United
States
EPA
822­
R­
03­
027
Environmental
Protection
November
2003
Agency
The
Biotic
Ligand
Model:
Technical
Support
Document
for
Its
Application
to
the
Evaluation
of
Water
Quality
Criteria
for
Copper
i
TABLE
OF
CONTENTS
1.0
INTRODUCTION
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1
2.0
THEORETICAL
BACKGROUND
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2
2.1
Description
of
Generalized
BLM
Model
Framework
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2
2.2
Model
Formulation
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3
2.2.1
Chemical
Model­
Inorganic
Metal
Speciation
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5
2.2.2
Chemical
Model­
Dissolved
Organic
Matter
Complexation
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5
2.3
Relationship
of
Copper
Accumulation
to
Acute
Toxicity
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7
2.4
Description
of
Species
on
the
Biotic
Ligand
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8
2.5
Alternative
Computational
Modes
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8
2.5.1
Metal
Speciation
Computations
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9
2.5.2
Metal
Toxicity
Computations
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9
3.0
MODEL
CALIBRATION
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10
3.1
Sources
of
Thermodynamic
Information
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10
3.1.1
Inorganic
Metal
Speciation
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10
3.1.2
Interactions
of
Copper
with
Organic
Matter
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10
3.2
Calibration
of
the
BLM
to
Copper
Accumulation
at
the
Biotic
Ligand
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11
3.3
Response
of
the
BLM
to
Variation
in
Hardness,
DOC
and
pH
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12
3.3.1
Effect
of
Dissolved
Organic
Carbon
on
Copper
Accumulation
and
Toxicity
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13
3.3.2
Effect
of
Hardness
on
Copper
Accumulation
and
Toxicity
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13
3.3.3
Effect
of
pH
on
Copper
Accumulation
and
Toxicity
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14
3.3.4
Summary
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15
3.4
Application
of
the
BLM
to
Fish
Toxicity
Data
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16
3.4.1
Relationship
of
Biotic
Ligand
Accumulation
Level
to
Effect
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16
3.4.2
Evaluation
of
the
Predicted
LC50
Using
the
BLM
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16
3.4.3
Application
of
the
BLM
to
a
Bioassay
Dataset
for
Fathead
Minnow
With
Water
Treatments
in
Synthetic
and
Natural
Waters
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17
3.5
Parameter
Estimation
for
Other
Organisms
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19
4.0
MODEL
TESTING:
A
DESCRIPTION
OF
MODEL
VALIDATION
EFFORTS
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20
4.1
WER
Datasets
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20
4.1.1
Model
Testing
­
Water
Effect
Ratio
Studies
Using
Fathead
Minnow
20
5.0
MODEL
APPLICATION
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22
5.1
Applicability
and
Limitations
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22
5.1.1
Equilibrium
Assumptions
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22
5.1.2
Aquatic
Organisms
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23
5.1.3
Ranges
of
Input
Parameters
Used
in
Calibration
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23
5.1.4
Other
Considerations
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23
6.0
REFERENCES
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24
ii
TABLES
Table
1.
Inorganic
Copper
and
Organic
Speciation
Reactions
in
the
WHAM
Database
(
Tipping,
1994).
Table
2.
Stoichiometry
and
Thermodynamic
Constants
for
Adsorption
of
Metals
and
Protons
on
Gills
of
Larval
Fathead
Minnows.
Table
3.
Average
Composition
of
Waters
Used
in
the
Fathead
Minnow
Copper
Toxicity
Experiments
of
Erickson
et
al.,
(
1987)
in
Exposures
Without
Chemical
Modifications.

FIGURES
Figure
1.
Schematic
diagram
of
the
generalized
biotic
ligand
model
(
BLM)
framework
for
acute
metal
toxicity.
Figure
2.
Relationship
between
mortality
of
juvenile
rainbow
trout
after
120
hours
of
exposure
and
copper
concentration
on
the
gill
of
the
fish
after
24
hours
of
exposure.
Data
from
MacRae
(
1999).
Figure
3.
Calibration
of
the
WHAM
model,
Version
V.
(
A)
Cu:
effect
of
ionic
strength:
0.001
M
(

)
0.01
M
(

)
(
B)
Cu:
effect
of
Ca:
0.001
M
NaNO
(

)
0.001
M
Ca(
NO)
(

)
0.01
M
Ca(
NO)
(
G)
(
C)
Cu:
effect
of
pH:
5.14
(

)
7.00
(

)
8.44
(
G)
(
D)
Ca:
effect
of
pH:
5.00
(

)
7.00
(

)
9.00
(
G)
(
E)
Cd:
effect
of
pH:
4.00
(

)
6.00
(

)
8.00
(
G)
(
F)
Pb:
effect
of
pH:
4.00
(

)
5.00
(

)
6.00
(
G).
Redrawn
from
Tipping
and
Hurley
(
1992).
Figure
4.
Schematic
diagram
of
the
biotic
ligand
model
(
BLM)
framework
for
acute
copper
toxicity,
showing
inorganic
and
organic
complexation
in
the
water
and
interaction
of
metals
and
cations
on
the
biotic
ligand.
Figure
5.
Measured
copper
accumulation
on
fathead
minnow
gills
from
Playle
et
al.,
(
12)
and
Biotic
Ligand
Model
predictions
as
a
function
of
cupric
ion
concentration.
Figure
6.
Relationship
of
copper
LC50s
to
variations
in
DOC
concentration.
The
lines
are
drawn
by
eye
to
represent
the
data.
(
A)
LC50
expressed
as
the
concentration
of
total
dissolved
copper.
(
B)
LC50
expressed
as
the
concentration
of
the
free
ion
activity
of
copper.
(
C)
LC50
expressed
as
the
concentration
of
the
copper
sorbed
to
the
gill.
Data
from
Erickson
(
1996).
Figure
7.
Relationship
of
copper
LC50s
to
variations
in
calcium
concentration.
The
lines
are
drawn
by
eye
to
represent
the
data.
(
A)
LC50
expressed
as
the
concentration
of
total
dissolved
copper.
(
B)
LC50
expressed
as
the
concentration
of
the
free
ion
activity
of
copper.
(
C)
LC50
expressed
as
the
concentration
of
the
copper
sorbed
to
the
gill.
Data
from
Erickson
(
1996).

FIGURES
(
continued)
iii
Figure
8.
Relationship
of
copper
LC50s
to
variations
in
pH.
The
lines
are
drawn
by
eye
to
represent
the
data.
(
A)
LC50
expressed
as
the
concentration
of
total
dissolved
copper.
(
B)
LC50
expressed
as
the
concentration
of
the
free
ion
activity
of
copper.
(
C)
LC50
expressed
as
the
concentration
of
the
copper
sorbed
to
the
gill.
The
LC50s
in
(
B)
are
the
measured
copper
activities
using
a
specific
ion
electrode.
Data
from
Erickson
(
1996).
Figure
9.
Response
of
measured
and
predicted
fathead
minnow
Cu
LC50
to
changes
in
pH.
BLM
predictions
assume
that
only
Cu2+
is
bioavailable.
Figure
10.
Distribution
of
complexed
Cu2+
and
CuOH+
on
natural
organic
matter
as
simulated
in
the
WHAM.
Figure
11.
Distribution
of
adsorbed
Cu2+
and
CuOH+
on
gill
membrane
as
simulated
in
the
revised
BLM.
Figure
12.
Response
of
measured
and
predicted
fathead
minnow
Cu
LC50
to
changes
in
pH.
BLM
predictions
assuming
only
Cu2+
is
bioavailable
are
compared
with
the
revised
model
that
assumes
both
Cu2+
and
CuOH+
are
bioavailable.
Figure
13.
Method
of
calculating
the
LC50
using
the
BLM.
Relationship
of
copper
concentration
sorbed
on
the
gill
and
dissolved
copper
as
computed
using
the
BLM
for
laboratory
water
and
100%
effluent.
Figure
14.
Biotic
Ligand
Model
predicted
versus
measured
LC50
values
for
fathead
minnow
in
static
toxicity
exposures
from
Erickson
et
al.,
(
1996).
Note
that
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.
Figure
15.
Simulated
changes
in
free
copper
over
time
during
a
static
toxicity
test.
Kinetics
of
copper
binding
to
natural
organic
matter
are
based
on
results
of
Ma
et
al.,
1999.
Figure
16.
Simulated
changes
in
free
copper
over
time
during
a
static
toxicity
test
with
a
24
hour
pre­
test
equilibration
period.
Kinetics
of
copper
binding
to
natural
organic
matter
are
based
on
results
of
Ma
et
al.,
1999.
Figure
17.
Simulated
changes
in
free
copper
over
time
during
a
static
toxicity
test
with
a
24
hour
renewal
frequency.
Kinetics
of
copper
binding
to
natural
organic
matter
are
based
on
results
of
Ma
et
al.,
1999.
Figure
18.
Simulated
changes
in
free
copper
over
time
during
a
flowthrough
toxicity
test.
Kinetics
of
copper
binding
to
natural
organic
matter
are
based
on
results
of
Ma
et
al.,
1999.
Figure
19.
Biotic
Ligand
Model
predicted
versus
measured
LC50
values
for
fathead
minnow
in
flow­
through
toxicity
exposures
from
Erickson
et
al.,
(
1996).
Note
that
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.

FIGURES
(
continued)

Figure
20.
Predicted
versus
measured
values
for
D.
pulex
copper
LC50
in
iv
Connecticut
streams
(
23).
Note
that
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.
Figure
21.
Comparison
of
BLM
predictions
for
copper
toxicity
to
a
number
of
invertebrate
aquatic
organisms
from
the
US
EPA
ambient
water
quality
criteria
document.
Figure
22.
The
aqueous
concentrations
of
TOC
(
taken
to
be
equivalent
to
DOC
in
the
application
of
BLM),
alkalinity,
hardness,
and
pH,
in
laboratory
water
(
LAB),
upstream
water
(
U/
S),
and
at
the
indicated
percentages
of
effluent
dilutions
in
upstream
water.
Data
from
Diamond
et
al.
(
1997).
Figure
23.
Comparison
of
measured
and
calculated
LC50s
and
the
water­
effect
ratios.
Data
from
Diamond
et
al.
(
1997).
Figure
24.
Predicted
versus
measured
values
for
fathead
minnow
copper
LC50s
in
Water
Effect
Ratio
studies
(
Diamond
et
al.,
1997;
Dunbar,
1996).
The
results
from
static
exposures
from
Erickson
et
al.,
1987
are
included
for
comparison.
Note
that
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.
Figure
25.
Predicted
versus
measured
values
for
C.
dubia
copper
LC50s
in
Water
Effect
Ratio
studies
(
Hall
et
al.
1998).
Note
that
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.

APPENDICES
Appendix
A.
Chemical
Speciation
Equations
for
Copper
Appendix
B.
BLM
Input
files
for
Toxicity
Datasets
1
1.0
INTRODUCTION
The
importance
of
explicitly
considering
bioavailability
in
the
development
of
water
and
sediment
quality
criteria
for
metals
has
been
recognized
for
some
time
(
Di
Toro
et
al.,
1991
a,
b;
Allen
and
Hansen,
1996;
Ankley
et
al.,
1996).
Criteria
that
incorporate
this
concept
are
being
recommended
to,
and
are
being
considered,
for
application
by
regulatory
authorities
(
Bergman
and
Dorward­
King,
1997;
Renner,
1997).
A
long
history
of
experiments
demonstrates
the
importance
of
water
chemistry
on
the
degree
of
toxicity
of
metals.
What
has
been
missing
is
a
practical
modeling
implementation
that
can
predict
these
variations
in
toxicity
with
some
degree
of
generality
and
reliability.

The
Biotic
Ligand
Model
(
BLM)
was
developed
in
response
to
this
need.
The
BLM
represents
a
synthesis
of
ideas
that
have
a
long
history
of
development.
These
ideas
have
been
combined
into
an
operational
model
of
metal
bioavailability
and
toxicity.
The
model
is
suitable
for
use
in
evaluating
differences
in
the
availability
and
toxicity
of
metals
such
as
copper
and
other
metals,
differences
that
occur
as
a
result
of
changes
in
water
chemistry
from
site
to
site,
and
at
a
given
site
over
time.

BLM
for
copper
and
silver
have
undergone
an
initial
review
by
the
USEPA
Ecological
Processes
and
Effects
Committee
Science
Advisory
Board
(
SAB;
USEPA,
1999).
The
purpose
of
this
SAB
review
was
to
assess
the
technical
validity
of
the
BLM
approach.
With
regard
to
the
question
of
whether
or
not
the
BLM
could
improve
the
Agency's
ability
to
predict
toxicity
to
water
column
organisms
in
comparison
to
the
currently
applied
dissolved
metal
concentration
criterion,
the
SAB
concluded
that
the
BLM
could
predict
with
"
reasonable
accuracy
(
generally
within
a
factor
of
two
of
measured
values
the
acute
toxicities
of
copper
and
silver
to
fish"
(
USEPA,
2000)).
The
SAB
also
agreed
that
it
had
been
shown
to
predict
acute
toxicity
to
a
limited
number
of
water
column
organisms,
for
selected
metals,
under
equilibrium
conditions.
[
italicized
text
reflects
emphasis
by
SAB].
Further,
it
was
concluded
that
the
scientific
underpinnings
of
the
BLM
appeared
to
be
sound.
It
would
not
necessarily
reduce
uncertainty
associated
with
metals
bioavailability
and
toxicity
as
a
site­
specific
adjustment,
relative
to
empirical
data,
but
"
its
predictiveness
over
a
wide
range
of
environmental
conditions
makes
the
BLM
a
more
versatile
and
effective
tool
for
deriving
site­
specific
WQC."
Finally,
the
SAB
concluded:

"
It
appears
premature
to
use
the
BLM
to
revise
the
protocol
for
deriving
national
ambient
water
quality
criteria
at
this
time,
primarily
because
the
model
has
not
yet
been
validated
for
a
sufficiently
diverse
set
of
aquatic
organisms
and
endpoints,
coupled
with
the
full
range
of
water
quality
conditions.
.
.
.
the
BLM
could
have
current
practical
applications
.
.
.
as
an
alternative
or
complementary
method
to
the
current
water­
effects
ratio
(
WER)
approach."

Pursuant
to
their
review,
the
SAB
made
several
recommendations
with
regard
to
the
BLM
before
it
could
be
used
in
developing
site­
specific
criteria
for
silver
(
USEPA,
2000).
Again,
quoting
from
this
review:

"
Finally,
the
Committee
provided
recommendations
for
further
research
to
provide
additional
validation
in
the
following
areas:

a)
Prediction
of
chronic
and
sub­
acute
toxicities
not
currently
supported
by
the
BLM.

b)
Broadening
the
supporting
database
to
include
greater
taxonomic
and
functional
2
diversity
and
additional
comparisons
with
the
water­
effect
ratio
method.

c)
Gaining
better
mechanistic
and
kinetic
understanding,
i.
e.,
distinguishing
relative
differences
in
binding
affinity
and
toxicity
mitigation
among
hardness
cations
(
e.
g.,
Ca,
Mg,
Mn)
and
other
"
biotic
ligands"
besides
the
fish
gill,
and
evaluating
predictability
of
the
model
under
non­
equilibrium
water
quality
conditions.

d)
Distinguishing
the
events
and
kinetics
of
DOC
complexing
with
divalent
cations
and
biological
uptake
to
improve
interpretation's
of
model
predictions.

e)
Applicability
to
multiple
metals,
and
sensitivity
analyses
for
varying
water
chemistry
conditions."

In
view
of
the
need
to
ultimately
incorporate
the
BLM
into
the
criteria
evaluation
process,
supplemental
analyses
have
been
performed
since
the
time
of
the
SAB
report,
in
part
to
address
SAB's
concerns
and
recommendations.
This
report
provides
an
updated
summary
of
the
technical
basis
of
the
BLM
for
copper,
with
further
descriptions
of
these
updated
analyses.

2.0
THEORETICAL
BACKGROUND
2.1
Description
of
Generalized
BLM
Model
Framework
The
conceptual
framework
for
the
BLM
is
an
adaptation
of
the
Gill
Surface
Interaction
Model,
(
GSIM)
originally
proposed
by
Pagenkopf
(
Pagenkopf,
1983)
and
more
recently
utilized
by
Playle
and
coworkers
(
Playle
et
al.,
1992;
Playle
et
al.,
1993b;
Janes
and
Playle,
1995;
Hollis
et
al.,
1996;
Hollis
et
al.,
1997;
Playle,
1998;
Richards
and
Playle,
1998;
Wood,
1999),
and
the
Free
Ion
Activity
Model
(
FIAM),
as
previously
reviewed
by
Morel
(
Morel,
1983;
Morel,
1993)
and
Campbell
(
1995).
The
generalized
framework
is
illustrated
in
Figure
1.
The
model
is
based
on
the
hypothesis
that
toxicity
is
not
simply
related
to
total
aqueous
metal
concentration,
but
that
both
metal­
ligand
complexation
and
metal
interaction
with
competing
cations
at
the
site
of
action
of
toxicity
need
to
be
considered
(
Pagenkopf,
1983;
Meyer
et
al.,
1999).
Mortality
occurs
when
the
concentration
of
metal
bound
to
the
biotic
ligand
exceeds
a
threshold
concentration.

The
BLM
simply
replaces
the
fish
gill
as
the
site
of
action
with
a
more
generally
characterized
site,
the
biotic
ligand.
The
reason
for
this
replacement
is
to
emphasize
that
this
model
should
be
applicable
to
other
aquatic
organisms
for
which
the
site
of
action
is
not
readily
accessible
to
direct
measurement.
In
fact,
it
is
likely
that
these
principles
should
apply
to
any
organism
for
which
metal
toxicity
is
associated
with
a
discrete
site
of
action
and
when
the
chemical
speciation
of
the
metal
has
an
effect
on
availability
of
the
metal
to
the
biological
receptor.

The
role
of
metal
complexation
is
critical,
because
formation
of
organic
and
inorganic
metal
complexes
renders
a
significant
fraction
of
the
total
metal
less
bioavailable.
In
fact,
this
modeling
framework
provides
an
operational
definition
for
the
expression
"
bioavailability
of
metals"
(
Meyer
2002a).
As
shown
in
Figure
1,
dissolved
metal
exists
in
solution
partially
as
free
metal
ion.
This
species
is
hypothesized
to
be
the
toxic
species
in
more
simplified
versions
of
the
free
ion
activity
model
of
toxicity.
The
inorganic
and
organic
complexes
may
or
may
not
directly
contribute
to
toxicity.
The
bioavailability
of
these
compounds
is
inferred
from
experimental
observations
of
changes
3
in
metal
toxicity
with
changing
chemistry.
It
is
for
this
reason
that
we
concentrate
on
comparing
predicted
and
observed
toxicity
as
the
test
of
the
model's
utility.

The
toxicity
of
metals
to
organisms
is
assumed
to
occur
as
the
result
of
metal
reacting
with
the
physiologically
active
binding
sites
at
the
site
of
action
resulting
in
the
formation
of
a
metal­
biotic
ligand
complex
(
Figure
1,
right­
hand
side).
For
fish,
the
biotic
ligand
appears
to
correspond
to
sites
on
the
surface
membrane
of
the
gill
responsible
for
regulating
sodium
ion
uptake
(
McDonald
et
al.,
1989).
In
the
BLM
metal
ions
or
complexes
may
bind
to
the
biotic
ligand
as
well
as
other
cations
(
e.
g.,
Ca
²
+
,
Na+,
and
H+;
Figure
1).
As
a
result,
the
presence
of
these
cations
in
solution
can
mitigate
toxicity,
with
the
degree
of
mitigation
depending
on
their
concentrations
and
on
their
strength
of
binding
to
the
biotic
ligand.

2.2
Model
Formulation
The
BLM
is
based
on
the
hypothesis
that
the
metal­
biotic
ligand
interaction
can
be
represented
in
the
same
way
as
any
other
reaction
of
a
metal
species
with
an
organic
or
inorganic
ligand.
Consider
a
ligand
L
b
­,
in
this
case
the
biotic
ligand,
and
a
divalent
metal
cation
M
i
²
+
.
The
charge
on
the
biotic
ligand
is
unknown.
We
assign
a
negative
charge
to
be
definite
because
it
binds
positive
cations.
However,
this
choice
has
no
practical
significance.
The
concentration
of
the
metal­
biotic
ligand
complex,
M
i
L
b
+,
is
determined
by
the
mass
action
equation
[
M
i
L
b
+]
=
K
MiLb[
M
i
2+][
L
b
­]
(
1)

where
K
MiLb
is
the
stability
constant
for
the
metal­
ligand
complex
and
the
square
brackets
denote
molar
concentration.
It
is
assumed
that
protonation
can
also
occur
with
the
formation
of
a
protonbiotic
ligand
complex
HL
b
with
concentration
[
HL
b]
and
stability
constant
K
HLb.

[
HL
b]
=
K
HLb[
H+][
L
b
­]
(
2)

The
mass
balance
equation
associated
with
the
biotic
ligand
L
b
­
is
[
L
b
­]
T
=
[
L
b
­]
+
[
HL
b]
+

i=
1
NMi[
M
i
L
b
+]
(
3)

where
[
L
b
­]
T
is
the
total
binding
site
density
of
the
biotic
ligand
(
e.
g.,
nmol
of
available
sites/
g
of
tissue),
[
HL
b]
is
the
concentration
of
protonated
sites,
and
N
Mi
is
the
number
of
metal
complexes
M
i
L
b
+
e.
g.,
CuL
b
+,
CaL
b
+,
etc.,
that
form
with
the
biotic
ligand
L
b
­.

The
analogous
equations
for
the
metal
cation
M
i
²
+
and
the
other
aqueous
ligands
L
j
­
that
form
metalligand
complexes
are
[
M
i
L
j
+]
=
K
MiLj[
M
i
²
+
][
L
j
­]
(
4)
[
HL
j]
=
K
HLj[
H+][
L
j
­]
(
5)
[
L
j
­]
T
=
[
L
j
­]
+
[
HL
j]
+

i=
1
NMi[
M
i
L
j
+]
(
6)

where
K
MiLj
and
K
HLj
are
the
stability
constants
for
these
ligands.
The
mass­
balance
equations
for
the
metal
cations
in
the
solution
are
[
M
i
2+]
T
=
[
M
i
2+]
+
[
M
i
L
b
+]
+

j=
1
NLj[
M
i
L
j
+]
(
7)
4
where
N
Lj
is
the
number
of
metal­
ligand
complexes,
including
hydroxyl
complexes,
that
M
i
²
+
forms.

In
the
BLM
it
is
assumed
that
the
quantity
of
metal
bound
to
the
biotic
ligand
[
M
i
L
b
+]
is
insignificant
relative
to
the
aqueous
species
(
Morel,
1983;
Meyer,
1999a).
Therefore
Equation
7
becomes
[
M
i
2+]
T
=
[
M
i
²
+
]
+

j=
1
NLj[
M
i
L
j
+]
(
8)

The
aqueous
chemistry
speciation
equations
(
Equations
4­
6,
8)
can
be
solved
as
discussed
below.
Then
the
biotic
ligand
equations
(
Equations
1­
3)
can
be
evaluated.
This
convenient
approach
is
adopted
below.

The
parameters
required
that
are
specific
to
the
BLM
are
the
conditional
stability
constants,
K
HLb
and
K
MiLb
i
=
1, 
N
Mi
for
the
proton­
and
metal­
biotic
ligand
complexes
(
Equations
1­
2),
and
the
total
site
density
[
L
j
­]
T
(
Equation
3).
For
fish,
the
site
densities
and
stability
constants
are
determined
on
the
basis
of
experimental
fish
gill
measurements.
These
are
currently
available
for
a
number
of
metals,
including
copper,
cadmium
(
Playle
et
al.,
1993a;
Playle
et
al.,
1993b)
and
silver
(
Janes
and
Playle,
1995).
For
other
organisms,
the
values
are
obtained
by
fitting
the
model
to
observed
mortality
data,
as
discussed
below.
The
relevant
mole
balance
equations
and
species
formation
reactions
and
related
constants
that
apply
to
the
copper
BLM
model
are
summarized
in
Appendix
A.

The
model
is
based
on
the
idea
that
mortality
(
or
other
toxic
effect)
occurs
if
the
concentration
of
metal
on
the
biotic
ligand
reaches
a
critical
concentration
C
Mi*.

C
Mi*
=
[
M
i
L
b
+]
(
9)

This
critical
concentration
for
mortality
can
only
be
determined
from
toxicity
experiments
that
establish
the
LC50
(
or
EC50)
concentrations
for
a
variety
of
toxic
metal
and
competing
cation
concentrations.
Once
the
site
densities
and
stability
constants
are
known,
the
critical
concentration
can
be
determined
by
computing
the
biotic
ligand
concentration
corresponding
to
the
aqueous
LC50
concentration.
The
validity
of
the
BLM
can
be
established
only
if
the
critical
concentration
C
Mi
*
is
the
same
over
the
entire
range
of
water
chemistry
tested.
Examples
of
this
analysis
will
be
given
below.
This
critical
concentration
is
referred
to
as
the
"
LA50",
or
the
lethal
accumulation
of
metal
on
the
biotic
ligand
associated
with
50%
mortality
(
Meyer
et
al,
1999b;
Meyer
et
al.,
2002).

2.2.1
Chemical
Model­
Inorganic
Metal
Speciation
The
chemical
speciation
computations
are
standard
and
may
be
performed
with
any
of
several
models
that
exist:
for
example,
MINEQL
(
Westall
et
al.,
1976),
MINTEQA2
(
Brown
and
Allison,
1987;
Allison
et
al.,
1991),
or
the
program
used
for
the
computations
presented
below,
CHESS
(
CHemical
Equilibria
in
Soils
and
Solutions;
Santore
and
Driscoll,
1995).
The
inorganic
speciation
is
the
straightforward
part
of
the
computation
because
the
ligands
are
well
characterized,
for
the
most
part,
and
their
binding
constants
are
known
(
e.
g.,
Smith
and
Martel,
1993).
The
difficult
part
is
modeling
the
complexation
of
metal
cations
by
organic
matter.
Although
Pagenkopf
(
1983)
recognized
the
ameliorating
effect
of
organic
matter
on
toxicity,
the
effect
of
organic
matter
was
neglected
in
his
original
model
formulation.
It
was
applied
to
test
results
using
laboratory
waters
with
low
organic
matter
content.
However,
dissolved
organic
matter
is
known
to
be
an
important
ligand
for
most
metals
in
most
natural
waters.

2.2.2
Chemical
Model­
Dissolved
Organic
Matter
Complexation
5
There
is
no
shortage
of
models
that
have
been
proposed
for
modeling
the
complexation
of
metals
to
dissolved
and
particulate
organic
matter;
e.
g.,
models
by
Van
Riemsdijk
and
colleagues
(
Benedetti
et
al.,
1995;
Kinniburgh
et
al.,
1996)
being
a
recent
example
of
a
comprehensive
modeling
framework.
For
many
of
these
models,
the
parameters
that
have
been
estimated
apply
to
a
specific
experimental
data
set.
What
is
required
is
a
model
that
has
been
calibrated
to
multiple
data
sets,
and
for
as
many
metals
as
possible.

Since
this
is
an
important
criterion,
Version
V
of
the
Windermere
Humic
Aqueous
Model
(
WHAM),
developed
by
Tipping
and
coworkers
(
Tipping
and
Hurley,
1992;
Tipping,
1993)
has
been
selected
for
use.
The
model
is
fully
described
and
the
computer
code
is
available
(
Tipping,
1994).
It
contains
a
detailed
model
of
proton
binding.
This
is
then
expanded
to
include
metal
cation
binding.
The
idea
is
that
the
proton
and
the
metal
cations
are
competing
for
the
same
sites,
so
a
detailed
model
of
proton
binding
is
the
essential
first
step.

This
description
follows
that
provided
by
Tipping
and
co­
workers
(
Tipping
and
Hurley,
1992;
Tipping,
1993).
Protons
bind
to
carboxyl
(
type
A)
and
phenolic
(
type
B)
sites.
A
uniform
distribution
of
pKs
is
specified
for
each
type
of
site
for
which
pK
=
­
log
10
K
and
K
is
the
stability
constant
for
the
proton­
site
binding
reaction.
The
site
distributions
are
parameterized
by
the
median
pK
A
and
pK
B
and
their
ranges
 
pK
A
and
 
pK
B.
Each
uniform
distribution
is
approximated
using
four
discrete
pK's
for
each
type:
K
H1
, ,
K
H4
and
K
H5
, ,
K
H8,
respectively,
where
pK
H1
=
pK
A
­
 
pK
A/
2
(
10)
pK
H2
=
pK
A
­
 
pK
A/
6
(
11)
pK
H3
=
pK
A
+
 
pK
A/
6
(
12)
pK
H4
=
pK
A
+
 
pK
A/
2
(
13)

and
the
analogous
equations
for
pK
H5,
 ,
pK
H8.
The
site
density
of
type
A
sites
is
n
A.
Because
humic
and
fulvic
acids
have
fewer
B
sites,
their
site
density
is
assumed
to
be
n
B
=
n
A/
2.
The
electrostatic
interactions
are
modeled
using
an
empirical
formulation
with
one
adjustable
parameter,
P,
which
is
related
to
the
surface
complexation
model
formulations
(
Westall
and
Hohl,
1980;
Dzombak
and
Morel,
1990).
Tipping
and
co­
workers
have
fit
this
model
to
various
sets
of
acid­
base
titrations
of
organic
matter
to
determine
the
six
model
parameters:
n
A,
the
pK's
and
 
pK's,
and
the
electrostatic
parameter
P.

The
stability
constants
for
metal
binding
are
parameterized
by
only
two
additional
constants.
This
is
a
remarkably
parsimonious
construct.
The
idea
is
to
specify
the
metal
binding
constants
using
the
proton
binding
pK's.
The
metal
stability
constants,
K
Mi,
i=
1, ,
8
are
defined
relative
to
the
proton
binding
constants
K
i
via
two
parameters:
K
MA
and
K
MB
K
Mi
=
K
MA/
K
Hi
i
=
1, ,
4
(
14)

K
Mi
=
K
MB/
K
Hi
i
=
5, ,
8
(
15)

where
the
K
Mi
are
the
discrete
metal
stability
constants
analogous
to
the
K
Hi
proton
binding
stability
constants.
In
addition
to
binding
to
the
proton
sites
individually,
binding
to
two
sites
at
once
(
bidentate
sites)
is
also
allowed.
The
binding
constants
for
these
sites
K
Mij
are
computed
from
the
product
of
the
metal
monodentate
binding
constants
K
Mij
=
K
Mi
K
Mj
(
16)
6
For
the
sake
of
simplicity,
only
11
of
the
possible
pairs
are
used.
From
data
fitting,
Tipping
and
Hurley
(
1992)
developed
the
following
relationship
between
K
MA
and
K
MB:

pK
MB
=
1.38
pK
MA
+
2.57
(
17)

Use
of
this
relationship
reduces
the
number
of
metal
specific
parameters
to
one.
This
is
the
most
parsimonious
parameterization
possible.
For
each
metal,
only
one
parameter
K
MA
is
required.
The
rest
follow
from
the
equations
given
above
(
Equations
14­
17).

The
status
of
the
level
of
calibration
of
Version
V
of
WHAM
will
be
summarized
in
Section
3.
The
model
equations
and
parameter
values,
as
employed
herein
for
copper,
are
summarized
in
Appendix
A.

2.3
Relationship
of
Copper
Accumulation
to
Acute
Toxicity
To
date,
the
BLM
has
been
used
to
describe
the
toxicity
to
freshwater
fish
such
as
fathead
minnows
(
Pimephales
promelas)
and
rainbow
trout
(
Oncorhynchus
mykiss)
and
invertebrates
such
as
Daphnia
magna,
Daphnia
pulex,
Ceriodaphnia
dubia,
Hyallela
azteca,
Lumbriculus
variegatus,
and
Mytilus
edulis.
Due
to
the
relative
ease
with
which
gill
tissue
can
be
excised
for
the
measurement
of
accumulated
metals,
information
on
metal
binding
to
gill
membranes
that
has
been
used
for
all
organisms
has
come
from
fathead
minnow
and
rainbow
trout.
These
species
have
comparable
sensitivities
to
copper
and
have
been
studied
extensively
(
USEPA,
1985)
.
Several
studies
have
shown
that
when
juvenile
fathead
minnows
and
rainbow
trout
are
exposed
to
copper,
there
is
a
relatively
rapid
increase
above
background
levels
of
copper
bound
to
the
gill.
Playle
and
co­
workers,
working
with
fathead
minnows,
showed
that
this
rapid
initial
increase
takes
place
over
a
time
scale
of
a
few
hours
to
a
day
(
Playle
et
al.,
1992).
Similar
data
for
juvenile
rainbow
trout
indicates
that
this
rapid
initial
increase
in
gill
copper
is
followed
by
a
more
gradual,
longer
term,
increase
(
MacRae
et
al.,
1999).
It
is
believed
that
the
rapid
initial
increase
in
gill
copper
reflects
binding
to
physiologically
active
receptor
sites
at
the
gill
surface.
More
specifically,
the
accumulation
reflects,
at
least
in
part,
an
interaction
of
copper
with
Na­
K
ATPase,
an
enzyme
that
is
essential
for
the
proper
functioning
of
the
iono­
regulatory
control
processes
of
fish.
For
acute
toxicity
then,
this
enzyme
is
considered
to
be
the
biotic
ligand
for
fish,
and
it
is
associated
with
the
gill.
Hence,
it
is
necessary
to
predict
metal
accumulation
at
the
gill
surface,
presumably
metal
that
is
associated
with
this
enzyme,
to
be
able
to
predict
metal
toxicity
to
fish.

If
the
approach
is
to
be
viable,
it
is
necessary
that
there
be
a
relationship
between
gill
accumulation
and
mortality.
Information
on
the
amount
of
copper
bound
to
gills
that
will
result
in
lethality
comes
from
determinations
of
copper
toxicity
and
mortality
in
juvenile
rainbow
trout
(
MacRae,
1994;
MacRae
et
al.,
1999).
Juvenile
(
15­
40
g)
rainbow
trout
(
Oncorhynchus
mykiss)
were
exposed
to
sublethal
copper
concentrations
for
24
hours.
The
total
copper
concentrations
were
kept
constant
(
10
ug/
L)
for
this
series
of
exposures,
but
the
copper
activity
was
varied
by
adding
different
organic
ligands,
with
varying
affinities
for
copper,
to
the
test
water.
After
24
hours,
individual
fish
were
removed
from
the
water,
their
gills
were
excised,
and
copper
accumulation
was
determined.
As
a
result,
measured
gill
accumulation
was
shown
to
be
related
to
copper
activity.

In
a
parallel
set
of
exposures
with
replicated
chemical
conditions,
a
120­
hour
LC50
was
determined.
7
A
plot
of
24­
hour
gill
accumulation
versus
120­
hour
LC50
yields
a
dose­
response
relationship
based
on
gill
copper
(
Figure
2).
As
shown,
the
gill
copper
LC50
­­
the
total
copper
concentration
on
the
gill
that
causes
50%
mortality
­­
is
estimated
to
be
22
nmol/
gram
wet
weight
(
nmol/
g
w).
There
is
a
background
gill
copper
concentration
­­
the
concentration
associated
with
control­
level
mortality
(
i.
e.,
<
about
25%)
­­
of
approximately
12
nmol/
g
w.
This
compares
well
with
the
fathead
minnow
background
gill
copper
level,
approximately
12
nmol/
g
w,
that
was
measured
by
Playle
and
co­
workers
(
1992)
in
the
absence
of
added
copper.
Based
on
these
results,
the
gill
copper
LA50
should
be
approximately
10
nmol/
g
w
­­
the
gill
Cu
LC50
of
22
nmol/
g
w
minus
the
background
concentration
of
12
nmol/
g
w.
Although
subsequent
analyses
of
toxicity
data
(
Section
3)
have
led
to
a
refined
estimate
of
the
gill
Cu
LA50,
acceptance
of
the
existence
of
a
cause­
effect
relationship
such
as
that
shown
by
the
data
of
Figure
2,
one
that
is
invariant
of
water
chemistry,
is
a
fundamental
premise
upon
which
the
BLM
is
based.
A
similar
result
has
been
demonstrated
for
the
toxicity
of
copper
to
an
oligochaete
worm
(
Lumbriculus
variegatus),
for
which
the
copper
LA50
was
apporximately,
0.17­
0.34
umol
Cu/
g
dry
wt.
(
Meyer
et
al.,
2002).
While
in
a
strict
sense,
water
chemistry
is
known
to
have
additional
physiological
effects
upon
the
organism,
the
idea
that
there
exists
a
unique
level
of
accumulation
at
the
biotic
ligand
that
is
associated
with
a
fixed
effect
is
a
significant
step
forward
in
comparison
to
a
hardness­
based
WQC,
at
least
with
regard
to
being
able
to
predict
the
degree
of
effect
that
is
associated
with
alternative
exposure
conditions.

2.4
Description
of
Species
on
the
Biotic
Ligand
As
noted
previously,
the
biotic
ligand
in
fish
is
associated
with
the
gill
and
is
considered
to
be
Na,
KATPase
an
enzyme
that
has
an
important
role
in
the
regulation
of
sodium
levels
not
only
in
fish,
but
in
essentially
all
forms
of
aquatic
life.
Cu
and
other
metals
will
interact
with
this
enzyme,
with
the
level
of
complexation
of
the
metal­
biotic
ligand
being
related
to
the
degree
of
effect,
that
being
an
inhibition
of
the
active
uptake
of
sodium
in
freshwater
organisms
(
or
active
excretion
of
sodium
in
saltwater
organisms).
Because
of
the
need
to
evaluate
the
level
of
accumulation
of
the
available
toxic
metal
species
at
the
biotic
ligand,
it
is
introduced
as
an
additional
biotic
component
that
must
be
considered
in
the
mass
balance
of
substances
in
the
chemical
model.
The
total
site
density
is
set
at
30
nanomoles
per
gram
wet
weight
of
gill
(
30
nmol/
g
w)

The
principal
copper
species
that
is
assumed
to
result
in
adverse
effects
is
often
considered
to
be
Cu2+,
but
it
need
not
be
limited
to
Cu2+
only,
and
other
species
such
as
CuOH+
may
also
bind
to
the
biotic
ligand
and
result
in
adverse
effects
as
well.
The
bioavailability
of
CuOH+
has
been
implicated
in
other
studies
(
Chakoumakos
et
al.,
1979;
Pagenkopf,
1983;
Brown
and
Markich,
2000).
It
is
known
that
other
cations
in
solution
will
also
affect
and
to
some
degree
mitigate
the
toxicity
of
metals
such
as
copper.
In
the
context
of
the
biotic
ligand
model,
the
mechanism
of
this
protective
effect
is
represented
as
a
competitive
binding
effect,
whereby
another
cation,
such
as
Ca2+
or
H+
or
Na+,
can
decrease
the
binding
of
copper
to
the
biotic
ligand.
This
decreases
the
accumulation
of
copper,
thereby
decreasing
the
degree
of
effect
on
the
organism.
Hence,
the
increase
in
the
dissolved
copper
LC50
in
the
presence
of
increasing
concentrations
of
competing
cations.
Although
other
physiological
mechanisms
might
also
be
partially
responsible
for
observed
mitigation
of
toxicity
(
e.
g.,
the
effect
of
sodium
on
sodium
uptake
kinetics
and
of
calcium
on
membrane
permeability
and,
thus,
on
the
sodium
loss
rate),
the
use
of
competitive
cation
interactions
with
the
biotic
ligand
offers
an
expeditious
way
to
account
for
these
effects
in
the
context
of
the
well­
established
framework
of
a
chemical
equilibrium
model.
8
The
cation­
gill
complexes
that
are
considered
in
the
model
at
this
time
are
Cu2+
and
CuOH+,
the
metal
species
that
are
associated
with
adverse
effects,
and
Ca2+,
H+
and
Na+,
the
competing
cations
that
mitigate
toxicity.
The
total
concentrations
of
each
of
the
chemical
components
that
are
included
in
the
model
are
present
in
the
form
of
a
variety
of
chemical
species.
The
sum
of
the
concentrations
of
all
of
these
species,
with
the
appropriate
stoichiometric
relationships
applied,
must
equal
the
total
concentration
of
the
chemical
component.
These
mole
balance
relationships
are
listed
in
Appendix
A1.

2.5
Alternative
Computational
Modes
The
BLM
has
been
structured
to
operate
in
two
distinct
operational
modes.
In
the
first
mode,
the
relevant
chemical
characterization
of
the
water
of
interest
is
specified,
and
the
model
is
used
to
evaluate
the
chemical
speciation
in
the
sample
for
a
given
dissolved
concentration
of
the
metal
of
interest.
In
the
second
mode,
the
chemical
characterization
of
the
water
of
interest
is
still
required.
However,
in
this
case
the
dissolved
concentration
of
the
metal
of
interest
that
will
result
in
the
end
point
of
interest
for
a
given
organism
(
e.
g.,
50%
mortality
in
96
hours),
is
predicted.
The
method
used
to
perform
each
of
these
tasks
is
described
in
further
detail
below.

2.5.1
Metal
Speciation
Computations
First,
chemical
components
are
defined
as
a
subset
of
all
available
chemical
species.
Components
must
be
selected
such
that
no
component
can
be
formed
as
the
product
of
a
reaction
involving
only
other
components,
and
all
remaining
species
can
be
defined
as
the
product
of
a
reaction
involving
only
components.
From
these
components,
a
generic
set
of
equations
that
describe
the
chemical
equilibrium
system
can
be
summarized
following
the
conventions
described
in
Santore
and
Driscoll
(
1995).
A
set
of
mole
balance
equations
is
defined
for
the
chemical
components
to
account
for
all
chemical
species
in
the
equilibrium
system.

T
j
=

i
S
i
a
i,
j
Where
the
concentration
of
an
individual
chemical
species
is
represented
by
S
i
and
the
stoichiometric
coefficient
representing
the
contribution
of
species
S
i
to
mole
balance
T
j
is
indicated
by
a
i,
j.

The
species
concentrations
can
be
expressed
as
a
function
of
the
concentrations
of
each
of
the
chemical
components
by
the
use
of
mass
action
expressions.
The
mass
action
expressions
for
the
formation
of
each
of
the
species
in
the
BLM
are
listed
in
Appendix
A2.
These
expressions
include
specification
of
the
interactions
at
the
gill
that
will
be
needed
for
evaluating
the
accumulation
and,
hence,
toxicity
of
copper
to
fathead
minnow
(
Pimephales
promelas).
For
each
reaction,
the
concentration
of
a
species
i,
S
i,
can
be
calculated
as:

S
i
=
K
i

C
k
a
ik
where
the
stoichiometric
coefficient
between
species
i
and
component
k
(
a
ik)
and
the
K
i
for
each
reaction
are
known
(
Appendix
A2),
and
the
concentration
of
each
component
C
k
is
an
unknown.
The
values
of
K
i
in
Appendix
A2
are
modified
for
the
specific
conditions
of
ionic
strength
and
temperature.
Ionic
strength
corrections
can
be
provided
by
the
extended
Debye­
Huckel
Equation
(
Morel,
1983)
for
inorganic
species,
and
by
a
Donnan­
layer
expression
for
organic
species
(
Tipping,
1994).
Substituting
these
mass­
action
expressions
into
the
mole­
balance
equations
generates
a
system
9
of
26
equations
(
T)
in
26
unknowns
(
C).
This
system
of
equations
can
be
solved
simultaneously
to
derive
the
final
chemical
distribution
at
equilibrium.

2.5.2
Metal
Toxicity
Computations
When
the
BLM
is
used
to
predict
toxicity,
the
dissolved
copper
concentration
is
not
known
a
priori.
In
fact,
the
primary
utility
of
the
BLM
is
that
it
provides
a
computational
basis
for
predicting
the
amount
of
dissolved
metal
that
will
be
toxic
to
an
organism.
The
BLM
adapts
the
above
chemical
speciation
calculation
to
predict
toxicity
by
considering
the
critical
accumulation
or
LA50
associated
with
a
given
toxicological
endpoint
for
a
given
organism.
In
this
case,
the
total
metal
concentration
is
determined
such
that
the
sum
of
all
toxic
metal
species
bound
to
the
biotic
ligand
equals
the
LA50.
10
3.0
MODEL
CALIBRATION
This
section
summarizes
the
sources
of
information
and
the
data
and
modeling
analyses
that
have
been
performed
to
arrive
at
the
current
calibration
of
the
BLM.
Information
will
first
be
summarized
with
regard
to
both
the
inorganic
and
organic
speciation
sub­
models.
The
application
of
the
model
to
accumulation
and
toxicity
data
will
also
be
presented.

3.1
Sources
of
Thermodynamic
Information
3.1.1
Inorganic
Metal
Speciation
Inorganic
metal
speciation
requires
the
specification
of
the
total
concentrations
of
the
inorganic
components
that
are
input
to
the
model.
This
information
is
typically
assigned
on
the
basis
of
measurements
that
are
made
for
the
water
sample
of
interest.
The
log
K's
are
typically
set
on
the
basis
of
the
NIST
database,
though
in
the
case
of
the
BLM,
where
WHAM
is
used,
the
log
K's
that
have
been
used
by
Tipping
are
employed.
Some
exceptions
to
log
K's
that
are
reported
in
the
NIST
database
are
therefore
used.
This
is
considered
to
be
a
reasonable
approach,
in
light
of
the
good
agreement
that
has
been
achieved
in
the
application
of
WHAM
to
datasets
that
have
been
used
to
characterize
copper­
organic
matter
interactions.
The
calibration
of
the
organic
binding
parameters
will
depend,
to
some
extent,
on
the
values
of
the
inorganic
stability
constants
used
when
WHAM
was
developed.
Values
for
log
K's
that
are
used
in
the
model
are
summarized
in
Appendix
A.

3.1.2
Interactions
of
Copper
with
Organic
Matter
As
stated
previously,
the
approach
that
is
employed
by
the
BLM
to
evaluate
the
complexation
of
copper
by
organic
matter
is
based
on
Version
V
of
WHAM.
The
formulation
and
structure
of
this
model
was
presented
previously
in
Section
2.
Briefly,
competing
reactions
are
simulated
as
simultaneous
equilibrium
reactions,
and
equilibrium
metal
speciation
includes
formation
of
inorganic
and
organic
complexes
(
Table
1).
The
WHAM­
based
formulation
includes
a
complex
description
of
reactive
functional
groups
that
are
designed
to
emulate
a
continuous
distribution
of
sites
on
humic
and
fulvic
acids.
Organic
complexation
includes
a
proton­
dependent
description
of
net
molecular
charge.
The
molecular
charge
is
used
to
calculate
an
electrostatic
adjustment
to
chemical
binding
of
metals.
Non­
specific
ion
binding
is
simulated
using
a
Donnan­
type
double
layer
model.
Model
V
and
WHAM
have
been
previously
calibrated
with
a
number
of
metals
and
sources
of
dissolved
organic
matter.
Given
this
prior
extensive
development
effort
by
Tipping
and
co­
workers
(
Tipping
and
Hurley,
1992
and
Tipping,
1993),
the
model
input
parameters
related
to
metal:
organic
matter
interactions
that
are
used
in
the
BLM
are
consistent
with
Version
V
of
WHAM.
A
brief
overview
of
the
results
of
this
calibration
effort
is
provided
here.

Figure
3
presents
a
selection
of
the
titration
data
used
to
evaluate
the
requisite
WHAM
parameters.
Each
graph,
redrawn
from
Tipping
and
Hurley
(
1992),
utilizes
the
following
convention.
The
y­
axis
variable
 
is
the
concentration
of
metal
bound
to
DOC
(
mol/
g
DOC)
and
the
x­
axis
variable
is
the
free
metal
concentration
(
mol/
L).
Both
are
plotted
as
­
log
of
the
concentrations
following
the
chemist's
convention
for
pH
=
­
log
10[
H+].
Thus,
small
concentrations
correspond
to
large
numerical
values.
In
order
to
retain
the
usual
sense
that
increasing
concentration
corresponds
to
increasing
distance
from
the
origin,
the
numerical
values
decrease
with
increasing
distance
from
the
origin.
11
Figures
3A­
3C
present
the
data
for
copper.
Figure
3A
illustrates
the
effect
of
increasing
ionic
strength
(
I
=
0.001
M
to
0.01
M).
Increasing
the
ionic
strength
slightly
reduces
the
amount
of
copper
complexed
to
DOC.
Figure
3B
illustrates
the
effect
of
calcium
competition
([
Ca]
=
0
M,
0.001
M
and
0.01
M)
on
copper
binding.
Increasing
the
calcium
concentration
decreases
the
quantity
of
complexed
copper
because
Ca
²
+
competes
with
Cu
²
+
for
the
same
binding
sites.
Since
calcium
also
competes
with
copper
at
the
biotic
ligand,
the
proper
modeling
of
this
competition
for
DOC
sites
is
important.
Figure
3C
illustrates
the
effect
of
pH
=
5.14,
7.00,
and
8.44.
As
the
pH
decreases
the
increasing
concentration
of
H+
competes
with
Cu
²
+
for
the
binding
sites
and
less
copper
is
complexed
to
the
DOC.
The
deviations
at
the
more
highly
complexed
copper
concentrations
are
of
less
concern
in
this
application
since
they
are
usually
above
toxic
concentrations
(
i.
e.,
[
Cu]

10­
9
M
=
0.06
ug
Cu/
L,
which
is
well
below
most
acute
LC50s
for
[
Cu
total].
But
it
would
be
more
appropriate
for
[
Cu2+]).
The
low
concentrations
are
important.
Figures
3D­
3F
present
the
effect
of
pH
on
the
complexation
of
calcium,
cadmium
and
lead.
As
with
copper,
less
metal
binds
to
DOC
at
lower
pH
levels.
The
careful
and
complete
calibration
of
the
WHAM
model,
illustrated
in
Figure
3,
was
the
principal
reason
for
its
selection
for
use
in
this
application.

The
description
of
dissolved
organic
carbon
includes
humic
and
fulvic
molecules.
Adjusting
the
percent
of
organic
matter
in
humic
and
fulvic
forms
can
by
used
to
specify
variation
in
organic
matter
chemistry.
Inorganic
speciation
includes
aqueous
hydroxide
and
carbonate
complexes
(
Table
1).
Although
the
chemical
description
of
dissolved
organic
matter
comes
from
Model
V
and
WHAM,
all
equilibrium
speciation
reactions
are
simulated
by
CHESS.

In
view
of
the
preceding
results,
it
appears
that
WHAM
provides
a
robust
model
for
the
most
complex
aspect
of
the
chemical
speciation
calculation:
the
complexation
of
metals
to
organic
matter.
Nevertheless,
it
is
expected
that
further
refinements
will
be
incorporated
into
the
model
in
the
future,
particularly
at
lower
metal
concentrations
where
even
stronger
binding
sites
may
need
to
be
included.
This
is
almost
certainly
the
case
for
low
concentrations
of
silver,
for
which
binding
to
sulfurcontaining
ligands
has
been
found
to
be
important
(
Bell
and
Kramer,
1999).
Studies
are
currently
in
progress,
both
in
the
United
States
and
in
Europe,
to
obtain
additional
data
that
can
be
used
to
further
refine
the
representation
of
copper
interactions
with
organic
matter.
The
BLM
itself
is
of
sufficient
flexibility
that
refinements
will
be
able
to
be
readily
incorporated
into
the
chemical
model,
at
such
time
in
the
future
when
it
is
appropriate
to
do
so.

3.2
Calibration
of
the
BLM
to
Copper
Accumulation
at
the
Biotic
Ligand
A
variation
of
the
generalized
BLM
framework
diagram
that
was
presented
previously
(
Figure
1)
is
shown
on
Figure
4,
as
it
applies
to
copper.
Pursuant
to
the
BLM
methodology,
acute
copper
toxicity
is
directly
related
to
a
predetermined
level
of
copper
accumulation
at
the
biotic
ligand.
By
specifying
the
chemical
characteristics
of
this
biotic
ligand
and
evaluating
the
concentration
of
copper
accumulation
associated
with
it,
it
is
possible
to
predict
the
dissolved
copper
level
that
will
be
associated
with
an
prescribed
effect,
such
as
50%
mortality.
What
needs
to
be
determined
then
are
the
values
of
model
parameters
that
can
be
used
to
evaluate
the
level
of
accumulation
at
the
biotic
ligand.

As
described
in
Section
2,
acute
metal
toxicity
in
freshwater
fish
has
been
associated
with
the
disruption
of
Na
ion
regulation
(
Playle
et
al.,
1993a).
Accumulation
of
copper
at
the
gills
of
freshwater
fish
has
been
shown
to
inhibit
Na
ion
influx
and
reduce
Na­
K
ATPase
activity
(
Playle
et
12
al.,
1993b).
For
freshwater
fish
the
biotic
ligand
associated
with
acute
copper
toxicity,
therefore,
is
assumed
to
involve
the
transport
mechanisms
for
Na
ion
regulation
in
the
gill.
Analytical
techniques
for
measuring
specific
metal
adsorption
on
the
biotic
ligand
have
not
been
developed.
However,
the
adsorption
of
copper
on
gill
surfaces
has
been
measured
over
a
wide
range
of
water
quality
conditions
(
Playle
et
al.,
1992;
Playle
et
al.,
1993a
and
1993b).
For
this
study,
metal
accumulation
on
the
gill
is
assumed
to
be
a
surrogate
measurement
for
specific
accumulation
on
the
biotic
ligand.

The
biotic
ligand
site
density
and
binding
constants
for
copper
and
other
cations
to
the
biotic
ligand
were
originally
derived
from
the
experimental
investigations
of
Playle
and
co­
workers
(
1992
and
1993a).
The
amount
of
copper
adsorbed
to
fathead
minnow
(
Pimephales
promelas)
gills,
over
a
range
of
total
copper
concentrations,
was
measured
in
these
investigations
and
these
measurements
used
to
evaluate
the
binding
site
density
and
stability
constants
for
copper
adsorption
(
Playle
et
al.,
1993b).
This
gill­
binding
model
for
fathead
minnows
was
adopted
for
use
in
the
present
analysis.
However,
this
model
did
not
include
binding
of
Na
(
Playle
et
al.,
1993b).
Evidence
from
copper
toxicity
determinations
suggests
that
Na
also
has
a
protective
effect
(
Erickson
et
al.,
1987
and
1996)
so
binding
of
Na
was
evaluated
and
added
to
the
fathead
minnow
database
for
the
BLM
for
copper.

Using
these
parameter
values
and
application
of
the
BLM
to
predict
Cu
accumulation
in
fathead
minnow
gills
results
in
good
agreement
with
gill
accumulation
levels
measured
by
Playle
and
coworkers
(
1993a;
Figure
5).
Although
there
is
a
considerable
scatter
of
the
data
about
the
simulated
line
of
fit,
the
overall
trend
in
the
data
is
reproduced
by
the
model.
For
these
data
only
the
accumulation
above
the
background
gill
Cu
loading
(
12
nmol/
g
w)
that
is
associated
with
pristine
conditions
is
shown.
Copper
binding
shows
a
typical
Langmuir­
type
adsorption
pattern
with
an
assumed
maximum
binding
site
density
of
30
nmol/
g
in
excess
of
background.
These
initial
estimates
of
the
biotic
ligand
binding
constants
have
been
adjusted
in
some
cases
on
the
basis
of
the
calibration
of
the
model
to
the
results
of
toxicity
studies,
as
described
subsequently.

3.3
Response
of
the
BLM
to
Variation
in
Hardness,
DOC
and
pH
The
next
application
of
the
BLM
will
be
made
using
a
very
complete
and
well­
characterized
set
of
experiments
by
Erickson
and
co­
workers
(
1987
and
1996)
who
investigated
copper
toxicity
to
larval
fathead
minnows.
Fish
were
exposed
to
increasing
concentrations
of
copper
in
these
experiments
and
the
LC50s
were
determined.
Systematic
variations
of
important
water
quality
characteristics
were
employed
to
produce
LC50s
as
a
function
of
the
concentrations
of
these
variables.
Three
sets
of
experimental
results
will
be
used
to
illustrate
the
effects
of
dissolved
organic
carbon
(
DOC),
hardness
and
pH
on
model
performance,
specifically,
the
prediction
of
biotic
ligand
accumulation
levels.
(
These
same
data
will
also
be
presented
subsequently,
where
the
model
is
used
to
predict
toxic
effect
levels.)
The
thermodynamic
constants
used
for
WHAM,
the
gill/
biotic
ligand
computations,
and
the
base
water
chemistry
are
listed
in
Tables
1,
2
and
3,
respectively.

3.3.1
Effect
of
Dissolved
Organic
Carbon
on
Copper
Accumulation
and
Toxicity
The
effect
on
copper
LC50
of
variations
in
DOC
concentration
is
shown
in
Figure
6.
The
pH
and
hardness
were
held
approximately
constant
for
these
experiments.
The
added
DOC
is
Alrich
humic
acid.
The
results
of
Figure
6A
demonstrate
that
the
measured
total
Cu
LC50
(
filled
data
points
and
associated
trend
line)
increases
with
increasing
DOC
concentration,
as
is
often
observed.
This
is
13
rationalized
in
the
model
by
assuming
that
the
copper
that
forms
a
complex
with
DOC
is
not
bioavailable.
As
a
result,
as
DOC
increases
more
copper
is
needed
to
exert
the
same
degree
of
toxicity.
Figure
6B
shows
the
corresponding
free
copper
(
Cu
²
+
)
LC50s.
These
LC50s
were
calculated
using
WHAM
(
V)
and
the
reported
chemistry
and
the
total
copper
LC50'
s
in
Figure
6A.
The
results
are
somewhat
variable,
but
they
are
approximately
independent
of
DOC
concentration.
This
is
consistent
with
the
free
ion
activity
model
of
toxicity,
where
toxicity
is
directly
related
to
the
concentration
(
actually
the
activity)
of
free
copper.
Figure
6C
presents
the
calculated
gill
copper
concentrations
associated
with
the
measured
total
copper
LC50
data.
The
gill
copper
concentrations
were
calculated
using
WHAM
to
compute
the
metal­
humic
acid
complexes,
and
CHESS
to
compute
the
gill
accumulation.
The
Cu
²
+
­
gill,
Ca
²
+
­
gill
and
H+­
gill
conditional
stability
constants
and
gill
site
density
estimated
by
Playle
et
al.
(
1993)
from
measured
gill
copper
concentrations
were
used.
The
exchangeable
gill
copper
LA50
averages
slightly
less
than
5
nmol/
gw.
This
level
of
fathead
minnow
gill
copper
accumulation
is
a
factor
of
two
lower
than
the
measured
exchangeable
gill
copper
LA50
for
rainbow
trout
of
10
nmol/
gw
(
Figure
2),
which
is
quite
encouraging.
The
fact
that
the
gill
copper
LA50
is
approximately
constant
across
the
DOC
range
tested
indicates
that,
as
was
the
case
with
free
copper,
gill
copper
concentration
can
also
be
used
to
predict
acute
mortality
when
DOC
is
varied.

3.3.2
Effect
of
Hardness
on
Copper
Accumulation
and
Toxicity
The
effect
of
variations
in
calcium
concentration
on
copper
LC50
is
shown
in
Figure
7.
The
experiments
were
performed
with
DOC
and
pH
held
approximately
constant.
Over
the
range
of
experimental
conditions
of
0.5
to
2.5
meq
Ca/
L,
the
ratio
of
Ca:
Mg
was
approximately
2:
1
and
the
corresponding
hardness
range
was
75
to
375
mg
CaCO
3/
L.
The
data
are
displayed
as
before
except
that
the
LC50
results
are
plotted
versus
calcium.
As
was
the
case
with
increasing
DOC,
the
measured
total
Cu
LC50
increases
with
increasing
Ca
concentration
(
Figure
7A).
This
increase
in
LC50
with
hardness
is
qualitatively
consistent
with
the
current
water
quality
criteria
(
WQC)
for
copper,
which
increases
as
a
function
of
hardness
as
well
(
USEPA,
1985).
However,
as
discussed
below,
the
magnitude
is
significantly
less
than
expected.

Free
copper
LC50s
corresponding
to
the
total
copper
LC50s
are
shown
in
Figure
7B.
Like
the
total
copper
LC50s,
the
free
copper
LC50s
varied
over
the
range
of
calcium
levels
tested.
Therefore,
a
single
free
copper
concentration
is
no
longer
uniquely
associated
with
50%
mortality.
This
is
not
unexpected
because
copper,
a
cation,
does
not
form
complexes
with
calcium,
another
cation.
Therefore,
except
for
a
relatively
minor
ionic
strength
effect
(
see
Figure
3A),
there
is
no
interaction
of
calcium
with
copper
in
the
water.
Note
that,
in
combination
with
the
results
from
the
DOC
experiments
shown
in
Figure
6B,
these
results
indicate
that
there
is
more
than
a
10­
fold
range
in
variation
of
free
copper
concentration,
from
less
than
0.015
to
0.15
µ
mol/
L,
associated
with
the
fathead
minnow
free
copper
LC50.
These
results
indicate
that
considering
only
the
free
ion
as
the
bioavailable
ligand
cannot
be
used
to
rationalize
these
data.

In
contrast
to
the
free
copper
results,
the
calculated
gill
Cu
concentrations
shown
in
Figure
7C
indicate
a
relatively
consistent
concentration
for
the
range
of
calcium
concentrations
tested.
The
average
fathead
minnow
gill
copper
concentration,
12
nmol/
gw
,
is
in
reasonably
good
agreement
with
the
gill
copper
concentration
of
slightly
less
than
5
nmol/
gw
calculated
for
the
DOC
experiments
(
Figure
6C)
and
with
the
gill
Cu
LA50
of
about
10
nmol/
gw
of
Figure
2.
The
reason
that
the
gill
copper
tends
to
be
relatively
constant,
even
as
the
free
copper
concentration
increases,
is
that
the
calcium
competes
with
the
free
copper
for
binding
at
the
biotic
ligand
on
the
gill.
Hence,
a
higher
free
14
copper
concentration
is
required
to
achieve
the
same
gill
Cu
concentration
associated
with
mortality.

It
is
interesting
to
note
that
for
the
calcium
experiments
the
observed
increase
in
total
copper
LC50
­­
slightly
more
than
a
factor
of
two
over
the
range
of
conditions
tested
­­
is
half
as
much
as
is
expected
from
the
hardness
correction
incorporated
in
the
current
copper
WQC
­­
4.5­
fold,
for
hardness
increasing
from
75
to
375
mg
CaCO
3/
L
(
USEPA,
1985).
The
BLM
framework
provides
an
explanation
for
this
difference
(
Meyer,
1999).
The
experiments
by
Erickson
(
1996)
with
varying
hardness
were
conducted
with
constant
alkalinity,
by
adding
calcium
in
the
form
of
CaSO
4.
Thus,
as
hardness
is
increased
in
these
experiments,
the
only
factor
that
mitigates
toxicity
is
competition
between
Cu2+
and
Ca2+
for
the
gill
sites.
In
contrast,
for
most
studies
from
which
the
WQC
is
based,
the
hardness
was
adjusted
by
adding
CaCO
3
to
the
water.
As
a
result,
bicarbonate
alkalinity
increased
as
well.
The
added
CO
3
²
­
reacts
with
Cu
²
+
to
form
CuHCO
3
+
and
CuCO
3
0.
The
resulting
"
hardness"
effect
is
actually
a
calcium
carbonate
effect
(
Meyer,
1999).
Hence
toxicity
is
mitigated
to
a
greater
degree
than
in
the
experiments
by
Erickson
et
al.
(
1996)
in
which
the
sulfate
ion
had
no
effect.
This
explains
the
smaller
than
expected
effect
of
calcium
hardness
on
copper
LC50.

3.3.3
Effect
of
pH
on
Copper
Accumulation
and
Toxicity
The
effect
of
changes
in
pH
on
total
copper
LC50
is
shown
in
Figure
8A.
The
total
copper
LC50
increases
from
about
0.1
to
2
µ
mol/
L
as
the
pH
increases
from
6.5
to
8.8.
In
addition
to
the
total
Cu
concentrations,
the
free
copper
ion
activity
was
also
measured
with
a
selective
ion
electrode.
It
is
fortunate
that
Erickson
(
1996)
made
these
measurements.
When
the
concentration
of
total
Cu
is
used
to
predict
the
free
copper
in
solution
using
WHAM,
the
computed
results
for
Cu
activity
were
significantly
less
than
the
measured
data.
The
apparent
difficulty,
which
is
limited
to
this
set
of
data
only,
and
its
solution
are
discussed
in
Section
3.4.3.
However,
the
measured
free
copper
activity,
shown
in
Figure
8B,
can
be
used
to
compute
gill
copper
concentrations,
which
are
shown
in
Figure
8C.
The
variation
in
predicted
gill
copper
concentrations
reflects
the
variation
in
the
cupric
ion
activity
measurements.
The
average
gill
copper
concentration
of
approximately
7
nmol/
g
w
is
within
the
range
of
the
results
for
the
two
previous
sets
of
experiments
in
which
DOC
and
calcium
were
varied.
The
slight
decreasing
trend
of
gill
Cu
with
increasing
pH
might
be
explained
in
part
by
the
provision
for
CuOH+
binding
to
the
biotic
ligand.
This
effect
is
not
included
in
the
calculations,
presented
thus
far,
but
if
it
was
accounted
for,
the
pH
response
would
be
flattened.
Results
shown
on
the
two
previous
plots
would
not
be
significantly
impacted,
since
the
pH
was
generally
lower,
and
thus
CuOH+
was
also
present
at
a
lower
concentration.

In
the
context
of
the
BLM
framework,
pH
affects
copper
toxicity
in
several
ways.
First,
the
model
predicts
that
toxicity
will
decrease
with
increasing
pH
as
a
result
of
the
effect
of
pH
on
speciation
and
complexation
of
copper.
As
pH
increases,
the
fraction
of
Cu
that
exists
as
copper
carbonate
complexes
increases,
thereby
reducing
toxicity.
Further,
the
deprotonation
of
DOC
at
higher
pH
levels
increases
the
degree
to
which
the
copper­
DOC
complex
forms,
which
reduces
bioavailability
as
well.
These
effects
on
toxicity
are
offset
to
some
degree
by
the
competition
between
the
H+
and
Cu
²
+
ions
binding
to
the
biotic
ligand,
a
factor
that
by
itself
would
result
in
an
increase
in
toxicity
as
pH
increases
(
i.
e.,
as
the
H+
concentration
decreases).

However,
there
is
an
indication
in
Figure
8B
that,
at
the
LC50,
free
copper
might
actually
be
decreasing
with
increasing
pH
above
pH
8.0.
Reduced
free
copper
concentrations
at
high
pH
when
total
copper
equals
the
LC50
would
indicate
the
copper
is
more
toxic
at
high
pH
then
complexation
15
reactions
would
predict.
If
we
compare
predicted
copper
LC50
based
on
the
BLM
formulation
assuming
only
free
copper
is
bioavailable
with
measured
copper
LC50
at
high
pH,
it
is
clear
that
the
BLM
does
predict
that
copper
is
less
toxic
at
high
pH
than
measured
LC50
values
indicate
(
Figure
9).
Agreement
between
measured
and
predicted
copper
LC50
seems
to
be
good
at
pH
values
below
8.0,
but
at
pH
values
above
8.0
the
model
predicts
LC50s
that
are
too
high.
This
discrepancy
suggests
that
another
copper
species,
in
addition
to
free
copper,
is
bioavailable
and
can
exhibit
toxic
effects.

From
a
chemical
standpoint,
it
is
reasonable
to
suggest
that
additional
copper
species
are
capable
of
sorbing
onto
gill
membranes.
For
example,
the
WHAM
model
assumes
that
both
Cu2+
and
CuOH+
species
bind
to
natural
organic
matter
(
Figure
10).
At
pH
values
below
8.2
to
8.5
(
depending
on
the
total
metal
concentration)
the
predominant
form
of
copper
bound
to
NOM
is
the
free
copper
ion.
However,
at
high
pH
values
CuOH+
is
the
dominant
form
of
copper
bound
to
NOM.
The
gill
surface
may
also
bind
Cu2+
and
CuOH+
in
relatively
similar
amounts.
Further
support
for
this
assumption
comes
from
observations
that
the
pH
at
which
we
would
expect
the
predominant
copper
species
to
shift
from
free
ion
to
copper
hydroxide
is
exactly
the
pH
at
which
the
model,
formulated
only
with
bioavailable
free
copper,
predicts
reduced
toxicity.
Incorporating
the
adsorption
of
both
Cu2+
and
CuOH+
onto
gill
surfaces
can
be
accomplished
by
assuming
relative
binding
strengths
for
these
ions
that
are
similar
to
what
we
would
expect
for
adsorption
onto
natural
organic
matter.
The
result,
show
in
Figure
11,
shows
that
at
the
LC50
we
would
expect
to
see
predominately
free
copper
bound
to
the
biotic
ligand
at
pH
values
below
8.5,
and
predominately
CuOH+
bound
to
the
biotic
ligand
at
pH
values
above
8.5.
It
was
determined
by
comparison
with
toxicity
data
from
Erickson
et
al.,
1996
result
that
slightly
reduced
binding
of
CuOH+
gave
the
closest
approximation
of
the
observed
pH
response
which
is
why
the
pH
at
which
the
conversion
from
Cu2+
to
CuOH+
occurs
at
a
slightly
higher
pH
on
the
biotic
ligand
(
Figure
11)
than
it
does
on
natural
organic
matter
(
Figure
10).
The
resulting
model
that
includes
both
Cu2+
and
CuOH+
bioavailable
species
matches
the
observed
pH
response
much
more
closely
(
Figure
12).

3.3.4
Summary
The
results
presented
above
indicate
that
the
BLM
describes
the
variation
in
copper
toxicity
to
fathead
minnows.
The
calculated
fathead
minnow
gill
Cu
LC50s,
averaging
5
to
12
nmol/
gw
over
the
range
of
DOC,
hardness
and
pH
conditions
tested,
are
in
reasonable
agreement
(
approximately
±
a
factor
of
2)
with
the
reported
rainbow
trout
exchangeable
gill
Cu
LC50
(
10
nmol/
g
w,
Figure
2).
This
finding
is
consistent
with
comparable
sensitivity
of
fathead
minnows
and
rainbow
trout
to
copper
(
USEPA,
1985).
It
is
also
consistent
with
recent
findings
that
fathead
minnows
and
rainbow
trout
accumulate
copper
on
their
gills
in
a
similar
manner,
and
that
binding
constants
for
metal­
gill
interactions
determined
for
one
species
can
be
generalized
to
other
fish
species
(
Hollis
et
al.,
1997).
The
copper­
gill
pKs
for
rainbow
trout
(
7.5)
and
brook
trout
(
7.2)
found
by
MacRae
et
al.
(
1999)
are
quite
close
to
pK
=
7.4
as
determined
by
Playle
et
al.
(
1993a)
for
fathead
minnows.
These
results
indicate
that
the
BLM
can
explicitly
account
for
variation
in
toxicity
resulting
not
only
from
changes
in
hardness,
but
from
site­
specific
variations
in
DOC,
pH
and
alkalinity
as
well.

3.4
Application
of
the
BLM
to
Fish
Toxicity
Data
The
BLM
will
next
be
applied
in
the
analysis
of
96­
hour
toxicity
data
for
fathead
minnow
(
Erickson
et
al.,
1987
and
1996)
16
3.4.1
Relationship
of
Biotic
Ligand
Accumulation
Level
to
Effect
Information
on
the
amount
of
copper
bound
to
gills
associated
with
lethality,
described
previously
in
Section
2,
is
derived
from
the
determinations
of
copper
accumulation
and
mortality
to
juvenile
rainbow
trout
(
MacRae,
1994;
MacRae
et
al.,
1999).
It
was
shown
that
approximately
10
nmol/
g
w
of
copper
at
the
gill
is
the
lethal
accumulation
level
that
is
associated
with
50%
mortality,
the
LA50.
Ideally
a
similar
experiment
would
be
performed
to
determine
a
gill­
Cu
dose
response
relationship
for
other
fish,
including
fathead
minnows.
Although
the
rainbow
trout
gill­
Cu
LC50
was
determined
for
a
different
species
and
using
a
longer
duration
toxicity
exposure,
an
LA50
of
10
nmol/
g
w
was
used
as
an
initial
estimate
of
the
Cu
LA50
for
fathead
minnow.
This
value
was
later
adjusted
based
on
calibration
to
larval
fathead
minnow
LC50
data
(
see
section
3.4.3).

3.4.2
Evaluation
of
the
Predicted
LC50
Using
the
BLM
The
LA50
is
used
in
the
BLM
to
predict
the
dissolved
copper
LC50
by
evaluating
the
amount
of
dissolved
metal
that
will
result
in
this
critical
gill
Cu
accumulation.
Conceptually,
the
LC50
determination
can
be
thought
of
as
a
titration
of
copper
on
the
gill
in
the
test
water.
For
example,
accumulation
of
copper
on
the
gill
in
response
to
copper
additions
in
a
clean
laboratory
water
with
low
concentrations
of
DOM
would
result
in
rapid
accumulation
on
the
gill
(
Figure
13).
From
the
point
in
the
titration
when
gill­
Cu
equals
the
LA50,
the
dissolved
copper
LC50
can
be
determined
by
interpolation.

The
BLM
uses
a
root­
finding
approach
to
determine
values
of
acute
metal
LC50.
The
model
assumes
an
initial
LC50
value,
and
this
concentration
is
used
to
determine
the
amount
of
metal
that
is
bound
to
the
gill.
The
calculated
gill­
metal
concentration
is
compared
to
the
critical
value
and
a
new
approximation
is
determined
with
a
higher
or
lower
copper
concentration
as
necessary.
New
approximations
are
determined
by
expanding
the
range
of
trial
values
using
an
exponentially
expanding
step
size
until
the
critical
gill
concentration
has
been
bracketed.
The
LC50
value
is
then
found
iteratively,
using
false
position
to
update
trial
values.

3.4.3
Application
of
the
BLM
to
a
Bioassay
Dataset
for
Fathead
Minnow
With
Water
Treatments
in
Synthetic
and
Natural
Waters
An
excellent
dataset
is
available
for
the
development
and
testing
of
the
ability
of
the
BLM
to
predict
copper
toxicity
over
a
range
of
water
quality
characteristics
(
Erickson
et
al.,
1987
and
1996).
In
these
experiments,
acute
copper
toxicity
(
96­
hour
LC50)
determinations
were
made
for
fathead
minnow,
in
both
static
and
flow­
through
exposures,
and
in
natural
and
synthetic
waters.
The
test
conditions
were
manipulated
so
that
the
effects
of
changes
in
pH,
DOC,
cations
(
Ca2+,
Mg2+,
K+,
and
Na+),
and
anions
(
HCO
3
­,
Cl­,
SO
4
2­)
could
be
independently
examined.

The
BLM
was
originally
used
to
predict
acute
copper
toxicity
(
96­
hour
LC50)
to
fathead
minnow
using
gill
binding
parameters
as
originally
determined
by
Playle
and
coworkers
(
1993b)
and
the
LA50
value
from
MacRae
and
coworkers
(
1999).
However,
the
fathead
minnow
bioassay
results
(
Erickson
et
al.,
1987
and
1996)
suggested
that
beneficial
effects
from
Na
additions
were
sufficient
to
justify
modification
of
the
gill
binding
model
to
include
these
effects.
A
provision
for
Na
accumulation
on
the
gill
was
incorporated
in
the
BLM
application.
Log
K
values
for
Na­
gill
and
Ca­
gill
binding
were
calibrated
or
refined
using
the
Erickson
et
al.
fathead
minnow
data
(
see
Appendix
B
of
Erickson
et
17
al.,
1987
and
Table
2
in
Erickson
et
al.,
1996).
Refinement
of
the
value
of
the
copper
LA50
for
fathead
minnow
was
also
made
on
the
basis
of
BLM
analyses
of
these
data.
These
analyses
led
to
a
determination
that
an
LA50
of
6.2
nmol
Cu/
g
w,
was
best
suited
for
use
in
predicting
the
96­
hour
dissolved
copper
LC50
for
fathead
minnow.

An
input
dataset
was
constructed
from
measured
water
chemistry
when
available,
or
from
nominal
concentrations
calculated
from
base
water
chemistry
plus
chemical
additions
when
measured
values
were
not
available
(
Erickson
et
al.,
1987).
Concentrations
of
DOC
were
not
measured
by
the
authors
in
the
exposure
water,
however
a
background
DOC
concentration
of
1.0
mg
C/
L
for
exposures
conducted
in
Lake
Superior
water
and
0.1
mg
C/
L
in
the
synthetic
waters
was
assumed
(
personnel
communication
with
R.
Erickson).
Background
concentrations
of
dissolved
organic
carbon
(
DOC)
were
assumed
to
be
composed
of
10%
humic
acid
and
90%
fulvic
acid.
Additions
of
DOC
made
with
Aldrich
Humic
Acid
were
assumed
to
be
100%
humic
acid.

Predictions
of
fathead
minnow
copper
toxicity
using
the
BLM
were
compared
to
measured
LC50
values.
Individual
experiments
reported
by
Erickson
et
al.
(
1987)
were
designed
to
test
the
effect
of
specific
water
quality
adjustments
on
copper
toxicity.
Comparison
of
BLM
predictions
for
all
static
test
results
in
the
fathead
minnow
dataset
are
shown
in
Figure
14.
Shown
in
the
figure
is
the
line
of
perfect
agreement
(
solid)
and
dashed
lines
showing
plus
or
minus
a
factor
of
two
for
reference.
Measured
LC50
values
cover
a
wide
range
from
10
to
over
1000
ug/
L
due
to
effects
of
water
chemistry
on
copper
toxicity.
Despite
the
wide
range
in
toxicity,
nearly
all
predicted
values
are
within
a
factor
of
2
of
measured
values.
For
comparison
with
toxicity
test
results,
agreement
within
a
factor
of
two
is
quite
good
given
the
variability
between
replicate
measurements.
For
example,
the
replicate
Cu
LC50
values
measured
in
Lake
Superior
water
by
Erickson
and
co­
workers
(
1987)
range
over
a
factor
of
six
from
lowest
to
highest
(
13
observations,
minimum
Cu
LC50
28
ug/
L
and
maximum
of
172
ug/
L).
Note
that
several
of
the
outlying
points
are
comparisons
of
the
model
results
to
exposures
with
high
K
concentrations
(
plotted
with
open
symbols).
Erickson
et
al.
found
that
elevated
K
resulted
in
an
increase
in
copper
toxicity.
This
effect
has
not
been
incorporated
in
the
Cu
BLM
and
therefore,
the
LC50
values
that
are
predicted
by
the
BLM
are
higher
than
the
measured
values
for
these
exposures.
With
the
exception
of
these
results,
the
BLM
can
generally
explain
the
effects
of
water
chemistry
on
copper
toxicity
to
fathead
minnow.

Given
the
very
good
level
of
agreement
that
was
observed
between
measured
and
predicted
copper
LC50
values
in
static
test
exposures,
it
was
initially
somewhat
surprising
to
see
that
model
could
not
predict
the
flowthrough
test
results.
The
explanation
for
this
discrepancy
is
believed
to
be
associated
with
the
kinetics
of
copper
complexation
with
natural
organic
matter.
In
a
recent
study
by
Ma
et
al.
(
1999),
the
cupric
ion
activity
that
was
measured
shortly
after
mixing
copper
with
natural
organic
matter
(
NOM)
was
significantly
greater
than
the
activity
that
was
measured
following
24
hours
of
equilibration
between
the
copper
and
the
NOM.
Toxicity
tests
with
Ceriodaphnia
dubia
in
flowthrough
bioassay
chambers
were
sensitive
to
the
equilibration
time
of
copper
and
DOC
mixtures
used
in
the
exposure
chambers.
Toxicity
tests
with
1­
hour
hydraulic
residence
times
(
HRTs)
resulted
in
lower
total
Cu
LC50s
than
tests
with
longer
HRTs
(
Ma
et
al.,
1999).

This
kinetic
information
has
important
implications
for
how
we
design
and
interpret
toxicity
tests.
If
the
kinetics
of
the
binding
reaction
is
estimated
from
the
Ma
et
al.
(
1999)
data,
we
can
simulate
the
time
series
of
free
copper
under
various
test
conditions.
For
a
static
test
where
the
metal
and
sample
containing
NOM
are
mixed
just
before
the
start
of
the
test,
the
free
copper
concentration
would
be
18
initially
high
and
would
gradually
fall
to
equilibrium
concentration
levels
throughout
the
experiment
(
Figure
15).
As
the
Ma
et
al.
(
1999)
results
indicated,
it
would
take
approximately
24
hours
for
this
equilibration
to
occur.
Equilibrium
conditions
could
more
closely
be
matched
throughout
the
test
if
a
24­
hour
pre­
equilibration
period
is
used
(
Figure
16).
In
this
test
design,
the
metal
is
added
to
the
sample
containing
NOM
24
hours
before
the
organism
is
introduced.
Most
of
the
test
duration
after
this
24­
hour
period
will
exhibit
equilibrium
conditions.
Other
test
designs
show
even
greater
sensitivity
to
these
kinetic
effects.
If
a
static
test
is
employed
where
the
solution
is
renewed
every
24
hours
with
a
sample
aliquot
with
fresh
metal
addition,
then
this
period
of
elevated
free
copper
is
repeated
with
each
renewal
(
Figure
17).
Finally,
a
flowthrough
test
with
a
1­
hour
HRT
should
have
constant
but
elevated
free
copper
over
then
entire
test
duration
compared
to
the
free
copper
concentrations
we
would
expect
at
equilibrium
(
Figure
18).
The
conditions
shown
in
Figure
18,
which
are
designed
to
emulate
the
conditions
typical
of
the
Erickson
et
al.
(
1996)
flowthrough
tests
with
fathead
minnow,
indicate
that
copper
may
easily
be
10
times
more
bioavailable
than
they
would
be
after
a
24­
hour
equilibration
period.

Comparison
of
BLM
predictions
to
measured
LC50
values
in
the
flow­
through
exposures
conducted
by
Erickson
et
al.
(
1987,
1996)
show
that
the
BLM
over­
predicts
the
measured
LC50
values
(
Figure
19).
The
amount
that
the
model
over­
predicts
LC50
values
is
well
within
this
estimate
that
kinetic
factors
may
make
copper
10
times
more
bioavailable
in
flowthrough
tests
with
a
1­
hour
HRT
used
in
Erickson
et
al.
(
1996).
Issues
that
might
arise
from
this
equilibrium
assumption
and
its
applicability
to
the
use
of
the
BLM
in
a
regulatory
context
should
be
addressed.
However,
it
should
also
be
noted
that
the
current
water
effect
ratio
procedure
does
not
require
that
toxicity
tests
are
performed
in
such
a
way
as
to
mimic
any
non­
equilibrium
conditions
at
a
site.

3.5
Parameter
Estimation
for
Other
Organisms
The
BLM
input
parameters
that
have
been
evaluated
on
the
basis
of
the
accumulation
datasets
of
Playle
and
co­
workers
(
1992
and
1993a)
and
the
calibration
of
the
model
with
the
fathead
minnow
toxicity
dataset
of
Erickson
and
co­
workers
(
1987
and
1996)
serve
as
the
principal
basis
for
model
input
values
for
other
organisms.
This
approach
is
adopted
out
of
necessity,
given
the
absence
of
accumulation
studies
for
the
variety
of
organisms
for
which
computations
would
need
to
be
performed.
The
practical
reason
for
this
datagap
is
that
it
would
be
exceedingly
difficult
to
sample
the
gill
or
other
respiratory
tissue
in
an
organism
as
small
as
some
of
the
sensitive
invertebrates
that
are
commonly
used
for
test
purposes
(
e.
g.,
D.
magna
or
C.
dubia).
The
possibility
that
a
generally
consistent
set
of
biotic
ligand
parameter
values
for
binding
to
the
biotic
ligand
would
be
applicable
across
organism
types
is
considered
plausible,
however,
if
the
mechanism
of
toxicity
is
the
same
across
all
organism
types
to
which
the
model
is
applied.
This
seems
to
be
a
reasonable
expectation,
given
that
essentially
all
aquatic
organisms
must
regulate
the
ionic
composition
of
their
internal
fluids
in
order
to
survive
and
further,
that
essentially
all
forms
of
aquatic
life
utilize
Na,
K­
ATPase,
the
presumed
biotic
ligand,
to
do
so.

The
principal
model
parameter
value
that
is
adjusted
for
different
organisms
is
the
LA50.
The
reason
is
that
different
organisms
appear
to
exhibit
varying
sensitivities
to
copper,
and
increasing
or
decreasing
the
LA50
has
the
effect
of
increasing
or
decreasing
the
predicted
dissolved
copper
concentration
that
would
be
in
equilibrium
with
the
LA50.
The
reasons
for
this
varying
sensitivity
across
organism
types
are
not
well
understood,
and
this
is
currently
an
area
of
active
investigation.
One
explanation
that
is
related
to
the
known
inhibition
of
active
sodium
uptake
by
copper
is
that
the
19
more
sensitive
organisms
have
a
relatively
high
turnover
rate
of
exchangeable
whole­
body
sodium
levels
(
Grosell
et
al.
2002).
Thus,
if
the
process
of
sodium
uptake
is
inhibited,
lethal
changes
in
internal
sodium
pools
will
occur
relatively
quickly.
Similarly,
for
a
fixed
perturbation
of
internal
concentrations
of
sodium,
less
inhibition
of
the
sodium
uptake
is
required,
such
that
lower
concentrations
of
copper
may
be
needed
to
achieve
this
lesser
degree
of
inhibition.
If
this
explanation
is
correct,
than
it
would
be
necessary
to
evaluate
these
changes
in
internal
sodium
levels
to
predict
toxic
effects.
Although
such
models
are
being
developed,
they
are
not
currently
at
the
stage
of
development
where
they
can
be
routinely
applied.
As
a
practical
expedient
then,
the
LA50
is
adjusted
as
a
way
to
effectuate
this
change
in
sensitivity
in
the
context
of
a
chemical
equilibrium­
based
model
framework.

The
initial
dataset
to
which
the
BLM
was
used
to
test
its
applicability
to
invertebrates
was
a
WER
dataset
in
which
D.
pulex
was
the
test
organism.
Calibration
of
the
LA50
resulted
in
a
value
of
0.035
nmol
Cu/
g
w
used
for
this
analysis.
The
water
chemistry
in
these
model
simulations
represents
conditions
in
Connecticut
streams
to
which
wastewater
effluent
is
discharged
(
Dunbar,
1996
).
In
consideration
of
the
simplified
approach
that
was
used
to
adapt
the
fathead
minnow
model
to
reproduce
these
data
(
i.
e.,
it
was
achieved
with
the
adjustment
of
a
single
model
parameter,
the
LA50),
the
resulting
agreement
between
model
and
data
is
encouraging
(
Figure
20).
The
use
of
the
LA50
as
a
means
for
adjusting
the
response
of
the
model
to
more
sensitive
organisms
is
attractive
from
a
practical
perspective
because
only
the
sensitivity
of
the
model
is
affected.
The
response
of
the
model
to
changes
in
chemistry
is
determined
by
log
K
values
and
is
not
affected
by
changes
in
the
LA50.
In
the
absence
of
any
specific
information
about
the
nature
of
the
biotic
ligand
in
D.
pulex,
the
adjustment
of
the
LA50
is
the
simplest
means
of
adapting
the
fathead
minnow
parameter
set.

This
approach
seems
to
also
work
across
numerous
datasets.
Additional
copper
toxicity
data
for
D.
pulex
were
obtained
from
Table
1
of
the
US
EPA
ambient
water
quality
criteria
for
copper
(
J.
Mitchell
and
C.
Roberts,
personal
communication).
The
same
LA50
used
for
the
Dunbar
WER
study
predicts
copper
toxicity
that
agrees
well
with
measured
LC50s
for
these
data
as
well
(
Figure
20).
The
adjustment
of
the
LA50
value
appears
to
be
a
simple
way
to
adjust
the
model
to
match
the
varying
sensitivity
of
various
organisms
to
copper
toxicity,
while
avoiding
the
need
to
develop
independent
sets
of
thermodynamic
parameters
to
different
organisms.
Additional
testing
of
this
approach
with
data
for
additional
organisms
from
Table
1
further
shows
the
practical
utility
of
adjusting
the
LA50.
Using
this
approach,
the
model
was
developed
for
several
invertebrates
including
daphnids
(
D.
magna,
D.
pulicaria,
D.
pulex,
and
C.
dubia)
as
well
as
H.
azteca.
Despite
the
practical
benefits
of
adjusting
the
LA50
this
way,
the
low
value
for
the
LA50
that
results
in
the
D.
pulex
calibration
is
not
likely
to
be
mechanistically
meaningful.

4.0
MODEL
TESTING:
A
DESCRIPTION
OF
MODEL
VALIDATION
EFFORTS
This
section
focuses
on
the
testing
of
the
BLM
by
its
application
to
bioassay
datasets
obtained
with
natural
water
samples,
or
mixtures
of
natural
waters
and
Publically
Owned
Treatment
Work
(
POTW)
effluents.

4.1WER
Datasets
20
The
ability
of
the
BLM
to
reproduce
the
effect
of
variations
in
water
chemistry
on
copper
toxicity
to
fish
is,
in
itself,
of
interest.
However,
of
more
practical
significance
is
its
potential
use
in
setting
permit
limits
and
defining
site­
specific
water
quality
criteria
(
WQC).
One
component
of
this
procedure
is
to
conduct
bioassays
to
develop
water
effect
ratios
(
WERs)
(
USEPA,
1994;
Allen
and
Hansen,
1996).
The
WER
is
defined
as
the
ratio
of
the
LC50
in
the
receiving
water
to
the
LC50
in
laboratory
water
for
the
species
being
tested.
The
WQC
is
then
multiplied
by
the
WER
to
define
a
site­
specific
WQC.

4.1.1
Model
Testing
­
Water
Effect
Ratio
Studies
Using
Fathead
Minnow
An
example
of
this
procedure
is
the
WER
study
by
Diamond
et
al.
(
1997)
for
copper
in
a
stream
in
Pennsylvania.
The
water
quality
characteristics
of
the
laboratory,
upstream,
effluent,
and
mixtures
of
the
effluent
and
receiving
water
are
summarized
in
Figure
22.
The
thermodynamic
constants
used
for
WHAM
and
the
gill
computations
are
listed
in
Tables
1
and
2,
respectively.
Total
organic
carbon
(
TOC)
concentrations
were
approximately
1
mg/
L
in
the
lab
water,
3
mg/
L
in
the
upstream
receiving
water
(
U/
S),
and
12
mg/
L
in
the
effluent.
Alkalinity
(
70
to
100
mg
CaCO
3/
L)
and
hardness
(
75
to
160
mg
CaCO
3/
L)
varied
to
a
lesser
degree,
while
the
pH
was
relatively
constant
in
these
waters
(
pH

8).
The
water
quality
characteristics
of
the
mixtures
of
upstream
and
effluent
water
were
generally
consistent
with
what
would
be
predicted
from
mass
balances,
with
the
exception
of
the
75%
effluent
sample
for
alkalinity
and
hardness.

The
procedure
used
to
predict
the
WER
for
fathead
minnows
is
as
described
above.
That
is,
the
water
quality
characteristics
for
a
test
sample
are
used
in
the
BLM
to
compute
the
gill
copper
concentration.
As
with
the
other
natural
water
datasets
that
have
been
analyzed
with
the
model,
dissolved
organic
carbon
(
DOC)
inputs
to
the
BLM
was
assumed
to
be
10%
humic
acid
and
90%
fulvic
acid
for
these
waters.
A
numerical
titration
is
performed
in
which
the
dissolved
copper
is
varied
over
a
range
of
concentrations,
and
the
computed
gill
copper
concentration
is
determined
for
each
concentration
of
copper
added.
Representative
results
are
illustrated
for
an
effluent
sample
and
a
laboratory
sample
in
Figure
13.
For
the
effluent
sample
the
gill
copper
concentration
initially
increases
hardly
at
all
as
copper
is
added
to
the
system,
reflecting
the
complexation
of
the
copper
by
DOC
high­
affinity
binding
sites.
Once
the
high­
affinity
binding
sites
are
saturated,
the
gill
copper
concentration
begins
to
increase
more
rapidly
as
copper
is
added.
The
dissolved
copper
concentration
corresponding
to
a
gill
copper
concentration
of
6
nmol/
g
w,
the
gill
copper
LC50,
is
1450
µ
g/
L.
This
dissolved
copper
concentration
is
used
as
the
predicted
LC50
for
copper
in
the
effluent.

In
contrast,
the
predicted
gill
copper
concentration
in
laboratory
water
increases
much
more
rapidly
as
copper
is
added.
The
more
rapid
increase
occurs
because
of
the
lower
concentration
of
DOC
in
laboratory
water.
Hence,
less
Cu­
DOC
complex
forms.
This,
together
with
lower
alkalinity
that
produces
a
lower
concentration
of
copper
carbonate
complexes,
and
lower
hardness
so
that
there
is
less
calcium
competition,
results
in
a
faster
rate
of
increase
in
gill
copper
concentration
as
dissolved
copper
concentration
increases.
The
result
is
that
the
predicted
gill
copper
concentration
reaches
the
gill
Cu
LC50
of
6
nmol/
g
w
at
a
much
lower
dissolved
copper
concentration
of
about
200
µ
g/
L.
This
concentration
is
the
predicted
LC50
for
copper
in
the
laboratory
water.
The
ratio
of
the
predicted
effluent
to
laboratory
water
LC50s,
1,450/
200
=
7.25,
is
the
predicted
WER.

A
summary
of
the
observed
and
predicted
results
of
the
WER
analysis
for
the
January
test
data
is
shown
in
Figure
23.
The
dissolved
copper
LC50s
for
the
lab
water,
upstream
water,
mixtures
of
21
upstream
and
effluent
(
53
and
75
percent
effluent),
and
100
percent
effluent
are
compared
in
Figure
23
(
upper
panel).
The
general
trend
of
increasing
LC50
with
increasing
effluent
is
reproduced
for
both
the
observed
results
and
model
predictions,
with
the
exception
of
the
75%
effluent
sample
for
which
the
measurements
of
alkalinity
and
hardness
are
inconsistent
with
the
mixing
of
the
endmembers
(
Figure
22).
Analogous
results
for
the
predicted
WERs
are
also
shown
in
Figure
23
(
lower
panel).
Since
both
the
predicted
and
measured
lab
water
LC50s
are
used
to
compute
the
WER,
the
lab
water
WER
equals
one
(
by
definition).
The
predicted
WER
values
for
the
remaining
samples
agree
well
with
measured
values,
showing
the
utility
of
BLM
results
for
calculating
a
site­
specific
water
quality
criteria
in
an
approach
that
is
analogous
to
the
WER.

Additional
test
datasets
were
obtained
from
WER
studies
using
fathead
minnow
to
determine
sitespecific
water
quality
criteria
for
copper
in
effluent
impacted
streams
in
Connecticut
(
Dunbar
et
al.,
1996
).
Since
it
is
not
yet
known
how
organic
matter
in
municipal
waste
streams
compares
to
that
from
natural
sources,
it
is
assumed
here
that
the
DOC
can
be
described
using
the
same
distribution
of
10%
humic
and
90%
fulvic
acids.
Given
these
assumptions,
application
of
the
BLM
to
the
Connecticut
dataset
yields
good
agreement
between
predicted
and
measured
values
(
Figure
24).
In
summary,
considering
both
the
Erickson
et
al.
(
1996)
laboratory
test
data
and
the
Pennsylvania
and
Connecticut
WER
data,
nearly
all
of
the
predicted
results
are
within
a
factor
of
two
of
the
measured
values.

Another
WER
data
from
Pennsylvania
rivers
used
to
test
the
BLM
was
developed
by
Hall
et
al.
(
1998)
for
the
Pennsylvania
Copper
Group.
These
data
included
a
group
of
10
municipal
wastewater
treatment
plants
that
discharge
to
ten
streams
in
Pennsylvania.
The
C.
dubia
bioassays
were
run
with
laboratory
water
and
for
two
different
dilutions
of
wastewater
with
receiving
water.
As
a
result,
there
as
considerable
variation
in
copper
toxicity.
The
BLM
predictions
for
these
same
conditions
compare
favorably
with
these
measurements
as
well
as
for
other
C.
dubia
data
from
Table
1
of
the
copper
criteria
document
(
Figure
25),
showing
the
ability
of
the
BLM
to
account
for
differences
in
copper
toxicity
over
a
wide
range
of
conditions.

5.0
MODEL
APPLICATION
The
BLM
is
applicable
to
a
variety
of
water
and
organism
types.
However,
there
are
limits
with
regard
to
the
applicability
at
its
current
state
of
development.
This
section
describes
some
of
the
conditions
over
which
the
model
has
been
applied,
and
limitations
of
BLM
applicability
as
well.

5.1
Applicability
and
Limitations
5.1.1
Equilibrium
Assumptions
To
date
the
BLM
has
primarily
been
applied
in
the
analysis
of
toxicity
results
obtained
under
laboratory
test
conditions,
with
both
synthetic
waters
and
natural
waters.
It
is
assumed
that
equilibrium
conditions
prevail
amongst
the
various
chemical
components
in
the
test
water,
including
the
biotic
ligand,
and
the
model
has
been
calibrated
under
this
assumption.
Results
presented
in
Section
4
highlighted
the
problem
that
can
be
encountered
when
this
is
not
the
case.
As
stated
above,
22
issues
that
might
arise
from
this
equilibrium
assumption
and
its
applicability
to
the
use
of
the
BLM
in
a
regulatory
context
should
be
addressed.
However,
it
should
also
be
noted
that
the
current
water
effect
ratio
procedure
does
not
require
that
toxicity
tests
are
performed
in
such
a
way
as
to
mimic
any
non­
equilibrium
conditions
at
a
site.
Thus,
under
the
current
state
of
development
of
the
BLM,
this
limitation
should
not
be
viewed
as
a
disadvantage
of
the
BLM
relative
to
other
methods
that
are
currently
available
to
set
WQC.

5.1.2
Aquatic
Organisms
To
date
the
BLM
for
copper
has
been
calibrated
with
acute
toxicity
datasets
for
the
following
aquatic
organisms:

Freshwater:
fathead
minnow
(
P.
promelas),
rainbow
trout,
Daphnia
magna,
D.
pulex,
D.
pulicaria,
Hyallela
azteca,
Ceriodaphnia
dubia.

Saltwater:
Mytilus
edulis
The
degree
of
calibration
varies
by
organism,
as
does
the
range
of
water
quality
conditions
tested.

Preliminary
analyses
have
been
performed
with
USEPA
WQC
Table
1
data
in
instances
where
sufficient
water
chemistry
was
available
or
could
be
reasonably
estimated
(
USEPA,
2003a).
While
these
analyses
are
not
considered
definitive,
on
balance
it
appears
that
the
BLM
reduces
the
degree
of
uncertainty
in
the
results,
with
regard
to
its
ability
to
predict
LC50
levels,
in
comparison
to
a
more
simplified
hardness­
based
analysis.
This
is
so
in
spite
of
the
fact
that
the
preponderance
of
the
data
in
the
WQC
document
tend
to
reflect
hardness
variation,
in
comparison
to
other
test
conditions,
such
as
pH,
alkalinity
and
DOC.
As
a
result,
it
is
concluded
that
the
BLM
for
copper
provides
an
improved
assessment
tool
in
comparison
to
the
hardness­
based
approach.

Other
studies
are
ongoing
to
develop
bioassay
datasets
that
can
be
used
to
refine
the
current
parameterization
of
the
BLM.
Such
results
will
be
able
to
be
readily
incorporated
into
updated
releases
of
the
BLM,
over
time,
as
appropriate.

5.1.3
Ranges
of
Input
Parameters
Used
in
Calibration
Input
parameters
upon
which
the
BLM
calibration
is
based
are
summarized
previously
in
Section
3.0.
This
summary
does
not
reflect
any
multi­
variable
interactions
that
are
present
in
the
database.
Further
information
on
the
applicable
range
of
water
quality
characteristics
and
organism
types
is
presented
in
the
BLM
Users
Guide
(
USEPA,
2003b).

5.1.4
Other
Considerations
Only
a
limited
effort
has
been
put
forth
in
the
application
of
the
BLM
to
saltwater
datasets
to
date
(
Di
Toro
et
al.,
2000).
Thus,
the
Version
A008
of
the
BLM
is
not
currently
viewed
as
being
suitable
for
use
in
the
evaluation
of
saltwater
WQC.
As
a
result,
standard
hardness­
based
WQC
methods
will
be
applied
to
evaluate
saltwater
WQC
in
the
immediate
future.
23
To
date
the
model
is
only
considered
to
be
appropriate
for
use
in
the
evaluation
of
acute
toxicity.
Although
future
work
is
planned
to
extend
the
applicability
of
the
model
to
chronic
toxicity,
it
is
not
recommended
that
Version
A008
of
the
BLM
be
used
for
chronic
toxicity
evaluations
at
this
time.
Thus,
existing
procedures,
involving
application
of
an
acute
to
chronic
ratio
(
ACR),
will
be
used
until
a
BLM­
based
chronic
toxicity
model
has
been
developed
and
judged
to
be
acceptable
for
use.

6.0
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the
Department
of
Zoology
and
Physiology
and
The
Graduate
School
of
the
University
of
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in
partial
fulfillment
of
the
requirements
for
the
degree
of
Master
of
Science
in
Zoology
and
Physiology.

MacRae,
R.
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prepared
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(
Pimephales
promelas)
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71­
83.
30
Table
1.
Inorganic
copper
and
organic
speciation
reactions
in
the
WHAM
database
(
Tipping,
1994).

Organic
Complexes
Proton
Exchange
Constant,
pK
­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­
Cu­
Humic
1.5
Cu­
Fulvic
0.8
CuOH­
Humic
1.5
CuOH­
Fulvic
0.8
Ca­
Humic
3.2
Ca­
Fulvic
2.2
Mg­
Humic
3.3
Mg­
Fulvic
2.2
Inorganic
Species
Formation
Reactions
Log
K
­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­
Cu
+
OH
=
Cu(
OH)
6.48
Cu
+
2*
OH
=
Cu(
OH)
2
11.78
Cu
+
SO4
=
CuSO4
2.36
Cu
+
CO3
=
CuCO3
6.55
Cu
+
2*
CO3
=
Cu(
CO3)
2
9.92
Cu
+
Cl
=
CuCl
0.4
Cu
+
H
+
CO3
=
CuHCO3
14.32
31
Table
2Stoichiometry
and
Thermodynamic
Constants
for
Adsorption
of
Metals
and
Protons
on
Gills
of
Larval
Fathead
Minnows.

Reaction
Log
K
Source
H
+
gill
=
H­
gill
5.4
Playle
et
al.,
1993b
Na
+
gill
=
Na­
gill
3.0
Santore
et
al.,
2001
Ca
+
gill
=
Ca­
gill
3.6
Playle
et
al.,
1993b
Cu
+
gill
=
Cu­
gill
7.4
Playle
et
al.,
1993b
Table
3.
Average
composition
of
waters
used
in
the
fathead
minnow
copper
toxicity
experiments
of
Erickson
et
al.
(
1987)
in
exposures
without
chemical
modifications.

Water
source
DOC
pH
Ca
Mg
Na
K
Cl
SO4
Alkalinity
mg/
L
mg/
L
mg/
L
mg/
L
Mg/
L
mg/
L
mg/
L
mg
CaCO3/
L
Lake
Superior
Water
1.0
7.9
13.5
2.9
1.6
0.4
1.4
6.7
42.5
Synthetic
Water
0.1
8.0
91.5
30.3
59.5
5.0
61.7
168.8
146.7
Note:
Concentrations
are
measured,
except
for
DOC
concentrations
which
were
provided
by
the
lead
author
(
Erickson,
2000,
Personal
Communication).
32
Ca
Na
H
2+

+
+

M2+
M­
DOC
M­
Biotic
Ligand
MOH
MHCO
MCI
3
BIOTIC
LIGAND
MODEL
Organic
Matter
Complexation
Site
of
Action
Competing
Cations
Free
Metal
Ion
Inorganic
Ligand
Complexation
+

+
+

Figure
1
Schematic
diagram
of
the
generalized
biotic
ligand
model
(
BLM)
framework
for
acute
toxicity
of
a
divalent
cationic
metal.
33
GILL
LC50
~
10
nmol/
gw
24­
Hour
Gill
Cu
(
nmol/
g
wet
weight)
0
0
20
40
60
80
100
(
Data:
MacRae,
12/
94)

TOTAL
Cu
=
10
ug/
L
Test
A
Test
B
10
20
30
40
50
120­
Hour
Juvenile
Rainbow
Trout
Mortality
(%)

Figure
2
Relationship
between
mortality
of
juvenile
rainbow
trout
after
120
hours
of
exposure
and
copper
concentration
on
the
gill
of
the
fish
after
24
hours
of
exposure.
Data
from
MacRae
et
al.
(
1999).
34
p[
Cu]

7
6
5
4
3
2.5
3.0
3.5
4.0
4.5
5.0
pN
p[
Cd]
Cd
4.5
3.5
2.5
6.0
5.0
4.0
p[
Pb]
pN
Pb
11
9
7
5
3
pN
5.0
4.0
3.0
2.5
3.5
4.5
Cu
3
4
5
10
8
6
4
p[
Cu]
pN
Cu
Figure
3
Calibration
of
the
WHAM
model,
Version
V.
(
A)
Cu:
effect
of
ionic
strength:
0.001
M
(

)
0.01
M
(

)
(
B)
Cu:
effect
of
Ca:
0.001
M
NaNO
(

)
0.001
M
Ca(
NO)
(

)
0.01
M
Ca(
NO)
(
G)
(
C)
Cu:
effect
of
pH:
5.14
(

)
7.00
(

)
8.44
(
G)
(
D)
Ca:
effect
of
pH:
5.00
(

)
7.00
(

)
9.00
(
G)
(
E)
Cd:
effect
of
pH:
4.00
(

)
6.00
(

)
8.00
(
G)
(
F)
Pb:
effect
of
pH:
4.00
(

)
5.00
(

)
6.00
(
G).
Redrawn
from
Tipping
and
Hurley
(
1992).
35
H
Ca
Active
Metal
Sites
Gill
Surface
(
biotic
ligand)

Cupric
ion
NOM
Cu
+

2+

Organic
Complexes
Inorganic
Complexes
e.
g.
:
Cu
­
Hydroxides
Cu
­
Carbonates
CONCEPTUAL
DIAGRAM
OF
COPPER
SPECIATION
AND
COPPER­
GILL
MODEL
(
After
Pagenkopf,
1983)

Figure
4
Schematic
diagram
of
the
biotic
ligand
model
(
BLM)
framework
for
acute
copper
toxicity,
showing
inorganic
and
organic
complexation
in
the
water
and
interaction
of
metals
and
cations
on
the
biotic
ligand.
36
0
5
10
15
20
25
30
35
40
0
50
100
150
200
250
300
Free
Copper
(
nmol/
L)
Gill­
Cu
(
nmol/
g
wet)
Playle
et
al.,
1993
BLM
Calibration
Figure
5
Measured
copper
accumulation
on
fathead
minnow
gills
from
Playle
et
al.
1993b;
and
Biotic
Ligand
Model
predictions
as
a
function
of
cupric
ion
concentration.
37
0
1
2
3
4
5
6
7
8
MEASURED
LC50
(
umol/
L)

Total
Cu
Ca
=
constant
0.000
0.015
0.030
0.045
0.060
0.075
MEASURED
LC50
(
umol/
L)

Cupric
Ion
0
5
10
15
20
25
0
1
2
3
4
5
6
7
CALCULATED
LC50
(
nmol/
g
wet
tissue)

DOC
(
mg
C/
L)
Gill
Cu
Figure
6
Relationship
of
copper
LC50s
to
variations
in
DOC
concentration.
The
lines
are
drawn
by
eye
to
represent
the
data.
(
A)
LC50
expressed
as
the
concentration
of
total
dissolved
copper.
(
B)
LA50
expressed
as
the
concentration
of
the
free
ion
activity
of
copper.
(
C)
LC50
expressed
as
the
concentration
of
the
copper
sorbed
to
the
gill.
Data
from
Erickson
et
al.
(
1996).
38
0
1
2
3
4
5
6
7
8
MEASURED
LC50
(
umol/
L)

Total
Cu
DOC
and
pH
constant
0.00
0.05
0.10
0.15
0.20
0.25
CALCULATED
LC50
(
umol/
L)

Cupric
Ion
0
5
10
15
20
25
0.0
0.5
1.0
1.5
2.0
2.5
3.0
CALCULATED
LC50
(
nmol/
g
wet
tissue)

Ca
(
meq/
L)
Gill
Cu
Figure
7
Relationship
of
copper
LC50s
to
variations
in
calcium
concentration.
The
lines
are
drawn
by
eye
to
represent
the
data.
(
A)
LC50
expressed
as
the
concentration
of
total
dissolved
copper.
(
B)
LC50
expressed
as
the
concentration
of
the
free
ion
activity
of
copper.
(
C)
LA50
expressed
as
the
concentration
of
the
copper
sorbed
to
the
gill.
Data
from
Erickson
et
al.
(
1996).
39
0
1
2
3
4
MEASURED
LC50
(
umol/
L)

Total
Cu
0.000
0.015
0.030
0.045
0.060
0.075
MEASURED
LC50
(
umol/
L
)

Cupric
Ion
0
5
10
15
20
25
6.0
6.5
7.0
7.5
8.0
8.5
9.0
CALCULATED
LC50
(
nmol/
g
wet
tissue)

pH
Gill
Cu
Figure
8
Relationship
of
copper
LC50s
to
variations
in
pH.
The
lines
are
drawn
by
eye
to
represent
the
data.
(
A)
LC50
expressed
as
the
concentration
of
total
dissolved
copper.
(
B)
LC50
expressed
as
the
concentration
of
the
free
ion
activity
of
copper.
(
C)
LC50
expressed
as
the
concentration
of
the
copper
sorbed
to
the
gill.
The
LA50s
in
(
B)
are
the
measured
copper
activities
using
a
specific
ion
electrode.
Data
from
Erickson
et
al.
(
1996).
40
Experiment
15
0
100
200
300
400
500
600
700
800
900
7.1
7.3
7.6
7.7
8.1
8.4
8.7
pH
Cu
LC50
(
ug
/
L)
Measured
BLM
with
Cu
only
Figure
9
Response
of
measured
and
predicted
fathead
minnow
total
Cu
LC50
to
changes
in
pH.
BLM
predictions
assume
that
only
Cu2+
is
bioavailable.
41
0
1
2
3
4
5
6
3.5
4.5
5.5
6.5
7.5
8.5
9.5
pH
Conc
(
umol
/
L)
NOM­
Cu
NOM­
CuOH
Figure
10
Distribution
of
complexed
Cu2+
and
CuOH+
on
natural
organic
matter
as
simulated
in
the
WHAM.
42
0
1
2
3
4
5
6
7
4.5
5.5
6.5
7.5
8.5
9.5
pH
Conc
(
umol
/
L)

Gill­
Cu
Gill­
CuOH
Figure
11
Distribution
of
adsorbed
Cu2+
and
CuOH+
on
gill
membrane
as
simulated
in
the
revised
BLM.
43
Experiment
15
0
100
200
300
400
500
600
700
800
900
7.1
7.3
7.6
7.7
8.1
8.4
8.7
pH
Cu
LC50
(
ug
/
L)
Measured
BLM
with
Cu
and
CuOH
BLM
with
Cu
only
Figure
12
Response
of
measured
and
predicted
fathead
minnow
Cu
LC50
to
changes
in
pH.
BLM
predictions
assuming
only
Cu2+
is
bioavailable
are
compared
with
the
revised
model
that
assumes
both
Cu2+
and
CuOH+
are
bioavailable.
44
0
5
10
15
20
25
30
0
500
1000
1500
2000
2500
3000
3500
4000
GILL
Cu
(
nmol/
g
wet)

DISSOLVED
Cu
(
ug/
L)
LABORATORY
SITE­
WATER
Figure
13
Method
of
calculating
the
LC50
using
the
BLM.
Relationship
of
copper
concentration
sorbed
on
the
gill
and
dissolved
copper
as
computed
using
the
BLM
for
laboratory
water
and
100%
effluent.
45
10
100
1000
10000
10
100
1000
10000
Measured
Cu
LC50
(
ug/
L)
Predicted
Cu
LC50
(
ug/
L)
Erickson
et
al.,
1987
Fathead
minnow,
96h
static
exposures
Figure
14
Biotic
Ligand
Model
predicted
versus
measured
LC50
values
for
fathead
minnow
in
static
toxicity
exposures
from
Erickson
et
al.
(
1996).
The
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.
46
1
10
100
1000
0
24
48
72
96
Time
(
hours)
Free
Copper
(
nmol
/
L)

Total
Dissolved
Copper
=
1.57E­
7
mol/
L
=
10
ug/
L
Equilibrium
Figure
15
Simulated
changes
in
free
copper
over
time
during
a
static
toxicity
test.
Kinetics
of
copper
binding
to
natural
organic
matter
are
based
on
results
of
Ma
et
al.
(
1999).
47
1
10
100
1000
0
24
48
72
96
120
Time
(
hours)
Free
Copper
(
nmol
/
L)

Pre­
equil.
Test
duration
Equilibrium
Figure
16
Simulated
changes
in
free
copper
over
time
during
a
static
toxicity
test
with
a
24
hour
pre­
test
equilibration
period.
Kinetics
of
copper
binding
to
natural
organic
matter
are
based
on
results
of
Ma
et
al.
(
1999).
48
1
10
100
1000
0
24
48
72
96
Time
(
hours)
Free
Copper
(
nmol
/
L)

Equilibrium
Figure
17
Simulated
changes
in
free
copper
over
time
during
a
static
toxicity
test
with
a
24
hour
renewal
frequency.
Kinetics
of
copper
binding
to
natural
organic
matter
are
based
on
results
of
Ma
et
al.
(
1999).
49
1
10
100
1000
0
24
48
72
96
Time
(
hours)
Free
Copper
(
nmol
/
L)

Equilibrium
Free
Copper
with
1
hour
HRT
Figure
18
Simulated
changes
in
free
copper
over
time
during
a
flowthrough
toxicity
test
with
1
hour
of
contact
time
of
the
copper
in
the
exposure
water.
Kinetics
of
copper
binding
to
natural
organic
matter
are
based
on
results
of
Ma
et
al.
(
1999).
50
10
100
1000
10000
10
100
1000
10000
Measured
Cu
LC50
(
ug/
L)
Predicted
Cu
LC50
(
ug/
L)

Erickson
et
al.,
1987
Fathead
minnow,
96­
h
flowthrough
exposures
Figure
19
Biotic
Ligand
Model
predicted
versus
measured
LC50
values
for
fathead
minnow
in
flow­
through
toxicity
exposures
from
Erickson
et
al.
(
1996).
The
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.
51
1
10
1
00
1000
1
10
100
1000
PREDICTED
LC50
(
ug/
L)

MEASURED
LC50
(
ug/
L)
CT
DEP
(
Dunbar,
1996)

Table
1,
WQC
Document
Data
Figure
20
Predicted
versus
measured
values
for
D.
pulex
copper
LC50
in
Connecticut
streams
(
CT
DEP;
1996b
).
The
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.
52
1
10
100
1000
1
10
100
1000
Measured
Cu
LC50
(
ug/
L)
BLM
Predicted
Cu
LC50
(
ug/
L)
D.
magna
D.
pulicaria
H.
azteca
C.
dubia
D.
pulex
Figure
21
Comparison
of
BLM
predictions
for
copper
toxicity
to
five
aquatic
species
from
the
US
EPA
draft
ambient
water
quality
criteria
document
(
USEPA
2003b).
53
0
50
100
150
ALKALINITY
(
mg/
L)

LAB
U/
S
53%
75%
100%
EFFLUENT
0
50
100
150
200
HARDNESS
(
mg/
L)

LAB
U/
S
53%
75%
100%
EFFLUENT
0
5
10
15
TOC
(
mg/
L)

LAB
U/
S
53%
75%
100%
EFFLUENT
0
2
4
6
8
10
pH
LAB
U/
S
53%
75%
100%
EFFLUENT
FATHEAD
MINNOW
WATER­
EFFECT
RATIO
STUDY
­
JANUARY
(
SOURCE:
DIAMOND
et
al.,
1997)

Figure
22
The
aqueous
concentrations
of
TOC
(
taken
to
be
equivalent
to
DOC
in
the
application
of
BLM),
alkalinity,
hardness,
and
pH,
in
laboratory
water
(
LAB),
upstream
water
(
U/
S),
and
at
the
indicated
percentages
of
effluent
dilutions
in
upstream
water.
Data
from
Diamond
et
al.
(
1997).
54
0
1000
2000
3000
4000
5000
DISSOLVED
COPPER
LC50
(
ug/
L)

­
MEASURED
­
CALCULATED
LAB
U/
S
53%
75%
100%

EFFLUENT
0
2
4
6
8
10
WATER­
EFFECT
RATIO
­
MEASURED
­
CA
LCULATED
LAB
U/
S
53%
75%
100%
EFFLUENT
Figure
23
Comparison
of
measured
and
calculated
LC50s
and
the
watereffect
ratios.
Data
from
Diamond
et
al.
(
1997).
1
10
100
1000
10000
1
10
100
1000
10000
PREDICTED
LC50
(
ug/
L)

MEASURED
LC50
(
ug/
L)
+
+
+
+

+
+

+
+
+
+

+
+
+

+
+
+
+
+
D.
pulex
(
CT
DEP,
Dunbar,
1996)
Fathead
minnows,
Field
Fathead
minnows,
Lab
Figure
24
Predicted
versus
measured
values
for
fathead
minnow
copper
LC50s
in
water
effect
ratio
studies
(
Diamond
et
al.,
1997;
Dunbar,
1996).
The
results
from
static
exposures
from
Erickson
et
al.
(
1987;
fathead
minnow
lab)
are
included
for
comparison.
The
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.
Figure
25
Predicted
versus
measured
values
for
C.
dubia
copper
LC50s
in
Water
Effect
Ratio
studies
(
Hall
et
al.,
1998).
The
1:
1
(
solid),
2:
1
and
1:
2
(
dotted)
reference
lines
are
drawn
for
comparison.
APPENDIX
A.
Chemical
Speciation
Equations
for
Copper
A1
APPENDIX
A
CHEMICAL
SPECIATION
EQUATIONS
FOR
COPPER
The
water
quality
criteria
for
copper
will
be
developed
using
the
Biotic
Ligand
Model
(
BLM;
Renner,
1997;
Meyer
et
al.,
1999;
Di
Toro
et
al.,
1999;
Paquin
et
al.,
1999;
Santore
et
al.,
1999a).
The
conceptual
framework
for
the
BLM
is
an
adaptation
of
several
previous
attempts
to
predict
metal
toxicity
and
bioavailability
including
the
Gill
Site
Interaction
Model
(
GSIM:
Pagenkopf,
1983)
and
recent
extensions
by
Playle
and
coworkers
(
Playle
et
al.,
1992,
1993a,
b;
Janes
and
Playle,
1995;
Wood
et
al.,
1999)
and
the
Free
Ion
Activity
Model
(
FIAM:
Morel,
1983b;
Campbell,
1995).
The
BLM
synthesizes
these
previous
efforts
and
combines
these
conceptual
models
with
state
of
the
art
descriptions
of
metal
chemistry
and
the
latest
information
on
the
physiology
of
metal
bioavailability.

The
underlying
equations
in
the
BLM
include
descriptions
of
the
amounts
of
all
the
chemical
components
in
the
model
(
the
mole
balance
equations),
and
how
these
amounts
are
distributed
amongst
all
of
the
chemical
species
possible
for
each
component
(
the
mass
action
equations).
For
an
examination
of
the
underlying
mathematical
structure
of
the
model,
it
is
helpful
to
start
with
the
mole
balance
relationships.
The
user
of
the
BLM
must
specify
a
total
concentration
for
each
chemical
component
in
the
model.
The
total
concentrations
for
these
components
include
T.
H,
T.
Cu,
T.
DOC,
T.
Ca,
T.
Mg,
T.
Na,
T.
K,
T.
SO4,
T.
Cl,
T.
CO3.
For
each
of
the
following
equations,
we
will
introduce
a
notation
such
that
the
prefix
"
T"
indicates
a
total
concentration,
and
the
suffix
identifies
the
individual
chemical
components.
These
total
concentrations
can
also
be
expressed
in
matrix
notation
such
that
the
vector
of
all
total
concentrations
is
expressed
as
T,
and
an
arbitrary
element
is
identified
as
Tj.
In
addition
to
the
components
identified
as
user
inputs,
the
following
components,
derived
from
the
Windermere
Humic
Aqueous
Model
(
WHAM:
Tipping,
1994),
are
introduced.

T.
HA1H
=
DOM
*
f
*
NHA
*
0.7
/
5.78
T.
HA2H
=
DOM
*
f
*
NHA
*
1.0
/
5.78
T.
HA3H
=
DOM
*
f
*
NHA
*
1.0
/
5.78
T.
HA4H
=
DOM
*
f
*
NHA
*
0.7
/
5.78
T.
HB1H
=
DOM
*
f
*
NHA
*
0.7
/
5.78
T.
HB2H
=
DOM
*
f
*
NHA
*
0.49
/
5.78
T.
HB3H
=
DOM
*
f
*
NHA
*
0.49
/
5.78
T.
HB4H
=
DOM
*
f
*
NHA
*
0.7
/
5.78
T.
FA1H
=
DOM
*
(
1
­
f)
*
NFA
*
0.7
/
5.78
T.
FA2H
=
DOM
*
(
1
­
f)
*
NFA
*
1.0
/
5.78
T.
FA3H
=
DOM
*
(
1
­
f)
*
NFA
*
1.0
/
5.78
T.
FA4H
=
DOM
*
(
1
­
f)
*
NFA
*
0.7
/
5.78
T.
FB1H
=
DOM
*
(
1
­
f)
*
NFA
*
0.7
/
5.78
T.
FB2H
=
DOM
*
(
1
­
f)
*
NFA
*
0.49
/
5.78
T.
FB3H
=
DOM
*
(
1
­
f)
*
NFA
*
0.49
/
5.78
T.
T.
FB4H
=
DOM
*
(
1
­
f)
*
NFA
*
0.7
/
5.78
Where:

DOM
=
DOC
*
2
/
1000
(
units
of
g/
L
of
Organic
Matter)
f
=
fraction
of
DOM
in
humic
substances
(
input
by
the
user)
NHA
=
Number
of
reactive
sites
in
humic
acids
=
3.29
E
­
3
moles
per
g
HA
NFA
=
Number
of
reactive
sites
in
fulvic
acids
=
4.73
E
­
3
moles
per
g
HA
WHAM
is
a
state­
of­
the­
art
representation
of
the
interactions
between
natural
organic
matter
and
metals,
including
copper.
The
BLM
has
adopted
the
chemical
description
in
WHAM
for
organic
matter
interactions.
A2
Finally,
a
component
is
introduced
for
mass
balance
of
substances
on
the
gill:

T.
Gill
=
.000030
moles
per
kg
wet
weight
of
gill
=
30
nmol/
g
w
Each
of
these
chemical
components
can
be
distributed
among
a
variety
of
chemical
species,
such
that
the
sum
of
all
species,
with
appropriate
stoichiometric
relations,
must
equal
those
total
quantities.
These
mole
balance
relationships
are
listed
in
Table
A1.

Together,
the
mole
balance
relationships
comprise
a
set
of
26
equations,
and
the
proper
description
of
copper
chemistry
must
satisfy
all
equations
simultaneously.
A
generic
expression
for
these
equations
can
be
summarized
as
follows:

T
j
=

i
S
i
a
i,
j
Where
the
concentration
of
an
individual
chemical
species
is
represented
by
S
i
and
the
stoichiometric
coefficient
between
S
i
and
T
j
is
indicated
by
a
i,
j.

A
solution
can
be
obtained
by
first
substituting
the
species
concentrations
in
each
of
the
mole
balance
equations.
The
species
concentrations
can
be
expressed
as
a
function
of
the
concentrations
of
each
of
the
chemical
components
by
the
use
of
mass
action
expressions.
The
mass
action
expressions
for
the
formation
of
each
of
the
species
in
the
BLM
are
listed
in
Table
A2.
Table
A2
contains
a
description
of
interactions
on
a
gill
suitable
for
determining
copper
toxicity
to
fathead
minnow
(
Pimephales
promelas).
For
each
reaction,
the
concentration
of
a
species
can
be
calculated
as:

S
i
=
K
i

C
k
a
ik
Where
the
K
i
for
each
species
is
given
in
Table
A2,
the
stoichiometric
coefficients
between
species
i
and
component
k
is
ai,
k.,
and
the
concentration
of
each
component
C
k
is
an
unknown.
The
values
of
K
in
Table
A2
are
modified
for
the
specific
conditions
of
ionic
strength
and
temperature.
Ionic
strength
corrections
can
be
provided
by
the
extended
Debye­
Huckel
Equation
(
Morel,
1983a)
for
inorganic
species,
and
by
a
Donnan­
layer
expression
for
organic
species
(
Tipping,
1994).
Substituting
these
mass
action
expressions
into
the
mole
balance
equations
generates
a
system
of
26
equations
(
T)
in
26
unknowns
(
C).
These
can
be
solved
simultaneously
to
derive
the
final
chemical
distribution
at
equilibrium.
Conversely,
an
iterative
approach
can
be
applied
to
solve
for
the
dissolved
copper
concentration
that
would
be
needed
for
the
Cu­
biotic
ligand
concentration
to
equal
the
critical
effect
level
that
is
associated
with
the
LC50.
This
is
the
approach
that
is
used
in
the
BLM
to
predict
metal
effect
levels.

Table
A1.
Mole
Balance
Equation
for
Chemical
Components
in
the
BLM
T.
H
=+
H
+
Gill­
H
­
HA1
­
HA2
­
HA3
­
HA4
­
HB1
­
HB2
­
HB3
­
HB4
A3
­
FA1
­
FA2
­
FA3
­
FA4
­
FB1
­
FB2
­
FB3
­
FB4
­
HA1­
Mg
­
HA2­
Mg
­
HA3­
Mg
­
HA4­
Mg
­
HB1­
Mg
­
HB2­
Mg
­
HB3­
Mg
­
HB4­
Mg
­
FA1­
Mg
­
FA2­
Mg
­
FA3­
Mg
­
FA4­
Mg
­
FB1­
Mg
­
FB2­
Mg
­
FB3­
Mg
­
FB4­
Mg
­
HA1­
Ca
­
HA2­
Ca
­
HA3­
Ca
­
HA4­
Ca
­
HB1­
Ca
­
HB2­
Ca
­
HB3­
Ca
­
HB4­
Ca
­
FA1­
Ca
­
FA2­
Ca
­
FA3­
Ca
­
FA4­
Ca
­
FB1­
Ca
­
FB2­
Ca
­
FB3­
Ca
­
FB4­
Ca
­
HA1­
Cu
­
HA2­
Cu
­
HA3­
Cu
­
HA4­
Cu
­
HB1­
Cu
­
HB2­
Cu
­
HB3­
Cu
­
HB4­
Cu
­
FA1­
Cu
­
FA2­
Cu
­
FA3­
Cu
­
FA4­
Cu
­
FB1­
Cu
­
FB2­
Cu
­
FB3­
Cu
­
FB4­
Cu
+
HCO3
+
2H2CO3
+
MgHCO3
+
CaHCO3
+
CuHCO3
­
HA1­
CuOH
­
HA2­
CuOH
­
HA3­
CuOH
­
HA4­
CuOH
­
HB1­
CuOH
­
HB2­
CuOH
­
HB3­
CuOH
­
HB4­
CuOH
­
FA1­
CuOH
­
FA2­
CuOH
­
FA3­
CuOH
­
FA4­
CuOH
­
FB1­
CuOH
­
FB2­
CuOH
­
FB3­
CuOH
­
FB4­
CuOH
T.
Cu
=
+
Cu
+
Gill­
Cu
+
HA1­
Cu
+
HA2­
Cu
+
HA3­
Cu
+
HA4­
Cu
+
HB1­
Cu
+
HB2­
Cu
+
HB3­
Cu
+
HB4­
Cu
+
FA1­
Cu
+
FA2­
Cu
+
FA3­
Cu
+
FA4­
Cu
+
FB1­
Cu
+
FB2­
Cu
+
FB3­
Cu
+
FB4­
Cu
+
CuOH
+
Cu(
OH)
2
+
HA1­
CuOH
+
HA2­
CuOH
+
HA3­
CuOH
+
HA4­
CuOH
+
HB1­
CuOH
+
HB2­
CuOH
+
HB3­
CuOH
+
HB4­
CuOH
+
FA1­
CuOH
+
FA2­
CuOH
+
FA3­
CuOH
+
FA4­
CuOH
+
FB1­
CuOH
+
FB2­
CuOH
+
FB3­
CuOH
+
FB4­
CuOH
+
CuSO4
+
CuCO3
+
Cu(
CO3)
2
+
CuCl
+
CuHCO3
T.
Ca
=+
Ca
+
Gill­
Ca
+
HA1­
Ca
+
HA2­
Ca
+
HA3­
Ca
+
HA4­
Ca
+
HB1­
Ca
+
HB2­
Ca
+
HB3­
Ca
+
HB4­
Ca
+
FA1­
Ca
+
FA2­
Ca
+
FA3­
Ca
+
FA4­
Ca
+
FB1­
Ca
+
FB2­
Ca
+
FB3­
Ca
+
FB4­
Ca
+
CaHCO3
+
CaCO3
+
CaSO4
Table
A1.
Continued
T.
Mg
=
+
Mg
+
HA1­
Mg
+
HA2­
Mg
+
HA3­
Mg
+
HA4­
Mg
+
HB1­
Mg
+
HB2­
Mg
+
HB3­
Mg
+
HB4­
Mg
+
FA1­
Mg
+
FA2­
Mg
+
FA3­
Mg
+
FA4­
Mg
+
FB1­
Mg
+
FB2­
Mg
+
FB3­
Mg
+
FB4­
Mg
A4
+
MgHCO3
+
MgCO3
+
MgSO4
T.
Na
=+
Na
+
Gill­
Na
T.
K
=
+
K
T.
SO4
=+
SO4
+
MgSO4
+
CaSO4
+
CuSO4
T.
Cl
=
+
Cl
+
CuCl
T.
CO3
=
+
CO3
+
HCO3
+
H2CO3
+
MgHCO3
+
MgCO3
+
CaHCO3
+
CaCO3
+
CuCO3
+
2Cu(
CO3)
2
+
CuHCO3
T.
HA1H
=
+
HA1H
+
HA1
+
HA1­
Mg
+
HA1­
Ca
+
HA1­
Cu
+
HA1­
CuOH
T.
HA2H
=
+
HA2H
+
HA2
+
HA2­
Mg
+
HA2­
Ca
+
HA2­
Cu
+
HA2­
CuOH
T.
HA3H
=
+
HA3H
+
HA3
+
HA3­
Mg
+
HA3­
Ca
+
HA3­
Cu
+
HA3­
CuOH
T.
HA4H
=
+
HA4H
+
HA4
+
HA4­
Mg
+
HA4­
Ca
+
HA4­
Cu
+
HA4­
CuOH
T.
HB1H
=
+
HB1H
+
HB1
+
HB1­
Mg
+
HB1­
Ca
+
HB1­
Cu
+
HB1­
CuOH
T.
HB2H
=
+
HB2H
+
HB2
+
HB2­
Mg
+
HB2­
Ca
+
HB2­
Cu
+
HB2­
CuOH
T.
HB3H
=
+
HB3H
+
HB3
+
HB3­
Mg
+
HB3­
Ca
+
HB3­
Cu
+
HB3­
CuOH
T.
HB4H
=
+
HB4H
+
HB4
+
HB4­
Mg
+
HB4­
Ca
+
HB4­
Cu
+
HB4­
CuOH
T.
FA1H
=
+
FA1H
+
FA1
+
FA1­
Mg
+
FA1­
Ca
+
FA1­
Cu
+
FA1­
CuOH
T.
FA2H
=
+
FA2H
+
FA2
+
FA2­
Mg
+
FA2­
Ca
+
FA2­
Cu
+
FA2­
CuOH
T.
FA3H
=
+
FA3H
+
FA3
+
FA3­
Mg
+
FA3­
Ca
+
FA3­
Cu
+
FA3­
CuOH
T.
FA4H
=
+
FA4H
+
FA4
+
FA4­
Mg
+
FA4­
Ca
+
FA4­
Cu
+
FA4­
CuOH
T.
FB1H
=
+
FB1H
+
FB1
+
FB1­
Mg
+
FB1­
Ca
+
FB1­
Cu
+
FB1­
CuOH
T.
FB2H
=
+
FB2H
+
FB2
+
FB2­
Mg
+
FB2­
Ca
+
FB2­
Cu
+
FB2­
CuOH
T.
FB3H
=
+
FB3H
+
FB3
+
FB3­
Mg
+
FB3­
Ca
+
FB3­
Cu
+
FB3­
CuOH
T.
FB4H
=
+
FB4H
+
FB4
+
FB4­
Mg
+
FB4­
Ca
+
FB4­
Cu
+
FB4­
CuOH
T.
Gill
=
+
Gill
+
Gill­
Cu
+
Gill­
Ca
+
Gill­
H
+
Gill­
Na
A5
Table
A2.
Species
Formation
Reactions
Species
Formation
Reaction
Log
K
­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­
Gill­
Cu
=
+
Gill
+
Cu
7.4
Gill­
Ca
=
+
Gill
+
Ca
3.6
Gill­
H
=
+
Gill
+
H
5.4
Gill­
Na
=
+
Gill
+
Na
3.0
HA1
=
+
HA1H
­
H
­
4.91
HA2
=
+
HA2H
­
H
­
4.316667
HA3
=
+
HA3H
­
H
­
3.723333
HA4
=
+
HA4H
­
H
­
3.13
HB1
=
+
HB1H
­
H
­
10.265
HB2
=
+
HB2H
­
H
­
9.121667
HB3
=
+
HB3H
­
H
­
7.978333
HB4
=
+
HB4H
­
H
­
6.835
FA1
=
+
FA1H
­
H
­
4.93
FA2
=
+
FA2H
­
H
­
3.816667
FA3
=
+
FA3H
­
H
­
2.703333
FA4
=
+
FA4H
­
H
­
1.59
FB1
=
+
FB1H
­
H
­
12.4
FB2
=
+
FB2H
­
H
­
10.56
FB3
=
+
FB3H
­
H
­
8.72
FB4
=
+
FB4H
­
H
­
6.88
HA1­
Mg
=
+
HA1H
­
H
+
Mg
­
3.3
HA2­
Mg
=
+
HA2H
­
H
+
Mg
­
3.3
HA3­
Mg
=
+
HA3H
­
H
+
Mg
­
3.3
HA4­
Mg
=
+
HA4H
­
H
+
Mg
­
3.3
HB1­
Mg
=
+
HB1H
­
H
+
Mg
­
3.3
HB2­
Mg
=
+
HB2H
­
H
+
Mg
­
3.3
HB3­
Mg
=
+
HB3H
­
H
+
Mg
­
3.3
HB4­
Mg
=
+
HB4H
­
H
+
Mg
­
3.3
FA1­
Mg
=
+
FA1H
­
H
+
Mg
­
2.2
FA2­
Mg
=
+
FA2H
­
H
+
Mg
­
2.2
FA3­
Mg
=
+
FA3H
­
H
+
Mg
­
2.2
FA4­
Mg
=
+
FA4H
­
H
+
Mg
­
2.2
FB1­
Mg
=
+
FB1H
­
H
+
Mg
­
2.2
FB2­
Mg
=
+
FB2H
­
H
+
Mg
­
2.2
FB3­
Mg
=
+
FB3H
­
H
+
Mg
­
2.2
FB4­
Mg
=
+
FB4H
­
H
+
Mg
­
2.2
Species
Formation
Reaction
Log
K
­­
­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­
HA1­
Ca
=
+
HA1H
­
H
+
Ca
­
3.2
HA2­
Ca
=
+
HA2H
­
H
+
Ca
­
3.2
HA3­
Ca
=
+
HA3H
­
H
+
Ca
­
3.2
HA4­
Ca
=
+
HA4H
­
H
+
Ca
­
3.2
HB1­
Ca
=
+
HB1H
­
H
+
Ca
­
3.2
HB2­
Ca
=
+
HB2H
­
H
+
Ca
­
3.2
HB3­
Ca
=
+
HB3H
­
H
+
Ca
­
3.2
HB4­
Ca
=
+
HB4H
­
H
+
Ca
­
3.2
F
A1­
Ca
=
+
FA1H
­
H
+
Ca
­
2.2
FA2­
Ca
=
+
FA2H
­
H
+
Ca
­
2.2
FA3­
Ca
=
+
FA3H
­
H
+
Ca
­
2.2
FA4­
Ca
=
+
FA4H
­
H
+
Ca
­
2.2
FB1­
Ca
=
+
FB1H
­
H
+
Ca
­
2.2
FB2­
Ca
=
+
FB2H
­
H
+
Ca
­
2.2
FB3­
Ca
=
+
FB3H
­
H
+
Ca
­
2.2
FB4­
Ca
=
+
FB4H
­
H
+
Ca
­
2.2
HA1­
Cu
=
+
HA1H
­
H
+
Cu
­
1.5
HA2­
Cu
=
+
HA2H
­
H
+
Cu
­
1.5
HA3­
Cu
=
+
HA3H
­
H
+
Cu
­
1.5
HA4­
Cu
=
+
HA4H
­
H
+
Cu
­
1.5
HB1­
Cu
=
+
HB1H
­
H
+
Cu
­
1.5
HB2­
Cu
=
+
HB2H
­
H
+
Cu
­
1.5
HB3­
Cu
=
+
HB3H
­
H
+
Cu
­
1.5
HB4­
Cu
=
+
HB4H
­
H
+
Cu
­
1.5
F
A1­
Cu
=
+
FA1H
­
H
+
Cu
­.
8
F
A2­
Cu
=
+
FA2H
­
H
+
Cu
­.
8
FA3­
Cu
=
+
FA3H
­
H
+
Cu
­.
8
FA4­
Cu
=
+
FA4H
­
H
+
Cu
­.
8
FB1­
Cu
=
+
FB1H
­
H
+
Cu
­.
8
FB2­
Cu
=
+
FB2H
­
H
+
Cu
­.
8
FB3­
Cu
=
+
FB3H
­
H
+
Cu
­.
8
FB4­
Cu
=
+
FB4H
­
H
+
Cu
­.
8
Table
A2.
(
Continued)
A6
Species
Formation
Reaction
Log
K
­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­
HCO3
=
+
H
+
CO3
10.329
H2CO3
=
+
2H
+
CO3
16.681
MgHCO3
=
+
H
+
Mg
+
CO3
11.4
MgCO3
=
+
Mg
+
CO3
2.98
MgSO4
=
+
Mg
+
SO4
2.37
CaHCO3
=
+
H
+
Ca
+
CO3
11.44
CaCO3
=
+
Ca
+
CO3
3.22
CaSO4
=
+
Ca
+
SO4
2.3
CuOH
=
+
Cu6.48
HA1­
CuOH
=
+
HA1H
­
H
+
Cu
­
1.5
HA2­
CuOH
=
+
HA2H
­
H
+
Cu
­
1.5
HA3­
CuOH
=
+
HA3H
­
H
+
Cu
­
1.5
HA4­
CuOH
=
+
HA4H
­
H
+
Cu
­
1.5
HB1­
CuOH
=
+
HB1H
­
H
+
Cu
­
1.5
HB2­
CuOH
=
+
HB2H
­
H
+
Cu
­
1.5
HB3­
CuOH
=
+
HB3H
­
H
+
Cu
­
1.5
HB4­
CuOH
=
+
HB4H
­
H
+
Cu
­
1.5
Species
Formation
Reaction
Log
K
­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­
FA1­
CuOH
=
+
FA1H
­
H
+
Cu
­.
8
FA2­
CuOH
=
+
FA2H
­
H
+
Cu
­.
8
FA3­
CuOH
=
+
FA3H
­
H
+
Cu
­.
8
FA4­
CuOH
=
+
FA4H
­
H
+
Cu
­.
8
FB1­
CuOH
=
+
FB1H
­
H
+
Cu
­.
8
FB2­
CuOH
=
+
FB2H
­
H
+
Cu
­.
8
FB3­
CuOH
=
+
FB3H
­
H
+
Cu
­.
8
FB4­
CuOH
=
+
FB4H
­
H
+
Cu
­.
8
Cu(
OH)
2
=
+
Cu
11.78
CuSO4
=
+
Cu
+
SO4
2.36
CuCO3
=
+
Cu
+
CO3
6.75
Cu(
CO3)
2
=
+
Cu
+
2CO3
9.92
CuCl
=
+
Cu
+
Cl
.4
CuHCO3
=
+
H
+
Cu
+
CO3
14.62
The
predicted
LC50
values
can
be
used
to
modify
a
water
quality
criterion
for
site­
specific
conditions
(
Santore
et
al.,
1999b).
The
USEPA
allows
the
use
of
a
water
effect
ratio
procedure
using
LC50
values
measured
in
a
site
water.
The
BLM
predicted
LC50
values
can
be
used
in
the
same
way.
One
possible
method
of
criteria
development,
is
to
use
the
LC50
predicted
for
fathead
minnow
compared
to
the
species
mean
acute
value
(
SMAV)
obtained
for
this
organism
in
laboratory
waters
(
111
ug
Cu/
L).
The
WER
would
then
be
determined
as
:

WER
=
LC50BLM
/
SMAV
The
WER
would
then
be
used
to
modify
the
water
quality
criteria
for
copper
based
on
site­
specific
conditions.
The
WQC
in
this
case
would
be
the
secondary
water
criteria
for
copper
listed
in
Table
A3.

WQCSITE
=
WQC
*
WER
Application
of
the
BLM
to
a
variety
of
water
quality
conditions
has
been
performed
and
is
included
here
for
reference
(
Table
A3).
A
range
of
values
for
chemical
concentrations
in
typical
freshwaters
was
input
to
the
BLM
and
the
copper
toxicity
and
WER
values
were
determined.

Table
A3.
Predicted
WERs
for
Representative
Ranges
in
the
Chemistry
of
Typical
Freshwater
Bodies
A7
Water
Chemistry
Effect
on
Toxicity
DOC
pH
Ca
Na
Alk
Cu
LC50
Cu
WER
mg/
L
mg/
L
mg/
L
mg/
L
ug/
L
1.0
6.0
12.0
4.6
40
80.6
0.7
1.0
6.0
12.0
4.6
80
123.8
1.1
C1
APPENDIX
B.
BLM
INPUT
FILES
FOR
TOXICITY
DATA
SETS
