**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.

+--------+---------+-------+---------+---------+---------+---------+
| **Ta   |         |       |         |         |         |         |
| ble 1. |         |       |         |         |         |         |
| Comp   |         |       |         |         |         |         |
| arison |         |       |         |         |         |         |
| of     |         |       |         |         |         |         |
| 2-     |         |       |         |         |         |         |
| Sample |         |       |         |         |         |         |
| S      |         |       |         |         |         |         |
| tudent |         |       |         |         |         |         |
| t-test |         |       |         |         |         |         |
| R      |         |       |         |         |         |         |
| esults |         |       |         |         |         |         |
| for    |         |       |         |         |         |         |
| Three  |         |       |         |         |         |         |
| Sets   |         |       |         |         |         |         |
| of     |         |       |         |         |         |         |
| Model  |         |       |         |         |         |         |
| Ca     |         |       |         |         |         |         |
| lculat |         |       |         |         |         |         |
| ions** |         |       |         |         |         |         |
+--------+---------+-------+---------+---------+---------+---------+
| *      | **Peak  | *     | **S     | **Lower | **Upper | **      |
| *Model | Mean    | *Year | tandard | Bound** | Bound** | Range** |
| Run**  | Dose**  | of    | Devi    |         |         |         |
|        |         | Peak  | ation** | **(mre  | **(mre  | **(mre  |
|        | **(mre  | D     |         | m/yr)** | m/yr)** | m/yr)** |
|        | m/yr)** | ose** | **(mre  |         |         |         |
|        |         |       | m/yr)** |         |         |         |
+--------+---------+-------+---------+---------+---------+---------+
| **DOE  | 125     | 73    | 300     | 99      | 151     | 52      |
| PDM**  |         | 0,000 |         |         |         |         |
|        |         |       |         |         |         |         |
| **(n=1 |         |       |         |         |         |         |
| 000)** |         |       |         |         |         |         |
+--------+---------+-------+---------+---------+---------+---------+
| **DOE  | 160     | 83    | 438     | 90      | 230     | 140     |
| PDM**  |         | 5,000 |         |         |         |         |
|        |         |       |         |         |         |         |
| **(n=  |         |       |         |         |         |         |
| 300)** |         |       |         |         |         |         |
+--------+---------+-------+---------+---------+---------+---------+
| **     | 152.5   | 47    | 290.6   | 106     | 199     | 93      |
| FEIS** |         | 6,000 |         |         |         |         |
|        |         |       |         |         |         |         |
| **(n=  |         |       |         |         |         |         |
| 300)** |         |       |         |         |         |         |
+--------+---------+-------+---------+---------+---------+---------+

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 5^th^ percentiles values of 0 for all
scenarios and the 25^th^ 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
95^th^ percentile to the 50^th^ 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 75^th^
percentile. These ratios are generally near 1, indicating that the peak
mean dose often is near the 75^th^ 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

<table style="width:100%;">
<colgroup>
<col style="width: 3%" />
<col style="width: 25%" />
<col style="width: 11%" />
<col style="width: 11%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 7%" />
</colgroup>
<tbody>
<tr class="odd">
<td>ID</td>
<td>One-Off Scenario</td>
<td>Peak Mean Dose (mrem/y)</td>
<td>Year of Peak Dose</td>
<td><p>5<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>25<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>50<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>75<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>95<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>Ratio</p>
<p>95th/50th</p></td>
<td><p>Ratio</p>
<p>Mean/75th</p></td>
</tr>
<tr class="even">
<td>0</td>
<td>Base Case</td>
<td>125</td>
<td>730,000</td>
<td>0</td>
<td>0</td>
<td>5</td>
<td>126</td>
<td>570</td>
<td>121</td>
<td>1.0</td>
</tr>
<tr class="odd">
<td>1</td>
<td>Low Infiltration Case</td>
<td>84</td>
<td>870,000</td>
<td>0</td>
<td>0</td>
<td>31</td>
<td>104</td>
<td>339</td>
<td>11</td>
<td>0.8</td>
</tr>
<tr class="even">
<td>2</td>
<td>Medium Infiltration Case</td>
<td>136</td>
<td>690,000</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>124</td>
<td>639</td>
<td>-</td>
<td>1.1</td>
</tr>
<tr class="odd">
<td>3</td>
<td>High Infiltration Case</td>
<td>162</td>
<td>690,000</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>151</td>
<td>770</td>
<td>-</td>
<td>1.1</td>
</tr>
<tr class="even">
<td>4</td>
<td>WP Corrosion Rate times 5</td>
<td>253</td>
<td>225,000</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>130</td>
<td>1,144</td>
<td>-</td>
<td>1.9</td>
</tr>
<tr class="odd">
<td>5</td>
<td>Full Temperature Dependence (FTD)</td>
<td>3<sup>(a)</sup></td>
<td>1,000,000</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>-</td>
<td>-</td>
</tr>
<tr class="even">
<td>6</td>
<td>DS Corrosion Rate times 5</td>
<td>151</td>
<td>690,000</td>
<td>0</td>
<td>0</td>
<td>7</td>
<td>156</td>
<td>664</td>
<td>92</td>
<td>1.0</td>
</tr>
<tr class="odd">
<td>7</td>
<td>Remove DS Functionality</td>
<td>154</td>
<td>690,000</td>
<td>0</td>
<td>0</td>
<td>8</td>
<td>157</td>
<td>674</td>
<td>80</td>
<td>1.0</td>
</tr>
<tr class="even">
<td>8</td>
<td>2nd Phase Np Solubility Control</td>
<td>111</td>
<td>865,000</td>
<td>0</td>
<td>0</td>
<td>36</td>
<td>126</td>
<td>484</td>
<td>14</td>
<td>0.9</td>
</tr>
<tr class="odd">
<td>9</td>
<td>SZ Transport Length Set to 0</td>
<td>2,497</td>
<td>775,000</td>
<td>0</td>
<td>0</td>
<td>288</td>
<td>2,719</td>
<td>11,139</td>
<td>39</td>
<td>0.9</td>
</tr>
<tr class="even">
<td>10</td>
<td>Non Collapsed Drifts (NCD)</td>
<td>37</td>
<td>860,000</td>
<td>0</td>
<td>0</td>
<td>0.7</td>
<td>28</td>
<td>183</td>
<td>250</td>
<td>1.3</td>
</tr>
<tr class="odd">
<td>11</td>
<td>WP &amp; DS Corrosion Ratex5</td>
<td>768</td>
<td>180,000</td>
<td>0</td>
<td>0.1</td>
<td>106</td>
<td>486</td>
<td>3,819</td>
<td>36</td>
<td>1.6</td>
</tr>
<tr class="even">
<td>12</td>
<td>Vary Pu242 BDCF +20%</td>
<td>138</td>
<td>730,000</td>
<td>0</td>
<td>0</td>
<td>5</td>
<td>140</td>
<td>648</td>
<td>133</td>
<td>1.0</td>
</tr>
</tbody>
</table>

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

[]{.mark}

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

[]{.mark}

<table>
<colgroup>
<col style="width: 3%" />
<col style="width: 25%" />
<col style="width: 11%" />
<col style="width: 11%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 7%" />
</colgroup>
<tbody>
<tr class="odd">
<td>ID</td>
<td>Combined Scenario</td>
<td>Peak Mean Dose (mrem/y)</td>
<td>Year of Peak Dose</td>
<td><p>5<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>25<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>50<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>75<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>95<sup>th</sup></p>
<p>(mrem/y)</p></td>
<td><p>Ratio</p>
<p>95th/50th</p></td>
<td><p>Ratio</p>
<p>Mean/75th</p></td>
</tr>
<tr class="even">
<td>1</td>
<td>NCD &amp; WP Corrosion Ratex5</td>
<td>55</td>
<td>420,000</td>
<td>0</td>
<td>0</td>
<td>0.2</td>
<td>31</td>
<td>283</td>
<td>1,415</td>
<td>1.8</td>
</tr>
<tr class="odd">
<td>2</td>
<td>NCD &amp; WP+DS Corrosion Ratesx5</td>
<td>118</td>
<td>190,000</td>
<td>0</td>
<td>0</td>
<td>1.5</td>
<td>34</td>
<td>401</td>
<td>267</td>
<td>0.3</td>
</tr>
<tr class="even">
<td>3</td>
<td>FTD &amp; WP Corrosion Ratex5</td>
<td>209</td>
<td>390,000</td>
<td>0</td>
<td>0</td>
<td>5</td>
<td>198</td>
<td>1,052</td>
<td>210</td>
<td>0.9</td>
</tr>
<tr class="odd">
<td>4</td>
<td>FTD &amp; WP+DS Corrosion Ratesx5</td>
<td>304</td>
<td>390,000</td>
<td>0</td>
<td>11</td>
<td>108</td>
<td>347</td>
<td>1,216</td>
<td>11</td>
<td>0.9</td>
</tr>
</tbody>
</table>

![](media/image1.png){width="6.376388888888889in" height="4.4375in"}

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

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

![](media/image2.wmf){width="5.999305555555556in"
height="3.9444444444444446in"}

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

![](media/image3.wmf){width="5.999305555555556in"
height="3.9444444444444446in"}

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

![](media/image4.png){width="5.99375in" height="4.25in"}

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

![](media/image5.png){width="5.99375in" height="4.25in"}

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

![](media/image6.wmf){width="5.998611111111111in"
height="3.9472222222222224in"}

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

![](media/image7.wmf){width="5.998611111111111in" height="3.95in"}

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

![](media/image8.wmf){width="5.999305555555556in" height="4.2125in"}

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

![](media/image9.wmf){width="5.999305555555556in"
height="3.942361111111111in"}

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

(Enlarged view)

![](media/image10.wmf){width="5.997222222222222in"
height="4.551388888888889in"}

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

![](media/image11.wmf){width="5.993055555555555in"
height="5.942361111111111in"}

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

![](media/image12.wmf){width="5.996527777777778in"
height="5.256944444444445in"}

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]{.underline}*. 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*]{.underline} 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]{.underline}*. 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]{.underline}* 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 CO~2~ 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]{.underline}* 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 CO~2~ 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]{.underline}* 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]{.underline}* 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[.]{.mark} 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]{.underline} 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.

**References**

BSC, 2001a. FY01 Supplemental Science and Performance Analyses, Vol. 2,
Performance Analyses. TDR-MGR-PA-000001 REV 00. Las Vegas, Nevada:
Bechtel SAIC Company. Prepared for the Office of Civilian Radioactive
Waste Management.

BSC, 2001b, FY01 Supplemental Science and Performance Analyses, Vol.1,
Scientific Bases and Analyses, TDR-MGR-MD-000007 REV 00 ICN 01, Las
Vegas, Nevada: Bechtel SAIC Company. Prepared for the Office of Civilian
Radioactive Waste Management.

CRWMS M&O, 2000. Total System Performance Assessment for the Site
Recommendation. TDR-WIS-PA-000001 REV 00 ICN 01. Las Vegas, Nevada:
CRWMS M&O.

EPA 2001, *Public Health and Environmental Radiation Protection
Standards for Yucca Mountain, Nevada -- Final 40 CFR 197, Evaluation of
Potential Economic Impacts of 40 CFR Part 197*, EPA 402-R-01-004, June
2001.

EPA 2005*. Public Health and Environmental Protection Standards for
Yucca Mountain, Nevada: Proposed Rule*, Code of Federal Regulations,
Monday, August 22,2005, 49014-49065.

DOE (U.S. Dept. of Energy), 1998. Viability Assessment of a Repository
at Yucca Mountain - Total System Performance Assessment, vol. 3,
DOE/RW-0508, Office of Civilian Radioactive Waste Management,
Washington, D.C.

DOE (U.S. Dept. of Energy), 2002. Final Environmental Impact Statement
for a Geologic Repository for the Disposal of Spent Fuel and High-Level
Radioactive Waste at Yucca Mountain, Nye County, Nevada. DOE/EIS-0250.
Washington, D.C.: U.S Department of Energy, Office of Civilian
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
~~e~~xamine 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.[^1] 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.

![](media/image13.wmf){width="6.780555555555556in" height="4.23125in"}

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

![](media/image14.png){width="5.909027777777778in" height="4.14375in"}

Figure A2.

![](media/image15.wmf){width="5.992361111111111in"
height="4.284722222222222in"}

Figure A3

![](media/image16.wmf){width="6.031944444444444in"
height="4.3069444444444445in"}

Figure A4.

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

+---------+---------+--------+---------+---------+---------+---------+
| Model   | Peak    | Year   | S       | Lower   | Upper   | Range   |
| Run     | Mean    | of     | tandard | Bound   | Bound   |         |
|         | Dose    | Peak   | De      |         |         | (m      |
|         |         | Dose   | viation | (m      | (m      | rem/yr) |
|         | (m      |        |         | rem/yr) | rem/yr) |         |
|         | rem/yr) |        | (m      |         |         |         |
|         |         |        | rem/yr) |         |         |         |
+---------+---------+--------+---------+---------+---------+---------+
| DOE PDM | 125     | 7      | 300     | 99      | 151     | 52      |
|         |         | 30,000 |         |         |         |         |
| (       |         |        |         |         |         |         |
| n=1000) |         |        |         |         |         |         |
+---------+---------+--------+---------+---------+---------+---------+
| DOE PDM | 160     | 8      | 438     | 90      | 230     | 140     |
|         |         | 35,000 |         |         |         |         |
| (n=300) |         |        |         |         |         |         |
+---------+---------+--------+---------+---------+---------+---------+
| FEIS    | 152.5   | 4      | 290.6   | 106     | 199     | 93      |
|         |         | 76,000 |         |         |         |         |
| (n=300) |         |        |         |         |         |         |
+---------+---------+--------+---------+---------+---------+---------+

**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  |      |      |                       |                      |
| P      |      |      |                       |                      |
| ackage |      |      |                       |                      |
| Perfo  |      |      |                       |                      |
| rmance |      |      |                       |                      |
| Assum  |      |      |                       |                      |
| ptions |      |      |                       |                      |
| and    |      |      |                       |                      |
| Dose   |      |      |                       |                      |
| Proj   |      |      |                       |                      |
| ection |      |      |                       |                      |
| R      |      |      |                       |                      |
| esults |      |      |                       |                      |
| in     |      |      |                       |                      |
| V      |      |      |                       |                      |
| arious |      |      |                       |                      |
| DOE    |      |      |                       |                      |
| Total  |      |      |                       |                      |
| System |      |      |                       |                      |
| Perfo  |      |      |                       |                      |
| rmance |      |      |                       |                      |
| Asses  |      |      |                       |                      |
| sments |      |      |                       |                      |
| (T     |      |      |                       |                      |
| SPA)** |      |      |                       |                      |
+========+======+======+=======================+======================+
| **DOE  | **   | **   | **C                   | **Waste Package      |
| TSPA** | Peak | Mean | orrosion/Radionuclide | Performance          |
|        | Dose | Peak | Release Assumptions   | Results**            |
|        | Time | Dose | for EBS Releases**    |                      |
|        | (    | (mr  |                       |                      |
|        | year | em/y |                       |                      |
|        | s)** | r)** |                       |                      |
+--------+------+------+-----------------------+----------------------+
| **T    | \~   | \~   | Considered general,   | Relatively rapid     |
| SPA-VA | 300  | 140  | local, pitting; rates | failure of pkgs.     |
| 1998** | K    |      | span 25-100 ^o^C;     | because corrosion    |
|        |      |      | general corrosion by  | resistant metal is   |
| *      |      |      | dripping proportional | inside and more      |
| *(DOE, |      |      | to seepage with flow  | susceptible to       |
| 1      |      |      | focusing from seeps   | localized corrosion  |
| 998)** |      |      | onto failed metal,    | after stainless      |
|        |      |      | corrosion rates       | steel outer metal is |
|        |      |      | correlated to         | degraded             |
|        |      |      | dripping variations;  |                      |
|        |      |      | juvenile failures     |                      |
|        |      |      | (1-10) included;      |                      |
|        |      |      | cladding credit       |                      |
|        |      |      | taken; volumetric     |                      |
|        |      |      | flux through failed   |                      |
|        |      |      | package scaled with   |                      |
|        |      |      | increasing corroded   |                      |
|        |      |      | areas on the package  |                      |
+--------+------+------+-----------------------+----------------------+
| **TSPA | \    | \~   | General corrosion,    | Three different      |
| --SR** | (1\) | 490  | local corrosion, SCC; | models used as       |
|        | 270  |      | Temperature           | follows: (1) 10 K    |
| **     | K    | \~   | independent corrosion | model simply         |
| 2000** |      | 30   | rate used; cladding   | extrapolated to peak |
|        | \    |      | credit taken; no      | dose beyond 10 K     |
| *      | (2\) | \~   | credit for inner      | yrs., (2) secondary  |
| *Three | 1    | 120  | stainless steel       | actinide phases      |
| se     | ,000 |      | container, diffusion  | control solubility   |
| parate | K    |      | thru SCC (assumed     | in the very          |
| models |      |      | continuous pathway)   | long-term, (3)       |
| used** | \    |      | and advective flow,   | multiple glacial     |
|        | (3\) |      | volumetric flux       | periods.             |
| *      | \~   |      | through failed        |                      |
| *(DOE, | 700  |      | package scaled with   |                      |
| 2      | K    |      | increasing corroded   |                      |
| 000)** |      |      | areas on the package  |                      |
+--------+------+------+-----------------------+----------------------+
| **TSPA | \~   | \    | General corrosion,    | SR models modified   |
| --     | 120  | ~140 | local corrosion, SCC; | for newer            |
| SSPA** | K    | *(   | Full temperature      | data/assumptions,    |
|        |      | TI)* | dependent (FTD) and   | Peak shown for       |
| **     | 1    |      | temperature           | nominal case (no     |
| 2001** | ,000 | \    | independent (TI)      | disruptive events),  |
|        | K    | ~110 | corrosion rates used; | SSPA analyzed a      |
| *      |      | *(F  | cladding credit       | high-temp model      |
| *(DOE, |      | TD)* | taken; volumetric     | (HTOM) and a         |
| 2      |      |      | flux through failed   | lower-temp model     |
| 001)** |      |      | package scaled with   | (LTOM) -- both with  |
|        |      |      | increasing corroded   | dose history still   |
|        |      |      | areas on the package  | rising at one        |
|        |      |      |                       | million yrs.         |
+--------+------+------+-----------------------+----------------------+
| *      | \    | \    | General corrosion.    | FEIS analyses        |
| *TSPA- | ~475 | ~120 | Local corrosion, SCC; | assumed larger       |
| FEIS** | K    | -150 | Temperature           | repository than SR   |
|        |      |      | independent corrosion | and SSPA analyses,   |
| **     |      |      | rate used (faster     | also assumed         |
| 2002** |      |      | rates assumed);       | different BDCFs and  |
|        |      |      | cladding credit       | 3,000 acre-ft rep    |
| *      |      |      | taken; volumetric     | vol. not used in     |
| *(DOE, |      |      | flux through failed   | previous PAs         |
| 2      |      |      | package scaled with   |                      |
| 002)** |      |      | increasing corroded   |                      |
|        |      |      | areas on the package  |                      |
+--------+------+------+-----------------------+----------------------+
| **TSPA | *\>1 | \~ 2 | General corrosion --  | 10% of packages get  |
| -FSEIS | mil  |      | full temperature      | general corrosion    |
| 2008** | lion |      | dependence enhanced   | breaches by one      |
|        | y    |      | by microbial          | million yrs. Only    |
| *      | rs.* |      | corrosion, local and  | 0.4% of package      |
| *(DOE, |      |      | stress corrosion      | surface removed; SCC |
| 2      |      |      | cracking; juvenile    | failures begin at    |
| 008)** |      |      | failures considered;  | 400 K yrs -- no flow |
|        |      |      | no cladding credit;   | through SCC          |
|        |      |      | volumetric flux       | failures; releases   |
|        |      |      | through failed        | from gen. corr.      |
|        |      |      | package scaled to     | Failures are well    |
|        |      |      | drip rate through     | after one million    |
|        |      |      | failed shield and     | years, releases      |
|        |      |      | increasing corroded   | within one million   |
|        |      |      | areas on the package  | 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       **Nature of          **Effect on Projected
  Modifications to the Modification to      Performance (From DOE, 2001,
  TSPA-SR Sub-Models** TSPA-SR Model**      Chapters 3. 2 & 4) against
                                            TSPA-SR base case model (\~60
                                            mrem/yr at 100 K yrs. reference
                                            mark)**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  Biosphere Dose       Modified factors     Small lowering ( less than 10
  Conversion Factors   used                 mrem/yr )\
                                            relative to the SR base case

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

[^1]: There is an earlier, lower peak of 153 mrem/yr at 635,000 years,
    not used in this analysis.