1
Memorandum
To:
Lynne
Tudor
and
Tom
Wall,
U.
S.
EPA
From:
Liz
Strange
and
Dave
Cacela,
Stratus
Consulting
Inc.

Date:
5/
28/
02
Subject:
Outline
of
§
316(
b)
Case
Study
Evaluation
of
Impingement
and
Entrainment
Data
with
Examples
Drawn
from
the
Salem
Case
Study
Per
your
request,
this
memorandum
provides
an
outline
of
the
links
among
facility
impingement
and
entrainment
(
I&
E)
data
that
were
inputs
to
case
study
analyses,
the
methods
used
by
Stratus
Consulting
to
evaluate
these
data,
and
results
of
our
evaluation.
It
is
intended
as
an
aid
to
reviewers
who
have
requested
clarification
of
the
data
evaluation
process
and
related
docket
entries.

There
are
two
major
components
of
each
case
study
analysis:
(
1)
the
evaluation
of
facility
I&
E
data,
including
the
development
of
metrics
that
express
I&
E
losses
in
ways
that
are
suitable
inputs
to
economic
analyses
(
e.
g.,
the
conversion
of
egg
and
larval
losses
to
an
equivalent
number
of
adult
fish);
and
(
2)
the
monetary
valuation
of
I&
E
losses
and
the
economic
benefits
expected
to
result
from
reducing
these
losses.
This
memorandum
focuses
on
the
first
component,
including
the
steps
that
Stratus
Consulting
followed
to
convert
I&
E
numbers
into
metrics
used
in
the
case
study
economic
analyses,
and
the
corresponding
docket
entries
for
input
data,
methods,
and
results.
Section
1
is
an
overview
of
the
general
approach
used
to
compile
and
evaluate
I&
E
data,
and
Section
2
provides
an
example
for
a
specific
case
study
facility.

1.
General
Approach
Used
to
Compile
and
Evaluate
I&
E
Data
For
each
case
study,
raw
I&
E
data
were
first
compiled
from
facility
documents
and
entered
into
an
EXCEL
workbook.
One
EXCEL
workbook
was
prepared
for
each
case
study
facility
and
labeled
according
to
the
name
of
the
facility.
Each
of
these
workbooks
is
a
separate
docket
entry,
listed
in
the
docket
index
under
Author,
Stratus
Consulting
Inc.
Electronic
copies
of
the
files
are
contained
in
a
CD­
ROM
located
at
DCN
4­
1305,
as
noted
in
the
Comment
field
of
each
workbook
docket
entry.

The
facility
I&
E
data
in
the
EXCEL
workbooks
were
evaluated
using
the
methods
presented
in
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
this
document
is
DCN
4­
0003).
Chapter
A5
provides
the
equations
used
to
calculate
age
1
equivalents
(
Section
A5­
3.1),
foregone
fishery
yield
(
Section
A5­
3.2),
and
production
foregone
(
Section
A5­
3.3)
from
the
I&
E
numbers
obtained
from
facility
reports.
The
relationships
among
facility
raw
loss
data
and
these
metrics
are
outlined
in
Figure
A5­
1
in
Chapter
A5.
Chapter
A5
also
discusses
the
approach
used
to
estimate
Stratus
Consulting
5/
28/
02
2
Results
Chapter
3
of
Case
Study
Report
(
Case
Study
Reports
are
Parts
B
through
I
of
Case
Study
Document)

DCN
4­
0003
Evaluation
Methods
Chapter
A5
of
Part
A
of
Case
Study
Document
DCN
4­
0003
Input
Data
Facility
I&
E
Data
Species
Life
History
Data
DCN
4­
1305
reductions
in
harvested
species
resulting
from
the
impingement
and
entrainment
of
forage
species
(
Section
A5­
3.4).
Figure
A5­
2
outlines
this
procedure.

The
results
of
the
calculations
discussed
in
Chapter
A5
are
presented
for
each
case
study
in
the
third
chapter
of
the
case
study
report,
entitled
"
Evaluation
of
I&
E
Data"
(
case
study
reports
are
contained
in
Parts
B
through
I
of
the
Case
Study
Document,
DCN
4­
0003).
Tables
in
the
chapter
"
Evaluation
of
I&
E
Data"
present
facility
estimates
of
numbers
of
organisms
impinged
and
entrained
per
year
and
these
numbers
expressed
as
age
1
equivalents,
foregone
fishery
yield,
and
production
foregone.
An
appendix
to
this
chapter
presents
species­
specific
life
history
data
used
to
perform
these
calculations.
The
References
section
of
the
Case
Study
Document
(
DCN
4­
0003)
provides
a
complete
listing
of
all
information
sources.

In
some
cases,
the
I&
E
data
provided
by
the
facilities
required
some
additional
manipulation
in
order
to
calculate
age
1
equivalents,
foregone
fishery
yield,
or
production
foregone
(
e.
g.,
conversion
of
daily
or
monthly
I&
E
rates
to
annual
rates).
Such
case­
study
specific
analyses
are
discussed
in
the
chapter
"
Evaluation
of
I&
E
Data"
of
the
corresponding
case
study
report
(
contained
in
the
Case
Study
Document,
DCN
4­
0003).

The
figure
below
outlines
the
links
among
data
input
files,
methods,
and
results,
and
the
corresponding
docket
numbers.
Stratus
Consulting
5/
28/
02
3
2.
Example
of
Links
Among
Data
Input
Files,
Methods,
and
Results
This
section
provides
an
example
of
the
links
among
data
input
files,
methods,
and
results
for
the
Salem
facility,
which
was
evaluated
as
part
of
the
Delaware
case
study
(
Part
B
of
the
Case
Study
Document,
DCN
4­
0003).
EPA
converted
Salem's
records
of
annual
total
numbers
of
impinged
and
entrained
organisms
to
age
1
equivalents,
foregone
fishery
yield,
and
production
foregone
using
the
equations
presented
in
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
DCN
4­
0003).
The
facility
I&
E
data
that
were
used
for
these
calculations
are
presented
in
worksheet
1
of
the
EXCEL
workbook
"
salem.
input.
data.
xls,"
indexed
in
the
docket
as
DCN
4­
2051.
An
electronic
copy
of
this
workbook
is
contained
in
the
CD­
ROM
filed
under
DCN
4­
1305.
The
results
of
these
calculations
are
provided
in
the
third
chapter
of
the
case
study
report,
Chapter
B3
of
Part
B
of
the
Case
Study
Document
(
DCN
4­
0003).
This
chapter
is
entitled
"
Evaluation
of
I&
E
Data."

The
following
example
gives
a
detailed
elaboration
of
the
steps
involved
in
calculating
the
number
of
age
1
equivalents
using
data
for
weakfish
entrainment
at
Salem
in
1981
and
1982.
Section
2.1
presents
the
equations
involved
(
discussed
in
detail
in
Chapter
A5
of
Part
A
of
the
Case
Study
Document,
DCN
4­
0003).
Section
2.2
shows
how
these
equations
are
implemented.

2.1
Equations
Used
to
Calculate
Age
1
Equivalents
As
discussed
in
Section
A5­
3.1
of
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
DCN
4­
0003),
the
Equivalent
Adult
Model
is
a
method
for
expressing
I&
E
losses
as
an
equivalent
number
of
individuals
at
some
other
life
stage,
referred
to
as
the
age
of
equivalency.
EPA
used
this
model
to
convert
facility
impingement
and
entrainment
numbers
to
age
1
equivalents.

The
basic
equation
used
by
EPA
to
calculate
stage­
specific
age
1
equivalent
losses
is
presented
as
Equation
5
in
Section
A5­
3.1
of
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
DCN
4­
0003),
and
duplicated
below:
Stratus
Consulting
5/
28/
02
4
AE1
j,
k
=
L
j,
k
S
j,
1
(
Equation
1)

where:

AE1
j,
k
=
the
number
of
age
1
equivalents
killed
during
life
stage
j
in
year
k
L
j,
k
=
the
number
of
individuals
killed
during
life
stage
j
in
year
k
S
j,
1
=
the
cumulative
survival
rate
for
individuals
passing
from
life
stage
j
to
age
1
(
defined
in
Equation
4)

The
main
elements
of
this
equation
include
L
j,
k,
the
numbers
of
individuals
impinged
or
entrained
during
life
stage
j
in
year
k,
and
S
j,
1
the
cumulative
survival
rate
for
individuals
passing
from
life
stage
j
to
age
1.

In
general,
the
loss
rates,
L
j,
k
,
used
by
EPA
for
age
1
equivalent
calculations
in
the
case
studies
are
the
annual
impingement
and
entrainment
rates
reported
by
each
facility.
However,
in
some
cases
EPA
adjusted
facility­
reported
annual
loss
rates
to
account
for
current
conditions
or
to
estimate
entrainment
assuming
100%
mortality.
Such
adjustments
are
described
for
particular
case
studies
in
the
third
chapter
of
the
relevant
case
study
report
("
Evaluation
of
I&
E
Data")
(
Parts
B
through
I
of
the
Case
Study
Document,
DCN
4­
0003).

In
order
to
calculate
S
j,
1
for
use
in
Equation
1
above,
it
is
necessary
to
compile
species­
specific
life
history
data,
including
stage­
specific
values
for
natural
mortality
(
M
j),
fishing
mortality
(
F
j),
and
the
fraction
of
individuals
vulnerable
to
fishing
mortality
(
FV
j).
In
cases
where
a
particular
life
stage,
j,
is
not
fully
recruited
to
the
fishery,
the
effective
fishing
mortality,
F
effective
is
derived
from
F
and
FV
as
F
effective,
j
=
­
log
e(
(
FV
j
*
e(
Fj))
+
(
1
­
F
j)
)
(
Equation
2)

As
discussed
in
Section
A5­
3.1
of
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
DCN
4­
0003),
these
life
history
data
are
used
to
estimate
stage­
specific
survival
rates,
S
j:
Stratus
Consulting
5/
28/
02
5
i
j
j
i
j
j
S
S
S
 +
=
=
max
1
*
1
,
S
j
=
e
(­
Zj),
(
Equation
3)

where:

Zj
=
M
j
+
F
effective,
j
and
Z
j,
M
j,
are
as
defined
above.

S
j,
1,
the
expected
cumulative
survival
rate
from
the
stage
of
impingement
or
entrainment,
j,
to
age
1,
is
then
given
by
the
product
of
all
stage­
specific
survival
rates
to
age
1.
The
equation
used
to
calculate
S
j,
1
is
presented
as
Equation
4
in
Section
A5­
3.1
of
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
DCN
4­
0003),
and
duplicated
below:

where:

S
j,
1
=
cumulative
survival
from
stage
j
until
age
1
S
j
=
survival
fraction
from
stage
j
to
stage
j
+
1
S*
j
=
2S
j
e­
log(
1+
Sj)
=
adjusted
S
j
j
max
=
the
stage
immediately
prior
to
age
1
(
Equation
4)

An
adjustment
to
S
j,
S*
j,
describes
the
effective
survival
rate
for
the
group
of
organisms
entrained
at
stage
j,
considering
the
fact
that
the
individual
fish
were
entrained
at
various
specific
ages
within
stage
j.
This
adjustment
is
necessary
because
the
amount
of
time
spent
in
that
stage
before
entrainment
occurs
is
unknown.

The
annual
total
number
of
age
1
equivalents
lost
to
impingement
or
entrainment
is
the
sum
of
age
1
equivalents
lost
at
each
life
stage
during
a
particular
year.
The
equation
used
to
calculate
this
total
is
presented
as
Equation
6
in
Section
A5­
3.1
of
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
DCN
4­
0003),
and
duplicated
below:
Stratus
Consulting
5/
28/
02
6
j,
k
k
AE
j
j
j
AE
1
1
max
min

=
=

where:

AE1
k
=
the
total
number
of
age
1
equivalents
derived
from
losses
at
all
stages
in
year
k
(
Equation
5)

Each
term
in
the
summation
represented
by
Equation
5
is
found
using
Equation
1.

2.2
Example
Calculation
of
Age
1
Equivalent
Weakfish
Lost
to
Entrainment
at
Salem
in
1981
and
1982
This
section
uses
the
equations
presented
above
in
Section
2.1
to
show
how
EPA
calculated
age
1
equivalent
numbers
of
weakfish
entrained
at
Salem
in
1981
and
1982.
Note
that
these
equations
are
consistent
with
those
used
by
Salem
in
its
1999
Permit
Renewal
Application.

2.2.1
Example
Calculation
of
S
j
and
S*
j
Table
1
illustrates
the
calculation
of
S
j
and
S*
j,
which
are
used
in
Equation
4
to
calculate
S
j,
1,
the
expected
cumulative
survival
rate
from
the
stage
of
entrainment,
j,
through
age
1.
Each
row
of
Table
1
gives
the
basic
and
derived
parameters
that
are
specific
for
each
particular
life
stage
of
weakfish.
The
two
right­
most
columns
in
the
table
present
S
j
and
S*
j.
The
life
history
data
presented
in
Table
1
are
found
in
the
docket
in
worksheets
2
to
4
of
the
EXCEL
workbook
"
salem.
input.
data.
xls"
(
DCN
4­
2051).
These
data
were
taken
from
Salem's
1999
Permit
Renewal
Application.
Stratus
Consulting
5/
28/
02
7
Table
1.
Stage­
specific
weakfish
life
history
parameters
(
M,
F,
Feffective)
used
to
derive
stagespecific
weakfish
survival
rates
(
S
j)
at
Salem.

Life
history
parameter
Life
stage
(
j)
M
j
F
j
Fraction
of
life
stage
(
j)
vulnerable
to
fishery
F
effective,
j
a
Z
j
=
M
j
+
F
effective,
j
S
j
=
e­
Zj
S*
j
b
Egg
1.04
0.00
0.00
0.00000
1.0430
0.3524
0.5211
Yolk­
sac
larvae
1.34
0.00
0.00
0.00000
1.3410
0.2616
0.4147
Post
yolk­
sac
larvae
6.33
0.00
0.00
0.00000
6.3325
0.0018
0.0035
Juvenile
1
2.44
0.00
0.00
0.00000
2.4399
0.0872
0.1604
Juvenile
2
1.48
0.00
0.00
0.00000
1.4838
0.2268
0.3697
Age
01
0.35
0.25
0.10
0.02237
0.3709
0.6901
0.8166
a.
F
effective,
j
represents
the
stage­
specific
fishing
mortality
rate
(
F)
adjusted
for
fraction
of
age
class
vulnerable
to
fishery.
b.
S*
j
represents
the
stage­
specific
survival
rate
(
S
j)
adjusted
to
account
for
the
fact
that
the
precise
within­
stage
age
of
entrained
fish
is
unknown.

2.2.2
Example
Calculation
of
S
j,
1
Table
2
illustrates
the
calculation
of
S
j,
1,
the
expected
cumulative
survival
rate
from
the
stage
of
entrainment,
j,
to
age
1
(
Equation
4
in
Section
2.1).
The
rows
of
Table
2
give
the
stage­
specific
values
of
S
j
or
S*
j
used
in
the
calculation
of
S
j,
1
for
weakfish
entrained
at
Salem.
The
rows
contain
different
numbers
of
values
for
the
survival
fraction
from
stage
j
to
stage
j
+
1
depending
on
the
number
of
life
stages
that
an
organism
would
have
passed
through
until
reaching
age
1.
The
final
column
of
Table
2
is
the
stage­
specific
cumulative
survival
rate
from
entrainment
to
age
1,
S
j,
1.

Table
2.
Elaboration
of
Equation
4:
Example
derivation
of
S
j,
1,
the
stage
specific
cumulative
survival
rate
(
as
a
fraction)
from
stage
at
entrainment
(
j)
to
age
1
for
weakfish
entrained
at
Salem.
The
definition
of
S
j,
1
includes
accommodation
for
unknown
within­
stage
age
at
entrainment.

Life
stage
(
j)
Egg
Yolk­
sac
larvae
Post
yolk­
sac
larvae
Juvenile
1
Juvenile
2
S
j,
1
Egg
0.52114a
0.26158
0.00178
0.08717
0.22678
0.0000048
Yolk­
sac
larvae
0.41469a
0.00178
0.08717
0.22678
0.0000146
Post
yolk­
sac
larvae
0.00355a
0.08717
0.22678
0.0000702
Juvenile
1
0.16036a
0.22678
0.0363669
Juvenile
2
0.36971a
0.3697119
a.
S*
j,
stage­
at­
entrainment
adjusted
survival
rate.
Stratus
Consulting
5/
28/
02
8
2.3
EPA
Procedure
for
Estimating
Annual
Entrainment
Under
an
Assumption
of
100%
Through­
Plant
Mortality
As
discussed
in
Section
B3­
3.2
of
Chapter
B3
of
the
Case
Study
Document
(
DCN
4­
0003),
Salem
discounted
the
number
of
organisms
entrained
by
species­
and
life
stage­
specific
through­
plant
survival
rates
(
discussed
in
Appendix
F,
Attachment
2,
of
Salem's
1999
Permit
Renewal
Application).
For
example,
if
Salem
estimated
that
1,000
individuals
of
a
particular
species
were
entrained
on
a
particular
day,
and
they
believed
that
15%
of
those
fish
could
survive
passage
through
the
facility
cooling
system,
Salem
used
the
survival
rate
as
a
discount
factor
and
reported
that
daily
entrainment
rate
as
850
fish
rather
than
1,000
fish.

An
independent
review
of
Salem's
1999
Application
(
ESSA
Technologies,
Ltd.,
2000)
concluded
that
Salem's
entrainment
rates
were
most
likely
underestimated
because
their
assumptions
about
through­
plant
survival
of
entrained
organisms
was
not
well
supported.
EPA
concurred
and
therefore
based
the
case
study
benefits
analysis
on
an
assumption
of
100%
through­
plant
mortality.
Thus,
EPA
recalculated
Salem's
entrainment
losses
to
disregard
the
survival
factors
that
Salem
had
used
in
its
calculations,
as
discussed
below.

2.3.1
Equations
used
by
EPA
to
Estimate
Salem's
Entrainment
Losses
Assuming
100%
Through­
Plant
Mortality
The
basic
equation
used
by
EPA
to
estimate
the
losses
under
an
assumption
of
100%
through­
plant
mortality
is
presented
below:

E'
=
E
/
F
where:

E'
=
Number
of
fish
entrained
assuming
100%
through­
plant
mortality
E
=
Number
of
fish
entrained
assuming
non­
zero
through­
plant
survival
(
i.
e.,
Salem
records
including
through­
plant
survival)
F
=
Through­
plant
mortality
rate
(
from
all
stresses
combined)
(
Equation
6)

Records
of
the
discounted
number
of
fish
entrained
(
E)
were
provided
in
Salem's
1999
Application,
Appendix
L,
Tab
8
and
duplicated
in
Table
B3­
6,
Chapter
B3
of
the
Case
Study
Document
(
DCN
4­
0003).
Through­
plant
mortality
(
F)
was
not
explicitly
presented
in
Salem's
Stratus
Consulting
5/
28/
02
9
1999
Application,
so
EPA
estimated
these
factors
based
on
the
stress
mortality
models
presented
in
the
1999
Application
(
Appendix
F,
Attachment
2).
This
procedure
is
discussed
below.

2.3.2
Salem's
General
Model
of
Through­
Plant
Mortality
Salem's
1999
Application
used
model­
based
estimates
of
thermal
mortality
in
conjunction
with
empirical
estimates
of
mechanical
mortality
to
determine
the
total
through­
plant
mortality
rate.
Mechanical
mortality
rates
were
based
on
studies
conducted
at
the
Indian
Point
Generating
Station
on
the
Hudson
River
in
the
1980'
s
and
using
data
from
the
1984
Salem
§
316(
b)
demonstration.
Chemical
mortality
was
considered
negligible.
The
general
model
for
the
joint
effects
of
these
mortality
factors
is
presented
in
Appendix
F,
Attachment
2,
p.
19
of
Salem's
1999
Application
and
duplicated
below:

F
i
=
1­
(
1
­
M
i)
×
(
1
­
C
i)
×
(
1
­
T
i)
(
Equation
7)

where:

F
i
=
Through­
plant
mortality
on
the
ith
day
M
i
=
Probability
of
death
resulting
from
mechanical
and
physical
stresses
in
the
ith
day
C
i
=
Probability
of
death
resulting
from
chemical
(
i.
e.,
antifouling
chemicals)
exposure
on
the
ith
day
T
i
=
Probability
of
death
resulting
from
exposure
to
elevated
temperatures
on
the
ith
day
The
species­
and
stage­
specific
mechanical
mortality
factors
that
apply
in
Equation
7
are
provided
in
Salem's
1999
Application
in
Appendix
F,
Attachment
2,
Table
12
and
are
duplicated
in
Appendix
B1
of
the
Case
Study
Document
(
DCN
4­
0003).
Equation
7
is
expressed
on
a
daily
basis.
However,
for
reasons
described
below,
EPA
used
this
model
without
consideration
of
daily
variations.

Salem's
1999
application
did
not
provide
a
complete
description
of
the
F
factors
that
were
used,
nor
did
it
provide
explicit
records
of
T.
However,
because
the
Application
did
provide
explicit
values
for
M,
and
because
C
was
considered
to
be
effectively
zero,
EPA
was
able
to
algebraically
solve
for
F
using
a
suitable
value
of
T.
The
procedure
that
EPA
used
to
identify
T
is
described
below
in
Section
2.3.3.
Stratus
Consulting
5/
28/
02
10
2.3.3
EPA
Procedure
for
Deducing
Salem's
Values
for
Thermal
Mortality
Parameters
Salem's
1999
Application
provided
values
of
mortality
rates
associated
with
mechanical
and
chemical
stress,
and
details
of
species­
specific
regression
models
used
to
estimate
thermally­
induced
mortality
rates.
The
actual
calculations
were
performed
on
daily
records
of
entrainment
and
daily
records
of
thermal
conditions
at
the
plant,
as
indicated
by
the
subscripts
i
in
Equation
7.
However,
daily
numbers
of
entrained
organisms
were
not
available
to
EPA,
which
precluded
EPA
from
performing
calculations
that
would
back­
out
the
effects
of
non­
zero
through­
plant
survival
on
a
daily
basis.
Instead,
the
curve
presented
in
Figure
4
of
Attachment
2
of
Appendix
F
of
Salem's
Application
made
it
possible
for
EPA
to
derive
values
of
average
thermal
conditions
at
the
facility.
EPA
used
the
average
values
estimated
in
this
way
with
Salem's
regression
models
of
thermal
mortality
provided
in
the
Application
to
generate
estimates
of
average
thermal
mortality
rates
on
a
species­
specific
basis.
This
procedure
is
described
in
detail
below.

In
order
to
calculate
the
thermal
mortality
factors
(
T
i)
for
use
in
Equation
7,
EPA
used
the
probit
models
of
thermal
mortality
that
were
presented
in
Salem's
1999
Application
in
Appendix
F,
Attachment
2,
p.
20.
As
part
of
this
effort,
EPA
identified
a
discrepancy
within
the
Application
with
regard
to
the
model
definition.
According
to
Table
13
of
Appendix
F,
Attachment
2,
the
coefficient
B
1
modifies
the
acclimation
effect,
and
the
coefficient
B
2
modifies
the
exposure
effect.
This
representation
disagrees
with
the
representation
of
the
equation
on
p.
20
of
Appendix
F,
Attachment
2.
EPA
concluded
that
the
discrepancy
was
due
to
a
clerical
error
and
concluded
that
the
coefficients
B
1
and
B
2
were
inadvertently
mislabeled
in
the
equation
on
p.
20
of
Appendix
F,
Attachment
2
and
therefore
used
the
following
equation
with
the
coefficients
B
0,
B
1,
B
2,
and
B
3
as
provided
in
the
Application
in
Appendix
F,
Attachment
2,
Table
13.
EPA
estimated
the
acclimation
temperature
(
T
a)
from
Appendix
F,
Attachment
2,
Figure
3
as
16.7
°
C.
The
exposure
duration
(
D)
was
obtained
from
the
Application,
Attachment
2,
Table
5
(
Unit
1),
and
is
equal
to
2.35
min.
:

probit
(
T)
=
B
0
+
B
1
T
e
+
B
2
T
a
+
B
3
log
10
D
(
Equation
8)

where:

B
0,
B
1,
B
2,
and
B
3
=
Coefficients
estimated
using
regression
analysis
in
Hudson
River
studies
of
thermal
tolerance
T
e
=
Exposure
temperature
(
°
C)
T
a
=
Acclimation
temperature
(
°
C)
D
=
Exposure
duration
(
minutes)
T
=
Fraction
killed
Stratus
Consulting
5/
28/
02
11
EPA
calculated
the
exposure
temperature
(
T
e)
using
the
following
equation
presented
in
the
Application
in
Appendix
F,
Attachment
2,
p.
20:

T
e
=
T
a
+
T
delta
(
Equation
9)

where:

T
a
=
Acclimation
temperature
(
°
C)
T
delta
=
Temperature
change
through
condensers
(
°
C)

The
temperature
change
through
the
condensers
(
T
delta)
was
obtained
from
Section
II
of
Appendix
F
of
the
Application
and
was
estimated
as
9.27
°
C,
which
is
the
mean
of
the
reported
minimum
of
14.8
°
F
and
maximum
of
18.6
°
F.
Table
3
provides
a
complete
depiction
of
the
particular
regression
model
and
thermal
regime
values
that
were
combined
by
EPA
to
yield
an
estimate
of
through­
plant
mortality
rates
due
to
thermal
mortality
for
weakfish
(
T).
The
relationship
between
thermal
mortality
rates,
mechanical
mortality
rates,
and
combined
mortality
(
Equation
7)
for
weakfish
is
presented
in
Table
4.

Table
3.
Use
of
Salem's
thermal
tolerance
model
(
Equation
8)
and
Salem
thermal
conditions
to
determine
thermal
mortality
rates
among
early
life
stages
of
weakfish
entrained
by
Salem.

Probit
model
coefficients
Thermal
variables
Estimates
B
o
B
1
B
2
B
3
T
a
T
e
D
probit(
T)
T
­
9.016
­
0.092
0.427
1.286
16.7
25.98
2.35
1.0173
0.845
Table
4.
EPA's
derivation
of
stage­
specific
through­
plant
mortality
rates
(
F)
from
factors
associated
with
mechanical
and
thermal
stress
for
weakfish.

Life
stage
Mechanical
mortality
Thermal
mortality
(
T)
F
Egg
1
0.845
1.000
Yolk­
sac
0.64
0.845
0.944
Post
yolk­
sac
0.64
0.845
0.944
Juvenile
1
0.5
0.845
0.923
Juvenile
2
0.5
0.845
0.923
Stratus
Consulting
5/
28/
02
12
2.4
Example
Calculation
of
Weakfish
Annual
Entrainment
Assuming
100%
Through­
Plant
Mortality
This
section
uses
the
equations
presented
in
Section
1
above
and
the
mortality
factors
in
Table
4
to
show
how
EPA
calculated
numbers
of
weakfish
entrained
at
Salem
assuming
100%
through­
plant
mortality.

2.4.1
Example
Calculation
of
Annual
Total
Age
1
Equivalents
Table
5
shows
how
EPA
used
stage­
specific
entrainment
estimates
(
number
of
fish
entrained)
and
stage­
specific
cumulative
survival
rates
(
S
j,
1)
to
calculate
stage­
specific
age
1
equivalent
losses
and
the
total
annual
age
1
equivalent
losses
of
weakfish
in
1981
and
in
1982
at
Salem.
The
rows
of
Table
5
present
stage­
specific
values.
Column
1
presents
Salem's
estimates
of
entrainment
losses
in
1981
and
1982
[
presented
in
Appendix
L,
Tab
8
of
Salem's
1999
Application
and
duplicated
in
Table
B3­
6
of
Chapter
B3
of
Part
B
of
the
Case
Study
Document
(
DCN
4­
0003)],
Column
2
presents
EPA's
estimates
of
through­
plant
mortality
rates,
Column
3
presents
Salem's
entrainment
rates
adjusted
for
100%
through­
plant
mortality
(
Table
B3­
7
of
Chapter
B3),
and
Column
4
presents
EPA's
estimates
of
S
j,
1.
Column
5
depicts
the
stage­
specific
and
annual
total
age
1
equivalent
losses
as
calculated
by
Equation
1
and
Equation
5,
respectively.
EPA's
estimates
of
annual
age
1
equivalent
losses
of
all
species
are
presented
in
Table
B3­
8
of
Chapter
B3
of
Part
B
of
the
Case
Study
Document
(
DCN
4­
0003).
Stratus
Consulting
5/
28/
02
13
Table
5.
EPA's
calculation
of
annual
age
1
equivalent
weakfish
entrainment
at
Salem
during
1981
and
1982
assuming
100%
through­
plant
survival.

Column
1
Column
2
Column
3
Column
4
Column
5
Year
Life
stage
(
j)
Number
of
fish
entrained
Deduced
throughplant
mortality
rate
Loss
assuming
100%
mortality
S
j,
1
Age
1
equivalent
losses
1981
Egg
2,190,647
1.00000
2,190,647
0.00000479
10.5
Yolk­
sac
larvae
15,818,220
0.94438
16,749,874
0.0000146
244.1
Post
yolk­
sac
larva
23,921,054
0.94438
25,329,945
0.0000702
1,777.0
Juvenile
1
3,628,034
0.92275
3,931,772
0.0364
142,986.5
Juvenile
2
206,985
0.92275
224,314
0.370
82,931.4
Age
1
0
1.00000
0
0.817
0.0
Total
(
1981)
45,764,940
48,426,552
227,950
1982
Egg
9,723,584
1.00000
9,723,584
0.00000479
46.6
Yolk­
sac
larvae
10,505,108
0.94438
11,123,833
0.0000146
162.1
Post
yolk­
sac
larva
44,235,698
0.94438
46,841,071
0.0000702
3,286.2
Juvenile
1
9,902,183
0.92275
10,731,191
0.0364
390,260.5
Juvenile
2
90,332
0.92275
97,895
0.370
36,192.8
Age
1
0
1.00000
0
0.817
0.0
Total
(
1982)
74,456,905
78,517,574
429,948
