PHYSICO-CHEMICAL MODEL OF TOXIC SUBSTANCES
IN THE GREAT LAKES
by
Robert V. Thomann
and
Dominic M. Di Toro
Manhattan College
Environmental Engineering and Science
Cooperative Agreement No. CR805916
Cooperative Agreement No. CR807853
Project Officer
William L. Richardson
Large Lakes Research Station
Environmental Research Laboratory - Duluth
Grosse lie, Michigan 48138
August 1983

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CONTENTS
PAGE
ABSTRACT		iii
FIGURES		v
TABLES		x
ACKNOWLEDGEMENTS		xii
SECTION 1 - INTRODUCTION		1
The Problem		1
Objectives of Research		1
Scope of Research		5
SECTION 2 - CONCLUSIONS		6
SECTION 3 - RECOMMENDATIONS		10
SECTION 4 - MODEL FRAMEWORK-COMPLETE EQUATIONS		11
Toxicant Mass Balance Equations		11
Local Equilibrium Equations		20
Suspended Solids & Sediment Solids Equations		24
Toxicant Equations - Several Solids Classes		25
SECTION 5 - SIMPLIFIED MODEL ANALYSES		27
Simplification Due to Chemical Behavior		27
Steady State Simplifications		31
SECTION 6 - STEADY STATE MODEL OF PCBs IN SAGINAW BAY		45
Segmentation and Transport		45
Suspended Solids Calibration		45
PCB Calibration		53
SECTION 7 - GREAT LAKES MODEL CALIBRATION		62
Introduction		62
Solids Balance		66
Plutonium-239 Calibration		72
SECTION 8 - PCB MODEL OF GREAT LAKES		96
Contemporary External PCB Loads		96
PCB Mass Balance		99
SECTION 9 - PLUTONIUM AND PCB RESPONSE TIMES		Ill
PCB		113
SECTION 10- EFFECT OF SOLIDS DEPENDENT PARTITIONING
AND SEDIMENT DIFFUSION		117
Introduction		117
Sensitivity of Plutonium Calculation		117
Sensitivity of PCB Calculation		122
SECTION 11- APPLICATION OF MODEL TO BENZO(a) PYRENE AND CADMIUM..	131
Benzo(a) Pyrene		131
Cadmium		138
REFERENCES		155
ii

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ABSTRACT
A physico-chemical model of the fate of toxic substances in the
Great Lakes is constructed from ass balance principles and incorporates
principal mechanisms of particulate sorption-desorption, sediment-water
and atmosphere-water interactions, and chemical a_nd biochemical decay.
The steady state mass balance model of the suspended solids in the open
lake water yields net solids settling velocities from 0.02 ra/d for
Saginaw Bay to 1.33 m/d for Lake Ontario. Calibration of the toxic
model is through comparison to plutonium-239 data collected in the
i970's using a 23 year time variable calculation. The calibration at a
239
Pu partition coefficient of 400,000 1/kg, a particulate settling
velocity of 2.5 m/d, associated lake specific net sedimentation and
resuspension velocities provided a good calibration to the observed time
239
variable Pu behavior. An assumption of zero resuspension of the
sediment did not provide a good calibration. The results indicate that,
in general, the sediments are interactive with the water column in the
Great Lakes through resuspension and horizontal transport. Fifty
239
percent response times of Pu following a cessation of load extend
beyond 10 years with sediment resuspension.
The calibrated model was applied to polychlorinated biphenyl (PCB)
using a high and low estimate of contemporary external load and with and
without volatilization. The results of the application indicate that
the upper load level (lake range of 400-9500 kg/yr) without volatiliza-
tion is not representative of the surface sediment data and very limited
water column data. The lower load level (lake range 640-1390 kg/yr)
with volatilization (at an exchange rate of 0.1 m/d) appears to be more
representative of observed surface sediment data for the open lake
waters. Calculated water column concentrations for the lower load level
with and without volatilization ranged from 0.25 to 0.90 ng/ for open
lake waters. Fifty percent response times for PCB following cessation
of load and including volatilization varied from less than 5 years to
10-20 years for the other lakes without volatilization. Comparison of
these response times to decline of concentrations of PCB in Lake Michigan
indicates that at least for that lake volatilization is occurring at an
exchange rate of about 0.1 m/d.
Calculations using a solids dependent partition coefficient for PCB
indicate that the total and dissolved PCB concentration in the water
column and sediment PCB concentration are affected to less than an order
of magnitude. Interstitial PCB concentration however increases by about
two orders of magnitude over the case with a solids independent partition
coefficient. Higher exposure concentrations to benthic organism may
then result with a potential route of PCBs to the top predators in the
food chain.
iii

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Calibration of the model to limited data on benzo(a) pyrene is
obtained with a partition coefficient about one order of magnitude
higher than published empirical relationships. The model confirms that
on a lake-wide scale the principal external source is the atmosphere and
for the larger lakes such as Michigan the response time of the lake to
external loads is about 6-10 years while for Lake Erie response time is
about 2 years.
Application of the model to cadmium in the lakes, using a solids
dependent partition coefficient Indicates that the lakes do not reach
equilibrium over a 100 year period. For constant partitioning, cadmium
concentrations reach steady state in about 10-25 years. An estimate of
the preceding 50 year average cadmium input ranges from 200-600
2	2
gCd/km -yr for the upper lakes to 2000-10,000 gCd/km -yr for Lake Erie.
Calculated high concentrations of cadmium in interstitial water (e.g.
10 wg/X.) indicate the importance of measuring interstitial cadmium con-
centrations .
iv

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FIGURES
Pa8e
1.	The Great Lakes Drainage Basin	 2
2.	Distinction between fate and effects of a hazardous substances. 3
3.	Principal components of overall modeling framework for fate of
toxic chemicals	 4
4.	General schematic of principal features of physical-chemical
fate model	 12
5.	Definition sketch for toxicant mass balance equation	 13
6.	Illustration of downward advection due to net sedimentation:... 21
a)	without sediment mixing
b)	with sediment mixing
7.	Fraction of particulate and dissolved toxicant for different
solids concentrations, partition coefficients and chemical
water solubility	 30
8.	Notation for toxicant distribution in completely mixed lake.... 34
9.	Relationship between hydraulic loading, net loss rate of chem-
ical and chemical loading/in-lake concentration ratio. Net
loss always positive (sink)			 37
10.	Ratio of net chemical loss to solids loass as function of sus-
pended solids concentration and partition coefficient. Dis-
solved loss = 0	 39
11.	Lake Ontario correlation of particulate metals concentration
on suspended solids in water column and particulate metals
concentration in surficial sediments (calculated from data
in Nriagu, et al., 1981)	 42
12.	Segmentation for Saginaw Bay and estimated long-term average
transport coefficients	 46
13.	Transport calibration for Saginaw Bay using long-term averaged
chloride data	 47
14.	Solids calibration using long-term solids data. Data, mean i
1 standard deviation; calculation, solid line	 50
v

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FIGURES (continued)
15.	Mass balance of Saginaw Bay total suspended solids under
long-term average conditions	 52
16.	Components of PCBs in water column, Saginaw Bay, 1979, Data,
mean  1 standard deviation; calculation, solid line	 55
17.	Particulate PCB calibration, 1979, water column (upper panel),
sediment (lower panel) Saginaw Bay. Data, mean 1 standard
deviation; calculation, solid line	 56
18.	Mass balance of total PCBs for Saginaw Bay under long-term
average conditions	 58
19.	Effects of external loads and boundary conditions on total PCB
average concentrations in water column of Saginaw Bay	 59
20.	Saginaw Bay mass balance of total PCBs-external loads only	 60
21.	Saginaw Bay mass balance of total PCBs-boundary conditions only. 61
22.	Great Lakes and Saginaw Bay and sediment segmentation used in
model	 64
23.	Long term variations in turbidity at Chicago water intake
(after Hall, 1980)	 74
239 240
24.	Annual areal deposition of ' Pu loading to Great Lakes
(from Wahlgren, et al., 1981), with constant loading
1973-1977	 75
239 240
25.	Comparison of calculated Lake Michigan ' Pu concentration
(fC /.) in the water column to 1971-1977 data for three
conditions of the particulate settling velocity, n = 400,000
/kg, (Data from Wahlgren, et al., 1981). 39. Mass balance of
PCB Lakes Michigan and Erie after 20 years of steady input of
low level of PCB load	 77
239 240
26.	Comparison of calculated ' Pu concentration (fC /S.) in the
water column for all lakes to 1971-1977 data for tnree condi-
tions of the particulate settling velocity, tt = 400,000 Jl/kg.
(Data from Wahlgren, et al. , 1981)	 78
239 240
27.	Comparison of calculated ' Pu concentration (pC./g(d)) in
the sediment of Lake Michigan to observed data for 1973-1974.
w = 2.5 m/d, v = 400,000 H/kg. (Data from Edington, et al.,
a
1975)	 79
vi

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FIGURES (cont'd)
FaSe
28.	Calculated time history of particulate plutonium concentration
(vg/g(d)) in (a) water column (vertical bar in 1974 is range
reported by Wahlgren and Marshall, 1975) and (b) surface
sediment for Lake Michigan and Central Lake Erie (data shown
in 1979 is mean 1 standard deviation for Lake Michigan from
Edington, et al., 1975)	 81
29.	Ratio of resuspension velocity to sedimentation velocity as a
function of particulate settling velocity	 85
30.	Calculated plutonium flux for Lake Michigan in year 20 under
different particulate settling velocities	 86
31.	Calculated plutonium flux for Western Central and Eastern Lake
Erie in year 20; wa = 2.5 m/d	 88
32.	Sensitivity of water column plutonium concentrations to parti-
tion coefficient; w = w _			 89
a net
33.	Behavior of Lake Michigan plutonium water column concentration
under two partition coefficients; w = w 	 92
a net
34.	Calculated sediment plutonium concentration for Western Basin,
Lake Erie; it = 400,000 Jl/kg.	 93
35.	Long term calculation of plutonium concentration in surface
sediment of Western Lake Erie for two partition coefficients,
w = 2.5 m/d....					 94
a
36.	Calculated water column total PCB concentration (ng/,) for
conditions on external load (see Table 17) and volatiliza-
tion rate	 102
37.	Calculated surface sediment PCB concentration (ng/g) for condi-
tions on external load (see Table 17) and volatilization rate
and comparison to observed data (see Table 19)	 103
38.	Relationship between net loss of solids (top), fraction of PCB
in particulate form (middle) and range of net loss of PCB
(bottom), calculated from Eq. 63	 106
39.	Mass balance of PCBs, Lakes Michigan and Erie after 20 years of
steady inputof low level of PCB load......			107
40.	Mass balance of PCBs, Lakes Michigan and Erie, after 20 years
of steady input of high level of PCB load	 108
239 240
41.	Calculated time history for * Pu load reduced to zero
after 1973 for two conditions on water column-sediment
interaction: w =w (resuspension = zero) and w = 2.5 m/d.... 112
an	a
42.	Calculated water column PCB concentration response to an
instantaneous drop in upper level PCB load at time t = 0	 114
vii

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FIGURES (cont'd)
Page
43.	Calculated surface sediment PCB concentration response to an
instantaneous drop in upper level PCB load at time t = 0	 115
44.	Assumed variation of plutonium partition coefficient with solids
concentration used in sensitivity analysis	 116
45.	Sensitivity of total plutonium water column cocentration for Lake
Michigan to three assumptions on mass dependence of partition
coefficient (see Figure 44)	 119
46.	Comparison of Lake Michigan plutonium total water column concen-
tration calculations under different assumptions on particulate
settling	 120
47.	Calculated variation of Lake Michigan particulate plutonium
concentration in water column and surface sediment:
(a) base run, (b) with solids dependent partitioning and
w =2.5 and 5.0 m/d	 121
a
48.	Summary of reported PCB partition coefficients and solids con-
centrations and relationships assumed in sensitivity analyses. 123
49.	Comparison of measured particulate PCB concentration in water
column and surface sediment, Lake Michigan	 124
50.	Comparison of calculated total water column PCB concentration
(ng/1) using different solids dependent partitioning; low
load level with volatilization	 126
51.	Comparison of calculated surface sediment PCB concentration
(ng/g) using different solids dependent partitioning; low
load level with volatilization	 127
52.	Comparison of calculated dissolved water column PCB concen-
tration (ng/1) using different solids dependent partition-
ing; low load level with volatilization	 128
53.	Comparison of calculated interstitial PCB concentration (ng/1)
in surface sediment using different solids dependent parti-
tioning; low load level with volatilization.....	 129
54.	Steady state water column and surface sediment BaP concentra-
tions compared to observed data from Eadie (1983)	 133
55.	Comparison between calculated surface sediment BaP concentration
after 20 years and observed concentration	 137
56.	Time variable BaP response in Lake Michigan under two partition
coefficients with 20 year constant loading	 139
viii

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FIGURES (cont'd)
Page
57.	Calculated total cadmium concentration (mg/2,) in water column
at t = 50 years with partition coefficient as a function of
solids concentration	 146
58.	Calculated surface sediment concentration ( g/g(d)) at t = 50
years with partition coefficient as a function of solids
concentration	 147
59.	Comparison of calculated cadmium concentration under two assump-
tions on partition coefficient. Low load estimate	 148
60.	Comparison of calculated cadmium concentration under two assump-
tions on partition coefficient. High load estimate	 149
61.	(Top) Calculated load normalized cadmium time variable response
(Bottom) Calculated sediment/water column partition coeffi-
cient time variable response	 154
ix

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TABLES
Page
1.	Definition of Terms	 14
2.	Two applications of simplified chemical model	 40
3.	Estimated long term average suspended solids inputs-
Saginaw Bay	 49
4.	Sediment solids concentrations - Saginaw Bay	 49
5.	Estimated total PCB loading for 1979 - Saginaw Bay	 54
6.	Total PCB partition coefficients - Saginaw Bay	 54
7.	Geometric and transport parameters of water column used
in Great Lakes model	 65
8.	Estimated shoreline erosion and tributary solids loading
range			 67
9.	Estimated percent of soil types in shore erosion loads	 68
10.	Solids loading concentration and net solids loss rates
used in model	 69
11.	Reported ranges of solids flux and net sedimentation rates
for Great Lakes	 71
239
12.	Some partition coefficients for Pu	 73
239
13.	Comparison of approximate response times for Pu in
water column and sediment of Lakes Michigan and Erie	 83
14.	Resuspension velocites for different particulate settling
velocities		 84
15.	Sensitivity of plutonium sediment concentration to settling
velocity and partition coefficient in Lake Michigan	 90
16.	Some reported concentrations of PCB in precipitation		97
17.	Estimated range of contemporary total PCB loading (kg/yr)		98
18.	Some reported PCB concentrations in Great Lakes tributaries...	100
19.	Some reported PCB surface sediment concentrations		104
20.	Chemical properties of benzo(a) pyrene (from Neff, 1979)		131
x

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TABLES (cont'd)
Paee
21.	Atmospheric load of BaP to the Great Lakes (from
Eisenreich et al., 1980)			 132
22.	Comparison of calculated and observed BaP under
different solids partition assumptions	 136
23.	Summary of some observed cadmium concentrations
in the Great Lakes	 140
24.	Summary of contemporary external cadmium loads	 142
25.	Estimate of approximate background cadmium concen-
tration for Great Lakes	 144
26.	Estimate of preceding 50 year average loading con-
sistent with observed data in 1970's	 152
xi

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ACKNOWLEDGEMENTS
Although the research described in this report has been funded
wholly or In part by the United States Environmental Protection Agency
through Cooperative Agreements CR805916 and 807853 to Manhattan College,
it has not been subjected to the Agency's required peer and policy review
and therefore does not necessarily reflect the views of the Agency and
no official endorsement should be inferred.
The initial formulation of the model and preliminary data compila-
tion and calibration of this model were conducted under Cooperative
Agreement CR805916. Further development, data analysis, calibration and
additional applications were completed under Cooperative Agreement
CR807853. The encouragement and support of the U.S. Project Officer,
Mr. William Richardson of the Large Lakes Research Station at Grosse lie,
Michigan and Nelson Thomas, Chief, Water Quality USEPA Laboratory in
Duluth, Minnesota is gratefully acknowledged and specially recognized.
Research assistants of the Environmental Engineering and Science
Program at Manhattan College who contributed to this work through their
diligent running of the model through its development are John Hall, R.
Kabaliswaran, Jian Li, Janice Rollwagen, K. Subburamu, and Robert J.
Thomann. Special thanks go to them for their consistent performance.
Colleagues at Manhattan College who also contribued to this work
and are acknowledged gratefully are Drs. John Connolly and John Mueller
and Messrs. Walter Matystik and Richard Wlnfield. Ms. Cynthia O'Donnell
and Mrs. Eileen Lutomski are recognized with grateful thanks for their
fine and careful typing of the report.
xii

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SECTION 1
INTRODUCTION
THE PROBLEM
The input of potentially toxic substances to the Great Lakes (Figure
1) has been the subject of considerable interest over a number of years.
The problem contexts have included elevated concentrations of mercury in
fish in Lake St. Clair and Lake Erie, atmospheric and nuclear power plant
input of radionuclides throughout the Lakes, mirex contamination in "Lake
Ontario and excessively high concentration of polychlorinated biphenyl
(PCB) in the lake trout of Lake Michigan. Several reviews of these and
other problem areas associated with toxicants are given by Swain (1980),
Delfino (1980) and IJC (1978). In recent years, some problems such as DDT
and mercury have declined in significance as concentrations in fish
species have dropped to acceptable levels (UC, 1980). Local near-shore
problems, (e.g. mercury in the fish of the Ontario shoreline of Lake
Superior) continue however to be a problem. Also, other problem areas
appear to be emerging (IJC, 1980). Polychlorinated terphenyls (PCT) have
been'identified In Lake Erie herring gull eggs and trace levels of dioxin
were identified in 1978 in fish taken from Lake Ontario and Saginaw Bay.
Indeed over 300 organochlorine compounds and metals such as lead, mercury,
zinc and cadmium have been identified in the Great Lakes. The fact that a
substance has been Identified is not however necessarily representative of
a toxic substances problem. The number of such different identifications
does indicate that the Great Lakes are receiving a spectrum of complex
chemical inputs - some of which may pose a problem if inputs of a
particular substance were to increase. Figure 2 shows this distinction.
A specific concentration of a chemical in water or in the food chain only
reflects the fate of the chemical and not the effect. The effect and
consequence of a given "hazardous" substance is a topic of a separate
evaluation and is not covered here. The general context of this report
then Is addressing the problem of the fate of chemicals in the Great Lakes
with specific reference to the chemicals that are known to be potentially
toxic or hazardous.
OBJECTIVES OF RESEARCH
In order to properly assess the fate of a given toxic substance in
the Great Lakes, some overall framework must be available that relates
external inputs of the chemical to the resulting concentration of the
substance in the water column, sediment and food chain. An understanding
of the relative contribution to the distribution of a given chemical from
atmospheric, direct discharges, and tributary sources is necessary Eor
effective decision making. Accordingly, the objectives of this research
are:
1) to develop a modeling framework for toxic substances in the
Great Lakes incorporating the principal features of the
physical and chemical mechanisms that determine the fate of
an externally inputted chemical,
1

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International
^ Boundary
Lake Superior v
St. Marie
t. Mary's River
Toroni
I
ORochester
Niagar
St. Claii/River
Lake St.Claii;
Detroit 0
Detroit Rive
Toledo
miles
0 50
hi;ago
Sanitary and Ship Canal
Figure 1. The Great Lakes drainage basin

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Input

p
Distribution and FATE
of hazardous substance
EFFECT and consequence
of hazardous substance
Biomass
(phytoplankton,
zooplankton,
fish, etc.)
Concentration in
food chain
(web)
Lake, bay, estuary,
river (flow, geometry)
Effect on man and
man's activities
Effect of concentration
on aquatic ecosystem
- -#
Figure 2.
Distinction between fate and effects of a hazardous substance.

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Laboratory and controlled
field experiments
Sub-system
compartment models
Kinetic behavior
(uptake, clearance,
trophic transfer]
Hazardous
substance
inputs
Water body
Flow .
Dispersion
Exchange
Sediment
Adsorption
settling
Concentration in
food chain (web]
Figure 3. Principal components of overall modeling framework for fate of toxic chemicals.

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2)	to calibrate the model using existing data on toxic sub-
stances, and
3)	to describe, via the modeling framework, the expected response
times of the lakes as a whole to reductions in external
inputs.
SCOPE OF RESEARCH
Figure 3 shows principal components of the overall framework for
assessing the fate of a chemical. Such a framework should include the
major features of transport in the water body, particulate sorption,
desorption and settling, and sediment exchange. The components of the
food chain or food web are of central importance in a credible framework.
Finally, the output from laboratory and controlled field experiments are
incorporated in sub-system compartment models to assess the kinetic
behavior of the given substance in terms of uptake, clearance and trophic
level transfers. The estimation of lake response and recovery due to
reduction in external chemical inputs therefore involves a complex
interaction of field data, laboratory experiments and a theoretical
construct that provides the synthesizing framework for making predictions.
The model framework is divided into two broad components: the
physical-chemical sector and the biological sector.
Mechanistically, this research is confined to development of a toxic
fate model for the physical-chemical sector of the environment. The
development of a model of the fate of a chemical in the aquatic ecosystem
is discussed in Thomann (1981) and Thomann and Connolly, (1983).
Geographically, the scope of the research is on a Great Lake scale.
With the exception of Saginaw Bay, the modeling framework is considered as
representative of the fate of a chemical in the open lake waters.
Localized problem areas in the vicinity of harbors, entering tributaries
or direct discharge inputs are therefore not part of the geographical
scope. The modeling framework is intended to answer questions related to
overall open-lake response to external inputs and the interaction of
upstream lakes on downstream lakes and the interaction of a large lake
such as Lake Huron on a bay such as Saginaw Bay.
The application of this research is also focused principally on toxic
substances that are sorbed to particulates and tend to be persistent and
not subject to segnificant losses due to, for example, bacterial
degradation. The modeling framework however as derived in Section 4 is
general and can address the complete spectrum of toxic substances.
Therefore,substances that are readily biodegradable, volatilize easily and
are not sorbed significantly into particulates present no new difficulties
in the modeling structure. Substances that interact strongly with
particulates on the other hand introduce the entire domain of solids
transport, settling, resuspension and sedimentation. For this reason,
this research is focused principally on persistent hydrophobic toxicants;
specifically as noted below plutonium -239 as a calibrating variable and
polychlorinated biphenyl (PCB) as a contemporary chemical of specific
interest.
5

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SECTION 2
CONCLUSIONS
A physico-chemical model of Che fate of toxic substances in the
Great Lakes can be constructed from mass balance principles to incor-
porate principal mechanisms of particulate sorption-desorption, sediment-
water and atmosphere-water interactions, and chemical and biochemical
decay. Valuable insight into the behavior of the fate of chemicals in
the lakes or regions of the lakes can be obtained from both steady state
models of water column and sediment interactions and time variable
models. For the latter models, and for the open waters of the lakes the
relevant time scale for toxic substances fate calculations is in the
order of years.
Steady state modeling in general does not require specification of
the sediment resuspension effects but requires only estimates of the net
exchange (settling-resuspension) between the sediment and water column.
A limited comparison to observed metal data for Lake Ontario appears to
confirm the general structure of the steady state model. Calibration of
a two-dimensional steady state model to the PCBs of Saginaw Bay in 1979
indicates the following:
1)	Approximately 30% of the total PCBs entering Saginaw Bay from
external loads is incorporated into the sediments of the Bay and
approximately 70% is exchanged with Lake Huron.
2)	Approximately 25% of the peak concentration in the Bay is due to
the boundary condition vjith Lake Huron and the remaining 75% is the
effect of the external loads. Complete removal of the Saginaw
River loads and maintenance of the Lake Huron boundary at 10 ng/
would result in at least a 75% reduction in the peak PCB concentra-
tion under the new steady-state condition. Additional reduction
would occur since some significant fraction of the local Lake Huron
boundary concentration is probably caused by the loads to Saginaw
Bay.
The time variable model of the physio-chemical behavior of poten-
tially toxic substances discharged into the Great Lakes can be calibrated
in an internally consistent manner through use of data on the historical
loading and resulting response of plutonium-239. The calibration is in-
ternally consistent but not necessarily unique. Other Internally consis-
tent sets of parameters are possible given the available data.
The available solids data including solids loading, water column
concentrations and sediment porosity and density permit an estimate of
the net flux of solids to the sediments but do not permit a separation
of settling and suspension effects. The steady state mass balance model
of the suspended solids in the open lake water yields net solids settling
velocities from 0.02 m/d for Saginaw Bay to 1.22 m/d for Lake Ontario.
Further calibration using the tracer plutonium-239 was required to delin-
eate settling and resuspension effects.
6

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The following conclusions may be drawn from the calibration of the
239 240
model to the ' Pu data and the associated sensitivity analyses.
(1)	Particulate settling velocity of 2.5 m/d to 5 m/d with result-
ing resuspension velocity to maintain a solids balance is operative
throughout the Lakes. The resuspension velocity should be viewed as a
parameter of the model representing the complex interaction of near shore
resuspension, horizontal transport and deposition and open lake resuspen-
sion and transport. Chambers and Eadie (1981) in their work on particu-
late matter in Lake Michigan report transient resuspension phenomena
vertically and horizontally that tend to result in large scale resuspen-
sion of particulates.
(2)	The result of the inclusion of the resuspension phenomena is
to retain concentrations of plutonium in the water column over longer
periods of time than would occur without the mechanism. This appears to
be consistent with the observed data.
(3)	The calibration to the observed sediment data in Lake Michigan
indicates that some sediment mixing between the 2 cm layers may be occur-
ring as a result of mechanisms such as bioturbation.
(4)	The sensitivity analyses indicate that the dynamic behavior of
the water column concentration of plutonium is most sensitive to varia-
tions in settling and resuspension velocities, and partition coeffi-
cients. The 0-2 cm sediment plutonium concentrations do not vary sig-
nificantly as a function of settling and resuspension characteristics or
partition coefficient indicating that data over the 0-2 cm depth is not
a sensitive calibrating data set for use in determining model parameters
of settling and resuspension.
(5)	The time variable calculations result in system behavior of a
chemical such as plutonium that is different than the steady state. For
example, the calculations indicate that the particulate plutonium de-
creases with increasing partition coefficient for certain Lakes (e.g.
Western Lake Erie).
It is concluded from the application of the plutonium calibrated
model to PCBs in the Great Lakes that:
a)	the estimated upper level of present PCB loading (ranging from
4080 kg/yr for Lake Ontario to 9500 kg/yr for Lake Superior) without vol-
atilization is probably too high,
b)	from the available data, it is not possible, at the present
time, to distinguish the appropriate combination of loading and loss due
to volatilization,
c)	lower levels of PCB in Lake Erie are probably due to the higher
net loss of PCB from elevated solids concentrations and resulting frac-
tion of PCB in the particulate form.
7

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d)	the response time for Lake Michigan to equilibrate to a steady
PCB load with volatilization is less than 20 years for the water column
but greater than 20 years for the sediment.
e)	the Western Basin ot Lake Erie delivers the highest net flux
of PCB to the sediment of the three basins of the Lake.
f)	volatilization ot PCB is significant for Lake Michigan (about
65% of incoming load) but is less significant for Lake Erie (about 8%)
due to the higher solids concentration in that lake.
It is concluded from calculations of response times that for large
lakes such as Michigan where response times are relatively long, a water
column/sediment equilibrium model is not appropriate since the sediment
response time is markedly different than the water column. The Inclusion
of sediment resuspension and interaction increases the response time of
nonreactive but particulate sorptive substance such as plutonium by about
an order of magnitude over the case where resuspension is assumed to be
zero.
For PCB, the response times due to load reduction of external
sources of PCB may vary by an order of magnitude depending on the magni-
tude of the volatilization of 5-10 years or longer without volatiliza-
tion. Comparison of these response times to observed declines in concen-
trations of PCB bloaters indicate that volatilization of PCB is
occurring at an exchange rate of about 0.1 m/d at least for that lake.
Model calculations were also perfomed using a solids dependent par-
tition coefficient for plutonium 239 and PCB. For plutonium, the results
indicate that particulate settling velocities of 2.5-5.0 m/day, with or
without solids dependent partitioning (at a log slope for solids of
-.435) and associated sediment diffusion provide an approximately equal
representation of the observed data. A more marked solids dependence
(log slope of -1) of the partition coefficient did not provide an accept-
able comparison to the observed data.
From the calculation on the sensitivity of the PCB distribution in
the Great Lakes to a sediment dependent partition coefficient, it is
concluded that:
(1)	such a relationship is more representative of the observed
particulate and sediment PCB data in Lake Michigan;
(2)	total and dissolved PCB concentration in the water column and
sediment PCB concentration are not affected significantly (i.e. by at
least one order of magnitude) under a solids dependent partitioning
assumption;
(3)	interstitial PCB concentration in the sediment is affected
markedly by such an assumption and an increase of about two orders of
magnitude is calculated.
(4)	since the increased interstitial PCB concentration in the sedi-
ment is about two orders of magnitude higher than the overlying water
8

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dissolved PCB concentrations, one would expect benthic organisms to carry
a significantly higher body burden than organisms exposed solely to the
water column and as a result would be a potential significant source of
PCBs to top predators in the food chain.
Additional applications were made to benzo(a) pyrene (BaP) and
cadmium for the Great Lakes. For BaP, it is concluded that:
(1)	the estimate of the BaP partition coefficient obtained from
published empirical relationships is probably low by about an order of
magnitude for the Great Lakes system,
(2)	with an increased BaP partition coefficient and assuming loss
due to volatilization, the	physico-chemical toxic substances model of
the Great Lakes approximate observed BaP water column and sediment data
to order of magnitude,
(3)	the model confirms that on a lake-wide scale, the principal
external source of BaP is the atmosphere,
(4)	for the larger lakes such as Michigan, the 50X response time
of the lake to a step increase in external loads is about 6-10 years for
the water column - sediment system while for Lake Erie the response time
is about two years,
(5)	lake to lake variations in calculated BaP water column and
sediment concentrations are less than a factor of two.
It is concluded from this application of the physico-chemical model
to cadmium in the Great Lakes that
1)	The degree of any dependence of the cadmium partition coeffi-
cient with solids has a marked effect on time to steady state
and interstitial cadmium concentration.
2)	Under a solids dependent cadmium partition assumption, the
Great Lakes, especially the upper Lakes, do not reach a steady
state condition after 100 years of constant loading.
3)	Under a constant partition coefficient for cadmium, the Lakes
do reach an equilibrium condition varying from about 25 years
for Lake Michigan to 10 years for Lake Erie.
4)	The concentration of cadmium in the Lakes would be expected to
increase by about 60% over the next 50 years if the average
cadmium loading for the preceding 50 years continues.
5)	Based on assumed sediment cadmium concentrations for Lake Erie,
it is estimated that the cadmium concentration in the water
column is about an order of magnitude higher than the other
Lakes.
6)	If loads are projected to increase then cadmium concentrations
in the Lake system may increase to levels of concern.
9

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SECTION 3
RECOMMENDATIONS
The following recommendations are offered as a result of this
research.
1.	The development of the physico-chemical model of the Great Lakes
should be continued and additional areas to be explored should include
additional calibration analyses, where possible, of PCB isomers and of
other chemicals of contemporary interest. Suspended solids data should
also be collected from the open waters of the Lakes.
2.	Because of the significance of PCBs in the Great Lakes, additional
field sampling is necessary for:
a)	input load of PCB, e.g. atmospheric, tributary, and point
sources,
b)	water column PCB concentration, both dissolved and particulate,
c)	sediment and interstitial PCB concentration as a function of
the depth of sediment,
d)	concentration of PCB in the food chain including intermediate
organisms (e.g. benthic species, zooplankton, small fish) and top
predators (e.g. lake trout).
3.	Models of the physico-chemical fate of potential toxic chemicals
should be developed for the near-shore and estuarine environment of the
lakes with ultimate extension to point sources of chemicals in a given
basin. Models on these scales will then provide a basis for assessing the
resultant input of chemicals from up-basin discharges on the lake proper
and be an important part of an overall waste load chemical allocation
scheme.
4.	Since there is evidence to indicate a dependence of partition
coefficient for PCB and cadmium (among other substances), laboratory
work should be conducted over the range of Great Lake solids concentra-
tions to determine the degree of such dependence for representative
chemicals.
5.	Under assumptions of solids dependent partition coefficient for
PCB and cadmium, interstitial water concentrations are calculated at
levels several orders of magnitude higher than overlying water concentra-
tions. Field sampling of interstitial water concentrations and benthic
organisms of representative substances such as PCB, cadmium and benzo(a)
pyrene should be conducted to confirm or deny these estimates.
10

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SECTION 4
MODEL FRAMEWORK
COMPLETE EQUATIONS
The development of a mathematical model for the physical-chemical
fate of a toxic substance in water must include the following features:
1.	sorption-desorption mechanisms of the chemical with suspended
particulates in the water column
2.	similar mechanisms with solids in the sediments
3.	loss of the chemical due to mechanisms such as biodegradation,
volitilization, chemical and biochemical reactions, photolysis
4.	transport of the toxicant due to advective flow transport, and
dispersion and mixing
5.	settling and resuspension mechanisms between sediment and
water column
6.	direct inclusion of external inputs that may be subject to
environmental control.
Figure 4 shows these principal features in a schematic form. The model
proceeds from these general features by development of the basic mass
balance equations; first for the suspended and sedimented solids in the
system and then for the toxicant. For the sake of simplicity in model
derivation only a single solids class is considered at this point; i.e.,
a distinction is not made between sands, silts, or organic particles.
The extension to more than one solid class is discussed later.
TOXICANT MASS BALANCE EQUATIONS
The concentration of a toxicant in the water column and in the sedi-
ment is given by a mass balance around each of the finite segments of the
water body. Referring to Figure 5 and Table 1, Definition of Terms, a
mass balance equation can be written around segment 2 as a typical inter-
ior segment. The toxicant is composed of two forms: 1) the dissolved
form, c1 ,, where "dissolved" is considered in an operational manner, i.e.
d
all toxicant passing for example a 0.45 um filter and 2) the particulate
form, c , i.e. the toxicant sorbed onto particulate matter in the water
column or sediment. As noted above in this derivation, only a single
solids class is considered here. The total toxicant concentration is
then
P
(1)
11

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Biodegradation

Biodegradation
Photolysis...

Toxicant Input
Desorption
Sorption
Suspended
Solids	*
Transport
Toxicant
on
Suspended
Particulates
Dissolved
Form
Toxicant
Settling
Resuspension
Diffusive
Exchange
//"// /V/7/7/// 7/7 //'//'/////// 7 ///r/ / /
Biodegradation
Biodegradation
Toxicant
on
Sediment
Particulates
Dissolved
Toxicant
in
Interstitial
Water
Net Sedimentation
Figure 4. General schematic of principal features of
physical chemical fate model.
12

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Wo~,
Water
Column
Sediment
TT
Ql,2T-
c' '
E|.a!Sf~
Wa2 Wfrs2

( / f
'#2,3
Figure 5. Definition sketch for toxicant mass balance equation.

-------
TABLE 1
DEFINITION OF TERMS
Symbol	Definition	Units*'
2
A	Interfacial area	[L ]
c.	Dissolved toxicant concentration-porosity	[M_/T3 ]
d	corrected	T/L s+w
3
c'j	Dissolved toxicant concentration	[Hp/L ]
3
c^	Gas phase toxicant concentration	[M^/L ]
3
c	Particulate toxicant concentration	[M~/L 1
p	T s+w
3
c^,	Total toxicant concentration	[M^,/L s+w]
3
cw	Solubility of chemical in water	[M^/L w]
2
E	Dispersion coefficient	[L /T]
3
E'	Bulk mixing/dispersion coefficient	[L S+W/T]
2
F	Net sedimentation flux of solids	[M /L -T]
s	s
f^	Fraction of toxicant concentration in
dissolved form
f	Fraction organic carbon
oc	
f	Fraction of toxicant concentration in
^	particulate form
H	Water column or sediment depth	[L]
3	3
H	Henry's constant for toxicant	[Mt/L -M^/L ]
6	1 g 1 W
K	Overall loss rate of total toxicant	[1/TJ
Loss rate of dissolved toxicant	[1/T]
K	Gas film rate coefficient for evaporative
	loss of dissolved toxicant	[L/T]
Sediment-water diffusive transfer	[L/T]
coefficient
14

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TABLE i (continued)

Symbol
Definition
Units1
K
Liquid film rate coefficient for evapora-
tive loss of dissolved toxicant
[L/T]
k
u
Sorption (uptake) coefficient
[L3 /M -
s+w s
m
Solids concentration
[M /L3 +v]
s s
r
Toxicant concentration on solids
[Mt/L3w]
t
o
Hydraulic detention time
[T]
Q
Advective flow transport
[L3 A /T]
s+w
q
Hydraulic overflow rate
[L/T]
V
Volume of water column or sediment segment
[L3 ]
s+w
w
a
Surface loading rates of chemical
[mt/l3-t]
W
m,d,p,T
Mass input of solids or dissolved particu-
late and total toxicant respectively
[mt/t]
W
ma
Areal loading of solids
[ms/l2-t]
wio
Wind speed 10 m above water surface
[L/T]
w
a
Particulate settling velocity
[L/T]
Wd
Net dissolved sedimentation velocity
[L/T]
w
n
Net loss rate of solids from water column
[L/T]
w
rs
Particulate resuspension velocity
[L/T]
w
s
Net particulate sedimentation velocity
[L/T]
WT
Net removal of toxicant from water column
[L/T]
Ax
Characteristic length
[L]
*P.g
Viscous coefficient for liquid and gas sub-
layer respectively

V
w,a
Kinematic viscosity of water and air
respectively
[L /T]
tt	Toxicant-solids partition coefficient [M.j./M^M.j./L w]
15

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Symbol	Definition	Units^
ir'	Toxicant-solids partition coefficient-	^
porosity corrected	[M_/M -s-M_/L ]
r	T s T s+w
3	3
tt	Octanol-water partition coefficient	[M/L *M_/L ]
ow	r	T o T w
3
ir	Partition coefficient-organic carbon basis [M^/M *M/L ]
oc		T oc T w
3
p	Density of water, air or solids respectively [M/L ]
w,a, s
4>	Porosity	[L^ l\? ]
w s+w
(fij	Drag coefficient
^ [M] = Mass
[M ]	= Mass of solids
s
[M^,]	= Mass of toxicant
[L]	= Length
[L3 ]= Volume of solids
s+w
3
[L ] = Volume of water
w
[L3 "
g] = Volume of gas
[T] = Time
and water, i.e. bulk volume
16

-------
or
cT = cp + cd	(2)
where
cd - *c'd	<3)
Note chat since the dissolved toxicant concentration is the mass of
toxicant per volume of water and the total toxicant concentration the mass
of toxicant per volume of water plus solids, the porosity of the volume
() must be introduced to maintain a consistent mass balance.
Recognizing the concentration as mass per volume of solids plus water
permits a consistent equation set between the water column and the
sediment. The quantity, c^, therefore represents the porosity corrected
dissolved form of the toxicant.
Figure 5 is the definition sketch and Table 1 lists the terms, their
definition and units. Note that the water column is divided into a series
of finite volumes and as shown in Figure 5 are one dimensional, but the
configuration of the segmentation can be multidimensional in the water
column. The Great Lakes application discussed below is two dimensional
(horizontally) in the water column. The water column segments are the
primary numbering sequence. The underlying sediment segments are further
numbered depending on the overlying water column segment. Thus a variable
that is subscripted i, j would be located in the jth sediment layer under
the ith water column.
Dissolved toxicant. The mass balance for the dissolved toxicant in the
water column segment 2 is given by
dcd2
V2~ = ^12Cdl~ ^23Cd2+ E12^Cdl~Cd2^ + E23^Cd3~Cd2^ (Transport)
dt
+ ^(j2V2Cp2 ~ ^u2m2V2Cd2	(Sorption-desorption)
- + Kt_A_ ,(c'_ i-c',-) (Sediment diffusive exchange)
L4 /)1	dfa ^1
-	^(j2^2Cd2	(Decay & losses)
-	k A0(c /H - c' )	(Volatilization)
HZ Z g e al
+ Wd2	(Input)(4)
The group of terms in brackets represents the transport and
dispersion of the dissolved toxicant. The net transport flows, Q, are
17

-------
written in an equivalent backward difference approximation to the
underlying partial differential equation. The dispersion or mixing
between segments is given by the bulk dispersion coefficient which in
turn is related to the dispersion coefficient by
EA
E' = 	(5)
Ax
The second line on the left of Eq. (4) is the balance between the
desorption of the toxicant in the particulate phase (^2,^2 2}
increases the dissolved form and the adsorption from the aissrolved phase
onto the particulates given by k 2^2^2Cd2" Note that this latter
term depends on the mass of solids available for sorption from the
dissolved phase.
The third line of Eq. (4) represents the diffusive exchange between
the sediment dissolved toxicant concentration c^ i the interstitial
water and the dissolved toxicant concentration In'the water column, c^-
The sediment-water diffusive transfer coefficient, K^ can be considered
as an overall interfacial transfer coefficient relating to the diffusion
of the toxicant across the sediment water interface.
Decay and loss mechanisms such as biodegradation, photolysis etc. of
the dissolved form are included in the fourth line of the equation.
Therefore, K  represents the sum of individual rates some of which in
turn may represent rather complex mechanisms. Note that for this model
all the loss rates are assumed to be first order.
Volatilization of the dissolved toxicant is given by the fifth line
of Eq. (4). The overall volatilization transfer coefficient is given by
(O'Connor, 1982) as
1 1 1
k~ = K7 + H~K	(6)
Z Z eg
Specific formulae for calculating K. and K due to winds for open
S
bodies of water such as the Great Lakes are from O'Connor (1982) as
L 2/3 "a 1/2 U10
\	[~ -1 17	V)
- w	w	Z
Dg 2/3 pa 1/2 1Q
and K - (-J (~ j-] j-	(8)
e a	w	g
The last line represents all external sources or inputs of dissolved
toxicant from point direct discharge sources as well as non-point and
tributary inputs.
An equation similar to Eq. (4) can be written for the dissolved
toxicant in the sediment layer underneath the typical water column segment
2. This layer is designated 2,1. Thus,
18

-------
= kd2,l V2,l Cp2,1 " ku2,l m2,l V2,l cd2,l
+ \2 A2,l (c'd2 ~ C'd2,l)
 K	V r
d2,1 2,1 d2,1
" Wd2,12 A2,l-2 Cd2,1
+ ^2,1*2 A2,l-2 (c'd2,2 " C'd2,l)	(9)
The first three lines of the left side of Eq. (9) have already been
discussed relative to the water column. The fourth line of Eq. (9)
expresses the "burial" or transfer down into the sediment of the dissolved
toxicant due to net sedimentation or build-up of the sediment layer. Note
that the subscript 2, 2.1 refers to the interface between sediment
segments //1 and //2 under the second water column segment. The last line
of Eq. (9) is the diffusive exchange of dissolved toxicant between the
first and second sediment layers under the water column. Similar
equations can be written for each successive sediment layer. Note that
there are no dissolved transport terms for the sediment thereby indicating
that the sediment is assumed to be stationary in the horizontal direction.
dc
d2,1
2,1
dt
Particulate toxicant. The mass balance equation for the toxicant
sorbed onto the particulates in the water column segment 2 is given by
dc 0
.El
= [Q,oC , " Qc  + E' -(c,-c9)+E'(c.-c)](Transport)
2 dt	12 pi 23 p2 12 pi p2' 23v p3 p2
-	kd2 V2 cp2 + k^2 m2 V2 cd2	(Desorption-sorption)
-	w  . A_ . c _	(Particulate settling)
a2,l 2,L p2
+ w  , A . c _ ,	(Particulate resuspension)
rs2,l 2,1 p2,l
" Kp2 V2 Cp2	(DeC3y)
+ W	(Input)(10)
P2
The first line of this equation is the transport of the particulate
toxicant due to net advection (Q) and dispersion (ET). The particulate
toxicant is assumed to be transported in the same manner as the dissolved
form. The second line is the sorption-desorption mechanism discussed
above and as can be noted for the particulate form, sorption is a source
and desorption is a sink of toxicant. The third and fourth lines are
respectively the particulate settling of the toxicant from the water column
and the resuspension of particulate toxicant from the sediment into the
water column. The settling velocity, w^ and the resuspension velocity w^g
are functions of particle type (sand, silt, organics) and the hydrodynamics
of the water-sediment interface. The fifth line represents any decay mech-
anisms (e.g. bacterial degradation) of the toxicant on/in the particulates
and the last line is the external mass input of particulate toxicant.
19

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The particulate toxicant in the sediment is given by an equation
similar to Eq. (10) except that, for this work, the sediment is assumed to
be stationary in the horizontal direction. That is, bed load transport or
sediment movement horizontally throughout the water body is not
considered.
The particulate toxicant equation for the sediment segment underlying
segment 2 (i.e. segment 2,1) is then given by
dCp2,1
V2,l ~ = "kd2,l V2,l Cp2,1 + ku2,l m2,1 V2,l Cd2,l
+w A. c _ - w _ A_
a2,1 2,1 p2 rs2,l 2,1
-K V c
P2,1 2,1 p2,1
~Ws2,l-2 A2,l-2 Cp2,1
+E'2,12 (cp2,2~Cp2,l)
Cp2,1
(11)
The first three lines of this equation parallel the equivalent
mechanisms in the water column (sorption-desorption, settling-resuspension
and decay). The fourth line represents the net downward flux of sediment
particulate toxicant due to the net sedimentation velocity and the fifth
part of the equation is the nixing of the sediment due to factors such as
bioturbation or deep sediment mixing. (The dissolved form of the toxicant
may also diffuse and exchange downward as noted in Eq. 9). Figure 6
illustrates the net sedimentation velocity and sediment mixing effects.
As shown in Fig. 6(a), without sediment mixing, assume a layer of sediment
at the surface receives at time t=0 an input of a tracer substance, such
as a radionuclide or a pollen pulse or a dye input. At some time At
later, the surface layer will be buried and will appear at a depth Az as a
well defined plug with no exchange with adjacent sediment segments. From
the surface of the sediment then, the layer with the concentration of the
tracer substance appears to be moving away at a velocity w , the net
sedimentation velocity. This velocity is equivalent to the net build-up
of the sediment over time. Fig. 6(b) shows a similar effect but including
some mixing between the sediment particles or diffusive mixing of the
dissolved form. The sediment and diffusive mixing induces some spread and
the uniqueness of the tracer layer is not maintained. The downward
movement of a toxicant is therefore representative of a classical
dispersive-advective transport system in the vertical direction.
LOCAL EQUILIBRIUM EQUATIONS
Eqs. (4) and (9) for the dissolved component and Eqs. (10) and (11)
for the particulate component in the water column segments and sediment
segments respectively represent the complete set of interactive equations.
Note that the coupling of the dissolved and particulate components is
through the reaction kinetics of sorption and desorption. Now, for a
large number of chemicals, these reaction kinetics tend to be "fast" (i.e.
completion times on the order of minutes-hour) compared to the kinetics
20

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water
sediment

at t=0
	sz_
K2S
0j
Depth
(a)
at t=At
dZ
x vryx x v x
cone.
ZZZ3
Depth
(b)


sediment
mixing
Depth
cone.
Depth
Figure 6. Illustration of downward advection due to net sedimentatio
(a) without sediment mixing, (b) with sediment mixing
21

-------
inherent in other mechanisms of the problem. These latter mechanisms
Include bacterial decay, net loss rates to the sediment and sedimentation
rates that have reaction times on the order of days to years. The equa-
tions noted above thus include the entire spectrum of reaction kinetics
and as a consequence are quite difficult to solve numerically. Di Toro
(1976) has discussed this problem with specific references to water quality
models.
The "fast" kinetics of sorption-desorption indicate that for time
scales of days to years, there will be a virtually continuous equilibration
of the dissolved and particulate forms depending on the local solids con-
centration. This partitioning between the two components permits the
specification of the fraction of dissolved and particulate toxicant to the
total. The dissolved and particulate toxicant are therefore assumed to be
always in a "local equilibrium" with each other. Assuming that the sorp-
tion is reversible (desorption) and that the sorption/desorption kinetics
are linear, then a partition coefficient can be defined as follows:
or
since c' = c /
T = r/c'd	(12)
tt' = 7t /  = r/cd	(13)
Eqs. (12) and (13) describe tt as the ratio of the toxicant on the
particulate, r, (in units of mass of toxicant per unit mass of dry solids)
to the toxicant in the dissolved form.
The particulate toxicant concentration relative to the bulk volume is
given by
c = rm	(14)
P
and then the relationship between c and c. is
p	d
c = Tr'mc,	(15)
P	a
Substituting Eq. (15) into Eq. (2), for the total toxicant gives
c_ = (1 + Tr'm)Cj
or
cd = fdcT	(16)
where f^ is the fraction of the total that is dissolved and is given by
-1
Recalling that
fd = (1 + ir'm)	(17)
cd = *c'd
22

-------
then	cd =* (fd/<*>)cT or cd = fdcT for
fd = V*	(18)
Also, the particulate toxicant as a fraction of total toxicant is
given by
c= f c	(19)
P P T
for
f
(20)
p 1 + Tr'm
The local equilibrium assumption therefore permits specification at
all times and places of the fraction of the total toxicant in the
dissolved and particulate form. It should be stressed again here that this
local equilibrium assumption assumes complete reversibility between the
solid and liquid phases. There is evidence (e.g. DiToro, et al. 1982a)
that this is not the case for PCBs. However, this development will
proceed on the assumption of reversibility.
Also in these relationships it is assumed that the partition
coefficient does not depend on the concentration of the sorbing solids.
There is evidence, however, as given by O'Connor and Connolly (1980) that
such may not be the case for all chemicals. Di Toro, et al. (1982a)
indicate that for PCB the partition coefficient does apparently depend on
the concentration of solids. The effect of this dependence with respect
to PCBs in the Great Lakes is discussed in Section 10. The development
continues here on the assumption of a constant partition coefficient.
Attention can then be focused solely on the mass balance equation
for the total toxicant. The total toxicant in the water column or
sediment is given by Eq. (2). Adding the water column equations for
dissolved toxicant (Eq. 4) and particulate toxicant (Eq. (10)) gives
dcT2
v2  = [Qi2cTrQ23CT2+E12 ^CT1~CT2) + E23 ^CT2~CT2^
dt
+ KL2 A2,l (c'd2,l"C'd2) ~ Kd2V2Cd2 + k2 A2,1(Cg/He"C'd2)
-w-,A01c0+w _.A01c0I-K_Vc+ W	(21)
a2,l 2,1 p2 rs2,l 2,1 p2,l p2 2 p2 T2
Note that the kinetics of sorption-desorption do not appear in this
equation because it represents a mass balance of the total. The net loss
rates and exchanges that are dependent on the form of the toxicant do
however, remain.
Substituting Eqs. (16) and (19) for the dissolved and particulate
forms gives an equation entirely in terms of the total toxicant, i.e.
23

-------
V2 ~dt~  tQ12CTl " Q23CT2 + E12 *cTl""CT2* + E23 (cT3_CT2)1
+ ^L2 A2,l ((f'd CT)2,1 " *f'dCT*2* ~ Kd2 V2 (fdCT^2
+ kl2 A2,l (cg/He(f'dCT)2) " Wa2,l A2,l (fpCT*2
+ Wrs2,l A2,l ^p^^.l " Kp2 V2 (fpcT*2 + WT2	(22)
This equation represents the mass balance of the total toxicant for
the typical water column segment //2. Note that the suspended solids
concentration is incorporated in the fraction dissolved and particulate of
the total and therefore requires a specification of the concentration or a
separate equation for the suspended solids transport.
A total toxicant equation for the sediment segment (number 2,1)
underlying segment 2 can be obtained in a similar manner. Thus adding
Eqs. (10) and (11) and substituting Eqs. (16) and (19) gives
V2,l dt = ^L2 A2,l((fdCT)2 " ^^T^.l* ~ Kd2, 1V2,1 (fdCT)2,1
" Kp2,lV2,l(fpCT)2,l + Wa2,lA2,l(fpCT)2
~ Wrs2,l A2,l (fpCT)2,l " wd2,l-2 A2,12(f'dCT)2,1
~ Ws2,12 A2,12 (fpCT)2,l + KL2,1*2 A2,1  2((f'dCT)2,2
(f'dCT)2,l) + E'2,12 ((f'pCT)2,2~(fpCT)2,1*	(23)
Eqs. (22) and (23) are the fundamental total toxicant mass balance
equations for a typical water column and underlying sediment segment.
SUSPENDED SOLIDS AND SEDIMENT SOLIDS EQUATIONS
As noted in the above equations, the toxicant equations are coupled
parametically to the suspended solids and sediment solids concentrations.
The concentrations can be specified externally as input. However, the
mechanisms of solids settling and resuspension must therefore be determined
by other tracer variables. The solids concentrations can also be computed
and calibrated to observed solids concentrations using mass balance equa-
tions. The latter course is followed in this work.
Thus for water column segment #2, the solids equation is
24

-------
dm2
V2 	 = [Q12 m1 - Q23 m2 + E[2 (n^-n^) + E3 (m3-m2) J
' Wa2,l A2,l n2 + Wrs2,1 A2,l m2,l + Wm2	(24)
Again, the term in brackets is the advective-dispersive transport of
the suspended solids. Note that the dispersion is assumed to be the same
for the solids as for the toxicant. The settling and resuspension of
solids are given by the term involving w and w and the external
input of solids is given by wm2*
For the solids in the sediment segment underlying segment #2 the
equation is
dm2,l
V2,l ~ = Wa2,l A2,l m2 " Wrs2,l A2,1 m2,l ~ WS2,1*2 A2,l-2 m2,l
+ e'2>1.2	(25)
This sediment solids equation represents a balance between solids
settling into the sediment, resuspension from sediment, net sedimentation
of solids and solids mixing in the sediment.
Since solids concentrations are given	in mass of solids per bulk
volume, the concentration is related to the	density of the solids and the
porosity by
m = pg(l - 
-------
*k mk
(28)
pk 1+ElTkmk
and
fd-	8a>
k
The concentration of particulate toxicant in the kth size class is
Cpk = fPkCT	<29>
and the dissolved concentration is given as before (Eq. 16). With these
expressions, the previously derived toxicant equations for the water
column (Eq. 22) and the sediment (Eq. 23) and the solids equations (Eqs.
24 and 25) can be viewed as representing several size classes. The only
difference is that all terms involving particulate toxicant must include
the sum of the individual size classes. Therefore in Eq. (22), the
settling, resuspension, and decay terms for the particulate become
dcT2	m
V2 ~dt~ *	A2,l ^pkcT^ 2 * ("rs2, 1* k A2,1 ^pkV 2,1
" (KpL>k V2 "pk'xV	0)
Similar extensions can be made for Eq. 23, the toxicant in the sediment
layer. For the solids concentrations, a separate equation must now be
written for each of the solids class. Equations (24) and (25) are then
subscripted for each solids class. The total number of equations for a
given segment that must then be solved is equal to the number of solids
classes plus one equation for the total toxicant or m + 1.
26

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SECTION 5
SIMPLIFIED MODEL ANALYSES
The preceding development of the complete time variable, multi-solids
class and spatially variable equations does not by itself increase
understanding of toxicant behavior. This is precisely because of the many
complex interactions between the water column and sediment, and the
particulate and dissolved toxicant. It is of value then to explore
several simplifications of the general equations to further elucidate the
role that key mechanisms play in the fate of a specific chemical. Also,
simplifications of the general model may prove useful in rapidly assessing
and screening potential new chemicals that may enter systems such as the
Great Lakes. Finally, simplifications may be possible for certain classes
of chemicals that exhibit mechanistic behavior in broadly similar
fashions. Two categories of simplification are considered then in this
section:
1)	Simplification due to chemical behavior
2)	Steady state simplification
a)	completely mixed lake
b)	multi-dimensional lake
SIMPLIFICATION DUE TO CHEMICAL BEHAVIOR
The general equations indicate that the characteristics that are
chemical specific are
1)	Partition of chemical between solids and water
2)	Volatilization of chemical across air-water interface
3)	Decay of chemical due to photolysis, bacterial degradation,
hydrolysis.
The structural properties of chemicals determine the degree to which
a given chemical exhibits certain behavior after discharge into a natural
body of water. Chemicals will tend to fall into certain groupings
reflective of these structural properties nad therefore groups of
chemicals can be examined to determine possible simplifications of the
preceding equations. Numerous attempts have been made to relate the
kinetics of chemicals to specific properties, most notably the
octanol/water partition coefficient and the solubility of the chemical in
water.
Empirical Relationships of Chemical Kinetics Octanol/water-solubility
equations
Chiou et al. (1977) in investigations into the bioconcentration
factors for fish suggested the following relationship between the
octanol/water partition coefficient and water solubility:
27

-------
Ior ir = 5.00 - 0.67 log c
6 ow	w
(31)
m5 ~-67
or tt = 10 c
ow	w
where tt is the octanol-water partition coefficient and c , the chemical
ow	w
solubility in water is in u mol/A. Chiou et al. (1977) indicate that this
relationship is valid for estimating tt to one order of magnitude. This
relationship however does not distinguish between liquids and solids.
Banerjie et al. (1980) examined this latter distinction and provided the
following overall equation
log tt = 5.2- 0.68 log c	(32)
ow	 w
which does not differ significantly from Chiou et al. (1977). Inclusion
of the melting point by Banerjie et al. (1980) resulted in the following
log tt = 6.5 - 0.89 log c - 0.015 (mp)	(33)
ow	 w	r
for melting point (mp) in C.
Solids-water partition coefficient equations. Kenaga and Goring (1978)
reviewed the literature on equations relating the chemical partitioning
into solids and indicated that the range of partition coefficients is
significantly reduced when the organic content of the solids is used as
the independent variable. They suggest
log tt = 1.377 + 0.544 log tt	(34)
oc	6 ow
Note that the relationship between the toxicant partition
coefficient on a solids basis (tt) and the partition coefficient on an
organic carbon basis (tt ) is
oc
TT = TT / f	(35)
oc	oc
for f as the fraction of organic carbon associated with the solids,
oc
Karickhoff et al. (1979) in measurements of hydrophobic chemicals
in natural sediments obtained a linear relationship as
tt = 0.63 rr	(36)
oc	ow
or tt = 0.63 f tt
oc ow	(37)
and tt = 6.3  10^ f c	(38)
oc w
28

-------
Eq. (34) differs rather considerably from Eq. (36) and reflects the
variability to be expected in attempting to estimate partition
coefficients for a broad spectrum of solids types. For a whole sediment
with varying solids composition,
" -|"if1	(39)
for f^ as the fraction of the total mass given by a specific size class,
Using the organic carbon partition coefficients,
* " *<\>cfocf)i	<40>
Karickhoff et al. (1979) thus suggest that from information on
organic carbon content, f , distribution of various solids classes and
oc
octanol/water coefficient, a reasonable (a factor of 2) estimate of
sorption partition coefficient can be made. They maintain however that
reported values for tt in the literature may vary by several orders of
magnitude due principally to experimental error.
These expressions can be utilized in assessing the relative
fractions of particulate toxicant and dissolved toxicant for different
sediment solids concentrations, using Eqs. (17) and (20). These latter*
equations are plotted in Figure 7 for varying levels of solids partition
coefficient, tt. The solids concentrations are shown for the ranges of
100-1,000,000 mg/2. and the range of solids on Great Lakes sediment is
shown. As shown, the fraction of toxicant in the particulate phase in
the sediment is 99% or larger for all substances with it of 102-10J /kg
or greater (or conversely water solubilities of less than about 1-10 u
mol/Jl). Using Eqs. (31) and (36) and an organic carbon content of 2%
(f = .02), a conversion between it and c (u mol/2.) is shown and some
oc	w
representative organic chemicals are indicated. Examination of Eq.
(23), the toxicant sediment equation together with Figure 7 shows that
there is a broad group of chemicals where the fraction dissolved in the
sediment will be less than .01. Hence, dissolved decay terms, exchange
of interstitial dissolved chemical concentration and impacts of
dissolved toxicant in the sediment on the overlying water column
concentration will tend to be small.
It should be noted, however, the the particle concentration dependency
of the partition coefficient is ignored in this analysis and it may mark-
edly affect these results. This issue is addressed in more detail
subsequently.
29

-------
(A
O
I 2
w	00
>	O
&	CL
w
J	*
o	r
<0
o
10?
I
n C
- - " " &
O
+*.
at
a	*  n	tQ
2	O ^ a JQ
Solubility In Water ifjimol/)
Y 1,0 i iji1
Ui
a
a
CO
o
a.

to

M
IO
102
*-163
Ol |
Partition Coef.- (/kg)
'd
Fraction
Dissolved
IP?
0.75
0.90
0.99
\V
Range of
Great Lakes Sediment
P,
Fraction
Particulate
0.999
ire 7. Fraction of particulate and dissolved toxicant for different solids
concentrations, partition coefficients and chemical water solubility.
30

-------
STEADY STATE SIMPLIFICATIONS
Completely Mixed Lake
Considerable insight into the behavior of the general equations can
be gained by considering a special case: equilibrium or steady state
conditions for a lake that is completely mixed in the water column and
interacts with one sediment layer. The steady state assumption does
not, of course, permit estimation of how long a sediment would take to
depurate when the external load is eliminated. This is a time variable
question addressable by the general equations and applied later to the
Great Lakes. The steady state assumption is particularly useful for
estimating concentrations for chemicals that will continue to be
discharged or for screening chemicals to estimate maximum expected
concentrations in water column and sediment.
Suspended Solids Model
Since it is known that many chemicals, such as PCBs, sorb to
suspended particulate matter, the first step in the development of a
simplified model is the mass balance of suspended solids. In this work,
a single class of solids is considered and is intended to incorporate
inorganic solids and organic particulates.
For a single completely mixed body of water, the mass balance
equation for the solids in the water column is given from Eqs. (24) and
(25) as:
dm
V  = W - Qm-w Ara + w Am	(41)
dtm	arss
where as before ra and m are the concentration of solids in the water
s
column and sediment respectively on a mass per bulk volume basis
3
[M /L ^ ] W is the mass input of solids [M /T], w is the overall
s s+w m	r	s	a
lake-wide average particle settling velocity [L/T] of the particulates
and wrg is the overall lake-wide resuspension velocity [L/T] of the
solids from the sediment to the water column and include parametization
of all sediment water particle interactions. Eq. (41) represents a
balance of solids between: (a) input of solids externally (W ) and
J m
internally from the flux due to sediment resuspension (w Am), (b)
rs s
losses of solids due to flow transport from the lake (Qm) and settling
from the water column (w Am), and (c) the time rate of change of the
cl
solids mass in the water column (V dm/dt). Since Eq. (41) depends on an
interaction with the sediment, a similar equation must be written for
the sediment segment underlying the water column. Thus following Eq.
(25)
31

-------
dm
s
V - = w A m - w Am - w Am	(42)
sdta	rssss
where wg is the overall lake-wide average net sedimentation velocity of
the surface sediment segment [L/T]. The equation for the solids in the
sediment then is a flux balance between the incoming solids due to
settling from the water column, loss due to resuspension, loss due to
net sedimentation (w Am) and the time rate of change of solids in the
sediment (V dm /dtf. Note that the sediment is assumed to be
S	3
stationary and interacting only with the overlying water column. For
the Great Lakes model discussed here, the available data on the open
lake solids concentration do not permit definition of the time variable
behavior of the solids either in the water column or sediment. Although
long term secular changes may be occuring in external solids Inputs
(e.g. from shore line erosion due to variable lake levels), it is not
possible to detail such changes nor on the time scale used in this
model, does the determination of year to year variation in solids appear
necessary. As a result of these considerations, it is assumed that the
solids concentrations are at steady state. Therefore, dm/dt and dm /dt
in Eqs. (41) and (42) are zero. Eq. (42) can then be solved for thl
sediment concentration and substitution into Eq. (41) yields an equation
only in terms of the water column solids concentration, i.e.
0 = W -Qm-wAm	(43)
m	n
where w is the ret loss of solids from the water column [L/T] and is
given by
w w
a s
w = 				(44)
n w + w
rs s
Eq. (43) can be expressed on an areal loading basis as
W
ma
m = 		(45)
q + w
^ n
2
where W is the areal load [m /L -T] and q is the ratio of flow to
raa	s
surface area [L/T], the "overflow rate" and is also given by
q = H/tQ	(46)
for depth H[L] and hydraulic detention time tQ [T],
With data on input solids, W and observed solids concentration,
ma
m, in the water column, Eq. (45) then permits direct estimation of the
net loss of solids, w . A mass balance around the sediment segment
yields (on an areal basis)
w m = w m	(47)
s s n
32

-------
which states that he net solids flux into the sediment layer from the
water column [M /L -T] is balanced by the solids flux leaving the
sediment segment due to net sedimentation. Note that normal solids
budget calculation describe only the balance of the fluxes of solids as
in Eq. (43). For a toxic chemical model, however, it is necessary to
separate out the solids concentration from the net sedimentation flux.
Also, since the solids concentration in the sediment represents the bulk
density, the concentration is given by Eq. (26). Then if the density of
the solids and the average porosity of the sediment are known, the net
effective sedimentation velocity can be estimated from Eqs. (47) and
(26) as
w m
w = 	. v	(48)
s ps (1-)
All of the above relationships apply in principle to a multi-
dimensional system where water column segments interact due to advective
transport and dispersive mixing as in Eqs. (24) and (25). The equations
must then be expanded to include additional terms to reflect the
interaction between wagr segments. Thus, if m^ represents the solids
concentration in the i segment, then at steady state
0 = Qi-l,I ml-l "	+ Ei-l,i '"l-l-10!1
* Ei,i*l	" wniml * "mi	(49)
where ra . and m . are the solids concentration in the i-1 and i+1
3	th
segments, [Lg+w/T] anc* wn^ gi-ven again by Eq. (44) for the i
segment.
Toxic Substances Model
Under the steady state assumption, Eqs. (22) and (23) become (where
the subscript "s" is the sediment segment, see Figure 8):
0 - WT - Q=t * KLA((fdcT)s - fdcT) - Kd V fd CT
+ k A(c /H -f ,c_) - w Af c + w A f c_ - K V f c_ (50)
I g e d T a p T rs ps Ts p ps Ts
0 = - KLAfdCT)s " Cfyl - Cd V fdcT)s - (Kp V fpCT)s
* V fpcT " wrs A fpsCTs " "d A fdSTS " "a A pscTs	(51)
If the equations are divided by the lake surface area (assumed
equal to the sediment-water interfacial area), and terms are grouped,
the result is
(q + a..)c + a. c = W + k c /H = W'	(52a)
II T LZ Ts a l g e a
a21cT + a22 CTs = 	(52b)
33

-------

Figure 8. Notation for toxicant distribution in completely mixed lake.
34

-------
where
W& = W^/A, the surface loading rate of the chemical
and au- (1^ - ^ - KdH)d - (a ~ K H)f
a12 *4.ds wrsps
a2l" ' Vd " Wap
a22= ,
ps s ps
Eq. 52b shows that the sediment concentration is a function only of
the overlying water column concentration. Therefore, the concentration
of the toxicant in the sediment can be solved from Eq. 52b in terms of
the concentration in the overlying water as:
cTs = aT CT	(53a)
where
w f + K. f I
a p L d
aT = Tw ^~w He H )f + (w +KT/ + K, H )f.	(53b)
rs s ps s ps s L. s ds s ds
Substituting Eq. (53a) into Eq. (52a) and simplifying gives
0 = - qcT - wT cT	(54)
where w^, is the net removal rate of the chemical from the water column.
A variety of expressions can be developed for w^ based on the above
derivation. A convenient form is given by Di Toro, et al. (1981, 1982b)
who have shown that the net loss rate can be expressed as
r
s
w_ = (K + B  (K + K ))H	(55)
, T l r I s
where
Ki - (Kd * VH)d * KP P	<56>
K, - K. f . + K f	(57)
2 ds ds ps ps
w f
s ps
Ks = 		(58)
s
and
m H f
s s p
6  ~	<59)
ps
35

-------
r (w	+ w ) f + IC. (ir /ir) f.
s rs s ps L s as
~ =	+ w ) f + H, f. + K, H	(60)
rs s ps L as 2s
Eq. (54) is informative since it is in a form similar to standard
water quality models where all the complex sediment and atmospheric
interactions are included in the net removal rate of the toxicant, w .
This provides for an immediate simplification since now only the water
column need be considered. If data are available on the load and
resulting water column concentration of a chemical, the net loss rate
can be computed from Eq. (54) or if fundamental information is known
about the chemical and sediment interactions, w_ can be calculated from
Eqs. (55)-(60).	1
The concentration for the water column is then given from Eq. (54)
by
W1
CT = q + wT	(61)
r
Figure 9 shows the relationship of Eq. (61) for a range of
hydraulic loading rates; net loss rates and resulting ratio of chemical
loading to in-lake concentration. For the Figure, w^ is assumed as
always negative (sink) although it need not be in general. It can be
noted that for hydraulic loading of >100 m/yr., the ratio of the
allowable loading to in lake concentration is constant over a wide range
of i.e. the lake hydraulics dominate the kinetics and "flushing" is
more important than all of the chemical interactions. For other water
bodies, however, such in not the case, although for lakes with lower
overflow rates, there is a range over which the allowable loading is
independent of w^,.
Eq. (60) shows that if there is no decay of the toxicant in the
sediment, and the partition coefficients are equal between the water
column and sediment then
(62)
which says that the particulate toxicant concentration in the sediment
is equal to the particulate concentration in the water. Also, it can
then be shown that for this case
wt = +	+ (w + K H)f	(63)
l	 d d	n p p
This latter result shows that if r =r, the net loss of chemical
g
from the water column at steady state is readily computed from
information on the solids net loss and concentration and properties of
the chemical such as decay, volatilization, and solids partitioning.
Finally, Eq. (62) indicates that for chemicals that do not appreciably
decay or volatilize (as approximated for example by heavy metals and
long lived radionuclides),
w_ = f w	(64)
T p n
36

-------
-looor
Wn =100 m/yr.
100
Wp=10 m/yr.
>
10
CD
wn =1 m/yr

wn =Om/yr.
.Great Lakes
1	10
HYDRAULIC LOADING
1000
100
Depth
(m/yr.)
Detention Time
Figure 9. Relationship between
rate of chemical and
concentration ratio.
hydraulic loading, net loss
chemical loading/in-lake
Net loss always positive(sink)
"*7

-------
This result shows that for kinetlcally conservative chemicals as
previously mentioned, the only loss of the chemical from the water column
is through the net settling of the fraction of the chemical in the par-
ticulate phase.
Figure 10 shows the behavior of the ratio of the net loss of toxi-
cant to solids from Eq. (23) for the case of no volatilization and decay.
The heavy metals and long lived radionuclides are examples. The fraction
particulate, therefore, is equivalent to the ratio of net toxicant loss
to net solids loss. With an estimate of the latter then, the toxicant
loss can be estimated.
Also if an estimate is available of the net sedimentation flux rate
of solids, F [M/L -T], i.e.
s
F = w m	(65)
s n	^ '
then the net loss of chemical is from Eqs. (64) and (20)
it1 F
WT 1 + ir'm
(66)
recognizing that this is for the case of no volatilization or decay. On
the other hand, if the chemical loss rate is known from observed data,
the equation permits estimate of either the net sedimentation flux, F
for known solids concentration in the water column, m or estimate of thl
"effective" steady state solids concentration for known sedimentation
flux. Again, all of these relationships are at steady state employ
various assumptions and do not apply in general for the time variable
situations.
Examples - Steady State
The preceding simplified steady state analyses for the fate of chem-
icals in lakes indicated that under certain assumptions, the ratio of
the concentration of the chemical on the suspended particulate matter is
equal to the concentration in the surficial sediments (Eq. 62). Nriagu,
et al. (1981) provide data on five metals for Lake Ontario which permit
a test of this assumption. The results are shown in Figure 11. In
these data, about 20 samples were obtained for the water column and four
for the sediment. As shown, for the five metals, the assumption that
the particulate concentrations in the water column and sediment are equal
is reasonably good. Cadmium is low however by about a factor of two and
nickel is high by about a factor of two. To within an order of magni-
tude, however, these metals appear to behave in accord with the simpli-
fied theory.
Table 2 shows the results of the application to two different chemi-
cals in different lakes. The first application, 1,4 dichlorobenzene in
Lake Zurich draws on the input data given by Schwarzenbach, et al. (1979).
This substance has a low partition coefficient to solids (estimated at
70 yg/kg -i- yg/) and, hence, the fraction particulate (for a solids con-
38

-------
8 0 75
M " IOOmg/1
M - 10 mg/l
% S 0.25
I-
<
-1
D
O
H
CC
<
a.
Z
O
0.25 
ac
100 1,000 10,000 100,000
PARTITION COEFFICIENT- it Ug/kg ~ *tg/l)
10. Ratio of net chemical loss to solids loass as function of
suspended solids concentration and partition coefficient,
Dissolved loss = 0.
39

-------
TABLE 2
q
TWO APPLICATIONS OF SIMPLIFIED CHEMICAL MODEL
Part Chem. Diss. Chem.	_ ,	
,.	r	T	Calc.	Obs.
Loading	Loss	Loss		
n	2	J	2	Cone.	Cone.
Lake	(m/yr) Chemical (tig/kgi)ig/)	g/m -yr	(m/yr)	(m/yr) (ng/1) (ng/1)
Zurich3 40 1,4 dichloro- 70	1 -3 10~3	0	106	8.9	10
benzene
/	r	r
Michigan 0.8 Cadmium	200,000	0.58*10	12.4	0	43.7	20
o
1	Calculated from (nM/(1+nM))w
n
2	Calculated from (l/(l+nM))K^
3	Input data from Schwarzenbach, et al. (1979)
4	Input data from Muhlbaier & Tisue (1981)
5	From Nriagu, et al. (1981)
6	Lake may not be in equilibrium with load (See Muhlbaier & Tisue (1981))

-------
centration of 4 mg/A, (Kelts and Hsii, 1978) is approximately zero. The
net loss of the chemical then as shown in Eq. 63 does not depend on set-
tling of the chemical out of the water column but only on the loss of
the dissolved fraction. Following the work of O'Connor (1982) using a 5
m/sec. wind, a molecular weight for DCB of 200 and a Henry's constant of
0.2 (Schwarzenbach, et al., 1979), a volatilization exchange rate of 0.29
m/d is calculated (compared to 0.24 calculated by Schwarzenbach, et al.
1979 from a mass balance). The net loss rate for DCB for Lake Zurich is
thus about 106 m/yr., all from the dissolved form. Eq. 61 then allows
computation of the in-lake concentration of 8.9 ng/Jt compared to the
approximate 10 ng DCB/J, observed for Lake Zurich.
The second application was the metal cadmium, which can be highly
adsorbed to particulate matter in contrast to DCB. Laboratory data on
the partitioning of cadmium indicate a coefficient of about 1000 ug/kg *
p g/i (O'Connor and Connolly, 1980) but Nriagu et al. (1981) obtained
data on Lake Ontario cadmium that permit an estimation of the partition
coefficient of about 200,000 y g/kg*y g/ . The latter value was used in
the calculation shown in Table 2. Muhlbaier and Tisue (1981) provide
estimates of loading to southern Lake Michigan which were applied on an
areal basis over the entire lake. Net losses of solids for Lake Michigan
is estimated at about 137 m/yr. (as discussed later). For 0.5 mg/2. sus-
pended solids and a partition coefficient of 200 ug/gTyg/, the fraction
particulate, f is equal to 0.09. If no other loss of cadmium is assumed
then the net lBss of cadmium is from settling only and is about 12.4 m/yr.
Since the outflow loss from Lake Michigan is small (q=0.8 m/yr.), the
loss of cadmium is dominated by the sedimentation of particulate cadmium.
The calculated in-lake concentration (from Eq. 61) as shown in Table 2
is 44 ng/ or about two times higher than the 20 ng/Jl considered as ob-
served by Muhlbaier and Tisue (1981). They discuss, at some length, the
hypothesis that Lake Michigan because of its long detention time is not
in equilibrium with the assumed cadmium load. The simplified steady
state model, therefore, approximates the observed cadmium concentration
only to order of magnitude (i.e to tens of ng/Jl) and more reliable data
on input and water column, together with a time variable analysis, would
be necessary to determine the degree of nonequilibrium for cadmium in
Lake Michigan.
Multi-Dimensional Lake
When significant gradients exist in the particular lake or region
of lake under study then the completely mixed assumption does not hold.
The flux between various regions due to net transport and mixing must be
included in the overall steady state simplification. The previous
principles for the completely mixed case will be seen to apply in
general to the non-homogeneous lake.
Consider then a steady state condition for Eqs. (22) and (23), i.e.
41

-------
-s 1.000
100 -
01 via tion
NICKEL

PA R TtCULA TE WA TER
CONCENTRA TtON / PARTtCULA TE SED/UENT
CONCENTRATION
10	100	1,000
PARTICULATE CONCENTRATION IN
WATER COLUMN (jig/g)
11. Lake Ontario correlation of particulate metals concentration
on suspended solids in water column and particulate metals
concentration in surficial sediments (calculated from data
in Nriagu, et al., 1981).
42

-------
d CT2 d CT2,1
dt	dt
and assume no interaction with the deeper sediment, i.e. consider a
single sediment layer with a net downward advection. The result upon
adding the two equations is
 = WT2 + ka2A2cg He + tQ12cTl ~ Q23cT2 + E12 (ct1"ct2) + E23(ct3"cT2^
[Kd2v2 + k2A2)fd2 + Kp2fp2V2lcT2
t(Kd2,lV2,l + Wd2,1.2A2,l)fd2,l
+ (ws2,1.2A2,l + Kp2,l V2,l)fp2,llcT2,l	(67)
It can be noted that all the interaction terms between the sediment
and the water column are eliminated. This is a result of taking the
mass balance around the water column and sediment so that the only loss
terms are those that are net from the entire system. These net losses
are fluxes out due to transport and dispersion, decay in the water
column and sediment and net sedimentation of mass out of the sediment
segment. Of course, Eq. (67) still includes the sediment total toxicant
concentration. Therefore let
where
CT2 1 m2 1
a = _i-L = n	(68)
*	T2	p2,1
r2 1
n =	(69)
CT2,1
The quantity a is related to the ratio of the chemical
concentration in the solids in the sediment and water column and the
quantity II is the ratio of the sediment chemical concentration to the
total water concentration, a quantity that is sometimes available from
data. Note also from the solids balance (Eq. (44) that
T2 = ^	> (Ti-> -f11	<70)
s2,1.2 p2,1	2
Substituting Eq. (68) into (67) and simplifying gives
 = Wt2 + kSi2A2Cg/He + ^Q12CTrQ23CT2+E12(CTrCT2) + E23 (CT3~CT2) 1
- WT2A2CT2
43

-------
where w,^ is the net loss of toxicant from the water column for segment
//2 and is given by Eqs. (55) to (60) with parameters particular to seg-
ment //2. Since the net loss rate is segment specific with respect to the
water column in a multi-dimensional system, calibration to observed data
permits in principle estimates of the net loss of chemical from the water
column. Such a net loss includes all interactions with the sediment and
atmosphere. Therefore, even for multi-dimensional systems (with a sta-
tionary sediment), the net loss rate of the chemical from the water col-
umn can be calculated directly from laboratory data on decay and net
solids loss rates from Eqs.(55) to (60). This completes the theoretical
development of the basic equations and simplifications. Application can
now be made to the Great Lakes system including first an application on
a steady state basis to solids and PCB in Saginaw Bay and then an analy-
sis of the solids balance and time variable calibration to the radio-
nuclide, plutonium-239,240 on a Great Lakes scale. An application then
is made to the PCB distribution also on a Great Lakes scale and the be-
havior of the response using a solids dependent PCB partition coefficient
is explored. Finally, applications of the model are made to benzo(a)
pyrene and cadmium.
44

-------
SECTION 6
STEADY STATE MODEL OF PCBs IN SAGINAW BAY
Saginaw Bay affords an opportunity to test the simple steady state
model for PCBs. Richardson, et al. (1983) have summarized the basic
data base for Saginaw Bay and the overall properties of the Bay. This
application uses the steady-state model previously discussed that
incorporates horizontal transport, net solids settling and
resuspension and sedimentation, and the interaction of the solids with
PCBs.
SEGMENTATION & TRANSPORT
The segmentation is from Richardson, et al., (1983) and includes
segment volumes, areas, and depths. The dispersive exchange
coefficients and the flows between each of the segments and Lake Huron
were also obtained from hydrodynamic modeling conducted by the Grosse
lie Laboratory. That work, however, concentrated on the time variable
aspects of 1977 and 1979 and, as a result, the coefficients of turbulent
exchange and flow have to be modified to represent a long-term
steady-state condition. The temporally averaged flows and exchange
coefficients that were used in the steady-state computation for the five
segments in the water column are as shown in Figure 12 together with the
segmentation.
A chloride calibration was then performed using these flows and
bulk dispersion values. Chloride data were obtained from STORET for the
years 1974 through 1977 and all data found in a segment were averaged
for each annual period for that segment. Loadings consisted of the
Saginaw River discharge and atmospheric sources (6670 kg/day). Saginaw
River chloride loadings for 1974 were estimated to be from 1.04 to 1.15
million kg/day and the 1977 discharge was 0.8 million kg/day. For the
calibration, the 1977 value was used. Boundary conditions were selected
to be 6.3 mg/Jl for both segment 4 and 5 on the basis of available STORET
data nearest the open lake boundary of the model. The comparison of
calculated concentrations of chlorides with the 1974-1977 data in Figure
13 indicates good agreement and, therefore, confirms the transport and
dispersion regime as representative of steady state conditions.
SUSPENDED SOLIDS CALIBRATION
The Saginaw River and smaller tributaries to the Bay, shoreline
erosion, atmospheric fallout and phytoplankton biomass are the
components of solids loads used to calibrate the solids in Saginaw Bay.
U.S. EPA (1982) provided a long-term estimate of the Saginaw River load,
whereas the contributions of other tributary drainage areas were
estimated from average flows and a long-term average suspended solids
concentration estimated for the Saginaw River. Bank erosion values were
derived from county by county erosion volumes in Monteith and Sonzogni
(1976) and proportioned to Saginaw Bay on the basis of shoreline length.
Volumes of eroded material were converted to mass loadings by assuming a
porosity of approximately 60% and a specific gravity of 2.65. To
account for immediate settling of heavier fractions, a 50% reduction was
45

-------
SEGMENTATION SAG R/rj)i

L. HURON
FLOW
(m3/sec)
113.3

BULK DISPERSION
(nWsec)
I
127.4 | T 6020 I
- - i	
1QB bCv' * 8219.7
12. Segmentation for Saginaw Bay and estimated long-term
average transport coefficients
46

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 YR. 1974
 1975
A 1976
~ 1977
25
20
CALCULATED
BC mg/l
USES 1977 ESTIM. SAG. R.
CHLORIDE LDQ.
SEGMENT
20
L. HURON
DISTANCE (km)
13. Transport calibration for Saginaw Bay using long-term averaged
chloride data.

-------
used to obtain the final estimates. Phytoplankton biomass was obtained
from algal model simulations. A summary of all segment loads by class
is contained in Table 3. The predominance of the Saginaw River and
phytoplankton loadings is apparent.
Boundary conditions, consistent with limited available data, were
selected primarily on the basis of trial and error. Preliminary
computations indicated that initial estimates of approximately 2 rog/
solids at the open lake boundary were too low since calculated solids
concentration in segments 4 and 5 were well below observed values and
mass balances of these segments indicated that the boundary fluxes
dominated these segments. Final values of 4.3 mg/Jl for segment 4 and
5.5 mg/2, for segment 5 were selected. The former value is thought to be
more associated with advective flow entering the Bay from Lake Huron and
the latter value more representative of observed segment 5
concentrations leaving the Bay with the net advective flow (see net
circulation, Figure 12).
Net removal rates of the suspended solids were then assigned to
segments 2,4, and 5 where solids deposition zones are either documented
to occur (segment 2) or estimated to occur (segments 4 and 5). No net
removal rates were assigned to segments 1 and 3 since sedimentation
appeared to be minimal there on the basis of sediment solids and PCB
data in sediment cores. Initial values of the net removal rates were
made from mass balances of each segment using observed water column
solids concentrations. These were then input to the 5 segment Saginaw
Bay model, using the transport coefficients previously calibrated, and
adjusted until the calculated and observed suspended solids
concentrations were in agreement. As seen in Figure 14, the calculated
values in the water column are in good agreement with the observed data
of 1976 through 1979, when values of the net removal rate of 12.7, 13.8,
and 9.7 meters/year are used for segments 2,4, and 5 respectively.
Sensitivity analyses indicate that the differences in the net loss rates
in segments 2,4, and 5 are not significant. Equally acceptable
calibrations are obtained for values between 10 and 20 m/yr. for
segments 2, 4, and 5.
With the estimated net removal rate of solids w from the water
n
column, the flux of solids into the bed is calculated as w jAm.fm /T].
ni il s
This is equal to the sedimentation flux which is calculated as w .Am. .
si is
Since both wg^ and m^g vary with sediment depth, no single value can be
specified. However, from Eq. (47) the relationship between w . and m.
si	is
is unique. If wg^ is selected, then m^g is determined. Log-log plots
of the relationships between the sedimentation rate and the bed solids
concentration are included in the bottom of Figure 14.
A considerable amount of effort was expended in determining the
sediment concentrations of solids (i.e. the bulk density of the
sediment) drawing on the work of Robbins (1980). From sediment cores
48

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TABLE 3
ESTIMATED LONG-TERM AVERAGE SUSPENDED SOLIDS INPUTS - SAGINAW BAY
Tributary	Bank Atmospheric Phytoplankton Total
Model	Loads	Erosion Loads	Mass	Loading
Segment (lb/day) (lb/day) (lb/day)	(lb/day)	(lb/day)
1
1,232,000*
28,200
10,100
132,200
1,402,500
2
123,900
92,600
31,400
341,600
589,500
3
34,900
63,900
15,100
143,300
257,200
4
21,900
124,100
23,700
176,300
346,000
5
43,700
50,700
24,700
251,300
370,400
Total
1,456,400
359,500
105,000
1,044,700
2,965,600
*
Saginaw
River 1,208
,000



TABLE 4
SEDIMENT SOLIDS CONCENTRATIONS^1^ - SAGINAW BAY
Core Solids Concentrations (mg/l(Bulk))
at Following Depths
Station	5 cm	12.5 cm	17.5 cm
1A
510,000
1,350,000
1,130,000
6A
250,000
700,000
730,000
11A
230,000
560,000
620,000
24-1
280,000
390,000
507,000
37-1
900,000
1,040,000
730,000
43-1
340,000
420,000
450,000
46-1
280,000
450,000
850,000
50-A
250,000
340,000
420,000
28-A
450,000
. 790,000
1,070,000
Mean
390,000
670,000
720,000
Std.Dev.
200,000
320,000
240,000
(1>DaCa
from Robbins (1980)

(2)
Stations all in
Saginaw Bay model
segment 2
49

-------
20
5
9
OO |> 10
Wqj J
a|fi
si
0)>
 1976 MEAN
 1977
A 1978
~ 1979
NET REMOVAL
RATE (m/yr)
13.8
2 SEGMENT 1
12.7	0
CALCULATED
3
0
5
9.7
SEG. 4
3 mm/yr
SEG. 2
OBSERV
RANGE
100
1000 10
100
1000
SEG. 5
100
1000
SEDIMENT SOLIDS CONCENTRATION (gm/l)
14. Solids calibration using long-term solids data. Data, mean +
1 Standard Deviation; calculation, solid line.

-------
located primarily in segment 2 of the Saginaw Bay model, a selected num-
ber of cores were examined for the sediment solids concentration at the
midpoints of a 10 cm well-mixed layer and at the midpoints of two deeper
5 cm layers. The results are summarized in Table 4. For the well-mixed
surface sediment layer, sediment concentrations average approximately
390,000 mg/Jl for nine cores with a range of approximately 230,000 to
900,000 mg/H. This range is shown in Figure 14 for segment 2. If the
lower value of the range is used, the corresponding sedimentation rate
for the 10 cm well-mixed layer would be approximately 0.8 mm/yr., some-
what less than a previously reported value of 3 mm/yr. (Robbins, 1980).
These results indicate the utility of the simple steady state solids
balance. The water column solids data are known in this case with some
accuracy and do not exhibit marked spatial gradients. Note that the max-
imum spatial differences in the average water column suspended solids is
about a factor of four. In contrast, the spatial heterogeneity of the
sediment is quite marked with regions of deposition, scour and no appar-
ent net deposition. Sediment solids may then vary markedly in the given
segment horizontally, but, more importantly, vertically. Boundary layers
of sediment solids, i.e. nepheloid or "fluff" layers may be available for
interaction with the surface water column at concentrations less than
sediment data from cores. Conversely, estimated net sedimentation velo-
cities are often cited only for those regions of deposition and not over
an area equivalent to a model segment of Saginaw Bay. The calculation
discussed above provides a good estimate of the net flux to the sediment
over the entire segment area and sediment solids concentrations is shown
in the lower figures of Figure 14. If, as noted above, the solids data
from the sediment cores are used, then the net sedimentation velocity
varies from 0.25 to 0.8 mm/yr. or almost one order of magnitude less than
the 3 mm/yr. previously cited. If, on the other hand, an average net
sedimentation over the entire area of segment 2 is fixed at say 3 mm/yr.,
then the sediment solids concentration that is consistent with that sedi-
mentation velocity is about 45,000 mg/Jl or one order of magnitude less
than the average sediment solids in the top 5 cm of the cores. The re-
sults indicate, therefore, that with only the net flux of solids to the
sediment (over a segemtn area) known with some confidence, then it is
difficult to uniquely specify the net sedimentation or boundary layer
sediment solids (or equivalently the boundary layer porosity and solids
density as per Eq. (48). Additional tracers (of which the radionuclides
or PCBs are examples) would provide additional information that could aid
in specifying the net sedimentation and sediment solids concentrations.
A mass balance of suspended solids for the entire model is presented
in Figure 15 for three flux categories: the external and internal loads,
the net flux removed from the water column and the boundary transport.
In the lower right panel, it is seen that 2,970,000 lb/day of solids
enter the Bay, 40% (1,190,000 lb/day) is incorporated into the sediments,
and the remaining 60% (1,780,000 lb/day) leaves the Bay and enters Lake
Huron.
51

-------
LOADS
9.8 X 10 7 5.8X 10 7
NET SETTLING ,,, x 1Q7 4.5 x 10 7
23 X 10
BC=4.3
BC =5.5
4.3 X 10
6.1 X 10 7
3.5 X 10
BOUNDARY TRANSPORT
SUMMARY
4.9 X 10
1 2.2 X 10 8
' 5.1 X 10
8AQINAW BAY
 L. HURON
8
1	* 2.9 X 10
2.0 X 10
NOTE: All Values in kg/yr
15. Mass balance of Saginaw Bay total suspended solids under
long-term average conditions

-------
PCB CALIBRATION
With the horizontal transport and net loss rate of suspended solids
calibrated, analysis of the PCB concentrations can proceed. Total PCB
loadings were obtained from U.S. EPA (1982) for 1979, the first year for
which total PCB field data were available. As noted in Table 5, the
Saginaw River load is approximately 75% of the total load and atmospheric
sources contribute an additional 25%. Although open lake concentrations
are reported to be in the 1 ng/Jl range, the boundary condition was
selected as 10 ng/JI - the value needed to calibrate observed data in seg-
ments 4 and 5.
Partition coefficients were selected on the basis of abserved dis-
solved and particulate fractions and values of 10,000, 50,000, and
100,000 yg/kg per iig/fc were selected for segments 1,2, and 3,4, and 5
respectively. These are in accord with values calculated from field
measurements, as seen in Table 6. With the partition coefficients
selected, the removal rates of total PCBs are then calculated as the par-
ticulate fraction of the suspended solids net settling rate (see Gq. (63)
for k = 0). Thus, in this calculation, exchange of PCBs with the
atmosphere, diffusive exchange with the sediment and decay processes are
zero. For segment 2, for example, the net removal rate w^^ is:
WT2 - "s2 (fp2>
= (12.7) (.37) = 4.7 m/yr.
Similarly, the net total PCBs removal rates for segments 4 and 5 are
4.8 and 3.5 m/yr., respectively.
With the loads, boundary conditions, and net removal rates described
above, together with the horizontal transport, the steady state model is
used to calculate total PCB concentrations in the water column. The top
panel of Figure 16 shows the agreement between calculated values and data
observed in 1979. Dissolved and particulate fractions also agree well
with observed data, as noted in the next two panels of the figure. The
bottom panel displays the particulate PCBs per unit weight of solids
and, again, agreement between observed means and calculated values is
good for the water column.
In the previous theoretical Section 5 of this report, it was shown
that, for zero sediment diffusion and decay the PCBs per unit weight of
solids in the water column (r^) is equal to the sediment toxicant concen-
trations Crjg) Figure 17 shows this comparison. The upper panel is a
reproduction of the bottom panel of Figure 16. Directly below, is a plot
of the PCBs in the sediment (r^g) where the solid line is the calculated
value of r^ assuming r2s=rj* The data are segment averaged sediment
concentrations for 1979, provided by the Grosse lie Laboratory. Agree-
ment between calculated and observed means is good for segments 1 and 2.
It is hypothesized that segment 3 may be a net erosion zone (see sus-
pended solids calibration, Figure 13) in which case the assumption chat
r^g = rj is not appropriate.
53

-------
TABLE 5
ESTIMATED TOTAL PCB LOADING FOR 1979^
SAGINAW BAY
Tributary Atmospheric Total
Loads	Loads	Loading
1 1.61(2)
0.05
1.66
2
0.16
0.16
3
0.07
0.07
4
0.12
0.12
5
0.12
0.12
Totals 1.61
0.52
2.13
^Source: USEPA LLRS
Grosse
He
(2)
Saginaw River


TABLE 6
TOTAL PCB PARTITION COEFFICIENTS ^
SAGINAW BAY
Partition Coefficient (it) from Observed
(2)
Segment	Concentrations	tt Used in
Model
Mean	Approx. Range
1	10,000	700- 30,000	10,000
2	80,000	7,000-190,000	50,000
3	60,000	20,000-160,000	50,000
4	90,000	10,000-250,000	100,000
5	280,000	10,000-920,000	100,000
(1)	All values in ng/kg per ]ig/l
(2)	Data from Grosse lie Laboratory (1982)
54

-------
1600
a>
O)
Z 800
SEGMENT 4
16. Components of PCBs in water column, Saginaw Bay,
1979, Data, mean + 1 standard deviation; calcu-
lation, solid line.

-------
 1979 MEAN
1600
CALCULATED

0 	1	
SEGM. 4
Tf -yug/kg 100,000
NET REMOVAL
RATE (m/yr)
2
1
3
5
50,000
10,000
50,000
100,000
3.5
4.8
4.7
1600
J1977 MEAN & RANGE
SEGM.
17. Particulate PCB calibration, 1979, water column (upper panel),
sediment (lower panel) Saginaw Bay. Data, mean + standard
deviation; calculation, solid line.

-------
A mass balance of total PCBs is shown in Figure 18 for the Saginaw
River and atmospheric loads, net settling fluxes and boundary fluxes.
As noted in the lower right panel, approximately 30% of the total PCBs
entering Saginaw Bay from external loads is incorporated into the
sediments of the Bay and approximately 70% is exchanged with Lake Huron.
The separate effects of the external PCB loads (Saginaw River and
atmospheric) and the boundary conditions are illustrated in Figure 19.
The total PCB due to both external loads and boundary conditions is
compared with observed data in the top panel of the figure, where the
peak concentration in segment 1 is seen to be approximately 24 ng/. Of
the 24 ng/, approximately 6 ng/ is due to the boundary condition
(center panel) and the remaining 18 ng/jt is the effect of the loads.
Thus, complete removal of the Saginaw River loads and maintenance of the
boundary at 10 ng/Jl would result in at least a 75% reduction in the
segment 1 PCB concentration under this new steady-state condition.
Additional reduction would occur since some significant fraction of the
boundary concentration is probably caused by the loads. Therefore,
reducing the boundary concentration to lower open Lake Huron levels
would reduce the concentration in segment 1. If, for example, the
boundary decreased to a value of 5 ng/2,, the concentration in segment 1,
under the no-load situation, would be approximately 3 ng/.
A mass balance of PCBs for the external loads alone (Figure 20)
shows that approximately 10% of the load entering the Bay is
incorporated in the sediment and 90% enters Lake Huron - the bulk of it
from segment 5. A similar balance for the boundary condition reveals a
net source from Lake Huron Into segment 4, and a net sink into the Bay
sediments before the remaining mass returns to Lake Huron from segment 5
(Figure 21).
This steady state analysis, therefore, provides a reasonable
approximation to the observed data with a minimum amount of parameter
specifications. Indeed, as noted previously, by virtue of the steady
state analysis, it is not necessary to specify the solids settling and
resuspension velocities. Only the net loss of solids is required.
Additional analyses of the role of PCB volatilization and sediment
diffusion due to variable partition coefficients would also prove useful
in further describing the distribution of PCB in the Bay. Finally, a
steady state model evaluation of the distribution of the various PCB
isomers, representing a range of chemical behavior would increase the
overall credibility of the modeling framework.
57

-------
LOADS*
26.5
19.9
274.8
BC= 10
BC=10
NET SETTLING
61.3 29.8
* ESTIMATED 1979 VALUES
23.2
BOUNDARY TRANSPORT
SUMMARY
352.7
L. HURON
675.5
*-+~ 913.9
8AQINAW BAY
I	^ 238.4
114.2
NOTE: All Values in kg/yr
18. Mass balance of total PCBs for Saginaw Bay under
long-term average conditions

-------
S? 40
LOADS*BC
o 20
0.
SEGM. 4
40
DUE TO BC
P 20
40
DUE TO LOADS
I- 20
19. Effects of external loads and boundary conditions on
total PCB average concentrations in water column
of Saginaw Bay
59

-------
LOADS
NET SETTLING
26.49
19.87
1.66
34.77
BC =0.0
274.83
-J mg/l
|BC=0.0
11.59
19.87
1.66
SUMMARY
352.65
BOUNDARY TRANSPORT
~ L. HURON
*-314.57
SAGINAW BAY |
38.08
NOTE: All Values in kg/yr
20. Saginaw Bay mass balance of total PCBs-external loads only.

-------
ON
LOADS
NET SETTLING
28.16
28.15
BC = 10
-J mg/l
!bc= 10
19.87
BOUNDARY TRANSPORT
SUMMARY
 L. HURON
 76.16
SAGINAW BAY
740.06
76.16
NOTE: All Values in kg/yr
21. Saginaw Bay mass balance of total PCBs-boundary conditions only.

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SECTION 7
GREAT LAKES MODEL CALIBRATION
INTRODUCTION
Radionuclide Models
A credible analysis of toxicant fate and response should draw on
existing data for testing and comparison purposes - such data are not
yet available in any consistently accurate form for many contemporary
toxic chemicals. Information on input loads is sparse and data on water
column levels have been subject to wide variability, due principally to
changes in analytical techniques.
However, relatively complete data sets exist for some radionuclides
such as those associated with previous weapons testing. Examples
include plutonium-239 and cesium-137. Data on input loads (principally
atmospheric) are known or can be estimated over a period of several
i	239 2A0	137
decades. In addition, much work on the fate of ' Pu and Cs in
the water column, sediments and food chain has been accomplished through
the Argonne National Laboratory (e.g. Edgington, et al. 1976; Robbins
and Edgington, 1975; Wahlgren and Nelson, 1975; Wahlgren and Marshall,
1975; Wahlgren, et al., 1981). The models utilized by these
investigators are generally of two types. In the first type, sediment
flux models are constructed where the focus is on modeling the
depositional flux of a chemical, resulting sedimentation rate and
comparison to sediment core data. For example, Edgington and Robbins
(1976) modeled the deposition of lead to the Lake Michigan sediments
where Eq. (22) was solved for the net depositional flux of lead given by
w_ c^. In earlier work on plutonium and cesium in Lake Michigan,
Edgington and Robbins (1975) focused their modeling effort on the
sediment core data using a version of Eq. (23) where from the available
sediment data estimates were derived of the flux of plutonium and cesium
delivered to the surface sediment layer. This sediment flux is related
to the external load via introduction of a "flux normalization factor"
which incorporates the interactions shown in Eq. (22).
The second type of model is focused on the behavior of
radionuclides in the water column. For example, Wahlgren, et al. (1981)
present a time variable model that considers the net loss from the water
column as a single parameter. The model equation used replaces all
sediment interaction terms on the right side of Eq. (22) with an overall
apparent settling velocity. Plutonium data from the Great Lakes are
then used to obtain estimates of this net loss parameter. In general,
however, it is seen that for the time variable case only if there is no
interaction with the sediment can one obtain the single equation with a
single loss parameter. At steady state, however, as shown in Eq. (61),
such a single loss parameter (w^) does result and incorporates sediment
interactions as noted previously.
62

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It is precisely the dynamic behavior of chemicals that sometimes is
of importance as in questions related to the length of time required for
the lakes to respond to external reductions (or increases) in chemical
input. The mechanisms of sediment interaction, partitioning and exchange
then become important in estimating the time variable behavior of a body
of water. The difficulty with the previous models of radionuclide behav-
ior in the Great Lakes is the lack of inclusion of those fundamental
mechanisms which would permit extension of the model to other chemicals.
This difficulty of previous models is also recognized by Chapra
(1982) in his work. The model of Chapra follows similar lines to that
developed and applied here and Chapra also included the use of radio-
nuclides as a calibrating variable for a toxicant model for the Lakes.
The resuspension of sediment particulates into the water column however
was not explicitly included in the calibration of the model to the radio-
nuclide data. In the model discussed here, therefore, emphasis is on
application of the theory presented previously which incorporates the
partitioning and sediment interactions into a more complete and general
framework. Since plutonium sorbs to particulate matter, does not vola-
tilize or appreciably decay, it becomes a useful water quality variable
for calibration. Following the calibration, the model is then further
applied to the PCB problem context in the Lakes.
Model Segmentation
Since the time scale of the model is considered to be long term,
i.e. year to year, the physical segmentation of the model considers the
Lakes to be completely mixed with the exception of Lake Erie (Figure 22).
This Lake is divided into three basins: west, central, and east to re-
flect varying regions of solids deposition and water column solids con-
centrations. In addition, Saginaw Bay is included as a separate embay-
ment from Lake Huron to represent a more local region interacting with a
large lake. Table 7 shows the physical parameters used in the model.
Three sediment segments of 2 cm each in depth are included under each of
the lakes or region of lake. This results in a model with eight water
column segments and twenty-four sediment segments for a total of thirty-
two segments.
Calibration Procedure
The suspended and sediment solids are considered to be at steady
state so that Eqs. (43) and (49) are appropriate. As noted in the toxi-
cant equations (Eqs. 50-51) it is necessary that the solids concentra-
tions be known (for calculation of the fraction of the chemical sorbed
to particulates, f ) as well as the settling and resuspension velocities
of the solids. As^such, overall flux balance or solids budget estimates
do not provide the level of detail necessary for the general chemical
model. On the otherhand, it is not possible to uniquely calculate the
solids concentration in the open waters of the Great Lakes because of
uncertainty in the settling and resuspension velocities, the external
solids loading and even the water column solids concentrations. Thus,
the use of a variable such as plutonium in the chemical model is essen-
63

-------
Lake Michigan
west
Statute Miles
2 2. Great Lakes and Saginaw Bay and sediment segmentation used in model.

-------
TABLE 7
GEOMETRIC AND TRANSPORT PARAMETERS OF WATER COLUMN
USED IN GREAT LAKES MODEL
Flow	Horizontal
Lake or	Volume Depth Surface In	Out Exchange
3	2 3	3	2
Region	km	m	Area km ra /s	m /s m /s
Superior
11,326
137
82,882
2,033
2,033
-
Michigan
4,716
82
57,772
1,470
1,470
-
Huron
3,243
56
57,437
3,503
4,967
-
Saginaw Bay
25
6
4,222
153
153
1,229
Erie-West
-Central
-East
23
288
175
8
18
28-
3,026
15,716
6,254
4,967
5,282
5,517
5,282
5,517
5,692
4,425
23,354
Ontario
1,666
86
19,485
5,692
6,740
_
65

-------
tially for calibration of solids interactions rather than as a calibra-
tion of plutonium itself.
Accordingly, the calibration procedure proceeded along the following
lines, (a) A review was made of data on fine grain solids loading to the
Lakes, net depositional flux of solids, and water column suspended solids
concentrations. Since the solids model is considered as steady state,
Eq. (45) was used to provide first estimates of w , the net loss rate of
solids from the water column. From assigned porosity in the surface sed-
iment layer, particle density and net flux of solids to the sediment, the
net sedimentation rate is computed from Eq. (48). (b) With the estimate
of the net loss of solids, w , a range of particle settling velocities
were assigned and the resuspension velocity necessary to maintain the
solids balance was computed from Eq. (44) as
w
w
rs
= w
w
- 1)
(72)
(c) Since there are an infinite number of combinations of settling and
resuspension velocities that will result in the same solids balance, an
additional calibrating variable is needed. For the solids concentration,
net loss rate and assigned settling and resuspension velocities, the time
variable chemical model with sediment interaction (Eqs. 22-23) was numer-
ically solved using plutonium as the calibrating variable. All decay
mechanisms and sediment diffusion were assumed to be zero and a sensitiv-
ity analysis using three values of plutonium solids partitioning was con-
ducted. (d) The plutonium calculation was therefore used to evaluate
the settling and resuspension parameters of the lakes for use in subse-
quent calculations of other chemical concentrations.
SOLIDS BALANCE
As noted previously, the toxic chemical model interacts with the
solids concentrations in both the water column and sediment. The degree
of chemical partitioning on to particulates determines the importance of
the solids concentration in the fate of the toxicant. It is relevant
then to undertake a gross solids balance for the Great Lakes to estimate
settling and resuspension velocities and the net loss rate of solids to
the sediment. The first step is the estimation of external solids load-
ing. The results of using these loads in a simplified steady state cal-
culation and a steady state model using the preceding segmentation are
then given and discussed.
Suspended solids loading to the Great Lakes results from many
sources. Tributaries and shoreline erosion, and atmospheric inputs are
important loads of solids to the Lakes. Direct input of municipal and
industrial sources are generally insignificant on a Great Lakes scale.
Erosion and Tributary Loads
The principal sources for estimating the solids loading due to
shoreline erosion are Monteith and Sonzogni (1976), (drawing on the work
66

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Lake
Shoreline Erosion
U.S.	Can.
TABLE 8
ESTIMATED SHORELINE EROSION AND TRIBUTARY
SOLIDS LOADING RANGE1
(All Units in 10^ mt/yr)
Tributary
Total	U.S.	Can. Total
Total Erosion
& Tributary
Soil Erosion
% of Total
Superior
Michigan
Huron
Erie
Ontario
4.6-18.3
(11.3)2
7.8-40.0
(21.8)2
0.4- 2.8
(1 - 3)2
1.4- 7.3
(4.0)2
0.5- 2.9
4.1-16.2 9.7-34.5 0.7-1.4 1.5-3.0 2.2-4.4	11.9-38.9
7.8-40.0
(21.8)
0.6-0.7
0.6-0.7	8.4-40.7
0.3- 1.0 0.7- 3.8 0.5-0.8 1.0-1.7 1.5-2.5	2.2- 6.3
8.7-14.0 10.1-21.3
(25.4)*
1.2- 1.4 1.7-4.3
6.0	2.1	8.1
18.1-33.5
1.0-1.5 0.6-1.0 1/6-2.5 3.3- 6.8
82-89
93-98
32-60
56-64
52-63
Based on Monteith and Sonzongni (1976), Thomas and Haras (1977), and Sonzongni, et al. (1978)
Estimated average (Monteigh and Sonzongni, 1976)
Estimated based on average U.S. loading per km shoreline
Estimated by Apmann (1975)

-------
of Seibel, et al., (1976), and Thomas and Haras (1977). These estimates
vary widely and reflect the substantial difficulty in estimating this
source of solids. Monteith and Sonzogni, (1976) gave shoreline erosion
loads by county for the United States shoreline. Erosion varies widely
from county to county, with Lake Michigan having the highest loading
rate per kilometer of shoreline, followed by Superior, Erie, Ontario,
and Huron respectively. The range of shoreline erosion loads is shown
in Table 8. With respect to the character of the eroded material,
Monteith and Sonzogni (1976) report that of the total average annual
volume of shoreline material eroded, 53% is estimated to be "sandy
material," 34% is estimated to be "loamy material," and 13% is estimated
to be "clayey material." On a lake by lake basis, Monteith and Sonzogni
(1976) estimate the values shown in Table 9.
TABLE 9
ESTIMATED PERCENT OF SOIL TYPES
IN SHORE EROSION LOADS
(From Monteith and Sonzogni, 1976)


Percent

Lake
Sand
Loam
Clay
Superior
17
43
40
Michigan
75
23
2
Huron
57
43
0
Erie
44
40
16
Ontario
15
74
11
Total
53
34
13
Tributary loading of solids are estimated by Sonzogni, et al-,
(1978) and also tend to be quite variable due to the difficulty in
estimating input loads from a tributary where only occasional grab
samples of solids concentrations are available. Estimates of tributary
loads are obtained by a ratio of the Canadian tributary drainage areas
given in IJC (1978). Table 8 shows the estimated loading ranges.
As shown in Table 8, shoreline erosion loads relative to tributary
loads are most significant for Lake Michigan and Table 8 indicates that
for Michigan, about 75% of the shoreline erosion load is of a sandy
material. The shoreline erosion loads are, therefore, of significance
and reflect an Important source of solids to the lakes. However,
because of the sandy nature of these solids, the impact is probably more
local and near-shore due to high settling velocities. The range in the
estimates should be carefully noted and variations in the loadings for a
given year and specific location may be expected.
Table 10 shows the areal solids loading rate of fine grain solids
used in the model calculation below. These loadings were arrived at by
(a) determination of solids concentration in the lake giving the term QM
in Eq. (43), (b) evaluation of the net depositional loading of solids
68

-------
TABLE 10
SOLIDS LOADING, CONCENTRATION AND NET SOLIDS	LOSS RATES USED IN MODEL
Lake/ Fine Grain Solids Overflow Solids	Net solids Net Sed. Net Sed.
Region	Loading Rate	Rate Cone.	Loss Rate Depos.Rate Vel.(4)
2(1)	2
g/m -yr	m/yr. mg/1	m/yr(m/d) g/m -yr mm/yr
Superior
98
0.8
0.5
195(0.53)
98
0.41
Michigan
69
0.8
0.5
137(0.38)
69
0.29
Huron
109
3.4
0.5
213(0.58)
107
0.45
Saginaw Bay
146
10.3(2)
8.0
8(0.02)
64
0.27
Erie-West
3762
101.1(3)
20.0
87(0.24)
1740
7.24
Central
1414
66.8(3)
5.0
216(0.59)
1080
4.52
East
1658
146.5(3)
5.0
185(0.51)
927
3.87
Ontario
229
11.0
0.5
447(1.22)
224
0.93
(1) Includes
upstream
loads and turbulent exchange loads


(2) Includes
turbulent
exchange with Lake Huron


(3) Includes
turbulent
exchange between
Lake
Erie basins


(4) Using porosity of
surface sediment :
= 0.9
throughout p
G
= 2.4 and _

and Eq. (9); porosity = 0.85 and 0.82 for 2-4 cm and 4-6 cm sediment
layers respectively.
69

-------
(discussed below) which yields the quantity w m in Eq. (43), (c)
estimation of external load from the previous?y discussed source so that
a steady state consistent mass balance was achieved. Actually, in the
toxics model, the external load of solids is not really needed; only the
concentration and net depositlonal velocities are required. The
loadings shown however in Table 10 are within the reported ranges from
Tables 8 & 9.
Suspended Solids Concentrations
Open lake suspended solids concentrations were difficult to
estimate since data reported in the U.S. EPA STORET system included a
lower bound of 1.0 mg/ thereby resulting in apparently unrealistically
high average levels. Turbidity levels appeared more realistic based on
solids concentrations measured at low levels for Lake Ontario by Nriagu,
et al. (1981) who reported average open lake concentration of 0.5 mg/JI.
Torrey (1976) reported that of 170 samples collected, 10 km offshore in
Lake Michigan, only 20% were greater than 1 mg/Jl of suspended solids.
Also, for southern Lake Michigan, Chambers and Eadie (1981) give results
for a cross section from Grand Haven, Michigan to Milwaukee, Wisconsin
during August, 1979. Excluding the solids concentration very close to
the bottom, the average suspended solids concentration in the water
column was 0.8 mg/ with a standard deviation of 0.47 rag/H. Finally,
IJC (1979) indicated that solids concentrations for the open water of
Lake Superior is about 0.2 mg/. Average turbidity levels as reported
in the STORET data base range from 0.3-0.6 (JTU) for Lakes Superior,
Michigan, Huron, and Ontario, and of course range upward to 20-25 JTU
for the more turbid western and central Lake Erie. Considerable
variation from year to year and for near shore regions throughout the
year are to be expected. Hall (1980) has examined these variations for
southern Lake Michigan and Figure 23 is a plot of the year to year
variation in turbidity at the Chicago water intake.
Also, Hall (1980) in an analysis of the relationships between
suspended solids and turbidity data for Lake Michigan shows that for
turbidity less than 1 JTU, the solids concentrations is almost linear to
the turbidity. As a result of these reported levels and from a balance
between reported net depositlonal fluxes of solids, suspended solids
concentration that were used are shown in Table 10. It should be noted
that overall, the data on open lake suspended solids concentrations are
generally weak and more data need to be obtained.
Sediment and Sedimentation Rates
A very large literature exists for the sediments of the Great
Lakes. There is no intention here to exhaustively review that
literature. For the purposes of the overall preliminary model, some
ranges of net sedimentation velocity and sediment solids fluxes and
porosity are sufficient. Table 11 summarizes the reported values for
the open Lakes and some regions of the Lakes. As noted, the range
within a lake is very large reflecting heterogeneous regions of
deposition. The Western and Eastern basins of Lake Erie are shown to
have the highest flux and net sedimentation rates. These fluxes and
sedimentation velocities generally reflect the fine grain solids.
70

-------
TABLE 11
REPORTED RANGE OF SOLIDS FLUX AND NET SEDIMENTATION RATES
FOR GREAT LAKES
Range of Range of
Solids Fli^to Sediments Net Sedimentation
Lake		g/tn -yr		Rate (mm/yr) Reference
Superior-N.W.Basin
155-3040
0.6-2.8
1
Central
50- 255
0.2-1.0
1
Southern
25- 700
0.1-2.3
1
Michigan
60-1015
0.2-3.2
2
Huron -
65- 495
0.3-2.2
3
Georgian
35- 90
0.2-0.4
3
Saginaw Bay
780
3.1
3
Erie - West
830-6450
1.7-7.4
4
Central
150- 790
0.8-1.7
4
East
40-3790
0.2-8.5
4
Ontario
85-1225
0.3-2.2
5
1.	Kemp, et al. (1978)
2.	Edington and Robbins (1976)
3.	Kemp and Harper (1977)
4.	Kemp, et al. (1977)
5.	Kemp and Harper (1976)
71

-------
Porosities of sediment samples also vary widely. For example, Robbins
and Edgington (1975) for Lake Michigan show porosities of 0.9 at 1 cm to
0.86 at 32 cm for one core and 0.86 at 1 cm to 0.75 at 32 cm for another
core.
With the estimate of solids loading and concentration and the over-
flow rate, q, the net loss rate of solids w was computed from Eq. (72) .
In order to "close" the solids balance, the net depositional flux calcu-
lated from this solid balance was compared to estimates from sediment
analyses and budget estimates as shown in Table 11 and reported for Lakes
Superior, Huron, Erie, and Ontario by Kemp, et al. (1976, 1977a,b, 1978),
Evans, et al. (1981) and for Lake Michigan by Edgington and Robbins
(1976). The complete steady state solids balance, resulting net loss
rates from the water column and net sedimentation are given in Table 10.
The net loss rates range from 8 m/yr. for the shallow Saginaw Bay to 487
m/yr. for Lake Ontario.
PLUT0NIUM-239 CALIBRATION
With the estimates of the net loss rate of solids and associated
concentration, the time variable model given by Eqs. (22) and (23) was
applied to the fate of plutonium in the Grat Lakes using the settling
velocity of the particulates as a parameter and calculating the resus-
pension velocity from Eq. (72) to maintain the solids balance. The
settling velocity, w , was set at one of three levels: w =w (i.e. no
resuspension) w = m/d, and w =5.0 m/d.	3 n
a	a
The partition coefficient for plutonium must also be specified.
Table 12 summarizes some of the reported coefficients. The reported
range for algae, inorganic solids and marine sediment (Noshkin, 1972;
Hetherington, et al., 1975; Marshall, et al., 1975; Thompson, 1975;
Hetherington, 1978; as well as from Wahlgren and Nelson, 1976 and
4 5	6
Edgington, et al., 1979 is from about 10 " to 10 ./kg. Hetherington
(1978) showed some dependence of the partition coefficient with particle
size and reported values of about 10 2-/kg for particles from 1-10 pm
4.5
and then a decrease to about 10 * for particles from 10 um to about 70
pm. As a result of the range of reported values, levels of 150,000-
400,000 and 10^ /kg were investigated as part of the sensitivity analy-
sis to partition coefficient.
For the calculations, the external plutonium input was as given by
Wahlgren, et al. (1981) with a constant loading from 1973 to 1977. Fig-
ure 24 shows the time history of the plutonium load. As shown, peak
loadings occurred in the late 1950's and early 1960's corresponding to
increased weapons testing during that period. Unfortunately, water col-
umn data were not collected during this time, but began in 1971. Sedi-
ment core data have, however, been obtained in Lake Michigan and as noted
below can form a basis for calibrating the time variable model over the
entire load history. Only the atmospheric input was considered.
Wahlgren, et al. (1981) discuss the potential importance of the plutonium
contribution from watershed runoff although lack of data on tributary con-
centrations precludes an accurate assessment of this source. At 0.5-1.0
fci11 in tributary waters (Wahlgren, et al., 1981),
72

-------
TABLE 12
SOME PARTITION COEFFICIENTS FOR 239PU
Partition
Coefficient
Bq/kg(d)*Bq/ Type and or Location	Reference
104-5-105'5 Marine Sediment; Irish Sea Hetherington (1978)
10^ -10^ Algae, seston; Rocky Flats,
Utah	Thompson (1975)
4 5 5
10 * -10 Particulates, Phytoplankton;	Marshall, et al.
Great Lakes	(1975)
4.5
10 * Algae; No. East Irish Sea	Hetherington,
et al. (1975)
10^*3 Algae; Oceanic	Noshkin (1972)
73

-------
ffi

o
Ui
*
<
i-
S
<
*
o
o
<
0
1
o
I-
<
3
>-
b
6
m
oc
D
V-
ffi
o
z
<
UJ
-
z
o
I
1963 ^
1965
1964
1960
1966
1967
1968
1969
1970
1972
1973
1974	1975 ' 1976	1977	1978
Figure 23 . Long terra variations in turbidity at Chicago water intake(after Hall, 1980).

-------
40
CM,
30
Ln
O
z
5
<
o
_i
3
Q.
o
cv
0)
C3
CJ
20
10
1953
	|	
1957
I
1961
1965
1969
1973
==
1977
YEAR
2 39 240
24. Annual areal deposition of	' Pu loading to fireat
Lakes (from Wahlgren, et a 1. , 1981), with constant
loading 1973-1977.

-------
however, the runoff input ranges from 1-8% of the total atmospheric
1970's load to Lake Michigan.
The data available for calibration in the water column have been
compiled by Wahlgren, et al., (1981). For all lakes, data were obtained
beginning in 1971, i.e. towards the end of the loading time history
shown in Figure 24. In the sediments, data on plutonium concentration
with depth have been reported for Lake Michigan by Edgington, et al.,
(1975).
The calibration procedure described above was then applied to the
fully time variable equations for the period 1953-1977 beginning with
zero plutonium concentration everywhere. Figure 25 shows the full time
history calculated for Lake Michigan under three conditions in the
settling velocity and for a partition coefficient of 400,000 Jl/kg.
Since the available data began only in 1971, particular interest centers
around the latter years where the data can be better compared to the
dynamic calculation. Figure 26 shows the results for the five lakes for
1971-1977 and the conditions of settling velocity. When attention is
focused more directly on these latter years, the calibration is clearly
not favorable for w = w , i.e. resuspension equal to zero. For Lakes
Superior and Michigan, ftiis case results in concentrations that are
substantially higher than the observed data due to the low loss rate
from the water column. For the other lakes however,the no resuspension
case underestimates the data. At a settling rate of 2.5 m/d, and
associated resuspension the results are much more favorable. The
increase in settling to 5 m/d with increased resuspension does not
result in any substantial change in the calculation in these later years
since under both cases the sediment as the primary driving force has
reached an equilibrium that is independent of the sediment interactions.
Sensitivity analyses also indicated that increasing the partition
coefficient to 1,000,000 Jl/kg and considering zero resuspension (w =
w ) does not adequately reproduce the data. The increased partition
coefficient does result in lowered water column concentration but the
dynamic behavior is not representative of the data shown in Figure 26.
Figure 27 shows the calibration to the plutonium sediment data for
Lake Michigan in 1973-1974 reported by Edgington, et al. (1975). The
sediment concentration as calculated approximately reproduces the
observed data. The introduction of sediment mixing (as for example due
to bioturbation) would smooth the sediment calculation to more
adequately reflect the observed data. Also it should be noted that the
observed data are for areas of net deposition while the calculation is
for a lakewide sediment average. The comparison then implies that the
model overestimated the mass of plutonium in the sediment. It may be
hypothesized, however, that the nondepositional areas of the lake do not
have zero concentration but may include a layer of particulate matter of
unknown thickness but at the approximate concentrations shown in Figure
27. (Edgington, et al., 1975 discuss this possibility and the reported
plutonium concentrations of surface sediment floe are similar to the
surface values shown in Figure 27.) The remaining mass of plutonium
that was not observed is then hypothesized to be contained in this layer
of particulate matter in the nondepositional zones.
76

-------
= 8

z
o
p
<
cc
H
Z
UJ
o
z
o
o
3
n,
O
CM
t
0>
CO
CM
-I
<
H
O
H
6
wnet
2.5 m/d
5.0 m/d

1953 1955
1960
1965
1970
1975 1977
TIME (Year)
2 3 g 2^0
2 5. Comparison of calculated Lake Michigan ' Pu concentration (fC^/o
in the water column to 1971-1977 data for three conditions of the
particulate settling velocity. n = 400,000 /kg, (Data from Wahlgren,
et al . , 1981).

-------
MICHIGAN
SUPERIOR
1971
Year
wa = wnet
1971
74 75
Year
 1.0
o
a
o
CM
m
CD
CO
CM
0.5
A
X
_L
-L
1971 72 73
74 75
Year
76 77
ONTARIO
s=Sept.
A= Aug.
? 0.5
1971 72
1S71 72
Year
Year
239 240
26. Comparison of calculated ' Pu concentration (fC^/) in
the water column for all lakes to 1971-1977 data for three
conditions of the particulate settling velocity.
Jl/kg. (Data from Wahlgren, et al., 1981).
7 8
tt = 400,000

-------
239,240p|| [|jCi/g(dry wt.)J
0.05
0.10
0.15
0.20
0.25
0.G
T
T
y
/
/
1.0
2.0
.s s	^ s s s f	s s
Calculated
' / ' / / s / / s	
3.0
X1
X
/
X
/
/
~
~
4.0

-i*
5.0
6.0
Key:	_Mean istd. dev.
over 1 cm depth
intervals
*=Mean 1 std. dev. w/o
open circle data
*^39 2AO
27. Comparison of calculated ~ ' Pu concentration (pC /g(d)) in the
sediment of Lake Michigan to observed data for 1973-^974. w = 2.5
m/d, it = 400,000 A/kg. (Data from Edington, et al., 1975).a
79

-------
Figure 28 shows the calculated time history of the particulate
plutonium concentration in the vater column and surface sediment of Lake
Michigan and Central Lake Erie. The concentration calculated for Lake
Michigan in the mid-1970's of 0.27 pC^/g(d) is at the upper end of the
range of values reported by Wahlgren and Marshall (1975) of 0.13 to
0.26 pC^/g(d). This may be due to an overestimation of the effective
partition coefficient. A similar comment applies to the overestimation
in the surface sediment. The calculation indicates that the water
column and sediment particulate plutonium concentration for Lake
Michigan are not in equilibrium due to the small net solids deposition
velocity. On the otherhand, for a region such as Central Lake Erie
(Fig. 28 (b)), the particulate concentrations are calculated to be in
equilibrium because of the more responsive coupling of sediment and
water column as a result of higher net depositional velocities. The
substantially lower particulate concentration for Lake Erie is coupled
to a lower dissolved concentration resulting from the increased solids
concentrations in that basin.
The relevant time variable response for the sediment is given
approximately from a simplified version of Eqs. (22 and 23), i.e.
dc TT c	w	w
	 W	a -	rs ,
-j = 77 r	 fc	+ t: f c	(73)
dt V t	H, p	H, ps s
o 1	1 r
dc w f c w	w
Scio rs	p s / ^ / \
-J = 		U	f C -  f C (74)
dt H H	ps s H ps s
s s	s r
If resuspension is neglected, i.e. w =w , then the sediment does not
interact with the water column and tfie 2wo equations are decoupled. An
approximate response time can then be readily calculated. The solution
for the sediment equation for a constant input beginning at time t=0
from the water column is:
cs - -2J a-exp-(	O	(/5)
s	s	s
Similarly, the water column is
<=- i/t"C f /H (1 - P<-a/vaym)	(76)
o a p
So that for the sediment, the approximate time to respond to one half of
an equilibrium level from an input from the water column is:
\	0.69
(t. ,J , = 		(77)
1/2 sed.	w
(ir> fps
s r
and for the water column is:
80

-------
0.8
cf-S *7
^ K
ct t 0.6
* z ? -5 
Z03
Lake Michigan
w O 0.2
< P
*5 0.1
Central
Lake Erie
55
60
65
75
80
70
YEARS
o
CM
at
O)
CO
CM
a- O
P
<
cc
i-
z
UJ
o
111
s
Q
Ui
(0
UI
O
<
u.
re

-------
Table 13 shows the approximate response times for the two cases of
Lakes Michigan and Erie. As seen, the sediment response time is about
an order of magnitude greater than the response time of the water column
for both lakes. For Lake Erie, however, the response time of both the
water column and the sediment is about an order of magnitude lower than
that of Lake Michigan. This is due to several factors associated with
239
Lake Erie: a) the more shallow depth, b) the higher fraction of Pu in
the particulate form, and c) the higher net sedimentation velocity.
The sediment for a lake, such as Lake Michigan, therefore, is esti-
mated to respond with a time frame of tens of years to external load
changes whereas for a more shallow lake, such as Lake Erie, the surface
sediment might be expected to track the water column concentration. An
equilibrium calculation using the fugacity concept of Mackay and Paterson
(1981) or of Eadie, et al (1981) between water column and sediment would
not result in a response similar to that shown in Figure 16. For example,
in the latter calculation, the water column and sediment are assumed to
be always in equilibrium with each other and, therefore, the sediment
concentration behaves in a similar manner to the water column. The cal-
culation shown in Figure 28 and as the simple equations (77) and (78) and
Table 13 show, an equilibrium assumption for a well-mixed sediment layer
of 2 cm for Lake Michigan may not be a good one. Of course, one"could
argue that the assumption of a well-mixed layer is not valid and that the
sediment-water interface is always in equilibrium. In this model, how-
ever, the well mixed assumption appears to be reasonable in the light of
the data. Nevertheless, the dynamic relationships between the sediment
and the water column is sensitive to the assumption of the depth of the
well-mixed sediment layer.
Table 14 shows the magnitude of the resuspension velocities for each
of the Lakes or regions and the ratio of the resuspension velocity to the
sedimentation velocity. Figure 29 shows this ratio as a function of the
particulate settling velocity. These results are calculated from Eq.
(72) with the net loss of solids and sedimentation rates given from Table
10. As seen, for the range of settling velocity from 2.5-5.0 m/d, the
resuspension velocity is about 2-10 times the net sedimentation velocity
for the upper lakes and about 10-20 times the net sedimentation velocity
for Western Lake Erie. Saginaw Bay, a more shallow body of water (see
Table 7) involves a high degree of turnover of internal solids where the
ratio of resuspension to sedimentation velocities is on the order of 100-
200. This presumably reflects the larger impact of wind induced resus-
pension. The lowest ratio of w to w is for Lake Ontario.
rs s
Figure 30 shows the fluxes of plutonium for year 20 (1973) in Lake
Michigan under the three conditions on the particulate settling velocity.
82

-------
TABLE 13
COMPARISON OF APPROXIMATE RESPONSE TIMES FOR 239PU IN
WATER COLUMN AND SEDIMENT OF LAKES MICHIGAN AND ERIE
(w = w : No resuspension)
a net
Det.
Time (t )
o
yr.
Depth
(Hx)
m
Water Column
Sett.
Fract
Vel (w ) Part.
m/yra (fpo}
en
50% Response Depth
Time(t, )	(H2>
(yr)	cm
Sediment
Sedim.
Vel. (w )
mm/yr
50% Response
Time (t, )
yr
Lake Michigan 100
Lake Erie	2.9
90
20
137
200
0.17
0.67
2.6
0.1
2.0
2.0
0.3
4.0
46.0
3.4
@ tt = 400,000 pC^/kg t pC^/Jl; Michigan @0.5 mg/Jl; Erie @ 5 mg/

-------
TABLE 14
RESUSPENSION VELOCITIES
FOR DIFFERENT PARTICULATE SETTLING VELOCITIES
w =Resuspension Velocity	_ ,
rs , I v f	J	w =Sed.
w =Particula?e^et?Eng Velocity of SVel.	Ratio
Lake or Region 2.5 m/day 5.0 m/day nun/yr w /w
		rs s
Superior

1.51
3.43
0.41
3.7-
8.4
Michigan

1.64
3.58
0.29
5.6-
12.3
Huron

1.35
3.26
0.56
2.4-
5.8
Saginaw Bay

30.53
61.33
0.27
113.1-
227.1
Western Lake
Erie
68.80
144.85
7.25
9.5-
20.0
Central Lake
Erie
14.50
33.50
4.50
3.2-
7.4
Eastern Lake
Erie
11.20
25.25
2.85
3.9-
8.9
Ontario

0.89
2.80
1.02
0.9-
2.7

-------
Sag. B
12	3	4
PARTICULATE SETTLING VELOCITY (m/day)
29. Ratio of resuspens ion velocity to sedimen-
tation velocity as a function of particu-
late settling velocity.
85

-------
0.44
0 1.99 1.99
Li
77!
"w mn\
I	
T
1.11
0.08
wa =wn
(No Resuspension)
0.44
6.33 6.83 0.50
) Is ^N * **}
	2U
T
1.15
0.04
wa = 2.5 m/d
(Calibration Run)
0.44
13.72 14.18
I I I
0.46
/ / // R //S//N / /"/ /
		Sd
7i
7
1.15
0.04
Wo =5 m/d
NOTE: All Fluxes - Ci/yr
R = Resuspension Fiux
S = Settling Flux
S(j= Sedimentation Flux
N = Net Flux to Sediment
30. Calculated plutonium flux for Lake Michigan in year 20
under different particulate settling velocities.
86

-------
The outflow from the Lake is relatively small and represents only about
10% of the incoming load. Far all cases, net loss to the deep sediment
is virtually independent of particulate settling and reflects the 20 year
loading of the sediment. Also, the net input of plutonium to the sedi-
ment is not affected by the particulate settling velocity since the re-
suspension flux increases by a factor of.two to compensate for the doub-
ling of the settling velocity.
Figure 31 shows the calculated plutonium flux for the three basins
of Lake Erie for year 20 and the calibration settling velocity of 2.5
m/d. It is seen that the water column for each basin is in approximate
equilibrium. The surface sediment, however, is not in equilibrium at
year 20 for each of the basins reflecting the sediment detention times
of abut 3 years, 4 years, and 7 years for the western central, and east-
ern basins respectively. Thus, the surface sediment is still fluxing to
the deeper sediment the plutonium flux from the earlier higher loading
to the lake system. Also, in terms of total flux (and areal flux), the
surface sedimentation loss to the deeper sediment is highest for the
central basin of Lake Erie.
Additional Sensitivity Calculations
The sensitivity of the plutonium calculation was also examined
through other model calculations where in addition to varying the set-
tling and resulting resuspension velocities as in the calibration analy-
sis, and the partition coefficient was varied to evaluate the sensitivity
of the calculation.
Figure 32 shows the sensitivity of the plutonium water column con-
centration in Lake Michigan to the partition coefficient for the case of
zero resuspension, i.e. w = w . The objective of this calculation was
to determine whether an increased partition coefficient with no resuspen-
sion would equally well represent the observed data. Although the con-
centration at tt = 1,000,000 Jl/kg is approximately equal to the data, the
dynamic response indicates that it undershoots the data by 1973-1974.
In general, increasing the partition coefficient decreases the water col-
umn concentration as shown and therefore the water concentration is sen-
sitive to a one order magnitude Increase in the partition coefficient
even at the solids level of 0.5 mg/. In the sediment of Lake Michigan,
however, the sensitivity is not as marked as shown in Table 15.
The surface sediment concentration (0-2 cm) as noted varies from
0.22 to 0.31 for an approximate order of magnitude increase in partition
coefficient for the no resuspension case (w = wneC)  This range is
within the range of data as shown in Figure if. Also, for the fixed par-
tition coefficient, the variation in sediment concentration as calculated
by the model is not sensitive to the settling and resuspension condition
that was assigned. These results indicate that the sediment plutonium
data in a large lake such as Lake Michigan is not sensitive enough to
distinguish between settling and resuspension characteristics. However,
the approximate 30% change in calculated particulate concentration as a
result of tbe approximate one order of magnitude change in partition co-
87

-------
0.11
0.84	0.89 0.05
u > i ^ ) ) )) ) > >	/1
0.07
S> 0.09
LAKE ERIE WESTERN BASIN
0.18

2.60 2.81 0.21
t i 



s"W"
SdT 0.81
LAKE ERIE CENTRAL BASIN
0.04
1.52

)))}))'*> if ) ) )
 R
1.51 -0.01
1 i
V' W'
V 027
0.01
NOTE: ALL UNITS- C,/yr
R s RESUSPENSION FLUX
S= SETTLING FLUX
N- NET FLUX TO SEDIMENT
Sj= SEDIMENTATION FLUX
*- INCLUDES HORIZONTAL
EXCHANGE FLUX
0.06
LAKE ERIE EASTERN BASIN
31. Calculated plutonium flux for Western Central and Eastern
Lake Erie in year 20; w = 2.5 m/d.
a
88

-------
00
v>
O
3
a
o
04
a>
CO
CM
O
P
<
oc
t-
z
HI
o
z
o
o
oc
UJ
H
<

<
I-
o
I-
7T =150,000
\7T =400,000
7r = 1,000,000
j
1953 1955
1960
1965
TIME (year)
1970
32. Sensitivity of water column plutonium concentrations to partition
coefficient; w = w
net

-------
TABLE 15
SENSITIVITY OF PLUTONIUM SEDIMENT CONCENTRATION TO SETTLING VELOCITY AND PARTITION COEFFICIENT -
LAKES MICHIGAN AND ERIE, 1973 CALCULATED VALUES
Lake Michigan
239 240
Calculated Sediment ' Pu Cone. (pC^/g)

0-2 cm
2-4 cm
4-6 cm
tt = 150,000 /kg)



w = w
a net
.22
.017
.0007
n=l,000,000(/kg)



w = w
a net
.31
.030
.0014
tt = 400,000(/kg)



w = w
a net
.29
.25
.0011
w = 2.5 m/d
a
.30
.033
.0017
w = 5.0 m/d
a
.30
.033
.0017
Lake Erie
239 240
Calculated Sediment ' Pu Cone. (pC^/g)


0-2 cm


2-4 cm


4-6 cm


West
Cent.
East
West
Cent.
East
West
Cent.
East
tt = 150,000 /kg









w = w
a net
.059
.063
.078
.091
.095
.084
.094
.075
.044
IT = 1,000,000 /kg









w = w
a net
.016
.045
.060
.036
.078
.074
.046
.066
.044
ir = 400,000 /kg









w = w
a net
.026
.049
.053
.051
.082
.080
.062
.068
.058
w = 2.5 m/d
a
.018
.046
.053
.031
.077
.074
.040
.064
.044
w = 5.0 m/d
a
.017
.046
.053
.030
.076
.073
.038
.064
.044

-------
efficient may prove useful in calibration of sediment data with variable
partition coefficient.
Figure 33 shows the dynamic behavior of the plut6nium water column
concentration under the two conditions on partition coefficient, again
for the case of zero resuspension. The upper panel indicates the behav-
ior of the dissolved fraction which varies as might be expected, i.e.
increasing the partition coefficient sorbs more plutonium on to the
solids and therefore reduces the dissolved concentration. As seen in the
lower panel, the effect of increasing partition is to increase the net
loss out of the water column and thereby reduce the total. The middle
panel, however, shows a rather peculiar behavior in the particulate form.
This form of plutonium is increased with increasing partitioning until
abut year 14 where a cross-over occurs and the particulate plutonium
under the higher partitioning is less than that under the lower parti-
tioning. This appears to be due to the overall net loss of total pluto-
nium for the higher partitioning and resulting reduced dissolved pluto-
nium to sorb onto the particulates.
Table 15 also show the sensitivity of the calculated plutonium sedi-
ment concentration for Lake Erie. As indicated, for a fixed partition
coefficient of 400,000 1/kg, the more interactive Western Basin sediment
is sensitive to the settling and resuspension characteristics whereas the
Central and Eastern Basins are not. Resuspension in the Western Basin
reduced the surface sediment plutonium concentration by about 30%. The
penetration into the sediment of the Western Basin is illustrated in
Figure 34 where again the sensitivity to including resuspension is not
marked. Also, the calculations shown in Table 15 are interesting since
they indicate that for 1973, the higher partition coefficient of
1,000,000 /kg resulted in the lowest concentration in the sediment in
almost all basins and sediment depths. One would have expected (as in
Lake Michigan) that increasing the partition coefficient would sorb more
plutonium onto the sediment solids whereas the opposite effect is calcu-
lated for Lake Erie. This appears to be due to the dynamic, nonsteady
state nature of the loading to a system such as Lake Erie. Continuing
the calculation under a constant loading would according to the steady
state theory result in a return of surface sediment concentrations at a
lower level with lower partition coefficient. Figure 35 shows, however,
that this is not the case since for an additional 40 years of constant
loading (year 20-60), the surface plutonium concentration at the higher
partion coefficient is still less than at the lower partition coefficient.
The only explanation for this behavior is that the response of the
Western Basin is still a nonsteady state response and that the relatively
simple behavior of the steady state model is not always appropriate.
This appears to be the case especially when it is recognized that the
detention time of the surface 2 cm sediment of Lake Huron is about 36
years and for Lake Michigan about 69 years. Figure 33 already displayed
the rather anamolous behavior of the particulate form for Lake Michigan
and since Western Lake Erie is responding to the long term response of
the upper Lakes, one can not readily apply the simple reasoning of the
steady state model to the time variable nature of the entire system.
91

-------
10
5
0
2.0
1.0
0
10
5
0
i
Be]
tr
LEGEND: 7T= 150,000	
IT = 106	
5
10
20
TIME (years)
avior of Lake Michigan plutonium water column concen-
tion under two partition coefficients; wfl => wnet*

-------
wa =*2.5 m/day
0.10
,0-2 cm
E
o>
2-4 cm
a 0.05
3
a.
0>
m
CM
10
TIME (years)
15
20
0.10 -
E
o>
N
O
a
0.05 -
a.
0>
m
CM
^ wnet
0-2 cm
2-4 cm
10
TIME (years)
34. Calculated sediment plutonium concentration for Western
Basin, Lake Erie; it = 400,000 J./kg.
 3

-------
0.20
0.15
n**
0)
\
o
a
x
S
a.
0.05
7T = 10
5 10 15 20 25 30 35 40 45 50 55 60
0
TIME (years)
35. Long term calculation pf plutonium concentration in surface sediment
of Western Lake Erie for two partition coefficients, w = 2.5 m/d.

-------
Conclusions
The following conclusions may be drawn from the calibration of the
239 240
model to the. ' Pu data and the associated sensitivity analyses.
(1)	Particulate settling velocity of 2.5 m/d to 5 m/d with resulting
resuspension velocity to maintain a solids balance is operative through-
out the Lakes. The resuspension velocity should be viewed as a parameter
of the model representing the complex interaction of near shore resuspen-
sion, horizontal transport and deposition and open lake resuspension and
transport. Chambers and Eadie (1981) in their work on particulate matter
in Lake Michigan report transient resuspension phenomena vertically and
horizontally that tend to result in large scale resuspension of particu-
lates .
(2)	The result of the inclusion of the resuspension phenomena is to
retain concentrations of plutonium in the water column over longer
periods of time than would occur without the mechanism. This appears to
be consistent with the observed data.
(3)	The calibration to the observed sediment data in Lake Michigan
indicates that some sediment mixing between the 2 cm layers may be
occurring as a result of mechanisms such as bioturbation.
(4)	The sensitivity analyses indicate that the dynamic behavior of
the water column concentration of plutonium is most sensitive to varia-
tions in settling and resuspension velocities, and partition coeffi-
cients. The 0-2 cm sediment plutonium concentrations do not vary sig-
nificantly as a function of settling and resuspension characteristics or
partition coefficient indicating that data over the 0-2 cm depth is not
a sensitive calibrating data set for use in determining model parameters
of settling and resuspension.
(5)	The time variable calculations result in system behavior of a
chemical such as plutonium that is different than the steady state. For
example, the calculations indicate that the particulate plutonium de-
creases with increasing partition coefficient for certain Lakes (e.g.
Western Lake Erie).
95

-------
SECTION 8
PCB MODEL OF GREAT LAKES
239 240
The analysis of suspended solids and ' Pu can also be applied
to calculate PCB levels in the Lakes as an example of the model
framework utility. However, there is a great deal of difficulty in
calculating a mass balance for PCBs in the Great Lakes in spite of the
preceding analyses. This is due to a) uncertainty in input loads, b)
uncertainty in the significance of certain PCB mechanisms such as
volatilization, and c) a wide range of reported levels of PCB in the
water column. The calculation of PCB in the water column and sediment
is, at best, therefore an order magnitude calculation and, therefore,
239,240
quite dissimilar to the ' Pu results discussed previously.
CONTEMPORARY EXTERNAL PCB LOADS
In these calculations, estimates are made of the contemporary PCB
input loads (i.e. approximately within the past 5-10 years). A complete
load history of PCB input over the past 30 years for the Great Lakes
system is not available at the present time.
The principal external sources of PCB to the Great Lakes are:
a) atmospheric input from precipitation and dry deposition,
2)	tributary inputs representing up-basin discharges of PCB and
subsequent transport to the Lakes,
3)	direct inputs of municipal and industrial PCB loads to the
Lakes.
Atmospheric Input
The concentration of PCB in precipitation over the Great Lakes has
been determined by Murphy and Rzeszutko (1978) and Strachan and Hunealt
(1979). These results and the data reported by Wells and Johnstone
(1978) are summarized in Table 16.
As seen, the mean concentrations differ by almost a factor of five
which may reflect sampling or analytical variations. (The reported
concentration for the East Coast of Scotland is included for reference.)
Strachan and Hunealt (1979) reported significantly different levels for
the various stations located in the Lake's basins, i.e. mean values of
26 ng/fc for Superior, 11 ng/2. for Huron, 9 ng/i for Erie, and 32 ng/JI
for Ontario. Because of the variability in reported values of PCB
precipitation concentration, a range of 10-100 ng/ was chosen for an
input load estimate.
Dry deposition has been estimated by Eisenreich, et al. (1979) for
Lake Superior. In their estimate^ 10% of the measured PCB air
concentrations (range 0.1-10 ng/m ) was assumed to be in the particulate
form and a deposition velocity of 0.005 m/s was used. The inpvjt of PCB to
Lake^Superior then from dry deposition was e^gi^ated at 0.1*10 to
1*10 kg which for a surface are^ of 8.21*10 m is an areal loading
of from 0.12 to 1.2*10 g PCB/m -yr. This range in the areal
96

-------
TABLE 16
SOME REPORTED CONCENTRATIONS OF PCB IN PRECIPITATION
Concentration
(ng/)
Location	Mean	Std. Dev.	Reference
Lake Michigan



(35 samples)
111

(1)
Lakes Superior,



Huron, Erie,



and Ontario
21
30
(2)
East Coast
Scotland	15	-	(3)
(1)	Murphy and Rzeszutko (1978)
(2)	Strachan and Huneult (1979)
(3)	Wells and Johnstone (1978)
97

-------
TABLE 17
ESTIMATED RANGE OF CONTEMPORARY TOTAL PCB LOADING (kg/yr)
Lake
Atmos-
pheric
(a)
Tribu
tary
Tb>
Mun. &
Ind.
(c)
Total
Atmospheric Load
as % of Total
Superior
60-
7550
630-
1890
5-
60
1390-
-9500
28-92
Michigan
530-
-5310
460-
1380
70-
700
1060-
-7390
20-91
Huron
310-
-3080
410-
1510
5-
80
730-
-4670
16-88
Saginaw Bay
30-
- 330
270-
530
5-
50
310-
- 910
5-55
Erie-West
30-
- 280
100-
300
160-
1620
290-
-2200
2-52
-Central
140-
-1450
80-
220
40-
450
260-
-2120
17-92
-East
60-
- 580
60-
160
10-
100
130-
- 840
19-89
Ontario
180-
-1830
330-
990
130-
1260
640-
-4080
7-80
(a)	Atmospheric loading range: precipitation, 10-100 ng/1; dry
	_ C	J
deposition, 1-2*10 to 1210 g/m -yr.
(b)	Tributary loading @ 10-30 ng/1, except Saginaw Bay where
tributary input data were directly available.
(c)	Mun. & Ind. direct point source loading @ 0.1-1.0 ug/1 @ municipal
direct point source flows.
98

-------
deposition rate was used for each of the segments in the model. Table
17 presents the atmospheric input loading ranges (precipitation plus
dry deposition) for each of the Great Lakes and regions.
Tributary Input
Konasewich, et al. (1978) have summarized a variety of isolated data
on concentration of PCB in tributaries to the Great Lakes and that work
together with work on the Saginaw River and the Canadian rivers is
summarized in Table 18. The range is quite large for any given
tributary and reflects transient events associated with suspended solids
resuspension, probable differences in analytical techniques throughout
the Great Lakes region and, of course, variable point and non-point
source loadings to the tributaries. In view of the range in the data and
the difficulty of determining, in detail, the effect of each upon basin
loading, it was decided to assign a range of concentration from 10-30
ng/ to the tributary flows into each Lake or region. The resulting
range of tributary loading by segment and for the Lakes as a whole is
shown in Tables 17.
Municipal and Industrial Input
Data on the concentration of PCBs in municipal and industrial point
sources throughout the Great Lakes have been summarized by Konasewich, et
al. (1978). Again, the range of reported concentrations is wide (from
about 0.1-100 ug/). Also, Mueller and Anderson (1978) in a survey of
data on PCB in municipal plants (including Canadian plants in the Great
Lakes basin) reported a range in average concentration from <0.2-1.2 ug/.
Given the range in reported concentrations, and the unavailability of any
detailed reliable data base on individual point source inputs directly to
the Lakes (as opposed to the tributary inputs which include up-basin point
sources), a range of concentration of PCB from 0.1-1.0 ng/4 was used.
This range was applied to the estimated municipal point source discharge
flows directly entering the model segments and the totals are shown in
Table 17.
PCB MASS BALANCE
As noted in Table 17, the range in the total input PCB loads is
consequently estimated to be about a factor of 5-8 from lowest to
highest estimates depending on assumptions made regarding PCB levels in
precipitation and loading due to other sources, such as tributary,
municipal, and industrial inputs. Also, the time history of all of the
PCB inputs is not known with certainty. Accordingly, in this
computation, the inputs are held steady at the two levels shown in Table
17 and the results therefore are reflective of a range of concentrations
for a range of input loads.
The partition coefficient was assumed at 100,000 /kg (Di Toro, et
al., 1982a; Richardson, et al., 1983; Thomann, 1981) throughout the
Lakes. As indicated by both Di Toro, et al., (1982a) and Eadie, et al.
(1983), the PCB partition coefficient may be a function of the solids
99

-------
TABLE 18
SOME REPORTED PCB CONCENTRATIONS IN GREAT LAKES TRIBUTARIES
PCB Cone,
on Susp.
Lake or Total Water Solids
Region	ng/1	ng/g	Remarks
Reference
(a)
SUPERIOR
27
20
(10- 30)
MICHIGAN
Platte R.
15
HURON
Cheboygan R. 500
Saginaw R.	74
ERIE
Grand R.	2.6.65
84
(20- 370)
20
( 8- 30)
60
(10- 330)
Calc. from reported trib.
load of 1740 kg/yr.
Mean and range of Canadian
tribs. (1975)
Aroclor 1254
1979 mean and range
(1
(2
(1
(1
(3
Mean and range of Canadian (2
tribs. (1974)
Mean and range of Canadian (2
tribs. (1975)
Mean and range of Canadian (2
tribs. (1975)
Mean  95% limits, 9 samples,(1
(1976)
Cuyahaga R.
39 -589

1973 data

(1)
p. 28
Tribs. to






Cuyahaga R.
48 -482

1973 data

(1)
p. 28
Agricult.






Plots
38

1975-1976 data

(1)
p. 35

ND-110






25

1976-1977 data

(1)
p. 35
ONTARIO

194
Mean and range of
Canadian
(2)
p. 75


( 2-1800)
tribs. (1974)



Oakville Cr.
3.51.2

Meant 95% limits,
9 samples,
(1)
p. 39
p.	215
p.	75
p.	289
p.	164
p.	75
p.	75
p.	75
p.	39
(1976)
(a) (1) Konasewich, et al. (1978)
(2)	Frank (1977)
(3)	U.S. EPA Grosse lie Laboratory
100

-------
concentration and at the high solids concentration in the sediment may
decrease by one to two orders of magnitude or more. The sensitivity of
the calculation to a solids dependent partition coefficient is discussed
in Section 10.
The PCB volatilization transfer rate for PCB was estimated using
the general approach of O'Connor (1982). A Henry's constant of 0.114 mm
Hg/mg/s, and a 5 m/s wind were used from which the liquid film
coefficient is 0.11 m/d and the gas film coefficient of 71.4 m/d can be
calculated using 1254 PCB. The lake-atmosphere exchange process is then
liquid film controlled and for this work an overall exchange rate of 0.1
m/d was used. In order to show the effect on the calculation of
volatilization at this rate, a zero exchange was also used.
The results of the four conditions (high and low load levels, with
and without volatilization) after running the preceding calibrated model
for 20 years to an approximate steady state are shown in Figures 36 and
37. Zero initial conditions were assumed throughout. The water column
calculations shown in Figure 37 can be compared to only a few
contemporary measurements of PCB concentration. Past reported data have
often fluctuated by an order of magnitude. For example, results for
Lake Ontario were reported in 1972 at 55 ng/ (Haile et al., 1972) but
were later questioned by Veith (1976a, 1976b) who indicated that the
actual value may be only on the order of several ng/. For Lake
Superior, Swain (1978) reported values for open waters (in 1974-1976) at
5 ng/ji, Eisenreich, et al (1983) reported lakewide average levels of 1.3
ng/, (1978), 3.6 ng/ (1979), and 0.9 ng/2, (1980), and Rice, et al.
(1982) reported values in the range of 1-11 ng/ for 1979-1980 in Lake
Michigan. The model results shown in Figure 36 range from 3 to 9 ng/
for the upper load level without volatilization of 0.25 to 0.5 ng/Jl for
the lower load level with volatilization. Comparison to the very
limited water column data indicates that the upper load level without
volatilization overestimates the data in the open lake waters. The
effect of volatilization of PCB as indicated in Figure 36 is to reduce
the steady state water column concentration by 50-70% except for Lake
Erie where the reduction due to volatilization is about 30%. This
reflects the higher fraction of PCB in the particulate phase for Lake
Erie due to the higher solids concentration. THe inclusion of
volatilization also has a significant effect on the time to reach
equilibrium. For example, for Lake Michigan at the upper level of
loading without volatilization, the time to equilibrium in the water
column is greater than 20 years in contrast to less than 10 years when
volatilization is included.
The comparison to sediment PCB data as shown in Figure 37 is
complicated by different years of sampling of the surface sediment.
Table 19 lists the reported PCB surface sediment concentrations and as
noted, the sampling dates vary from 1968 for Lake Ontario to 1978-1980
for Saginaw Bay. To order of magnitude, the reported data are in the
range from 10-100 ng/g(d) with some indication of higher concentrations
in lower lakes although as noted the reported data for Lakes Erie and
Ontario are for 1971 and 1968 and may be reflecting higher loadings
101

-------
800
600
400-
= 600
ui 400
(2)

SUPERIOR
800r
600-
400
200
800h
J AJ

800r
600
400
101=73
(8)
_Efca_
HURON
(7)
soor
west
(9)

(8)
CTrra
(8)

central
ERIE
east
Extended Load
Condition
Volatilization Rate
Cm/d)
0.0
0.1
Upper Level
1
n
Lower Level
m
0
i
- Mean & Range; ( )=Ref. No.
Table 4
MICHIGAN
SAGINAW BAY
ONTARIO
36. Calculated water column total PCB concentration (ng/JO for conditions on external
load (see Table 17) and volatilization rate.
102

-------
800r
800-
400-
(2)
^ j
5?
SUPERIOR
I 80
r 0
Ji 400
2 20
800
600-
400
200
(773

800
600
400
Jgfea.
<8)

west
HURON
(7)
800r
(9)

MICHIGAN
SAGINAW BAY
ONTARIO
(8)
Ik Hun.
(8)
iXzo.
central
ERIE
east
Extended Load
Condition
Volatilization Rate
(m/d)
0.0
0.1
Upper Level
1
n
Lower Level
R
0
i
- Moan A Range; ( )=Ref. No.
Table 4
37. Calculated surface sediment PCB concentration (ng/g) for
conditions on external load (see Table 17) and volatiliza-
tion rate and comparison to observed data (see Table 19).

-------
TABLE 19
SOME REPORTED PCB SURFACE SEDIMENT CONCENTRATIONS (ng/g)
Lake
Mean
Std.Dev.
Range No.
of Samples
Year
Remarks
Ref.
Superior
3.3
5.7
<2.5- 57
405
1973
0-3 cm
(1)



5-290

1977
0-0.5 cm
(2)
Michigan
9.7
15.7
< 2-190
286
1975
0-3 cm
(3)



64-160
3
1980
0-1 cm
(4)

132
48
91-201
5
-
0-1.5 cm
(5)
Huron
13
-
3- 90
174
1969
0-3 cm
(6)
Sag. Bay
118
-
2-968
59
1978-
80
(7)
Erie
-West
252
156
4-660
24
1971
0-3
cm
(8)
-Central
74
56
12-330
71
1971
0-3
cm

-East
86
85
12-320
29
1971
0-3
cm

Ontario
57
56
< 5-280
229
1968
0-3
cm
(9)
Ref. (1)
Frank,
et al.
(1980)





(2) Eisenreich, et al. (1979)
(3)	Frank, et al. (1981)
(4)	Eadie, et al. (1981)
(5)	Armstrong and Swackhamer (1983)
(6)	Frank, et al. (1979a)
(7)	Richardson (Private Communication)
(8)	Frank, et al. (1977)
(9)	Frank, et al. (1979b)
104

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prior to or during that period. As shown in Figure 37, the upper load
level without volatilization overestimates the reported values in all
Lakes except Erie. Better agreement to observed sediment data is ob-
tained at the other conditions. From the comparison to water and sedi-
ment data then, the upper level without volatilization is not considered
to be a representative condition. For Lakes Superior, Michigan and
Huron, the lower level of loading with volatilization represents the
observed data more adequately than other conditions.
As with the water column, the calculated time to equilibrium in the
sediment is markedly influenced by volatilization. For Lake Michigan,
the sediment does not reach equilibrium even after 20 years without vola-
tilization but approaches equilibrium within 20 years with volatiliza-
tion. In contrast, western Lake Erie is calculated to reach equilibrium
with volatilization in about 10 years. The observed 0-3 cm data shown
in Figure 37 and Table 19 therefore represent a long term integration of
previous load inputs and the calculations using the calibrated model In-
dicate that the range of conditions on loading and volatilization encom-
passes to order of magnitude the previous load history. The comparison
of calculated PCB sediment concentrations to observed PCB data tends to
Indicate that volatilization may be a significant mechanism although the
data do not permit a definitive conclusion. The model results do indi-
cate that if the range of present loading continues, the water column and
sediment concentrations shown in Figure 37 can be expected to continue.
Discussion
The effect of the higher solids concentrations in Lake Erie is seen
in Figure 38 where the net loss of PCB (as estimated from Eq. 63) is sig-
nificantly higher for that Lake. Eq. 63 indicates that the higher frac-
tion particulate for Lake Erie coupled with the net deposition of solids
results in a higher net loss rate of PCB from the water column. Further,
since the fraction particulate for Lake Erie is relatively high, the
resulting dissolved concentration will tend to be lower, providing at
least a partial explanation for the lower levels of PCB in the fish of
Lake Erie.
The mass balance of PCB as calculated from the model after 20 years
of steady input is shown for Lakes Michigan and Erie in Figures 39 and
40. Volatilization is included.
For Lake Michigan, it is seen that the downstream transport of PCB
is small (about 1% of the input) indicating that the PCB load remains in
the Lake and enters the sediment via net deposition. Resuspension flux
of PCB is about 50% of the incoming load and net deposition is about 30%
of the incoming load. About 65% of the incoming load is lost due to vol-
atilization. Also for Lake Michigan, the water column is in approximate
equilibrium but the sediment is not although the flux difference results
in a small change in sediment concentration so that for practical pur-
poses, the sediment can be considered at approximate equilibrium (see
also Fig. 28).
105

-------
500
w
>
I
 250
-j	O
H	W
HI	L_
Z	O
1.0
0.5
Q	=>
P	E
o	fc
<	5
QC	<
U.	Q-
100
>s
E
8 so
J 0.
t LL
LU O
ERE
38. Relationship between net loss of solids (top), fraction of PCB in
particulate form (middle) and range of net loss of PCB (bottom),
calculated from Ea. 63.	'
106

-------
694.4
1066-
v		*15.3
TTTTTT71
522.9
^}})>))})})
$3
~~r
859.7 I
3 |
)}>) A
-I
MASS BALANCE FOR LAKE MICHIGAN
26.2
333.6-
t

-*181.3
1183.7
1309.8
t Is !
1r Al * 1
'W
125.5
MASS BALANCE FOR LAKE ERIE WESTERN BASIN
97.8
444.6-
r
958.7
V	1	*45.0
1256.9 |
I
I
' t	3
CIlf* A""i"'"*
"^298.1
MASS BALANCE FOR LAKE ERIE CENTRAL BASIN
37.0
167.1
549.4
464.7
46.3
MASS BALANCE FOR LAKE ERIE EASTERN BASIN
NOTE: All Fluxes - kg/yr
R = Resuspension Flux
S = Settling Flux
S
-------
5187.1
7903.4
V
j	3952.8
I
I
6407.3
S
j22	
4728.6
T7T
f / f / f
-^117.3
J
MASS BALANCE FOR LAKE MICHIGAN
196.4
2491.8	
|	8870.5
I

9815.8
S
>)>>>>>) >> ) ,) >>>l
R -sd
p
T940>
-*-1350.9
MASS BALANCE FOR LAKE ERIE WESTERN BASIN
3473.6
753.2
, I
1
i	*-398.1
7383.5
11
Vt7
>))>>,
L
9677.1 |
S J
>)>}>>>)>)}v))))\
R ,Sh
	&5T
J
MASS BALANCE FOR LAKE ERIE CENTRAL BASIN
,274.8
1241.1
I
-X+-
3451.5
>>>)))>
4080.1
S
77777777777^
R	*
*343.7
-f2	
^610.9
MASS BALANCE FOR LAKE ERIE EASTERN BASIN
NOTE: All Fluxes - kg/yr
R = Resuspension Flux
S = Settling Flux
Sd= Sedimentation Flux
V = Volatilization Flux
N = Net Flux to Sediment
Mass balance of PCBs, Lakes Michigan and Erie, after 20 years
steady input of high level of PCB load.
108

-------
In contrast to Lake Michigan, Lake Erie in all basins and for both
water column and sediment has reached an approximate equilibrium during
the 20 year calculation period. As noted previously, (see Eqs. 77 and
78 and Table 13), the rapid equilibrium for Lake Erie is due to the more
shallow depth and the higher sedimentation velocity for that Lake. Also,
in contrast to Lake Michigan, the advective and dispersive transport out
of the Western Basin in particular is about 50% of the incoming load with
only 8% being lost to volatilization (versus 65% for Lake Michigan). The
lower flux due to volatilization is a function of the higher solids con-
centration in the Western Basin and the resulting lower concentration of
dissolved PCB available for exchange to the atmosphere. Also, in con-
trast to plutonium, the Western Basin of Lake Erie receives the highest
areal flux of PCB of the three basins of the Lake (42-312 g PCB/km^-yr).
The resulting sediment PCB concentration, however, does not differ mark-
edly from the other basins because of the higher sedimentation velocity
for the Western Basin. This can be seen from Eq. (51) where
W  /A
cTs "	(79)
s
where W /A is the net areal flux of PCB delivered to the sediment. As
net
indicated in Table 10, the sedimentation velocity for the Western Basin
is higher than the other two basins resulting in a difference in PCB
sediment concentrations of about 35%. This difference is less than the
difference in observed sediment concentrations between the Western Basin
and the Central and Eastern Basins as shown in Table 19. The observed
mean surface sediment concentration of 252 ng/g in the Western Basin in
1971 may reflect a higher loading to the basin during that time.
Conclusions
It is concluded from the application of the plutonium calibrated
model to PCBs in the Great Lakes that:
a)	the estimated upper level of present PCB loading (ranging from
4080 kg/yr for Lake Ontario to 9500 kg/yr for Lake Superior) without
volatilization is probably too high,
b)	from the available data, it is not possible, at the present time,
to distinguish the appropriate combination of loading and loss due to
volatilization,
c)	lower levels of PCB in Lake Erie are probably due to the higher
net loss of PCB from elevated solids concentrations and resulting frac-
tion of PCB in the particulate form.
d)	the response time for Lake Michigan to equilibrate to a steady
PCB load with volatilization is less than 20 years for the water column
but greater than 20 years for the sediment.
e)	the Western Basin of Lake Erie delivers the highest net flux of
PCB to the sediment of the three basins of the Lake.
109

-------
f) volatilization of PCB is significant for Lake Michigan (about
65% of incoming load) but is less significant for Lake Erie (about 8%)
due to the higher solids concentration in that lake.
110

-------
SECTION 9
PLUTONIUM AND PCB RESPONSE TIMES
PLUTONIUM
The response time of the toxic substance model applied in this re-
search has been analyzed by Di Toro, et al. (1981) who indicate that the
response is composed of two parts following a load decrease: a rather
rapid reduction in the water column due to initial water column-sediment
equilibration and a much slower change in the water column due to the
removal mechanisms and the water column-sediment interactions. The re-
sponse time is therefore a function of how long the load into the lake
has been occurring with consequent transport of the toxicant to the sedi-
ment. If there is no sediment interaction, then, of course, the water
column response depends only on the net settling velocity and other
losses. With sediment interaction and considering the load to have been
discharged over a time sufficient to contaminate the sediment then the
water column will continue to receive a flux from the sediment and re-
sponse times will be lengthened.
The calculated response times for plutonium and the five Lakes under
two conditions on the water column - sediment interaction are shown in
Figure 41. These plots were calculated assuming that at the end of 1973
(i.e. at the end of the 20 year loading pattern), the external input of
plutonium is eliminated; the results, therefore, represent the responses
due to an instantaneous elimination in the external load. The concentra-
tions shown at t=0 are those at the end of 1973. The response times in-
clude the effects of hydraulic residence, vertical settling of particu-
lates and interaction with the sediments.
The most striking aspect of these calculations is the range in re-
sponse times under different conditions on sediment resuspension. For
example, for Lake Michigan, if no sediment resuspension is included (i.e.
w = w ), the 50% response time (i.e. the time to reach one half of the
a net	r
initial value) is less than 5 years and the plutonium clears out
rapidly. With resuspension from a 2 cm sediment layer; however, a
condition used in the preceding solids and plutonium balance, the 50%
response time is extended by about an order of magnitude. In Central
Lake Erie, with the sediment as a sink (no resuspension), the 50%
response time is less than one year; whereas with suspension, the
response time increases to greater than 5 years.
Note that these response times are markedly different than the times
associated with the calculated plutonium history during the period of
1953-1965. Figure 24 shows a peak load in 1963 with a rapid decline by
almost one order of magnitude within about 8 years. The water column re-
sponse shown in Figure 25 paralleled this decline but levelled off as a
result of the sediment resuspension included in the calculation. Also
Figure 17 shows that for Lake Michigan the sediment particulate concen-
tration reached an approximate equilibrium by about 1965.
Ill

-------
1.0
SUPERIOR
s
O
0)
0
M
z
s
D
-I
O
o
HURON
5
TIME (Yr)
0.5
MICH GAN
\


I

\

\



PRIP
ONTARIO
10 0
TIME (Yr)
TIME (Yr)
5
TIME (Yr)
239 Pu Load =0.0
Initial Year is 1973
	wa =2.5 m/d
	wa = wnet
TIME (Yr)
41. Calculated time history for * Pu load reduced to zero after 1971 for two conditions
on water column-sediment interaction: w = w (resuspension = zero) and w - 2,5 o/d.
an	a

-------
ECB
It Is also informative to simulate the response of PCB levels in the
Lakes due to a reduction in loading after the water column sediment have
reached the levels shown in Figures 36 and 37. Such a simulation for the
upper load level is shown in Figures 42 and 43. In this calculation, all
solids and sediment Interactions are as previously used for the plutonium
model where resuspension is Included. The external PCB load is assumed
to drop to zero following the attainment of equilibrium. The two condi-
tions used in the simulation Include the case of no volatilization of PCB
and a volatilization exchange rate of 0.1 m/d. As shown in Figures 42
and 43 for the water column and sediment respectively, the effect on the
response time of volatilization is marked. For example, for Lake
Michigan, the time to decline to 50% of the intial concentration varies
from 15-20 years without volatilization to 1-2 years with volatilization.
The relatively rapid response of Lake Erie under both conditions is also
clearly indicated by Figures 42 and 43. It can also be noted that the
sediment concentration decline parallels the water column concentration.
A comparison of these response times can be made to the response of fish
concentrations of PCB (IJC, 1981). For eastern Lake Michigan bloaters,
the time for PCB concentrations to decline by one-half beginning in 1972
is about 5 years. This decline may be presumed to reflect a reduction
in external load. Form this comparison, it is concluded that volatiliza-
tion of PCB is occurring at an exchange rate of approximately 0.1 m/d for
Lake Michigan.
Conclusions
It is concluded from these calculations of response times that for
large lakes such as Michigan where response times are relatively long, a
water column/sediment equilibrium model is not appropriate since the sed-
iment response time is markedly different than the water column. The
inclusion of sediment resuspension and interaction increases the response
time of a nonreactive but particulate sorptive substance such as pluto-
nium by about an order of magnitude over the case where resuspension is
assumed to be zero.
For PCB, the response times due to load reduction of external
sources of PCB may vary by an order of magnitude depending on the magni-
tude of the volatilization exchange rate; 50% response times vary from a
few years with volatilization to 5-10 years or longer without volatili-
zation. Comparison of these response times to observed declines in con-
centrations of PCB bloaters indicate that volatilization of PCB is occur-
ring at an exchange rate of about 0.1 m/d at least for that lake.
113

-------
SUPERIOR
_L
o 5 10 15 20
Years
10'
101
161
HURON

5 10 15 20
Years
101
10
10 1
west
central
east
"\
\
\
N
S
1 1
\
\\
\ N.
\
\
i	k	1	
\ ^
 1 1_
0 5 10 15 0
5 10 15
Years
5 10 15 20
MICHIGAN
\
f- s
10 15 20
Years
10'
10*
10
-1
SAGINAW BAY
10 15 20
Year-.
10
10'
JO
r 1
ONTARIO
PA

5 10 15 20
Years
	Volatilization=0.0
	Volatilization = 0.1 m/ d
42. Calculated water column PCB concentration response to an instantaneous drop in upper
level PCB load at time t = 0.

-------
SUPERIOR
103
102
 N
o>
\
O)
3
o1Dl
o10(
Q. '
Z
UJ
2
5
111

UJ
<103
LL
DC
3
0)
X
_L
5 10 15 20
YEAR
MICHIGAN
10'
\
N
10T
10 15 20
YEAR
HURON
10*
10'
10'
 * 1 *
0 5 10 15 20
YEAR
SAGINAW BAY
10*
10'
10
10 15 20
YEAR
103
10'
10
west
ERIE
central
east
\
^ i	1	
xv\
\ X
\ \
\ N.
. \
\ \
\ \
\ \
\ \
\ x
* ^ \
5 10 15
0 5 10 15
YEAR
0 5 10 15 20
ONTARIO
103
10'
10
Volatilization = 0.0
	Volatilization=0.1 m/d
20
YEAR
43. Calculated surface sediment PCB concentration response to an Instantaneous drop In upper
level PCB load at time t = 0.


-------
(I/kg)
10
10
10
10
-1
10
CURVE:
Tr
TT
TT
10
-1
354,000(M)'1755
296.000(M)'435
200,000(M) 1 
E E
(C.E) 
10
.400.000
Surface
Sediment
10
10
10
SOLID CONCENTRATION (mg/l)
44. Assumed variation of plutonium partition coefficient with
solids concentration used in sensitivity analysis.
116

-------
SECTION 10
EFFECT OF SOLIDS DEPENDENT PARTITIONING AND SEDIMENT DIFFUSION
INTRODUCTION
It has been noted by O'Connor and Connolly (1980) in a summary of
the literature that there Is for some chemicals an apparent dependence
of the partition coefficient on the concentration of solids. The mech-
anisms for this dependence are not clear but may be related to some
interaction between solids which affects the available sites for sorp-
tion. The dependence of the partition coefficient on solids concentra-
tion had also been noted by Seymour, et al (1979) for Americium-241.
O'Connor and Connolly (1980) analyzed a variety of data relating
partition coefficient to solids concentration using the general form of
* = + 		^	(80)
m + m
o
where is the lower limiting partition coefficient at high solids and
m bounds the upper limiting partition coefficient at low solids concen-
tration. Assuming that and m are zero and generally over the range
4 00	
of solids from 10-10 mg/, O'Connor and Connolly (1980) computed values
for a ranging from 0.19 to 0.92. The work of Seymour, et al. (1979)
resulted in a values of 1.4 for desorption of Americium and 2.0 for ad-
sorption.
If a chemical displays an inverse dependence of partition coeffi-
cient on the concentrations of solids, then at the high solids concen-
trations found in bed sediment, the partition coefficient would be ex-
pected to be lower than for the water column. Less chemical would then
be sorbed onto sediment particles and an increase in interstitial dis-
solved chemical would occur. A gradient between the dissolved chemical
in the bed and the dissolved chemical in the overlying water would then
develop and depending on the magnitude of the exchange between the sedi-
ment and water column, a flux of the chemical from the sediment to the
water may occur. In this section, the sensitivity of the previous pluto-
nium and PCB calculations to this effect is calculated and discussed.
SENSITIVITY OF PLUTONIUM CALCULATION
No laboratory data were available on the dependence of the plutonium
partition coefficient on solids concentration. Accordingly, three rela-
tionships were examined where, in all cases, the partition coefficients
was fixed at 400,000 Jl/kg at a solids concentration of 0.5 mg/SL and the
slope of the change in partition coefficient with solids concentration
was varied. The three relationships as showin in Figure 44 are
(a) it = 354,000 (M)	a one order of magnitude decrease from
0.5 mg/ to surface sediment concentrations of 240,000 mg/2,
117

-------
- 435
(b)	ir = 296,000 (M) * ; a slope equal to that used for the PCB
sensitivity analysis (discussed subsequently)
(c)	tt = 200,000 (M)	an approximate upper bound of the slope.
-5 2
A sediment diffusion coefficient of 10 cm /sec (Hesslein, 1980; Lerman
and Weiler, 1970; Lerman and Lietzke, 1975) was used throughout all cal-
culations.
Figure 45 shows the sensitivity of the 20 year plutonium calculation
for Lake Michigan to the three, assumed relationships. The data as shown
239 240
in Figure 26 indicate that the ' Pu concentration in the years 1971
-1973 (years 18-20) is less than 1 fci/A. The sensitivity of the mass
dependent effect with a slope of -1, (curve c in Figure 44) is most
marked and results in a completely different time dependence and equilib-
rium values that are substantially greater by more than one order of mag-
nitude then the observed data. This is due to the increased dissolved
plutonium, (by about an order of magnitude) and subsequent flux to the
overlying water column. It is also interesting to note that the increase
in water column concentration is not directly related to the slope of the
mass dependent relationships since curve "b" results in a lower concen-
tration in the water column than curve "a." Based on Figure 45 and the
observed data in Figure 26, it is concluded from the sensitivity analysis
that a dependence of partition coefficient on solids concentration at a
slope of -1 is too high and results in calculated water column concentra-
tions that are about an order of magnitude higher than observed data.
Further sensitivity runs were therefore made using curve "b" (slope of
-.435) as approximately representative of the solids dependent effect.
Figure 46 summarizes earlier calculations and the sensitivity of the
solids dependence for Lake Michigan. The base run with resuspension con-
sistent with a settling velocity of 2.5 m/day has already been compared
to the case of no resuspension and no diffusion (curve 2). As shown,
including solids dependent partitioning (curve 3) results in a higher
concentration over the base run case due to sediment diffusion. The
question addressed at this point then was "Could an equally good cali-
bration to observed data be obtained with sediment diffusion but in-
creased settling velocity of particulate from the water column?" Curve
4	indicates that indeed increasing the particulate settling velocity to
5	m/day and maintaining solids dependent partitioning can give an approx-
imately equivalent calibration. In the total concentration of plutonium
in the water column then it is not possible to distinguish the appro-
priate settling velocity from the appropriate sediment diffusion and,
therefore, one must look to other representations of the plutonium to
determine any change as a result of the trade-off between particulate
settling velocity and solids dependent partitioning.
Figure 47 shows the particulate concentration in the water column
and sediment under three conditions, a) partitioning independent of
solids concentration, b) solids dependent partitioning and w =2.5
3
m/day, c) solids dependent partitioning and w =5 m/day. Including
8
118

-------
CURVE:
0TT = 354,000(M) 1755
TT = 296,000(M)"435
@7T = 200,000(M) 1'
10
15
20
0
5
TBME (years)
45. Sensitivity of total plutonium water column concentration for Lake Michigan to three
assumptions on mass dependence of partition coefficient (see Figure A).

-------
3
2
1
0
15
10
20
TIME (YEAR)
BASE RUN 1? =400.000 (l/kg) ^RESUSPENSION,
NO SOLIDS PARTITIONING AND SEDIMENT DIFFUSION
_ NO RESUSPENSION, NO SOLIDS PARTITIONING AND
SEDIMENT DIFFUSION
-0.435
	If (l/kg) = 296,000 (M)
wfe =2.5 M/DAY ;RESUSPENSION, SEDIMENT DIFFUSION
-0.435
.... 296,000 (M)
wa =5.0 M /DAY; RESUSPENSION, SEDIMENT DIFFUSION
Comparison of Lake Michigan plutonium total water column concentra-
tion calculations under different assumptions on particulate set-
tling.
120

-------
1.0
TJ
w
O)
o
Q.
z
o
H
<
oc
H
Z
LU
o
z
o
o
Water Column
(a) BASE RUN:
Partitioning Independent
of Solids Concentration
400,000 l/kg; wa = 2.5 m/day
Surface Sediment (0-2cm)
10	15
TIME (YEAR)
20
o
CNI
a
o
CM
111
Z)
o
H
CC
<
0.
Tf s 296 (M)
Tf ~ 400.000 l/kg
Water Column
(b) Solids Dependent Partitioning
-0.435
a = 2.5 m/day
v"c wa = 5 m/day
Surface Sediment (0-2cm)
	,	JTr" 1360 l/kg
Tf; 1360 l/kg
10
15
20
TIME (YEAR)
47. Calculated variation of Lake Michigan particulate plutonium concen-
tration in water column and surface sediment: (a) base run, (b)
with solids dependent partitioning and w = 2.5 and 5.0 m/d.
121	a

-------
solids dependent partitioning in the base run case Increased the particu-
late plutonium concentration in the water column even though the parti-
tion coefficient at water column solids concentration (0.5 mg/fl,) was the
same as for the base run (400,000 Jtkg). This is due to the fact that the
increased flux of dissolved plutonium from the sediment increases the
sorption onto the particulates. Surface sediment concentrations, how-
ever, decrease by almost one-third and bracket the surface sediment data
shown in Figure 27. Note that in Figure 47(b), the water column particu-
late concentration is about 3-4 times sediment concentration reflecting
the disequilibrium between water column and sediment under tine variable
conditions. Although one might have hoped that the particulate plutonium
concentration would be definitive in separating out particulate settling
and diffusion effects such is not the case. Figure 47(b) does indicate,
however, that if detailed data were available on the water column partic-
ulate concentration and surface sediment concentration that a determina-
tion could be made in principle of the appropriate settling velocity and
solids dependence.
It is, therefore, concluded form this sensitivity analysis that par-
ticulate settling velocities of 2.5-5.0 m/day, with or without solids
dependent partitioning (at a log slope of -.435) and sediment diffusion
provide an approximately equal representation of the observed plutonium
data. As noted earlier, a more marked solids dependence (log slope of
-1) of the partition coefficient does not provide an acceptable compari-
son to the observed data.
SENSITIVITY OF PCB CALCULATION
Figure 48 shows a compilation of PCB partition coefficients as a
function of solids concentration ranging from approximately 0.1 mg/fl, as
reported for Lake Superior (Eisenreich, et al., 1983) to Lake Michigan
sediment solids of 200,000 mg/JL as reported by Eadie, et al. (1983). The
data indicate a dependence of the PCB partition coefficient on solids
concentration where for concentrations at about 10 mg/fl, and higher, the
partition coefficient declines logarithmically at a slope of about
-0.435. This depends heavily, however, on the one point of a sediment
partition coefficient reported by Eadie, et al. (1983). The data of Di
Toro, et al. (1982) Indicate, for Saginaw Bay sediments, that the parti-
4
tion coefficient may be leveling off at about 10 fl,/kg at solids concen-
trations greater than about 1000 mg/fl,. The data of Eisenreich, et al.
(1983) for Lake Superior extend into the concentration of solids at less
than I mg/fl. and show a steap increase in partition coefficient at the
lower solids concentration. The data from Lederman and Rhee (1982) are
for Great Lakes algae and the higher partitioning may reflect the pres-
ence of lipids in the algae.
If the partition coefficients differ between the water column and
the sediment, then one would expect the particulate PCB concentration in
the water column to be higher than that of the sediment. There is some
evidence to indicate that this may be the case for Lake Michigan as shown
in Figure 49. Rice and Frez (1981) reported water column particulate PCB
concentrations ranging from 213 ng/g(d) to 1147 ng/g(d) with indications
122

-------
10
10
10
10
10"





A
Dltoro el al (1982)

\ # #
N 
0
G



0
Elsenrelch al (1882)
Pavlou+Dexter (1979)
V

O 0
O 0
0
0
0
~
Eadie et at (1983) -


o
o
0
0
Rice et al (1683)
 >

0

0
Richardson et al
(1983)
w

*
0
0
 0
Lederman & Rhee
(1982)
V

\0
CA


Partition Coeff./Solids Relationships
0 Constant partition coeff.
0 435
@7T = 73,990(M) '
7T =
JL
- 10'
i.
_L
~ j 1242
1254
- 10
Total
10
0.1
1.0
10
10'	10*	10
SOLIDS CONCENTRATION ( mg/l )
10
10
48. Summary of reported PCB partition coefficients and solids concentrations and relation-
ships assumed in sensitivity analyses.

-------
^ 10,000
0)
c
z
o
p
<
oc
H
Z
UJ
O
z
o
o
CO
o
a
Ul
l-
<
3
O
P
cc
<
a.
1000
100
10
WATER
COLUMN
Rice and
jFrez (1981]
I
I 9
1978
SURFACE SEDIMENT (0-3 cm)
I
Mean and
Range

-------
of a decrease of tbe concentration with depth. The average of their data
is 537 ng/g(d). The surface sediment PCB data as shown in Figure 49
varies by an order of magnitude although it should be recognized that the
data of Frank, et al. (1981) represents 286 samples throughout the Lake
while Armstrong and Swackhamer (1983) and Eadie, et al. (1983) represent
only 12 and 4 samples respectively. If the data of Frank, et al. (1981)
is used then there is about a two order of magnitude decrease in the par-
ticulate PCB concentration between the water column and the sediment.
In the model used here, the only way that sucti a decrease can be calcu-
lated is through a solids dependent partition coefficient.
Two cases ot solids dependent partitioning of PCBs were therefore
examined:
a) it = 73,990 M * D
and b) tt = 25,120 M * _ for solids < 10 ng/I
tt = 73,990 M	for solids >_ 10 ng/fl
Figures 50 through 53 summarize the results under the lower level
of loading of PCBs and including volatilization. Several points can be
noted. As shown in Figures 50 and 51, the total and dissolved water con-
centrations are not sensitive in a significant way to the assumption on
partitioning. The principal effect on the dissolved component is in
Western Lake Erie where the dissolved concentration increases by a factor
of three. In all other lakes, however, for practical purposes, the total
and dissolved concentrations are unaffected by the partitioning assump-
tion. Figure 52 shows that the surface sediment concentration is also
not markedly affected (to order of magnitude) by the partitioning assump-
tion although a decline of about 50% is evident in the lake sediment and
a decline of about 70% is calculated for the surface sediment of Saginaw
Bay.
These reductions in sediment PCB particulate concentration reflect
the assumed reduced partitioning at the high solids concentrations and
are, therefore, subsequently reflected in the PCB concentration of the
interstitial water of the surface sediment as shown in Figure 53. It is
in the interstitial water that the effect of the solids dependent parti-
tioning is most pronounced. Here increases in the dissolved PCB concen-
tration of about two orders of magnitude are calculated as seen in Figure
53.
For Lake Michigan, as an example, the interstitial concentration of
PCB as calculated for a constant partition coefficient is about 0.25
ng/Jl. For a variable partition coefficient (Relationship No. 3 in Figure
53), the concentration increases to about 30 ng/Jl. Eadie, et al. (1983)
reported values of pore water PCB at three stations in southern Lake
Michigan of 159, 214, and 342 ng/Jl which is about one order of magnitude
higher than that calculated in Figure 53. However, the estimate shown
in that Figure 53 represents a lake-wide average incuding regions of non-
deposition. One would, therefore, expect an observed lake-wide average
to be less than individual core samples. Indeed, the high value of 342
ng/Jl reported by Eadie, et al. (1983) is for a station off Benton Harbor,
Michigan with the highest recorded accumulation rate in Lake Michigan of
2
3 g/m /day. This accumulation is 16 times the lake-wide average net dep-
125

-------
~ 1.0
1.0
0.5
0.5
1.0
0.5
it
V\
Superior

V\
/
-4
Huron
Michigan
Saginaw Bay
v\
/
/
/
/
..z.
West
I
N
\
\
\
_\r
Central
Erie
1
1
East
/
/
/
/
4
Partition Coeff./Solids Relationships
J (D Constant: 7f = 150,000 l/kg
.-0.4346
7T = 73990(M)
-0.435
@i 7T = 73.990(M) M10 mg/l
-1.2
i if  251,190(M) M *10 mg/l
Ontario
; ^

-------
60
E
09
c 40
Z
o
p
<
H 20
z
Ul
O
z
o
o
CO 0
o
Q.
E
o
? 60
o
H
Z
Ul
2
5 40
Ul
(0
Ul
o
<
!r 20
3
CO
JSL
Superior
JSL
60
40
20
i
JSL
Huron
60
40
20

Michigan
Saginaw Bay
West
1
am
Central
Erie
I

East
Partition Coeff./Solids Relationships
Jjj Constant: "jf ~ 150,000 l/kg
a
(2)^= 73,990(M)
0.435
-0.435
7T = 73,990(M) M10 mg/l
-1.2
7f  251,190(M) M^IO mg/l
Ontario


-------
o 1.0
0.5

SUPERIOR
1.0
0.5
Mi
MICHIGAN
1.0
0.5
I
P
HURON
SAGINAW BAY
1.0
0.5
-
I
PI
WEST
1
P
/
~
J
CENTRAL
ERIE
1
P
EAST
1.0
Partition Coeff./Solids Relationships
Constant: IT = 150.000 I/Kg
-0.435
0.5

d)T= 73,990(M)
-0.435
IT = 73,990(M) M10 mg/l
7f = 251,190(M)1'2 M*10 mg/l
ONTARIO
'"i
\L>

-------
E
o
SUPERIOR
MICHIGAN	SAGINAW BAY
/

/

/

/

/

/

/

/

/

/

/

/

/

/

WEST
F]
1/
p

*
V
1
*
*
/
0
1.64
(10 >
CENTRAL
ERIE
/
Y
/
y
Y
/
*
/
/
EAST
Partition Coeff./Solids Relationships
| Constant: 7T= 150,000 l/kg
*
(2)TT~ 73,990(M)
-0.435
-0.435
7T = 73,990(M) M10 mg/l
V =251,190(M~)1'2 M*10 mg/l
ONTARIO

-------
osition as used in the preceding solids balance calculation. It can also
be noted that the calculation 9howti in Figure 53 is for the low loading
condition for PCB. The higher loading condition would result in an in-
crease in interstitial water PCB concentration approximately proportional
to the load or a factor of about 7 over the lower load condition.
In any event, it appears from this calculation on the sensitivity
of the PCB distribution in the Great.Lakes to a sediment dependent parti-
tion coefficient that:
(1)	such a relationship is more representative of the observed par-
ticulate and sediment PCB data in Lake Michigan;
(2)	total and dissolved PCB concentration in the water column and
sediment PCB concentration are not affected significantly (i.e. by at
least one order of magnitude) under a solids dependent partitioning
assumption;
(3)	Interstitial PCB concentration in the sediment is affected mar-
kedly by such an assumption and an increase of about two orders of magni-
tude is calculated.
(4)	since the increased interstitial PCB concentration in the sedi-
ment is about two orders of magnitude higher than the overlying water
dissolved PCB concentrations, one would expect benthic organisms to carry
a significantly higher body burden than organisms exposed solely to the
water column and as a result would be a potential significant source of
PCBs to top predators in the food chain.
Since the interstitial PCB component is potentially significant and
since the issue of solids-dependent partitioning is of contemporary
interest on constructing mass balances of PCB, it is recommended that
additional sampling of pore water PCB and PCB concentration in benthic
organisms be conducted in various Great Lakes regions.
130

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SECTION 11
APPLICATION OF MODEL
TO BENZO (a) PYRENE AND CADMIUM
As noted in the earlier Sections of this report, the physico-chemi-
cal model is developed to provide a means for assessing the fate of chem-
icals entering the Great Lakes system. The credibility of such a model
depends to some considerable degree on the ability of the framework to
explain observed chemical concentrations. The preceding Sections dealt
with the use of plutonium as a calibrating variable for the model and
also the application to PCBs, a contemporary chemical of some interest.
In this Section, the model is further applied to two other chemicals:
a) benzo(a)pyrene, a polycyclic aromatic hydrocarbon (PAH), and b) cad-
mium, .a representative metal. For both chemicals some data exist for the
application of the model framework.
BENZO(a)PYRENE
The distribution of this chemical, one of the PAH compounds result-
ing from incomplete combustion of organic materials has been widely stud-
ied (Neff, 1979) because of its potential carcinogenicity. The fate of
benzo(a)pyrene (BaP) in the Great Lakes has recently been evaluated in a
series of papers by B.J. Eadle (Eadie, et al., 1982; Eadie, 1983; Eadie,
et al., 1983). In that work, data are presented for the range of concen-
tration of BaP in the water column and surficial sediments as well as
preliminary data on the BaP concentration in the pore water of the sedi-
ment. It is those data (together with estimates of loading) that can be
used as a further application of the physico-chemical model.
Table 20 shows some of the basic chemical properties of BaP.
TABLE 20
CHEMICAL PROPERTIES OF BENZO(a)PYRENE
(From Neff, 1979)
Molecular Weight - 252
-9
Vapor Pressure (mmHg) - 5.49*10
Saturation Vapor Concentration
(Mg/1000 m3) - 75
Water Solubility (yg/i) - 0.172(1977)l; 0.5 (1971); 6.05(1946;
4.0 (1942)
* Date parentheses is date of publication as cited in Neff (1979)
131

-------
As seen, BaP is sparingly soluble in water (especially if the more
contemporary value of solubility is accepted) and as such would be ex-
pected to have an affinity for solids. The partitioning on to particu-
lates and in addition, the extent of volatilization of the BaP must be
estimated. Although BaP is known to undergo photolysis (Neff, 1979) this
pathway is not considered in this application.
BaP Loads
As discussed in Gadie (1983), the principal source of BaP is from
the atmosphere. Eisenreich, et al. (1980) have estimated the airborne
load to the Great Lakes and their estimates are shown in Table 21, to-
gether with the calculated areal loading rate.
TABLE 21
ATMOSPHERIC LOAD OF BaP TO GREAT LAKES
(From Eisenreich, et al. (1980))
Lake
Load
103 kg/y
Superior
7.9
Michigan
5.6
Huron
5.8
Erie
2.5
Ontario
1.8
Areal
Area	Loading Rate
(km2)	g/km2-yr
82882	95.3
57772	96.9
61659	94.1
24996	100.0
19485	92.4
As seen, the estimated atmospheric loading on an areal basis is
2
about 95 g BaP/km -yr across all of the lakes but as noted by Eadie
(1983), all BaP load estimates are based on quite limited data and there-
fore may vary as additional information becomes available.
Solids Partition Coefficient
Smith, et al. (1978) reported solids partition coefficients for BaP
ranging from 17,000 to 150,000 JL/kg with a correlation to organic carbon
(range .06 to 3.8%). Eqs. (31) and (34) with a solubility of 0.17 vig/Jl
and an organic carbon range of 5-10% yield coefficients from 9000 to
18,000 Jl/kg which are lower by about an order of magnitude and therefore
somewhat suspect.
132

-------
From the data given in Eadie (1983) for Lake Michigan, a field value of
it for BaP can be calculated to be between 143,000 and 287,000 i/kg. The
low estimate of 10,000 i/kg is therefore probably not representative.
However, like the PCB, the partition coefficient may be dependent on the
solids concentration. From the limited data of Eadie (1983) the sediment
partition coefficient can be estimated at about 600 /kg. The low solids
concentration of Lake Michigan (<1 mg/Z) results in a considerably higher
partition coefficient. In the absence of enough data to formulate a
solids dependent partition coefficient, the model for BaP was run for it
= 10,000 to 100,000 ifkg, thereby providing a range of one order of mag-
nitude in the solids partition coefficient.
Volatilization
For the conditions given in Table 19, the Henry's constant for BaP
is calculated from
He-16ff	(8D
w
where M is the molecular weight, p is the partial pressure (mm Hg),
c is the water solubility (mg/), T is temperature (K) and H is the
W	, G
dimensionless Henry's constant and is calculated at 4.60*10~ . Following
Eqs. (7) and (8) and using a 4 m/s wind speed and diffusivity relation-
ships to molecular weight as given in O'Connor (1982), the liquid film
coefficient is calculated at 0.15 m/d and the product of the gas film
coefficient and the Henry's constant is calculated at 0.040 m/d so that
both the liquid and gas film control the volatilization of BaP. The
overall water-air transfer coefficient is then calculated from Eq. (6)
as 0.032 m/d and this value was used in the calculation.
Preliminary Calculations
The simplified steady state model discussed in Section 5 can provide
a rapid means for calculating the in-lake and surface sediment concentra-
tion for BaP for an upstream lake such as Lake Michigan. (The concentra-
tion in the downstream lake can, of course, also be calculated given the
upstream concentration; the concentrations in the overall Lake system are,
therefore, best computed with the overall framework.) For Lake Michigan,
water column BaP concentrations, Eq. (61) can be used with the estimate
of the net loss of BaP given by Eq. (63) and the particulate BaP concen-
tration can be calculated using Eq. (62). The net loss of the solids
from Lake Michigan is taken from Table 10 at 137 m/yr. Since there is
some uncertainty in the BaP partition coefficient as noted above, the
steady state BaP concentration can be readily calculated over a range of
coefficients and compared to observed data. The results of this steady
state calculation are shown in Figure 54 where it is seen that at it for
4
BaP of 10 (JL/kg), the calculated water column concentration is within
the observed data but the surficial sediment concentration is low by
133

-------
o>
j= 100
<
cc
H
Z
UJ
o
z
o
o
OBSERVED
MEAN  s
FOR
SURFACE
WATER SED.
COL. (ng/gj
(ng/l)
o
Y-
Q.

r-
00
(1>
o
o
o
o
m
100
WATER COL. CONC.
10
39
>
H
3

-------
almost an order of magnitude. At u = 10 H/kg, the calculated surficlal
sediment concentration is approximately equal to the observed data, but
the water column concentration is lower than the observed mean by a fac-
tor of about two but is still within the mean  one standard deviation.
The lower concentration is due to the increased loss of BaP to the sedi-
ments. The steady state calculation shown in Figure 54 tends to support
the higher partition coefficient of about 10^ which is the order obtained
directly from the field data. It should, of course, be recalled that the
loading estimate is subject to some considerable uncertainty as is the
loss mechanisms of volatilization and photolysis. Nevertheless, the cal-
culation tends to indicate that the estimate of the BaP partition coeffi-
cient obtained from the empirical relationships may be low by an order
of magnitude and thus highlights the need to utilize the empirical rela-
tionships with caution.
Time Variable Calculations
Although the preceding steady state calculation provides important
insight into the fate of BaP, it is recognized from the preceding work
reported on in this report, that the time to reach the steady state
values is long and that over a 20 year period for lakes such as Michigan,
the resulting concentration is at about 75% of the ultimate steady state
values. Therefore, a series of time variable calculations were also con-
ducted with constant BaP loading as shown in Table 20 beginning at time
t = 0 with zero initial conditions. The results at two levels of BaP
partitioning are summarized in Table 22 and Figure 55.
As shown in Table 22, the lake to lake variation in BaP concentra-
tions either in the water column or the sediment differs by less tha
about a factor of two. The highest concentration of BaP in the surface
sediments for tt = 10,000 is in Saginaw Bay. It can also be noted in
Table 22 and Figure 55 that at u = 10,000 I /kg the comparison to the
observed data is not satisfactory. Figure 55 shows that at it = 10,000
the surface sediment concentration for Lakes Michigan and Erie is about
45 ng/g(d) or about one order of magnitude lower than the observed data.
These time variable results, therefore, are confirmatory of the previ-
ously discussed steady state calculations. Figure 56 shows the time
history under the two partition coefficients. For it = 10,000 Jl/kg, the
water column and sediment are at about 80 and 60% of steady state
respectively while for it = 100,000 I /kg, the water column and sediment
are at about 20% of steady state.
Figure 55 and Table 22 indicate that a more favorable (but not
totally desirable) comparison to observed data is obtained at the higher
BaP partition coefficient of 100,000 /kg. The results also indicate the
need to determine the partition coefficient for BaP, as a representative
PAH for Great Lakes solids concentrations. On the basis of this applica-
tion of the physico-chemical model to BaP in the Great Lakes, it is con-
cluded that:
(1) the estimate of the BaP partition coefficient obtained from pub-
lished empirical relationships is probably low by about an order of mag-
nitude for the Great Lakes system,
135

-------
TABLE 22
Comparison of Calculated and Observed BaP
Under Different Solids Partition Assumptions
Calculated Range of BaP Across All Lakes	Observed Mean
it = 10,000 g./kg	rr = 100,000 A/kg 	of BaP	 	Ref.	
Total Water (conc. (ng/ J.)	5-6	1-2	12  8^	Eadie et al.(1983)
Mich:480  246(7)(c)
Surficial Sediment	Erie:255  152(3) Eadie (1983)
Conc. (ng/g(d))	38-60	46-133	Sup.:28(l)
Hur.:294(1)
Ont.: 306(1)
Sediment Pore	3-5	0.5-1.3	850  1260	Eadie et
al.(1983)
Water Conc(ng/)
Particulate Conc.	46-64	46-165	Mich:200-400	Eadie (1983)
in Water Column(ng/g(d))
^ After 20 years with loading of Table 20
^ Mean  Std. Dev.
(c)
( ) = No. of samples

-------
PARTITION COEF. (I/kg)
100,000
10.000
OIOOO
E 100
CALCULATED = OBSERVED
100	1000
CALCULATED BaP CONC. (ng/g(d))
SURFACE SEDIMENT (0-2 cm)
AFTER 20 YEARS LOADING
KEY:
o- Individual Data
Lake Michigan (Eadie.1983)
+ - Mean	I
I - Mean  Std. Dev.J Lake Erle (Eadie.1983)
1 (n=3>	)
55. Comparison between calculated surface sediment BaP concentration
after 20 years and observed concentration.
137

-------
(2)	with an increased BaP partition coefficient and assuming loss
due to volatilization, the physico-chemical toxic substances model of the
Great Lakes approximate observed BaP water column and sediment data to
order of magnitude,
(3)	the model confirms that on a lake-wide scale, the principal
external source of BaP is the atmosphere,
(4)	for the larger lakes such as Michigan, the 50% response time of
the lake to external loads is about 6-10 years for the water column-sedi-
ment system while for Lake Erie the response time is about two years,
(5)	lake to lake variations in BaP water column and sediment concen-
trations are less than a factor of two.
CADMIUM
Water Column and Sediment Data
The distribution of cadmium in the water column and sediments of the
Great Lakes has been sampled for a number of years and a summary of much
of the earlier data up to about 1977 is given by Konasewich, et al.
(1978). As noted earlier in Section 5, Muhlbaier and Tisue (1980) have--
sampled for cadmium in southern Lake Michigan and have applied a simple
mass balance model of cadmium for that basin. They point out that
earlier measurements of cadmium in the water column (with a detection
limit of usually 100 ng/iL) may be in significant error because of poten-
tial contamination during collection, handling and analysis. Muhlbaier
and Tisue (1980) concluded that values of cadmium lower than 100 ug/& are
probably more representative of the actual concentrations. Indeed, in
their work, they used an average from careful sample collection and analy-
sis of 20 ng/&. Thus, retrievals from the USEPA Storage and Retrieval
System (STORET) for cadmium in all of the Lakes which were made as part
of this research are suspect since concentrations for the years 1972-1978
are about one-two orders of magnitude higher than the much lower levels
indicated by Muhlbaier and Tisue (1978). For Lake Ontario, (Nriaga), et
al. (1981) reported mean values of about 50 ng/J, total cadmium for 1978
as opposed to reported concentrations of dissolved cadmium in STORET for
1971-1974 of about 200 ng/H.
As a result, the STORET data base for water column cadmium concen-
trations were not used in this work, but reliance was placed on the more
recent observations. Table 23 summarizes some of the data for the water
column where the limit of detectability was below 100 ng/S, and where
presumably special care was taken in sample analysis. As seen in Table
22, average water column data for Lakes Michigan and Ontario and Saginaw
Bay are below 100 ng/l although the variation is quite large. The lower
cadmium concentration reported for 1978 should not necessarily be taken
as evidence of a cadmium decline from the 1973-1975 reported values;
again because of potential contamination problems. The data for Saginaw
Bay when examined at a more detailed spatial level indicate that the
waters of the outer Bay adjacent to Lake Huron and receiving inflow from
Huron averaged about 80 ng/ total cadmium during 1976.
138

-------
n =10,000 I/kg
10
SEDIMENT
STEADY
STATE
STEADY
STATE
WATER COLUMN
CO
m
a
i
m
-100 zS
10,000
1000
3 2
(O H
\ >
00
o
O
O
z
o
10	15
TIME (years)
100
20
-10
-1
10
100.000 l/kg
SEDIMENT

/
/
WATER COLUMN
10,000

o
o
z
o
400-
H100
-10
-1
10	15
TIME (years)
56. Time variable BaP response in Lake Michigan under two partition
coefficients with 20 year constant loading.
139

-------
TABLE 23
Summary of Some Observed Cadmium Concentrations
in the Great Lakes
Lake
Date
Total Concentrations
Water Column (ng/J.)
Mean Std. Dev. It of Obs.
Ref .
Date
Surface Sediment (ug/g(d))
Mean Std. Dev. # of Obs.
Ref.
Superior




<
1976
1.2
3.0
0.8
0.7+4.6(b)
404
40
(9)
(10)
Michigan
1973-75 70
1978 27
70
9.3
60
17
(1)
(3)
%
1978
1860
1.0
0.57
0.52
0.12
6
3
(4)
(4)
Huron




<
<
1976
1760
1.4
1.0
3.9
197
(9)
(9)
Saginaw Bay	1976 59 ^ 20-30	130	(5)
Erie
1970
5.4*c) 3.8
11
(9)

1972
1
,0
r--
O
8
(8)

^ 1920
0.44(d) 0.57 (d)
6
(8)
Ontario	1969 90	-	* 300	(7)
1973 160, v	1	(1)	1978 5.4	0.6	3	(2)
1978 50U' 11	3	(2)
"Background
" Cone.


Shale


0.3 (6)
Deep Sea
Clays

0.43
Granitic
Rocks

0.13
References:
(1) Elzerman and Armstrong (1979)
Notes: (a)
"Labile" + particulate, May/June

(2) Nriagu et al. (1981)
(b)
Range

(3) Muhlbaier & Tisue (1981)
(c)
Western Basin

(4) Christensen & Chien (1981)
(d)
"Background" conc. at depths as cal-

(5) USEPA Crosse lie (data communication) and

culated from (8).

Dolon & Bierman (1982)


(6)	Forstner and Wittmann (1979) from Turekian &
Wedpohl (1961)
(7)	Chau et al. (1970)
(8)	Walters et al. (1974)
(9)	Konasewich et al. (1978)
(10) Robbins & Edinefon (1976), onnt-pH in MuhlKiiior i Ticno fionn

-------
Table 23 also shows some data on the cadmium concentration in the
surface sediments of the Lakes although this summary does not include all
data as compiled by Konasewich, et al. (1978). The range of sediment
cadmium concentration is about 1-5 yg/g(d) with some tendency for the
higher concentration to occur in the downstream lakes. "Background" sed-
iment levels, i.e. cadmium concentration at depth equivalent to about 100
years ago for some Lake Michigan cases is about 0.4-0.5 yg/g(d)
(Christensen and Chien, 1981). For Lake Erie, a background deep sediment
concentration of 0.14 ug/g(d) has been reported (Forstner and Wittmann,
1979, p. 148) and Kemp, et al. (1974, 1976)(as reported in Forstner and
Wittmann, 1979) indicated that the sediment cadmium enrichment factor (an
aluminum normalized elemental ratio at the sediment surface to the
Ambrosia horizon) was 4.0, 0.8 and 2.7 for the West, Central, and Eastern
basins respectively.
For Lake Michigan, Elzerman, et al. (1979) reported particulate cad-
mium concentration in the water column of 5 yg/g(d) for a sample which
is higher than the approximate 1 ug/g(d) in the surface sediment but be-
cause of the limited data it is not possible to conclude that this is a
real difference. As noted earlier in Section 5 (Figure 11), the data of
Nriaga, et al. (1982) indicated that to order of magnitude the surface
sediment cadmium data and particulate water column data are equivalent
although the concentrations do differ by a factor of about two with the
particulate water column concentration higher than the surface sediment
concentration.
Cadmium Loads
A variety of estimates of the external cadmium loads to the Great
Lakes or to individual lakes or bays has been made. Recent examples
include Casey, et al. (1977) for Lake Ontario, Muhlbaier and Tisue
(1980) for Lake Michigan; Dolan and Bierman (1982) for Saginaw Bay and
IJC (1980) for Great Lakes system. All of the load estimates indicate
the significance of the atmospheric input of cadmium and the possibility
that individual industrial point sources may discharge significant loads
of cadmium to Great Lakes tributaries but that sampling is not yet defin-
itive enough to provide detailed estimates of these sources. Indeed the
range in atmospheric estimates is also quite large (as given below).
Earlier attempts as part of this research to arrive at external loads of
cadmium to the Great Lakes by carefully going through each major sector
of a Great Lake basin were abandoned because of the wide variability in
industrial load components.
Instead an approach similar to the load estimates for PCB was used;
i.e. a range was assigned to each principal load component (atmospheric,
tributary and municipal and industrial) and subsequent time variable
model calculations were made for an upper and lower load estimate. A
summary of the range of external loads is given in Table 24 and as seen
for any given lake or region, the difference from low to high estimate
is one-half to one order of magnitude. There is a general tendency for
the loading to increase in the downstream direction with the highest
areal loads in Western Lake Erie and Lake Ontario. This is principally
due to the apparent increased atmospheric input and tributary loads for
the downstream lakes.
141

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TABLE 24


Summary of Contemporary External Cadmium Loads




(not including upstream loads)



Atmospheric^
3)
Tributary
Mun. + Ind.^

Total 2
Lake/Region
mt/yr
mt/yr
(mt/yr)
mt/yr
g/km -yr
Superior
41-108
13-126
0-0.3
54-234
651- 2823
Michigan
12-120
9-92
0.4-4
21-216
363- 3739
Huron
23-57
14-136
0.1-1
37-194
644- 3378
Sag. Bay
3
2
0
5
1184
Erie- West
1-18
2-20
1-8
4-46
1321-15202
- Central
3-94
2-16
0.2-2
5-112
318- 7126
- East
1-38
1-12
0.1-0.5
2-51
320- 8155
Ontario
10-44
7-66
0.6-6
18-116
924- 5953
^	From Allen and Halley (1980)
2)	From Dolan and Bierman (1982)
3)	Assuming tributary flow at total cadmium conc. of 0.2-2.0 ug/JL
4)	At 0.5-5.0 yg/ for direct municipal point sources

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Background Concentrations and Load9
An approximate calculation can be made of the background (I.e. con-
ditions prior to any external anthropogenic input) cadmium concentrations
and associated equivalent external loads using the steady state formula-
tions discussed In Section 5. As shown in Table 22, the cadmium concen-
tration of shale clays and rocks varies from about 0.1 to 0.4 yg/g(d).
For the Great Lakes, however, the deep sediment cadmium concentration
tends to be somewhat higher. For Lake Michigan, Christensen and Chieu
(1981) show for three cases, a cadmium concentration corresponding to
about the year 1860 of 0.57 pg/g(d). A "pre-colonial" value of 1.0
Ug/g(d) for Lake Huron is tabulated in Konasewlch, et al. (1978) from the
work of Kemp and Thomas (1976). Walters, et al. (1974) provide data from
which a mean background level (approximately for the year 1920) can be
calculated at about 0.44 ug/g(d) with a standard deviation of 0.57
Ug/g(d) and range of 0.0-1.5 yg/g(d). A range of 0.5-1.0 ug/g(d) was
chosen to estimate background concentrations and loads.
Under equilibrium conditions and the assumptions discussed in Sec-
tion 5, the concentration of particulate cadmium in the surface (back-
ground) sediment would be expected to be approximately equal to the par-
ticulate concentration in the water column (Eq. (6)). The total cadmium
water concentration can then be computed from Eq. (19) and (15) as
cT = -p	(82)
P
The areal load can be computed from Eq. (61) with the net deposi-
j1 rate, wT gi'
shown in Table 25.
tional rate, wT given by Eq. (64). The results of the calculations are
As shown in that Table, the estimated background total cadmium con-
centration in th water column is about 4 ng/ for the upper Lakes and
Lake Ontario and 8-20 ng/ for Lake Erie. The elevated concentration in
Lake Erie Is due to the increased solids concentration (and associated
loading)-into that Lake. The resulting estimated external background
load, as shown, increases In the downstream direction to maximum levels
in Lake Erie which are about an order of magnitude higher than the upper
lakes. The last column of Table 25 indicates that the contemporary cad-
mium loads (Table 23) are about 10-50 times the background load for the
Upper Lakes, Western Lake Erie, and Lake Ontario. Central and Eastern
Lake Erie, however, have a lower bound of this ratio of less than one
indicating present loads (at the lower bound) are approximately equal to
historical background loads. This seems unlikely. The upper bound for
these basins is about ten times background loads, a more plausible ratio
from the sediment data (Table 23, Lake Erie).
Partition Coefficient
As previously discussed in Section 5 where a simple steady-state
calculation of cadmium in Lake Michigan is discussed, Nriagu, et al.
(1981) provide data for Lake Ontario from which a cadmium partition
143

-------
TABLE 25
Estimate of Approximate Background Cadmium Concentration for Great Lakes
Range in Total Background Cone.
Lake/Region
Background Water
Col. Conc.
(ng/I)1
Used in Load
Estimate
(ng /)
Background
Total Load
(mt/yr)2
External Background
Load
3 2
(mt/yr) g/km -yr
Ratio:
Contemp. Load (Tab. 23)
Background Load
Superior
2.8- 5.6
4.0
6.1
6.1
37
18-76
Michigan
2.8- 5.6
4.0
3.1
3.1
54
7-69
Huron
2.8- 5.6
4.0
5.2
4.8
83
8-41
Sag. Bay
6.5-13.0
10.0
0.6
0.4
105
U
Erie-West
12.5-25.0
20.0
10.3
8.6
283
5-54
-Central
5.0-10.0
8.0
22.0
10.0
635
0.5-11
-East
5.0-10.0
8.0
12.0
4.7
754
0.4-11
Ontario
2.8- 5.6
4.0
4.0
2.6
132
7-45
^ At assumed background sediment conc. of 0.5-1.0 ygcd/g(d); r = r and Eq. (82) with tt = 200,000 /kg.
s
2)
Includes any upstream or exchange loads.
3)
Not including any upstream or exchange loads.

-------
coefficient of about 200,000 &/kg can be calculated. HydroQual (1982)
in a compilation of cadmium partition coefficients, calculated from
available field data, determined tbe following relationship from regres-
sion analysis of data for lakes:
n = (3.52  106)K"'9246	(83)
for a range of solids concentration of about 2-80 mg/. Tbe  one stan-
dard deviation error bars span about one order of magnitude and the
standard deviation of the exponent is .0593. The data, however, show a
clear decrease of the partition coefficient with solids concentration.
In the model calculations, two conditions were examined: a) constant par-
titioning at 200,000 /kg and b) solids dependent partitioning according
to Eq. (82) with associated sediment diffusion of dissolved cadmium.
Model Results
Model calculations were made using the low and high	load estimate
of Table 24 and two assumptions on the cadmium partition	coefficient:
a)	variable partition with solids concentration as given	in Eq. (83) and
b)	a constant partition coefficient of 2 * 10^ Jl/kg. Cadmium was assumed
to be conservative kinetically. For all calculations, zero initial con-
ditions were assumed and the loads were inputted as constant over time.
It became apparent from initial runs that the time to steady state espec-
ially for the upper lakes is long so that the computation was carried out
for a 100 year period. The computation therefore represents the response
of the Great Lakes system to a constant loading and such loading can be
viewed as a loading in addition to the background loading and cadmium
concentrations shown in Table 25. If increased loading of cadmium is
assumed to have begun in approximately the 1920's then the output from
the model calculation at t = 50 years would be representative of the
1970's, the period during which some reliable data are available.
Figures 57 and 58 show the calculated lake to lake cadmium concen-
trations for the water column and surface sediment respectively under the
high and low load estimate at t = 50 years. A solids-dependent partition
coefficient is assumed. The comparison of the calculation to the limited
water column and surface sediment data in Figure 57 shows that the high-
load estimate substantially overestimates the concentration at 50 years
for all lakes except Lake Erie. This is not surprising since it is un-
likely that the upper bound of the cadmium load estimate has been persis-
ting for the preceding 50 years. However the calculation does indicate
that a loading close to the upper load estimate is not unreasonable for
Lake Erie where the lower load estimate substantially underestimates the
surface sediment concentration as shown in Figure 58. An estimate of the
loading that is consistent with both the upper Lakes and Lake Erie is
given below.
Figures 59 (low load estimate) and 60 (high load estimate) show the
full 100 year calculation for Lake Michigan and central Lake Erie as
illustrations. The sensitivity of the calculation to the assumptions in
the partition coefficient is shown. As Indicated, the effect of the
solids dependent partition coefficient Is to greatly Increase the time
145

-------
600 -
500 -
400 
300 -
200 -
100 
0 -
600
500 "
400 -
300 -
200 -
100 
0 _
SUPERIOR
HURON
WEST
CENTRAL ERIE
EAST
J- MEANSTD. DEV. (REF. SEE TABLE 22)
I
(1)
1(3)
J(5)
(1)	
> I
- HIGH
- LOW
)
LOAD ESTIMATES
(SEE TABLE 23)
MICHIGAN
SAGINAW BAY
ONTARIO
57. Calculated total cadmium concentration (mg/1) in water column at t = 50 years with par-
tition coefficient as a function of solids concentration.

-------
12r
10
Cd 8
6
4
2
0
i
(9)
SUPERIOR
(9)
HURON
(9)
WEST
RANGE
(8)
CENTRAL ERIE
EAST

Cd
(g/g)
12
10
8
6
4
2
0
 (10)
J (4)
MICHIGAN
I
SAGINAW BAY
J (2)
ONTARIO
I
MEAN + STD. DEV. (REF. SEE TABLE 22)
- HIGH
I
- LOW
}
LOAD ESTIMATE
(SEE TABLE 23)
58. Calculated surface sediment concentration (yg/g(d)) at t = 50 years with partition
coefficient as a function of solids concentration.
t\\

-------
LOW LOAD ESTIMATE
->
00
LAKE MICHIGAN
o 100
>
O)
c
w Z
ii
So
s
-II-
<<
50
25
50
75
100
CENTRAL LAKE ERIE
~ 100 r
o>
c
 2
2^
2 O
Q O
O UJ
n
o
50
/
/

25
50
75
i
100
	Tf - 3.52 '10 (M)~*9240 (l/kg)
	7T = 2-105 (l/kg)
TIME , (yrs)
100
^ z
"D in
oil
o>S
3Lii
CO
5 uj
2 o
5 <

-------
HIGH LOAD ESTIMATE
LAKE MICHIGAN
CENTRAL LAKE ERIE
i P
00
o>
1

-------
Co steady state as a result of the diffusive flux of cadmium from the
sediment due to the lower partition coefficient. For Lake Michigan, the
surface sediment concentration decreases with the variable partition co-
efficient but for Lake Erie the surface sediment concentration increases.
This is similar to the response shown for PCB and discussed in Section
10. The continual Increase in concentration for central Lake Erie re-
flects the non-equilibrium condition of the upstream Lakes.
If a constant partition coefficient is assumed (as in Muhlbaier and
Tisue, 1981 and in Section 5 of this report, then it is seen that for
the water column a steady state is reached in about 25 years for Lake
Michigan and about 10 years for Lake Erie. A calculation then for Lake
Michigan that attempts to calibrate to the mean concentration of 27 ng/K,
(Table 22) then is simply a matter of estimating the approximate average
load and may not reflect a non-steady state condition as concluded by
Mulhbaier and Tisue (1981). However under a solids dependent partition
coefficient for cadmium (which as noted earlier appears to be supported
by field data for lakes, in general) the Great Lakes are not in equilib-
rium with the external load and for all practical purposes never reach a
steady state condition. Clearly then, under this model construct, it is
important to determine the solids dependence of cadmium for the range of
solids encountered in the Great Lakes water column and sediments (i.e.
0.5-240,000 mg/). If however it is temporarily assumed that a solids
dependent partition coefficient as given by Eq. (83) is applicable to
the Great Lakes, then the system is not in equilibrium with respect to
the external load.
Analysis of Model Results
Since the model equations are linear to the external load some fur-
ther analysis of the Lake cadmium response can provide additional insight.
Basically, a more appropriate estimate of the probable average load over
the past 50 years can be made exactly for the upper Lakes (e.g. Michigan)
and approximately for the lower Lakes (e.g. Erie). Let the rate (a) of
cadmium response in the water column to external areal loading be given
by
cT(t)
a(t) = -i		(84)
a
and also let II be the ratio of the surface (0-2 cm) sediment cadmium
concentration to the total water concentration, i.e. Eq. 69:
> - Mil
cT(t)
Figure 61 shows the load normalized water column response and the sedi-
ment/water column partition coefficient. For Lake Michigan as an up-
150

-------
stream lake, the normalized response as required In the water column and
sediment is linear to the load. Therefore, at 50 years, with a solid
dependent partition coefficient, the normalized response is about 0.11
ng/Jl t g/km2-yr. As noted, the difference in the partitioning between
the surface sediment and water column under the two partitioning schemes
is about an order of magnitude. Muhlbaler and Tisue (1981) using 20
ng 1% and 3 yg/g(d) concluded that II = 150,000 /kg. However their data
averaged 27 ng/Jl and the sediment concentration may vary at least from
1-3 ug/g(d). At 30 ngtl and 1 ug/g(d) II = 33,000 or a factor of two
above the variable partition coefficient case. The data therefore do
not permit a distinction between the constant or variable partition
assumption. However, since the compilation of data from other lakes
resulting in Eq. (83) clearly indicates a solids dependence of che
partition coefficient over the range of solids indicated, additional
analyses are made on that assumption.
For central Lake Erie, because of the upstream load time variable
behavior, the normalized response is dependent on the load level. (A
more detailed analysis using individual load responses would provide
exact load-independent normalized responses. However, time did not per-
mit a full examination of the individual temporally variable responses).
It is interesting to note however that the differences in the normalized
response for a given partition coefficient assumption are not great.
Also, the sediment/water column partitioning is essentially the same as
for Lake Michigan. Figure 61 provides a basis therefore for estimating
the water column and sediment response due to any load level constant in
time.
If it is assumed, as indicated above, that the Lake system has been
receiving an average increased load for about 50 years (i.e. a load in
addition to the background load), then an estimate of that load can be
made that is approximately consistent with the observed data of the
1970's. The results are shown in Table 26. As shown in this Table,
either water column or sediment cadmium data were assigned to represent
the condition of the 1970's. From the normalized response and the sedi-
ment/water column partition, either the water column or sediment concen-
tration was computed and then the associated average 50 year load was
calculated.
The calculations indicate that an average load of about 200-600
gCd/km2-yr for the upper Lakes over the preceding 50 years results in a
water column concentration of about 30 ng/ Jl and a surface sediment con-
centration of about 0.5 yg/g. Since background concentrations for these
lakes are about 3-6 ng/Jl and 0.5-1.0 Mg/g, the total concentration is
about 35-40 ng/Jl and 1-1.5 yg/g(d). For Lake Michigan the water column
concentration is higher than the 20 ng/Jl used by Muhlbaier and Tisue
(1981) and the sediment concentration is lower than the 3.0 pg/g(d) used
in their work. The estimates in Table 26 however are within the range
shown in Table 23. The loadings for the upper Lakes are below the lower
loading level shown in Table 24. This reflects the fact that the load-
ings of Table 24 are estimates of contemporary (e.g. 1970's) loading
whereas the estimated loading of Table 26 represent an average loading
condition for the preceding 50 years.
151

-------
TABLE 26
Estimate of Preceding 50 Year Average Cadmium Loading
Consistent With Observed Data in 1970's
(Solids dependent partition coefficient)
Lake
(ng/J.
m2-yr)(1)
n(2>
U/kg)

15,000

16,500
(A)
15,500
(4)
30,000
(A)
12,000
(4)
15,000
(4)
13,000
(A)
17,000
Assumed 1970's
(3)
Concentration
Water Col. Surface
(ng/fc)	yg/g
Calculated
Sed. Water Col. Surface Sed.
(ng/Jl)	yg/g
Approximate
Average
50 Yeaj Load
g/km -yr
Superior
Michigan
Huron
Saginaw Bay
Erie-West
-Central
-East
Ontario
0.114
0.125
0.114
0.103
0.041
0.111
0.105
0.098
30
60
0.5
0.5
5.0
3.5
3.5
75
33
33
417
233
269
0.5
1.8
1.3
290
240
290
580
10,160
2,100
2,560
765
(1)
(2)
(3)
(4)
Calculated normalized response at 50 years =
Calculated surface/sediment water column partition coefficient
Not including "background" concentration
Average of high and low normalized response

-------
For Lake Erie however the situation Is different and average load-
ings as shown In Table 26 are towards the high end of the contemporary
loading estimates. The calculated concentrations of 200-400 ng/Jl are an
order of magnitude higher than the upper Lakes and reflects the assumed
higher sediment cadmium concentration for Lake Erie.
Figure 61 shows that for Lake Michigan and solids dependent parti-
tion coefficient that if the average load shown in Table 25 were to con-
tinue that the normalized response would increase to about 0.2 or about
a 60% increase in the cadmium concentration over the next 50 years. The
concentration however would still be less than 100 ng/H, a level below
any apparent toxic effects.
If however the load Increases due to increased industrial usage and
manufacture then the concentration may approach levels of several hundred
ng/Jl as projected by Muhlbaier and Tlsue (1981). As such, cadmium should
be monitored for the upper Lakes both In the water column, sediment and
biota and periodic estimates should be made of the external cadmium load
to the Lakes.
The computations also indicate that Lake Erie concentrations are
about an order of magnitude higher than the upper Lakes. The estimates
should be checked by a field sampling program to determine present cad-
mium concentrations In the water column and sediment. The calculations
also indicate, in a manner similar to PCB, the significance of the par-
tition assumption in the calculated interstitial cadmium concentrations.
At a solids dependent partition coefficient, interstitial cadmium concen-
trations rise by about two-three orders of magnitude to levels of 10-100
Ug/Jl. It is of some importance then that the partition coefficient
solids dependence be determined and more directly that measurements be
made of the interstitial cadmium concentration In the sediment.
Conclusions
It is concluded from this application of the physico-chemical model
to cadmium in the Great Lakes that
1)	The degree of any dependence of the cadmium partition coeffi-
cient with solids has a marked effect on time to steady state
and Interstitial cadmium concentration.
2)	Under a solids dependent cadmium partition assumption, the Great
Lakes, especially the upper Lakes, do not reach a steady state
condition after 100 years of constant loading.
3)	Under a constant partition coefficient for cadmium, the Lakes
do reach an equilibrium condition varying from about 25 years
for Lake Michigan to 10 years for Lake Erie.
A) The concentration of cadmium In the Lakes would be expected to
increase by about 60% over the next 50 years if the average cad-
mium loading for the preceding 50 years continues.
5)	Based on assumed sediment cadmium concentrations for Lake Erie,
it is estimated that the cadmium concentration in the water col-
umn is about an order of magnitude higher than the other Lakes.
6)	If loads are projected to increase then cadmium concentrations
in the Lake system may increase to levels of concern.
153

-------
LAKE MICHIGAN
CENTRAL LAKE ERIE
25
50
75
100
L = LOW LOAD ESTIMATE
H = HIGH LOAD ESTIMATE
L . H
L , H
25	50
TIME . (yrs)
75
100
1.0
L
H

.01
JL
25
50
	7T = 3.52-106(M)~-9246(l/kg)
	7T = 2-105 (l/kg)
10
10
10
L , H
L . H
75
25	50
TIME , (yrs)
75
100
100
61. (Top) Calculated load normalized cadmium time variable response
(Bottom) Calculated sediment/water column partition coefficient time variable response

-------
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