actual realizations.  When the
DOE PDM was exercised at 300 realizations (n=300 in Table 1) the bounds
were observed to be considerably wider around a higher peak dose.  These
variations are to be expected, since the number of realizations sampled
in the analyses is only a small fraction of all the possible
combinations of possible parameter values.  If enough realizations were
done, the results would converge on the true mean for the population of
all possible combinations and aleatoric uncertainty would be minimal. 
Increasing the number of realizations usually will decrease the
uncertainty of the estimated mean, as measured by the standard error of
the mean, which may increase or decrease before stability is reached. 
In practice, the number of realizations performed with large PA codes is
a compromise between efficiency and confidence building in the model’s
output.  Doing large numbers of realizations easily consumes large
blocks of time.  If the results of various “runs” (sets of
realizations) of equivalent size do not show results significantly
different, a professional judgment may be made that no new insights into
the system performance would be obtained by ever increasing larger runs
of the model.

The results in Table 1 for the FEIS results are based on 300
realizations.  The uncertainty range for this model is ± 45 mrem/yr.,
approximately one-third of the mean. In exercising the FEIS model, the
number of realizations was determined by obtaining a “stable” mean,
i.e., one that did not move significantly after a certain number of
realizations were included (with 300 realizations the mean was observed
not to differ significantly with the addition of more realizations). 
The FEIS model is a larger and more comprehensive model than the DOE
PDM, (which is a simplified site performance model), and may have the
effect of damping down the variations shown in the simpler DOE PDM,
which was developed to assess the impacts of the major “driver”
parameters affecting peak dose.  The larger changes in the mean for the
DOE PDM may well reflect the effects of driver parameters not otherwise
constrained by all the other parameters contained in the larger FEIS
model.

While the results of these two model exercises are illustrative of the
nature of the aleatoric uncertainty, the results should not be directly
transferred to another model.  For another model, more specifically a
model DOE will use for the performance assessments submitted for the
licensing process, the magnitude of the aleatoric uncertainty will be
different, varying as a function of the number of realizations needed to
observe a “stable” mean and the inherent characteristics of the
model itself (the details of the processes included in the model and the
specific pdfs used in the model).  However it is interesting that the
FEIS analyses, which were done using a complex total system performance
model, carried an aleatoric uncertainty around the mean that is a
significant percentage of the estimated mean dose.  The larger the
aleatoric uncertainty in a given model results, the more likely an
alternate conceptual models of the disposal system performance may be
statistically indistinguishable from the given model results.

Table 1.  Comparison of 2-Sample Student t-test Results for Three Sets
of Model Calculations

Model Run	Peak Mean Dose

(mrem/yr)	Year of Peak Dose	Standard Deviation

(mrem/yr)	Lower Bound

(mrem/yr)	Upper Bound

(mrem/yr)	Range

(mrem/yr)

DOE PDM

(n=1000)	125	730,000	300	99	151	52

DOE PDM

(n=300)	160	835,000	438	90	230	140

FEIS

(n=300)	152.5	476,000	290.6	106	199	93



There is an intersection of both aleatoric and epistemic uncertainty
involved in the example discussed above.  The large model used in the
DOE TSPA analyses combines a number of alternative conceptualizations
for some the operative processes in the disposal system.  While it is
considered a single model for the purposes of the examination above, the
model is actually a combination of alternative conceptualizations of
various processes involved in the total system performance.  For
example, corrosion of the waste packages is a function of the mechanisms
that operate under various physical and chemical conditions.  Knowledge
of the exact corrosion rates for the various possible mechanisms
operating over the lifetime of the disposal system may be lacking for
any number of reasons.  To simulate the effects of these various
mechanisms, the parameter distributions used in the model may be an
amalgamation of estimates for the individual processes based on the
expert judgment of the modelers.  To represent the different mechanisms
the corrosion rate variations compiled from laboratory testing would be
expanded to simulate the possible effects of the lesser know processes. 
The corrosion rates chosen for each realization may then be reflective
of different corrosion mechanisms rather than a single mechanism
consistently used for all the realizations.  Similar bounding type
approaches to developing parameter value distributions are used for
radionuclide solubility in ground waters in the emplacement drifts,
radionuclide sorption coefficients in the natural barrier, hydrologic
parameters describing the flow field, etc.  This combination of
alternate conceptualizations in a single model must be understood to
avoid erroneous comparisons of different models.

Some conclusions about aleatoric uncertainties in performance
assessments can be formulated from the analyses described above. 
Aleatoric uncertainties can be a significant portion of the calculated
dose for assessments with a limited number of realizations, in the
examples examined above 30 percent for different dose models were
observed.  Since separate sets of assessments using the same
conceptual/calculational model are of equal statistical validity (they
are both equally defensible projections of performance from which a mean
value can be calculated), it would be difficult to make a regulatory
compliance decision if the two sets of realizations straddle the
regulatory marker.  In such case, additional numbers of realizations
could be done to reduce the uncertainty and make a compliance decision
less difficult.  Performing additional sets of realizations for large
performance models is time consuming and typically sets of realizations
are performed and compared to examine the “stability” of the
calculated mean doses.  A professional judgment may be required to
determine when increasing the number of realizations no longer results
in a meaningful reduction in the aleatoric uncertainty.  There may
remain a minimal level of aleatoric uncertainty judged by regulatory
authorities to be sufficient for the purpose of compliance decisions. 
This decision rests with the compliance decision makers and is a
function of the specific performance model involved in the applicant’s
safety assessment. 

 For the purpose of our standard setting, aleatoric uncertainty in
performance assessments is not a major determinant in evaluating the
implementability of particular dose limits, because additional
realizations can be performed to lower it.  Observing that aleatoric
uncertainty in assessments using a large site performance model can be a
relatively high proportion of the peak dose (as noted above), it is not
unreasonable to conclude that for a two-tiered standard the tiered dose
limits should be sufficiently separated that aleatoric uncertainties do
not cloud the compliance evaluation for either marker.  In the case of
the Yucca Mountain standard, this would suggest that a separation of
10-20 mrem/yr would be a reasonable adjustment to minimize the potential
for aleatoric uncertainty alone to cloud the compliance decision.  It
must be stressed that setting the actual standard is a decision on the
protectiveness of the respective dose limits and not predicated on an
assumption of any particular level of aleatoric uncertainty in the
performance assessments, which in fact cannot be determined a priori.

  

Moving from the consideration of aleatoric uncertainty, a more important
area of uncertainty relative to standard setting and regulatory decision
making are the epistemic uncertainties – those arising from how well
we understand and can confidently quantify the expected behavior of the
disposal system over the compliance period.  These uncertainties are
discussed below.  Many of the comments on the proposed standards
addressed this topic, i.e., the proposition that uncertainties in
modeling site performance increase with time over the geologic stability
period.

V	Epistemic Uncertainties in Yucca Mountain Performance Assessments

Epistemic uncertainties, those concerning our understanding of the
disposal system’s anticipated performance, are the most important
source of uncertainty in disposal system performance projections.  This
section will examine these kinds of uncertainties for the Yucca Mountain
disposal system.  Results from our modeling efforts will be discussed in
terms of the effects of the assumptions about the processes used in the
modeling the disposal system and their inherent uncertainties spatially
and temporally.  The confidence we have in understanding the processes
that will operate over the compliance period is key to establishing
confidence that the disposal system will perform satisfactorily and meet
the requirements in the standard.  Understanding these uncertainties is
also important in setting performance standards in that a standard must
be capable of implementation for successful regulatory decision making. 
An extensive discussion of the epistemic uncertainties in modeling the
Yucca Mountain disposal system and assumptions used in DOE modeling can
be found in SC&A 2005.  Many of the comments received on the 2005
proposed standards (referenced in the introduction to this document)
concerned the nature of these uncertainties and their variation over
time.  The treatment below addresses these comments, and describes the
insights we gained through our modeling of the disposal system.

V-1a    Modeling Approach for Uncertainty Analyses

Our modeling focused on uncertainties involved the use to two site
models that are closely related.  In response to requests for comment on
the 2005 draft of the Yucca Mountain standards (EPA 2005), DOE submitted
a Yucca Mountain site model designed to examine the behavior of driver
parameters contributing to the peak dose.  This model, referred to here
as the DOE PDM, is a smaller scale model in contrast to the larger TSPA
models used in previous disposal system performance assessments
performed by DOE.  We used this model to explore alternative
conceptualizations of the processes operative in the disposal system,
the results of which are described and discussed below.  For the second
model, the Agency modified the DOE PDM and used it (referred to as the
EPA Uncertainty Model in SC&A, 2006) to examine the effects of
uncertainties in the natural barrier performance for a hypothetical
disposal system.  As part of the Agency’s Quality Assurance process
supporting the studies reported in SC&A 2006, the DOE PDM was reviewed
for its capabilities to model the disposal system and found adequate for
that purpose (SC&A, 2007).  The DOE PDM model proved useful in examining
the relative performance of alternative conceptual models for the
disposal system, as discussed below.  

V-1b	Modeling Uncertainties –  Results and Discussion of Uncertainties

  For the purposes of the analyses reported here, the DOE PDM was used
as submitted to the Agency without any additional modifications.  The
DOE PDM (DOE, 2005) offers a useful tool for examining the epistemic
uncertainties involved in assessing peak doses from the disposal system.
 The DOE PDM has a useful feature for examining the impact of some
epistemic uncertainties on peak dose calculations.  A number of
“switches” (Checkboxes) are built into the model, which allows
various components of the model to be changed, effectively examining
alternate conceptualizations of the system.  This is an important point
for interpreting the results presented here.  Each of the Checkboxes in
the DOE PDM should be regarded as allowing an alternative
conceptualization of the disposal system performance.  By examining the
results of various combinations, it is possible to see the effects of
uncertainties arising from these alternatives, i.e., to the extent to
which we “know” how the system could operate over the very
long-term.

To establish a baseline, the DOE PDM was run initially with no checkbox
selections. This base case model forecasts a peak mean dose of 125
mrem/yr at 730,000 years.  The 1,000 realizations span the range of
results shown in Figure 1.  Using this model as the baseline, a series
of one-off sensitivity scenarios was conducted using of the checkbox
controls (provided on the model “Dashboard” `feature).

The checkbox scenarios programmed into the model include:

A.  Deterministic Infiltration Scenarios

1.  Deterministic Infiltration Rate:  Low Infiltration 

2.  Deterministic Infiltration Rate:  Medium Infiltration 

3.  Deterministic Infiltration Rate:  High Infiltration 

B.  Corrosion Scenarios

4.  Full General Corrosion Rate Temperature Dependence for WPs 

5.  Waste Package (WP) General Corrosion Rates Increased by a Factor of
5 

6.  Drip Shield (DS) General Corrosion Rates Increased by a Factor of 5 

7.  WP and DS General Corrosion Rates Increased by a Factor of 5 

C.  Other Uncertain Parameters/Conceptual Models

8.  Secondary Phase Neptunium Solubility Control; 

9.  Non Collapsed Drift Seepage Conditions

10.  Saturated Zone Transport Pathway Length Set Equal to 0 

11.  Drip Shield Performs No Function

12.  Pu-242 Biosphere Dose Conversion Factor (BDCF) by +20%

The sensitivity scenarios include three deterministic long-term average
infiltration cases: Low, Medium and High.  In the base case model, the
infiltration case for each realization is selected randomly from these
three alternatives with probabilities 0.24, 0.41, and 0.35,
respectively.  In the infiltration sensitivity scenarios, the case
selected with the checkbox is used in all realizations.  

Four scenarios address the general corrosion rate of the waste package
(WP) and drip shields (DS).  These include increasing the WP general
corrosion rate by a factor of 5, increasing the DS general corrosion
rate by a factor of 5, increasing both WP and DS general corrosion rate
by a factor of 5, and using the full temperature dependence general
corrosion model rather than assuming that the dependence of corrosion
rate on temperature is limited to a maximum of 45 º C.  

Five additional sensitivity scenarios were examined: non collapsed
drifts, complete removal of drip shield functionality, setting the
length of the transport pathway in the saturated zone (SZ) to zero,
using secondary phase neptunium solubility controls, and varying the
Pu-242 Biological Dose Conversion Factor (BDCF) by +20%.  In this study,
all but two sensitivity runs from the list above were run using a single
checkbox selection.  One run (#7 in Table 2) was conducted using two
checkbox selections.  This scenario is only one of the many possible
checkbox scenarios that could be created using multiple checkbox
selections.  The first eleven scenarios are discussed in the PDM report
(OCRWM 2005).  The Pu-242 scenario was not included in the PDM report. 
The scenario was implemented manually by adding a multiplicative factor
of 1.2 in the BDCF table entry for Pu-242 in the DOE PDM.  The Pu-242
sensitivity scenario was added since this radionuclide is a major
contributor to long-term doses. 

The DOE  PDM was run initially with no checkbox selections to establish
a baseline (#0 in Table 2).  This base case model forecasts a peak mean
dose of 125 mrem/yr at 730,000 years.  The 1,000 realizations span the
range of results shown in Figure 1.  Using this model as the baseline, a
series of one-off sensitivity scenarios was conducted using of the
checkbox controls provided on the model Dashboard (see DOE 2005 for a
description of the Dashboard feature of the DOE PDM).  

 	The mean annual dose projections from the set of three infiltration
cases are compared with the base case forecast in Figure 2.  The low
infiltration rate scenario has a peak dose of  84 mrem/yr at 870,000
years, while the high infiltration rate scenario has a peak dose almost
twice as high, 162 mrem/yr at 690,000 years.  As expected, these values
bound the peaks for the medium infiltration scenario and the base case.

The mean annual dose estimates from the four general corrosion rate
sensitivity scenarios are compared with the base case in Figure 3.  The
two sensitivity scenarios which include increasing the WP general
corrosion rate by a factor of 5 have earlier and large peak doses mainly
due to the release of Pu-239.  Figure 4a shows the mean annual dose by
radionuclide for the scenario with the WP general corrosion rate
multiplied by a factor of 5.  This may be compared with the same plot
for the base case in Figure 4b.  In the base case and in all other
sensitivity scenarios, this nuclide has essentially decayed away before
the waste packages begin failing.  The full-temperature-dependence
sensitivity scenario (Table 2, ID #5, Figures 3, 6 and 7) rises to a
peak dose of 3 mrem/yr at 1,000,000 years, the end of the time period
covered by the model.  A higher peak dose occurs after this time.  The
Supplemental Environmental Impact  Statement (SEIS) recently published
by DOE (DOE, 2008) used the assumption of full temperature dependence
for the waste package corrosion rates and calculated that only 10% of
the waste packages were breached by general corrosion within the 1
million year geologic stability period, illustrating a consistent with
the DOE PDM.  Doses projections for this scenario in the SEIS show a
mean value of approximately 2 mrem/yr. at 1 million years.  

Mean annual dose estimates from the five additional sensitivity
scenarios are compared with the base case in Figure 5a, and in a zoom
view in Figure 5b.  Based on examination of Figure 5a, the most
significant change in the magnitude of the peak dose occurs for the
Saturated Zone (SZ) Transport Pathway Length set to 0 scenario with the
highest peak dose estimate of all scenarios examined in the study at
2,497 mrem/yr.  In this scenario, the lack of actinide retention in the
saturated alluvium leads to relatively large doses occurring at
approximately the same time as the peak in the base case, near 750,000
years.  This scenario has no direct physical meaning in reality since
the saturated zone cannot be eliminated from the disposal system. 
However it provides two useful insights into the functioning of the
disposal system.  The dose level can be regarded as approaching an upper
limit for the doses that could possibly come from the system, in that
the results represent a complete failure of the saturated zone to
provide any retardation.  For this scenario essentially the leachate
from the failed waste packages is delivered directly to the biosphere
pathway for the dose projections to the RMEI.  This is of course an
impossible situation, but illustrates the contribution of the natural
barrier to the disposal system performance. The second insight from this
scenario comes from comparison of the high dose to the base case result
(125 mrem/yr.).  The difference is an indication of the magnitude
(semi-quantitative due to the simplifications and assumptions in the DOE
PDM) of the contribution of the natural barrier to total system
performance, illustrating that the natural barrier plays a very
significant role in reducing doses.  These results also illustrate that
epistemic uncertainties concerning the retardation capabilities of the
natural barrier can have dramatic effects on the timing and magnitude of
the dose projections.  This bounding, but unrealistic scenario, can also
serve as a measure against which to compare the effects of uncertainties
contained in other scenarios as they affect dose projections. 

All twelve sensitivity scenarios are compared with the base case using a
logarithmic vertical scale in Figure 6a.  The most significant changes
from the base case in the timing of the peak mean dose occur for the
three WP general corrosion rate sensitivity scenarios (#’s 4, 5, & 11
in Table 2) – WP Rate times 5, WP and DS Rate times 5, and the Full
Temperature Dependence scenarios.  Increasing the WP general corrosion
rate by a factor of 5 leads to initial WP failures at times that are
approximately a factor of 5 earlier, resulting in higher, earlier peak
doses than in the base case.  Reduced corrosion rates are encountered in
the Full General Corrosion Temperature Dependence scenario in the later
years when the repository has cooled.  The reduced corrosion rates lead
to a distribution of initial failure times with only a few WP failures
occurring before the end of the 1,000,000-year time frame used in the
current model.  It must be remembered that the DOE PDM uses an
abbreviated travel path, and therefore the times for peak dose to the
RMEI are artificial and of relevance only in comparing the results of
various variations within the model.  They do not indicate the actual
time to peak dose projections for the site models used in the past to
simulate actual site performance.

A summary of the results of the analysis is shown in Table 2.  The
results include the peak mean dose, the year it occurs, and selected
percentiles of the distribution of annual dose estimates from each of
the 1,000 realizations at the time of the peak.  In most cases, the peak
dose occurs during the time period before all the waste packages have
failed.  This is the reason for the 5th percentiles values of 0 for all
scenarios and the 25th percentiles values of 0 for almost all scenarios.
 The sole exception is the multiple checkbox  scenario with WP and DS
corrosion rates increased by a factor of 5.  The ratio of the 95th
percentile to the 50th percentile provides one measure of the spread of
the realizations at the time of peak dose.  The spread ratios range from
a low of 11 to a high of 250 for the non-collapsed drifts scenario.  The
geometric mean of the spread ratios is 51.  The final column of Table 2
shows the ratio of the peak mean dose to the 75th percentile.  These
ratios are generally near 1, indicating that the peak mean dose often is
near the 75th percentile of the realizations.

The peak mean doses in Table 2 are shown in a bar graph in Figure 7. 
Omitting the dramatically low full-temperature-dependence scenario which
has a higher peak after 1 million years, the next lowest peak dose
estimate in Table 2 (non-collapsed drifts) is a factor of 3.4 lower than
the Base Case peak dose of 125 mrem/yr.  Omitting the extreme SZ
Transport Length 0 scenario, the next highest peak dose estimate (WP and
DS corrosion rates times 5) is a factor of 6.1 higher than the base
case.  

A log normal distribution was fit to the 11 middle peak mean dose
estimates shown in Table 2, with a geometric mean (GM) of about 145, and
a standard deviation (GSD) of 2.44.  The upper limit of the
corresponding 95% confidence interval would b 834, or about 5.75 times
greater than the GM, and about 5.75 2  = 33 times greater than the lower
limit.  This is reasonably consistent with the “central” base case
peak dose of 125 mrem/yr. and the approximate range of values as
suggested by inspection of Table 2.  In summary, peak dose estimates in
the DOE PDM may range higher or lower by a factor of 5 to 6 from the 125
mrem/yr. base case peak dose as a result of reasonable one-off
variations in modeling assumptions and parameters.  The effect of
simultaneous variation of two or more sensitivity scenario parameters is
expected to generate a broader range of peak dose estimates, depending
on whether the effects of the assumptions compound or compensate for
each other.  These results are specific to the assumptions and
alternatives included in the DOE PDM.  The DOE PDM does not consider all
possible alternative assumptions that can be made in a total system
performance model.  A discussion of additional possibilities, and how
uncertainties in the disposal system’s behavior and evolution over
long time frames, is presented below.

Another approach to characterizing and quantifying the variability of
the mean dose estimates is to average the mean dose functions shown in
Figure 2 at each time to construct an ensemble mean for the scenarios
examined.  An estimate of the uncertainty of the ensemble mean was
derived based on the standard deviation of the 13 forecasts at each
time.  A plot of the ensemble mean and fits 75% confidence interval is
shown in  Figure 9.  The peak of the ensemble mean annual dose is 290
mrem/yr at 685,000 years.  The lower and upper bounds of the 75%
confidence interval for the ensemble mean ranges from 159 to 422 mrem/yr
at this time.  The “Remove DS Function” scenario was not included in
the data for this plot due to the close similarity with the DS Rate time
5 scenario results seen in Figure 7 and Table 2.  Inclusion of both
would over-weight the drip shield scenarios.

It can be seen from the two statistical treatments of the sensitivity
scenarios analyzed that there is considerable spread in the mean dose
estimates across the scenarios examined, even with some scenarios
excluded because of their large deviations from the rest.  Except for
the scenario excluding the saturated zone, all the scenarios are
reasonable assumptions about possible behavior of the disposal system. 
The spread of mean dose projections can vary over a range of several
hundreds of mrem/yr.  It should be borne in mind that the DOE PDM was
developed to examine the sensitivity of the peak dose to the driver
variables included in the model, and not as a tool for examining the
performance of the disposal system in detail.  The larger total system
models used for that purpose will produce different results because more
parameters and more of the detail of the operative processes are built
into these models.  It is possible that the more complex model may show
less spread in the mean estimates because other processes, or a more
rigorous treatment of the same processes, may attenuate the effects,
producing less variation in the means.  It is also possible that a more
complex model may contain synergistic effects not modeled in the DOE PDM
which could increase or decrease mean dose variations to some degree  A
further discussion of uncertainties over time is presented below.



Table 2.  Peak Mean Dose and Selected Percentiles in Year of Peak Dose
for Base Case and 12 Alternative Scenarios

ID	

One-Off Scenario	Peak Mean Dose (mrem/y)	Year of Peak Dose	5th

(mrem/y)	25th

(mrem/y)	50th

(mrem/y)	75th

(mrem/y)	95th

(mrem/y)	Ratio

95th/50th	Ratio

Mean/75th

0	Base Case	125	730,000	0	0	5	126	570	121	1.0

1	Low Infiltration Case	84	870,000	0	0	31	104	339	11	0.8

2	Medium Infiltration Case	136	690,000	0	0	0	124	639	-  	1.1

3	High Infiltration Case	162	690,000	0	0	0	151	770	-  	1.1

4	WP Corrosion Rate times 5	253	225,000	0	0	0	130	1,144	-  	1.9

5	Full Temperature Dependence (FTD)	3(a)	1,000,000	0	0	0	0	0	-  	-  

6	DS Corrosion Rate times 5	151	690,000	0	0	7	156	664	92	1.0

7	Remove DS Functionality	154	690,000	0	0	8	157	674	80	1.0

8	2nd Phase Np Solubility Control	111	865,000	0	0	36	126	484	14	0.9

9	SZ Transport Length Set to 0	2,497	775,000	0	0	288	2,719	11,139	39	0.9

10	Non Collapsed Drifts (NCD)	37	860,000	0	0	0.7	28	183	250	1.3

11	WP & DS Corrosion Ratex5	768	180,000	0	0.1	106	486	3,819	36	1.6

12	Vary Pu242 BDCF +20%	138	730,000	0	0	5	140	648	133	1.0

(a)  A higher peak is reached after the end of the one-million-year
timeframe used in the current model.

Table 3.  Peak Mean Dose and Selected Percentiles in Year of Peak Dose
for 4 Combined Scenarios

ID	

Combined Scenario	Peak Mean Dose (mrem/y)	Year of Peak Dose	5th

(mrem/y)	25th

(mrem/y)	50th

(mrem/y)	75th

(mrem/y)	95th

(mrem/y)	Ratio

95th/50th	Ratio

Mean/75th

1	NCD & WP Corrosion Ratex5	55	420,000	0	0	0.2	31	283	1,415	1.8

2	NCD & WP+DS Corrosion Ratesx5	118	190,000	0	0	1.5	34	401	267	0.3

3	FTD & WP Corrosion Ratex5	209	390,000	0	0	5	198	1,052	210	0.9

4	FTD & WP+DS Corrosion Ratesx5	304	390,000	0	11	108	347	1,216	11	0.9





Figure 1.  Mean and Percentiles of Base Case Annual Dose Forecasts

(Peak mean dose is 125 mrem/yr at 730,000 yr)



Figure 2.  Mean Annual Dose, Base Case and Three Infiltration Rate
Scenarios



Figure 3.  Mean Annual Dose, Base Case and Four General Corrosion Rate
Sensitivity Scenarios



Figure 4a.  Mean Annual Dose by Radionuclide for the Increase WP General
Corrosion Rate by a Factor of 5 Sensitivity Scenario



Figure 4b.  Mean Annual Dose by Radionuclide for the Base Case Scenario 



Figure 5a.  Mean Annual Dose, Base Case and Five Uncertain Parameter
Sensitivity Scenarios



Figure 5b.  Mean Annual Dose, Base Case and Five Uncertain Parameter
Sensitivity Scenarios (Enlarged view)



Figure 6a.  Mean Annual Dose, Base Case and 12 Alternative Sensitivity
Scenarios



Figure 6b.  Mean Annual Dose, Base Case and 12 Alternative Sensitivity
Scenarios

(Enlarged view)



Figure 7.  Comparison of 12 Peak Dose Model Sensitivity Scenarios with
Base Case



Figure 8.  Normal Score Plot of Middle 11 Peak Dose Estimates with
Best-Fitting Regression Line

 

Figure 9 Plot of Ensemble Mean Annual Dose for Base Case and 11
Alternative Scenarios with 75% Confidence Interval for Mean

V-2	Some Significant Uncertainties in the Disposal System Performance
(DOE-PDM)

An examination of the results of these sensitivity studies with the DOE
PDM points to some significant uncertainties that affect the degree of
confidence that can be placed on the results of performance assessments.
 These uncertainties are discussed more extensively below.  Some cannot
be reduced entirely by additional field and laboratory studies (such as
field studies of the flow system around the repository and the
far-field).  Others reflect the inherent uncertainty in extrapolating
field and laboratory data far into the future and for conditions that
can only be approximated from relatively short-term laboratory and field
studies (such as the extrapolation of corrosion rates into the tens to
hundred of thousands of years).  The spatial and temporal nature of
these uncertainties is also discussed under each of the alternative
scenarios examined with the DOE PDM.

V-2.1 	Corrosion and Drip Shield Performance- Modeling Results

The largest dose estimates for the DOE PDM studies (Fig. 7) were
observed for runs where increased corrosion rates for the drip shields
and waste packages were used (ID#’s 4, 5, 6, 7, &11 in Table 2). 
Variations in performance ranged from the Full Temperature Dependence
scenario (ID# 5) where doses were below 10 mrem/yr., to scenarios where
doses close to 800 mrem/yr. were projected (ID# 11), approximately a
six-fold increase over the base case results.  For these latter
scenarios, the high doses result from a factor of five increase in the
waste package and drip shield corrosion rate (using the switches” in
the DOE PDM).  For these higher rates, Figure 4a shows that the peak
dose is moved forward into the 100,000 year time-frame, and the peak
dose is higher.  This is not an unexpected result since more packages
fail earlier in time and release more radionuclides into the natural
barrier.  Examination of these alternatives indicates that the corrosion
rate is the dominant variable controlling the timing and magnitude of
the peak dose.  Variations of hundreds of mrem/yr are projected
depending on the corrosion rates assumed for any assessment.  The rest
of the alternative scenario results in Fig. 7 show much smaller
differences from the base case results.  The spread in projections
illustrates a fundamental uncertainty in making projections over these
extremely long periods (discussed more fully in the temporal and spatial
uncertainty heading below).  The only other alternative that produces a
dramatic effect on the DOE PDM projections is the drift collapse
alternatives discussed below.

 Temporal and Spatial Aspects of the Uncertainties In Drip Shield
Performance.  For drip shield performance, the temporal and spatial
uncertainties involved in assessing performance are closely aligned and
involve the degree of contact with intruding ground water during the
post-closure period.  Corrosion failure rates for the drip shields are
determined by the amount of water contacting them, and will vary
depending on their location within the heterogeneous fractured
repository host rock.  Over long time periods, the drip shields will
also be subjected to damage from roof collapse occurring primarily as a
consequence of seismic activity.  This uncertainty has a temporal aspect
in that the degree of damage to the drip shields, and their
susceptibility to failure from rock falling from the emplacement drift
ceiling, will vary with time.  A drip shield that has experienced
significant thinning from corrosion is more likely to fail from the
impacts of roof collapse than one that has its original thickness and
mechanical strength.  Both the corrosion failures and failures from roof
collapse would be expected to increase with time over the stability
period as the repository area is subjected to repeated seismic events
during the stability period.  The exact history of the failures would be
difficult to impossible to predict with high confidence because the
seismic events affecting the repository have considerable uncertainty. 
Bounding assumptions would probably be used to simulate these processes
in performance assessments, but considerable uncertainty is present
within any bounding assumptions.

 

	Temporal and Spatial Aspects of the Uncertainties in Waste Package and
Drip Shield Corrosion Performance  Making projections of metal barrier
performance is a site-specific task, particularly under the unique
conditions at the site, i.e., an unsaturated zone with varying thermal
and fluid flow conditions in the emplacement drifts (see SC&A, 2005,
Chapter 5, and BSC, 2001b for an extensive discussion of the
uncertainties and assumptions used in DOE PA of corrosion processes and
total system performance).  

 Spatial uncertainties involved in projecting waste package performance
involve both the placement of the packages in the emplacement drifts
within the repository, and also the distribution of pathways by which
ground water can intrude into the drifts.  These uncertainties can be
resolved to an extent by noting the configuration of fractures in the
emplacement drifts and avoiding placing packages where fracture
densities are high.  However it is not possible to eliminate all
uncertainty, since it is not possible to predict with certainty which
fractures will conduct ground water  into the drifts and to what extent.
 Attempting such predictions is also complicated by the potential for
thermal effects to alter fracture characteristics around the drifts and
alter pre-thermal pulse behavior patterns that may be observed in
testing within the repository, adding a temporal aspect to this
particular uncertainty.  Seismic activity over long time periods also
has the potential to alter the transmissive behavior of the fractures in
the repository host rock.  Seismic activity causing roof fall at long
time periods when the drip shields are significantly thinned and loose
their structural integrity can directly damage waste packages, adding
another time dependent aspect to the effects of seismic activity.

Another aspect of spatial uncertainties involves extrapolating corrosion
testing results to waste package performance in the repository. 
Laboratory testing is of necessity performed on small pieces of metal,
sometimes put under stress to simulate expected in-service conditions,
but the results of such testing remains an extrapolation that cannot be
verified practically.  Here again, an extrapolation must be made from
industrial experience with container fabrication and weld failure
mechanisms in various in-service environments, which are limited to time
frames of decades at most.  As noted by some comments, the highly
corrosion resistant alloy used for the waste packages has only been in
existence for a short time and little real time experience is available
from industrial applications.  Extrapolating laboratory performance is
unavoidable, but the longer the extrapolation the more uncertainty is
involved.  The strength of welded metals can also be tested on the
laboratory scale, but again using such data for performance projections
for full-size waste containers containing many long welds done in
fabrication remains an extrapolation that cannot be verified in any
practical sense.  

Temporal uncertainty in the use of corrosion rate data arises from
extrapolating the corrosion rates measured for specific corrosion
mechanisms into unprecedented time frames, i.e., how confident can we be
that we fully understand, and can confidently predict, which corrosion
mechanisms will predominate over the times spans involved and changing
conditions in the emplacement drifts.  Corrosion rates are derived from
relatively short-term laboratory testing for various potential corrosion
mechanisms, but their use in the performance assessments is an
extrapolation of these data both in time and scale (extrapolation of
tests on small pieces of metal to behavior of full-size welded
containers).  Laboratory corrosion testing is also typically done under
“accelerated” conditions, where higher temperatures or more
corrosive fluids are used in the testing relative to those anticipated
in the in-service environment.  There is an inherent uncertainty in
using such data, in that the data are intended to be deliberately
conservative.  How conservative such data actually will be is largely
speculative since projections of container performance in the repository
environment cannot be confirmed in practical time frames.  Without an a
priori understanding of all possible corrosion mechanisms operative for
the physical and chemical conditions evolving over time, important
mechanisms may be ignored inadvertently.  Lower temperature testing to
measure very low corrosion rates is also difficult due to measurement
uncertainties and always limited by available time frames for testing. 
For the highly corrosion resistant alloys used for the waste package,
the amounts of metal removed from the test samples is so small that 
analytical sensitivity is close to, and sometimes below, the ability of
the techniques to measure (CRWMS M&O, 2000, sec 5.2.3.3).  Synergistic
effects involving the actual in-service environment may not be addressed
by laboratory testing at all.  The projections of performance cannot be
confirmed in any real time sense, whereas performance for engineered
materials placed in service can be confirmed over the operational time
scales concerned.  Although additional laboratory testing can always be
performed, the extrapolation uncertainty will always be present. 
Intuitively one would suspect that the longer the time frame of the
extrapolation the higher will be the uncertainty in the performance
projections and dose assessments.  Therefore, we are presented with an
essentially irresolvable uncertainty involving the data extrapolations. 


Uncertainty in data extrapolation is present whether the performance
projections are made over a 10,000 year time frame or a 1 million year
time frame.  In that sense, this uncertainty could be likened to the
uncertainties in projecting natural processes, such a seismicity, over
the stability period.  However in the case of geologic processes, the
geologic record at the site provides some confirmation of the effects of
ongoing processes, by allowing examination of what has taken place in
the site’s geologic record.  Industrial applications of corrosion data
deal with in-service life times of decades typically, whereas for deep
geologic disposal the operational life time is essentially unbounded in
practical terms.  For the case of corrosion rate data for the C-22 alloy
used in the DOE waste packages, we have no such record for testing our
extrapolations from a backward look at what’s happened in the past.  

 In summary, the uncertainties in the application of corrosion rates in
performance projections is one that can only be limited to a degree, and
becomes more uncertain with time as the extrapolations extend to
progressively longer time frames, and conditions in the repository that
limit access of intruding ground waters to the waste packages degrade
over time.  From the variations shown in the DOE TSPA results published
in the past, corrosion rate assumptions are the dominant control on peak
dose timing and the magnitude of the projected doses.  Results of
various DOE TSPA efforts using differing waste package designs and
corrosion rate assumptions are listed in Table B1 in Appendix B. 
Additional results of sensitivity studies for a TSPA analyses are given
in Table B2.

V-2.2	Drift Collapse Modeling Results

From the sensitivity analyses presented here, the second most important
variable for projecting dose histories is the extent of emplacement
drift collapse over time.  The properties of the host rock in the
repository are such that for intact cylindrical walls in the emplacement
drifts, water moving through the unsaturated zone is significantly
deflected around the drifts as long as the walls remain intact, thereby
limiting the amount of ground water that can enter the drifts (BSC,
2001b, sec 4.2).  Collapse of the drift walls may occur as a consequence
of seismic activity around the site, and the timing and extent of such
collapse is uncertain because there is considerable uncertainty in the
recurrence intervals of larger seismic events around the site ( TRW,
2000, Fig.2-10, also in EPA Docket No. EPA-HQ-OAR-2005-0083-0379, DOE
2007).  There is also a significant uncertainty involved in
extrapolating the results of laboratory testing of the mechanical
strength of solid rock cores to predicting the behavior of the
heterogeneous fractured rock  mass of the repository host rock  Over
very long periods of time, increasingly greater drift wall collapse
should be anticipated, but the rate and extent of collapse will remain
uncertain.  Roof collapse is an example of the type of uncertainty that
can only be reduced to an extent by laboratory testing and seismic event
frequency analyses.  Conservative approaches assume extensive drift
collapse, allowing “worse case” situations to be analyzed, but these
bounding analyses must be considered cautiously.  While a degree of roof
collapse can be assumed, the nature of the collapse will also have an
effect on performance estimates.  If large blocks result from collapse,
they may deflect much of the intruding ground waters away from contact
with the waste packages in comparison to small blocks which might act
more as a porous flow medium in the collapsed drift.  However, larger
blocks may physically damage the drip shields causing rupture and more
immediate access for the ground water to the waste packages and  the
release of radionuclides.

Results from the modeling show that releases for the non-collapse
situation produce doses in the tens of mrem/yr at peak dose (#10 in
Table 2).  Similar results were observed in modeling using the EPA
Uncertainty Model (SC&A, 2006, Fig. 11).  These results illustrate the
significant effect roof collapse can have on performance.  Intuitively
one might expect maximum roof collapse to precede and be the initiator
for the peak dose, under that the assumption that the greater the degree
of collapse, the higher the ground water influx into the emplacement
drifts with consequent increased corrosion induced failure of the waste
packages and release and transport of radionuclides into the natural
barrier, as well as physical breaching of weakened packages by the
falling rock.  While this scenario appears reasonable, it may not occur
in that way since general corrosion will occur even under potentially
reduced water influx and the highly corrosion resistant metals may
maintain waste package integrity even with significant roof collapse if
the packages are not physically breached by the fallen rock.  The
calculations for the full temperature-dependence scenario (#10 - results
shown in Fig 7) include a degree of roof collapse, but the results show
greatly reduced doses controlled by the slow corrosion rate temperature
dependence.  

Temporal and Spatial Aspects of the Uncertainties.  The question of
predicting the deterioration of emplacement cavities in repository host
rock is a generic issue for any geologic setting, not only temporally
but spatially as well since the repository host rocks are not
homogeneous and fractured uniformly.  For a saturated zone site,
eventual drift deterioration may be a minor issue since the emplacement
drifts would be assumed to become flooded quickly after closure. 
However, the uncertainties connected to roof collapse are unique to the
Yucca Mountain setting because of the nature of the setting in the
unsaturated zone, and the important effect intact drifts have on keeping
doses low.  The complexity of flow through the unsaturated zone around
the emplacement drifts makes the prediction of water movement into the
drifts uncertain and the uncertainty in predicting the timing and
magnitude of roof collapse adds to the overall uncertainty in projecting
water movement into and out of the emplacement drifts over the long-term
as some collapse inevitably will take place in the drifts.  Projecting
the effects of large block versus small block collapse on the physical
integrity of the drip shields and waste packages over long time spans
adds another layer of uncertainty to performance projections.  A
conservative approach, assuming widespread collapse, can be taken to
make bounding projections, but that does not decrease the inherent
uncertainty in the total system analyses.  Such a conservative
assumptions may significantly overestimate releases since intact drift
walls significantly reduce ground water entry into the drifts, as
suggested by the results from the DOE PDM modeling described above.  

In summary, the timing and extent of roof collapse and its effects on
waste package corrosion rates and failure is an uncertainty that would
be difficult to reduce dramatically, and can have significant effects on
projected dose levels.  Relative to the base case results shown on Fig 7
(peak dose of about 125 mrem/yr.), reduced roof collapse lowers the
projected mean dose calculations by about 90 mrem/yr., a significant
decrease from the base case.  

V-2.3	Infiltration Rates/Climatic Fluctuations – Modeling Results

Infiltration rates do not appear to be a controlling variable for site
performance.  The difference between the high and low infiltration rate
cases is approximately 60 mrem/yr., a level well below the hundreds of
mrem/yr variations caused by alternate corrosion rates for the waste
packages and drip shields (Table 2, scenarios ID#s 1-3).  This is not
unexpected since the natural barrier above the repository location tends
to attenuate the effect of increased precipitation on the surface (BSC
2001b, Chapter 3), both because of the inbibition effects in the
unsaturated zone (the tendency of water moving down fractures to be
drawn into the porous tuff) and lateral diversion along discontinuities
between the volcanic rock units in the stratigraphic column above the
repository..  The largest uncertainty for infiltration rate input to the
performance assessments is in the magnitude of infiltration rate changes
from climate fluctuations over the long term.  There is relative
certainty that climate changes will occur and fairly high certainty in
the pattern of cyclical variations that can happen.  This uncertainty
could be addressed by bounding approaches for infiltration data since
the most uncertain aspect is the magnitude of the changes.  Relative to
the base case results shown in Fig 7, changes in infiltration rates to
higher or lower rates results in changes in the mean dose estimates of
about 40 mrem/yr on either side of the base case estimate of about 125
mrem/yr.  This uncertainty is about the same as the aleatoric
uncertainty seen in the FEIS data set, suggesting that the uncertainty
due to infiltration rate assumptions may not be distinguishable from the
uncertainty arising solely from random selection of parameter values
from the sampled distributions in the larger models used for the FEIS
calculations and the licensing performance assessments.  In light of the
ability of the rock units above the emplacement drifts to damp out sharp
variations in infiltration through lateral flow toward thru-going
fractures/faults (BSC, 2001b, Sec 3.2.3), an approach to performance
modeling that uses averaged infiltration rates to approximate the
changes anticipated from climatic fluctuations would be a way of
removing an uncertainty that does not appear to be a significant driver
for the estimates.

Temporal and Spatial Aspects of the Uncertainties for Infiltration  The
general question of how ground water can move through the geologic
strata above and below the repository is a generic issue applicable to
any geologic setting.  Projecting ground water infiltration rates is a
uniquely site-specific issue for any geologic setting and would produce
site-specific uncertainties.  The technical challenges are unique for
the Yucca Mountain site because of its unique geologic setting, in
fractured rock, in a thick unsaturated zone, and in an arid climate. 
For a repository location in a saturated zone, the uncertainties would
not be as great since the ground-water flow through a saturated zone
repository location would not be as strongly affected by climatic
fluctuations.  The spatial uncertainties controlling infiltration, and
also ultimately the movement rates of ground water in the unsaturated
zone, include: the degree of homogeneity of the rock, soil and
vegetation cover across the repository site; and the fractures exposed
on the surface.  These variants will probably remain relatively constant
over time with some changes in soil cover properties over time from
erosive processes and the development of poorly permeable soils typical
of arid environments, as well as from precipitation variations due to
climatic changes.  While rates of erosion and soil development in an
arid setting are low, over the course of a million year period, some
changes in the soil cover over the repository and its permeability, as
well as that of the near surface fractures can be reasonably expected in
response to climatic fluctuations.  It is not possible to predict such
changes with certainty, but they would be expected to be relatively
small, using the geologic record around the site as a guideline.  

The temporal uncertainty in precipitation variations is due to climatic
fluctuations and is more important than spatial variations.  While the
cyclical nature of climatic fluctuations is reasonably certain, the
magnitude and exact timing of the fluctuations will always remain
uncertain, also reflecting the uncertainty about the effects of carbon
dioxide increases in the atmosphere (SC&A, 2005, sec.1.2, 1.4). 
Modeling performed by DOE to examine the impact of climate variations on
projected doses (CRWMS M&O, 2000) showed increases of as much as 2-3
fold increase in the peak dose estimate (SC&A, 2005, Table I-5), but
these analyses did not consider the moderating effect of seepage
behavior of the unsaturated zone around the emplacement drifts.  

V-2.4	Radionuclide Solubility and Transport – Modeling Results

The DOE PDM assumes that the release of radionuclides into the natural
barrier is limited by the thermodynamic solubility controls for the
various actinides in the wastes.  This assumption limits the
concentrations of various actinides leaving the repository to levels
dictated by the chemistry of waters in the repository and the actinide
phases determined to be the thermodynamically stable phases under those
conditions. The results of the sensitivity assessments involving
changing neptunium solubility control show little effect relative to the
base case results.  The change in the mean dose level is only slightly
different (see Table 2, mean dose of 111 mrem/yr. for scenario ID# 8)
than the base case results (125 mrem/yr.).  While this result is
suggestive of a small effect from this source of uncertainty, these
results should not be taken too literally as demonstrating that this
source of uncertainty (i.e., thermodynamic control on radionuclide
solubility and mobilization in ground water) is insignificant, or
extending the result of the single alternative solubility control
assumption to all possible alternative controls.  Only one solubility
control alternative for one actinide was examined in the DOE PDM.

There are a number of uncertainties involved in making assumptions about
solubility controls on the actinides, all of which can affect
performance calculations.  These uncertainties include: (1) determining
how physical and chemical conditions in the repository environment will
evolve and affect the solubility controls; (2) identifying what actinide
phases, and secondary phases that could incorporate actinides, could
form in the waste package/repository environment over time and; (3)
determining the stability constants for these very low solubility
actinide phases or secondary phases.  Uncertainties about thermodynamic
phases that control actinide solubility exist for all the actinides, and
their effects on projected dose are not evaluated in the analyses
reported here.  Only one example among many possibilities for actinide
solubility control variations was analyzed in the results reported here.
 Extensive discussions about the evolution of ground water chemistry in
the emplacement drifts and the repository are contained in BSC 2001b. 
These discussions focus on changes in pH and CO2 while mentioning the
uncertainty in predicting which particular phases will control actinide
solubility.  The combined effects of assuming different thermodynamic
solubility controlling phases is a more complex effort, beyond the scope
of our relatively limited analyses.  The combined effects may be
greater, less or about the same as the dose projections for solubility
controls assumed in the base case.  The analyses reported here do not
explore the full range of possibilities, they examine only one
alternative.

In addition to the uncertainties associated with the thermodynamic
solubility control assumption, there is a fundamental uncertainty in
assuming that the solubility - (i.e., the concentrations of
radionuclides entering the natural barrier) will be controlled by the
thermodynamically stable phase(s) under the varying physical and
chemical conditions in the repository over time.  It is very common in
nature for the precipitation of solids to be controlled by metastable
phases rather than the thermodynamically prescribed phases.  This often
happens because the nucleation kinetics for precipitation of the
thermodynamically favored solid are too slow and another phase with
faster nucleation kinetics precipitates more rapidly.  Whether this will
happen for some or all of the actinides over the course of the geologic
stability period is unknowable, since the physical and chemical
environment in and around the waste packages is not possible to
duplicate in a laboratory because of the many variables that will
control it and their variations with time.  If metastable phases control
some or all of the actinide solubilities, higher concentrations of
actinides would be present in ground waters exiting the repository and
transporting radionuclides into the natural barrier.  The extent of
changes in concentrations is not easily estimated for many reasons
(complex and varying chemistry in the near-field, difficulties in
measuring actinide concentrations in very dilute solutions, etc.). 
Along with the uncertainties in the near-field, the solubility
constraints on concentration levels along the far-field flow path can
differ, i.e., the thermodynamically stable phase could control the
concentration levels in the far-field thereby lowering them to levels
that would have resulted if the same phase controlled the near-field
concentrations.  This alternative would give dose results essentially
equivalent to the thermodynamic control assumption.  

Another mechanism for enhanced radionuclide transport is colloidal
transport, either as a radionuclide colloid or adsorption of
radionuclides on other colloidal particles developed in the repository
environment.  Colloid formation in the near-field also can play a role
in the mobility and transport of certain radionuclides released from the
wastes (SC&A, 2005, Chap. 4).  The tendency for radionuclides to form
colloidal particles has been investigated, primarily for plutonium, and
the conditions under which the colloidal material can form are
reasonably well known.  The potential for radionuclides to adsorb on
other colloidal materials is less well known, and the question of when
and to what extent these colloids can form in the repository and how
well they can migrate through the natural barrier has many uncertainties
involved. 

 As the engineered barriers degrade over long time frames and corrosion
products (e.g., iron oxides of various types from the oxidation of
ferrous materials - SC&A, 2005, sec, 4.2.2) become more abundant, the
potential for colloids to form and to adsorb and transport radionuclides
would seem to increase, but the extent and rate of this process is
highly uncertain.  These processes are highly dependent on the
micro-scale changes in the waste package metal containers, the
dissolution behavior of the spent fuel and the flow conditions for
ground waters entering and exiting the packages.  Another uncertainty in
this potential transport mechanism is the extent to which the rocks
along the transport path act to “filter out” colloidal material due
to pore size and electrostatic effects.  Although over the long-term it
might appear reasonable to expect greater potential for colloidal
transport, the fracture pathways and pore spaces leading away from the
repository may well become “clogged” with material from the
degradation of the engineered barrier components and inhibit or
completely block colloidal transport.  The degree to which these
processes will affect radionuclide transport in the very long-term is
uncertain and not amenable to reliable quantification, because the exact
conditions in and around the waste packages over the very long-term
cannot be duplicated in laboratory testing. 

 In summary, the sensitivity results shown here for the variation of
neptunium concentration limiting phases lies well within the aleatoric
uncertainty  (~ 50 mrem/yr., see Table 1)) shown for these analyses. 
This result suggests that the DOE PDM could not meaningfully distinguish
between the two alternative actinide concentration limiting scenarios
examined.  However this result should not be broadened to conclude that
the uncertainties in projecting solubility controls cannot be
demonstrated to have a significant effect on dose projections.  This is
because of the fundamental, and in many respects irreducible,
uncertainties in determining the mechanisms that will control the mass
transfer of actinides through the disposal system.  In addition, the
release and transport of radionuclides in the near-field is determined
by the evolving chemistry of the ground water entering the emplacement
drifts and its interaction with the components of the engineered barrier
system (EBS).  Temporal and spatial uncertainties are discussed below
and more extensively in the SC&A, 2005 report mentioned above.

Temporal and Spatial Aspects of the Uncertainties in Radionuclide
Chemistry  The question of controls on the concentration of
radionuclides that may move from the engineered barrier into the natural
barrier is a generic question applicable to any geologic setting. 
Thermodynamic versus  metastable phase controls on solubility levels, as
well as the potential for colloid formation and transport, are part of
the broader issue of understanding the evolution of ground water
chemistry as these waters enter the repository, react with cement and
ferrous metal components of the EBS, and exit the repository.  The Yucca
Mountain disposal system presents some very unique additional
difficulties because of its location in an unsaturated zone setting.  In
an unsaturated zone setting, changes in physical and chemical conditions
due to heat effects and drying may have significant kinetic effects on
the nucleation of solid phases or their dissolution, which would affect
transport rates into the natural barrier for instance.  These physical
changes will also produce changes in the chemistry of the ground water
entering the emplacement drifts.  After entering the drifts, reaction
with the cement and ferrous metal components of the EBS would further
alter the ground water’s initial chemistry.  

Spatially, the seepage water in the drifts may contact the drip shields
or may not.  The water may run down along the drift walls with minimal
contact with the EBS components and retain a chemistry reflecting its
loss of  CO2  upon entering the drift and contact with the invert
material on the drift floor.  More ground water is likely to fall on the
drip shields and have its chemistry changed by the corrosion process and
eventual interactions with the waste packages and their contents.  All
these waters will also undergo chemical changes from heat generated by
the wastes.  Upon beginning to exit the EBS, these various differing
water chemistries will be mixed while traveling through the invert to
reach the surrounding host rock.  The exact chemistry of these waters
can only be approximated because of the heterogeneity of their travel
paths and the EBS materials they encounter.  The chemistry of these
waters will differ, reflecting their unique travel paths through the
emplacement drifts, and can only be approximated with bounding
assumptions made about their “average” or alternatively “worst
case” composition.

Temporally, as the repository moves through its thermal period the
chemistry of the ground waters will change in response to lessening
temperatures and the build up of corrosion products from the degradation
of the metallic EBS components.  In the long-term, the questions of what
phases will control the concentration of radionuclides in the ground
waters becomes more difficult.  Higher temperatures favor reaching
predictable thermodynamic equilibria.  At lower temperatures, metastable
phases are more likely to form and the increased amounts of corrosion
products present after the waste packages have breached lessen the
confidence in predicting exactly what phases will determine the aqueous
concentrations of radionuclides, what phases will sorb radionuclides in
the emplacement drifts, or become mobile in the ground water to allow
transport away from the EBS.  All these variables create increasing
uncertainties as the EBS degrades over time.  Conservative bounding
assumptions can be made for these various processes to simplify
calculations, but these kinds of assumptions simply mask the actual
uncertainties and may result in a significant over-estimation of
radionuclide mobility and transport out of the EBS.  It is not possible
to confirm assumptions about the actual variations in chemical
conditions in the degrading EBS because of the time frames involved and
the slow rates at which these processes operate.

 

V-2.5	Changes in Assumptions about Ingestion Pathway Doses – Modeling
Results

Like the neptunium solubility variation analyses, results from varying
the BDCF for plutonium-242 showed changes in the peak dose within the
aleatoric uncertainties (peak dose of 138 mrem/yr.).  These results
suggest that the assumptions about dietary intake are not significant in
terms of driving the dose estimates out of the envelope of the aleatoric
uncertainty.  This may be true in that the dose to the RMEI is largely
controlled by two requirements in the rule, i.e., that the RMEI is
located over the center line of the contamination plume and consumes a
fixed amount of contaminated drinking water.  These two requirements
overweigh the relatively smaller input from food ingestion assumptions. 
Also, the rule directs that the ingestion profile for the RMEI be based
on present-day consumption patterns.  Food items produced with
potentially contaminated ground water are produced at distances greater
than the RMEI location and would use less contaminated ground water.  

Temporal and Spatial Aspects of the Uncertainties for Ingestion Pathways
 Uncertainties about biosphere pathways and exposures apply to any
biosphere dose model for a disposal system, but must be considered on a
site-specific basis due to differences in relevant biosphere parameters
at any specific site.  While the standard approach for biosphere
exposure modeling has many fixed parameters, such as drinking water
consumption, the exposure pathways arising from the use of contaminated
ground waters are site-specific.  For example, the standards mandate
that food consumption patterns for the RMEI be based on present day
local food consumption patterns in the area down gradient from the
repository.  These characteristics would be different for a farming area
in a temperate location as opposed to the arid environment in Amargosa
Valley.  It is believed that assuming current day conditions for
ingestion patterns is a conservative measure (overestimating doses)
because of the heavy use of well water for irrigation.  It could be
argued that in future times when rainfall is more abundant, food could
be produced closer to the repository location and consequently become
more contaminated than present day conditions where food is produced
farther down gradient from the RMEI location.  However under such a
scenario, less well irrigation water may be necessary, possibly
counterbalancing the effect of producing food closer to the repository. 
Because population dynamics are not possible to forecast confidently,
even into the relatively near future period of hundreds of years, it is
reasonable to assume that the uncertainties in the biosphere pathways
model component of dose projections cannot reliably be reduced.

V-2.6	Removal of the Saturated Zone – Modeling Results

This alternative (setting the saturated path length to zero – ID #9,
Table 2) is largely hypothetical in nature since the saturated zone
cannot really disappear.  Effectively this scenario takes the
contaminated water from the floor of the emplacement drifts and delivers
it immediately to the well supplying ground water to the RMEI.  (The DOE
PDM excludes the unsaturated zone below the waste packages and the
fractured volcanic rocks in the saturated zone and considers only the
presence or absence of the alluvial portion of the saturated zone.) 
However this scenario illustrates some important points.  The scenario
quantitatively describes the contribution of the natural barrier beyond
the repository boundary to the dose projections.  Without this
contribution, the peak dose rises to well over 2 rem/yr., showing that
the natural barrier is a major contributor to total performance.  The
scenario also illustrates the potential effects of a generic uncertainty
– the confidence that can be placed on the retardation properties of
the far-field. 

Radionuclide retardation on the rocks along the flow paths to the RMEI
location is estimated primarily by laboratory testing of radionuclide
“sorption” on the rocks.  The extrapolation of such laboratory test
results to field conditions has always been a controversial subject, as
is the more immediate question of how the tests are designed and
executed to simulate expected conditions along the ground water flow
paths.  A conservative approach is generally taken in using the
laboratory data in contaminant transport modeling, usually by biasing
the selection of lab results to low-end values for use in the
contaminant transport calculations.  The issue of whether the laboratory
results are meaningful at the process level (do they actually test
retardation mechanisms under true site conditions), and to what extent
can they be used in modeling, is a generic uncertainty that can only be
addressed in a limited way for any site-specific application. 
Regardless of the geologic media under consideration, a significant
uncertainty will be present in the extrapolation of laboratory test data
to the field situation. 

Field testing using sorbing and non-sorbing tracers can be performed to
test the transferability of laboratory data.  However such tests have
significant uncertainties themselves concerning how well the tested
domain represents the entire flow path.  The questions typical for such
testing include:  comparisons of test flow rates versus in-situ ground
water flow rates; heterogeneity within the test domain in contrast to
the actual flow paths; kinetics of sorption processes and ability to
model the test domain flow paths precisely enough.  Multiple field tests
at the same or different locations can be performed but many of the
uncertainties will remain.

Temporal and Spatial Aspects of the Uncertainties – Far-Field
Radionuclide Sorption  The uncertainties involved with  transferring
laboratory retardation data, as well as field test data, to contaminant
transport assessments are largely spatial in nature.  Laboratory
measurements are done on isolated systems with few variables left
uncontrolled, and with fewer variables than are present in the actual
disposal system in nature. The transferability of such data is always
uncertain to a significant degree, leading to the conservative approach
of using lower-end values for modeling applications.  Field testing of
retardation is difficult and time-consuming and subject to all the
uncertainties mentioned above in attempting to scale up such data for
modeling purposes.  The conservative approach of using lower-end values
would tend to overestimate doses, however since it is not possible to
confirm the results of these calculations, the uncertainties remain only
partially resolved.  

Temporal uncertainty is introduced when the radionuclide inventory
changes with time.  However for the long-lived actinides which
constitute the overwhelming majority of the peak dose, their low
solubility and relative abundance in the wastes minimizes the
consequences of changing inventory after the shorter-lived radionuclide
inventory is depleted.  After a long-period of time, a more constant mix
of radionuclides is released into the natural barrier, consisting of
long-lived radionuclides.  Colloidal transport is proposed for some
radionuclides, either on natural colloids or colloids formed from the
degradation of the engineered barrier materials (BSC 2001b, Chapters
9-12).  The gradual degradation of the engineered barrier may introduce
some temporal variation in the radionuclide load delivered into the
natural barrier through colloid formation and transport, however it is
not possible to reliably quantify this source.  Intuitively, one would
expect colloidal transport to increase as the repository EBS components
progressively degrade over time and more colloid material (such as iron
hydroxides and oxide compounds from the oxidation of the waste packages)
becomes available to “sorb” radionuclides and move through the
disposal system.  As mentioned previously, there is a potential that at
long time frames the fractures and pores in the rocks around the
repository may become “clogged” with degradation products and impede
radionuclide movement into the far-field.  It is not possible to
reliably estimate the amounts of colloidal material available as a
discrete function of corrosion of the waste packages.  Another temporal
uncertainty in far-field transport may derive from long-term changes in
the ground water flow rates in the saturated zone, due to climate
fluctuations and changes in regional recharge and flow patterns.  A
conservative approach to modeling transport is usually taken to
compensate for the uncertainties, but the approach does not remove the
uncertainties or increase the confidence that can be placed on the
assessments as “predictors” of future behavior.

V-3 Summary of Epistemic Uncertainties in the DOE-PDM Results

The analyses performed with the DOE PDM illustrate the potential effects
on dose projections of a number of alternate descriptions of how the
Yucca Mountain disposal system would operate.  The dominant
uncertainties concern the projected performance of the waste package and
drip shield metal components, and the stability of the emplacement
drifts to collapse.  Relative to the base case performance (~125 mrem/yr
peak dose), the most dramatic range in dose projections arise from
assumptions for faster corrosion rates for the waste package and drip
shields (5X faster) and  assumptions of slower rates (the full
temperature dependence alternative).  The range of dose projections
range from 3 to 768 mrem/yr., essentially no significant doses at one
end of the spectrum to doses significantly higher than the 100 mrem/yr
peak dose limit in the final standards.  The analyses presented here
were done looking only at the variations (alternate conceptualizations)
separately and a few variations in combination (Table 3).  For example
the combination of non-collapsed drifts and increased corrosion rates 
(Table 3, # 1) produced  lower doses than the corrosion rate increase
alone  (Table 2, #4).  This is understandable since the non-collapsed
drift limits the amount of ground water that can flow through the
emplacement drifts and transport radionuclides into the natural barrier.
 Analyses looking at more combinations may give different results.  The
combination of full temperature dependence for corrosion rates and
limited roof collapse may produce essentially minuscule doses within the
stability period and beyond, where as a combination of increased
corrosion rates with added factors such as high infiltration or less
retardation in the far field would produce higher doses than the
increased corrosion rates alone.  

With the exception of removing the saturated zone from the disposal
system, all the variations examined with the DOE PDM are reasonable
alternatives for the processes that may operate in the long-term and
contribute to the peak dose.  Considering the aleatoric uncertainty in
the DOE PDM model for sets of 1000 realizations is approximately 50
mrem/yr.  (25 mrem/yr. on either side of the mean value, or
approximately 20 % of the dose), many of the alternatives examined would
not be distinguishable from the base case results statistically (at the
5% probability level).  However the uncertainties for some of the
processes in the PDM may well be more significant than the limited
options built into the DOE PDM allows, for example the uncertainties in
solubility controls for all of the radionuclides significantly
contributing to the dose projections.  It should be noted that these
conclusions refer to this model.  A more complex model may give
different results, although the trends show in these results should be
the same as long as the significant processes are included in the model.
 Note that the aleatoric uncertainty for the more elaborate model used
for the FEIS analyses is 45 mrem/yr. on either side of the mean – or
approximately 30% of the dose.  However this illustrative exercise shows
the approximate limits of an assessment model to make meaningfully
projections over the time frame involved.  The epistemic uncertainties
in the DOE-PDM analyses are more difficult to define precisely, but they
are the dominant ones.  Corrosion rate assumptions can reduce the base
case (125 mrem/yr at peak) to insignificant levels or increase the dose
many times over.  

VI 	Uncertainty Propagation Over the Very Long-Term

In another report, the propagation of uncertainty over long time frames
was examined (SC&A 2006).  For that exercise, the DOE PDM was modified
as described in that report to allow the analyses to be done.  A
hypothetical disposal system was developed that was at the “edge of
compliance”, i.e., gave a mean dose to the RMEI of 15 mrem/yr. at
10,000 years, by allowing a fixed number of waste packages to fail
within the 10,0000 year time frame.  This group of failed packages was
kept constant through the simulation (no additional failures were
allowed), and the dose histories were followed through peak dose.  The
spread in the dose histories (realizations) for the failed packages
(difference between the 5 and 95 percentiles) increased from one and a
half orders of magnitude at 10,000 years to three and a half orders of
magnitude at the time of peak dose (SC&A 2006, Table 10). These results
illustrate that as the time frame for the assessments increases into the
tens to hundred of thousands of years the uncertainty in the dose
histories also increases as reflected by the spread in dose projections.
 

Peak doses for various modeling variations (number of realizations,
sampling strategies, etc.) varied between a low of about 160 mrem/yr.,
to slightly over 400 mrem/yr (SC&A 2006, Table 2)., also illustrating
the “sharpness” of the PA tool (the EPA Uncertainty Model as
modified from the DOE PDM) for modeling the hypothetical disposal
system.  It is worth noting that the spread in peak dose estimates due
to these modeling variations (and not the underlying model itself) is
significant - more than a factor of two from the lowest to highest dose
estimate.  These analyses could be considered a low-end approach to
forecasting a peak dose for an “edge-of-compliance” system, since no
additional waste package failures were allowed after ten thousand years.
 In reality for a disposal system that might be actually at the 15
mrem/yr mean dose limit at ten thousand years, additional failures
beyond that time would be expected with corresponding increases in dose
above those seen for the fixed number of failed waste packages in the
hypothetical system.  An obvious conclusion of these analyses is that a
peak dose limit in the range of several hundred mrem/yr. would constrain
the disposal system to produce performance well below the 15 mrem/yr.
level within the ten thousand year compliance period, in light of the
uncertainties inherent in very long-term dose projections.  The addition
of a peak dose limit to the 10,000 year dose limit has the practical
effect of constraining the disposal system to limit waste package
failures and consequent releases to extremely low levels for well in
excess of 10,000 years in order to meet the peak dose limit (Docket
number for WM08 paper).

This conclusion is also supported by the results of the DOE PDM exercise
reported here.  For increases in corrosion rates from those used in the
base case, the time for the peak dose changes dramatically from the
700-800 thousand year range to less than 200 thousand years.  With
corrosion rates even faster, the time of peak dose would decrease
further and the peak dose would rise higher still.  At some point, the
rapidly rising part of the dose history curve would generate doses
approaching or exceeding the 15 mrem/yr limit at 10,000 years as the
time to peak dose continues to decrease due to the faster corrosion
rates.  The two tiered standard can then be seen as doubly constraining.
 While the 10,000 year standard limit constrains performance within that
period, the peak dose limit is a second measure that constrains
performance within 10,000 years.  The disposal system must perform below
the 10,000 year dose limit in order to demonstrate compliance with a
peak dose limit in the range of several hundred mrem/yr.  

 

While the results of the uncertainty study (SC&A 2006) support the
generalized conclusion that over-all uncertainties increase with time
for these complex simulations, another important question remains.  How
much confidence can be placed in PA analyses as reliable “forecasts”
of disposal system performance and consequent dose potential?  While
overall uncertainty may increase, does the PA tool give a reasonably
reliable picture of the most probable outcome?  The “sharpness” of
the PA tool in these long time frames is central to answering that
question.  Examining an actual site performance model (the FEIS results)
illustrates that the results for a given set of realizations has a
significant level of uncertainty in terms of how well alternative
conceptualizations of the disposal system can be distinguished from each
other.  For the FEIS analyses from Table 1, the mean dose was
approximately 150 mrem/yr., with an uncertainty band of about  45-50
mrem/yr. on either side of the mean.  The band indicates the
“sharpness” of the FEIS model for aleatory uncertainties.  For a
mean of 150 mrem/yr., there is a relatively wide band around the mean
value.  If we contrast  this uncertainty with  the aleatoric uncertainty
for the DOE PDM (for the 300 and 1,000 realizations sets) we can see a
similar aleatoric uncertainty would arise for assessments with
realization numbers between 300 and 1,000.  

For the DOE PDM model exercise (Table 1 and Figs 1-7), the alternate
conceptualizations produce a wide range in mean dose levels, from less
than 10 to close to 800 mrem/yr.  The alternatives scenarios examined
(the various “switches” in the model) are reasonable alternatives,
suggesting that, depending on which ones are considered credible
possibilities in the licensing assessments, the dose assessments could
differ dramatically and perhaps in ways that cannot be resolved.  For
example, assuming faster corrosion rates than those shown in short-term
laboratory test could be considered a more defensible approach than
simply assuming the laboratory testing results can be extrapolated
confidently to times in the many hundreds of thousands of years.  The
resulting dose projections would be much higher than the base case (see
Figs. 3, 4 & 6).  However if drift wall collapse were assumed to be
minimal or minor in extent, a compensating process would operate to
lower doses (by restricting ground water access into the drifts), with
the net result being little different than the base case.  This case is
illustrated by combined scenario #2 in Table 3 which links the non
collapsed drift (NCD) scenario from Table 2 with waste package and drip
shield corrosion rates accelerated by a factor of 5.  The forecasted
peak mean dose for this combined scenario is 118 mrem/yr.  This value is
approximately the same as the peak mean dose in the base case in Table
2, but occurs much earlier at 190,000 years versus 730,000 years in the
base case.  If the corrosion rate is accelerated for the waste packages,
but not the drip shields, then the peak mean dose is reduced in half to
55 mrem/yr at 420,000 years, as shown in combined scenario #1 in Table
3.  The difficulty with this situation in a licensing process is that
the two alternatives (high releases from faster corrosion versus low
releases due to limited roof collapse) cannot be confidently predicted
relative to each other.  The uncertainties cannot be reduced
significantly making it very difficult to discount either scenario or
give them relative weights for decision making against a fixed numerical
dose limit.

In moving from the ten thousand year standard dose limit of 15 mrem/yr.
to the question of an appropriate peak dose limit for the Yucca Mountain
disposal system several points are relevant.  The peak dose limit should
offer a measure of meaningful protection.  The engineered barrier cannot
be assumed to provide essentially complete containment indefinitely, at
some point releases beyond the 15 mrem/yr. level should be expected. As
the results of the sensitivity studies reported here show, without the
natural barrier contribution doses easily exceed 2 rem/yr.  A robust
metal barrier can constrain releases to levels well below that, but the
uncertainties in extrapolating the relevant laboratory data will remain,
and are generic uncertainties shared by any repository design and
geologic setting.  The uncertainties in very long-term assessments of
the Yucca Mountain system limit the degree of confidence that can be
placed on simulations and limit the degree to which they can be used to
define the “protectiveness” of the system relative to the 10,000
year standard (as well as mandate a specific repository design or set a
peak dose limit for a particular design).  As an example, an assessment
assuming full temperature dependence for the corrosion rates (Table 2
– peak dose 3 mrem/y) combined with a assumption for limited drift
collapse (Table 2 – peak dose 37 mrem/yr.) would give extremely low
peak doses.  However this scenario could not be argued as more likely,
or even as likely, as one with higher corrosion rates and more extensive
drift collapse that would give doses in the many hundreds of mrem/yr. 
Clearly the performance assessments, when uncertainties are considered,
should be regarded as only rough approximations to demonstrate the
“protectiveness” of the disposal system and the designated peak dose
limit.  Rather than deriving a peak dose limit from the range of
performance assessments for the site, another measure for an acceptable
dose limit should be derived.  The proposed rule offered the alternative
of deriving a peak dose limit based on natural background level of
exposure.  This route to setting a peak dose limit avoids the issue of
uncertainties in performance site projections, but still allows these
assessment to play their appropriate role as measures of how well the
system could meet the limit, giving consideration to the applicable
uncertainties.

VII	Aleatoric and Epistemic Uncertainties – Uncertainty and
Conservatism in Performance Assessments for the Yucca Mountain Site

The aleatoric uncertainties in a given performance assessment play a
role in determining the degree of confidence with which alternate
conceptualizations of the disposal system processes can be distinguished
from one another.  For the FEIS analyses shown in Table 1 (300
realizations to obtain a “stable” mean) the aleatoric uncertainty is
approximately 90 mrem/yr.  This suggests that dose histories produced
from alternate conceptualizations of the disposal system performance
could not be clearly distinguished from the nominal FEIS
conceptualization unless the results were different by more than 90
mrem/yr. (45 mrem/yr on either side of the mean value).  For
interpreting the implications of aleatoric uncertainty, it should be
noted that this uncertainty is unique to each individual performance
assessment exercise.  In the case of the FEIS analysis used here, 300
realizations using the large TSPA model produced the level of
uncertainty shown in Table 1.  This level could be reduced by increasing
the number of realizations in the analysis (this effect can be seen in
Table 1, by  comparing the spreads for the DOE PDM results shown for two
sets of realizations, n = 300, 1000).  Presumably the aleatoric
uncertainty for the higher number of realizations would be lower to some
degree.  

In examining epistemic uncertainties in the DOE PDM, the aleatoric
uncertainty for 1,000 realizations of the model was about 50 mrem/yr
(see Appendix A, Table A1).  From this starting point, the performance
assessments for alternative conceptualizations (the various
“switches” in the DOE PDM that allow realizations for alternate
scenarios – such as non-collapse of the drifts), could not be
statistically distinguished from the base case unless the mean dose for
the alternative scenario was more than approximately 25 mrem/yr. on
either side of the base case mean of approximately 125 mrem/yr.  From an
examination of the variations analyzed for the DOE PDM modeling (Fig.
7), many of the alternatives could not be distinguished statistically
from the base case (e.g., changes in the Pu -242 BDCF, neptunium
solubility controls, medium infiltration).  If an alternative scenario
were examined separately, i.e., a thousand realizations performed, there
would be an aleatoric uncertainty associated with it and an uncertainty
band around the mean.  It may be possible, for certain combinations of
parameters, for an alternative to have some results fall outside the
aleatoric band of the base case.  In that case, there would be a greater
chance that the alternative may be distinguishable from the base case
for the realizations where the projected dose is close to or outside of
the base case aleatoric uncertainty band.  But there would be
combinations of parameter values for which the alternative would still
be indistinguishable from the base case.  These relationships create a
situation that lessens the over-all confidence in the performance
assessment tool to make confident projections of how the disposal system
will actually behave in the long-term.  This results from the ambiguity
created when the performance assessment tool can sometimes tell the
difference between alternative scenarios and sometimes not.  This
ambiguity is essentially the “sharpness” of the tool for use in
confidently projecting performance and doses and subsequently making
regulatory compliance decisions, i.e., that the actual processes
operative at the site are understood sufficiently to have high
confidence that the projections are true representations of how the
disposal system will operate over time.  

 The epistemic uncertainties examined indicate that the “sharpness”
of the PA tool is not sufficient to distinguish between some alternative
scenarios (e.g., neptunium solubility control and plutonium BDCF) and
may not always be able to distinguish between some of the alternatives
(high and low infiltration scenarios).  For the FEIS PA analyses, the
aleatoric uncertainty around the mean value of approximately 45
mrem/yr., with added uncertainty in terms of how well that model can
distinguish between alternate conceptualizations.  Without an exhaustive
examination of uncertainties in that model, it is not possible to be
exact about the total range of uncertainty, as reflected by dose
variations, but it would not be surprising for the combination of
aleatoric and epistemic uncertainty to exceed the 45 mrem/yr. level
significantly.  This is a significant portion of the total dose
estimates shown in published assessments for the Yucca Mountain site
(DOE,1998, 2000, 2008, BSC, 2000 a&b, CRWMS, 2000), and has important
implications for interpreting the results of these assessments, as
discussed below.

The recognition that the PA tool has inherent limitations brings up
another relevant aspect of using performance assessment to project doses
for the disposal system.  To address uncertainties that are not possible
to reduce completely by laboratory and field studies, such as the degree
of drift wall collapse, or the solubility controlling phases for
actinides (see previous discussions on epistemic uncertainties),
conservative assumptions are often incorporated into the construction of
the PA model.  Conservative assumptions and associated uncertainties in
Yucca Mountain performance assessments were examined critically in
report supporting the proposed rulemaking (SC&A, 2005).  Conservatism
should not be confused, or thought of as synonymous, with uncertainty. 
The intent of conservative assumptions is to examine “worst-case” or
“high-end” situations to determine if projected performance can
still meet targeted levels in spite of the “worst-case” or
“high-end” assumptions.  Whereas uncertainties concern the limits of
our knowledge to construct and execute mathematical simulation models
and interpret their output.  If performance projections are well below a
regulatory limit, the uncertainty in the assessment may still be high
with respect to how much confidence can be given that the model is a
reliable description of how the disposal system will perform in the
long-term.  

Depending on how conservative assumptions and modeling approaches are
incorporated into the site PA model, it may be difficult to determine
the effect of uncertainties in the associated assumptions on the
projected doses.  If conservative assumptions are incorporated
implicitly by modifying parameter distributions alone, it may not be
possible to separate aleatoric from epistemic uncertainties.  In this
case the aleatoric uncertainty (estimated as described in Appendix A) in
a given set of realizations would be a mixture of both kinds of
uncertainty.  If many alternative scenarios are constructed and
weighted, and the parameter distributions used are tied to alternative
conceptualizations for system performance, it would be possible to
examine the alternatives separately in a transparent manner and clearly
identify the uncertainties and their effects on dose projections.  The
published Yucca Mountain assessments treat igneous intrusion scenarios
in this way (DOE, 2008) because the probability of these scenarios is
very low, potential exposures are very high, and the exposure pathways
so different from the nominal expected case that separate treatment of
the scenarios is unavoidable.  For other alternative conceptualizations,
such as infiltration rates, parameter distributions are simply modified
to incorporate the parameter ranges associated with the alternatives
into the nominal case data base.  For these approaches it is more
difficult to identify and quantify the uncertainty attributable to
alternative conceptualizations.  In addition, the “abstraction”
process used by DOE  to develop the over-all total system performance
model from more detailed subsystem process models selects the
“driver” parameters and processes from the lower tier models for
inclusion into the next level of the model abstraction process.  In
doing this, a measure of simplification is incorporated at every level
of the abstraction with an associated loss of “sharpness” in terms
of scientific rigor in the simulations and detailed quantification of
the uncertainties on the subsystem behavior.  For an abstraction
process, care must also be taken to examine the relative role of
conservative or bounding assumptions at different levels of the
abstraction.  It may be possible that a conservative assumption at one
level of the abstraction may not be a conservative assumption at a
higher level.  

VIII	Uncertainties in Performance Assessments – Implications for
Standard Development and Regulatory Decisions

A peak dose standard limit must be derived from considerations of
acceptable health impacts and safety not on how a particular disposal
system is “forecast” to perform.  Many of the questions surrounding
decisions about what is an acceptable dose limit over the extremely long
time frames in question are outside of the scope of this discussion,
which is focused more narrowly on the ability of the performance
assessment tool to distinguish between alternative conceptualizations of
the disposal system performance (epistemic uncertainties), as well as
the inherent uncertainties in making dose projections for a given
conceptualization (aleatoric uncertainties).  However, these
uncertainties have implications for the repository applicant and
regulatory decision maker in that both parties are concerned with having
a credible safety case for the disposal system.  Understanding the
“sharpness” of the performance assessment tool is important in this
respect.  As the time frame extends into hundreds of thousands of years,
uncertainties will increase and may well lessen the confidence that dose
projections are reliable simulations of repository performance and
challenge the credibility of a safety case relying heavily on
performance assessment results. 

 The sharpness of the performance assessment tool represents the limit
of the science concerning dose projections for the compliance period. 
Performance assessment technology has advanced over the course of the
repository effort since the late 1970s, as illustrated by the
progressively more complex models used in the disposal system
assessments over that time.  In parallel, site characterization studies
have generated considerably more information than available for
assessments performed early in the program and the design of the
disposal system has evolved in consort with the increased understanding
(EPA, 2001).  However considering the uncertainties discussed above,
there are some uncertainties that can never be completely reduced to
insignificance, and some that may not need to be studied further in
consideration of their relative effects on dose projections. For a
two-tiered standard for the disposal system, the ability of the
performance assessment tool to distinguish between the two dose limits
is an important consideration in compliance decision making.  If
projected performance over the entire stability period is well below the
standards, there is little difficulty in making a compliance decision as
long as the performance model has been demonstrated to acceptably
simulate the processes controlling peak dose to the RMEI.  If the dose
projections overlap the standard to some degree, a compliance decision
is potentially problematical.  In formulating a standard, attention
should be directed to understanding the limits of the tool, so that dose
limits, judged to be protective, are not so close together that it is
unlikely the tool can meaningfully distinguish relatively short-term
performance (within 10,0000 years) from performance over the entire 1
million year geologic stability period.

There are still some important implications of uncertainty in the
performance assessments that have a bearing on standard setting. 
Understanding these effects is also relevant to designing the structure
of a standard, so that uncertainties in dose projections do not
compromise the ability to make confident decisions about the safety of
the disposal system.  Performance assessment is the only tool available
to project performance of the disposal system over the regulatory time
frame in a standard.  As such, an understanding of the uncertainties on
a site-specific basis is necessary to avoid setting standards that
cannot be implemented with reasonable confidence that the disposal
system will perform adequately.  More specifically for example if tiered
standards are under consideration (e.g. different dose limits at varying
times), if the difference between these dose limits is well within the
uncertainty of the assessment tool to distinguish between them for the
various scenarios in the assessments, making a confident compliance
decision would be very difficult to impossible

  The site-specific aspects of aleatoric and epistemic uncertainties
present the applicant with the challenge of designing a disposal system
that can confidently be shown, through performance assessments of its
anticipated behavior, to meet the regulatory standards with a reasonable
degree of confidence.  From that perspective, the “sharpness” of the
performance assessment tool for regulatory decision making is a critical
issue.  If the projected performance of the disposal system, considering
the uncertainties, is below the regulatory limits the uncertainties
should not be an issue in the compliance decision.  If however the
envelope of uncertainties overlaps the regulatory markers, the nature of
the uncertainties will play a significant role in reaching a compliance
decision.  The analyses presented and discussed above illustrate the
quantitative effects of aleatoric and epistemic uncertainties on dose
projections for the complex Yucca Mountain disposal system. These
results present a reasonable picture of the capabilities of performance
assessments performed for exceedingly long time periods to confidently
distinguish between alternative conceptualizations of how the disposal
system may perform.  

In terms of formulating a standard and making compliance decisions, the
sharpness of the PA tool and the role of conservative assumptions in the
performance modeling both come into play.  For setting a standard,
understanding how well the assessment tool can distinguish between
alternatives is important to determine how well a standard can be
implemented for decision making.  Understanding the uncertainties
involved in an assessment submitted to the regulatory decision maker is
an important component in sound decision making.  As the results and
discussions in this report illustrate, there is considerable uncertainty
in the confidence that can be placed in any given performance
assessment.  Many of these uncertainties cannot be significantly lowered
by additional testing because of the spatial and temporal complications
involved in extrapolating test data.  Implications concerning the
“sharpness” of the performance assessment tool on various aspects of
the standards are discussed below.

From the results of the examination of uncertainties, we have drawn some
conclusions about how they affect performance assessments, and their
interpretation in a regulatory process.  These conclusions are
summarized below.  

A standard must be based on a societal decision on acceptable levels of
radionuclide release in the future.  The “protectiveness” of the
dose limits (i.e., the risks posed by radionuclide releases)  is not
determined by the ability of the disposal system to meet pre-set limits
nor the ability of the measurement tool to generate meaningful results. 
For the peak dose limit, a dose limit of 100 mrem/yr to the RMEI was
chosen as a protective standard, for reasons articulated in the preamble
to the final standards and in the Response to Comments document
accompanying the final rule, not from a consideration of disposal system
performance assessments performed by the Agency or those published in
the open literature.

Performance assessment is the main tool for assessing potential
performance of the disposal system.  Uncertainties inherent in the
understanding and mathematical modeling of the system should be
understood as they impact both the standard setting and compliance
decision process.

Uncertainties in the functioning of the disposal system and in making
simulations of its performance over the geologic stability period do
increase over time, particularly time periods extending into the many
hundreds of thousands of years.  These uncertainties compromise the use
of performance assessments as highly confident predictors of disposal
system performance and dose histories over the geologic stability
period.

For a tiered standard (multiple dose levels) as a function of time,
implementability of the standard is in part dependent on the
“sharpness” of the performance assessment tool.  If the difference
between the tiered dose limits is too small for the tool to meaningfully
distinguish between reasonable alternative performance scenarios when
the uncertainties in the model are taken into account, (i.e., the
uncertainty band around the calculated mean dose over time overlaps the
standard’s dose limits), confidence in the compliance decision may be
minimal, depending on the level of the projected doses and the
uncertainty.  The same consideration applies to a given safety case
being evaluated against a tiered standard.  If the tool cannot
adequately distinguish performance relative to the separation in the
tiered standard, the implementability of the standard is highly suspect.
Other considerations beyond the numerical results of performance
assessments would become important, if not deciding, factors in a
compliance decision.

A degree of aleatoric uncertainty may persist even if the number of
realizations used in calculating mean doses is increased, simply for
practical considerations of time and resource allocation in doing TSPA
type assessments.  With some effort to minimize this source of
uncertainty, the aleatoric uncertainty should not make a compliance
decision difficult as long as the difference between the two standards
is more than 10-20 mrem/yr.  Epistemic uncertainties in contrast can
amount to many tens to hundreds of mrem/yr depending on the specific
causes and may prove difficult to lower for some sources.  

Corrosion rates and drift collapse are the major driver parameters for
the peak dose estimates examined here.  A peak dose limit of 100 mrem/yr
provides sufficient separation between the 15 mrem/yr 10,000 year limit
and the dose limit for the remainder of the stability geologic period to
allow the performance assessment tool to distinguish between the 10,000
year safety case and that for a peak dose occurring at a later time. 
The 100 mrem/yr peak dose limit also imposes a significant burden to
understand and reduce epistemic uncertainties as low as possible to
establish a level of confidence that the assessments are meaningful
representations of the disposal system in the very long term.

An important insight gained from the modeling work we have performed, is
that a peak dose limit in the low hundreds of mrem/yr constrains the
disposal system to keep waste package failures low and minimal for many
tens and even hundreds of thousand of years to meet the peak dose
standard.  The choice of a 100 mrem/yr peak dose limit places a heavy
constraint on the disposal system performance assessment in that
epistemic uncertainties, as illustrated by our modeling, can be larger
than the 85 mrem/yr difference between the 10,000 year and peak dose
limits.  Considerable effort must be expended to demonstrate in the
safety case that the epistemic uncertainties have been reduced to a
level that permits the performance assessment tool to make meaningful
assessments for comparison against the standards and distinguish between
alternative conceptualizations that may be proposed.  

A relatively low peak dose limit should not be considered as a weakening
of the standard, but more correctly as recognition of the uncertainties
that develops and evolves over the course of the stability period, and
an understanding of the “sharpness” of the performance assessment
tool over these time frames.  This is essentially recognizing the limits
of the science relative to making these very long-term dose projections.
 Performance assessments of the site indicate that that a peak dose
limit not exceeding several hundred mrem/yr. would constrain the
disposal system to perform well enough to meet the 15 mrem/yr. 10,000 
year standard by a large margin, and perform well enough to keep doses
to relatively low levels in the longer term.  The constraint would focus
primarily on the need for a highly corrosion resistant waste package and
drip shield design, and the ability to support the use of laboratory
corrosion data in a licensing process where it will get critical
examination.  The protectiveness of the 100 mrem/yr dose limit is
explained in the preamble to the final standards.

Conservative assumptions are commonly used in performance assessments
for areas where uncertainty cannot be reduced significantly or where
judgments are made that the additional efforts to reduce uncertainties
would not significantly change the projected dose histories.  However,
they should be evaluated with a degree of caution in that they may
influence regulatory decision making more than their inherent
uncertainties would warrant.

Many of the significant uncertainties in very log-term dose projections
are generic in nature although their magnitude can be determined by
site-specific conditions. Some uncertainties, such as drift wall
collapse rates and extent cannot be reduced dramatically, and can have a
significant effect on dose projections.

Definitively assessing the magnitude of aleatoric and epistemic
uncertainties for a specific site performance assessment model is
possible only after an extensive assessment using the site data base and
all reasonable alternate conceptual models for the operative processes
at the site over the assessment period.  Understanding the nature and
role of these uncertainties in the licensing safety case for the Yucca
Mountain disposal system will be a major part of the licensing process. 
The insights gained from our examination of the site and the
uncertainties inherent in performance assessments, are important and
useful in developing a standard for the extremely long time period
covered by the Yucca Mountain standard.  Uncertainties in the
understanding the performance of the disposal system do change over the
million year stability period, as described in this paper.  Some
uncertainties decrease while others increase, and some uncertainties can
only be reduced, not eliminated, by site characterization and laboratory
testing efforts.

	As discussed in the introduction to this document, the analyses and
discussions presented here were done to provide insights into the import
of uncertainties in performance assessments of the Yucca Mountain
disposal system and their implications for our rulemaking.  We believe
these insights demonstrate that uncertainties become progressively
greater during the course of the geologic stability period, and more
important in making performance assessments and compliance decisions
over the geologic stability period.

   

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Radioactive Waste Management.

DOE (U.S. Dept. of Energy), 2005. Management and Technical Support -
Peak Dose Sensitivity Analysis, contained in EPA Docket No.
OAR-2005-0083-0352.  Department of Energy, Office of Civilian
Radioactive Waste Management.

DOE (U.S. Dept. of Energy) 2008, Final Supplemental Environmental Impact
Statement for the Disposal of Spent Fuel and High-Level Radioactive
Waste at Yucca Mountain, Nye County, Nevada. DOE/EIS-0250F-S1.
Department of Energy, Office of Civilian Radioactive Waste Management.

Sanford Cohen & Associates, 2005.  Conservatisms, Assumptions, and
Uncertainties in Yucca Mountain Performance Assessments. EPA Docket No.
EPA-HQ-OAR-2005-0083-0085.

 

 

Sanford Cohen & Associates, 2006. Modeling Uncertainty on a Reference
Dose Level – Task 4, Final Report.  EPA OAR Docket No.
OAR-2005-0083-0386

Sanford Cohen & Associates, 2007.  Quality Assurance Audit Report , QARR
3-06, Support to the Revision of 40 CFR Part 197 (“Yucca Mountain”),
in EPA Docket No. OAR 2005-0083-0400.

National Academy of Sciences (NAS), National Research Council (NRC),
1995.  Technical Bases for Yucca Mountain Standards, Washington, D.C.,
National Academy Press, TIC: 217588.

TRW Environmental Safety Systems Inc, 2000.  Disruptive event Process
Model Report, TRD-NBS-MD-000002 REV00 ICN 1, Civilian Radioactive Waste
Management System Management & Operating Contractor. 

Appendix  A

Aleatory Uncertainty in Performance Assessment Analyses of Disposal
System Performance

Two models of the Yucca Mountain disposal system and their results were
examined to estimate the aleatoric uncertainties.  This exercise is
intended to examine the “sharpness” of the PA tool to distinguish
between sets of realizations produced by these individual models
simulating site performance.  The two models examined here differ
significantly in complexity.  The DOE model used for the Final
Environmental Impact Statement (FEIS) analyses is very complex, with the
number of variables extending into the many hundreds.  It contains
complex submodels addressing subsystem performance by components of the
engineered and natural barrier system, such as corrosion models, models
for water movement into and out of the emplacement drifts, etc.  The DOE
Peak Dose model is less complex.  It was developed to examine the
relative effects of the most important “driver” parameters on
calculations of the peak dose.  The number of variable parameters in the
DOE PDM is about a hundred.  These two models offer an opportunity to
examine and compare the aleatoric uncertainties for two models that can
be used for the same purpose, calculating the peak dose, but differ
significantly in complexity.  Both of these models address various
scenarios for system performance.  The data bases sampled by the models
contain parameter distributions derived from site and laboratory
investigations performed during the site characterization studies. Both
models should be considered site-specific performance models for the
disposal system therefore, differing only in the level of detail
imbedded within the models.

Parameter distributions in the models were derived considering the
alternative physical and chemical conditions anticipated to operate
under the scenarios.  In that sense, the data  bases in the model
address many individual scenarios for performance.  In developing the
data bases for specific parameters, the possible values of parameters
attributable to different scenarios (such as changed water flow rates
through the mountain reflecting differing precipitation/infiltration
rates from climate changes) are aggregated into parameter distributions.
 The probability of parameter values for various scenarios are
aggregated into a single probability density function  (pdf) which is
sampled by the model for each individual calculation (“realization”)
generating a dose history. 

For each model, the analyses presented here attempt to determine with
what level of confidence can two sets of realizations (done with the
same model) be identified as statistically different from each other. 
The mean of the dose distributions was used as the performance measure,
and a  two-sample Student t-test was used to determine the degree to
which the means for separate sets of realizations from each model could
be identified as statistically different, i.e, representing something
other than random variation produced by simply sampling the parameter
distributions.  This is one way to examine the “sharpness” of the PA
tool to make meaningful discrimination between alternative sets of
realizations.  The other aspect of examining the “sharpness” of the
PA tool is to examine how well the model can distinguish between
alternative conceptualizations of disposal system performance.  This
aspect is related to the aleatoric uncertainty examined here in that the
aleatoric uncertainty will be present to greater or less extent in any
PA model.  Should the dose variations from modeling one
conceptualization fall within the range of the aleatoric uncertainty,
the different conceptualizations can not be distinguished from each
other, and the performance of the disposal system would be considered
equivalent – regardless of which conceptualization is more likely in
reality.  The aleatoric uncertainty alone is a measure of the
“sharpness” of the PA model.  Results for the DOE Peak Dose Model
and the FEIS model are described below.

The DOE Peak Dose Model Calculations

The peak dose from the DOE Peak Dose Model (DOE PDM) was found to be
approximately 125 mrem/y at 730,000 years based on the arithmetic
average of 1,000 realizations.  The frequency distribution of 1,000
realizations at the time of the peak dose is shown in Figure A1.  There
are 467 realizations which forecast an annual dose equal to 0 mrem/y at
that time, while the remaining 533 realizations range up to a dose of
5,098 mrem/y.  As noted in the figure, the mean annual dose is 125
mrem/y and the standard deviation is 300 mrem/y.  It is of interest to
compare the mean of this distribution with the mean of other possible
distributions of peak dose forecasts with a similar uncertainty.  The
1,000 DOE PDM peak dose forecast realizations will be referred to as
Population 1.  The mean of Population 1 will be compared to the mean a
second hypothetical population of annual dose forecasts with the same
variance as the DOE PDM peak dose forecast but with a different mean,
which may be higher or lower than that of Population 1.  

The distribution in Figure A1 is not normally distributed, but consists
of a substantial probability (0.467) at a dose of zero, while the
distribution of positive dose forecasts has a long tail to the right. 
Despite the lack of normality, the large sample size permits a
possibility of comparing mean annual dose forecasts using a 2-sample
t-test.  Figure A2 shows the p-level of a 2-sided, 2-sample t-test as a
function of the mean of Population 2.  The p-level of the test measures
that probability that the two means differ by chance alone. 

The t-test compares the means of the two populations using the standard
error of the mean as a measure of the ability to distinguish between the
two means.  For determination of a statistically significant difference
it is generally required that the p-level for the test be 0.05 or less,
i.e., a 5% or less chance that the observed difference would happen by
chance alone.  As shown in Figure 2, a p-level of 0.05 is achieved when
the mean of Population 2 is below 98.7 mrem/yr.  Symmetrically on the
upper end, the 0.05 p-level is achieved when the mean of population 2
exceeds 151.3 mrem/yr.  If the Population 2 mean is between 98.7 and
151.3 mrem/yr, the t-test will conclude there is no significant
difference in the means of the two populations since the p-level exceeds
0.05 in this interval.

Although the t-test is known to be fairly robust with respect to
deviations from normality, the results in Figure A2 must be considered
as only an approximation of the true power to distinguish between the
two population means.  The large number of realizations at a dose of  0
mrem/yr is the main concern in this respect.  The non-normality issue
may be addressed using nonparametric statistical tests for a difference
in means, or using a simulation model based on the empirical
distribution shown in Figure A1.  If Population 2 also contains a large
number of zeros, it may be even more difficult to distinguish between
the two populations using popular nonparametric methods like the
Mann-Whitney or the Wilcoxon Ranked Sum test because of the large number
of ties in rank at zero and a substantial degree of overlap between the
two distributions at higher dose levels

FEIS Peak Dose

The peak dose from the FEIS model  (the large model with many hundreds
of variable parameters) is approximately 152.5 mrem/yr at 476,000 years
based on the arithmetic average of 300 realizations (the typical number
of realizations calculated to obtain a “stable” mean, as described
previously).  The standard deviation is 290.6 mrem/yr.  In this section,
we compare the mean of this distribution with the mean of other possible
distributions of peak dose forecasts with a similar uncertainty.  The
300 FEIS peak dose forecast realizations will be referred to as
Population 1.  The mean of Population 1 is compared to the mean a second
hypothetical population of annual dose forecasts with the same variance
but with a different mean, which may be higher or lower than that of
Population 1.  Again, the large sample size permits a possibility of
comparing mean annual dose forecasts using a 2-sample t-test.  Figure A3
shows the p-level of a 2-sided, 2-sample t-test as a function of the
mean of Population 2.  The p-level of the test measures that probability
that the two means differ by chance alone.  For determination of a
statistically significant difference it is generally required that the
p-level for the test be 0.05 or less, i.e., a 5% or less chance that the
observed difference would happen by chance alone.  As shown in Figure
A3, a p-level of 0.05 is achieved when the mean of Population 2 is below
106 mrem/yr.  Symmetrically on the upper end, the 0.05 p-level is
achieved when the mean of population 2 exceeds 196 mrem/yr.  If the
Population 2 mean is between 106 and 196 mrem/yr, the t-test will
conclude there is no significant difference in the means of the two
populations, since the p-level exceeds 0.05 in this interval.

The FEIS mean comparison is based on a run with 300 realizations, while
the DOE PDM uses 1,000 realizations.  A better comparison of the
uncertainty in the two forecasts may be obtained when the DOE PDM model
also is run for only 300 realizations.  However, the DOE PDM results for
300 realizations are quite different than the results based on 1,000
realizations. Based on the arithmetic average of 300 realizations, the
peak dose from the DOE PDM is approximately 160 mrem/yr at 835,000
years.  The standard deviation is 438 mrem/yr at the time of the peak
dose.  With 1,000 realizations, the peak dose from the DOE PDM was
approximately 125 mrem/yr at 730,000 years, with a standard deviation of
300 mrem/yr.  The p-level plot for the DOE PDM run with 300 realizations
is shown in Figure A4.  With 300 realizations, the PDM has a higher peak
dose occurring 100,000 years later with a larger standard deviation at
that time.  

The two DOE PDM runs are compared with the FEIS results in Table 1.  The
large standard deviation for the DOE PDM model when there are 300
realizations results in a much broader range of values for the mean of
Population 2 for which there is no significant difference.  Results of
the DOE  PDM for two different numbers of realizations (n =300 or 1000)
illustrate an important point.  By doing higher numbers of realizations,
the ability to distinguish between sets increases, i.e., the range where
no statistical differentiation can be made decreases (140 to 52 mrem/yr
as shown in Table I).  To increase the “sharpness” of the PA model
relative to the aleatoric uncertainties, larger numbers of realizations
must be done.  For a smaller model like the DOE PDM, calculating more
realizations is not difficult, but for very large models the extra
computer time demands can be excessive.  A judgment is often made
concerning the time demands and the added precision to be obtained. 
Theoretically, if all the possible combinations of parameter values were
calculated there would be no uncertainty in the value of the mean for
the modeled system performance.



Figure A1.  DOE PDM Annual Dose Frequency Distribution at Time of Peak
Dose (n=1000 realizations)



Figure A2.  



Figure A3



Figure A4.



Table A1.  Comparison of 2-Sample t-test Results for Three Models

Model Run	Peak Mean Dose

(mrem/yr)	Year of Peak Dose	Standard Deviation

(mrem/yr)	Lower Bound

(mrem/yr)	Upper Bound

(mrem/yr)	Range

(mrem/yr)

DOE PDM

(n=1000)	125	730,000	300	99	151	52

DOE PDM

(n=300)	160	835,000	438	90	230	140

FEIS

(n=300)	152.5	476,000	290.6	106	199	93



Appendix B

DOE-TSPA Analyses with Varying Corrosion Rate Assumptions

Confirmation of the importance of corrosion rate assumptions on dose
projections and some additional insight into the importance of corrosion
rate uncertainty can be obtained from examining the results of previous
TSPAs published by DOE.  These assessments were done with the larger,
more detailed, assessment models than the DOE PDM, which contain more
complex inter-relationships between the model components and represent
the “state-of-knowledge” in terms of available data bases when they
were performed.  The TSPA models evaluated stress-corrosion cracking
(SCC) as well as general corrosion and other failure mechanisms for the
metallic components of the EBS.  

Table B1 describes briefly the waste package performance assumptions
used in DOE TSPA analyses, beginning with the Viability Assessments (VA)
published in 1998 (DOE, 1998) up to the recently published Supplemental
Environmental Impact  Statement (SEIS) analyses (DOE, 2007).  The
structure of these assessment models is basically the same, i.e., the
total system model is developed from abstractions of more complex
sub-system models and incorporates many assumptions to simplify the
integrated total system modeling.  Mean peak dose projections from the
various TSPAs range from a low of 2 mrem/yr in the most recent
assessment (DOE, 2007) to 120-150 mrem/yr in earlier analyses, with one
assessment going as high as 490 mrem/yr (DOE, 2000).  (This high number
came from an analysis that extended the calculations in a model,
designed only for processes active within the 10,000 year period, to the
one million year time frame.  It should not be considered as a realistic
simulation for the one million year stability period since many
assumptions were made for the 10,000 year analyses that are not valid
for much longer time periods, such as climatic fluctuations, cladding
failure rates, seismic activity and drift degradation rates.

 The most important aspect of the various TSPA models is the corrosion
rate assumptions used in each.  The full temperature dependence case
shown on Fig 7 (ID # 5 in Table 2 for the DOE PDM analyses) involves
using corrosion rate data that matches the thermal profile of the
repository over the performance period. The most recent performance
assessments published by DOE (DOE, 2008) also used this assumption. 
Very low failure rates from general corrosion were calculated, with mean
doses at one million years below 10 mrem/yr.  During the early times
when repository temperatures are relatively higher, higher corrosion
rates are used, followed by progressively lower corrosion rates
corresponding to the decreasing repository temperature.  In the very
long-term, the low corrosion rates in this conceptualization result in
delaying waste packages failures significantly beyond the end of the
stability period, with an eventual peak in the dose projections (due to
the eventual degradation of a large portion of the waste packages)
occurring beyond one million years.  Ideally, this is a more realistic
approach since the corrosion rates should reflect the thermal history of
the repository.  However there is significant uncertainty in assuming
that the low-temperature corrosion rates can be reliably extrapolated to
these time frames, as discussed more below.  In contrast, if a more
skeptical view is taken on how reliably laboratory measurements can be
extrapolated to repository in-service conditions, assuming a five-fold
increase in corrosion rates might not be an unreasonable assumption (as
was illustrated by the DOE PDM analyses shown in Fig. 7).  This case is
illustrated by combined scenario #3 in Table 3 which combines the Full
Temperature Dependence (FTD) scenario from Table 2 with the assumption
that waste package corrosion rates are accelerated by a factor of 5. 
The peak mean dose for this combined scenario is 209 mrem/yr, which is
significantly higher than the peak mean dose in the Base Case in Table
2.  The peak dose occurs much earlier, at 390,000 years versus 730,000
years in the base case.  If the corrosion rate also is accelerated for
the drip shields, then the peak mean dose is increased to 304 mrem/yr at
390,000 years in the combined scenario #4 in Table 3. The results from
the DOE PDM and the DOE SEIS analyses are in good agreement concerning
the implications of the full temperature-dependent assumption and its
effect on dose projections.

For the cases where the lowest corrosion rate was not assumed, higher
dose projections were calculated.  For the TSPA-SR and FEIS analyses
(Table B1), temperature independent corrosion rates were used and higher
peak dose projections resulted in time frames in the hundreds of
thousands of years.  For these analyses, corrosion rates were assumed to
be independent of temperature in the long-term, meaning that the
corrosion rate used after the repository had cooled significantly
corresponded to higher temperatures than the actual projected
temperatures in the very long-term.  

Along with the TSPA-SR results, Table B1) also contains the TSPA results
from the follow-on Supplemental Science and Performance Analysis (SSPA)
model.  For the SSPA modeling, the DOE TSPA-SR model was modified in
various ways and “one-off” sensitivity studies of the modified model
were performed to assess the impact of changes to the SR model.  Results
of these sensitivity studies were reported in the DOE TSPA-SSPA (DOE,
2001) document.  In the SSPA analyses, a temperature dependent corrosion
assumption was analyzed and results showed that the time for peak dose
moved outward to the end of the stability period, reflecting the slower
degradation of the waste packages, in agreement with the DOE-PDM and the
SEIS models .  

Unfortunately most of the sensitivity analyses in the SSPA report
compared the modified model results against the TSPA-SR results only to
the 100,000-year time line rather than to the later peak dose.  Since
most of the sensitivity studies only extended to 100,000 years, it is
not possible to quantitatively assess their individual contribution to
the spread of peak dose estimates.  However, the results offer some
insights into the effects.  Differences from the SR model results are
listed in Table B2 for the components of the TSPA-SR model that were
modified significantly.  A number of factors affect seepage rates into
the emplacement drifts.  Intuitively, it could be assumed that these
effects would amplify, to some extent, the effects of using the full
temperature-dependent corrosion rates, reducing dose estimates still
further.  Solubility control assumptions also contribute significantly
to mobilization of radionuclides from the waste package and transport
out of the EBS.

Results of these sensitivity studies on the TSPA-SR model show
variations in some parameters can cause changes in dose estimates of
many 10s of mrem/yr.  It is not possible to extrapolate these dose
changes from 100,000 years to the time of peak dose with high
confidence, but the trends in these results would probably continue as
the time frame extends outwards to the time of peak dose.  These results
generally confirm the observations made from the DOE-PDM modeling
exercise results discussed in the main body of this paper – that
epistemic uncertainties have the most significant effects on dose
projections and corrosion rate assumptions are the major driver in
determining the timing and magnitude of the peak dose.

Table B1 Waste Package Performance Assumptions and Dose Projection
Results in Various DOE Total System Performance Assessments (TSPA)  

DOE TSPA	Peak Dose Time (years)	Mean Peak Dose (mrem/yr)
Corrosion/Radionuclide Release Assumptions for EBS Releases	Waste
Package Performance Results

TSPA-VA 1998

(DOE, 1998)	~ 300  K 	~ 140	Considered general, local, pitting; rates
span 25-100 oC; general corrosion by dripping proportional to seepage
with flow focusing from seeps onto failed metal, corrosion rates
correlated to dripping variations;  juvenile failures (1-10) included;
cladding credit taken; volumetric flux through failed package scaled
with increasing corroded areas on the package	Relatively rapid failure
of pkgs. because corrosion resistant metal is inside and more
susceptible to localized corrosion after stainless steel outer metal is
degraded

TSPA –SR

2000

Three separate models used

(DOE, 2000)	(1) 270 K

(2) 1,000 K

(3) ~ 700 K	 ~ 490

~ 30

 ~ 120 	General corrosion, local corrosion, SCC; Temperature independent
corrosion rate used; cladding credit taken; no credit for inner
stainless steel container, diffusion thru SCC (assumed continuous
pathway) and advective flow, volumetric flux through failed package
scaled with increasing corroded areas on the package	Three different
models used as follows: (1) 10 K model simply extrapolated to peak dose
beyond 10 K yrs., (2) secondary actinide phases control solubility in
the very long-term, (3) multiple glacial periods.   

TSPA – SSPA

2001

(DOE, 2001)	~  120 K

1,000 K

 	~140 (TI)

~110 (FTD)	General corrosion, local corrosion, SCC; Full temperature
dependent (FTD) and temperature independent (TI) corrosion rates used;
cladding credit taken; volumetric flux through failed package scaled
with increasing corroded areas on the package	SR models modified for
newer data/assumptions, Peak shown for nominal case (no disruptive
events), SSPA analyzed a high-temp model (HTOM) and a lower-temp model
(LTOM) – both with dose history still rising at one million yrs.

TSPA-FEIS 

2002

(DOE, 2002)	~475 K	~120-150	General corrosion. Local corrosion, SCC;
Temperature independent corrosion rate used (faster rates assumed);
cladding credit taken; volumetric flux through failed package scaled
with increasing corroded areas on the package	FEIS analyses assumed
larger repository than SR and SSPA analyses, also assumed different
BDCFs and 3,000 acre-ft rep vol. not used in previous PAs

TSPA-FSEIS 2008

(DOE, 2008)	>1 million yrs.	~  2	General corrosion – full temperature
dependence enhanced by microbial corrosion, local and stress corrosion
cracking; juvenile failures considered; no cladding credit;  volumetric
flux through failed package scaled to drip rate through failed shield
and increasing corroded areas on the package	10% of packages get general
corrosion breaches by one million yrs. Only 0.4% of package surface
removed;  SCC failures begin at 400  K yrs – no flow through SCC
failures; releases from gen. corr. Failures are well after one million
years, releases within one million years largely from disruptive
scenarios



Table B2 Modifications to the DOE TSPA-SR Model for Sensitivity
Analyses Presented in the DOE TSPA-SSPA



Post TSPA-SR Modifications to the TSPA-SR Sub-Models  	Nature of
Modification to TSPA-SR Model	Effect on Projected Performance (From DOE,
2001, Chapters 3. 2 & 4) against TSPA-SR base case model (~60 mrem/yr at
100 K yrs. reference mark)

Climate  	Includes post-10K climate fluctuations in the nominal case
Seepage increases with higher infiltration.  Only 20% increases in waste
packages experiencing seepage over the SR base case 

Seepage  	More data for repository rock units	No significant increase in
dose over SR base case estimates

Seepage Flow Focusing	Used non-heterogeneous permeability field in
simulations to derive focusing factor	Increased seepage but only a small
difference from the SR base case – less than10 mrem/yr.

Episodic Seepage	New factors for episodic changes in seepage from
fractures	Raised 100 K yr. dose ~ 30 mrem/yr over the SR base case

Thermal Properties	Included newer data on rock units and invert
properties	Changes affect relative humidity in drifts – high temp.
case and SR base case very similar results, low-temp case significantly
different than the SR base case – longer time to failure

Thermal-Hydrologic Effects and Seepage	Calculations include newer data
on rock properties	Changes affect seepage rates – general lowering
relative to the SR base case

In-Drift Chemistry	Used  smaller range of thermodynamic data and host
rock mineralogy	No significant increase in dose over SR base case  

Stress Corrosion Cracking	Newer data on crack shape and propagation,
uncertainty and threshold values	Longer time to SCC failures, resulting
in lower doses than SR base case at 100 K yrs. ~ 10 – 30 mrem/yr.
(greater difference at less than one million yrs.)

General Corrosion	Include temperature dependence of corrosion rate
Reduces doses by 60 mrem/yr. at 100 K yr.. over SR base case, peak dose
extends beyond one million yrs.

Evaporative Seepage Reduction	New model added	No significant change over
the SR base case

Flow through Waste Package	Flow through drip shield not always on
package breaches, bathtub effect	Lower dose than the SR base case at 100
K yrs.  ~20 mrem/yr

In-Package Chemistry	Considers waste form and iron degradation products
on chemistry	Raises dose as much as 50 mrem/yr. at  100 K yrs. –
elevated solubility for actinides

Cladding Degradation	Newer data on creep, SCC, local corrosion and
unzipping	Slightly lower doses up to 100 K yrs – no significant
difference from the SR base case at one million years.

In-Package Solubility Limits	Increased uncertainty on controlling phases
Lower dose at  100 K yrs. by ~ 60 mrem/yr. relative to SR base case

EBS Diffusive Transport	Diffusive transport included	No significant
difference from the SR base case

EBS Sorption	Includes sorption on waste package degradation products and
the invert	Reduces dose at 100 K yrs. By ~ 10 mrem/yr

UZ Transport in Drift Shadow	Modified flow mechanisms	Delays transport
by 10 K yrs. Relative to SR base case, lowers  100 K yr. dose by ~ 25
mrem/yr.

SZ Transport	Modified bulk density and I and Tc coefficients in the
alluvium, other assumptions	No significant differences through entire
dose history to 100 K yrs relative to the SR base case

Biosphere Dose Conversion Factors	Modified factors used	Small lowering (
less than 10 mrem/yr )

 relative to the SR base case

Total System Releases from TSPA-SSPA Model	Effects of all modifications
to the TSPA-SR model	Releases delayed in time relative to the SR base
case for the low-temp model and projected doses lower than the SR base
case by 10-80  mrem/yr. at one million years



  There is an earlier, lower peak of 153 mrem/yr at 635,000 years, not
used in this analysis.

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