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

Date:
5/
21/
02
Subject:
Outline
of
§
316(
b)
Case
Study
Evaluation
of
Impingement
and
Entrainment
Data
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/
21/
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
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/
21/
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
Brayton
Point
case
study
(
Part
F
of
the
Case
Study
Document,
DCN
4­
0003).
EPA
converted
Brayton
Point
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
"
brayton.
input.
data.
xls,"
indexed
in
the
docket
as
DCN
4­
2037.
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
F3
of
Part
F
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
Brayton
Point
in
1979
and
1980.
Although
this
example
focuses
on
entrainment,
the
same
basic
procedure
applies
to
impingement.

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
in
Section
A5­
3.1
of
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
DCN
4­
0003),
and
duplicated
below:

AE1,
j,
k
=
L
j,
k
S
j,
1
(
Equation
5)

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
(
equation
4)

The
main
elements
of
this
equation
include
L
j,
k,
the
numbers
of
individuals
impinged
or
entrained
Stratus
Consulting
5/
21/
02
4
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
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
5
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
=
­
log
e(
(
FV
j*
e(
Fj))
+
(
1­
F
j)
)

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:

S
j
=
e
(­
Zj),

where
Z
j
=
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,
through
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
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/
21/
02
5
i
j
j
i
j
j
S
S
S
 
+
=
=
max
1
*
1
,

j,
k
k
AE
j
j
j
AE
1
1
max
min

=
=
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
in
Section
A5­
3.1
of
Chapter
A5
of
Part
A
of
the
Case
Study
Document
(
DCN
4­
0003),
and
duplicated
below:

where:

AE1
k
=
the
total
number
of
age­
1
equivalents
derived
from
losses
at
all
stages
in
year
k
(
Equation
6)

Each
term
in
the
summation
represented
by
Equation
6
is
found
using
Equation
5
(
presented
above).
Stratus
Consulting
5/
21/
02
6
2.2
Example
Calculation
of
Age
1
Equivalent
Weakfish
Lost
to
Entrainment
Brayton
Point
Station,
1979­
1980
This
section
uses
the
equations
presented
above
in
Section
2.1
to
show
how
EPA
calculated
age
1
equivalent
numbers
of
weakfish
entrained
at
the
Brayton
Point
Station
in
1979
and
1980.

2.2.1
Example
Calculation
of
Sj
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
"
brayton.
input.
data.
xls"
(
DCN
4­
2037).

Table
1.
Stage­
specific
weakfish
life
history
parameters
used
to
derive
stage­
specific
weakfish
survival
rates
(
Sj)
at
Brayton
Point
Station.
Life
history
parameter
Life
stage
(
j)
M
F
Fraction
of
life
stage
(
j)
vulnerable
to
fishery
F
effective,
j
a
Z
=
M+
F
effective,
j
S
j
=
e­
Z
S*
j
b
Egg
1.04
0.00
0.00
0.00000
1.0430
0.3524
0.5211
Larvae
7.67
0.00
0.00
0.00000
7.6735
0.0005
0.0009
Juv1
2.44
0.00
0.00
0.00000
2.4399
0.0872
0.1604
Juv2
1.48
0.00
0.00
0.00000
1.4838
0.2268
0.3697
Age01
0.35
0.50
0.10
0.04014
0.3887
0.6779
0.8081
a.
F
effective,
j
represents
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
Sj,
1
Table
2
illustrates
the
calculation
of
S
j,
1,
the
expected
cumulative
survival
rate
from
the
stage
of
entrainment,
j,
through
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
Brayton
Point.
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
.
Stratus
Consulting
5/
21/
02
7
Table
2.
Example
derivation
of
Sj,
1,
the
stage
specific
cumulative
survival
rate
(
as
a
fraction)
from
stage
at
entrainment
(
j)
to
Age
1
for
weakfish
entrained
at
Brayton
Point
Station.
As
noted
in
the
text,
the
definition
of
Sj,
1
includes
accommodation
for
unknown
within­
stage
age
at
entrainment.
Life
Stage
(
j)
Egg
Larvae
Juvenile1
Juvenile2
Age1
S
j,
1
Egg
0.5211a
0.00046
0.0872
0.2268
0.6779
0.00000479
Larvae
0.00093a
0.0872
0.2268
0.6779
0.0000184
Juvenile1
0.1604a
0.2268
0.6779
0.0364
Juvenile2
0.3697a
0.6779
0.370
Age1
1.190a
1.190
a.
S*
j,
stage­
at­
entrainment
adjusted
survival
rate.

2.2.3
Example
Calculation
of
Annual
Total
Age
1
Equivalents
Table
3
shows
how
stage­
specific
entrainment
estimates
and
stage­
specific
cumulative
survival
rates
are
used
to
calculate
stage­
specific
age
1
equivalent
losses
and
the
total
annual
age
1
equivalent
losses
of
weakfish
in
1979
and
1980
at
Brayton
Point.
The
rows
of
Table
3
present
stage­
specific
values.
Column
1
presents
Brayton
Point's
estimates
of
entrainment
losses
in
1979
and
1980,
column
2
presents
these
losses
adjusted
by
EPA
to
represent
current
conditions,
and
column
3
presents
EPA's
estimates
of
S
j,
1.
Annual
age
1
equivalent
losses
at
Brayton
Point
are
presented
in
Table
F3­
7
of
Chapter
F3
of
Part
F
of
the
Case
Study
Document
(
DCN
4­
0003).
An
explanation
of
EPA's
adjustment
of
Brayton
Point's
historical
I&
E
records
is
also
provided
in
Chapter
F3.
Stratus
Consulting
5/
21/
02
8
Table
3.
Example
application
of
weakfish
cumulative
survival
rates
(
Sj,
1)
to
derive
stage­
specific
and
annual
total
Age­
1
equivalent
losses
from
weakfish
entrainment
losses
at
Brayton
Point
Station
during
1979­
1980.

Year
Life
stage
(
j)
Number
of
fish
entrained
Flow­
adjusted
lossa
S
j,
1
Age
1
equivalent
losses
1979
Egg
67,093,115
76,620,337
0.00000479
367.0
Larvae
6,336,776.00
7,236,598
0.0000184
133.0
Juvenile1
0
0
0.0364
0.0
Juvenile2
0
0
0.370
0.0
Age1
0
0
1.190
0.0
Total
(
1979)
95,764,620
500
1980
Egg
294,679,948
336,524,501
0.0000048
1,612.1
Larvae
6,897,493.00
7,876,937
0.0000184
144.7
Juv1
0
0
0.0364
0.0
Juv2
0
0
0.3697
0.0
Age01
0
0
1.1900
0.0
Total
(
1980)
393,306,442
1,757
a.
Flow
adjustment
factor
=
1.142,
accounting
for
differences
in
intake
flow
rate
between
1979­
1980
and
the
present;
the
rationale
and
derivation
of
the
flow
adjustment
factor
is
explained
in
Chapter
F3
of
Part
F
of
the
Case
Study
Document
(
DCN
4­
003).
