ANL/ER-84-2
ANL/ER-84-2
TEN-YEAR FORECASTS OF
WATER QUALITY IN LAKE MICHIGAN
USING A DETERMINISTIC EUTROPHICATION MODEL
by
Barry M. Lesht
ARGONNE NATIONAL LABORATORY, ARGONNE, ILLINOIS
Operated by THE UNIVERSITY OF CHICAGO
for the U. S. DEPARTMENT OF ENERGY
under Contract W-31-109-Ena-38
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ANL/ER-84-2
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TEN-YEAR FORECASTS OF WATER QUALITY IN LAKE MICHIGAN
USING A DETERMINISTIC EUTROPHICATION MODEL
Barry M. Lesht
Environmental Research Division
March 1984
Report 1n Partial Fulfillment of
Interagency Agreement IAG AD-89 F-0-145-0
with
U.S. Environmental Protection Agency
Great Lakes National Program Office
536 South Clark Street
Chicago, Illinois 60605
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disclaimer
The Information In this document ha* * j .. u
United States Environmental Protection Anf!L> *? wholly or In part by the
number AD-89 F-0-145-0 with Argonne National ik ""J61" Int®ra9ency Agreement
to peer review by the EPA and by Arqonne * been subject
approved for publication. Any mention of tiEE! Laboratory and has been
does not constitute endorsement or recommendation nfms or commerc a products
11
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TABLE OF CONTENTS
Page
FIGURES 1v
TABLES vi
ACKNOWLEDGEMENTS v11
ABSTRACT 1
INTRODUCTION 1
LAKE MICHIGAN MODEL 4
Development 4
Five-Year Hlndcast 8
TEN-YEAR SIMULATIONS 12
Loading Scenarios . 12
Winter Scenarios 14
Limiting Simulations 15
Monte Carlo Simulations 19
DISCUSSION 21
Comparison with Mass-Loading Models 23
Historical Simulation with Accelerated Removal 25
Non-D1mens1onal Forms of Mass-Loading Model 27
LITERATURE CITED 32
111
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FIGURES
Number _r
1 State variables and interactions LAKE1 model
2 Segmentation 1n Lake Michigan eutrophlcation model
3 Comparison of model prediction with calibration and verification
data before modification to Include accelerated particle
removal . .
4 Comparison of model prediction with calibration and verification
data after modification to include accelerated particle removal . .
5 Five-year simulation of chlorophyll-a 1n the southern basin
epllimnlon using the unmodified model and the model modified to
Include accelerated removal
6 Five-year simulation of total phosphorus In southern basin
epllimnlon compared with calibration and verification data ....
7 Historical estimates of total phosphorus loads to Lake Mlchiqan
1975-1980 ! . . .
8 Ten-year simulations of chlorophyll-a in the southern basin
epllimnlon. Limiting cases - large loads, mild winters-
small loads, severe winters
9 Ten-year simulations of whole-lake-volume-averaged total
phosphorus. Limiting cases as In Figure 8
1° Sensitivity of the ten-year constant-condition simulation of peak
chlorophyll-a in the southern basin epllimnlon to winter
conditions .
11 Theoretical probability distributions and histograms of Monte
Carlo realizations for random phosphorus loads and Ice days ....
12 Results of Monte Carlo simulation for peak chlorophyll-a 1n the
southern basin epllimnlon, mean and one standard deviation
limits
iv
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FIGURES (Cont'd)
Number Page
13 Results of Monte Carlo simulation for whole-lake-volume-averaged
total phosphorus, mean and one standard deviation limits 22
14 Results of Monte Carlo simulation for peak chlorophyll-a In the
southern basin epIUmnlon, mean and one standard deviation
1Imlts • ••••••••••••••••••••••••••••• 23
15 Comparison of mass-loading and dynamic models for whole-lake-volume-
averaged total phosphorus after 10 simulation years—constant loads,
no Ice cover 26
16 Comparison of mass-loading and (Jynamlc models for whole-lake-volume-
averaged total phosphorus after 10 simulation years—constant
loads 1ce cover, as a function of 1ce cover 26
17 Historical total phosphorus loading to Lake Michigan 1850-1970
based on Chapra (1977) 28
18 Predicted total phosphorus concentration In Lake Michigan 1850-1970
using estimated loading shown 1n Figure 17 In model with accelerated
removal 28
19 Fraction phosphorus concentration change at equilibrium as a
function of loading and Ice days 30
20 Time to equilibrium for several phosphorus-loading conditions as
function of 1ce days 31
v
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TABLES
Number Page
1 Reported total phosphorus loads 1n Lake Michigan 1974-1980 9
2 Initial conditions used 1n multi-year simulations, southern
basin ep1Hmn1on 11
3 Days of greater than 30% Ice cover on Lake Michigan, 1976-1981 ... 15
4 Scenario for phosphorus loads and Ice days used 1n ten-year
simulations 16
vi
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ACKNOWLEDGEMENTS
This work was supported by the Great Lakes National Program Office of the
U. S. Environmental Protection Agency (IAG AD-89 F-0-145-0) and conducted in
cooperation with members of the Environmental Sciences and Engineering Program
at Manhattan College, New York. Thanks are due to Mr. David Rockwell of the
U.S. EPA, who served as Project Officer, and to Drs. Dominic DIToro, Richard
W1nf1eld, and John Connolly of Manhattan College.
vi 1
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TEN-YEAR FORECASTS OF WATER QUALITY IN LAKE MICHIGAN
USING A DETERMINISTIC EUTROPHICATION MODEL
by
Barry M. Lesht
ABSTRACT
A dynamic, deterministic lake eutrophlcation model was used
to forecast changes In Lake Michigan water quality over a ten-year
simulation period. Emphasis was placed on changes 1n eplllmlnon
phytopiankton blomass and In whole-lake total phosphorus concen-
tration 1n response to changes In Input phosphorus loads and
to variations 1n winter conditions. Constant-condition simula-
tions corresponding to current, Increased, and reduced loads and
to mild, average, and severe winters were used to establish bounds
for the projected changes In water quality. Monte Carlo-type
simulations were used to estimate the variance associated with the
projections. Given the assumptions and limitations Inherent In
the modeling process, water quality In Lake Michigan 1s projected
to Improve slightly (reduced concentrations of phy topiankton and
total phosphorus) over the next ten years. Year-to-year varia-
tions are significant, however, and will depend on loading and
winter conditions. The variation 1n the projected values associ-
ated with the assumed fluctuations 1n loads and winter conditions
1s approximately 20 percent.
INTRODUCTION
Dynamic, deterministic eutrophlcatlon models have been applied to several
of the Great Lakes (Thomann et al., 1975; Blerman and Dolan, 1981; DIToro and
Connolly, 1980; DIToro and Matystlk, 1980; Rodgers and Salisbury, 1981). One
of the primary reasons for the development of these models has been to provide
a method of simulating the biological and chemical response of the lakes to
environmental changes, particularly those changes that might result 1n alter-
ation of the trophic state of the lakes. The most common change considered 1n
this context 1s variation 1n the amount of the critical nutrient phosphorus
that enters the lake. In recent applications these models have been used both
1
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to evaluate the effect of established phosphorus control measures and to
predict the effect of proposed controls.
Although phosphorus controls are undoubtedly Important for the long-term
status of a lake, a surprising result of one of these model studies 1s the
discovery that naturally occurring processes may be much more significant than
enforced controls In reducing lake-water phosphorus concentration over short
periods (Rodgers and Salisbury, 1981). This was suggested during Rodgers and
Salisbury's development of a eutrophlcation model for Lake Michigan when they
found that accelerated particulate settling associated with winter 1ce cover
could be responsible for more than 85 percent of the unusually large (>35 per-
cent) phosphorus loss observed In Lake Michigan over the years 1976-1977
(Rockwell et al., 1980). In a separate study, Rockwell (1981) also found
strong historical evidence for a correlation between over-winter phosphorus
loss and winter 1ce cover In other Great Lakes, although he did not attribute
his findings to any specific mechanism. In terms of the eutrophlcation
models, this result Implies that long-term predictions of water quality based
on assumed nutrient loads must also Include some provision for nutrient
removal by natural processes.
The purpose of this report 1s to present the results of a study 1n which
a dynamic, deterministic eutrophlcation model that Included accelerated par-
ticle-removal processes during the winter was used to make long-term (ten-
year) forecasts of water quality in Lake Michigan. Following Rodgers and
Salisbury (1981), the hypothesized accelerated particle removal was para-
meterized In the model by an eight-fold increase 1n the assumed partlculate-
settUng velocity during those days when 30 percent or more of the lake was
ice covered. Historical data obtained from composite aerial and satellite
photographs (D.C. Rockwell, personal communication) were used to determine
days of 1ce cover from 1976-1981 and to estimate the statistical distribution
of yearly Ice cover. Estimates made by the International Joint Commission
(1975-1980) of total phosphorus Input to the lake were used to establish
loading scenarios for use 1n the simulations, and 1n conjunction with the
observed 1ce days, to bring the model forward from the last Intensive survey
year (1977) to 1981, the starting point for the ten-year forecasts.
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Two sets of simulations were conducted. In the first set, different
combinations of phosphorus loading and Ice conditions were assumed to remain
constant during the ten-year simulation period. In the second set, ice days
and loads were chosen randomly, In Monte Carlo fashion, from prescribed dis-
tributions. In all, more than 350 ten-year runs were made. These simulations
provided forecasts of the likely limits of lake response to loading and
extreme winter conditions, as well as an estimate of the variance, due to
uncertain loads and winters, associated with each forecast.
Assuming that Lake Michigan does Indeed experience accelerated par-
ticulate removal during the winter and responds to external loads as modeled,
the simulations show a steady Improvement In water quality from 1976 to
1981. Predicted peak chlorophyll-a levels In the southern basin eplllmnlon
dropped from 3.0 jig/L in 1976 to 1.6 yg/L in the summer of 1980, while total
phosphorus concentration decreased from just under 7 yg/L to 5 ug/L. These
Improvements were predicted even though the assumed yearly total phosphorus
load, based on International Joint Commission estimates, exceeded the 1978
water quality agreement target load of 5600 metric tons per year In every year
except 1977. The predicted Improvement thus Is due more to Incorporating the
effects of the exceptionally severe winters of 1977, 1978, and 1979 into the
model than to any changes in loading. The model does predict, however, that
total phosphorus In the lake did Increase In 1980 after the relatively mild
winter, as a result of excess loading.
Ideally, a model exercise such as this would be accompanied by collection
and analysis of field data to confirm the model results. Unfortunately, very
few data are available for Lake Michigan in the period 1977 to 1981. Those
data that are available for eplllmnlon chlorophyll-a and for total phosphorus
(one point in 1980) generally are within the bounds obtained from the calcu-
lated values. The calculated values, then, based on estimated phosphorus
loads and observed 1ce cover, were used to Initialize the ten-year simulations
conducted for the period 1981-1992.
The long-term model simulations suggest that given the initial conditions
provided by the hlndcast and the assumed limits of phosphorus loading and
winter ice cover, water quality in Lake Michigan, as measured by peak epi-
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4
Hmnion chlorophyll-a concentration and by whole-lake total phosphorus concen-
tration (volume-weighted average), can be expected to Improve or, at worst,
remain stable over the next ten years. However, the analysis also suggests
that 1f either the amount of phosphorus loaded Into the lake Increases
drastically, or the region experiences a long succession of very mild winters,
the trend toward Improvement would reverse. The ultimate trophic state of the
lake will depend on both factors.
LAKE MICHIGAN MODEL
DEVELOPMENT
The eutrophlcation model used 1n this study 1s one of a general class of
dynamic, deterministic water quality models developed by Hydroscience
(Westward, New Jersey 07675). The general model, based on a simple mass
conservation equation, allows the user to follow the time history of several
so-called state variables (water quality constituents) 1n many model segments,
representing discrete volumes of water, simultaneously throughout a simula-
tion. Included in the mass balance are the effects of advectlon and mixing
between segments, external loading of state variables and Internal sources and
sinks, which may Include chemical and biological transformations. The model
framework also provides a means of specifying external forcing functions as
may be required for the particular application, 1n this case, eutrophlcation
1n Lake Michigan.
Adapting the general model to a specific purpose 1s a complicated task.
Not only must the physical system that the model 1s to represent be described
1n terms compatible with the general model framework, but also the chemical
and biological components of the system must be selected and the Interactions
between them expressed mathematically. Furthermore, since the equations
representing the Interactions among state variables almost always Involve
parameters of unknown value, the model must be compared to field data to give
reasonable values to these parameters. Finally, once a model 1s calibrated
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(I.e., parameters assigned values based on comparison with data) the model
must be verified, that 1s, compared with Independent field data, before 1t can
be used for simulation. These steps may have to be repeated many times before
an acceptable model 1s found.
The Lake Michigan model was developed, calibrated, and verified by
Rodgers and Salisbury (1981). They based their development on the LAKE1
kinetic formulation used successfully In Lake Ontario (Thomann et al.,
1975). This formulation requires eight state variables (F1g. 1) and, for Lake
Michigan, six segments (F1g. 2). The state variables are total phytopiankton
blomass, expressed In terms of chlorophyll-a concentration; herbivorous and
carnivorous zooplankton; three forms of nitrogen (non-living organic nitrogen,
nitrate + nitrite, and ammonia); and two forms of phosphorus (non-living
organic phosphorus, and soluble reactive phosphorus). The segmentation scheme
represents the open lake (I.e., offshore) ep1limn1on, hypol1mn1on, and
sediments of both the northern and southern basins of the lake. Nearshore
areas are explicitly excluded from the model, although as pointed out by
Schelske (1980), nearshore areas receive most of the phosphorus load and may
have considerably different water quality than offshore, open-lake areas.
Data collected during the 1976 Intensive survey of Lake Michigan
(Rockwell et al., 1980) were used to calibrate the model, which was subse-
quently compared to data collected 1n 1977. This comparison showed that the
original LAKEl-type model failed to predict the decrease In peak chlorophyll-a
level (F1g. 3) and the large drop In total phosphorus observed In the 1977
data. After careful analysis of the data and several attempts at
recallbratlon, Rodgers and Salisbury hypothesized that the discrepancy between
observation and model output was related to the especially severe winter of
1976-1977. They experimented with several methods of working within the model
framework before they found that they could fit the model output to the
observations by Increasing the value of the parameter representing particu-
late-settUng velocity during the period when the lake was ice covered (F1g.
4). This Increase changed the assumed settling velocity from 0.2 m/day to 1.6
m/day during the 85 days that Lake Michigan was Ice covered during the winter
of 1976-1977.
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Figure 1. State variables and Interactions LAKE1 model.
SOUTHERN BFISIN NORTHERN BBS IN
EPILIMNION
HYPOLIMNION
SEDIMENT
Figure 2. Segmentation 1n Lake Michigan eutrophlcation
model.
SEGMENT 1
SEGMENT 2
SEGMENT 3
SEGMENT 4
SEGMENT 5
SEGMENT 6
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7
rJ 4-
CD
ZD
cc 3-
>-•
JZ
Q_ 2 H
o
•
CD
CJ 1
SOUTHERN BASIN EPILIMNION
T I I I I I I I—I 1 1 1 1 1 1—I 1—I 1 1 1 1 1 1
JFMflHJJflSONDJFMflMJJflSOND
SIMULATION MONTH
Figure 3. Comparison of model prediction with calibration and
verification data before modification to Include
accelerated particle removal.
SOUTHERN BASIN EPILIMNION
1—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—\—i—i—i—i—i
JFMRMJJRSONDJFMflMJJRSOND
SIMULATION MONTH
Figure 4. Comparison of model prediction with calibration and
verification data after modification to Include
accelerated particle removal.
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Although the modified parameter 1s called settling velocity, 1t 1s
actually a simplified way of representing many factors affecting patlculate
transport 1n the lake. These Include gravitational settling, sediment resus-
penslon, and transportation of nutrients from nearshore to offshore waters.
Rodgers and Salisbury's hypothesis 1s that severe winter conditions alter the
balance between these, and perhaps other, processes. Analysis Indicates that
the behavior of other particle-bound substances seems consistent with this
hypothesis (Blerman and Swain, 1982). Rodgers and Salisbury's solution,
although ad hoc, has the attraction of being simple, physically reasonable,
and consistent with the 1977 data. In the following, 1t 1s assumed that their
hypothesis 1s correct.
FIVE-YEAR HINDCAST
The overall purpose of this study 1s to use the eutrophlcation model to
project the likely state of water quality of Lake Michigan ten years Into the
future under different liypotheslzed phosphorus-loading scenarios. Rodgers and
Salisbury (1981) showed that winter conditions also must be specified 1n any
long-term projection. Since the last extensive data survey was made 1n 1977
and since phosphorus-loading and winter conditions are known, as well as can
be, for the period 1976-1981, the model was used to hlndcast this period to
provide a starting point for the ten-year simulations. The alternatives would
have been to begin all simulations at 1977 and run forward 14 years, or to
collect new data for Initialization 1n 1981. Because of the number of simu-
lations to be conducted, a 40 percent savings 1n computer time was achieved by
starting with 1981 Instead of 1977. Furthermore, mounting an Intensive field
effort, although desirable, would be prohibitively expensive.
The phosphorus-loading data used In the five-year hlndcast are listed 1n
Table 1. The total phosphorus load was divided Into fractions representing
available and non-living organic phosphorus (slowly available) using the same
method as Rodgers and Salisbury (1981). The fractions loaded into the
northern and southern basins were determined In the same manner (Lesht, 1982).
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Table 1. Reported total phoshorus loads (metric tons)
to Lake Michigan, 1974-1980
Year
Total
Municipal
Industrial
Tributaries
Atmosphere
1975
5359
1066
61.3
4231
no estimate
1976
6656
1040
32
38941
1690
1977
4666
660
50
22661
16902
1978
6245
494
46
40151
16902
1979
7659
371
13
43061
2969
1980
6574
431
37
31371
29693
^Includes adjustment for unmonltored tributaries.
*1976 estimate.
1979 estimate.
The results of the five-year hlndcast are shown 1n Figure 5, a time-
series plot of southern basin eplllmnlon chlorophyl1-a. Also plotted are data
collected by Parker et al. (1981) and by the U.S. Environmental Protection
Agency (D.C.Rockwell, personal communication). Although the peak levels
recorded by Parker were significantly higher than those predicted by the
model, agreement during most of the year Is very good. However, the trend
predicted by the model toward decreasing peak levels of chlorophyll-a 1s not
readily apparent 1n the data.
Such detailed data are not available fo? total phosphorus, the five-year
calculation shown In Figure 6. The data plotted are from the U.S. Environ-
mental Protection Agency for 1976-1977 (Rockwell et al., 1980) and 1980 (D. C.
Rockwell, personal communication). The effects of Increased winter settling
on the model output are obvious on this plot, accounting for the steep drops
1n predicted values early In the year. Overall, the amount of total phos-
phorus 1n the water Is predicted to have declined In the period 1976-1980.
Again, the 1980 datum 1s within the bounds suggested by the two limiting forms
of the model.
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Figure 5. Five-year simulation of chlorophyl1-a In the southern
basin ep1l1ron1on using the unmodified model (dashed
line) and the model modified to Include accelerated
removal (solid line). Data are from Parker et al
1982 (crosses) and U.S. EPA cruise (triangle).
In addition to providing some confidence 1n the adequacy of the model,
the five-year hlndcast provides a starting point for the ten-year simula-
tions. The initial conditions used 1n the ten-year simulations and those used
1n the five-year hlndcast are listed 1n Table 2. The starting point for both
the long-term simulation and the hlndcast was January 1. All other external
forcing functions, Including water temperature, solar radiation, vertical
mixing, and nitrogen loading, were assumed to remain constant from year to
year. Similarly, the value of each of the kinetic parameters used 1n the
model was assumed to be constant. The effects of these assumptions on the
Lake Michigan model are discussed by Lesht (1582). Scavla et al. (1981) show,
1n great detail, how uncertainty 1n key parameter values affects the output of
other models of this type. These sources oF model uncertainty are not con-
sidered here, and their effect on the output of the ten-year simulations 1s
unknown.
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SOUTHERN BASIN EPILIMNION
CD
3
CO
ZD
C£
O
JZ
Q_
CO
O
CE
E-h
O
E-h
\"0'
SIMULATION YEAR
Figure 6. Five-year simulation of total phosphorus In southern
basin eplllmnlon compared with calibration (triangles)
and verification (circles) data.
Table 2. Initial conditions used in multi-year
simulations, southern basin eplllmnlon
State Variable
5-Year
S1mulatlon
10-Year
Simulation
Chlorophyll-a (ug/L)
0.900
0.537
Herblvorus zooplankton (mg/L)
0.010
0.006
Non-living organic N (mg/L)
0.132
0.067
Ammonia N (mg/L)
0.003
0.002
Nitrate + nitrite N (mg/L)
0.236
0.220
Non-11v1ng organic P (mg/L)
0.005
0.004
Reactive P (mg/L)
0.0015
0.0008
Carnlvorus zooplankton (mg/L)
0.0065
0.0064
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TEN-YEAR SIMULATIONS
Although the eutrophlcation model could be used to make water quality
forecasts over any length of time, the long-term simulations reported here
were limited to ten years. The selection of this limitation was based 1n part
on a desire to conserve computer resources and 1n part on a preliminary
analysis suggesting that the Lake Michigan model would reach equilibrium,
under constant-loading scenarios, In 7 to 14 simulation years. Given all the
sources of uncertlnty 1n the model prediction (Scavia et al., 1981; Lesht,
1982) It seemed Imprudent to carry the simulation too far Into the future; on
the other hand, 1t was obvious that several simulation years would be required
to discern any trend forecast by the model. Thus, ten years was chosen as a
reasonable period over which to examine the predicted response of the lake to
changes 1n phosphorus loading.
LOADING SCENARIOS
The target total phosphorus load for Lake Michigan established under the
1978 Water Quality Agreement 1s 5600 metric tons per year. This load 1s con-
sidered achievable If all municipal sewage treatment plants discharging more
than 1 million gallons per day into the lake reduced their effluent phosphorus
concentrations to less than 1 mg/L. Historical estimates of phosphorus load-
ing (Fig. 7) show, however, that since 1974 this target has been met only 1n
1977 and that the reduced loading in 1977 was due to reduction 1n tributary
flow rather than to effluent control measures. Indeed, Figure 7 shows that
remaining controllable sources (direct municipal and Industrial) of total
phosphorus are small relative to the uncontrollable sources (atmosphere and
tributaries). Not Included 1n these amounts are phosphorus loads caused by
shoreline erosion.
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10000 -I
8000 A
2000
Legend
ESS Industrial
CZD direct
(SD Indirect
IB atmosphere
Y/\ tributaries
6000 A
4000
1975 1976
1980
Figure 7. Historical estimates of total phosphorus loads to
Lake Michigan 1975-1980.
Assuming that the estimates of phosphorus loads are fairly accurate, the
following loading scenarios were established for use in the simulations:
1) Water Quality Agreement target load of 5600 metric tons per year.
This represents a "best case" scenario in which all loads from 1981
on are at the target value.
2) Constant load of 6350 metric tons per year. This scenario represents
the situation in which direct municipal and industrial surces are
reduced to target values, but uncontrolled tributary and atmospheric
loads from 1981 to 1990 remain at recent levels.
3) Random samples from a truncated normal distribution with a mean of
5600 metric tons per year and standard deviation of 1000 metric tons
per year. The distribution is truncated so that the minimum possible
load is 4000 metric tons per year. This case models random fluctua-
tions in the tributary and atmospheric loads, added to municipal and
I .
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14
Industrial loads at their target levels, and should be considered the
most realistic of the loading scenarios based on the International
Joint Commission target load.
WINTER SCENARIOS
One of the major results of the work of Rodgers and Salisbury (1981) was
the modification of the LAKEl-type model to Include time-dependent particle-
settling velocity. They found that by Increasing the value of the particle-
settling- velocity parameter during the period of the year that the lake was
Ice covered, they could account for the large phosphorus loss (35 percent)
observed 1n Lake Michigan over the winter 1976-1977. Rockwell (1981) extended
Rodgers and Salisbury's analysis by analyzing historical data from other Great
Lakes. He found a strong correlation between over-winter phosphorus loss and
the annual maximum extent of 1ce cover. As was pointed out by Lesht (1982),
the factor by which settling velocity Is Increased 1n Rodgers and Salisbury's
model Is a calibrated parameter, that Is, 1t Is adjusted to fit the data.
Therefore, given an arbitrary definition of "1ce cover", a certain amount of
error can be accounted for by adjustment of the settling-velocity parameter.
For consistency, we have used Rodger's 30 percent definition of Ice cover and
his calibrated value of under-lce settling velocity. Somewhat less Informa-
tion 1s available for establishing the winter 1ce-cover scenarios than was
available for loading. The Lake Michigan 1ce-cover data compiled by the World
Data Center for Glaclology and provided by D. C. Rockwell (personal com-
munication) are summarized 1n Table 3. These data were obtained from
composite aerial and satellite photographs taken every two weeks. Based on
these data, the following winter scenarios were considered:
1) Average winters consisting of 45 days of 1ce cover. This 1s the
arithmetic mean and median of the observations listed In Table 3.
2) MlTd winters consisting of 16 days of Ice cover.
3) Severe winters consisting of 74 days of Ice cover.
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15
4) Random samples from a normal distribution with mean of 45 days and
standard deviation 29 days. Although the distribution Is normal,
samples less than zero are treated as zero, resulting In a trunca-
tion at zero days.
5) The unmodified model (I.e., Ice days equal to zero) was also
tested.
Table 3. Days of greater than 30X Ice cover
cover on Lake Michigan, 1976-1981
Winter
Ice Days
Onset*
1975-1976
7
February 3
1976-1977
83
January 6
1977-1978
56
January 18
1978-1979
70
February 5
1979-1980
21
January 21
1980-1981
35
January 14
Earliest 1ce days.
All combinations of the loading and winter scenarios outlined above were
used In the simulations; these are summarized 1n Table 4. Each simulation
Involving a random Input (either loads or Ice cover or both) was repeated 50
times. The random selections were made using subroutine GGfM. of the Inter-
national Mathematical and Statistical Library. Output consisted of time
series of the principal state variable values in the non-random simulations
and time series of the mean and standard deviation of the principal state
variables 1n the Monte Carlo simulations. Output was printed at flve-slmula-
tlon-day Intervals.
LIMITING SIMULATIONS
The limiting simulations considered here are those 1n which both loading
and winter conditions were held constant during each of the ten simulation
years. Since phosphorus loading and winter removal can be viewed as competing
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Table 4. Scenarios for phosphorus loads and 1ce days
used in ten-year simulations
Scenario
Val ue
Loading Scenario
Phosphorus Loads*
1978 Water Quality Agreement Target
5600
Probable limit of controlled loads
6350
Random from normal distribution
5600 + 1000 but >4000
Winter Scenario
Ice Cover (days)
Mild winter
16
Average winter
45
Severe winter
74
Random from normal distribution
45 t 29
Metric tons/year.
mechanisms, the combinations of the extremes of each can be viewed as best-
case and worst-case scenarios. The ten-year predictions for southern basin
chlorophyll-a resulting from these two extreme situations are shown 1n Fig-
ure 8. The difference 1n trends Is obvious, with the best case leading to
rapid Improvement 1n water quality and the opposite occurring 1n the worst-
case simulation. These differences are reflected 1n the ten-year prediction
for total phosphorus (F1g. 9). The saw-toothed pattern 1n this plot Is a
result of adding the modeled phosphorus load 1n equal Increments throughout
the year and removing phosphorus at an accelerated rate at the beginning of
the year. The available phosphorus data are too variable to confirm this
"w1th1n-year" pattern (Lesht, 1982); however, a close correspondence between
the model and data In this regard would not be expected since the model
assumes a constant rate of phosphorus loading throughout the year.In addition
to establishing limits of lake response, these constant-condition simulations
provide Information concerning the sensitivity of the model predictions to
variations 1n 1ce cover and phosphorus loading. As shown 1n Figure 10, for
the two fixed-load conditions, the model 1s quite sensitive to the assumed
winter conditions. This result may be compared with that presented by Thomann
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17
3i SOUTHERN BRSIN EPILIMNION
DFiSHED - 6350 TONS/YERR; 16 ICE DflYS/YEFIR
SOLID - 5600 TONS/YEAR; 71 ICE DFItS/YEFIR
_J
C9
3
0
1
_J
X
Q_
O
q:
o
_j
x
o
2-
1 -
1981
1983
1985
1987
1989
SIMULATION YEAR
1991
Figure 8. Ten-year simulations of chlorophyll-a In the southern
basin ep1l1mn1on. Limiting cases - large loads, mild
winters (dashed); small, loads, severe winter (solid).
WHOLE LAKE VOLUME AVERAGE
C9
o
CD
ID
OC
O
X
ci-
cn
o
x
Q_
6-
-J 2 -
-------
18
cs
o
2.5-1
2-
1.5-
£ H
CL.
O
QC
O 0.5H
_J
o
_J
\
CD
3
Q_
0
01
O
_J
X
o
0.5-
TRRGET LORDS
5600 METRIC TONS/YERR
0 1 2 3 4 5 6
2-5"i REALISTIC LORDS
6350 METRIC TONS/YERR
1.5-
7 8
0 1
n r
2 3
n r
4 5
"i
7
"T~
9
8 9
MILD
- flVERRGE
SEVERE
n
10
MILD
RVERRGE
SEVERE
\
10
Figure 10. Sensitivity of the ten-year constant-condition
simulation of peak chlorophyll-a 1n the southern
basin ep111mn1on to winter conditions.
et al. (1977) 1n which they examined the sensitivity of a Lake Ontario model
to various kinetic assumptions dealing with long-term decay of dissolved
Inorganic forms.
Also evident from Figure 10 1s that for both loading cases, "average"
conditions tend toward Improved water quality, Implying that average yearly
phosphorus removal exceeds loading even at higher load levels. However, It
should be recalled here that the "average" condition 1s based on only six
recent years, and that the assumed normal distribution has a high coefficient
-------
19
of variation (0.64), so that the probability of occurrence of an "average"
year, although higher than any other, 1s of the same order of magnitude as the
probability of occurrence of a mild or a severe winter.
MONTE CARLO SIMULATIONS
If the assumed distribution of 1ce days 1s fairly accurate and If the
number of 1ce days In any year 1s Independent of the number of Ice days 1n any
other year, then the probability of ten successive winters of any fixed number
of 1ce days 1s extremely low. Thus, although the constant-condition simula-
tions may represent extremes of lake response to variations 1n loading and
winter 1ce cover, these extremes would not be likely to occur. Since we are
Interested 1n the most likely response of Lake Michigan to input-controlling
factors that are assumed to be random, some stochastic representation of the
problem would be more appropriate than the constant-condition approach. The
approach taken here 1s to examine the statistics of results obtained using the
deterministic model when the yearly phosphorus loading and number of 1ce days
1s chosen at random from pre-speclfled probability distributions.
The exact probability distributions used are those specified above. Both
are normal but truncated on the low end. In the case of phosphorus load, the
truncation 1s 1.6 a below the mean; 1n the case of number of 1ce days, the
truncation 1s 1.55 a below the mean. The theoretical distributions, as well
as the distribution of values selected In the Monte Carlo process, are shown
1n Figure 11. With so few data available, the choice of probability distri-
bution 1s essentially arbitrary (Scavla, 1981). Although other distributions
could be used, the truncated normal 1s simple to calculate and a reasonable
first approximation.
Each of the Monte Carlo simulations consisted of 50 ten-year runs of the
model. Within each ten-year run, the phosphorus load and ice-cover condition
for each year was selected from the appropriate probability distribution.
Time series of the mean and standard deviations of the output state variables
were produced at the same five simulation-day interval used in the constant-
condition simulations.
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20
RNNURL PHOSPHORUS LORD
70 -|
0 30 60 90 120
RNNURL ICE DRYS
Figure 11.
Theoretical probability distributions and histograms
of Monte Carlo realizations for (A) random phosphorus
loads and (B) ice days.
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21
As would be expected, the mean of the Monte Carlo simulations follows the
same trend as the corresponding constant-condition simulation. Figure 12
Illustrates this for the case when both loads and 1ce days are assumed to be
random. Of particular Interest here 1s the band of solutions shown within the
one standard deviation limits. The fact that the band seems to be bounded
Implies an Inherent statistical stability In the modeled system. Thus, random
effects that may cause short-term variations maiy be compensated for In the
long-term. This 1s not to say that any particular ten-year trajectory will be
within these bands, but the statistical distribution of trajectories Is fairly
narrow.
A t1me-ser1es plot of total phosphorus concentration predicted by the
Monte Carlo simulations Illustrates much the same thing (Fig. 13). As In the
case of peak ep1l1mn1on chlorophyll, the phosphorus trend follows that pre-
dicted by the constant-condition simulation, and the one standard deviation
limits are also fairly small, approximately 10 percent of the mean value.
DISCUSSION
Two points must be kept 1n mind when Interpreting the results of this
study* The first point 1s that the output of the model simulations 1s a
product of the model, Its structure, and the assumptions made rather than of
Lake Michigan. Although this maty seem obvious, 1t 1s often overlooked when
models are developed for practical applications. The degree to which the
model actually represents the biological and chemical processes Important In
lake eutrophlcation 1s a problem not considered here. The second point 1s
that the variations In phosphorus loading and winter Ice cover are not the
only, nor necessarily the most significant, sources of uncertainty In models
of this type. As Scavla et al. (1981) demonstrate, uncertainty 1n many of the
key parameters considered fixed In this study may result 1n significant varia-
tion 1n model output. This source of uncertainty also Is not considered
here.
Given these two qualifications, this ten-year simulation study does have
Interesting positive results. Primary among them 1s the prediction that In-
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22
2.5-| SOUTHERN BASIN EPILIMNION
CD
Q_
O
cc
o
X
o
2.0-
1.5-
1.0
0.5-
0.0
ANNUAL LORD RANDOM
ICE 0RYS RANDOM
10
SIMULATION YERR
Figure 12. Results of Monte Carlo simulation (both
loads and ice days random) for peak
chlorophyll-a in the southern basin
epilimnion, mean and one standard devia-
tion limits.
CD
U
U~)
ZD
CD
X
Q_
CO
o
X
Q_
X
o
E—
WHOLE LRKE VOLUME HVERHGE
LORDS RANDOM RND ICE DAYS RANDOM
50 RUNS
1981 1983 1985 1987
SIMULATION YERR
1989
—I
1991
Figure 13. Results of Monte Carlo simulation (both loads and
ice days random) for whole-lake-volume-averaged
total phosphorus, mean and one standard deviation
1imits.
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23
place phosphorus control measures seem adequate to maintain the quality of the
open waters of Lake Michigan. In fact, the simulations show that the long-
term trend of water quality is stable even if the yearly phosphorus loads
exceed the agreement target by 13 percent (Fig. 14). This does not imply that
a 13 percent increase above target is an upper limit to allowable loads, but
that little change from current conditions would be expected even if loads
were that high.
CD
D
>1
X
CL
O
CC
O
o
2.5
2.0-
1.5
1.0
0.5-
0.0
SOUTHERN BASIN EPILIMNI0N
RNNUflL LOAD 6350 METRIC TONS
ICE 0RYS RANDOM
I
10
SIMULATION YEAR
Figure 14. Results of Monte Carlo simulation (fixed load, ice
days random) for peak chlorophyll-a in the southern
basin epilimnion, mean and one standard deviation
limits.
COMPARISON WITH MASS-LOADING MODELS
The target phosphorus loads for the Great Lakes were established using
simple mass-loading models. These models, such as the one presented by Chapra
(1977), can be written as:
V^P = W - Qp - vAsp (1)
-------
24
where V 1s lake volume, p 1s total phosphorus concentration, W 1s annual
phosphorus loading, Q Is advective outflow, v 1s the apparent settling velo-
city of total phosphorus, and A$ Is the surface area of the sediments.
Equation (1) 1s an expression of mass balance for total phosphorus 1n
which the change 1n water column phosphorus concentration 1s the net result of
loading, outflow, and sedimentation. Although more complicated in Its struc-
ture, the dynamic deterministic eutrophlcatlon model used 1n this stutjy 1s
based on the same type of mass-balance equation. The significant difference
between the two models 1s that the dynamic model calculates the mass balance
for each of the state variables, thereby providing direct predictions for many
of the quantities of Interest. Thus, 1f the problem at hand Involves a vari-
able other than total phosphorus, the dynamic model 1s the appropriate tool to
use. Other differences and advantages of each model type are discussed by
Thomann (1977).
Since both models are based on mass balances, it 1s reasonable to expect
them to agree, at least for long-term predictions of total phosphorus. In the
context of this study, however, some provision must be made for the variable
particle-removal rate that was Incorporated Into the dynamic model. The
Chapra model Involves a parameter, v, that represents the apparent settling
velocity for total phosphorus. Based on empirical evidence, Chapra and
Sonzogni (1979) determined a constant value of 12.4 m/yr for v in Lake
Michigan. This may be compared to the 73 m/yr base (without any 1ce cover or
accelerated settling) particle-removal rate assumed 1n the 4ynam1c model.
The difference between the numerical value of the two parameters 1s due
to the fact that even though both are called "settling velocity", they
actually represent different processes and scales. While this parameter
Incorporates particle settling, resuspenslon, and offshore transport 1n the
dynamic model, It Includes all these factors plus decay and re-solut1on
processes of Inorganic phosphorus 1n the mass-balance model. Thus, although
the parameters are conceptually related, there 1s no simple transformation of
one to the other.
-------
25
If the mass-balance model, Equation (1), is solved as a function of time,
one obtains:
P(t> * Peq ~ [P0 - Peq]e-<* (2)
where Peq 1s the equilibrium total phosphorus concentration, Peq = W/(Q+vAs);
P0 1s the initial total phosphorus concentration; and a = (Q+vAs)/V. Assuming
that v = 12.4 m/yr and that the phosphorus loading, lake volume, outflow, and
surface area are the same as 1n the dynamic model formulation, Equation (2)
may be solved for total phosphorus concentration after ten years of the hypo-
thesized loading. The solution to Equation (2) (v ¦ 12.4 m/yr) is compared
with that obtained using the dynamic simulation model, assuming v = 73 m/yr
(i.e., zero days of 1ce cover), 1n Figure 15. The agreement 1s quite remark-
able.
Carrying this analysis one step further, 1f we apply the same hypothesis
used by Rodgers and Salisbury (1981) concerning accelerated winter settling to
the Chapra model, we should be able to predict total phosphorus concentration
as a function of winter 1ce days and loading. Assuming that the total phos-
phorus removal rate 1n the mass-balance model 1s also Increased by a factor of
eight on those days that the lake 1s 1ce covered, we obtain the results Illus-
trated 1n Figure 16. In this figure, the curves show the solution of the
Chapra model for the two assumed loadings, and the points are the solutions
obtained using the dynamic simulation model. Once again, the agreement
between the two models Is quite striking.
HISTORICAL SIMULATION WITH ACCELERATED REMOVAL
Obviously, the realism of the model results depends entirely on the hypo-
thesized phosphorus-removal mechanism. Although agreement between the two
models shows that accelerated removal affects each consistently over the ten-
year simulation period, the real question is whether the accelerated removal
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26
DYNAMIC MODEL TOTRL PHOSPHORUS
Figure 15. Comparison of mass-loading and dynamic models for
whole-lake-volume-averaged-total phosphorus after
10 simulation years—constant loads, no 1ce cover.
10-,
WHOLE LAKE VOLUME AVERAGE
TEN YEAR SIMULATIONS
CONSTANT LOADING AND ICE COVER
6350 MTA
5600 MTA
2-
—r~
10 20 30 40 50 60
DAYS OF WINTER ICE COVER
40
~T~
50
1
70
I
80
Figure 16. Comparison of mass-loading (curves) and dynamic models
(points) for whole-lake-volume-averaged total phosphorus
after 10 simulation years—constant loads, Ice cover, as
a function of Ice cover.
-------
27
concept Is consistent with estimates of phosphorus loading and observed con-
centrations In Lake Michigan over very long time periods. The Chapra mass-
loading model, Equation (1), provides a mechanism for answering this question.
Chapra (1977) also presented a model for estimating phosphorus loads to
the Great Lakes. This model, based on census and land-use data, was used to
estimate Lake Michigan phosphorus loads for the period 1850-1970 (Fig. 17).
These loads were then used as input to the mass-loading model under the
assumption that the phosphorus-removal rate was 23.1 m/yr, corresponding to
the "average" winter used 1n the other simulations. Based on the additional
assumption that the lake was In pastoral equilibrium prior to 1850, the Ini-
tial phosphorus concentration was calculated to be 3.0 yg/L. Given the loads
shown 1n Figure 17 and the Initial condition specified above, the Chapra model
with accelerated removal predicts a 1970 phosphorus concentration of 9 yg/L
(Fig. 18). This 1s very close to the Lake Michigan observations reported by
Rousar and Beeton (1973). For comparison, 1f Chapra and Sonzongl's (1979)
removal rate (12.4 m/yr) Is used with the estimated loads, the model predicts
that the 1970 concentration would be 15.9 yg/L. Thus, accelerated removal is
consistent with Chapra's load estimates and the observed phosphorus levels in
Lake Michigan.
NON-DIMENSIONAL FORMS OF MASS-LOADING MODEL
Two Important quantities that can be predicted using the simple mass-
loading model, Equation (1), are equilibrium total phosphorus concentration
and time to reach equilibrium. Assuming that both loads and removal rates are
constant, one may Infer from Equation (1) that equilibrium concentration for a
given lake depends only on the phosphorus load and on removal rate. Time to
reach equilibrium will depend, of course, on these factors and on the Initial
condition of the lake. For the case of Lake Michigan, all of the ten-year
simulations presented so far are based on the assumed Initial conditions given
In Table 2. These conditions are unverified, however, and all of the expli-
citly predicted values are thus subject to this uncertainty.
-------
28
CO
-z.
o
t—
o
QL
t—•
LJ
O
O
o
o
-------
29
The mass-loading model, coupled with the accelerated settling hypothesis,
provides a method of forecasting equilibrium total phosphorus concentration
Independent of Initial conditions. Writing:
peQ = —"— (3)
eq Q+vA
and expressing the annual load, W, as a fraction (e) of the lake's Initial
total phosphorus burden,
W = $P0V (4)
one can write the percent concentration change at equilibrium,
Pon - Prt 3V - (Q+vA )
S3 o . s_ _ (5)
P„ QvA
0 s
This equation 1s plotted for Lake Michigan as a function of ice days 1n Figure
19. If, for example, Lake Michigan's Initial (1981) total phosphorus concen-
tration was not 5.25 yg/L and If the average number of Ice days was not 45 per
year as has been assumed, Figure 19 could be used to calculate either per-
missible loads for a desired equilibrium concentration change, or equilibrium
concentration change for a particular load. This would be done In the follow-
ing manner:
1) Select number of 1ce days/year (e.g., 29).
2) Calculate the Initial lake burden by multiplying lake concentration
by volume (e.g., 6 yg/L x 4420 krn^ = 26,520 metric tons).
3) To find the permissible annual load for a 25 percent (for example)
reduction In equilibrium concentration (to 4.5 yg/L), follow dashed
line (a) 1n Fig. 19 vertically to -0.25. This yields a normalized
load (point a') of 0.18. Thus the permissible annual load Is 4774
metric tons (0.18 x 26,520 metric tons Initial burden).
-------
30
4) To find the equilibrium concentration change for a particular load
(e.g., 7950 metric tons), calculate the normalized load by dividing
the assumed looad by the Initial lake burden (7950 metric tons/26,520
metric tons = 0.3). Follow the appropriate loading curve (0.3) to
dashed line (a) (29 Ice days) at point b'. Read the equilibrium con-
centration change on the ordinate (+0.25).
ICE DRYS PER YERR
Figure 19. Fraction phosphorus concentration change at
equilibrium as a function of loading and 1ce
days.
Again assuming constant annual load and removal rates, the time to equi-
librium (95 percent) can be written:
t., - - —— In '°'05 1f P„ < P (6a)
95 QfvA P„ 0 eq
S 0 1
p— 1
eq
-------
31
or
t
V 0.05
in ——
*v\ Po .
P 1
eq
(6b)
Figure 20 shows time to equilibrium, as calculated above as a function of the
number of annual Ice days (I.e., phosphorus removal rate). Zero values of the
ordinate Imply that the lake 1s Initially at equilibrium. This calculation
shows that all of the constant-condition dynamic simulations except one (high
loads, mild winters) should have reached equilibrium within ten simulation-
years .
Figure 20 can be used In the same way as Figure 19 to estimate the time
to reach equilibrium for any constant loading and ice-d^y scenario. Using the
previous example, 1n which the annual load was 7950 metric tons, the Initial
20-i
L OWING
0 10 20 30 40 50 60 70 80
ICE DRYS PER YERR
Figure 20. Time to equilibrium for several phosphorus-
loading conditions as function of Ice days.
-------
32
lake concentration was 6 yg/L, and the number of 1ce days was 29, we find the
normalized loading as 7950 metric tons/26,520 metric tons =0.3. Following
the 0.3 loading curve, we find that 1t Intersects dashed line (a) (29 1ce
days) at point a', or an ordinate value of approximately six years. This 1s
the projected time to reach the new equilibrium concentration.
The fact that the modified
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33
Chapra, S.C. 1977. Total phosphorus model for the Great Lakes. J. Environ.
Eng. Div., Am. Soc. Civil Engr. M3(EE2): 147-161.
Chapra, S.C., and W.C. Sonzogni. 1979. Great Lakes total phosphorus budget
for the mid 1970's. J. Water Poll. Contr. Fed. 51_(10): 2524-2532.
DIToro, D.M., and J.P. Connolly. 1980. Mathematical Modeling of Water
Quality 1n Large Lakes. Part 2: Lake Erie. Report on Grant R803030.
Environmental Engineering Program, Manhattan College, Bronx, NY. 230 pp.
DIToro, D.M., and W.F. Matystlk, Jr. 1980. Mathematical Modeling of Water
Quality 1n Large Lakes. Part 1: Lake Huron and Saginaw Bay. Report on
Grant R803030. Environmental Engineering Program, Manhattan College,
Bronx, NY. 165 pp.
International Joint Commission. 1975. Great Lakes Water Quality 1974, 3rd
Annual Report of the Great Lakes Water Quality Board to the International
Joint Commission, Windsor, Ontario. 170 pp.
International Joint Commission. 1976. Great Lakes Water Quality 1975, 4th
Annual Report of the Great Lakes Water Quality Board to the International
Joint Commission, Windsor, Ontario. 72 pp.
International Joint Commission. 1977. Great Lakes Water Quality 1976, 5th
Annual Report of the Great Lakes Water Quality Board to the International
Joint Commission, Windsor, Ontario. 72 pp.
International Joint Commission. 1978. Great Lakes Water Quality 1977, 6th
Annual Report of the Great Lakes Water Quality Board to the International
Joint Commission, Windsor, Ontario. 89 pp.
International Joint Commission. 1979. Great Lakes Water Quality 1978, 7th
Annual Report of the Great Lakes Water Quality Board to the International
Joint Commission, Windsor, Ontario. 82 pp.
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34
International Joint Commission. 1980. Great Lakes Water Quality 1979, 8th
Annual Report of the Great Lakes Water Quality Board to the International
Joint Commission, Windsor, Ontario. 68 pp.
International Joint Commission. 1981. Great Lakes Water Quality 1980, 9th
Annual Report of the Great Lakes Water Quality Board to the International
Joint Commission, Windsor, Ontario. 74 pp.
International Mathematical and Statistical Library. 1979. IMSL, Inc.,
Houston, TX.
Lesht, B.M. 1982. Lake Michigan eutrophlcation model: Calibration, sensi-
tivity and five-year Mndcast analysis. Interim Report on IAG AD-89 F-0-
145-0. Argonne National Laboratory, Argonne, IL.
Parker, J.I., C.W. Kennedy, and K.S. Stanlaw. 1982. Measurement of the
spatial and temporal distributions of chlorophyll and total suspended
solids 1n southern Lake Michigan by fluorometry and nephelometry, respec-
tively. Radiological and Environmental Research Division Annual Report,
January-December 1980, ANL-80-115, Part IV. Argonne National Laboratory,
Argonne, IL. pp. 74-79.
Rockwell, D. C. 1981. Maximum percent Ice cover as an Indicator mechanism
for changes 1n large lakes total phosphorus concentrations. XXIV Confer-
ence on Great Lakes Research, International Association for Great Lakes
Research, 28-30 April 1981. p. 38.
Rockwell, D. C., D. S. DeVault, M. F. Palmer, C. V. Marlon, and R. J. Bowden.
1980. Lake Michigan Intensive Survey, 1976-1977. EPA-905/4-80-003-A.
U.S. Environmental Protection Agency, Great Lakes National Program Office,
Chicago, IL. 154 pp.
Rodgers, P., and D. Salisbury. 1981. Water quality modeling of Lake Michigan
and consideration of the anomalous 1ce cover of 1976-1977. J. Great Lakes
Res. 2(4): 467-480.
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35
Rousar, B.C., and A.M. Beeton. 1973. Distribution of phosphorus, silicon,
chlorophyll a, and conductivity In Lake Michigan and Green Bay. Wise.
Acad. Sc1., Arts and Lett. 61_: 117-140.
Scavla, D., R.P. Canale, U.F. Powers, and J.L. Moody. 1981. Variance
estimates for a dynamic eutrophlcatlon model of Saginaw Bay, Lake Huron.
Water Resources Res. _17j4): 1115-1124.
Schelske, C.L. 1980. Dynamics of nutrient enrichment 1n large lakes: The
Lake Michigan case. In Restoration of Lakes and Inland Waters. Internat.
Symp. on Inland Waters and Lake Restoration, 8-12 Sept 1980, Portland,
Maine. EPA 440/5-81-010. U.S. Environmental Protection Agency, Office of
Water Regulations & Standards, Washington, D. C.,
Thomann, R.V. 1977. Comparison of lake phytoplankton models and loading
plots. Llmnol. Oceanogr. 22(2): 370-373.
Thomann, R.V., D.M. DIToro, R.P. W1nf1eld, and D.J. O'Connor. 1975. Mathe-
matical Modeling of Phytoplankton 1n Lake Ontario. 1. Model Development
and Verification. EPA-660/3-75-005. U.S. Environmental Protection
Agency. 189 pp.
Thomann, R.V., R.P. W1nf1eld, and D.S. Szumskl. 1977. Estimated response of
Lake Ontario phytoplankton blomass to varying nutrient levels. J. Great
Lakes Res. 3(1-2): 123-131.
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36
Distribution for ANL/ER-84-2
Internal
H. Drucker
P.E. Hess
D.L. Slsterson
D.R. Cook
I-Y. Lee
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B.M. Lesht (20)
M. Wastag
J.D. DePue
T.J. Martin
M.L. Wesely
A.J. Dvorak
J.E. Miller
ANL Patent Dept.
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ANL Contract File
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TIS Files (6)
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