# Transport, Pathway, and Dose Assessment

The primary purpose of this appendix is to summarize the mathematical
relationships used in Version 2 of GENII to model the transport of
radionuclides through the air from a release point to an exposure
location, the exposure of humans to radionuclides existing at that
exposure location, and the annual radiation dose and cancer risk
resulting from that exposure. Exposure of humans to radionuclides is
assessed through 18 exposure pathways -- 13 pathways associated with
radionuclides released to the air, and 5 pathways associated with
radionuclides released to surface water. Each pathway may cause
radiation exposure either through external exposure to radiation,
through ingestion of radionuclides, or through inhalation of
radionuclides.

The movement of radionuclides by air to an exposure location was
assessed in a different manner than the movement of radionuclides by
surface water to an exposure location. For air transport, the Gaussian
plume model contained in the GENII code was used. This Gaussian plume
model is described in [Section D.2](#transport-through-air).
Radionuclide concentrations in air at an exposure location, as
calculated using this Gaussian plume model, were used along with
GENII-calculated radionuclide deposition rates as source terms for the
subsequent GENII assessments of the 13 exposure pathways considered for
radionuclides released to the air.

For water transport, a procedure independent of the GENII code was used.
Radionuclide holdup in surface water sediments, as well as dilution by
surface water bodies, was considered as part of a procedure discussed in
[Appendix C](../Appendix_C%20-Ready%20for%20CDC_031405.doc) and [Chapter
7](../Chapter_07_Ready%20for%20CDC%20031405.doc). This procedure was
used to develop radionuclide concentrations that were used as source
terms for the subsequent GENII assessments of the 5 exposure pathways
considered for radionuclides released to surface water.

The mathematical relationships presented in this appendix have been
obtained from the GENII model (1). These mathematical relationships were
included to enable the reader to relate the results of the analyses to
their mathematical bases. The preparers of this report were concerned
that the lack of this information would have detracted from the report's
discussion of important variables that influenced the calculated doses
and risks, and believed that many readers would not possess a copy of
the \[GENII SDD\]. To enable easier referencing by the reader, the same
terminology and notation as those used in the GENII SDD was generally
used. This enabled easier referencing by the reader.

In addition, the mathematical relations described in Sections D.2
through D.4 are each composed of a set of parameters, each requiring a
numerical value. To avoid a voluminous and complicated appendix, we
generally defer a discussion of the assumed values for parameters that
are used in the base-case GENII calculations to other appendices.

## Overview of Transport, Pathway Exposure, and Dose and Risk Assessment

This section consists of two principal subsections. Subsection D.1.1
addresses some considerations that guided decisions about the transport
and exposure pathways to be addressed for this phase of the SRS Dose
Reconstruction Project. Subsection D.1.2 describes how the perparers
envisioned the assessment as a linked set of calculation modules, and
points the reader toward those parts of the report that address each
calculational module.

### Selection of Transport and Exposure Pathways

#### Background

This report provides a plausible, yet bounding, assessment of the
radiological impacts that may have resulted from release of radioactive
material to the environment from 39 years of SRS operation. The report
was prepared for the Center of Disease Control and Prevention (CDC), and
builds on the work performed by the Risk Assessment Company (RAC) to
characterize the principal sources of radionuclide release to the
environment. In \[Phase II\] (2), RAC provided estimates of
radionuclides and chemicals discharged over 39 years into the air and
into onsite surface waters.

As charged by CDC, the analysis was performed in terms of exposure
scenarios representing hypothetical families performing plausible
activities. The goal of reconstructing possible doses and risks from
past SRS operations dictated somewhat different considerations in
selecting pathways for analysis than would be the case if the goal was
to perform preoperational evaluation for comparison to a regulatory
requirement. Analyses performed for comparison against regulatory limits
are typically performed in a very conservative manner to assure that
doses or risks would not be underestimated even under unusual
circumstances. But this level of conservatism would have been
unwarranted for the SRS Dose Reconstruction Project. Rather, it was
preferable to conduct an assessment that more closely examined plausible
rather than extreme activities and pathways. Such an assessment would be
more reflective of the mass of the persons in the vicinity of SRS and
potentially exposed from site operations.

In addition, by the same logic that guided use of a screening process to
identify those radionuclides that contributed the great majority of the
possible health effects from site operations, it was desirable to focus
on the exposure pathways leading to the largest doses and risks. In
practice, the relative significance of different pathways was not
initially clear, which prompted a bias for completeness in the initial
stages of the analysis.

#### Pathways Considered

The Phase II report identified two principal sources of release of
radionuclides into the environment from SRS: release into the air, and
release into surface water (2). The Phase II report identified and
quantified the principal radionuclides that were released.[^1] To assess
the environmental consequences of these releases, an existing
state-of-the-art computer code was used, Version 2[^2] of the GENII
family of codes.[^3] The process for selecting this code over other
computer codes and options is summarized in [Appendix
H](../Appendix_H_Ready%20for%20CDC%20031405.doc).

Of the exposure pathways addressed in GENII, those considered
appropriate for this report are shown in Table D-1. Exposure pathways
consist of those associated with release of radionuclides into the air
(*air pathways)*, and those associated with release of radionuclides
into surface water (*water pathways*). Doses and risks experienced by
the receptors may have resulted from three exposure routes: external
exposure, ingestion, and inhalation. Exposures from each exposure route
represent the sum of exposures from all applicable exposure pathways.

An overview of the air and water exposure pathways considered for this
report is provided in Section D.1.1.2.1. Section D.1.1.2.2 addresses the
approach for addressing radiological impacts from ingestion of meat from
game animals. Both the CDC and the SRS Health Effects Subcommittee
identified the need to consider radiological impacts from ingestion of
meat from game animals (see [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc)).

Table D‑1 Exposure Routes and Pathways for Air and Water Pathways

+------------------------------------+----------+----------+----------+
| Exposure Route & Pathway           | Air      | Water    | All      |
|                                    | Pathways | Pathways | Pathways |
+------------------------------------+----------+----------+----------+
| **Externa**l **Radiation:**        |          |          |          |
+------------------------------------+----------+----------+----------+
| -   Immersion in a Plume of Air    | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Exposure to Contaminated Soil  | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Exposure to a Contaminated     |          | X        | X        |
|     Shoreline                      |          |          |          |
+------------------------------------+----------+----------+----------+
| -   Exposure to Contaminated Water |          | X        | X        |
|     While Swimming                 |          |          |          |
+------------------------------------+----------+----------+----------+
| -   Exposure to Contaminated Water |          | X        | X        |
|     While Boating                  |          |          |          |
+------------------------------------+----------+----------+----------+
| **Ingestion:**                     |          |          |          |
+------------------------------------+----------+----------+----------+
| -   Leafy Vegetable Consumption    | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Root Vegetable Consumption     | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Fruit Consumption              | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Grain Consumption              | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Beef Consumption               | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Poultry Consumption            | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Milk Consumption               | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Egg Consumption                | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Inadvertent Soil Consumption   | X        |          | X        |
+------------------------------------+----------+----------+----------+
| -   Fish Consumption               |          | X        | X        |
+------------------------------------+----------+----------+----------+
| -   Inadvertent Ingestion of Water |          | X        | X        |
|     While Swimming                 |          |          |          |
+------------------------------------+----------+----------+----------+
| **Inhalation:**                    |          |          |          |
+------------------------------------+----------+----------+----------+
| -   Inhalation of Contamination in | X        |          | X        |
|     the Air                        |          |          |          |
+------------------------------------+----------+----------+----------+
| -   Inhalation of Contamination    | X        |          | X        |
|     Resuspended from Soil          |          |          |          |
+------------------------------------+----------+----------+----------+

##### Pathways Associated with Release of Radionuclides into the Air and Water

Radionuclides discharged from SRS release points were transported to
various receptor locations, leading to receptor exposures from external
radiation and inhalation pathways. Radionuclides were also deposited on
the ground at receptor locations. Contaminated soil exposed receptors to
radiation through several pathways. Exposure pathways considered in this
report resulting from deposition of contamination on the ground were:

-   External radiation exposure to the contaminated soil.

-   Inhalation of resuspended soil.

-   Inadvertent ingestion of soil from working or playing in soil.

-   Consumption of food crops, where the crops were contaminated through
    root uptake of radionuclides in soil, direct deposition of
    radionuclides on plant surfaces, or deposition on plant surfaces
    from radionuclides resuspended from contaminated soil.

Consumption of food products from animals that had consumed forage crops
grown in contaminated soil. Forage crops ingested by animals were
contaminated through root uptake of radionuclides in soil, direct
deposition of radionuclides on plant surfaces, and deposition on plant
surfaces from radionuclides resuspended from contaminated soil.

Surface water exposure pathways considered in this study were:

-   Ingestion of aquatic animals (e.g., fish) obtained from Savannah
    River and Lower Three Runs Creek access locations.

-   External radiation exposure to radionuclides building up in sediment
    alongside Savannah River and Lower Three Runs Creek.

-   Exposures from swimming in contaminated water, including external
    exposure to water and accidental ingestion of water.

-   External exposures from boating on contaminated water.

Exposures from possible ingestion or inhalation of resuspended sediment
were not analyzed. Considering that sediment is normally saturated,
resuspension of sediment would have been less likely than resuspension
of dryer soil, particularly soil used for growing food and crops that
were abraded and dispersed by farm implements. Therefore, it was
concluded that this pathway was likely much smaller than other possible
pathways from contaminated surface water. It is also not considered in
GENII.

Radiation exposures caused by use of contaminated river or creek water
were not assessed for irrigation, drinking or cooking, or showering.

Two studies have considered the potential use of the Savannah River for
irrigation. The first study, published in 1991, was performed by the
Westinghouse Savannah River Company (WSRC), the primary contractor at
SRS. It summarized land and water use characteristics around SRS that
could be incorporated as site-specific information in dose models (3).
The author contacted the Georgia Department of Natural Resources and the
Clemson University Extension Cooperative. These organizations "provided
information regarding irrigation practices along the Savannah River from
Clark's Hill reservoir to the Atlantic Ocean." They found that "the only
known use of Savannah River water for irrigation is by a dairy farmer in
Edgefield \[County\], upstream of the SRS" (3). This statement implied
that the Savannah River was not used as a source of irrigation water
downstream of SRS, at least as of the late 1980s and early 1990s. The
author recommended that irrigation not be considered as a pathway for
ingestion of radionuclides in dose models used for SRS (3).

The second study, issued in 2002 by the South Carolina Department of
Health and Environmental Control (SCDHEC), was a critical pathway
assessment of SRS to be used to help assess the environmental monitoring
program at SRS (4). The author surveyed state employees. This report
states: "The state county extension offices report no knowledge of any
irrigation system originating from the Savannah River downstream of the
SRS. Pine plantations bordering the Savannah River in Allendale and
Jasper counties are used by deer hunters." In Georgia, "due to the high
elevation of the Georgia river bank, irrigation from the Savannah River
is not practical. Irrigation water, therefore, comes from other sources
such as groundwater or ponds" (4).

An extension engineer in Georgia was contacted who verified that, to his
knowledge, the Savannah River was not used for irrigation and that
irrigation water in Georgia was primarily from ponds and groundwater
(5). The SCDHEC author of the second assessment was contacted and the
author stated that the extension agents he contacted based their
information on their 20 to 30 years of experience (6). It was concluded
that the Savannah River most likely had not been used for irrigation
since at least the early 1970s.

In any event, this study considered two farming-family scenarios. The
closest to the SRS lived near Girard, Georgia. It would have been
unreasonable to assume that this family used the Savannah River as a
source of irrigation water. The family farm was about three miles from
the river, an unfeasible distance for piping Savannah River water to a
farm. Groundwater levels are normally less than 100 feet below the
surface in this part of South Carolina and Georgia, making groundwater
more easily available and cost effective to use for irrigation. Using
ponds that are commonly found on farms in the southeast U.S. is also
more cost-effective than pumping water from a river.

With respect to drinking and showering water, the only scenario
involving a dwelling located reasonably near a source of contaminated
surface water was the Family Near the River. It was assumed that the
family in this scenario lived in or near Martin, SC, which is near Lower
Three Runs Creek. There was no evidence that persons living in or near
Martin used Lower Three Runs Creek as a source of drinking water.

Considering this, it was concluded that incorporating use of water from
Lower Three Runs Creek into the scenario would have been unreasonable.

##### Game Animals

**Background.** Humans could have become exposed to radionuclides by
ingesting meat from game animals that had taken up radionuclides. It was
determined that these game animals could be represented by deer and wild
fowl.

\[ERDA-1537\] (7) documents that the deer herd before SRS was officially
closed to the public in December 1952 constituted about 20 animals. The
population as of the mid 1970s had grown to 5,000 to 8,000. The greatest
population densities occurred on the southern and northeastern portions
of SRS. Controlled public hunts began in 1965. From that time to the mid
1970s, about 10,000 deer were taken in public hunts, and about 500 were
killed for research programs (7). In addition, several domestic hogs,
abandoned in 1952, had reverted to the semi-wild state. SRS began a
control program for hog removal, and since 1969, about 125 wild hogs had
been killed as of the mid 1970s (7).

Therefore, deer were selected to represent all wild mammals assumed to
be taken for consumption. Deer was routinely taken by hunters between
1954 and 1992. Although wild hogs were also taken, the numbers killed by
hunters were apparently small in comparison to deer. From the mid 1960s
to the mid 1970s, the number of wild hogs taken by hunters was only
about 1% the number of deer.

With respect to wild fowl, there was no evidence that the consumption of
wild fowl constituted a major source of human intake of radionuclides
during the SRS operational period. Nonetheless, it was recognized that
waterfowl were present on the SRS, mainly during winter migrations. In
addition, other game birds such as quail and dove were abundant.
\[ERDA-1537\] (7) observed that the population of quail and dove in the
SRS vicinity did not initially decrease when the SRS land was removed
from agriculture, but probably reached a record high in the early 1960s.
Wild turkeys are also on the site, resulting from use of SRS as a
breeding ground.

Hence, it was felt plausible that hunters either onsite or in the
vicinity of SRS would have taken wild fowl during the period of SRS
operations, and that wild fowl represented a possible source of
ingestion exposures to some receptors.

**Analyzing exposures from contaminated game.** Development of exposure
pathways for game animals was difficult. For example:

-   It was not clear that such pathways were reasonable for game taken
    on the SRS. Persons would have done so voluntarily with knowledge
    that the game may have contained radionuclide contamination. This
    would arguably not have been the case for deer or other game animals
    taken off the SRS site.

-   Unlike animals used for food products such as beef or pork, game
    animals are generally not confined to a definable location. Game
    animals may have wandered from one widely separated location to
    another, consuming grass or other plant products as well as water
    from SRS streams.

-   There was a lack of basic information such as transfer coefficients
    for deer except for a few isotopes, as well as other computational
    difficulties (see below).

-   It was unclear whether exposures that may result from taking deer on
    or near SRS were significantly different from exposures elsewhere
    (see below).

Options for modeling doses from consumption of contaminated wild game
were considered as discussed in \[ATL white paper on venison\] (8). It
was determined that with respect to deer, transfer factors for most
isotopes of concern were not available. (A transfer coefficient value
for ^137^Cs to deer was available from \[IAEA 1994\] (9).) It was also
determined that for most years, data about the concentrations of
radionuclides in venison were available for one or a few nuclides
(^137^Cs and ^90^Sr) from SRS annual environmental reports. As discussed
in Chapter 11 of the Phase II report, there was a substantial body of
information about the concentrations of cesium in meat from deer killed
on the SRS and elsewhere in the region. "In general, ^137^Cs is the
radionuclide of greatest concern because of its relatively long
half-life (30 years) and its tendency to accumulate in edible (muscle)
tissues" (2). Nonetheless, concentration data for other radionuclides
and for missing years would have had to be derived or estimated.

Perhaps more significantly, the Phase II report notes, "Concentrations
measured in deer collected from offsite locations give no indication
that mean ^137^Cs burdens in SRS deer are elevated above the expected
background concentrations." The Phase II authors described comparisons
between SRS deer and deer taken from other locations in South Carolina
and Georgia, and discussed potassium levels in soils as the most likely
reason that the mean ^137^Cs concentrations in the SRS deer were
consistently lower. They discussed a study designed to use the fact that
the ^134^Cs/^137^Cs ratio from SRS releases differed from that in
fallout: the cesium ratios in deer in that study "were consistent with
global fallout and were comparable to those calculated for offsite deer"
(2).

In a 1999 report available on the web site of the University of
Georgia's Savannah River Ecology Laboratory, Dr. Michael Smith of the
University of Georgia and Peter Fledderman of Westinghouse Savannah
River Company provided additional information comparing levels of
^137^Cs found in deer at SRS with those at Fort Jackson, SC, Fort
Stewart, Georgia, Cedar Knoll Plantation, SC and Webb Wildlife Center,
SC. These authors provided data showing higher average concentrations of
^137^Cs in deer at the two military bases than at SRS. They described
the soils at the military bases as similar to those at SRS. Deer from
the other two locations had much lower concentrations of ^137^Cs, but
the authors maintained that fertilizers with potassium were used at
these locations and that this probably reduced the ^137^Cs levels in the
deer (10).

The Phase II authors suggested how the deer pathway might be further
explored in "future phases of the SRS Dose Reconstruction Project."
However, there was a lack of usable data that would have enabled the
perparers to confidently quantify human exposures via deer consumption
from radionuclides released by the SRS. As noted, information was
lacking about transfer coefficients for elements other than cesium. A
more difficult issue was the lack of data that showed that radionuclide
concentrations in venison from SRS were "above background"--- i.e,
larger than the concentrations in other deer. It was not possible to
discern a significant difference in the isotopic ratios between the
cesium in the SRS deer and the cesium from atmospheric fallout.[^4]
Furthermore, "radioiodine concentrations measured in deer thyroids have
consistently corresponded to periods of weapons testing" (2).

Therefore, the wild game consumption pathway was modeled as a form of
beef and poultry consumption.

### Dose and Risk Assessment

#### Assessment Modules 

Although the calculational procedure for determining dose and risk from
long-term operation of SRS is complex, the overall governing
relationship between the stages of the calculational procedure is
straightforward. For each year that SRS operated between 1954 and 1992,
the dose and risk to an individual can be mathematically envisioned for
each radionuclide as a set of separate calculational modules. The
outputs of each calculational module are multiplied in turn by the next
module. For each year and radionuclide, therefore, the annual dose to an
individual is:

  ------------ --- -----------------------------------------------------------
  D~i~         =   RE~i~ TR~i~ PA~i~ DF~i~

  And the          
  annual risk      
  to an            
  individual       
  is:              

  R~i~         =   RE~i~ TR~i~ PA~i~ RF~i~

  Where D~i~   =   Annual dose in Sieverts (Sv) for radionuclide i.

  R~i~         =   Annual risk for radionuclide i.

  RE~i~        =   *Release Module*. Quantity of radionuclide i released to
                   the air (as from a stack) or to a surface water body (Bq)

  TR~i~        =   *Air and Surface Water Transport Module.* Mathematical
                   relationships that model the transport of a radionuclide
                   through air or surface water to an exposure location --
                   i.e., a location occupied by a receptor or a location where
                   a receptor obtains foods such as vegetables, beef, or fish.
                   The calculational result of this module is the
                   concentration of the air or water containing that
                   radionuclide at that exposure location \-- i.e., m^-3^ of
                   air or L^-1^ of surface water. Note that RE~i~ x TR~i~ =
                   Bq/m^3^ or Bq/L.

  PA~i~        =   *Pathway Assessment Module.* Mathematical relationships
                   (pathway assessments) that model the movement of a
                   radionuclide through each of the exposure pathways listed
                   in Table D-1. The calculational result of this module is
                   the concentration or quantity of a radionuclide that the
                   receptor is exposed to, inhales, or ingests. The units
                   associated with this module depend on the pathway being
                   considered (see below).

  DF~i~        =   *Dose and Risk Module*. Dose conversion factor, a
                   relationship that gives the dose to a receptor for
                   radionuclide i for the particular exposure pathway of
                   interest (e.g., Sv per annual exposure to a concentration
                   of 1 Bq per m^3^ of air, Sv per Bq ingested from food,
                   water, or other sources of contamination).

  RF           =   *Dose and Risk Module*. Risk conversion factor, a
                   relationship that gives risk of cancer to a receptor for
                   radionuclide i for the particular exposure pathway of
                   interest (e.g., risk per annual exposure to a concentration
                   of 1 Bq per m^3^ of air, risk per Bq ingested from food,
                   water, or other sources of contamination), given as an
                   annual probability of cancer incidence or fatality.
  ------------ --- -----------------------------------------------------------

Each of these modules is briefly addressed below.

**Release Module.** The release of radionuclides into the air and
surface water is addressed in Appendices A and B. [Appendix
A](../Appendix_A%20-%20ready%20for%20CDC%20031405.doc) addresses the
determination of airborne release points for the assessment. [Appendix
B](../Appendix_B_ready%20for%20CDC%20031405.doc) lists the quantities of
radionuclides annually released into the air and water from each source
considered in this study, as well as the bases for these listed
quantities. From the information in these appendices, a series of data
files was created that list the quantities of radionuclides released
into the air as a function of major SRS facility and year, and the
quantities of radionuclides released into surface water as a function of
year. The files were input to GENII using the pre-processor, a program
was created to facilitate entry of data into GENII.

**Air and Surface Water Transport Module.** Different mathematical
procedures were used to model movement of radionuclides to exposure
locations, depending on whether the radionuclide release was to air or
to water. For release of radionuclides to air, a sector-averaged
Gaussian model was contained in the GENII code as described in Section
D.2. For release of radionuclides to surface water, simple dilution
models were considered that differed depending on whether the exposure
location being considered was Lower Three Runs Creek or was the Savannah
River ([Appendix C](../Appendix_C%20-Ready%20for%20CDC_031405.doc)). For
Lower Three Runs Creek, radionuclide concentration data considered as
measured in this creek are reported in SRS documents such as annual
environmental reports. For the Savannah River, a simple dilution model
was considered. The annual quantities of radionuclides that were
discharged into the Savannah River were first estimated from all major
surface water systems (including Lower Three Runs Creek), and then
diluted this annual discharge by a volume of water equal to the annual
river flow rate. The outcome of this module was a set of files
containing radionuclide concentrations in water. These files were input
into GENII for the pathway assessment.

**Pathway Assessment Module.** This portion of the assessment was
performed using the GENII code. For radionuclides released through the
air pathway, the starting point of the pathway assessment was the
concentration of radionuclides in air at an exposure location.
Radioactive exposures were then assessed for each of the 13 air pathways
listed in Table D-1, in accordance with the mathematical procedures
summarized in Section D.3. While the radionuclides were in the air, they
caused exposures to humans by the following pathways:

1.  Inhalation exposures from immersion in air containing radionuclides
    (Section D.3.3.1).

2.  External exposures from immersion in air containing radionuclides
    (Section D.3.2).

Radionuclides also fell to earth through depositional processes. This
deposition resulted in a concentration of radionuclides in the top part
of the soil. Radionuclides in this top part of the soil then caused
radionuclides through additional pathways. Three pathways caused by
ground contamination at an exposure location are:

1.  External exposures from proximity to contaminated soil (Section
    D.3.3.2).

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3.  Inhalation exposures from breathing radionuclides that had been
    resuspended from contaminated soil (Section D.3.3.3).

4.  Ingestion exposures from inadvertently ingesting contaminated soil
    (Section D.3.3.4).

In addition, radionuclides may be transported through the food chain to
humans. This transport mechanism has historically been a very important
mechanism for human exposure to radionuclides released to the
environment. In GENII, radionuclide transport through food chain
pathways are considered in two ways. First, GENII considers foods that
take up radionuclides from soil (or have radionuclides deposited on food
surfaces) and are directly eaten by humans. The four pathways considered
in this manner are:

1.  Ingestion exposures from eating leafy vegetables (Section D.3.4.1).

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5.  Ingestion exposures from eating root vegetables (Section D.3.4.1).

6.  Ingestion exposures from eating fruit (Section D.3.4.1).

7.  Ingestion exposures from eating grain (Section D.3.4.1).

Second, GENII considers animal products that are eaten by humans and
have previously consumed contaminated grass or forage. The four pathways
considered in this manner are:

1.  Ingestion exposures from eating beef (Section D.3.4.2).

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8.  Ingestion exposures from eating poultry (Section D.3.4.2).

9.  Ingestion exposures from drinking milk (Section D.3.4.2).

10. Ingestion exposures from eating eggs (Section D.3.4.2).

For radionuclides released into surface water, the starting point of the
pathway assessment was the concentration of radionuclides in water at an
exposure location. Radioactive exposures were then assessed for each of
the 5 water pathways listed in Table D-1, in accordance with the
mathematical procedures summarized in Section D.3. While the
radionuclides were in contained within the water, they could they caused
exposures to humans by the following pathways:

11. Ingestion exposures from eating fish (Section D.3.4.3).

12. External exposures from swimming in water (Section D.3.6.1).

13. Ingestion exposures from inadvertently drinking water while swimming
    (Section D.3.6.2).

14. External exposures from boating in water (Section D.3.6.3).

Note that eating fish is another very important mechanism for food-chain
transport of radionuclides to humans.

Finally, radionuclides may be deposited from the water onto river or
creek sediment. Persons standing or performing other activities along a
shoreline may receive external exposures from the radionuclides in these
sediments -- i.e.:

1.  External exposures from a contaminated shoreline (Section D.3.5).

**Dose and Risk Module.** This portion of the assessment was basically
calculated using the GENII code, although certain dose and risk
calculations were also performed using the post-processor. This module
calculated equivalent dose for 23 organs, effective dose, and cancer
risk as a function of radionuclide and year for each receptor. Almost
all dose and risk conversion factors used for this report were those
obtained from EPA's April 2002 update to its Federal Guidance Report No.
13 \[FGR-13U\] (11). Section D.4 contains a discussion of radiation dose
and risk concepts, and summaries the basic equations used by GENII to
calculate dose and risk from exposure to radioactive material.

#### Approach for Presenting Mathematical Relationships used in GENII

The remaining three sections of this appendix present the mathematical
relationships used in the GENII code to:

-   Model transport of radionuclides through air to an exposure location
    (Section D.2).

-   Perform pathway assessments, include food-chain transport
    assessments, of radionuclides through air and surface water pathways
    (Section D.3).

-   Assess human radiation doses and cancer risks from external exposure
    to radionuclides, inhalation of radionuclides, and ingestion of
    radionuclides (Section D.4).

It was recognized that a rigorous description of the mathematical
relationships set forth in GENII would be lengthy and would largely
repeat the information in the GENII SDD. Yet it was also recognized that
if the mathematical relationships were not presented in some detail,
most readers would be unable to easily relate the results of the
analyses to their mathematical bases. (It was believed that many readers
would not have access to a copy of the GENII SDD.) This would have
detracted from the report's discussion of important variables that
influenced the calculated doses and risks. Hence, the mathematical
relationships used in GENII are briefly summarized, hoping that this
summary would be sufficient for most persons interested in the technical
details of the analysis.

The preparers of this document used the same terminology and notation as
those used in the GENII SDD. This enabled easier referencing by the
reader. Also where appropriate, the equations cited in this section were
related to their application in GENII using the FRAMES software system.
In some cases the terminology for particular parameters is somewhat
different in the GENII SDD than in the FRAMES interface.[^5]

In addition, the mathematical relations described in Sections D.2
through D.4 are each composed of a set of parameters, each requiring a
numerical value. To avoid a voluminous and complicated appendix, we
generally defer a discussion of the assumed values for parameters that
are used in the base-case GENII calculations to other appendices. Some
parameters pertain to site-specific considerations such as the density
of soil (see [Appendix
F](../Appendix_F%20tables%20-%20Ready%20for%20CDC%20031405.doc)). Others
pertain to human activities that influence the uptake or exposure to
radionuclides (e.g., time spent in an exposure location) and are
determined in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

## Transport Through Air

### Fundamentals of Air Dispersion

Radioactive materials in the form of gases and particulates may be
released into the atmosphere and may result in radiation exposure to
humans from both external and internal pathways. External exposures may
result from immersion in contaminated air or from proximity to
radionuclides deposited on the ground, while internal exposures may
result from inhalation and ingestion of radionuclides. The magnitude of
exposure depends on the concentrations of radionuclides in contaminated
media contacted by, or in proximity to, a human receptor. In turn,
radionuclide concentrations in contaminated media depend on atmospheric
diffusion and deposition processes that affect the transport of
radionuclides from the point of release to the location of the receptor.

Figure D-1 and Figure D-2 depict many of the atmospheric processes that
affect airborne release and transport \[from Till & Meyer, IAEA SS-19\]
(12), (13). These include plume rise, dispersion, wind speed and
direction, depletion, release height, building effects, and topography
and geographic features.

![](media/image1.wmf){width="4.444444444444445in"
height="3.361111111111111in"}

Figure D‑1 Atmospheric Dispersion and Removal Processes

Adapted from \[IAEA SS-19\] (13).

![](media/image2.wmf){width="4.444444444444445in"
height="2.8055555555555554in"}

Figure D‑2 Air Flow Around a Building

Adapted from \[IAEA SS-19\] (13).

#### Plume Rise 

As a plume of air containing gaseous and particulate materials
(effluent) is released from a source such as a tall stack, the effluent
may initially rise. Some of the factors influencing plume rise include
the temperature of the effluent and the ambient air, the velocity of the
effluent leaving the stack, the inside radius of the stack, the wind
speed at the release height, and the atmospheric stability (see below).
Plume rise affects the "effective stack height" of the release point.
Plume rise may significant increase the effective stack height, which in
turn may significantly reduce near-field ground-level concentrations
(12).

#### Dispersion 

As the effluent plume is transported from the source by wind, turbulent
eddies in the atmosphere diffuse the effluent. Consistent with Fick's
Law, a concentration gradient exists in the effluent, so that the
effluent concentrations in the center of the plume are larger than those
toward the plume edges. The combined influences of diffusion and
transport are called dispersion.

As the plume moves with the wind, diffusion continues in the vertical
direction until certain "boundaries" are reached. Of course, vertical
diffusion from the depicted stack (Figure D-1) cannot continue below the
surface of the earth. In the other direction, the plume continues to
diffuse up to the mixing height, which generally ranges from about 200 m
to about 2,000 m above the surface of the earth.[^6] Within this
atmospheric "mixing layer", friction caused by ground surface roughness
and heating combine to generate turbulence that efficiently mixes the
effluent. But the top of the mixing layer is marked by a decrease in
turbulence brought about by stable atmospheric conditions above. Above
this "boundary," further diffusion in the vertical direction is
significantly reduced, and the vertical concentration distribution
becomes more uniform. The thickness of the mixing layer changes with
atmospheric conditions. The mixing layer is generally thickest during
the day and during periods having high wind speeds, and it is thinnest
at night during periods having low wind speeds. It also tends to be
thickest on summer afternoons and thinnest on autumn mornings.
Thicknesses also vary considerably by geographic location. In either
case, the mixing layer depth tends to increase with surface roughness
(12).

The stability of the atmosphere within the mixing layer largely
determines the intensity of turbulence within the mixing layer and
therefore the diffusion of effluent within it. Essentially, conditions
within the mixing layer are said to be stable, neutral, or unstable
depending on variations of temperature and air density. These variations
affect the movement of air particles from one location to another. If
the variations tend to retard movement of particles, then the
atmospheric conditions are said to be stable; if the variations have no
effect on the movement of the particles, then atmospheric conditions are
said to be neutral; and if the atmospheric conditions tend to promote
the movement of the particles, then atmospheric conditions are said to
be unstable. Clearly, unstable conditions promote dispersion of
particles within air, while stable conditions retard it.

A common method for describing stability conditions is to differentiate
meteorological conditions into stability classes. One of the original
classification systems was developed in 1962 by Pasquill, who
distinguished six stability classes ranging from Class A (highly
unstable) to Class F (highly stable). Pasquill's original classification
is reproduced here as Table D-2, and it considers the relationship of
wind speed, amount of incoming solar radiation, and cloudiness. Since
this classification system was developed, it has been modified by
various researchers and regulatory agencies, and other, similar,
classification systems have been developed (12). The choice of a
particular classification system, which affects the analyses performed
to numerically describe effluent diffusion in air, is somewhat
subjective.

Table D‑2 Pasquill Stability Categories

  --------------- ------------ ---------- --------------- --------------- --------------
  *A. Extremely                           *D. Neutral                     
  Unstable                                Conditions\**                   
  Conditions*                                                             

  *B. Moderately                          *E. Slightly                    
  Unstable                                Stable                          
  Conditions*                             Conditions*                     

  *C. Slightly                            *F. Moderately                  
  Unstable                                Stable                          
  Conditions*                             Conditions*                     

  Surface Wind    Daytime                                 Nightime        
  Speed at 10 m   Insolation                              Conditions      
  (m/s)                                                                   

                  Strong       Moderate   Slight          Thin Overcast   ≤ 3/8
                                                          or \> 3/8       Cloudiness
                                                          Cloudiness^†^   

  \<2             A            A-B        B                               

  2-3             A-B          B          C               E               F

  3-5             B            B-C        C               D               E

  5-6             C            C-D        D               D               D

  \>6             C            D          D               D               D
  --------------- ------------ ---------- --------------- --------------- --------------

\*Applicable to heavy overcast day or night.

^†^The degree of cloudiness is the fraction of the sky above the local
apparent horizon that is covered by clouds.

#### Wind Speed and Direction

Clearly, wind speed affects the airborne dispersion of effluent. Higher
wind speeds promote dispersion, while lower wind speeds retard it. Wind
speeds frequently fluctuate both temporally and with height, as does
wind direction.

#### Depletion

Removal mechanisms reduce effluent concentrations within the plume, and
include wet and dry deposition, radioactive decay, and chemical change.

Wet deposition processes include rainout and washout. Rainout refers to
the interaction of gaseous and particulate effluents with precipitation
formation processes within clouds. Effluents are subsequently removed by
the precipitation. Washout refers to the removal of gaseous or
particulate matter below the cloud layer from contact by falling
precipitation. Dry deposition processes include removal of effluent
through gravitational settling, or through contact with the ground,
vegetation, or other ground cover such as buildings. Although dry
deposition is continuous, compared to wet deposition that only occurs
during periods of precipitation, dry removal of effluent from air is a
less efficient process than wet removal.

Radioactive isotopes decay during transport. The significance of this
removal process for exposure to a downwind receptor depends on the
radionuclide half-life and the transport time. Chemicals may degrade or
otherwise change during transport.

#### Release Height

Generally speaking, the higher the effluent release point, the farther
the effluent travels from the release point before significant effluent
concentrations reach ground level. NRC notes that for a facility such as
a nuclear power plant, gaseous effluents released from tall stacks
generally produce peak ground-level air concentrations near the site
boundary, while near-ground-level releases usually produce
concentrations that monotonically decrease from the release point to all
locations downwind (15). Till and Meyer suggest that a common approach
is to assume an elevated release when the release point is 2.5 times the
height of nearby structures, and to assume a ground-level release when
the release point is below the height of the structures (see below) (12)
.

#### Building Effects 

The flow of air and effluent from a release point can be disturbed by
surrounding structures. Figure D-2 \[from IAEA SS-19\] illustrates
idealized flow around a single building. The three main zones of airflow
around this building are (13):

1.  The upwind displacement zone, where the approaching air is deflected
    around the building.

```{=html}
<!-- -->
```
15. The relatively isolated cavity zone immediately on the leeward side
    of the building.

16. The highly disturbed wake zone further downwind from the building.
    The exact distance of the downwind wake zone depends on the source
    configuration and meteorological conditions.

The prevailing dispersion pattern will depend on both the release height
and the building geometry. If the release height is greater than about
2.5 times the building height, then building effects on dispersion are
relatively small. Dispersion characteristics are similar to those in the
displacement zone. If the release height is less than about 2.5 times
the building height, the transition between the downwind cavity zone and
the wake zone occurs downwind of the release point at a distance of
about 2.5 times the square root of the surface area of the largest wall
of the building. Variations in dispersion patterns caused by buildings
can be considered through modifications of basic atmospheric dispersion
models such as the Gaussian plume model.

#### Topographic and Geographic Features 

Geographic features such as hills, valleys, and large bodies of water
influence dispersion and airflow patterns. For example, effluent
released in a well-defined river valley will likely follow the confines
of the valley rather than remain in a straight-line trajectory. Surface
roughness, including vegetative cover, affects the degree of turbulent
mixing. Sites having similar topographical and climatological features
can have similar dispersion and airflow patterns. Detailed dispersion
patterns, however, are usually unique for each site (12), (15).

### Gaussian Plume Model

One of the most widely used models for numerically describing the
movement and dispersion of effluent from a release point is the Gaussian
plume model. In theory, notes the IAEA, the Gaussian plume model is
limited to rather simple dispersion situations (13):

-   Dispersion over flat, non-complex terrain.

-   Short range transport (about 100 m to 20 km downwind).

-   Steady state meteorological conditions.

-   No elevated temperature inversions.

-   Quasi-continuous releases.

-   Transport and mixing in the lee of isolated point sources.

-   Non-depositing materials, such as noble gases.

But in practice, the Gaussian plume model has been successfully applied
to a wide variety of dispersion problems. This is possible because the
model is firmly supported by extensive experimental data, as well as
being one of the most widely validated of the general dispersion models
(13).

#### Basic Model

The basic model used for chronic release of effluent from a source is
provided below (1). It describes dispersion of effluent from a single
point source assuming that wind always flows in a single, straight-line
direction. Modifications to this model to address the release from
multiple sources, and the flow of wind from multiple directions, are
described in the next section.

A point source model was used for this report, rather than an area
source model, because a point source model best described the release of
most of the radioactive material into the air at SRS.[^7] Furthermore,
no attempt is made to consider plume rise or building effects. Regarding
plume rise, offgas from SRS stacks was not particularly elevated in
temperature. Therefore, plume rise from SRS stacks should have been
comparatively small. In any event, neglecting plume rise was
conservative because the assumption of no plume rise deposited more
radionuclides on the ground closer to the release point. Regarding
building effects, most release of radioactive material occurred from
stacks that were considerably taller than nearby buildings. In addition,
most receptor locations were several miles from release points,
minimizing the local effects of buildings. Finally, it was determined
that the calculational complications associated with consideration of
building effects was unwarranted considering the limited availability of
long-term meteorological data for SRS (see below).

Therefore, the complete straight-line Gaussian plume model used in this
study is, from \[GENII SDD\] (1):

![](media/image3.wmf)**\
**

  ------------------- --- --------------------------------------------------------
  Χ(x,y,z,H,h~eff~)   =   the concentration at distance x, crosswind position y,
                          and height z, in a plume with axis at height h~eff~
                          (Ci/m^3^)[^8]

  Q'(x)               =   the release rate, corrected for deposition and decay as
                          appropriate (Ci/s)

  U(h~s~)             =   the wind speed at release height, h~s~ (m/s)

  σ~y~                =   the horizontal diffusion coefficient (m)

  σ~z~                =   the vertical diffusion coefficient (m)

  G(z)                =   the vertical dispersion factor.
  ------------------- --- --------------------------------------------------------

The vertical dispersion factor includes plume reflection off the ground
and off the top of the mixing layer. It is given by (1):

![](media/image4.wmf)**\
**

  --------- --- ----------------------------------------------------------
  Where     =   the effective release height (h~s~ + plume rise) (m)
  h~eff~        

  H         =   the mixing layer thickness (m).
  --------- --- ----------------------------------------------------------

In GENII, the limits of summation in the second equation are truncated
between (-2 \< n \< 2), a simplification that should not significantly
affect the accuracy of the equations. The receptor height (z) is assumed
to be one meter.

If the distance from the source is sufficiently large, the value of the
vertical diffusion coefficient (in meters) approaches the thickness of
the mixing layer (H). Under this condition, the effluent is uniformly
mixed in the vertical direction, and the straight-line Gaussian plume
model is simplified to (1):

![](media/image5.wmf)**\
**

  --------- --- ----------------------------------------------------------
  Where     =   the height of the mixing layer, or the effective release
  H~u~          height, whichever is higher.

  --------- --- ----------------------------------------------------------

In GENII, the effluent is considered to be uniformly mixed in the
vertical direction when the vertical diffusion coefficient is at least
1.2 times the uniform depth (as defined above) (1).

Horizontal and vertical diffusion coefficients in the above equations
(i.e., σ~y~ and σ~z~) may be calculated using a variety of methods that
incorporate consideration of stability classes. Horizontal and vertical
diffusion coefficients are automatically calculated in GENII when
meteorological data is entered using the joint frequency distribution
approach. The joint frequency distribution approach is used for this
report.

#### Sector Average Model

Wind normally does not blow from the same direction for prolonged
periods. So for chronic or long-duration releases, the basic Gaussian
plume model is modified using a sector-average approximation. One first
draws an imaginary circle around the release point, and divides the
circle into a series of arcs. Historically, the circumference around the
release point has been divided into 16 sectors corresponding to the
16-major compass directions: N, NE, NNE, E, and so forth. Each sector is
a pie-shaped wedge describing a 22.5^o^ arc (360^o^ /16 sectors). (Since
1965, however, directions have been recorded in 10-degree sectors,
leading to 36 sectors.) One then estimates the dispersion of effluent in
each horizontal direction around the release point. One considers the
concentrations produced by each wind direction, wind speed, and
stability class, weighted by the frequency with which these conditions
occur (the joint frequency distribution), and obtains an average
effluent concentration within each sector as a function of distance from
the release point.

Although the straight-line Gaussian plume model discussed above is given
in Cartesian coordinates, the model when adjusted for sector averaging
is normally converted to cylindrical coordinates. The sector average
model as used in GENII is (1):

![](media/image6.wmf)

  ------------- --- --------------------------------------------------------
  Χ(θ~i~,r,z)   =   the concentration at distance r, in sector θ~i,~ at
                    height z (Ci/m^3^)

  Q'(r)         =   the total mass of material released, corrected for
                    deposition and decay

  θ~w~          =   the sector width, which is the larger of the arc length
                    in a 22.5^o^ sector, or 4 times σ~y~

  U             =   wind speed (m/s)
  ------------- --- --------------------------------------------------------

  ----------- --- --------------------------------------------------------
  σ~z~        =   vertical diffusion coefficient for distance r (or time t
                  = x/U)

  G(z)        =   vertical factor given by the above equation.
  ----------- --- --------------------------------------------------------

At long distances, the model further simplifies, because of uniform
mixing in the vertical direction, to (1):

![](media/image7.wmf)

In GENII, it is again assumed that the plume is uniformly mixed in the
vertical direction when the vertical diffusion program is 1.2 times the
uniform depth.

#### Joint Frequency Distribution (JFD)

The joint frequency distribution, P~pjk~, is a function of wind
direction sector, p, stability category, j, and wind speed class, k. The
joint frequency distribution is computed by compiling meteorological
data, usually determined and recorded for each hour, over an appropriate
time interval and computing the frequency of occurrence of each joint
frequency category. Each joint frequency category represents a band of
wind speeds, directions, and stability conditions.

#### Multiple Sources and Receptor Locations

The above discussions regarding the Gaussian plume model, and
modifications to account for sector averaging, are for a single source
emitting radionuclides into the air. But there are multiple SRS sources
as well as multiple receptors. A single receptor may receive radiation
exposures from all sources. Even if the release rate from each source
was the same, the exposure received by a receptor would differ for each
source because of distance and sector-averaging considerations.

The GENII code determines the total exposure received by each receptor
as summed over the contribution from all sources. (See Section 5.1.5 of
the GENII SDD.) It establishes the location of each receptor and source
on a polar grid, and then for each receptor determining the distance and
bearing from each source. For each radionuclide, the contribution from
each source is summed, leading to a total concentration in air at the
receptor's location. This average concentration is then used for further
exposure and pathway analyses as addressed in Section D.3.

#### Depletion Processes

As radionuclides transit from a source to a receptor, several processes
deplete the quantities of radionuclides in air. These processes include
dry and wet deposition and radioactive decay.

##### Dry Deposition 

Dry deposition is modeled in accordance with an assumption that the flux
of material reaching the ground in is proportional to the concentration
of the material in the air near the ground (1):

  ----------- --- --------------------------------------------------------
  ω~1ij~(t)   =   v~dd~ X~ij~(t)

  Where       =   the dry deposition rate at position i,j at time t (g/(s
  ω~1ij~(t)       m^2^)
  ----------- --- --------------------------------------------------------

  ----------- --- --------------------------------------------------------
  v~dd~       =   the dry deposition velocity (m/s), which is a function
                  of the height at which the concentration is measured or
                  calculated (assumed to be one meter for GENII).

  X~ij~(t)    =   the concentration at a height of one meter above the
                  ground at position i,j at time t.
  ----------- --- --------------------------------------------------------

Dry deposition velocities may be estimated using an analogy to
electrical resistance, in that particles resist falling to the ground
surface depending on their physical and chemical characteristics and
atmospheric conditions. (Because noble gases are inert, the deposition
velocity for noble gases is assumed to be zero.) For *small* particles,
the dry deposition velocity is given by:

  ----------- --- --------------------------------------------------------
  v~dd~       =   (r~a~ + r~s~ + r~t~)^-1^

  Where r~a~  =   aerodynamic resistance (s/m)

  r~s~        =   surface resistance (s/m)

  r~t~        =   transfer resistance (s/m).
  ----------- --- --------------------------------------------------------

Aerodynamic resistance is a parameter characteristic of the turbulence
in the lowest layer of the atmosphere, and can be calculated from the
wind speed as:

  ------------ --- --------------------------------------------------------
  r~a~         =   U(z) / u^2^

  Where z      =   the height at which the concentration is estimated

  u            =   the characteristic turbulence velocity, called the
                   friction velocity

  U(z)         =   the wind speed at height z.

  The surface      
  resistance       
  is a             
  function of      
  the friction     
  velocity,        
  where:           

  r~s~         =   2.6 / (0.4 u) = 6.5/u
  ------------ --- --------------------------------------------------------

where 2.6 is a dimensionless empirical constant and 0.4 is von Karman's
constant.

The transfer resistance is a mathematical device to establish an upper
limit on the deposition velocity. As a default, the transfer resistance
is assumed to be 10 s/m for iodine and 100 s/m for particles.

For *large* particles, the gravitational settling velocity of the
particles must be considered, and the deposition velocity becomes:

$$V_{\text{dd}} = \left( r_{a} + r_{s} + r_{t} + r_{a}r_{s}v_{s} \right)^{- 1} + v_{s}$$

Where v~s~ is the gravitational settling velocity, a function of
particle size and density. GENII uses the same settling velocity as that
used in the EPA ISC3 model, or \[GENII SDD\]:

![](media/image8.wmf)

  ----------- --- --------------------------------------------------------
  Where ρ     =   the particle density (g/cm^3^)

  ρ~AIR~      =   the air density (assumed to be 1.2E-3 g/cm^3^)

  d~p~        =   the particle diameter (μm)

  μ           =   the absolute viscosity of air (assumed to be 1.81E-4
                  g/cm/s)

  c~2~        =   air units conversion constant (assumed to be 1E-8 cm^2^/
                  μm^2^)

  S~CF~       =   the slip correction factor, which is computed as (1):
  ----------- --- --------------------------------------------------------

[]{.mark}

![](media/image9.wmf)

Where x~2~, a~1~, a~2~, and a~3~ are constants with values of 6.5E-6,
1.257, 0.4, and 0.55E-4, respectively.

##### Wet Deposition 

Wet deposition of gases is modeled under an assumption that the exchange
of gas between air and precipitation is sufficient to maintain
equilibrium between the concentrations in the air and in the
precipitation. The flux of gas to the ground surface is therefore
proportional to the concentration of gas in air at ground level, the
precipitation rate, and a solubility constant related to the Henry's Law
constant for the gas. The wet deposition rate is given by (1):

  ----------- --- --------------------------------------------------------
  ω~2ij~(t)   =   v~dw~ X~ij~(t).

  Where       =   the wet deposition rate for gas at position i,j at time
  ω~2ij~(t)       t (g/(s m^2^)).

  v~dw~       =   the wet deposition velocity (m/s).

  X~ij~(t)    =   the concentration at a one-meter height above ground
                  surface at position i,j at time t.

  And v~dw~   =   c S P~.~

  Where S     =   the solubility coefficient (dimensionless).

  P~r~        =   the precipitation rate in mm/hr.

  c           =   a conversion factor to convert P~r~ to m/s.
  ----------- --- --------------------------------------------------------

For gases, it is assumed for GENII that the gases are dissolved rapidly
by precipitation. The wet deposition model for snow is assumed to be
zero if the temperature is less than --3^o^C. (If temperature data are
not available, the wet deposition velocity is zero for all forms of
frozen precipitation.) This assumption is made because unless the
precipitation is liquid, or has a liquid exterior, the rate of exchange
of gases between air and ice is negligible.

For particulates, wet deposition is given by the following model,
assuming that the particles are irreversibly collected by impaction as
the precipitation falls through the plume (1):

![](media/image10.wmf)

Where Λ is the washout coefficient, a function of the type of
precipitation (liquid or frozen), the precipitation rate, and the
precipitation collection efficiency.

This integral can be approximated as follows for sector-averaged point
sources (1):

![](media/image11.wmf)

Where Q' is the release rate corrected for depletion and decay*.*

For rain and drizzle, GENII uses the following expression to calculate
the washout coefficient (1):

![](media/image12.wmf)

  ----------- --- --------------------------------------------------------
  Where Λ~r~  =   the washout coefficient for rain (hr^-1)^

  C           =   empirical constant with a value of 0.5

  E           =   the average collection efficiency, assumed to be unity

  P~r~        =   precipitation rate in mm/hr

  P~n~        =   normalized precipitation rate (P~r~/1 mm/hr)
  ----------- --- --------------------------------------------------------

During periods of hail, snow, and other frozen precipitation, GENII
calculates the washout coefficient as (1):

![](media/image13.wmf)

  ----------- --- --------------------------------------------------------
  Where Λ~s~  =   the washout coefficient for snow (hr^-1^)

  0.2         =   empirical constant with units of mm^-1^

  P~s~        =   precipitation rate in mm/hr, liquid water equivalent
  ----------- --- --------------------------------------------------------

##### Total Deposition 

Given the above formulas for wet and dry deposition, the surface
contamination that accumulated at any point during any short period is
given as (1):

![](media/image14.wmf)

Where D(x,y,T) is the total surface contamination (Ci/m^2^) at position
(x,y) and for time period T. ω~1ij~, ω~2ij~, and ω~3ij~ are the
deposition rates for dry deposition, rain deposition, and snow
deposition, respectively. The total deposition rate, which is calculated
for the GENII chronic models, is (1):

![](media/image15.wmf)

##### Radioactive Decay 

Radionuclide decay is considered as radionuclides transit between the
source and the receptor. For most radionuclides of interest, the decay
is negligible, as is the buildup of daughter products. The algorithm for
describing radionuclide decay during plume transit is given in Section
5.3.6 and Appendix C of the GENII SDD. The general procedure described
in Appendix C for calculating decay chains includes branching as
addressed in \[Kennedy and Strenge\] (16), and in \[Strenge 1997\] (17).
Appendix C of the GENII SDD also references \[Lederer and Shirley\] (18)
and the International Commission on Radiation Protection in ICRP
Publication 38 \[ICRP-38\] (19) for data on radionuclide half-lives,
decay chains, and fractional branching within chains. Half-lives for the
radionuclides considered in this report (including daughter products)
are listed, in units of days, in Table D-3. They were obtained from
Appendix E of \[Kennedy and Strenge\] (16). Half-lives are given as the
relationship, log~e~(2)/λ~i~, where λ~i~ is the radionuclide decay
constant in units (in this case) of days^-1^.

Table D‑3 Half-Lives (days) for Radionuclides Considered in This Report

  ----------- ----------- ----------- ----------- ----------- -----------
  Isotope     Half-Life   Isotope     Half-Life   Isotope     Half-Life

  ^3^H        4.51E+3     ^95^Nb      3.52E+1     ^231^Th     1.06E+0

  ^14^C       2.09E+6     ^95^mNb     3.61E+0     ^234^Th     2.41E+1

  ^32^P       1.43E+1     ^99^Tc      7.78E+7     ^234^U      8.93E+7

  ^35^S       8.74E+1     ^103^Ru     3.93E+1     ^235^U      2.57E+11

  ^41^Ar      7.63E-2\*   ^106^Ru     3.68E+2     ^236^U      8.55E+9

  ^60^Co      1.93E+3     ^129^I      5.73E+9     ^238^U      1.63E+12

  ^65^Zn      2.44E+2     ^131^I      8.04E+0     ^238^Pu     3.20E+4

  ^89^Sr      5.05E+1     ^134^Cs     7.53E+2     ^239^Pu     8.79E+6

  ^90^Sr      1.06E+4     ^137^Cs     1.10E+4     ^240^Pu     2.39E+6

  ^90^Y       2.67E+0     ^141^Ce     3.25E+1     ^241^Am     1.58E+5

  ^95^Zr      6.40E+1     ^144^Ce     2.84E+2                 
  ----------- ----------- ----------- ----------- ----------- -----------

\*From \[FGR-13\] (20).

##### Correction of Release Rate 

To determine the concentrations of radionuclides at the point of
interest, one must subtract those radionuclides that are lost through
deposition and decay before reaching the point of interest. This is done
for the basic Gaussian plume model by correcting the radionuclide
release rate. For a given distance, x, from the source, one calculates
an effective release rate, Q'(t), in units of Ci/s or Bq/s, which is
equal to the actual release rate from which one subtracts the loss up to
point x from deposition and decay. This assessment is done in GENII
through consideration of conservation of mass. For plume models, the
depletion of the source term per unit distance is given as (1):

![](media/image16.wmf)

This integral can be solved to give a second integral which is
approximated in GENII using a trapezoidal rule. Because the
calculational procedure breaks down very close to the source, no
depletion is assumed to occur within 100 meters of the source. (See
Chapter 5 of \[GENII SDD\].)

#### Calms

The straight line Gaussian plume model cannot be derived for zero wind
speeds. In GENII, a minimum wind speed (1 m/s) is assumed for calm
conditions, and a randomly-selected direction. Unless the user of GENII
supplies a distribution of low wind speed directions, all wind
directions are assumed for GENII to be equally likely (1).

### Application of Air Transport Models to SRS

Fifteen major sources of radionuclide release to air were identified.
These 15 sources were then collapsed to four virtual sources of which
three are represented by a release point of 61 meters above ground level
(AGL) and one of 10 meters AGL ([Appendix
A](../Appendix_A%20-%20ready%20for%20CDC%20031405.doc)).

To estimate transport from these virtual sources to exposure locations,
the preparers had to develop a set of meteorological data that reflected
the meteorological conditions that existed between 1954 and 1992. The
principal need for the meteorological data was to establish the joint
frequency distributions for input to the GENII computer code.

It would have been desirable to use SRS-specific meteorological data
that spanned the entire 39-year period of operations. Unfortunately, the
SRS meteorological program was only established in the early 1970's,
leaving a gap of about 20 years in SRS-specific meteorological data.

**Data from nearby weather stations.** To approximate meteorological
data for the entire 39 years of operation, data from nearby locations
was considered. Yet this approach would have contained pitfalls as
illustrated in \[Weber 2001\] (21).

\[Weber 2001\] documented the results of a study performed by
Westinghouse Savannah River Company and Oregon State University to
create a meteorological database for SRS for the years 1955 through 1961
(21). The authors of this study projected 1992-1996 data from reasonably
close National Weather Service (NWS) stations to the 1955-1961 time
period at SRS.

The two sets of NWS data used for the study were obtained from NWS sites
near the Columbia, South Carolina, airport (CAE) and Bush Field near
Augusta, Georgia (AGS). Figure D-3 \[from Weber 2001\] and Table D-4
\[from Weber 2001\] respectively illustrate the locations of these two
airports relative to SRS and summarizes the differences in measurement
parameters relative to SRS.

Columbia, South Carolina, and Augusta, Georgia, lie about 90 km apart
from one another in the South Carolina Piedmont, a primarily
agricultural area broken by forests, streams, and small communities. The
Augusta NWS station is about 30 km west-northwest of the SRS
meteorological station, while the Columbia NWS station is about 80 km
northeast of the SRS meteorological station. The terrain surrounding the
Columbia NWS station more closely resembles SRS than that surrounding
the Augusta NWS station, which is located near swampy terrain in the
Savannah River drainage basin. Fog and calm wind conditions occur much
more frequently at Augusta than at Columbia or SRS. Also, the wind
direction at the Augusta NWS is influenced by "channeling" caused by the
presence of the Savannah River.

Unlike the meteorological data for SRS, which are obtained from a
61-meter tower (the same height as the stacks at SRS that are primarily
responsible for airborne radionuclide release), the data at the Augusta
and Columbia NWS stations were obtained from a 10-meter tower. The
instrumentation at Augusta and Columbia was less sensitive than that at
SRS, so that low wind speeds at Augusta and Columbia were more likely to
be recorded as "zeros" (calms) than as actual measurements of speed and
direction. In addition, the meteorological data at the Augusta and
Columbia NWSs were 2-minute averages at the top of each hour (or 1/30 of
the weather conditions over each hour). The SRS data, however, are
averaged continuously over one-hour intervals.

To illustrate the variability in meteorological conditions that can
occur between locations that are nominally close, wind roses for the
years 1992 to 1996 are provided in Figure D-4 \[from Weber 2001\] for
Augusta, Columbia, and SRS. These wind rose plots depict the frequency
of the direction from which the wind is blowing along with the wind
speeds. As shown, the Columbia wind rose shows more frequently northerly
winds than does that for SRS, although in both cases winds seem to
predominately blow from either the north-through-east sectors or the
south-through-west sectors. SRS winds blow more frequently from the
southeast than do Columbia winds. The Augusta wind rose is more nearly
symmetrical than that for either SRS or Columbia.

The authors \[Weber 2001\] also compared long-term average data for
Augusta and Columbia NWSs. They determined that the 1948-1995 wind rose
for Columbia was similar to the 1992-1996 SRS wind rose, and that the
1948-1995 wind rose for Columbia was more similar to a 1955-1961
Columbia wind rose than to the 1992-1996 Columbia wind rose. "In spite
of the fact that the 1992-96 time period (as evidenced by the CAE wind
rose) is not representative of the longer-term trends, it was
nevertheless used to provide the basis for representing the wind
direction at SRS" (21).

Hence, the authors projected SRS meteorological conditions at a 61-meter
level for the years 1955 through 1961using recorded data at a 10-meter
level for the 1992-1996 time period from the Columbia NWS station. They
used three different statistical techniques: (1) a linear regression
method, (2) a similarity theory approach, and (3) a statistical
differences method. They judged the last method to give the "best"
\[quotes in original\] statistical distribution because of its superior
distribution function and lack of appreciable bias (21).

![](media/image17.png){width="4.672916666666667in"
height="4.486111111111111in"}

**Figure D‑3 Map of SRS Showing the Locations of Augusta and Columbia
National Weather Service Stations**[^9]

Table D‑4 Differences Between Measurement Parameters for Augusta and
Columbia National Weather Stations and for SRS

  ----------------- ----------------- ----------------- -----------------
  Difference        Savannah River    Columbia, SC NWS  Augusta, GA NWS
                    Site              (CAE)             (AGS)

  Height of Sensors 61 meters.        10 meters.        10 meters.

  Instrument        High sensitivity. Robust            Robust
  Sensitivity                         instrumentation   instrumentation
                                      but low           but low
                                      sensitivity.      sensitivity.

  Averaging Time    One hour          Two minute        Two minute
                    (continuous).     "snapshots".      "snapshots".

  Topographical     Pine tree forest. Airport location. Airport location.
  Influences        Mostly flat       Lies near         Lies at the edge
                    within 2 km of    partially         of the Savannah
                    the tower. Modest developed         River drainage
                    terrain changes   suburban          basin.
                    beyond.           landscape.        
  ----------------- ----------------- ----------------- -----------------

Source: \[Weber 2001\] (21).

**Decision to use twenty-year averages.** The preparers might have used
the projected metrological conditions determined in \[Weber 2001\] for
this report. The preparers did not do so, however, because it only
covered the years 1955 through 1961, leaving a meteorological data gap
about a decade long. The scope of this study did not include preparation
of this projected data. In addition, it was not apparent that use of the
information from \[Weber 2001\] would have added add appreciably, if at
all, to the accuracy of the doses calculated for this study.

Therefore, it was decided to use SRS-specific data from the SRS
meteorological station to represent the entire 39 years of operation.
Because joint frequency distribution data from the SRS meteorological
station was available only as five-year averages, the prepareres
averaged four five-year averages to arrive at a twenty-year average.

![](media/image18.png){width="3.5305555555555554in"
height="3.4166666666666665in"}\
![](media/image19.png){width="6.496527777777778in"
height="3.803472222222222in"}

**Figure D‑4 1992-1996 Wind Rose Plots for SRS and the Columbia and
Augusta National Weather Service Stations**[^10]

## Transfer and Exposure Pathways

This section presents the mathematical relationships used in GENII to
model the transfer of radionuclides through air and water exposure
pathways. The mathematical relationships are from Chapters 9 and 10 of
the GENII SDD. This section summarizes the equations used for most
radionuclides as well as those used for the behavior of tritium and
^14^C in environmental pathways.

The general form of the equations in this section can be depicted as
Figure D.5.

Given a concentration of a radionuclide in air (Ci/m^3^ or Bq/m^3^) or
water (Ci/L or Bq/L) at an exposure location, the mathematical
relationships model the movement of radionuclides through each pathway.
Each relationship is composed of a set of parameters, each requiring a
numerical value. To avoid a voluminous and complicated appendix, we
generally defer a discussion of the assumed values for parameters that
are used in the base-case GENII calculations to other appendices. Some
parameters pertain to site-specific considerations such as the density
of soil (see [Appendix
F](../Appendix_F%20tables%20-%20Ready%20for%20CDC%20031405.doc)).
Others, called Usage Factors in Figure D.5, pertain to human activities
that influence the uptake or exposure to radionuclides (e.g., time spent
in an exposure location) and are determined in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc) in accordance with
the exposure scenarios discussed in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

Figure D‑![](media/image20.wmf) Illustration of General Form of
Equations in Section D.3

The GENII mathematical relationships first determine the following
information:

-   Annual radionuclide activity ingested (Bq in a year) for ingestion
    exposure pathways

-   Annual radionuclide activity inhaled (Bq in a year) for inhalation
    exposure pathways

-   Annual average exposure factor for external radiation exposure
    pathways. Units depend on whether exposure results from immersion in
    air (Bq/m^3^) or water (Bq/L), or from proximity to soil or sediment
    (Bq/kg) or water (Bq/L).

GENII then multiplies this information by dose and risk relationships
that are described in \[GENII SDD\] and summarized in Section D.4.

Not all exposure pathways that are considered in this report may be
appropriate for a specific receptor. This situation is illustrated in
Table D-5. Although all of the scenario families were exposed to
radioactive material through all airborne pathways, only some of the
scenario families were exposed to radioactive material through the
surface water pathways. Also, the exposure of individual members of each
scenario family was different depending on the member. For example, the
adult female member of the Urban Family spent her entire time in
Augusta, GA. The adult male member of the Urban Family spent 2000 hours
a year on the SRS site and the remaining hours in Augusta.

### Inhalation of Contaminated Air

Section D.2.1 addresses models describing the movement of radionuclides
through the air pathway. The output of the model is the radionuclide
concentration (Bq/m^3^) at the receptor location, assuming a receptor
height of 1 meter, as a function of time (e.g., average concentration
over a year).

Exposure as a function of location and time is modeled as an average
concentration of radionuclides in air that is inhaled over the time
period of concern. The amount that is inhaled is a function of the
average breathing rate, which depends on the age of the receptor.

The total amount of radioactive material that is inhaled is given as
(1):

  ------------ --- --------------------------------------------------------
  I~aaig~(T)   =   C~aag~ U~aag~ T~aag~ ED~aag~

  Where        =   total intake of radionuclide i from air inhalation over
  I~aaig~(T)       the period T at air usage location a for individuals in
                   age group g (Bq)

  C~aag~       =   average air concentration for radionuclide i at air
                   usage location a over time period T (Bq/m^3^)

  U~aag~       =   inhalation rate at air usage location a for individuals
                   in age group g (m^3^/d)

  T~aag~       =   annual intake factor giving days per year that air
                   inhalation occurs at air usage location a for
                   individuals in age group g (d/y)

  ED~aag~      =   exposure duration for the air inhalation pathway at air
                   usage location a for individuals in age group g (y).
  ------------ --- --------------------------------------------------------

Assumed parameter values for exposure times per individual, and average
breathing rates as a function of age group, are provided in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

Table D‑5 Transport, Transfer, and Exposure Matrix

  ----------- --------------- ------------ --------- -------- -------- -------- ---------- ---------- -------- ---------
  Transport   Transfer        Exposure     Section   Rural    Rural    Urban    Delivery   Outdoors   Family   Migrant
  Mechanism   Pathway or      Route                  Family   Family   Family   Person     Person     Living   Family
              Activity                               One      Two               Family     Family     Near     
                                                                                                      River    

  Air         Plume           Inhalation   D.3.3.1   X        X        X        X          X          X        X
  (Sections   Inhalation                                                                                       
  D.3.1 &                                                                                                      
  3.3.2)                                                                                                       

              Plume Immersion External     D.3.2     X        X        X        X          X          X        X

              Ground          External     D.3.3.2   X        X        X        X          X          X        X
              Contamination   Exposure                                                                         

                              Inhalation   D.3.3.3   X        X        X        X          X          X        X

                              Ingestion    D.3.3.4                                                             
                              Soil                                                                             

              Plant and Food  Ingestion:   D.3.4.1   X        X        X        X          X          X        X
              Concentration   Vegetables                                                                       
                              Fruit Grains                                                                     

              Animal Product  Ingestion:   D.3.4.2   X        X        X        X          X          X        X
              Concentration   Beef Poultry                                                                     
                              Milk Eggs                                                                        

  Surface     Aquatic         Ingestion    D.3.4.3                              X          X          X        
  Water       Accumulation                                                                                     
  (Section                                                                                                     
  D.2.3)                                                                                                       

              Concentration   External     D.3.5                                X          X          X        
              in Sediment     Exposure                                                                         

              Recreational    External     D.3.6.1                              X                     X        
              Swimming        Exposure                                                                         

                              Ingestion    D.3.6.2                              X                     X        

              Recreational    External     D.3.6.3                              X                     X        
              Boating         Exposure                                                                         
  ----------- --------------- ------------ --------- -------- -------- -------- ---------- ---------- -------- ---------

### Immersion in Plume of Contaminated Air

External exposures from immersion in a plume of contaminated air is
given as (1):

  ------------ --- --------------------------------------------------------
  I~eaig~(T)   =   C~eai~ (T) U~eag~ TC~p~

  I~eaig~(T)   =   average exposure factor over the period T for external
                   plume immersion exposure for radionuclide i for an
                   individual in age group g (Bq/m^3^)

  C~eai~ (T)   =   average air concentration over the period T at the
                   location of the exposed individual for radionuclide i
                   (Bq/m^3^)

  U~eag~       =   daily exposure factor (daily plume immersion exposure
                   time) giving hours of plume immersion exposure per day
                   for individuals in age group g (h/d)

  TC~p~        =   time correction set to T~eag~/(8760 h/y) for chronic
                   releases

  T~eag~       =   annual exposure factor (yearly plume exposure time)
                   giving the number of days in a year of external plume
                   immersion for individuals in age group g (d in a y).
  ------------ --- --------------------------------------------------------

Parameter values for calculating external doses from immersion in
contaminated air are provided in [Appendix
F](../Appendix_F%20tables%20-%20Ready%20for%20CDC%20031405.doc).
Important considerations are the age of the receptor, and the duration
of exposure.

### Ground Contamination Pathways

Exposures and resulting doses arising from ground contamination pathways
are addressed here and include external radiation exposures from
contaminated soil, inhalation of resuspended soil, and ingestion of
contaminated soil.

#### Contamination Buildup and Loss in Soil

To assess doses resulting from ground contamination pathways, one must
first consider processes for buildup and loss of radionuclides in soil.
Radionuclides accumulate in soil by wet and dry deposition from the air,
and from deposition via irrigation. (However, irrigation was not
considered a reasonable pathway for the scenarios defined for this
report.) Radionuclides are lost by leaching from the surface soil zone,
by harvesting vegetation that has taken up radionuclides from the soil,
and by radioactive decay. The general model for expressing the buildup
and loss of radionuclides from soil is a differential equation of the
form (1):

  ----------- --- --------------------------------------------------------
  dA~i~(t) /  =   (R~bi~ + R~ai~) - (λ~Li~ + λ~i~) A~i~
  dt              

  Where A~i~  =   amount of radionuclide i in the surface soil zone at
                  time t (atoms)[^11]

  R~ai~       =   rate of input from atmospheric depletion (wet and dry
                  deposition) (atoms/y)

  R~bi~       =   rate of input from irrigation water (atoms/y)

  λ~i~        =   radioactive decay constant for radionuclide i (y^-1^)

  λ~Li~       =   rate constant for leaching radionuclide from the surface
                  soil zone (y^-1^).
  ----------- --- --------------------------------------------------------

This model is solved in GENII by an integrator that considers
radionuclide decay chains. For chronic releases, the initial activity of
radionuclide in the soil is assumed to be zero.

Losses from harvest are handled outside this differential equation
because they occur as isolated events during the year rather than as a
continuous process. Losses from harvest are subtracted from the
calculated radionuclide amount via a step function at the time of
harvest.

Below we discuss the deposition of radionuclides from the air, leaching
from the soil zone, and loss by harvest.

##### Deposition from the Air 

Accumulation from deposition from the air is determined using the
calculational relationships for airborne deposition as presented in
Chapter 5 of the GENII SDD and summarized in Section D.2.1.6 of this
report. For chronic and essentially uniform release of radionuclides
over the course of multiple years (see next paragraph), initial
radionuclide concentrations in the upper surface of the soil zone are
set equal to zero. In each subsequent year the soil concentrations at
the end of the year are evaluated based on the concentrations present at
the beginning of the year as modified by activity deposited during the
year, and by activity lost considering decay and other processes. The
average concentration from past years' contributions is represented by
the term C~si~(T~yr~), with units of Bq/m^2^. Decay evaluations are made
using the GENII decay processor, which considers branching and ingrowth
of radioactive chains as needed.

As implied by the above paragraph, the system used in GENII to calculate
buildup over the course of several years was designed under the
assumption that releases to air (and surface water), and deposition over
time, are essentially constant per year. This assumption would be
consistent with use of the GENII code for preoperational evaluation of a
nuclear facility. In addition, the system for calculating doses and
risks using GENII was designed under the assumption that the same dose
and risk conversion factors would be used for each year (i.e., one
assumes a constant receptor age over the time period of concern).

But GENII is being used for this project for reconstructing past doses
and risks rather than evaluating the doses and risks that may result
from operation of a new or existing nuclear facility. Different
radionuclide release rates were considered for each of the 39 years of
operation, and also doses and risks to receptors as they grow up in the
area were considered, meaning that over 39 years several sets of
age-specific dose and risk conversion factors may be used for each
receptor as that receptor grows from an infant to an adult. To address
these calculational needs, GENII was linked to a custom-designed pre-
and post-processor. Doses and risks are calculated for each receptor
according to the receptor's age group, and summed over all operational
years.

To do this, separate GENII computations had to be made for each year of
operation. Each time this was done, the radionuclide concentrations in
the upper surface of the soil zone were set equal to zero as discussed
in the first paragraph of this section. Hence, although buildup in soil,
and loss through leaching from the surface soil zone, are considered
over the course of a year, buildup and loss that may have taken place
over all 39 years of SRS operation are not considered directly in GENII.
The implications of this calculational limitation on the results of the
study are addressed elsewhere.

##### Leaching from the Surface Soil Zone 

Removal from surface soils through leaching into deeper soils may be
addressed in GENII in three optional ways:

1.  Calculate leaching using GENII default leach rates.

```{=html}
<!-- -->
```
17. Calculate leaching using a soil removal formula.

18. Calculate leaching using user-provided leach rate constants.

For this report, leaching from the surface soil zone was calculated
using the second option: a soil removal rate constant, λ~si~. This
constant is calculated in GENII according to a general formula developed
by Baes and Sharp (22):

![](media/image21.wmf)

  ----------- --- --------------------------------------------------------
  Where λ~si~ =   removal rate constant for activity of radionuclide i in
                  the surface soil layer (y^-1^)

  P           =   total annual precipitation (cm/y)

  I           =   total irrigation rate (cm/y)

  E           =   total evapotranspiration rate (cm/y)

  d~s~        =   surface soil thickness (cm)

  ρ~s~        =   surface soil bulk density (kg/m^3^)

  Θ~s~        =   surface soil volumetric water content (mL/cm^3^)[^12]

  Kd~si~      =   surface soil distribution coefficient for radionuclide i
                  (mL/g)

  10^-2^      =   units correction factor (m/cm)

  10^3^       =   units correction factor (g/kg)

  10^-6^      =   units correction factor (m^3^/ml).
  ----------- --- --------------------------------------------------------

In the above equation, the surface soil thickness is the average
thickness of the surface soil. If the surface soil is agricultural land,
the thickness should be set to represent the plow layer. And where, for
this report,

The total infiltration rate is evaluated in GENII as the sum of the
total annual precipitation plus the irrigation rate minus the
evapotranspiration rate. It represents the quantity, (P + I -- E), in
the numerator of the above equation. Note that for this report, the
total irrigation rate, I, is assumed to equal zero based on the
scenarios defined for this report.

##### Loss by Harvest 

Loss of radionuclides from the surface soil zone is modeled in GENII as
a step function applied at the end of each year. The model accounts for
plant concentrations at harvest, the annual plant yield, and the soil
concentrations at harvest (1):

  ------------- --- --------------------------------------------------------
  C~si~(t~+~)   =   C~si~(t~-~) \[ (C~si~ -- C~ci~(Th~c~) Y~c~) / C~si~ \]

  Where         =   surface soil concentration at soil location s for
  C~si~(t~+~)       radionuclide i after correction for harvest removal at
                    time t (Bq/m^2^)

  C~si~         =   average (over the year) value of surface soil
                    concentration at soil location s for radionuclide i
                    (Bq/m^2^)

  C~si~(t~-~)   =   surface soil concentration at soil location s for
                    radionuclide i before correction for harvest removal at
                    time t (Bq/m^2^)
  ------------- --- --------------------------------------------------------

  -------------- --- --------------------------------------------------------
  C~ci~(Th~c~)   =   Concentration of radionuclide i in crop c at time of
                     harvest (Bq/kg)

  Y~c~           =   annual harvested yield of crop c (kg/m^2^).
  -------------- --- --------------------------------------------------------

In the above equation, the term on the right, within the square
brackets, represents the average (over a year) ratio of the contaminant
in soil to that in crops. This term is used rather than a simple
subtraction of amount harvested because, for short-lived radionuclides,
the amount harvested over the year might be larger than the amount
remaining in the soil at the end of the year.

In addition, the radionuclide concentration in each food crop considered
in GENII (C~ci~(Th~c~)) is calculated using the relationships described
in Section D.3.4.1 for ingestion of radionuclides through food crops.
However, for purposes of the ground contamination pathways, the
radionuclides that are ingrown into harvested food crops would be
removed from the analysis. (Radionuclides ingrown into food crops are,
of course, considered in the food crop ingestion analysis considered in
Section D.3.4.1.) Note that GENII allows the user to consider, for
purposes of harvesting, a different set of food crop growth parameters
(e.g., interception fractions, standing biomass) from those considered
for food crop ingestion (see Section F.4.2.1). In any event, for this
study, loss through harvesting is conservatively not considered. This
conservatism maximizes the concentrations of radionuclides assumed to be
concentrated in the top surface of the soil.

#### External Radiation Exposures from Contaminated Soil 

To determine exposures one must first calculate, over the year of
exposure considered, average soil concentration in units of Bq/m^2^.
This value is then divided by the soil areal density (units of kg/m^2^)
to obtain an average concentration in units of Bq/kg. The general form
of the equation to calculate average soil concentrations is (1):

![](media/image22.wmf)

  --------------- --- --------------------------------------------------------
  Where           =   average surface soil concentration (including
  C~esi~(T~yr~)       deposition) at soil location s for radionuclide i
                      including deposition during the year (Bq/kg)

  C~si~(T~yr~)    =   average surface soil concentration at soil location s
                      for radionuclide i at the start of the current year
                      (Bq/m^2^)

  R~ait~          =   constant deposition rate of radionuclide i from air for
                      year t (Bq/(m^2^y))

  R~wit~          =   constant deposition rate of radionuclide i from
                      irrigation water for year t (Bq/(m^2^y))

  d~s~            =   thickness of soil containing radionuclide contamination
                      (m)[^13]

  ρ~s~            =   density of soil (kg/m^3^)

  T~yr~           =   one year integration period (y).
  --------------- --- --------------------------------------------------------

The term on the right side of the equation, following the \[R~ait~ +
R~wit~\] term, represents the evaluation of the time-integral from
deposition onto soil at a constant rate. Accumulation occurs over a
one-year period. Division by the one-year period provides the average
soil concentration during the year.

The deposition rate for atmospheric (wet and dry) deposition is
described in Section D.2.1.6. Deposition from irrigation is not
considered (R~wit~ = 0.)

Once average soil concentrations (Bq/kg) are determined, the average
exposure factor for exposure to surface-contaminated ground is
calculated as (1):

  ------------ --- --------------------------------------------------------
  I~esig~(T)   =   C~esi~ (T) U~esg~ \[SH~h~ FT~hg~ + SH~o~ FT~og~\] T~esg~

  Where        =   average exposure factor over time period T for external
  I~esig~(T)       exposure to contaminated ground for radionuclide i for
                   individuals in age group g (Bq/kg)

  C~esi~ (T)   =   average soil concentration at the location of individual
                   exposure for radionuclide i for time period T (Bq/kg)

  U~esg~       =   daily exposure factor (daily external ground exposure
                   time) giving hours of exposure to contaminated ground
                   per day for individuals in age group g (h/d)

  SH~h~        =   shield factor (indoor shielding factor) for exposure to
                   soil while inside a home (dimensionless)

  FT~hg~       =   fraction of time spent inside a home (indoors) for
                   individuals in age group g (dimensionless)

  SH~o~        =   shield factor (outdoor shielding factor) for exposure to
                   soil while outside (dimensionless)

  FT~og~       =   fraction of time spent outside (outdoors) for
                   individuals in age group g (dimensionless)

  T~esg~       =   annual exposure factor (yearly external ground exposure
                   time) giving external ground exposure for individuals in
                   age group g (d).
  ------------ --- --------------------------------------------------------

Assumed values for U~esg~, SH~h~, FT~hg~, SH~o~, FT~og~, and T~esg~ are
provided as a function of receptor in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

#### Inhalation of Resuspended Soil

GENII uses a model for inhalation exposure from resuspended
radionuclides that incorporates a parameter called the resuspension
factor, a factor relating the soil concentration (per unit area) to the
air concentration (per unit volume), and is in units of m^-1^. The
mathematical equation for the model is (1):

![](media/image23.wmf)

  --------------- --- --------------------------------------------------------
  Where           =   air concentration of radionuclide i at soil resuspension
  C~sai~(T~yr~)       exposure location a for a one-year period (Bq/m^3^)

  RF~a~           =   resuspension factor for soil exposure location s (m^-1^)

  C~si~(T~yr~)    =   average surface soil concentration over the current year
                      at the soil exposure location s from material deposited
                      in earlier years (Bq/m^2^).
  --------------- --- --------------------------------------------------------

Other terms are as defined previously.

The resuspension factor may be estimated in more than one way. GENII
offers three optional methods for doing so (1). The method used for this
report was to input an assumed resuspension factor in units of m^-1^.

The resuspension factor had a different value depending on the location
where soil resuspension occurs. As addressed in Section F.3.1, a larger
resuspension factor was assumed for locations where there was likely to
be farming.

Once air concentrations are calculated, the total intake of
contamination over the period of concern is given as (1):

  ------------ --- --------------------------------------------------------
  I~saig~(T)   =   C~sai~(T) U~sag~ F~sag~ T~sag~ ED~sag~

  Where        =   total intake of radionuclide i from resuspension
  I~saig~(T)       inhalation over the time period T at soil usage location
                   a for individuals in age group g (Bq)

  C~sai~(T)    =   average concentration of radionuclide i in soil over
                   time period T at soil usage location s (Bq/m^2^)

  U~sag~       =   inhalation rate of air for the resuspension pathway at
                   soil location s for individuals in age group g (m^3^/d)

  F~sag~       =   fraction of a day that resuspension inhalation exposure
                   occurs at soil usage location s for individuals in age
                   group g (dimensionless)

  T~sag~       =   annual intake factor (resuspended soil inhalation
                   period) giving days per year that resuspension
                   inhalation occurs at soil usage location s for
                   individuals in age group g (d/y)

  ED~sag~      =   exposure duration for the resuspension inhalation at
                   soil usage location s for individuals in age group g
                   (y).
  ------------ --- --------------------------------------------------------

The exposure duration (ED~sag~) accounts for possible multiple years of
exposure from deposition of radionuclides onto the ground during these
years at a constant rate. As addressed in Section D.3.3.1, this period
is set at one year because deposition is not constant from year to year,
and because multiple age-specific sets of risk and dose conversion
factors must be considered. Otherwise, assumed values for U~sag~,
F~sag~, and T~sag~ are provided in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

#### Inadvertent Ingestion of Soil

Inadvertent ingestion of soil is evaluated in the following manner (1):

$C_{\text{dsi}}\left( T_{\text{yr}} \right) = \frac{\text{10}^{3}}{\text{10}^{4}\rho_{s}d_{s}}\left\lbrack C_{\text{si}}\left( T_{\text{yr}} \right) + \frac{R_{\text{ait}} + R_{\text{wit}}}{\lambda_{i}T_{\text{yr}}}\left( T_{\text{yr}} - \frac{1 - e^{- \lambda_{i}T_{\text{yr}}}}{\lambda} \right) \right\rbrack$

  --------------- --- --------------------------------------------------------
  Where           =   average concentration at soil location s for
  C~dsi~(T~yr~)       radionuclide i in soil consumed during the current year
                      (Bq/kg)

  C~si~(T~yr~)    =   average surface soil concentration at soil location s
                      for radionuclide i during the current year (Bq/m^2^)

  ρ~s~            =   density of surface soil (g/cm^3^)

  d~s~            =   thickness of contaminated surface soil layer (cm)
  --------------- --- --------------------------------------------------------

  ----------- --- --------------------------------------------------------
  10^4^       =   units conversion factor (cm^2^/m^2)^

  10^3^       =   units conversion factor (g/kg).
  ----------- --- --------------------------------------------------------

Other terms are as previously defined.

The total intake is then calculated from the average soil concentration
(C~dsi~(T~yr~)) as follows (1):

  ------------ --- --------------------------------------------------------
  I~dsig~(T)   =   10^-6^ C~dsi~(T) U~dsg~ T~dsg~ ED~ds~

  Where        =   total intake of radionuclide i from inadvertent soil
  I~dsig~(T)       ingestion over time period T at soil usage location s
                   for individuals in age group g (Bq)

  C~dsi~(T)    =   average soil concentration for radionuclide i at soil
                   usage location s for time period T (Bq/m^2^)

  U~dsg~       =   ingestion rate for soil location s for individuals in
                   age group g (mg/d)

  T~dsg~       =   annual intake factor (soil contact days) giving days per
                   year that ingestion occurs at soil usage location s for
                   individuals in age group g (d/y)

  ED~ds~       =   exposure duration for the soil ingestion pathway at soil
                   usage location s for individuals in age group g (y)

  10^-6^       =   units conversion factor (mg/kg).
  ------------ --- --------------------------------------------------------

As above, the exposure duration (ED~ds~) accounts for possible multiple
years of exposure from deposition of radionuclides onto the ground
during these years at a constant rate. As addressed in Section D.3.3.1,
this period is set at one year because deposition is not constant from
year to year, and because multiple age-specific sets of risk and dose
conversion factors must be considered. Otherwise, assumed values for
U~dsg~, and T~dsg~ are provided in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

### Food-Chain Transport and Exposure

This section covers the following exposure pathways:

  --------- --------------------------------------------------------------
  Section   Section Description

  D.3.4.1   Ingestion of food crops contaminated with radionuclides,
            including deposition (surface) contamination as well as root
            uptake.

  D.3.4.2   Ingestion of animals (e.g., livestock) and animal products
            (e.g., eggs) that have taken up radionuclides through
            consumption of contaminated forage (from deposition) or
            consumption of contaminated surface water.

  D.3.4.3   Ingestion of contaminated aquatic foods (fish, shellfish,
            etc.)
  --------- --------------------------------------------------------------

These three exposure pathways model transfer of radionuclides through
food pathways. The calculations are normally performed using variables
generally called transfer factors that describe the ratio (at
equilibrium) between contamination levels in two types of media (or
environmental compartments). Some variables are partition coefficients
--- for example, the ratio of contamination levels in soil and in a
plant that grows in soil. Other variables describe the steady state
ratio between contamination levels in plant matter and contamination
levels in animal products (meat, eggs, or milk) that is produced from an
animal that consumes the plant matter at a unit intake rate. Still other
variables characterize bioaccumulation processes, such as those for fish
and shellfish..

Although a substantial body of literature exists for various transfer
values, there is considerable uncertainty in any single value assigned
to a transfer factor. For this reason, we discuss the selection of
values for transfer factor parameters in detail, mainly in [Appendix
F](../Appendix_F%20tables%20-%20Ready%20for%20CDC%20031405.doc).

#### Ingestion of Food Crops

This section addresses direct ingestion of crops and plants grown in
contaminated soil or dusted with deposited and resuspended soil. These
crops and plants include leafy vegetables, other vegetables, cereal
grains, and fruit. Special models for calculation of uptake of tritium
and ^14^C in food products are also described. Similar models are used
to calculate uptake by animals that are then used as food products by
humans. Human ingestion of animal products, including cow's milk, beef
and meat, poultry, and eggs from poultry, is considered in Section
D.3.4.2.

##### Radionuclide Concentration in Soil

Deposition considered for the terrestrial food pathways is the
deposition that is modeled to exist at the location where the farm
product is produced. This deposition is considered as an average value
obtained from the output of the atmospheric transport model addressed in
Section D.2. The annual average deposition is evaluated as the time
integral of the deposited activity for deposition at a constant rate.

Deposition, accumulation, and loss is modeled as a differential equation
of the following form (1):

$\frac{d\ C_{\text{ai}}(t)}{d\ t} = R_{\text{ait}} - \lambda_{i}C_{\text{ai}}(t)$

  ----------- --- --------------------------------------------------------
  Where       =   areal concentration from deposition from air to soil or
  C~ai~(t)        plants at location a for radionuclide i as a function of
                  time (Bq/m^2^).

  R~ait~      =   constant deposition rate of radionuclide i from air at
                  location a (Bq/m^2^ y).

  λ~i~        =   radiological decay constant for radionuclide i (y^-1^).
  ----------- --- --------------------------------------------------------

The atmospheric deposition rate is the sum of the dry and wet deposition
rates.

The soil concentration is used when estimating root uptake to plants, as
well as the resuspension and re-deposition of activity onto plant
surfaces. The concentration during the year is calculated as the sum of
the surface soil concentration from the soil model, C~si~(T~yr~),
discussed previously. The soil concentration is addressed as follows,
where the amount deposited is calculated as the time-integral of
deposition over the particular annual period considered (1):

$C_{\text{ci}}\left( T_{\text{yr}} \right) = C_{\text{si}}\left( T_{\text{yr}} \right) + \frac{R_{\text{ait}} + R_{\text{wit}}}{\lambda_{i}\ T_{\text{yr}}}\left\lbrack T_{\text{yr}} - \frac{1 - e^{- \lambda_{i}T_{\text{yr}}}}{\lambda_{i}} \right\rbrack$

  ------------------- --- --------------------------------------------------------
  WhereC~ci~(T~yr~)   =   average concentration of radionuclide i in farmland soil
                          for crop type c during the year considered (Bq/m^2^).

  C~si~(T~yr~)        =   the average concentration during the current year of
                          radionuclide i in surface soil in location s (where crop
                          c is grown) for deposition from earlier years (Bq/m^2^).
  ------------------- --- --------------------------------------------------------

Other terms are as previously defined.

##### Radionuclide Concentration in Food Crops

The concentration in plants at the time of harvest is calculated as the
sum of contributions from deposition onto plant surfaces, plus uptake
through roots. Deposition onto plant surfaces includes deposition
directly onto plant surfaces, as well as deposition from material
resuspended from soil. The general form of the model is given as (1):

$\begin{array}{r}
C_{\text{dci}}\left( T_{\text{yr}} \right) = \left\lbrack R_{\text{aitd}}r_{\text{dc}} + R_{\text{aitw}}r_{\text{we}} + 3\text{.}\text{15}E7C_{\text{ci}}\left( T_{\text{yr}} \right)\text{RF}_{c}\text{Vd}_{i}r_{\text{dc}} + R_{\text{wit}}\frac{\text{12}r_{\text{ic}}}{M_{c}} \right\rbrack \\
\frac{T_{\text{Vc}}}{B_{c}}\left\lbrack \frac{1 - e^{- \lambda_{\text{wi}}\text{Tg}_{c}2\text{.}\text{74}E - 3}}{\lambda_{\text{ei}}} \right\rbrack
\end{array}$

  --------------- --- --------------------------------------------------------
  Where           =   concentration of radionuclide i on plant type c at
  C~dci~(T~yr~)       harvest from deposition processes for a one-year period
                      (Bq/kg wet weight)

  T~yr~           =   one-year exposure period (y)

  r~dc~           =   interception fraction from airborne dry deposition for
                      plant type c (dimensionless)

  r~wc~           =   interception fraction for airborne wet deposition to
                      plant type c (dimensionless)

  C~ci~(T~yr~)    =   average concentration of radionuclide i in farmland soil
                      for crop type c for the current one-year period
                      (Bq/m^2^)

  RF~c~           =   resuspension factor for crop soil (m^-1^)

  Vd ~i~          =   deposition velocity of radionuclide i (m/s)[^14]

  12              =   months per year

  r~ic~           =   interception fraction for irrigation deposition to plant
                      type c (dimensionless), and assumed to be generally
                      equivalent to r~wc~

  M~c~            =   irrigation period for plant type c (month)

  T~Vc~           =   translocation factor for plant type c (dimensionless)

  B~c~            =   total standing biomass for plant type c (kg wet
                      weight/m^2^)

  λ~e~            =   λ~wi~ + λ~i~

  λ~wi~           =   weathering rate constant for crops for radionuclide i
                      (y^-1^)[^15]

  Tg~c~           =   crop growing period for plant type c (d)

  3.15E+7         =   units conversion factor (sec/y)

  2.74E-3         =   units conversion factor (y/d).
  --------------- --- --------------------------------------------------------

And where irrigation is assumed not to occur for scenarios defined for
this report.

The plant concentration at harvest from root uptake is given as (1):

$C_{\text{rci}}\left( T_{\text{yr}} \right) = \frac{C_{\text{ci}}\left( T_{\text{yr}} \right)\text{RP}_{\text{sc}}\text{Bv}_{\text{ci}}f_{c}}{P_{3}}$

  --------------- --- --------------------------------------------------------
  Where           =   concentration of radionuclide i in crop type c from root
  C~rci~(T~yr~)       uptake pathways for a one-year period (Bq/kg wet weight)

  Bv~ci~          =   concentration ratio for root uptake of radionuclide i in
                      crop type c (Bq/kg dry plant per Bq/kg dry soil)

  f~c~            =   dry-to-wet ratio for plant type c (kg dry plant/kg wet
                      plant)

  P~3~            =   areal soil density of farmland soil (kg/m^2^)

  RP~3~           =   fraction of plant type c having roots in surface soil
                      zone (dimensionless).
  --------------- --- --------------------------------------------------------

The total concentration in the plant at the time of harvest is the sum
of the contribution from the deposition and root uptake pathways, or:

$$C_{\text{hci}}\left( T_{\text{yr}} \right) = C_{\text{dci}}\left( T_{\text{yr}} \right) + C_{\text{rci}}\left( T_{\text{yr}} \right)$$

Where C~hci~(T~yr~) is the concentration in plant type c at harvest for
a one-year period (Bq/kg wet weight). Other variables have already been
defined.

##### Radioactive Decay

GENII has the capability of evaluating radionuclide decay between
harvest of food crops and consumption of the crops by humans. The decay
calculation is performed in GENII, considering decay chains and
branching, using the decay processor described in Section D.2.1.6 of
this report. For most radionuclides (those for which decay chains and
branching is not a factor), the decay calculation is calculated as
follows (1):

  --------------- --- --------------------------------------------------------
  C~csi~(T~yr~)   =   C~hei~(T~yr~) e^-\ λi\ Thc\ 2.74E-3^

  Where           =   concentration of radionuclide i in crop type c at
  C~csi~(T~yr~)       location s at the time of consumption over a one-year
                      period (Bq/kg wet weight)

  Th~c~           =   holdup delay time between harvest and consumption for
                      crop type c (d)

  λ ~i~           =   radiological decay constant for radionuclide i(y-1)

  2.74E-3         =   Conversion factor, years per day (1 year /365 days).
  --------------- --- --------------------------------------------------------

##### Interception Factor and Dry-to-Wet Ratio

This factor (also called interception fraction, or retention fraction)
accounts for the fact that not all material deposited from the air lands
on plant surfaces. A fraction deposited from the air lands on plant
surfaces, while the remaining fraction misses plant surfaces and lands
on soil. GENII provides two optional methods for performing calculations
using the interception fraction (1). These calculations were performed
using user-defined values for wet and dry interception (dimensionless).
The assumptions for the wet and dry interception factors, and for
dry-to-wet ratios, are presented in Section F.4.2.1.

##### Resuspension Factor 

The resuspension factor for crop soil (RFc) in the above equation is
essentially the same resuspension factor as that described in Section
D.3.3.3. RFc is in units of m^-1^ and is the ratio of the radionuclide
concentration in air (Bq/m^3^) to the areal concentration of
radionuclides in the top soil layer (Bq/m^2^). For this report, a larger
resuspension factor is assumed for locations where farming is assumed to
occur than for residential areas.

##### Translocation Factor and Weathering 

Material deposited on plant surfaces may be absorbed into the plant or
may be removed from the plant because of wind, rain, or other weathering
processes. The translocation factor (T~Vc~) is the fraction of the total
deposition on plant surfaces that is incorporated into the edible parts
of the plant. As a GENII default, a value of 0.1 is assumed for all
vegetation except for leafy vegetables and forage crops, for which a
value of unity is assumed. (The GENII user may input different assumed
parameter values, however.)

Weathering is accounted for by a rate constant, λ~wi~, in units of
days^-1^, and the GENII default value for this parameter is 14 d^-1^.

##### Tritium and ^14^C Calculations 

Concentrations of tritium and ^14^C in soil and plants are assumed to be
related to the specific activity of these radionuclides in the air or
water media. *Need better words.* The fractional content of hydrogen or
carbon in a plant or animal product is used to calculate the
concentration of tritium or ^14^C in the product.

**Tritium.** The hydrogen content in the aqueous (HTO) and dryer
portions of the food products is considered when calculating tritium
concentration. Also addressed is the creation of organically-bound
tritium (OBT) in plant (and animal) products.

Models for tritium are different depending on whether the tritium exists
as tritiated water (HTO) or as elemental hydrogen gas (HT).

The general equation for calculating concentrations of tritium as HTO in
plant products (Bq per kg of fresh matter) is (1):

  ----------- --- --------------------------------------------------------
  C~pp_HTO~   =   RF~pp~ C~am~ F~fw_pp~

  Where       =   the concentration of HTO in the "wet" (fresh matter
  C~pp_HTO~       (fm)) portion of plant products (Bq/kg fm).

  RF~pp~      =   a reduction factor that accounts for low soil
                  concentrations relative to concentrations in air
                  moisture (varies by vegetable type) (see below)

  C~am~       =   the concentration of tritium as HTO in air moisture
                  (Bq/L), which is determined by dividing the tritium
                  concentration in air (Bq/m^3^) by the absolute humidity
                  in units of (kg or L per m^3^)

  F~fw_pp~    =   the fresh weight fraction (the fraction of the plant
                  having a high aqueous content), which is dimensionless
                  and varies by plant type.
  ----------- --- --------------------------------------------------------

For GENII, it is assumed that the concentration of HTO in plant water
equals 0.9C~am~ for leafy vegetables and pasture and 0.8C~am~ for fruit,
root crops and other vegetables, and grain. (That is, RF~pp~ = 0.9 for
leafy vegetables and pasture, and RF~pp~ = 0.8 for fruit, root crops and
other vegetables, and grain.) These reduction factors account for
dilution from soil water, which has a lower tritium concentration than
does air moisture and which affects fruit and root crops more than
leaves.

The general equation for calculating concentrations of tritium as OBT in
plant products (Bq per kg of fresh matter) is (1):

  ----------- --- --------------------------------------------------------
  C~pp_OBT~   =   RF~1~ ID~pp~ C~am~ F~dm_pp~ W~eq_pp~

  Where       =   Tritium concentration existing as OBT in plant products
  C~pp_OBT~       (Bq/kg fw)

  RF~1~       =   Reduction factor for plant leaves (0.9)

  ID~pp~      =   isotopic discrimination factor for plant products (0.9)

  F~dm_pp~    =   the dry weight fraction (the fraction of the plant have
                  a very low aqueous content), which is dimensionless and
                  varies by plant type.

  W~eq_pp~    =   water equivalent factor (dimensionless), which varies by
                  plant type.
  ----------- --- --------------------------------------------------------

OBT concentrations are estimated assuming a plant water concentration of
0.9C~am~ for all types of plants (i.e., RF~1~ = 0.9.) OBT is assumed to
form exclusively in the leaves and be translocated to other parts of the
plant. Isotopic discrimination occurring in the formation of OBT is
conservatively assumed to result in an OBT concentration that is 0.9
times the concentration in plant water (ID~pp~ = 0.9.)

Parameter values for calculating HTO and OBT concentrations in plant
products (RF~pp~, RF~1~, ID~pp~, F~fw_pp~, F~dm_pp~, W~eq_pp~) are
"hard-wired" in GENII and are listed in Table D-6.

Table D‑6 Parameter Values for Calculating HTO and OBT Concentrations in
Plant Products

  -------------------------- ------------ ------- ------------ ------- ---------
  Parameter Values           Leafy        Fruit   Root & Other Grain   Pasture
                             Vegetables           Vegetables           

  Reduction Factor (RF~pp~)  0.9          0.8     0.8          0.8     0.9

  Reduction Factor for       0.9          0.9     0.9          0.9     0.9
  Leaves (RF~1~)                                                       

  Isotopic Discrimination    0.9          0.9     0.9          0.9     0.9
  Factor (ID~pp~)                                                      

  Fresh Matter Fraction      0.906        0.853   0.824        0.117   0.8
  (F~fw_pp~)                                                           

  Dry Matter Fraction        0.094        0.147   0.176        0.883   0.2
  (F~dm_pp~)                                                           

  Water Equivalent Factor    0.6          0.59    0.58         0.577   0.616
  (W~eq_pp~)                                                           
  -------------------------- ------------ ------- ------------ ------- ---------

Source: (1).

Calculation of tritium as elemental gas (HT) is performed in GENII as an
empirical relationship. Although elemental hydrogen is not readily taken
up into vegetation, HT is slowly oxidized into tritiated water by
microbes in soil. The GENII SDD references work by Peterson and Davis
who determined, after numerous observations, that the ratio of HTO in
air moisture to HT in air was about 8 (Bq/L)/(Bq/m^3^). This led to a
modification for GENII of the above model for uptake of HTO in plants,
where most terms remain the same but C~caH~ is approximated as 8C~caHT~
H, where H in this case is the absolute humidity. Peterson and Davis
also recommend that, for HT releases, the isotopic discrimination factor
ID~pp~ be set to 1.0, and the reduction factor for HTO, RF~pp~, be
replaced with a supplemental factor numerically equal to 1.5 (23). This
results in the following equation for uptake of tritium as HT in plants:

  -------------- --- ------------ ------------------------------------------------------
  C~pp_HT~       =   1.5          
                     (8C~caHT~)   
                     F~fw_pp~     

                 =   12 C~caHT~   
                     F~fw_pp~     

  And the uptake                  
  of tritium as                   
  HT in plants                    
  as OBT is                       
  given as:                       

  C~pp_OBT~          =            RF~1~ (8C~caHT~) F~dm_pp~ W~eq_pp~

                     =            8 RF~1~ C~caHT~ F~dm_pp~ W~eq_pp~

  Where:             =            Tritium concentration existing as OBT in plant
  C~pp_OBT,HT~                    products from HT (Bq/kg fw)

  RF~1~              =            Reduction factor for plant leaves (0.9)

  F~dm_pp~           =            the dry weight fraction (the fraction of the plant
                                  have a very low aqueous content), which is
                                  dimensionless and varies by plant type.

  W~eq_pp~           =            water equivalent factor, which is dimensionless and
                                  varies by plant type.
  -------------- --- ------------ ------------------------------------------------------

**Carbon-14.** It is assumed that plants obtain all carbon from airborne
CO~2~ and that animals obtain all carbon from ingestion of plants.
Because plants acquire most of their carbon from the air, transfer
through the root pathway is negligible. Models for ^14^C are similar to
those for tritium. The concentration of ^14^C in crops from atmospheric
contamination is (1):

$C_{\text{hcaC}}\left( T_{\text{yr}} \right) = \frac{C_{\text{aaC}}\left( T_{\text{yr}} \right)F_{\text{Cc}}}{P_{C}}$

  ---------------- --- -------------------------------------------------------
  Where            =   concentration of ^14^C in crop type c at harvest from
  C~hcaC~(T~yr~)       atmospheric deposition at year t (Bq/kg wet weight)

  C~aaC~(T~yr~)    =   annual average air concentration of ^14^C at usage
                       location a (Bq/m^3^)

  F~Cc~            =   fraction of carbon in crop type c (dimensionless)

  P~C~             =   concentration of carbon in the air (kg/m^3^).
  ---------------- --- -------------------------------------------------------

The concentration of ^14^C in crops from contamination in the surface
soil from initial or previous depositions is calculated from the average
annual soil concentration for ^14^C, or C~cC~(T~yr~) (1):

$C_{\text{hcsC}}\left( T_{\text{yr}} \right) = \frac{0\text{.}1F_{\text{Cc}}C_{\text{sC}}\left( T_{\text{yr}} \right)}{0\text{.}\text{01}\ P_{3}}$**\
**

  ---------------- --- -------------------------------------------------------
  Where            =   concentration of ^14^C in crop type c at harvest from
  C~hcsC~(T~yr~)       soil root uptake for one year (Bq/kg wet weight)

  C~sC~(T~yr~)     =   average surface soil concentration at soil location s
                       for ^14^C during the current year from material present
                       at the start of the year (Bq/m^2^)

  F~Cc~            =   fraction of carbon in crop type c (kg carbon/kg plant)

  P~3~             =   areal soil density of farmland soil (kg/m^2^)

  0.1              =   assumed uptake of 10% of plant carbon from soil
                       (dimensionless)

  0.01             =   average fraction of soil that is carbon (kg carbon/kg
                       soil).
  ---------------- --- -------------------------------------------------------

The total concentration in food crops is evaluated as the sum of the
contributions from air, water, and soil, or:

  ---------------- --- -------------------------------------------------------
  C~hcC~ (T~yr~)   =   C~hcaC~(T~yr~) + C~hewC~(T~yr~) + C~hcsC~(T~yr~)

  Where C~hcC~     =   concentration of ^14^C in crop type c at harvest for
  (T~yr~)              one year (Bq/kg wet weight).

  C~hewC~(T~yr~)   =   concentration of ^14^C in crop type c at harvest from
                       irrigation for one year (Bq/kg/wet weight) (assumed to
                       be zero).
  ---------------- --- -------------------------------------------------------

Other terms are defined above. No decay is considered between harvest
and consumption of crops containing ^14^C because the radiological
half-life of ^14^C is long.

##### Ingestion of Radioactive Material 

Ingestion of radioactive material is considered in GENII for leafy
vegetables, other vegetables, cereal grains, and fruit. Given an average
radionuclide concentration (C~csi~(T)) in food products, the quantity of
a given radionuclide ingested over a given time period is calculated as
(1):

  ------------ --- --------------------------------------------------------
  I~csig~(T)   =   C~csi~(T) U~csg~ T~csg~ ED~csg~

  Where        =   total intake of radionuclide i in food crop c over the
  I~csig~(T)       period T from ingestion at agricultural location s for
                   individuals in age group g (Bq)

  C~csi~(T)    =   average concentration in food crop c at agricultural
                   location s for radionuclide i (Bq/kg)

  U~csg~       =   ingestion rate (food crop consumption rate) of food crop
                   c at agricultural location s by an individual in age
                   group g (kg/d)

  T~csg~       =   annual intake factor (food crop consumption period)
                   giving the days per year that food crop c is eaten (at
                   the average rate) at agricultural location s by
                   individuals in age group g (d/y)

  ED~csg~      =   exposure duration for consumption of food crop c at
                   agricultural location s for individuals in age group g
                   (y).
  ------------ --- --------------------------------------------------------

The exposure duration (ED~csg~) is the number of years that exposure
occurs, which for this study is assumed to be one year. [^16] Assumed
parameter values for the ingestion rate and annual intake factor are
provided in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

#### Ingestion of Animals and Animal Products

Pathways describing the transfer of radionuclides to humans from animals
and animal products generally start with calculations such as those
described in Section D.3.4.1, except that transfer factors for forage
crops are used, as well as consumption rates and other parameters that
are appropriate for the animal. Then, animal-to-human transfer is
considered assuming animal products that are characteristic of the area
as well as typical rates of consumption.

##### Radionuclide Concentration in Animals and Animal Products

**Basic equation.** The basic radionuclide concentration in a given
animal product as determined at the time of harvest (slaughter, milking,
egg collection) is (1):

$C_{\text{hai}}\left( T_{\text{yr}} \right) = \text{Fa}_{i}\left\lbrack C_{\text{wi}}\left( T_{\text{yr}} \right)d_{\text{aw}}U_{\text{ae}} + C_{\text{ai}}\left( T_{\text{yr}} \right)d_{\text{as}}U_{\text{as}} + \sum_{f - 1}^{N_{\text{af}}}{C_{\text{cfi}}\left( T_{\text{yr}} \right)d_{\text{af}}U_{\text{af}}} \right\rbrack$**\
**

  --------------- --- --------------------------------------------------------
  C~hai~(T~yr~)   =   concentration of radionuclide i in animal product a at
                      harvest of the animal product for a one-year period
                      (Bq/kg)

  T~yr~           =   one-year exposure period (y)

  Fa~i~           =   transfer coefficient that relates daily intake rate by
                      an animal to the concentration in an edible animal
                      product a (Bq/L milk per Bq/d for milk, and Bq/kg meat
                      per Bq/d for meat)

  C~wi~(T~yr~)    =   average concentration of radionuclide i in water
                      consumed by animals for a year (Bq/L)

  C~ai~(T~yr~)    =   average concentration of radionuclide i in soil consumed
                      by animals for a year (Bq/kg dry soil)

  C~cfi~(Tyr)     =   concentration of radionuclide i in animal feed type f at
                      the time of consumption for a one-year period (Bq/kg wet
                      weight)

  d~aw~           =   fraction of animal type a water intake that is
                      contaminated (dimensionless)

  U~aw~           =   daily water intake rate for animal type a (L/d)

  d~as~           =   fraction of animal type a soil intake that is
                      contaminated (dimensionless)

  U~as~           =   daily soil intake rate for animal type a (kg/d)[^17]

  N~af~           =   number of feed types, f, fed to animal type a

  d~af~           =   fraction of animal type a feed type f intake that is
                      contaminated (dimensionless)

  U~af~           =   daily feed intake rate for animal type a of feed type f
                      (kg/d).
  --------------- --- --------------------------------------------------------

Where animal uptake of contaminated water is not considered for the
scenarios defined for this report. Other terms have been already
defined.

##### Radioactive Decay

GENII has the capability of considering two periods of radioactive decay
for human ingestion of animals and animal products: (1) radioactive
decay between harvesting and animal consumption of animal feed and
forage, and (2) radioactive decay between animal or animal product
harvest (e.g., animal slaughter, collection of eggs) and consumption of
the animal or animal product by humans.

The first period of radioactive decay is addressed in GENII as explained
in Section D.3.4.1.3, except that the calculation is performed for
animal feed and forage rather than food crops. Note that different
holdup (delay) times may be appropriate for animal feed and forage than
would be the case for food crops.

The second period of radioactive decay is again addressed in GENII using
the GENII decay processor. For most radionuclides (those for which decay
chains and branching is not a factor), the decay calculation is
calculated as follows (1):

  --------------- --- --------------------------------------------------------
  C~asi~(T~yr~)   =   C~hai~(T~yr~) e^-\ λi\ Tha\ 2.74E-3^

  Where           =   concentration of radionuclide i in animal product a at
  C~asi~(T~yr~)       usage location s at the time of consumption over a
                      one-year period (Bq/kg wet weight)

  Th~a~           =   holdup delay time between harvest and consumption for
                      animal product a (d)

  λ ~i~           =   radiological decay constant for radionuclide i (y^-1^)

  2.74E-3         =   Conversion factor, years per day (1 year /365 days).
  --------------- --- --------------------------------------------------------

##### Tritium and ^14^C Calculations 

**Tritium.** HTO concentrations in animals are assumed to equal the
average weighted tritium concentration of ingested water based on the
fraction of water supplied by each source, including skin absorption,
inhalation, drinking water, and food (from plant water and digested
organically bound molecules).

Concentrations of tritium as HTO in animal products are calculated as
(1):

$$C_{\text{HTOap}}\left( T_{\text{yr}} \right) = F_{\text{Wa}}\frac{C_{\text{wH}}\left( T_{\text{yr}} \right)U_{\text{wa}}d_{\text{aw}} + \sum_{f = 1}^{N_{\text{fa}}}{C_{\text{cfH}}\left( T_{\text{yr}} \right)U_{\text{af}}d_{\text{af}}}}{U_{\text{wa}} + \sum_{f = 1}^{N_{\text{fa}}}{F_{\text{fw}_{\text{pp}}}\text{RF}_{\text{pp}}U_{\text{af}}}}$$

Where:

  ----------------- --- --------------------------------------------------------
  C~HTOap~(T~yr~)   =   concentration of tritiated water in animal product a at
                        time of consumption by humans over a one-year period
                        (Bq/kg)

  F~Wa~             =   fraction of water in animal product a (dimensionless)

  C~wH~(T~yr~)      =   average concentration of tritium in water consumed by
                        animal type a over a one-year period (Bq/L)

  U~aw~             =   daily water intake rate for animal type a (L/d)

  d~aw~             =   fraction of animal type a water intake that is
                        contaminated (dimensionless)

  C~cfH~(T~yr~)     =   concentration of tritium, calculated as the sum of the
                        water and organic portions (see above), in animal feed
                        type f at the time of consumption for a one-year period
                        (Bq/kg wet weight)

  U~af~             =   daily intake rate for animal type a of feed type f
                        (kg/d)

  d~af~             =   fraction of animal type a feed type f intake that is
                        contaminated (dimensionless)

  N~fa~             =   number of feed crops eaten by animal type a.
  ----------------- --- --------------------------------------------------------

Other constants are previously defined. Tritium (as HTO) concentrations
in animal feed is evaluated using the above equations with values
defined for the animal feed crops.

Regarding tritium as OBT, the relationship used to calculate
concentrations in animal products was created under the assumption that
the specific activity in organic material equals the specific activity
in the aqueous phase apart from a discrimination factor. It is given,
after the derivation of Peterson and Davis (23) as:

$$C_{\text{ap}_{\text{OBT}}} = C_{\text{ap}_{\text{HTO}}}\frac{F_{\text{dm}_{\text{ap}}}}{F_{\text{fw}_{\text{ap}}}}W_{\text{eq}_{\text{ap}}}$$

Default values for the parameters needed for the above equations (9.30a
and 9.30b) are listed in Table D-7.

Table D‑7 Parameter Values for Calculating HTO and OBT Concentrations in
Animal Products

  ----------------------- --------- --------- --------- --------- ---------
  Parameter Values        Eggs      Milk      Beef      Pork      Poultry

  Fresh Weight Fraction   0.74      0.897     0.668     0.50      0.67
  (F~fw_ap~)                                                      

  Dry Matter Fraction     0.26      0.103     0.332     0.50      0.33
  (F~dm_ap~)                                                      

  Water Equivalent Factor 0.835     0.669     0.795     0.904     0.796
  (W~eq_ap~)                                                      
  ----------------------- --------- --------- --------- --------- ---------

Source: (1).

**Carbon-14.** GENII calculates the concentration of ^14^C in animal
products as (1):

$C_{\text{caC}}(t) = F_{\text{Ca}}\frac{\sum_{f = 1}^{N_{\text{fi}}}C_{\text{efC}}U_{\text{af}}d_{\text{af}}}{\sum_{f = 1}^{N_{\text{fi}}}{F_{\text{Ca}}U_{\text{af}}}}$**\
**

  --------------- --- -------------------------------------------------------
  Where           =   concentration of ^14^C in animal product a at time of
  C~caC~(T~yr~)       consumption by humans (Bq/kg)

  F~Ca~           =   fraction of carbon in animal product a (dimensionless)

  C~efC~(T~yr~)   =   concentration of ^14^C in animal feed type f at time of
                      consumption for a year (Bq/kg wet weight)

  U~af~           =   daily feed intake rate for animal type a of feed type f
                      (kg/d)

  d~af~           =   fraction of animal type a feed type f intake that is
                      contaminated (dimensionless)

  F~Cf~           =   fraction of carbon in animal feed type f
                      (dimensionless)

  N~fa~           =   number of feed crops eaten by animal type a.
  --------------- --- -------------------------------------------------------

##### Ingestion of radioactive Material 

Once average concentrations of radionuclides in animal products are
determined, the quantity of radioactive material ingested over a given
period of time is (1):

  ------------ --- --------------------------------------------------------
  I~asig~(T)   =   C~asi~(T) U~asg~ T~asg~ ED~asg~

  Where        =   total intake of radionuclide i in animal product a over
  I~asig~(T)       the period T from ingestion at agricultural location s
                   for individuals in age group g (Bq)

  C~asi~(T)    =   average concentration in animal product a at
                   agricultural location s for radionuclide i (Bq/kg)

  U~asg~       =   ingestion rate (animal product consumption rate) of
                   animal product a at agricultural location s by an
                   individual in age group g (kg per day on the days that
                   the food is eaten)

  T~asg~       =   annual intake factor (animal product consumption period)
                   giving the number of days per year that animal product a
                   is eaten (at the average rate) at agricultural location
                   s by individuals in age group g (d/y)

  ED~asg~      =   exposure duration for consumption of animal product a at
                   agricultural location s for individuals in age group g
                   (y).
  ------------ --- --------------------------------------------------------

As for ingestion of food crops, the exposure duration (ED~asg~) is
assumed to be one year. Assumed values for the ingestion rate and annual
intake factor are provided for each receptor in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

#### Aquatic Food Ingestion

Fish, crustaceans, mollusks, and other possible aquatic food products
may become contaminated with radionuclides and cause radiation doses to
humans when food products are consumed.

##### Radionuclide Concentration in Aquatic Foods

The radionuclide concentration in a particular type of aquatic food is
given as the radionuclide concentration in water multiplied by a
bioaccumulation factor. The basic equation to describe accumulation is
(1):

  -------------- --- -------------------------------------------------------
  C~hqi~ (T~yr~) =   C~wi~(T~yr~) B~qi~

  Where C~hqi~   =   concentration of radionuclide i in aquatic food type q
  (T~yr~)            at the time of harvest (Bq/kg).

  C~wi~(T~yr~)   =   average concentration of radionuclide i in water over
                     the year.

  B~qi~          =   bioaccumulation factor for radionuclide i in aquatic
                     food type q (Bq/kg in wet fish per Bq/L of water).
  -------------- --- -------------------------------------------------------

##### Radioactive Decay

Radionuclide concentrations in aquatic food products may be reduced by
means of radioactive decay between food product harvesting and food
product consumption. Radioactive decay is accounted for using the GENII
decay processor in a similar manner as that for food crops and animal
products. For most radionuclides (those without decay chains or
branching), radioactive decay is considered in the following manner (1):

  --------------- --- -------------------------------------------------------
  C~fwi~(T~yr~)   =   C~hqi~(T~yr~) e^-\ λi\ Tha\ 2.74E-3^

  Where           =   concentration of radionuclide i in aquatic food type q
  C~fwi~(T~yr~)       at water location w at the time of consumption over a
                      one-year period (Bq/kg wet weight)

  Th~a~           =   holdup delay time between harvest and consumption of
                      aquatic food type q (d)

  λ ~i~           =   radiological decay constant for radionuclide i (y^-1^)

  2.74E-3         =   Conversion factor, years per day (1 year /365 days).
  --------------- --- -------------------------------------------------------

##### Ingestion of Radioactive Material

Once the concentration of a radionuclide in aquatic food products are
calculated (fish, mollusks, invertebrates, and water plants), the
radionuclide quantity (Bq) ingested is calculated as (1):

  ------------ --- --------------------------------------------------------
  I~fwig~(T)   =   C~fwi~(T) U~fwg~ T~fwg~ ED~fwg~

  Where        =   total intake of radionuclide i from ingestion of aquatic
  I~fwig~(T)       food f over the period T at aquatic food location w for
                   individuals in age group g (Bq)

  C~fwi~(T)    =   average concentration in aquatic food f at aquatic food
                   location w for radionuclide i (Bq/kg)

  U~fwg~       =   ingestion rate (aquatic food product consumption rate)
                   of aquatic food f at aquatic food location w by an
                   individual in age group g (kg per day on the days that
                   the food is eaten)

  T~fwg~       =   annual intake factor (aquatic food product consumption
                   period) giving the days per year that aquatic food f is
                   eaten (at the average rate) at aquatic food location w
                   by individuals in age group g (d/y)

  ED~fwg~      =   exposure duration for consumption of aquatic food f at
                   aquatic food location w for individuals in age group g
                   (y).
  ------------ --- --------------------------------------------------------

The exposure duration (ED~fwg~) in this equation is assumed in this
report to be one year. Assumed values for the ingestion rate and annual
intake factor are provided as a function of receptor in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc).

### Sedimentation Pathways

Individuals involved in sun bathing, fishing, or other recreational
shoreline activities along contaminated surface water may be exposed to
radiation from radionuclides that have built up over the years in
sediment. The build up over time is evaluated as an integral that
considers the deposition of radionuclides from the water. The
concentration in sediment built up over a single year is (1):

$C_{\text{sri}}\left( T_{\text{yr}} \right) = \frac{\text{TC}\ C_{\text{ri}}\left( T_{\text{yr}} \right)\left( 1 - e^{- \lambda_{i}T_{\text{yr}}} \right)}{\lambda_{i}}$**\
**

  --------------- --- --------------------------------------------------------
  Where           =   concentration of radionuclide i in sediment after one
  C~sri~(T~yr~)       year of accumulation from deposition on the shoreline at
                      recreational water usage location r (Bq/m^2^)

  TC              =   transfer rate constant from water to sediment (L/m^2^/y)

  C~ri~(T~yr~)    =   average (constant) annual water concentration for
                      radionuclide i at recreational water usage location r
                      (Bq/L)

  T~yr~           =   one-year integrating period for deposition to sediments
                      (y).
  --------------- --- --------------------------------------------------------

The concentration over several years would be determined by integrating
over the appropriate time period (say five years), considering the
average concentration in the water over that time period.

In the above equation, the transfer rate constant (TC) is a parameter
that describes the transfer of radionuclides to sediment (Bq/m^2^) from
water (Bq/L) during a year (L/m^2^/y). In GENII, a transfer rate
constant of 35,400 L/m^2^/y is used, a value chosen from consideration
of data obtained for several radionuclides that compared concentrations
in river water and sediment. River and sediment samples were obtained
from the Columbia River between Richland, Washington, and the river
mouth, and from Tillamock Bay, Oregon, 75 km south of the river mouth
(1).

The exposure to an individual in any year is the time-integral of the
shoreline sediment concentration during that year, considering the
amount of time spent on the shoreline. The average concentration (Bq per
kg of sediment) is determined using a model of the following form (1):

$C_{\text{sri}}\left( T_{\text{yr}} \right) = \int_{0}^{T_{\text{yr}}}{C_{\text{sri}}(t)\frac{\text{dt}}{\left( T_{\text{yr}}d_{\text{ed}}\rho_{\text{sed}} \right)}}$

  --------------- --- --------------------------------------------------------
  Where           =   shoreline sediment time integral of exposure for
  C~sri~(T~yr~)       radionuclide i evaluated at the recreational usage
                      location r (Bq/kg)

  d~ed~           =   thickness of shoreline sediments (m)

  ρ~sed~          =   density of shoreline sediments (kg/m^3^)

  T~yr~           =   one-year exposure period (y).
  --------------- --- --------------------------------------------------------

In this case, the concentration within the integral is integrated over a
one-year period starting from the total concentration in sediment at the
beginning of the year. For example, if one wishes to evaluate the
exposure during the 6^th^ year of operations for a given radionuclide,
one would calculate the total average radionuclide concentration over
the year considering the concentration that had built up over the
previous five years, as well as the concentration as enhanced in
sediment over the course of the 6^th^ year.

In addition, neither D~sed~ nor ρ~sed~ is input into the GENII
calculations. Rather, to use GENII one inputs the shoreline areal
density, in units of kg/m^2^, which is the product of D~sed~ with ρ~sed~
(see Section F.5).

Recreational shoreline exposures are then calculated using the average
radionuclide concentration in shoreline sediment as (1):

  ------------ --- --------------------------------------------------------
  I~srig~(T)   =   C~sri~(T) SW~r~ FE~srg~ TE~srg~ T~srg~

  I~srig~(T)   =   average exposure factor over the period T for
                   radionuclide i from shoreline exposure at recreational
                   shoreline location r for individuals in age group g
                   (Bq/kg)

  C~sri~       =   average shoreline sediment concentration of radionuclide
                   i at recreational shoreline location r (Bq/kg)

  SW~r~        =   shoreline width factor for recreational shoreline
                   location r (dimensionless)

  FE~srg~      =   shoreline use event frequency (frequency of shoreline
                   use) at recreational shoreline location r for
                   individuals in age group g (events/d)

  TE~srg~      =   duration of each shoreline exposure event at
                   recreational shoreline location r for individuals in age
                   group g (h/event)

  T~srg~       =   annual exposure factor (shoreline days) for shoreline
                   exposure at recreational shoreline location r for
                   individuals in age group g (number of days in a year
                   that the shoreline exposure location is visited).
  ------------ --- --------------------------------------------------------

The annual exposure factor for shoreline exposure, T~srg~, is assumed to
be 365 days for chronic exposures, which is the situation considered for
this report. The daily exposure factor is the product of the event
frequency, FE~srg~, and the event duration, TE~srg~. Assumed values for
these parameters, and for T~srg~, are provided as a function of receptor
in [Appendix E](../Appendix_E%20ready%20for%20CDC%20031405.doc). The
shoreline width factor (SW~r~) is assumed to be 0.2 for the base case
evaluation (see Section F.5).

### Recreational Exposures from Surface Water Pathways

Recreational exposures to contaminated water are considered for two
cases: swimming and boating. Exposure pathways considered for swimming
include immersion in a contaminated plume of water, and inadvertent
ingestion of small quantities of water. The exposure pathway considered
for boating is external exposure to a volume-contaminated source. The
starting point for all pathways is the concentrations of radionuclides
in water, given as Bq/L.

#### External Exposure From Immersion in Water (Swimming)

Recreational swimming exposures are calculated in GENII as (1):

  ------------ --- --------------------------------------------------------
  I~wrig~(T)   =   C~wri~(T) FE~wrg~ TE~wrg~ T~Cs~

  I~wrig~(T)   =   average exposure factor over time period T for
                   radionuclide i from swimming at recreational swimming
                   location r for individuals in age group g (Bq/L)

  C~wri~(T)    =   average water concentration over time period T for
                   radionuclide i in surface water at recreational swimming
                   location r (Bq/L)

  FE~wrg~      =   frequency of swimming events at recreational swimming
                   location r for individuals in age group g (events per
                   day on the days when swimming occurs)

  Tc~s~        =   time correction set to T~wrg~/8760 h/y for chronic
                   releases

  TE~wrg~      =   duration of an average swimming event at recreational
                   swimming location r for individuals in age group g
                   (h/event)

  T~wrg~       =   annual exposure factor (swimming days) for swimming at
                   recreational swimming location r for individuals in age
                   group g (number of days in a year that swimming
                   occurs).[^18]
  ------------ --- --------------------------------------------------------

Here, the daily exposure factor is the product of the event frequency,
FE~wrg~, and the event duration, TE~wrg~. Assumed parameter values for
FE~wrg~, TE~wrg~, and T~wrg~ are provided in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc) as a function of
receptor.

#### Ingestion of Surface Water While Swimming 

Inadvertent consumption of surface water while swimming is calculated as
(1):

  ------------ --- --------------------------------------------------------
  I~wwig~(T)   =   C~wri~(T) FE~wrg~ TE~wrg~ T~Cs~ U~swg~

  I~wwig~(T)   =   average exposure factor over time period T for
                   radionuclide i from ingestion at swimming location w for
                   individuals in age group g (Bq)

  C~wri~(T)    =   average water concentration over time period T for
                   radionuclide I in surface water at the recreational
                   swimming location r (Bq/L)

  FE~wrg~      =   frequency of swimming events at water use location r for
                   individuals in age group g (events/d

  TE~wrg~      =   duration of an average swimming event at water use
                   location r for individuals in age group g (h/event)

  T~Cs~        =   time correction, set equal to T~wrg~/8760 h/y for
                   chronic releases

  T~wrg~       =   annual exposure factor (swimming days) for swimming at
                   water use location r for individuals in age group g
                   (number of days in a year that swimming occurs)

  U~wwg~       =   uptake rate of water while swimming (ingestion rate of
                   water while swimming) for age group g (L during an hour
                   of swimming).[^19]
  ------------ --- --------------------------------------------------------

Here, the daily exposure factor is the product of the event frequency,
FE~wrg~, and the event duration, TE~wrg~, in units of h/d. The ingestion
rate of water while swimming (U~wwg~) is provided in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc) as a function of
receptor. Otherwise, one assumes the same usage factors (FE~wrg~,
TE~wrg~, and T~wrg~) as those used to calculate direct radiation
exposure while swimming (Section D.3.6.2).

#### External Exposure While Boating

Exposure of humans during recreational boating may be calculated as (1):

  ------------ --- --------------------------------------------------------
  I~brig~(T)   =   C~bri~(T) SB FE~brg~ TE~brg~ T~Cb~

  I~brig~(T)   =   average exposure factor over time period T for
                   radionuclide I from boating at recreational boating
                   location r for individuals in age group g (Bq/L)

  C~bri~(T)    =   average water concentration of radionuclide i at
                   recreational boating location r (Bq/L)

  SB           =   shielding factor for boating exposures
                   (dimensionless)[^20]

  FE~brg~      =   average frequency of daily boating events at
                   recreational boating location r for individuals in age
                   group g (events/d)

  TE~brg~      =   duration of an average boating event at recreational
                   boating location r for individuals in age group g
                   (h/event)

  T~Cb~        =   time correction set equal to T~brg~/8760 h/y for chronic
                   releases

  T~brg~       =   annual exposure factor (boating days) for boating at
                   recreational boating location r for individuals in age
                   group g (number of days in a year that boating
                   occurs).[^21]
  ------------ --- --------------------------------------------------------

Here, the daily exposure factor is the product of the event frequency,
FE~brg~, and the event duration TE~bgr~, in units of h/d. Assumed values
for SB, Fe~brg~, Te~brg~, and T~brg~ are provided as a function of
receptor in [Appendix
E](../Appendix_E%20ready%20for%20CDC%20031405.doc). The shielding factor
for boating exposures (SB) is assumed to be 0.5 as addressed in Section
F.6.

## Dose and Risk Principles

Additional information about radiation assessment and protection
principles, and terminology, can be obtained from Internet sites on
radiation established by EPA (<http://www.epa.gov/radiation>) and the
University of Michigan (<http://www.umich.edu/~nradinfo>).

### Types of Radiation

Decaying radionuclides such as those considered for this portion of the
SRS Dose Reconstruction Study can each emit up to three basic types of
ionizing radiation:

-   *Alpha particles*: These particles are essentially the nuclei of
    helium atoms. Each particle contains two protons and two neutrons.
    Because of their relatively large size, alpha particles lose energy
    quickly as they collide with matter. They will not penetrate human
    skin. Therefore, human skin can be impacted by alpha particles
    (i.e., the human receives an *external exposure* to alpha particles)
    without harm. However, alpha particles can damage cells within the
    human body if they are taken into the body by breathing or by
    swallowing. In this case, a human receives *internal exposure* to
    alpha particles.

-   *Beta particles*: These particles are electrons identical to those
    that surround the nuclei of atoms. They are much smaller than alpha
    particles and can penetrate up to a few centimeters of water or
    human flesh. Therefore, both external and internal exposure to beta
    particles can damage human cells.

-   *Gamma rays and X-rays*: These rays are forms of electromagnetic
    energy. (Ordinary light is another form of electromagnetic energy,
    as are microwaves and radio waves). Gamma rays and X-rays are
    virtually identical except that gamma rays tend to have more energy
    and are emitted by atomic nuclei, while X-rays tend to have less
    energy and are emitted from the electrons surrounding atomic nuclei.
    Gamma rays and X-rays have considerable penetrating power. Both
    external and internal exposure to gamma rays and X-rays can damage
    human cells.

Ionizing radiation damages cells by imparting energy to the cells.
Energy absorbed by the cells can break chemical bonds, among other
impacts.

### Radiation Dose 

To estimate the effects of radiation on human (or other) tissue, one
must estimate the *dose* that the human receives. A radiation dose is a
measure of the amount of energy imparted to tissue (absorbed) by the
radiation. However, a strict calculation of the *absorbed dose* ---e.g.,
in units of joules of energy absorbed by a kilogram of tissue
(J/kg)---is insufficient. Different particles of radiation ---alpha,
beta, gamma--- impart energy to tissue in different ways. One accounts
for these differences through the concept of an *equivalent dose*,[^22]
which may be considered as:

  --------------- --- ----------------------------------------------------
  H               =   D W~R~

  Where H         =   equivalent dose (Sievert)

  D               =   absorbed dose (Gray)[^23]

  W~R~            =   weighting factor (dimensionless)

  The unit of         
  equivalent          
  dose, called        
  the *Sievert*       
  (Sv), is            
  therefore           
  defined as:         

  1 Sievert       =   1 J/kg = 100 rem, and

  1 milliSievert  =   1/1000 Sv = 100 millirem (mrem)
  (mSv)               
  --------------- --- ----------------------------------------------------

Where a "*rem*," or "Roentgen equivalent man," is a dose unit commonly
used in the United States, and, as indicated, is one one-hundredth of a
Sievert. A *millirem* (mrem) is one one-thousandth of a rem.

The weighting factor[^24] accounts for differences in how energy is
imparted to tissue by different types of radiation. X-rays, gamma rays,
and beta particles are generally assigned weighting factors of one,
while alpha particles are generally assigned weighting factors of
twenty.

One difficulty of estimating radiation doses to humans is that human
bodies are variable. To achieve agreement on standards for radiation
protection, and to help comparisons of different radiation dose
assessments, a concept was developed called a *standard* *man*, a
surrogate human having organs of both sexes of reference radii and
masses. Risk assessments are commonly performed using these standard
physiological assumptions.

Doses from internal exposures, such as those from inhalation or
ingestion of radioactive material, are determined using models
describing the movement and retention of the material in the body. Some
radionuclides may build up in the body as a person inhales or ingests
the radionuclides year after year. A radionuclide retained in the body
will impart a dose to a person not only for the first year of intake,
but in following years until the radionuclide decays or is eliminated.
This phenomenon causes a *committed dose*. It may be considered as:

  ----------- --- --------------------------------------------------------
  H~C~        =   ∫ H(t) dt

  Where H~C~  =   committed equivalent dose (Sv)

  H(t)        =   equivalent dose rate (Sv/y)
  ----------- --- --------------------------------------------------------

And the integral is evaluated over a specified period of time.[^25]

At one time, the usual practice was to calculate doses to individual
bodily organs or tissues. But in 1977, the ICRP recommended in ICRP-26
the concept of a weighted mean whole-body dose (24). It provides a
measure of the dose across multiple organs or tissues, and is determined
by multiplying the dose received by each organ or tissue by a weighting
factor, and then adding all of these weighted doses to arrive at a
single representative dose. ICRP originally called this dose an
*effective dose equivalent* (24). In a more recent recommendation
\[ICRP-60, issued in 1991\] (25), ICRP called this dose an *effective
dose*. It may be considered as:

  ----------- --- --------------------------------------------------------
  H~E~        =   Σ~T~ W~T~ H~T~

  Where H~E~  =   effective dose (Sv)

  W~T~        =   a weighting factor representing the ratio of the
                  stochastic risk from irradiation of tissue T to that for
                  the whole body when irradiated uniformly.

  H~T~        =   equivalent dose in tissue T.
  ----------- --- --------------------------------------------------------

Values for tissue weighting factors recommended by ICRP in 1977 (24) and
1991 \[ICRP-60\] (25) are listed in Table D-8. The weighting factors
recommended in ICRP-60 are different from those recommended in
ICRP-26.[^26]

The concept of effective dose is used for doses resulting from both
external and internal exposures. To calculate committed effective dose
from internal exposures, ICRP in ICRP-60 recommended using an
integration time of 50 years following intake for assessments of
occupational dose, and 70 years for members of the public.

Table D‑8 ICRP-26 and ICRP-60 Tissue Weighting Factors

  ----------------------- ----------------------- -----------------------
  Organ or Tissue         ICRP-26 Weighting       ICRP-60 Weighting
                          Factors                 Factors

  Gonads                  0.25                    0.20

  Breast                  0.15                    0.05

  Colon                                           0.12

  Red bond Marrow         0.12                    0.12

  Lungs                   0.12                    0.12

  Stomach                                         0.12

  Urinary Bladder                                 0.05

  Liver                                           0.05

  Esophagus                                       0.05

  Thyroid                 0.03                    0.05

  Bone Surface            0.03                    0.01

  Skin                                            0.01

  Remainder               0.30\*                  0.05^†,‡^
  ----------------------- ----------------------- -----------------------

\*The value 0.30 is applied to the average dose among the five remaining
organs or tissues receiving the entire dose, excluding the skin, lens of
the eye, and the extremities.

^†^The reminder consists of: adrenals, brain, small intestine, upper
large intestine, kidney, muscle, pancreas, spleen, thymus, and uterus.

^‡^The value 0.05 is applied to the average dose to the remainder tissue
group. However, if a member of the remainder receives a dose exceeding
the highest dose in any of the 12 organs for which weighting factors are
specified, a weighting factor of 0.025 is applied to that organ and
weighting factor of 0.025 is applied to the average dose to the rest of
the remainder.

### Risk from Radiation Exposure 

Ionizing radiation was first discovered and used in the last years of
the 19^th^ Century. The most urgent need was to avoid exposures causing
immediate or near-term effects on the health of individuals. These
health effects were seen after individuals had received very large
exposures above a *threshold* of received radiation. Below the threshold
the health effects did not occur, and above it the severity of the
health effects increased. These *nonstochastic* effects were avoided by
limiting exposures to levels below the threshold.[^27]

Scientists and health providers later observed that exposure to
radiation might lead to delayed health effects, either to exposed
individuals (called *somatic* effects) or to descendents (called
*genetic* effects). These effects are called *stochastic* effects,
because they occur with given frequencies in populations receiving
radiation exposures rather than predictably to an exposed individual.
The severity of stochastic effects, including cancer and hereditary
effects, is not related to the level of exposure.

From these observations came the development of procedures for
estimating the risks of negative health effects that may occur from
exposure to ionizing radiation. One way to express risks is the
probability of cancer *fatality* (*mortality*) occurring over a lifetime
from exposure to radioactive material. Fatality (mortality) is the risk
of dying of cancer. Another way to express risks is the probability of
cancer *incidence* *(morbidity)* occurring over a lifetime from exposure
to radioactive material. Incidence (morbidity) is the risk of radiogenic
cancer whether or not the cancer is fatal.

Modern estimates of risk have, particularly for low-LET ionizing
radiation,[^28] been largely based on information about Hiroshima and
Nagasaki atomic bomb survivors as documented in the Radiation Effects
Research Foundation's Life Span Study. The Study cohort was a large,
relatively healthy population at the time of exposure. The cohort was
exposed to a wide range of reasonably established doses to individuals,
and there exists a large, well-matched control group (people who
received only small doses of radiation but were present at the time the
bombs exploded). Additional information used for estimating radiation
risks has come from sources such as: (1) persons who have had large
intakes of radium into the body from occupational contamination or
supposedly therapeutic administration, (2) persons who have had large
intakes of a thorium preparation known as Throtrast as part of
diagnostic procedures, and (3) workers in uranium mines and other mines
resulting in exposure to radon gas.

Application of the various studies to estimations of risks from low
levels of radiation exposure is subject to considerable uncertainty, for
a variety of reasons, including:

-   Sampling uncertainties

-   Latency of health effects such as cancer following radiation

-   Transferability of risks from one population to another

-   Dose and dose rate dependence (e.g., although risk relationships
    have been developed based on observation of doses that have tended
    to be acute and much larger than doses at background levels, they
    have been primarily applied to assessment of risks from chronic
    doses at levels in the range of background).

There are also various ways to express risks, such as risks of disease
or adverse genetic change, the number of days of life shortening from a
given dose, and so forth. A common way to express risks, however, is the
probability of a radiogenic cancer fatality (mortality) occurring over a
lifetime from exposure to radioactive material. As used here, cancer
*fatality* *(mortality)* refers to the risk of dying of cancer. Another
way to express risks is the probability of radiogenic cancer incidence
(morbidity) occurring over a lifetime from exposure to radioactive
material. Cancer *incidence (morbidity)* refers to the risk of
experiencing radiogenic cancer whether or not the cancer is fatal.

In any event, to estimate the consequences of radiation exposures to
individuals and populations, and to regulate use of radioactive
materials, it is normally assumed that the probability of occurrence of
late stochastic effects is proportional to the radiation exposure that
is received and that there is no threshold for the probability of health
effects. This assumption is commonly known as the *linear no-threshold*
assumption. For roughly 50 years it has formed the basis for
international recommendations for protection of the public from
radiation. As summarized by the IAEA in Publication No. 26 \[ICRP-26\]
in 1977 (24):

-   No practice shall be adopted unless it introduction produces a
    positive net benefit.

-   All exposures shall be kept as low as reasonably achievable,
    economic and social factors being taken into account.

-   The dose equivalent limits to individuals shall not exceed the
    limits recommended for the appropriate circumstances by the
    \[ICRP\].

### Dose and Risk Coefficients

To calculate doses to individuals from exposure to radioactive
materials, most risk assessors normally use standard tables that relate
human doses or risks to the quantity of individual radioactive material
ingested, inhaled, or exposed to. These tables of *dose coefficients*
and *risk coefficients* are based on complicated models of physical and
human physiological factors. This avoids the need to repeatedly perform
these complicated calculations, and it is easier to compare different
assessments.

For this report, the most up-to-date dose and risk coefficients provided
in GENII were used. These dose and risk coefficients are almost all
based on EPA's April 2002[^29] Update \[FGR-13U\] (11) to Federal
Guidance Report No.13 \[FGR-13\] (20).

For exposures of persons from inhaling or ingesting radionuclides, the
following coefficients were used:

-   Age-dependent dose coefficients for 23 organs and bodily tissues,
    plus effective dose based on ICRP-60 weighting factors (see Table
    D-8).

-   Age-dependent cancer risk coefficients (fatality and incidence) for
    15 cancer sites, plus the sum of cancers across all cancer sites.

Table D-9 lists the organs and bodily tissues considered in the dose
coefficients, and the cancer sites considered in the risk coefficients.
Table D-10 lists the age categories considered for the dose and risk
coefficients. (Note that the age categories are different for the dose
and risk coefficients.)

Table D‑9 Organs, Tissues, and Lung-Compartments, and Cancer Sites,
Addressed in Dose and Risk Conversion Factors in the FGR-13 Update

  ------------------- -------------- -------------- -------------- --------------
  Organs, Tissues and                               Cancer Sites   
  Lung-Compartments                                 Addressed in   
  Addressed in Dose                                 Risk           
  Conversion Factors                                Conversion     
                                                    Factors        

  Adrenals            Kidneys        Skin           Esophagus      Breast

  Bone Surface        Liver          Spleen         Stomach        Ovary

  Brain               ET-Region\*    Testes         Colon          Bladder

  Breast              Lung           Thymus         Liver          Kidneys

  Stomach Wall        Muscle         Thyroid        Lung           Thyroid

  SI Wall\*           Ovaries        Uterus         Bone           Leukemia

  ULI Wall\*          Pancreas       UB Wall\*      Skin           Residual^†^

  LLI Wall\*          Red Bone       Effective\*                   Total
                      Marrow                                       
  ------------------- -------------- -------------- -------------- --------------

\*SI: small intestine; ULI: upper lower intestine; LLI: lower lower
intestine; ET: extra-thoracic; UB: urinary bladder; effective: effective
dose.

^†^Residual cancer sites.

Table D‑10 Age Categories Addressed in Dose and Risk Conversion Factors
Presented in the FGR-13 Update

  ----------------------------------- -----------------------------------
  Dose Conversion Factors             Risk Conversion Factors

  Infant                              0-5 Years

  1-Year Old                          5-15 Years

  5-Year Old                          15-25 Years

  10-year Old                         25-70 Years

  15-Year Old                         0-110 Years

  Adult                               
  ----------------------------------- -----------------------------------

For doses and risks from inhalation, specify dose and risk coefficients
had to be consistent with assumptions about the physical and chemical
form of each inhaled radionuclide. This was done because a
radionuclide's chemical and physical form affected the rate that it
could be absorbed into blood. It was assumed most radionuclides were
particulates assigned to one of three absorption types:

-   Type F: Fast dissolution and a high level of absorption to blood.

-   Type M: Intermediate rates of dissolution and levels of absorption
    to blood.

-   Type S: Slow dissolution and a low level of absorption to blood.

It was assumed some radionuclides existed as a gas or vapor. The
assumptions for the lung absorption types used in this report are listed
in Table D-11.

For Table D-11, a value of G was selected for carbon assuming that the
carbon was released as CO~2~. Carbon dioxide was considered the most
expected form of carbon that would have been inhaled because it is the
most chemically stable of the oxidized forms of carbon. For iodine, a
value of G for an organic gas was selected because it provides dose and
risk results that are intermediate between particulate and elemental
iodine. For ruthenium, a value of M was selected based on EPA's
recommended value for particulates. It is also an intermediate value.
For sulfur, a value of V was selected, which is EPA's recommended value
for sulfur dioxide. Limited data on the chemical form suggested that an
oxide would be more likely than the other choice of chemical form,
carbon disulfide (26), at least from reactor areas.

For external exposures resulting from (1) immersion in a "cloud" of
radionuclides in air, and (2) proximity to a contaminated ground
surface, the following coefficients were used:

-   Adult dose coefficients for 23 organs and bodily tissues, plus
    effective dose based on ICRP-60 weighting factors (see Table D-8).

-   Age-specific cancer risk coefficients (fatality and incidence) for
    15 cancer sites, plus the sum of cancers across all cancer sites.

GENII (and FGR-13U) provide only adult dose conversion factors for these
types of external exposures. The authors of FGR-13 believe that use of
adult external dose coefficients for all age groups should normally
result in small errors (usually \<30%). The FGR-13 authors believe that
these errors are likely to be negligible compared to the errors
associated with the simplified exposure scenarios assumed to calculate
the dose conversion factors (e.g., the phantoms were in constant
position in relation to the radiation source, and shielding was not
considered) (20).

Table D‑11 Assumptions for Lung Absorption Classes by Element

  ------------ ------------ -----------------------------------------------
  Element      Absorption   Comments^†^
               Class\*      

  Americium    M            Default absorption type recommended in ICRP-72
  (Am)                      (27).

  Argon (Ar)   NA           No absorption occurs for noble gases.

  Carbon (C)   G            Type G was assumed because it was recommended
                            in FGR-13 for CO~2~.

  Cesium (Cs)  F            Default absorption type recommended in ICRP-72
                            (27).

  Hydrogen     HT: G\       Type G was assumed for tritium released as a
  (^3^H)       HTO: V\      gas (HT) in accordance with FGR-13. Type G is
               OBT^‡^: V    also appropriate for tritium released as an
                            organic. Type V is assumed for tritium released
                            as water vapor (HTO) in accordance with FGR-13.

  Iodine (I)   G            Iodine was released in several forms. Type G
                            was assumed because it resulted in dose and
                            risk conversion factors between those for a
                            particulate and elemental I.

  Plutonium    M            Default absorption type recommended in ICRP-72
  (Pu)                      (27).

  Sulfur (S)   V            FGR-13 recommends Type V for sulfur dioxide.
                            (Note that if S is released as a particulate,
                            ICRP-72 (27) recommends Type M.)

  Strontium    M            Default absorption type recommended in ICRP-72
  (Sr)                      (27).

  Thorium (Th) S            Default absorption type recommended in ICRP-72
                            (27).

  Uranium (U)  M            Default absorption type recommended in ICRP-72
                            (27)

  Xenon (Xe)   NA           No absorption occurs for noble gases.
  ------------ ------------ -----------------------------------------------

\*F: fast; M: medium; S: slow; G: gas; V: vapor; NA: not applicable.

^†^Lung absorption classes are not listed for radioactive isotopes of
elements released only into surface waters. Although GENII requires that
lung absorption class assumptions be input for these isotopes, the
assumed values are not used in the dose and risk calculations because
inhalation exposure is not assessed for the surface water pathways
considered in this report.

^‡^OBT: organic bound tritium.

The ages considered in the risk coefficients for these types of external
exposures are the same as those listed in Table D-10.

For external exposures while swimming in water or while boating, dose
and risk coefficients are not available from the update to FGR-13. Dose
coefficients for water immersion and boating from \[FGR-12\] were used
(28). These (adult) dose coefficients are provided for fewer organs than
those in the FGR-13 update, and the weighting factors used to calculate
effective dose equivalent are from ICRP-26 rather than ICRP-60 (see
Table D-8). Risk was estimated by multiplying the calculated doses for
water immersion and boating by the following health effects conversion
factors:

-   Fatality: 0.05 Sv^-1^

-   Incidence: 0.06 Sv^-1^

Finally, the dose and risk coefficients were grouped into four age
groups: 0 to 5 years, 5 to 15 years, 15 to 25 years, and 25 to 70 years.
This assumption allowed for better correlation between the doses and
risks calculated as a function of age group. Dose and risk conversion
factors for these calculations were determined by interpolating between
appropriate dose and risk conversion factors obtained from the update to
FGR-13 and from FGR-12. The three combined age groups are summarized in
Table D-12. Also presented is the assumed duration of exposure for each
age group.

Table D‑12 Exposure Groupings and Corresponding Combined Dose and Risk
Factor Age Groups

  -------------------- --------------------------- ----------------------
  Age / Gender         Exposure Group (Duration    Dose and Risk Factor
                       \[years\])                  Age Group

  \<1 male             Infant (male only) \[1\]    0 -- 5

  1 -- 4 male          Preschool (male only) \[4\] 0 -- 5

  5 -- 11 male         Schoolage (male only) \[7\] 5 -- 15

  12 -- 17 male        Teenage (male only) \[6\]   15 - 25

  18 -- 70 male        Adult male \[varies\] \*    25 -- 70

  18 -- 70 female      Adult female \[varies\] \*  25 -- 70
  -------------------- --------------------------- ----------------------

> \*The exposure duration of the adult age groups depends on the year
> that the individual reaches age 18. Exposure duration lasts from the
> year of the 18^th^ birthday until the end of 1992, when one child
> would be 38 and the other 29.

### Calculation of Dose and Risk

Annual doses, and doses summed over all years of exposure, are
calculated for each member of the exposure scenario families described
in [Appendix E](../Appendix_E%20ready%20for%20CDC%20031405.doc). In
addition, for each year of exposure, the lifetime risk resulting from
that exposure is calculated, as well as the total lifetime risk caused
by all years of exposure. Total annual doses and risks are the sum of
doses and risks from each pathway. The pathways considered for each
family member, and other factors important for calculating doses and
risks (e.g., food consumption rates) may differ depending on the
scenario and family member.

Section D.3 addressed the calculational procedures used by GENII to
model each of the exposure pathways considered for this report. The
output of these calculations is a set of annual exposure factors as
summarized in Table D-13. Each exposure factor is calculated over a
period of time, T, which is one year for the scenarios in this report.

Some exposure factors may be calculated several times for each receptor,
and the individual calculations summed, to arrive at a total exposure
factor for that receptor. This would be the case, for example, for
exposure factors involving food crop ingestion, where the exposure
factor calculated from consumption of each food product is summed to
arrive at a total exposure factor for food crop ingestion.

The exposure factors for each pathway are then used in set of
calculational procedures involving multiplication by appropriate dose or
risk conversion factors as needed to determine the annual doses and
lifetime risks that would result from each of exposure.

Three sets of calculational procedures are used to address effective
dose, equivalent dose to various organs, and lifetime risks. Because the
calculational procedures are repetitive, they have been summarized in
tables. The equations used to calculate effective dose are listed in
Table D-14, while definitions for the various parameters listed in these
equations are summarized in Table D-15. Similarly, the equations used to
calculate equivalent dose are listed in Table D-16, while the
definitions for the various parameters used in these equations are
summarized in Table D-17. Finally, the equations used to calculate risk
are listed in Table D-18, while the definitions for the various
parameters used in these equations are summarized in Table D-19. For
these tables, the assumed values for the surface soil bulk density
(ρ~s~) and the thickness of the contaminated surface soil layer (d~s~)
are provided in Section F.7.

Table D‑13 Summary of Exposure Factors

  ------------ -------------- ------------ --------------------------------------------
  Exposure     Pathway        Exposure     Definition
  Route                       Factor       

  External     Plume          I~eaig~(T)   Exposure factor for plume immersion exposure
                                           for radionuclide i for an individual in age
                                           group g (Bq/m^3^) (Sec. D.3.2)

               Ground         I~esig~(T)   Exposure factor for exposure to contaminated
                                           ground for radionuclide i for individuals in
                                           age group g (Bq/kg) (Sec. D.3.3.2)

               Swim-ming      I~wrig~(T)   Exposure factor for radionuclide i from
                                           swimming at recreational swimming location r
                                           for individuals in age group g (Bq/L) (Sec.
                                           D.3.6.1)

               Boating        I~brig~(T)   Exposure factor for radionuclide i from
                                           boating at recreational boating location r
                                           for individuals in age group g (Bq/L) (Sec.
                                           D.3.6.3)

               Shoreline      I~srig~(T)   Exposure factor for radionuclide i from
                                           shoreline exposure at recreational shoreline
                                           location r for individuals in age group g
                                           (Bq/kg) (Sec. D.3.5)

  Ingestion    Farm Crops     I~csig~(T)   Intake of radionuclide i in food crop c from
                                           ingestion of agriculture location s for
                                           individuals in age group g (Bq) (Sec.
                                           D.3.4.1)

               Animal         I~asig~(T)   Intake of radionuclide i in animal product a
               Products                    from ingestion at agricultural location s
                                           for individuals in age group g (Bq) (Sec.
                                           D.3.4.2)

               Aquatic Foods  I~fwig~(T)   Intake of radionuclide i from ingestion of
                                           aquatic food f at aquatic food location w
                                           for individuals in age group g (Bq) (Sec.
                                           D.3.4.3)

               Inadver-tent   I~dsig~(T)   Intake of radionuclide i from inadvertent
               Soil                        soil ingestion at soil usage location s for
                                           individuals in age group g (Bq) (Sec.
                                           D.3.3.4)

               Inadver-tent   I~wwig~(T)   Intake of radionuclide i from inadvertent
               Swim                        water ingestion at swimming location w for
                                           individuals in age group g (Bq) (Sec.
                                           D.3.6.2)

  Inhalation   Air            I~aaig~(T)   Intake of radionuclide i from air inhalation
                                           at air usage location a for individuals in
                                           age group g (Bq) (Sec. D.3.1)

               Resus-pended   I~saig~(T)   Intake of radionuclide i from resuspension
               Soil                        inhalation at soil usage location a for
                                           individuals in age group g (Bq) (Sec.
                                           D.3.3.3)
  ------------ -------------- ------------ --------------------------------------------

Table D‑14 Equations for Calculation of Effective Dose

  -------------- -------------- ------------- ----------------------------
  Exposure Route Exposure       Dose          How Calculated
                 Pathway        Parameter     

  External       Plume          IE~eaig~(T)   I~eaig~(T) EC~iaa~ T~yr~
                                              3.15E+7

                 Ground         IEesig(T)     I~esig~(T) ECiag Tyr 3.15E+7
                                              / (ρ~s~ d~s~)

                 Swimming       IE~wrig~(T)   10^-3^ I~wrig~(T) EC~ia~w
                                              T~yr~ 3.15E+7

                 Boating        IE~brig~(T)   10^-3^ I~brig~(T) EC~iaw~
                                              T~yr~ 3.15E+7 / 2\*

                 Shoreline      IE~srig~(T)   I~srig~(T) EC~iag~ T~yr~
                                              3.15E+7 / (ρ~s~ d~s~)

  Ingestion      Farm Crops     IE~csig~(T)   I~csig~(T) EC~igoc~

                 Animal         IE~asig~(T)   I~asig~(T) EC~igoc~
                 Products                     

                 Aquatic Foods  IE~fwig~(T)   I~fwig~(T) EC~igoc~

                 Inadvertent    IE~dsig~(T)   I~dsig~(T) EC~igoc~
                 Soil                         

                 Inadvertent    IE~wwig~(T)   I~wwig~(T) EC~igoc~
                 Swim                         

  Inhalation     Air            IE~aaig~(T)   I~aaig~(T) EC~igrc~

                 Resuspended    IE~saig~(T)   I~saig~(T) EC~igrc~
                 Soil                         
  -------------- -------------- ------------- ----------------------------

\*The factor of two devisor reflects the different geometry of the
exposure situation for swimming vs. boating. The swimming pathway
entails immersion in the radioactive source, while the boating pathway
entails being in proximity to it.

Table D‑15 Definitions for Calculation of Effective Dose

  ------------- ------------------------------------------------------------
  Parameter     Definition

  IE~eaig~(T)   Effective dose from external exposure to radionuclide i from
                plume immersion at air usage location a for an individual in
                age group g (Sv)

  IE~esig~(T)   Effective dose from external exposure to radionuclide i in
                contaminated soil at soil usage location s for an individual
                in age group g for exposure over time period (T)

  IE~wrig~(T)   Effective dose from external exposure to radionuclide i in
                contaminated water at recreational water usage location r
                for an individual in age group g (Sv)

  IE~brig~(T)   Effective dose from external exposure to radionuclide i from
                boating in contaminated water at recreational water usage
                location r for an individual in age group g (Sv)

  IE~srig~(T)   Effective dose from external exposure to radionuclide i in
                shoreline sediment at recreational water usage location r
                for an individual in age group g (Sv)

  IE~csig~(T)   Effective dose from ingestion intake of radionuclide i in
                food crop c at soil usage location s for an individual in
                age group g for exposure over time period T (Sv)

  IE~asig~(T)   Effective dose from ingestion intake of radionuclide i in
                animal product a at soil usage location s for an individual
                in age group g for exposure over time period T (Sv)

  IE~fwig~(T)   Effective dose from ingestion intake of radionuclide i in
                aquatic food f at water usage location w for an individual
                in age group g for exposure over time period T (Sv)

  IE~dsig~(T)   Effective dose from ingestion intake of radionuclide i in
                soil at soil usage location s for an individual in age group
                g for exposure over time period T (Sv)

  IE~wwig~(T)   Effective dose from ingestion intake of radionuclide i in
                swimming water at water usage location w for an individual
                in age group g for exposure over time period T (Sv)

  IE~aaig~(T)   Effective dose from inhalation intake of radionuclide i in
                air at air usage location a for an individual in age group g
                for exposure over time period T (Sv)

  IE~saig~(T)   Effective dose from inhalation intake of radionuclide i in
                resuspended soil at air usage location a for an individual
                in age group g for exposure over time period T (Sv)

  EC~iaa~       Effective dose coefficient for external exposure from plume
                immersion for radionuclide i for an adult (Sv m^3^ per Bq s)

  EC~iag~       Effective dose equivalent factor for external exposure from
                ground exposure for radionuclide i for an adult (Sv m^2^ per
                Bq s)

  EC~iaw~       Effective dose equivalent factor for external exposure from
                water immersion for radionuclide i for an adult (Sv L per Bq
                s)

  EC~igoc~      Effective dose coefficient for ingestion intake of
                radionuclide i of class c for an individual in age group g
                (Sv/Bq)

  EC~igrc~      Effective dose coefficient for ingestion intake of
                radionuclide i for an individual in age group g (Sv/Bq)

  T~yr~         Time of exposure, one year.

  3.15E+7       Factor for correction of units (seconds per year)

  10^-3^        Factor for correction of units (m^3^ per liter)

  ρ~s~          Surface soil bulk density (kg/m^3^)

  d~s~          Thickness of surface soil layer (m)
  ------------- ------------------------------------------------------------

Table D‑16 Equations for Calculation of Equivalent Dose

  ------------ ---------------- ---------------- ------------------------------
  Exposure     Exposure Pathway Dose Parameter   How Calculated
  Route                                          

  External     Plume            IE~eaig~T(T)     I~eaig~(T) HC~iaa~T T~yr~
                                                 3.15E+7

               Ground           IE~esig~T(T)     I~esig~(T) HC~iag~T T~yr~
                                                 3.15E+7 / (ρ~s~ d~s~)

               Swimming         IE~wrig~T(T)     10^-3^ I~wrig~(T) HC~iaw~T
                                                 T~yr~ 3.15E+7

               Boating          IE~brig~T(T)     10^-3^ I~brig~(T) HC~iaw~T
                                                 T~yr~ 3.15E+7 / 2\*

               Shoreline        IE~srig~T(T)     I~srig~(T) HC~iag~T T~yr~
                                                 3.15E+7 / (ρ~s~ d~s~)

  Ingestion    Farm Crops       IE~csig~T(T)     I~csig~(T) HC~igoc~T

               Animal Products  IE~asig~T(T)     I~asig~(T) HC~igoc~T

               Aquatic Foods    IE~fwig~T(T)     I~fwig~(T) HC~igoc~T

               Inadvertent Soil IE~dsig~T(T)     I~dsig~(T) HC~igoc~T

               Inadvertent Swim IE~wwig~T(T)     I~wwig~(T) HC~igoc~T

  Inhalation   Air              IE~aaig~T(T)     I~aaig~(T) HC~igrc~T

               Resuspended Soil IE~saig~T(T)     I~saig~(T) HC~igrc~T
  ------------ ---------------- ---------------- ------------------------------

\*The factor of two devisor reflects the different geometry of the
exposure situation for swimming vs. boating. The swimming pathway
entails immersion in the radioactive source, while the boating pathway
entails being in proximity to it.

Table D‑17 Definitions for Calculation of Equivalent Dose

  ---------------------------------------------------------------------------
  Parameter      Definition
  -------------- ------------------------------------------------------------
  IE~eaig~T(T)   Equivalent dose to organ or tissue T from external exposure
                 to radionuclide i from plume immersion at air location a for
                 an individual in age group g (Sv)

  IE~esig~T(T)   Equivalent dose to organ T from external exposure to
                 radionuclide i from plume immersion at soil usage location s
                 for an individual in age group g for exposure over time
                 period T (Sv)

  IE~wrig~T(T)   Equivalent dose to organ T from external exposure to
                 radionuclide i while swimming at recreational water usage
                 location r for an individual in age group g for exposure
                 over time period T (Sv)

  IE~brig~T(T)   Equivalent dose to organ T from external exposure to
                 radionuclide i while boating at recreational water usage
                 location r for an individual in age group g for exposure
                 over time period T (Sv)

  IE~srig~T(T)   Equivalent dose to organ T from external exposure to
                 radionuclide i from shoreline sediment at recreational water
                 usage location r for an individual in age group g over time
                 period T (Sv)

  IE~csig~T(T)   Equivalent dose to organ T from ingestion intake of
                 radionuclide i in food crop c at soil usage location s for
                 an individual in age group g for exposure over time period T
                 (Sv)

  IE~asig~T(T)   Equivalent dose to organ T from ingestion intake of
                 radionuclide i in animal product a at soil location s for an
                 individual in age group g for exposure over time period T
                 (Sv)

  IE~fwig~T(T)   Equivalent dose to organ T from ingestion intake of
                 radionuclide i in aquatic food f at water usage location w
                 for an individual in age group g for exposure over time
                 period T (Sv)

  IE~dsig~T(T)   Equivalent dose to organ T from ingestion intake of
                 radionuclide i in soil at soil usage location s for an
                 individual in age group g for exposure over time period T
                 (Sv)

  IE~wwig~T(T)   Equivalent dose to organ T from ingestion intake of
                 radionuclide i in water at water usage location w for an
                 individual in age group g for exposure over time period T
                 (Sv)

  IE~aaig~T(T)   Equivalent dose to organ T from inhalation intake of
                 radionuclide i in air at air usage location a for an
                 individual in age group g for exposure over time period T
                 (Sv)

  IE~saig~T(T)   Equivalent dose to organ T from inhalation intake of
                 radionuclide i in resuspended soil at air usage location a
                 for an individual in age group g for exposure over time
                 period T (Sv)

  HC~iaa~T       Equivalent dose coefficient for air immersion to an organ T,
                 radionuclide i, for an adult (Sv m^3^ per Bq s)

  HC~iag~T       Equivalent dose coefficient to organ T for external exposure
                 to ground for radionuclide i for an adult (Sv per Bq s)

  HC~iaw~T       Equivalent dose coefficient to organ T for external exposure
                 from water immersion for radionuclide I for an adult (Sv L
                 per Bq s)

  HC~igoc~T      Equivalent dose coefficient to organ T for ingestion intake
                 of radionuclide c of class c for an individual in age group
                 g (Sv/Bq)

  HC~igrc~T      Equivalent dose coefficient to organ T for inhalation intake
                 of radionuclide i of class c for an individual in age group
                 g (Sv/Bq)

  EC~igrc~       Effective dose coefficient for ingestion intake of
                 radionuclide i for an individual in age group g (Sv/Bq)

  T~yr~          Time of exposure, one year.

  3.15E+7        Factor for correction of units (seconds per year)

  10^-3^         Factor for correction of units (m^3^ per liter)

  ρ~s~           Surface soil bulk density (kg/m^3^)

  d~s~           Thickness of surface soil layer (m)
  ---------------------------------------------------------------------------

Table D‑18 Equations for Calculation of Cancer Risk

  ------------ -------------- -------------- ----------------------------------
  Exposure     Exposure       Risk Parameter How Calculated
  Route        Pathway                       

  External     Plume          IR~eaig~T(T)   I~eaig~(T) RC~iga~T T~yr~ 3.15E+7

               Ground Contam. IR~esig~T(T)   I~esig~(T) RC~igg~T T~yr~ 3.15E+7
                                             / (ρ~s~ d~s~)

               Swimming       IR~wrig~T(T)   10^-3^ I~wrig~(T) HC~iaw~T HC~gh~
                                             T~yr~ 3.15E+7

               Boating        IR~brig~T(T)   10^-3^ I~brig~(T) HC~iaw~T HC~gh~
                                             T~yr~ 3.15E+7 / 2\*

               Shoreline      RH~srig~T(T)   I~srig~(T) RC~iag~T T~yr~ 3.15E+7
                                             / (ρ~s~ d~s~)

  Ingestion    Farm Crops     RH~csig~T(T)   I~csig~(T) RC~igoc~T

               Animal         RH~asig~T(T)   I~asig~(T) EC~igoc~T
               Products                      

               Aquatic Foods  RH~fwig~T(T)   I~fwig~(T) RC~igoc~T

               Inadvertent    RH~dsig~T(T)   I~dsig~(T) RC~igoc~T
               Soil                          

               Inadvertent    RH~wwig~T(T)   I~wwig~(T) RC~igoc~T
               Swim                          

  Inhalation   Air            RH~aaig~T(T)   I~aaig~(T) RC~igrc~T

               Resuspended    RH~saig~T(T)   I~saig~(T) RC~igrc~T
               Soil                          
  ------------ -------------- -------------- ----------------------------------

\*The factor of two devisor reflects the different geometry of the
exposure situation for swimming vs. boating. The swimming pathway
entails immersion in the radioactive source, while the boating pathway
entails being in proximity to it.

Table D‑19 Definitions for Calculation of Cancer Risk

  --------------------------------------------------------------------------
  Parameter      Definition
  -------------- -----------------------------------------------------------
  IR~eaig~T(T)   Risk to organ or tissue T from external exposure to
                 radionuclide i from plume immersion at air location a for
                 an individual in age group g (risk)

  IR~esig~T(T)   Risk to organ T from external exposure to radionuclide i
                 from plume immersion at soil usage location s for an
                 individual in age group g for exposure over time period T
                 (risk)

  IR~wrig~T(T)   Risk to organ T from external exposure to radionuclide i
                 while swimming at recreational water usage location r for
                 an individual in age group g for exposure over time period
                 T (risk)

  IR~brig~T(T)   Risk to organ T from external exposure to radionuclide i
                 while boating at recreational water usage location r for an
                 individual in age group g for exposure over time period T
                 (risk)

  RH~srig~T(T)   Risk to organ T from external exposure to radionuclide i
                 from shoreline sediment at recreational water usage
                 location r for an individual in age group g over time
                 period T (risk)

  RH~csig~T(T)   Risk to organ T from ingestion intake of radionuclide i in
                 food crop c at soil usage location s for an individual in
                 age group g for exposure over time period T (risk)

  RH~asig~T(T)   Risk to organ T from ingestion intake of radionuclide i in
                 animal product a at soil location s for an individual in
                 age group g for exposure over time period T (risk)

  RH~fwig~T(T)   Risk to organ T from ingestion intake of radionuclide i in
                 aquatic food f at water usage location w for an individual
                 in age group g for exposure over time period T (risk)

  RH~dsig~T(T)   Risk to organ T from ingestion intake of radionuclide i in
                 soil at soil usage location s for an individual in age
                 group g for exposure over time period T (risk)

  RH~wwig~T(T)   Risk to organ T from ingestion intake of radionuclide i in
                 water at water usage location w for an individual in age
                 group g for exposure over time period T (risk)

  RH~aaig~T(T)   Risk to organ T from inhalation intake of radionuclide i in
                 air at air usage location a for an individual in age group
                 g for exposure over time period T (risk)

  RH~saig~T(T)   Risk to organ T from inhalation intake of radionuclide i in
                 resuspended soil at air usage location a for an individual
                 in age groupg g for exposure over time period T (risk)

  RC~iga~T       Risk coefficient for air immersion to an organ T,
                 radionuclide i, for an individual in age group g (m^3^ per
                 Bq s)

  RC~igg~T       Risk coefficient to organ T for external exposure to ground
                 for radionuclide i for an adult (m^2^ per Bq s)

  HC~iaw~T       Equivalent dose coefficient to organ T for external
                 exposure from water immersion for radionuclide I for an
                 adult (Sv L per Bq s)

  HC~gh~         Health effects conversion factor for effect h and an
                 individual in age group g (risk/Sv)

  RC~iag~T       Risk coefficient to organ T for external exposure to ground
                 (the soil surface factor is used for sediment as well) for
                 radionuclide i for an adult (m^3^ per Bq s)

  RC~igoc~T      Risk coefficient to organ T for ingestion intake of
                 radionuclide c of class c for an individual in age group g
                 (Bq^-1^)

  RC~igrc~T      Risk coefficient to organ T for inhalation intake of
                 radionuclide i of class c for an individual in age group g
                 (Bq^-1^)

  RC~igrc~T      Risk coefficient for inhalation of radionuclide i for an
                 individual in age group g (Sv/Bq)

  T~yr~          Time of exposure, one year

  3.15E+7        Factor for correction of units (seconds per year)

  10^-3^         Factor for correction of units (m^3^ per liter)

  ρ~s~           Surface soil bulk density (kg/m^3^)

  d~s~           Thickness of surface soil layer (m)
  --------------------------------------------------------------------------

## References

1.  GENII SDD. Napier, B.A., et al. GENII Version II Software Design
    Document. PNNL for U.S. Environmental Protection Agency. November
    2002.

2.  Phase II. Till, J.E, et al. Savannah River Site Environmental Dose
    Reconstruction Project, Phase II: Source Term Calculation and
    Ingestion Pathway Data Retrieval, Evaluation of Materials Released
    from the Savannah River Site. RAC Report No. 1-CDC-SRS-1999-Final,
    Risk Assessment Corporation (RAC), 30 April 2001.

3.  Hamby 1991. Hamby DM. Land and Water Use Characteristics in the
    Vicinity of the Savannah River Site (U). Westinghouse Savannah River
    Company. WSRC-RP-91-17. March 1991; 7.

4.  Moore 2002. Moore MS. Critical Pathway Assessment of the Savannah
    River Site, Aiken South Carolina. South Carolina Department of
    Health and Environmental Control. May 2002; 17-18.

5.  Harrison 2003. Harrison K. Georgia Extension Engineer. Telephone
    Log. March 11, 2003.

6.  Moore 2003. Moore M. SCDHEC. Telephone Log. March 12, 2003.

7.  ERDA-1537. U.S. Energy Research and Development Administration
    (ERDA). Final Environmental Impact Statement: Waste Management
    Operations, Savannah River Plant, Aiken, South Carolina. ERDA-1537,
    September 1977.

8.  ATL White Paper on Venison.

9.  IAEA 1994. International Atomic Energy Agency. Handbook of Parameter
    Values for the Prediction of Radionuclide Transfer in Temperate
    Environment. Tech. Rep. Ser. No. 364. Vienna, Austria. 1994.

10. Smith & Fledderman. Smith, M. and P. Fledderman. Radiocesium in
    White-tailed Deer on the Savannah River Site. 14 May 1999. Cited 21
    August 2003. Available at:
    <http://www.uga.edu/srel/Graphics/deer_snapshoot.pdf>.

11. FGR-13U. U.S. Environmental Protection Agency. Federal Guidance
    Report 13 Cancer Risk Coefficients for Environmental Exposure to
    Radionuclides: CD Supplement. EPA 402-C-99-001, Rev. 1. Oak Ridge
    National Laboratory and U.S. EPA. April 2002.

12. Till & Meyer. Till, J.E. and H.R. Meyer. Radiological Assessment --
    A Textbook on Environmental Dose Analysis. NUREG/CR-3332. ORNL-5968.
    U.S. Nuclear Regulatory Commission, Washington, DC. 1983.

13. IAEA SS-19. International Atomic Energy Agency. Generic Models for
    Use in Assessing the Impact of Discharges of Radioactive Substances
    to the Environment. Safety Series Report No. 19. Vienna, Austria.
    2001.

14. FRAMES 1.3. FRAMES 1.3 Website. 2002. \[cited 23 September 2003\]
    Available from URL: <http://mepas.pnl.gov/FRAMESV1/index.html>.

15. RG 1.111. U.S. Nuclear Regulatory Commission. Methods for Estimating
    Atmospheric Transport and Dispersion of Gaseous Effluents in Routine
    Releases from Light-Water-Cooled Reactors. Regulatory Guide 1.111,
    Revision 1. Office of Standards Development. July 1977.

16. Kennedy and Strenge. Kennedy, W.E., Jr. and D.L. Strenge. Residual
    Radioactive Contamination from Decommissioning -- Technical Basis
    for Translating Contamination Levels to Annual Total Effective Dose
    Equivalent. NUREG/CR-5512. PNL-7994. Pacific Northwest Laboratory
    for U.S. Nuclear Regulatory Commission. October 1992.

17. Strenge 1997. Strenge, D.L. A General Algorith for Radioactive Decay
    with Branching and Loss from a Medium. Health Physics. 73(6):
    953-957. 1997.

18. ICRP-38

19. Lederer and Shirley. Lederer, C.M. and V.S. Shirley. Table of
    Isotopes. 7th Edition. John Wiley & Sons, Inc., New York. 1978.

20. FGR-13. Eckerman, K. F., et al. Cancer Risk Coefficients for
    Environmental Exposure to Radionuclides. Federal Guidance Report
    No. 13. EPA 402-R-99-001. Oak Ridge National Laboratory and U.S. EPA
    Office of Radiation and Indoor Air. September 1999.

21. Weber 2001. Weber, A.H., R.L. Buckley, M.J. Parker, R.P. Harvey, and
    D.M. Hamby. The Creation of an Historical Meterological Database for
    Dose Construction. WSRC-TR-2001-00275. Westinghouse Savannah River
    Company, Aiken, GA. 2001.

22. Baes &Sharp 1981. Baes, C.F. and R.D. Sharp. Predicting Radionuclide
    Leaching from Root Zone Soil From Assessment Applications.
    CONF-81606. Oak Ridge National Laboratory, Oak Ridge, Tennessee.
    1981.

23. Peterson & Davis 2001. Peterson, S.R. and P.A. Davis. Tritium Doses
    from Chronic Atmospheric Releases: A New Method Proposed for
    Regulatory Compliance. Health Physics, 82(2):213-225. 2001.

24. ICRP-26. International Commission on Radiation Protection.
    Recommendations of the International Commission on Radiation
    Protection. ICRP Publication 26. Pergamon Press, Oxford. 1977.

25. ICRP-60. International Commission on Radiation Protection.
    Recommendations of the International Commission on Radiation
    Protection. ICRP Publication 60. Pergamon Press, Oxford. 1991.

26. Johnson 1962. Johnson JE. Sulfur-35 Releases from Reactor Areas.
    Dupont Interoffice Memorandum to CM Patterson. Savannah River Plant.
    RAC reference no. SKR1994020129. July 19, 1962.

27. ICRP-72. International Commission on Radiation Protection.
    Age-Dependent Doses to Members of the Public from Intake of
    Radionuclides, Part 5. Compilation of Ingestion and Inhalation Dose
    Coefficients. ICRP Publication 72. Pergamon Press, Oxford. 1996.

28. FGR-12. Eckerman, K.F. and J.C. Ryman. External Exposure to
    Radionuclides in Air, Water, and Soil. Federal Guidance Report
    No. 12. EPA 402-R-93-081. Oak Ridge National Laboratory and EPA
    Office of Radiation Programs. September 1993.

[^1]: The estimates of release were reviewed from the Phase II report,
    and, using site-specific data, adjusted the Phase II estimates as
    needed to perform the analyses for this report (see [Chapter
    5](../Chapter_05_Ready%20for%20CDC%20031405.doc) and [Appendix
    B](../Appendix_B_ready%20for%20CDC%20031405.doc)).

[^2]: In the rest of this appendix, references to GENII mean Version 2
    of GENII.

[^3]: The original version of GENII was developed in the late 1980s for
    use at DOE's Hanford Reservation, although the codes were designed
    with the flexibility to accommodate input parameters for a wide
    variety of sites. GENII Version 2 incorporates improved transport
    models, exposure options, dose and risk estimates, and user
    interfaces.

[^4]: If either the concentrations of ^137^Cs in SRS venison were
    notably larger than venison from other areas, or the cesium isotopic
    ratios in SRS venison were notably different that that from venison
    in other areas, it could have been possible to calculated doses from
    venison consumed in different scenarios. But such differences cannot
    be discerned, based on available literature.

[^5]: Documentation for use of FRAMES is available on the Internet at
    the FRAMES Version 1.3 website
    (<http://mepas.pnl.gov/FRAMESV1/index.html>) \[FRAMES 1.3\] (14).

[^6]: Another name for the mixing layer is the planetary boundary layer
    (12).

[^7]: The great majority of airborne releases were from tall stacks from
    the reactor and separations areas. Relatively small quantities of
    radionuclides were released into the air (primarily tritium as
    evaporated water vapor) from seepage basins and other area sources.

[^8]: In the GENII SDD, radionuclide activity is described in units of
    curies (Ci) as well as Becquerals (Bq), where 1 Ci = 3.7E+10 Bq.

[^9]: Adapted from \[Weber 2001\] (21). Topographic contours are
    25-meter intervals above sea level, with highlighted 50- and
    100-meter intervals. Lightly-shaded filled areas denote locations of
    cities and towns.

[^10]: Adapted from \[Weber 2001\] (21).

[^11]: As indicated, the basic equation as presented in the GENII SDD is
    given in units of atoms. The quantity of a radionuclide in soil can
    be converted from radioactive atoms to activity (Bq) by multiplying
    by the decay constant, λ~i.~

[^12]: This unit sited in the \[GENII SDD\] is functionally
    dimensionless.

[^13]: For purposes of modeling for these and other exposure pathways
    considering deposition of radionuclides onto soil or sediment, one
    assumes that the radionuclides are uniformly concentrated throughout
    a narrow band of soil near the earth's surface (e.g., a thickness of
    about 15 cm (6 in), which is about the depth that a plow would
    penetrate soil).

[^14]: In fact, however, the deposition velocity as actually used in the
    GENII coding is not radionuclide-specific. A value for deposition
    velocity must be assumed that is the same for all radionuclides.

[^15]: Note that the value actually input when using GENII is the
    weathering half-life, in days, as calculated from the relation ln2/
    λ~wi.~ The GENII coding performs the needed conversion to λ~wi~ and
    corrects from d^-1^ to y^-1^. In addition, the weathering rate as
    used in GENII is actually constant for all radionuclides.

[^16]: Because the annual quantity of each radionuclide ingested may be
    different from year to year, radionuclide ingestion is recalculated
    for each year for each receptor rather than assuming ingestion of a
    uniform radionuclide quantity over several years.

[^17]: Inadvertent soil ingestion by animals is not at this time
    considered in GENII. Although the equation is coded into GENII
    including the inadvertent soil ingestion pathway, the user interface
    does not request input of any values for the animal soil ingestion
    rate, and the GENII variable (SLCONA) for this parameter is set to
    zero \[Napier 2003e\].

[^18]: On each of the days it is assumed for purposes of the GENII
    calculations that the individual swims the number of times specified
    by the frequency of swimming event and for the duration of swimming
    event for each of these events.

[^19]: Despite the terminology used by the GENII SDD and the
    documentation for the FRAMES interface, this parameter is used as a
    quantity rather than a rate.

[^20]: The shielding factor for boating accounts for the shielding to
    direct radiation that may be provided by the structure of the boat.
    It is different from the geometry factor, which accounts for the
    location of the receptor above the surface of the water (rather than
    being immersed in the water). The geometry factor is assumed by the
    GENII authors to be a factor of 2 reduction, and is incorporated
    into the dose and risk equations for boating exposures that are
    addressed in Section D.4.3.

[^21]: During each of the boating days, the individual is assumed for
    purposes of the GENII calculations to be involved in the number of
    events given by the frequency of boating events with each event
    lasting for the duration of boating events hours.

[^22]: Except where noted, ICRP-60 terminology is used in this chapter.

[^23]: A *Gray* is a unit of absorbed dose equal to 1 Joule/kilogram (1
    J/kg).

[^24]: In ICRP-60 and other ICRP recommendations preceding ICRP-60, a
    weighting factor was called a quality factor.

[^25]: ICRP-26 recommended a 50-year time period for members of the
    public as well as radiation workers. ICRP-60 recommends a 70-year
    time period for members of the public and a 50-year time period for
    radiation workers.

[^26]: These weighting factors were calculated under somewhat different
    assumptions. ICRP-26 weighting factors are based on the risk of
    fatal cancers and hereditary defects in the first two generations.
    ICRP-60 weighting factors are based on risks for both fatal and
    non-fatal cancers, the risk of hereditary defects over all future
    generations, and the relative loss of live expectancy given a fatal
    cancer or a severe generic disorder.

[^27]: Radiation exposures that members of the public may have received
    from SRS operations are several orders of magnitude below those
    levels that could result in nonstochastic effects.

[^28]: LET stands for "linear effective track." Low-LET radiation refers
    to radiation such as gamma rays and beta particles. High-LET
    radiation refers to more massive radiation particles such as alpha
    particles.

[^29]: A supplement was first issued in 2000, but this supplement
    contained errors in the viewer and was replaced by the April 2002
    version.