MODELING OF WATER QUALITY IN KE MICHIGAN AND THE EFFECT
OF THE ANO LOUS ICE COVER OF 1976-1977
BY
Paul W. Rodgers
DePaul University
-. . . . Chemistry Department
Large Lakes Research Station
Grosse ‘e, chigan B138

jc’ -
: -:
/ (
U.S. Environn ental Protection Acency
-.
-
—
• __- .—

Great Lakes Environmental Planning Study (GLEPS)
Great Lakes Bdsin Commission, Ann Arbor, iI 31O6
Contribution No. 44
February 1981
Douglas K. Salisbury
Large Lakes Research Station
Grosse .F e, Michigan
i3138

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MODELING OF WATER QUALITY IN LAKE MICHIGAN AND THE EFFECT
OF THE ANOMALOUS ICE COVER OF 1976-1977
BY
Paul W. Rodgers
DePaul University
Chemistry Department
Large Lakes Research Station
Grosse lie, Michigan 48138
Douglas K. Salisbury
Large Lakes Research Station
U.S. Environmental Protection Agency
Grosse lie, Michigan 48138
February 1981

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ABSTRACT
An intensive survey of water quality parameters was conducted on Lake
Michigan during 1976 and 1977. A nutrient-phytoplaflkton model (MICH1) was
developed and calibrated to data from 1976. MICH1 was then applied to data
from 1977 in an attempt to simulate an observed phosphorus depletion of up
to 3 ug-PIi. In order to account for this rapid phosphorus loss an implicit
representation of the extreme ice cover which separated these survey years
was necessary. This procedure included increasing the apparent settling
rate eight fold during ice cover. A time variable total phosphorus model
(TPM) was used in a hindcasting application which produced a reasonable
recreation of historical phosphorus concentrations. Two empirical models
were compared to the forecasting results of MICH1 and TPM. The forecasts
generally indicate a steady-state total phosphorus concentration of about
7 iig-P/Z, given a target load recorrrnended by the 1978 Water Quality Agree-
ment, which reflects a point source standard. The projected response time
by MICH1 is 7-14 years for obtaining 95% of steady-state concentrations.
11

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CONTENTS
Abstract . . .
Figures
Tables
Acknowledgements
1. Introduction
2. Conclusions
3. ReconinendatiOns
4. Data Presentdtiofl
4.1 Hydrology and physical definition
4.2 1976-1977 in—lake data
4.3 Historical data
4.4 Future loading scenarios
5. Model Development and Requirements
5.] Model types and requirements
5.2 MICH1 mode] kinetics
5.3 Model requirements
6. Calibration of MICH 1 to the 1976 Data
6.1 Calibration approach
6.2 Calibration coefficients
6.3 Calibration results and discussion
7. Model Application to 1977 Data
7.1 Approach and results
7.2 Consideration of ice cover effects
7.3 Discussion 0 f 1977 simulation .
8. Long Term Simulations
6.1 Rationale and approach
8.2 Historical simulation results .
8.3 Forecasting results
9. Surrmary
References
ii
iv
V
vi
1
3
5
7
7
9
11
13
15
15
17
19
22
22
24
28
35
35

38
41
41
41
43
47
49
lii

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FIGURES
NurT er Page
4—1 Lake Michigan station grid and cruise dates 10
4—2 Phosphorus concentration during days 260—263 in the
Southern Basin for the 1976—1977 survey years 12
4-3 Historic and future total phosphorus loading estimates
to Lake Michigan 13
5-1 Schematic of segmentation used by MICH1 16
5-2 Schematic of MICH1 model compartments and kinetic
interactions 18
6-1 Incident light input to MICH1 23
6-2 Vertical exchange coefficient from temperature
calibration 25
6-3 Model calibration results for chlorophyll-a
during 1976 29
6—4 Model calibration results for total phosphorus
duringl 97 G 30
7-1 MICH1 application to 1977 data for total phosphorus
and ch1orophyll- 36
7-2 Two year total phosphorus simulation incorporating an
eight fold increase in apparent net settling during
the ice cover period 39
7-3 Two year chlorophY1l— . . simulation incorporating an
eight fold increase in apparent net settling during
the ice cover period
8-1 TPM historical simulation output for Lake Michigan
for the years 1800-1980 . . . . . . 42
iv

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TABLES
Number Page
4—1 Lake Michigan Physical Characteristics 7
4—2 Lake Michigan Hydrology 8
4—3 Total Phosphorus to Lake Michigan in Metric Tonnes
Per Year 14
5—1 Sumary of Models Applied to Lake Michigan 20
6—1 Nutrient and Chemical Loads to Lake Michigan in 1976 . 22
6—2 Principal Coefficients 26
6—3 Reported Phytoplankton Stoichiometry 28
6—4 1976 Calibration Statistics 31
8—1 Model Comparisons of Forecasting Results for Steady-
State Total Phosphorus Concentration 44
V

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ACKNOWLEDGEMENTS
This work was conducted at the U.S. Environmental Protection Agency,
Large Lakes Research Station, Grosse lie, Michigan. Support was supplied
through EPA Grants 807412 and 805325, Dr. Michael D. Muliin, Project
Officer. Special gratitude is due William L. Richardson and Victor 3.
8 erman, Jr. for their professional guidance. This work was dependent upon
the many contributors in the development of WASP (Manhattan College). Laura
Betts contributed to the calibration and data management of MICH1. Debra L.
Caudill provided valuable editorial assistance and secretarial competence.
vi

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MODELING OF WATER QUALITY IN LAKE MICHIGAN AND ThE EFFECT
OF THE ANOMALOUS ICE COVER OF 1976-1977

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SECTION 1
I NTRODUCTION
Lake Michigan is the only member of the Laurentian Great Lakes to
lie entirely within the borders of the United States. Even so, Lake
Michigan is included in the Great Lakes International Surveillance Plan
(GLISP) as recomended to the International Joint Comission in 1974 by the
Water Quality Board. The reason for having Lake Michigan as part of GLISP
was attributed to the outfl contributing to the loading of Lake Huron.
During 1976 and 1977, Region V of the U.S. Environmental Protection Agency
and the University of Michigan, supported by the Large Lakes Research
Station, undertook an intensive study, which was part of the first phase of
the GLISP. The next such study is scheduled for 1985.
The field data obtained during the 1976-77 survey reflects the water
quality status of the system and provides the basis for analyzing nutrient
load responses. An analysis which includes deterministic modeling can assess
kinetic processes affecting chemical and biological behavior as well as
evaluate remedial programs. A challenging fact of this pursuit is for the
scientific cormiunity to distinguish between the influences of natural pro-
cesses upon chemical and biological dynamics and the concurrent impact of
remedial programs. This insight would have special import to the management
cormrnnity. Ecological modeling has demonstrated the ability in the past to
evaluate these influences. For example, Dolan and Clark (1981) were able to
conclude that the reductions in flow to Saginaw Bay between 1974-1979 was of
near equal importance in phosphorus load reduction as the phosphorus removal
by municipalities. By the end of the study there was about an 11 ug/2 reduc-
tion in chlorophyll-a evident during the late sumners. In analyzing the
1975 Lake Erie data set, DiToro and Connolly (1980) were able to attribute
reduction In the anoxic zone of the central basin to changes in the onset of
thermal stratification and not load reductions. In this study the concur-
1

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rent effects of a phosphorus load reduction in 1977 and a climatically in-
duced ice cover is examined for relative irnport nce. The ice cov r is hypo-
thesized to enhance net phosphorus losses by isolating the lake from wind
induced mixing and sediment resuspension.
The application of ecological models to the Lake Michigan basin was
the central focus of this research. A modified version of a deterministic
model, Lake 1 (Thomann et al. 1975), was first calibrated to the 1976 Lake
Michigan results. An attempt to simulate the 1977 data was the first appli-
cation of this calibrated Lake Michigan model, MICH1. During this verifica-
tion phase additional mod fications in the model became necessary. Specifi-
cally, attempts were made to implicitly reflect the effects that the exten-
sive ice cover observed during the winter of 1976—77 might have had. The
final application of MICH1 was to forecast lake response given several
loading scenarios.
Additional models were used in making long term simulations. A
time variable total phosphorus model was also used in forecasting as well as
in hindcasting simulation. This total phosphorus model, similar to the
Lorenzen (1976) model, provided valuable comparisons to MICH1 results. Two
empirical models, the loading plot model by Vollenweider (1976) and the
Dillon and Rigler (1975) model, were used for forecasting in order to gain
more insight. By using a variety of models of varying complexity a contrast
was made evident based on their performance versus their requirements.
2

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SECTION 2
CONCLUSIONS
The efforts of this study enabled the following conclusions to be
made:
1. A dynamic phytoplankton simulation model (MICH1) proved ap-
plicable to Lake Michigan for simulating field data.
2. MICH1 also proved useful, because of its versatility, in
approaching new problems. Specifically, the hypothesis
that an extraordinary ice cover may have enhanced an ob-
served loss of phosphorus from the water column was investi-
gated.
3. Changes in model forcing functions that may have been
affected by an ice cover (incident light; vertical ex—
change, and ambient temperature) proved inadequate in
providing a sufficient loss of particulate phosphorus.
4. The apparent settling rate had to be increased eight fold
(to 1.6 rn/day) during the ice cover period (the winter
separating the 1976—77 survey years) i order to simulate
the substantial phosphorus loss observed in the Southern
Basin of Lake Michigan.
5. A case that an extraordinary ice cover may have enhanced
removal of particulates from the water column was made in
this investigation. If the mechanism for this influence
is the isolation of the lake from wind induced circulation
and sediment resuspension then these rapid losses in phos-
phorus may create rich deposits available for subsequent
reintroduction into the lake.
3

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6. A time variable total phosphorus model (TPM) was able to
achieve an historical simulation of total phosphorus in
Lake Michigan from 1800 to 1980 which “predicted” peak
concentrations of total phosphorus during the early—l960’s
as well as the levels observed in the 1976 survey.
7. Two empirically derived models, the Vollenweider loading
plot model and the Dillon and Rigler model, proved appli-
cable to Lake Michigan for forecasting responses to various
steady-state loading scenarios. The Vollenweider model
suggested that long term loadings equivalent to 1976 loads
(6671 MT/yr) would result in marginally mesotrophic conditions,
whereas the long term target load recorr nended by the 1978 Water
Quality Agreement (5553 MT/yr) would result in oligotrophic
conditons. The Dillon and Rigler model predicted higher con-
centration responses than did MICH1 or TPM.
8. MICH1 and 1PM forecasting results were similar regarding
total phosphorus response. The recorrinended GLISP load re-
sults in an in—lake steady—state concentration of approxi-
mately 7 .ig-P/Z. The observed 95% response time was eight
to fourteen years.
9. MICH1 forecasted in-lake chlorophyll concentrations less
than 4 for all three future loading scenarios.
Nearshore responses were not modeled.
4

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SECTION 3
RECOMMENDATIONS
Based on the results and conclusions of this study the following
reconinendaticns are made:
1. Studies which are designed to assess the influence of
major ice cover events may be a necessity in modeling
lakes on a temporal scale.
2. If, indeed, ice cover can influence short term particle
dynamics then there is a strong case for at least limited
winter sampling.
3. Predictions of long term lake response should incorporate
significant meteorological events by utilizing their fre-
quency of occurrence as a stochastic model input.
4. An increased resolution of particle dynamics may be de-
sirable. This would include improved representation of
hcrizonal sediment and erosion transfer as well as resus-
pension phenomena.
5. A close look at the attainability of the GLISP recorrinended
load over the long term is appropriate given that it is
based on point source standards and appears to omit con-
sideration of population and industrial growth.
6. Certain difficulties encountered in model calibration and
application suggest the need for monitoring fundamental
variables (e.g., temperature, conductivity, etc.) on a more
regular basis. This change in sampling strategy would pro-
vide a basis for identifying the timing and magnitude of
5

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water exchange processes. This sampling should occur sea-
sonally at specific “master stations” on the major lakes,
thereby establishing continuity in reporting general lake
status.
6

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SECTION 4
DATA PRESENTATION
4.1 HYDROLOGY AND PHYSICAL DEFINITION
Lake Michigan is the second largest of the Great Lakes in terms of
volume and is the only one to lie entirely within the boundary of the United
States. The shores of Lake Michigan fall within Wisconsin 1 Illinois,
Indiana and Michigan. The drainage basin area for Lake Michigan is the
largest among the Great Lakes. For a sun nary of the physical characteris-
tics of Lake Michigan refer to Table 4—1. There are 25 major tributaries to
Lake Michigan and the outlet to Lake Huron is through the Straits of
Mackinac. The hydrology for Lake Michigan is sumarized in Table 4—2. Pro-
jected hydraulic detention times based only on each year’s flow are also re-
ported. The values presented in these tables were obtained from a variety
of sources and data from other sources may differ somewhat 1 but should be
essentially similar. Note that the annual flows for 1975-1978 have been
highly variable. The high flow year was in 1976 followed by the low flow
year of 1977. A 66% reduction in annual flows was observed in this short
period. This variation in flow and the projected detention times indicates
that flows measured or computed during any given year may not be representa-
TABLE 4-1. LAKE MICHIGAN PHYSICAL CHARACTERISTICS
Lake Surface
Drainage Area* Area
(km 2 ) (km 2 )
Mean Depth
(m)
Volume
(km 3 )
Lake
Michigan
117410
57800
86.1
4976.0
Green
Bay
43670
4213
16.0
67.2
Main
Lake
73740
53587
91.6
4908.8
*Does not include lake surtace.
7

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TABLE 4-2. LAKE MICHIGAN HYDROLOGY (cfs)
1975 1976 1977 — - 1978 Long Term
Northern Basin
1. Gaged FlOw* 14580 14784 9l 4 14726 l409d
2. Adjusted Flow 20935 21228 13130 21145 20238
3. Net Precipitation 10888 12980 -713 8729 6941
4. Infiltration 200 200 200 200 200
Sub-Total (2+3+4) 32023 34408 12617 30074 27379
Southern Basin
1. Gaged Flow 13764 15520 8057 11597 10514
2. Adjusted Flow 20822 23479 12189 17544 15906
3. Net Precipitation 11044 13166 —723 8854 7031
4. Infiltration 200 200 200 200 200
Sub—Total 32066 36845 11666 26598 23137
Total Inflow 64089 71253 24283 56672 50516
Projected Detention
Time (yrs. ) 87.0 78.2 229.5 98.3 110.3
*Approximately 78% of the basins were gaged.
**f\djusted for ungaged area plus additional flow to river mouth (1.12 in
North and 1.18 in South).
***precipjtation minus evaporation estimates (refer to Philips and
McCulloch, 1972).
8

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tive of long term averages. This water balance does not consider possible
deep layer return flows at the Straits of Mackinac discussed by Quinn (1977).
Quinn further noted the variability 1n annual flow by calculating a 26% vari-
ation in the mean for the years 1950—1966.
4.2 1976—1977 IN-LAKE DATA
During 1976 and 1977, Region V of the U.S. Environmental
Protection Agency and the University of Michigan undertook an intensive sur-
vey which was part of the first phase of the Great Lakes International
Surveillance Plan. The next such study is scheduled for 1985. The stations
sampled and the cruise dates are presented in igure 4—1. There were about
forty in-lake stations in the Southern Basin and seventy in the Northern
Basin, although not all stations were sampled on every cruise. An extensive
sampling of water quality parameters included physical, chemical, and biolo-
gical measurements. Those parameters relevant to this modeling effort in-
clude water and air temperature, transparency, chlorophyll—a, primary pro-
ductivity, total phosphorus, soluble reactive phosphorus, total Kjeldahl
nitrogen, amonia, nitrite + nitrate nitrogen, chloride, and zooplankton
bioniass. The time variable results for the most important of these param-
eters will be evident in the model comparison figures presented in “Calibra-
tion to 1976 Data,” Section 6, and “Application to 1977 Data,” Section 7.
In the subsequent years since those data were collected the results have
been reported by Rockwell et al. (1980) and separately by Bartone and
Schelske (1980). A more extensive treathient of the data will soon be avail-
able from the E.P.A. (Region V).
The inspection of this data has revealed the status of Lake
Michigan as compared to historical samples from less intensive surveys.
Comparison of the 1976—77 data to historical conditions in Lake Michigan re-
veals degradation of these waters as evidenced by an increase in chloride
and sulfate concentrations (conservative ions), increasing phytoplankton
populations, and decreased reactive silica concentrations (Rockwell et al.
1980). An analysis of anthropogenic phosphorus loads to the Great Lakes
basin by Chapra (1977) indicates that as much as two-thirds of recent loads
to Lake Michigan have been related to human influences within the basin.
9

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U.3. PV O M N’tA .L
PWflCT)OPd AC CT
Lak3 Michigan
£2
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Survey Cruise Stations
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ORTHERN 8ASIN
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J Northern Basin
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: ,/ &rists. 3. July 10-19, 1976
4. August 10-19, 1976
\Luc cn 5. 0c cber 5.15, 1975
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27 3mA
• . • S
Transect 8
312’4
F_S. 5 0 • USXZCCN
tILWAU [ J 21$ T nAeCt 5 • rand
• Haven
SOUTHERN BASIN
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Tri ris ct 2
17
0• 0
Tr n cct 1
Figure 4-1
New
uthern S sin
1. May 1.3, 1976
2. May 25-June 2. 1975
3. June 15•21, 1976
4. July 7-13, 1976
5. Aug. 3.10. 1976
6. Aug. 24- pt. 2. 1976
7. Seat. 14-20, 1975
8. Oct. 7-8, 1976
1. April 19-24, 1977
2. June 11-16, 1977
3. Aug. 20-25, 1977
4. Sept 17-24, 1977
sc - lu
10 5 0 10 20 30 40 50
- [
1050 1020 3040 50607080
3ia .ffa .lo ____________________
LJ t 1 1 1 i L _ i X I
Lake Michigan station grid and cruise dates.
Mertoe i ee
a ie t e
w .
••.
Port
3m 3m
S
Haver
I , .
S
farbQr
10

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This cultural impact upon phosphorus loads has resulted in increased phos-
phorus levels in nearshore zones (Rockwell et al. 1980) and throughout the
lake (IJC-Surveillance Subconinittee 1978). As a result Lake Michigan has
been identified as presently being on the borderline between oligotrophic
and mesotrophic conditions (Rast and Lee 1978). Since phosphorus has been
identified as the growth limiting nutrient throughout most of Lake Michigan
(Schelske et al. 1974; Rast and Lee 1978) the increased phosphorus loads are
no doubt the stimulus for the observed phytoplankton related water quality
problems. Confirming these observations is the trend in silica depletion
accompanied by a shift from diatom dominance to an increase in blue-green
phytoplankton abundance (Schelske and Stoermer 1971; Rockwell et al. 1980).
A linear increase in conservative ions over the past 100 years has also been
suggested as a cause for this shift to blue—greens (Stoermer and Tuchnian
1980).
The data from the two cruise seasons further indicated substantial
changes in important water quality parameters between 1976 and 1977 values.
A conclusive comparison of 1976 data to 1977 data is hampered because of the
reduction in sampling in 1977. As indicated in Figure 4—1, there were only
four cruises in 1977 and the Northern Basin was not sampled. However, the
data strongly indicates decreases in phosphorus, ariiiionia, chlorophyll-a and
phytoplankton cell counts, and increased silica concentrations in 1977 when
compared to the 1976 results (Rockwell et al. 1980). The magnitude of the
phosphorus reduction is particularly striking and is evident in Figure 4—2.
The data indicates approximately 6,500 metric tonnes of phosphorus were re-
moved from the water column in one year’s time. Yet the reduction in
loading to that basin was only about 1,100 metric tonnes. Therefore, even
if an in nediate response to the load reduction is assumed nearly 83% of the
phosphorus loss from the water column remains to be accounted for via other
influences.
4.3 HISTORICAL DATA
There exists no historical water quality data set for Lake Michigan
comparable to that of the intensive survey of 1976-77. Previous to this
time there were no organized attempts to obtain a comprehensive analysis of
11

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0
3
0
0
I
0
-J
0
Figure 4—2. Phosphorus concentration during days 260-263 in the
Southern Basin for the 1976-1977 survey years.
the Lake Michigan waters. Instead, the historical data is the combined pro-
duct of many research efforts in localized areas. This data usually re-
flects a relatively limited number of parameters collected for a short term
by single investigative efforts. The only consecutive long term data
available usually has been obtained from the routine sampling of water
treab’nent plant intakes. A synopsis of data sources and trends in biologi-
cal and chemical composition can be found in a series entitled, ‘ 1 Environ—
mental Status of the Lake Michigan Region, available from the National
Technical Information Service.
An advantageous application of models is to attempt the simulation
of the aquatic system over the dynamic historical period (that time frame
when nutrient loads were increasing due to anthropogenic influences). An
important requirement for this application is to reconstruct the nutrient
loading during the historical period. If the model accurately reflects the
lake response to these loads then it should “predict” present day condi-
tions. To aid in the historical simulation a sumiiary of historical loading
estimates was gathered from a variety of sources and is graphically pre-
sented in Figure 4-3. The absence or presence of atmospheric loading was
6.0
940.5 UT
LOSS
5573.0 UT
LOSS
EPILDvINION
HY POUMNION
12

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I-
16
E
.
U)
0
I
U)
0
I
A.
-J
—2
0
1800 1850 1900 1950 - 1960 1970 19
Figure 4-3. Historic and future total phosphorus loading estimates to Lake
Michigan (1O metric tonneslyr). Solid syi’nbols represent
historical loading model estimates:
• - Chapra (1977) — Patalas (1972).
Open syii bols represent estimated loads based on field measure-
rnents:
A - Eisenreich et al. (1977) o - GLWQB (1974)
v - jJc (1978) - IJC (1978),
G - Lee (1974) — PLUARG (1978)
X — Sonzogni et al. (1978) - U.S. Dept. HEW (1963)
o — Zar (1974)
Dashed lines (-—) represent the three loading cases presented
in Table 4-3 and used in forecasting.
normally found to be the difference In reported values within a particular
year. These loads are used as model input in Section 8.2, 0 Historical Simu-
lation Results.
4.4 FUTURE LOADING SCENARIOS
Three representative phosphorus loads were used for observing
steady state response frci various water quality models. Table 4—3 pre-
sents these loads on a whole lake basis. These loads are also indicated In
S
• .0I
0
e
S
h
• ‘ ———CMLI
0 V
0
x
x
13

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TABLE 4-3. TOTAL PHOSPHORUS LOADINGS TO LAKE MICHIGAN IN
METRIC TONNES PER YEAR
CASE 1
1976 Load 1
CASE 2
.
1977 Load
2
1976 Load
with 1 mg/2..
effluent standard
Atmospheric
1690
1690
1690
Point Sources
2268
1150
1623
Diffuse Sources
2713
2713
1353
TOTAL 3
6671
5553
4666
‘Reported in Fifth Year Review of Canada-United States Great Lakes Water
Quality Agreement, eds. J.R. Vallentyne and N.A. Thomas, a Report of Task
Group III, IJC, 1978.
2 Total load reported in Great Lakes Water Quality, Sixth Annual Reoort
Appendix B , IJC, 1978. Allocation between point and diffuse sources for
1977 is only an estimate based on the mid 1970’s portions reported in
Critical Assessment of U.S. Land Derived Pollutant Loadings to the Great
Lakes , Sonzogni et a]., IJC, 1979.
3 Total does not include shoreline erosion or re—entry from sediments.
Figure 4—3. Case 1 reflects the high flow, high load condition of 1976.
Case 2 is the target load recormnended by Task Group III in 1978 (Vallentyne
and Thomas 1978). This load was considered achievable through a 1 rng/ ef-
fluent standard applied to Case 1. The Task Group felt that this load would
result in the in—lake phosphorus concentration being held to 7 pq-P/2.. or
less. Case 3 represents the low end of the loading spectrum by reflecting
the extreme low flow, law loading condition observed in 1977. Note that the
atmospheric loading accounts for 25-36% of the total and thatkero$iofl inputs
are not included. When applying these loads to the water quality models a
steady input con nencing in 1978 was assumed. No attempt to predict changes
in loading due to industrial, agricultural, or population changes within the
basin was made. The use of the three loading scenarios proved sufficient
for demonstrating critical load and response sensitivity of Lake Michigan
(Section 8.3).
14

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SECTION 5
MODEL DEVELOPMENT AND REQUIREMENTS
5.1 MODEL TYPES AND REQUIREMENTS
A modified version of the Lake 1 model, MICH1, was used to evaluate
the 1976—1977 LaKe Michigan conditions. Lake 1 was chosen as the basic
framework on the basis of its proven application flexibility. Lake 1 was
originally developed for Lake Ontario (Thomann et al. 1975) and modified
versions have since been applied to Lake Huron (DiToro and Matystik 1980)
and Lake Erie (Diloro and Connolly 1980). The physical segmentation in
MICH1 utilizes the horizontal division between the Northern and Southern
Basins as depicted in Figure 4—1, but includes only the in—lake portion
greater than 15 meters in depth. Green Bay is also excluded from model re-
presentation. The mathematical representation of Lake Michigan further seg-
ments each of the two basins into two vertical layers at 20 meters in order
to represent sunTner thermal stratification. This segmentation scheme, de-
picted in Figure 5-1, succeeds in modeling over ninety-five percent of the
Lake Michigan volume without requiring the detailed data and segmentation
necessary for nearshore modeling.
The framework of MICH1 simulates both biological and chemical
parameters as state variables. There are three biological trophic levels
represented. Corrected chlorophyll—a represents phytoplanKton biomass and
equivalent carbon reflects the two zooplankton trophic levels. In addition
there are six chemical or nutrient state variables. These include two phos-
phorus ompartrnents, total and soluble reactive phosphorus. The three
nitrogen compartments simulated are total nitrogen, aninonia, and nitrite +
nitrate nitrogen. Chloride is modeled as a conservative substance and
served as a quantity of predictable behavior during the calibration phase.
15

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SOUTHERN BASIN NORTHERN BASIN fl
— EP LI .4N ON ( UPPER LAYER ) —
E
HYPOL!MNION (
LOWER LAYER
Figure 5—1. Schematic of segmentation used by MICH1.
Flow (- ) Water Exchange ( - )
In addition to MICH1 several additional models were applied to the
Lake Michigan ecosystem. A total phosphorus model (TPM) was chosen to pos-
sibly corroborate the phosphorus simulations observed in MICH1. Empirical
models by Vollenweider (1976) and Dillon and Rigler (1975) were also applied
to Lake Michigan for further general comparisons. TPM, a time variable
model of total phosphorus, is conceptually similar to that developed by
Lorenzen (1976) for use on Lake Washington and is numerically similar to a
variety of total phosphorus models (Rumer 1978; Dolan and Bierman 1980). In
essence this model invisions phosphorus as one compartment subject to one
kinetic loss, settling. However, the phosphorus in the sediments are made
available for reintroduction into the water column via resuspension ordif—
fusion and may be permanently loss to deeper unavailable sediments.
The Vollenweider model is empirical in its development, although
the relationship between areal loading (mass/area/time) and the overflow
rate (depth/time) can be derived from steady-state solutions to a mixed re-
actor mass balance model (Vollenweider 1975). The Dillon and Rigler model
(1975) is a mathematical formulation based on empirical observation and cor-
relation. However, its mathematical formulation can be derived from a
steady—state solution of a simplistic phosphorus model having only one kine-
tic loss term.
16

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5.2 MICH1 Model Kinetics
For the most part MICH1 is a specific application of the Lake 1
model (Thomann et al. 1975) to the Lake Michigan system. The interaction of
the nutrient and biological state variables is shown in Figure 5—2. Note
that the chloride compartment is not included in this kinetic representa-
tion due to its non—dynamic conservative nature. Whereas, all other corn—
partiients which comprise MICH1 interact with one or more additional compart-
ments. In addition, these compartments are subject to inter—segment mixing.
The unavailable nutrients and the phytoplankton chlorophyll are also subject
to sinking from the water column to the sediments.
The major kinetic change included in MICH1 as compared to the ori-
ginal Lake 1 framework is a parameterization of phytoplankton decomoosition
followed by a similar representation for phosphorus recycle. This change
was made to give the modeling framework an ability to be applied to lakes of
various trophic status. DiToro and Matystik (1979) observed that similar
models, when applied to lakes exhibiting a range of trophic states, required
more rapid phosphorus recycle as the trophic state increased. Th s observa-
tion was inconsistent with a genuine first order recycle mechanism and they
therefore hypothesized a recycle rate that is a saturating function of
chlorophyll (an indicator of trophic status).
Recent experimental results by Rodgers (1979) suggests an explana-
tion for the above observation by DiToro and Matystik (1979). These labora-
tory results indicated that making recycle rates a function of chlorophyll
concentration is probably an implicit representation of bacterial metabolic
activity responding to lake trophic status and, therefore, organic content.
Rodgers (1979) also demonstrated that the degradation rate of phytoplankton
biomass is enhanced when the physiological status of phytoplankton is
stressed. The saturation function representing phytoplankton decomposition
in Equation 1 is therefore proportional to an indicator of trophic status
(e.g., biomass concentration) and inversely proportional to an indicator of
phytoplankton physiology (e.g., growth rate).
DR - e(T 20 ) ‘K + A/T. ! ‘
- ‘ e Kmaxg+1 7 j1
17

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Ccirniv orous
Zoopkinkton
— - - BIOLOGICAL_SUB-MODEL —
PhytoptanktonLj Herbivoro
ChlorophyU Zooptonkton
1
—
Organic
Phosphorus
Organic
Nitrogen
1
___________________________________________________________ I
I
I
I
-a
AVAILABLE NUTRIENTS
I
UNAVAILABLE
p
Figure 5—2. Schematic of MICI-11 model compartments and kinetic interactions.

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where,
specific first crder phytoplar 1 ton decomposition ate (dayl)
I ambient temperature (°C)
6 = Arrhenius coefficient
Ke endogenous respiration rate necessary for cell main-
tenance at 20°C (dayl)
Kmax theoretical maximum first order decomposition rate due
to heterotrophic activity at 20°C (dayl)
A = chlorophyll biomass concentrat-ton (ug/Z)
calculated growth rate (day —i)
k = half-saturation coefficient ( UQ daY)
5.3 Model Requirements
The Great Lakes Environmental Planning Study (1978) has pointed out
the need for model requirement sumnaries. Such a sumary of requirements
necessary for MICH1, 1PM, the Vollenweider loading plot model, and the
Dillon and Rigler model is found in Table 5—1. MICH1 has the most extensive
requirements and its data are single system intensive. This investment of
data collection yields more detailed model output than do the other models.
Not only are nine water quality state variables tracked in time, but MICH1
has the versatility of representing the desired three dimensional segmenta-
tion. The versatility of MICH1 is due to foresight in the Lake 1 develop-
ment (Thomann et al. 1975). TPM is less sophisticated than MICH1 in its re-
presentation of a complex system. Yet, TPM is a dynamic, time variable
model whose conceptual framework has succeeded in simulating a number of
lakes. The simplified framework and reduced model requirements of 1PM lends
itself to more widespread application. The output of TPM, however, yields
no information regarding the nutrient fractions or the biological responses
of a lake. The mixing characteristics of a lake are also not represented by
1PM.
The last two total phosphorus models, Vollenweider’s loading plot
model and Dillon and Rigler s empirical model are both based on steady-state
19

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TAULE 5-i. SUF 1ARY OF HODELS APPLIED TO LId(E MICHIGAN
Pioae I
Model Type
progr am
I anqu age
No or
Coefficients Time Scale
N)
C D
MICH1 Deterministic Fortran
phytopiank ton
end nutrient
model
Lake hydrology and merpliometry,
incident light, se nent exchange
coefficients, loadlog and initial
conditions for nine state var -i—
ables (two phosphorus and three
nitrogen fractions, two uooplankton
trophic levelt, chlorophyll-a, and
chloride)
30-40 Time variable,
daily, seasonally,
Or annually
Iiorhiorral and
vertical
(4 seg nents)
Graphics of state variables
vs. time and comparison
with field data for each
spatial segment
TP 1I Dynamic mass
balance model
Fortran Lake hydrology and ienrphometry,
loading and initial conditions for
total phosphorus
3 Time variable,
annually
ilorizonal Total phosphorus concentra-
(2 segments) Lion In the water coltuno
and sediments
Dillon Empirical
and total phos—
itigler phorus
load ing
model
Mathema— Empirical interpretation of areal
tical total phosphorus loading, onerflow
equations rate, and In-lake total phosphorus
concentration for numerous lakes
Total phosphorus Concentra-
tion in the water colunvi
Vollen- Loading
weider pint
model
Hone
Plot of areal phosphorus load vs
overflow rate and the trophic
status for numerous lakes
none Steady-state
assumptions
None
Judgereent of permissable or
dangerous total phosphorus
loads for a given lake
moot Data
spat lal
Segmentation
Model Output
Steady-state
assumpt ions
None (basin
separation
possible)

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assumptions. The data required for the empirical development of these
models must come from many lakes of similar gea-physical and climatic class-
ification. Normally data from over 30 lakes and sometimes in excess of 100
lakes are utilized in empirical formulation. Although the application of
these models are comparatively easy, the predictions of lake response to
phosphorus loading has considerable uncertainty. The cautions regarding the
interpretation of results hinges on their empirical development. Their ap-
plication is best suited to yielding general indications of lake response
for lakes that are similar to the lakes for which the empirical relation-
ships were developed. No direct indication of transition concentrations or
response times are available from these models.
21

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SECTION 6
CALIBRATION OF MICH1 TO THE 1976 DATA
6.1 CALIBRATION APPROACH
There are three primary topics to be addressed when calibrating a
specific model to a given lake. First the mass loads that the model re-
quires must be measured or estimated. The total phosphorus load to Lake
Michigan in 1976 was represented by Case 1 in Table 4—3. In MICH1, however,
there are additional loads which must be quantified for an accurate repre—
sentaticri of the system. The nutrient and chemical loads required by MICH1
are presented in Table 6-1. The total loads are also divided between
Southern and Northern Basins, as the model requires. Note that loads for
the biological state variables are not included. This is because the pri-
mary source of chlorophyll-a is autochthonous generation within the euphotic
zone followed by responses in the zooplankton community.
TABLE 6—1. NUTRIENT AND CHEMICAL LOADS TO LAKE MICHIGAN IN 1976.
(Metric Tonnes/Yr.)
Unavailable
Organic
Phosphorus
Available
Phosphorus
Organic
Nitrogen
Arrinonia
Nitrogen
Nitrate +
Nitrite
Nitrogen
Chloride*
Southern
Basin
2686
895
24211
10126
26804
489700
Northern
Basin
2317
773
20869
8729
23104
221900
Total
5003
1668
45080
18855
49908
711600
*Total does not include direct industrial and municipal load of approximately
116000 metric tonnes/yr.
22

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790
S4e
C
z
0
0
-J
0
U)
a
Figure 6—1. Incident light input to MICH1.
Secondly, the field data has to be reduced and organized to fit the
spatial segmentation of the model. This step includes characterizing addi-
tional forcing functions such as incident light and temperature as well as
representing the status of the state variables. The time series for inci-
dent light used in the 1976 calibration is reported in Figure 6—1. These
values are similar to those developed by Thomann et al. (1975). In this
study, volume—weighted averages for the state variables were computed (Yui
1978), but since these values proved to be the same (within the variance of
the data) as the arithmetic averages the latter means were used. These data,
once prepared, are later compared to the model output, both graphically and
statistically.
The last primary responsibility in calibrating the model is to ad-
just the model coefficients within realistic value ranges so that the model
output of state variables will best simulate the observed data. The coeffi-
cients which govern the simulation of biological and chemical processes
within the water column depend upon known relationships which are charac-
terized through extensive field and laboratory experimentation. There are
nearly forty coefficients in MICH1. Although many coefficients are rea-
sonably well determined, others require calibration runs where coefficients
tea
oe 250
TIME ( Jutien dQys)
23

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are adjusted and model output is compared to field data in order to cali-
brate acceptable values. The state of the art knowledge of the processes
serve as a guideline which fixes the range within which the coefficients
must be calibrated. Therefore, a continuing effort must be made by the
modeler to not only mathematically simulate the state variables but to main-
tain external consistency.
6.2 CALIBRATION COEFFICENTS
A preliminary requirement of MICH1 is the characterization of water
exchange rates between adjacent segments. The vertical dispersion between
model layers, previously indicated in Figure 5—1, is time dependent. Con-
servative substances are often used when calibrating exchange coefficients.
However, there are no large gradients to be found in the open waters of Lake
Michigan for chloride (Rockwell et al. 1980). In order to calibrate the
dispersion between the vertical layers, conceptually equivalent to the
epilimnion and hypolimnion, it is necessary to simulate the temperature
dynamics. This process can be accomplished by directly evaluating the heat
flux (DiToro and Matystik 1980). Unfortunately, sufficient data to pro-
perly utilize this approach does not exist for Lake Michigan. This heat
flux can instead be modeled implicitly by using the upper 5 meter layer as a
boundary layer. The water and its associated heat can be mixed until the
model output fits the measured temperature throughout the year. The water
is first mixed into the remaining epilimnion and then into the hypolimnion.
The results of calibrating vertical exchange coefficients are presented gra-
phically in Figure 6—2 for the Southern and Northern Basin.
Note that the onset of stratification in the Northern Basin lags
behind that of the Southern Basin and that it is not as complete in the
North. The magnitude of vertical dispersion is also generally higher in the
North than in the South. These results are due to the more inclement
weather in the Northern sector mediating colder temperatures and greater
mixing from the winds. This calibrated dispersion set is very influential
in predicting the timing and magnitude of the first phytoplankton bloom and
should be an essential step in calibrating any new aquatic system.
24

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5C
V.,
U
/
I I
z I /
30- /
/
U-
U-
I I
o • q’ .
L) “ I /
1 1 ______
0 40 80 120 160 200 240 280 320 360
TIME (days)
Figure 6—2. Vertical exchange coefficient from temperature calibration.
— Southern Basin -— Northern Basin
The horizontal exchange coefficients were set at constant values of
1000 cm 2 /sec between the epilimnetic segments and 100 cm 2 /sec between
the hypolimnetic segments. Similar coefficients have been utilized for
other large systems.
The principal model coefficients are listed in Table 6-2. Many of
the values associated with these coefficients required a calibration pro-
cess. The general approach and guidelines to this calibration process have
already been discussed here and elsewhere (Thomann et al. 1975, Bier-man et
al. 1981). However, the specific details regarding the calibration of
several of these coefficients is appropriate.
Nutrient to Chlorophyll Ratios: There are four cellular components
which MICH1 must simulate, chlorophyll (Chl), phosphorus (P), nitrogen (N),
and carbon (C). The framework of MICH1 kinetically simulates chlorophyll,
but tracks the cellular nutrients by assigning constant nutrient to chloro-
phyll ratios. This approach lacks accurate representation of known nutrient
kinetics. Namely, nutrient ratios are known to vary depending on phyto-
25

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Nanie
K1C
KiT
Is
CCHL
NCHL
PC ML
KMP
Ke
Kmax
k
K2T
RHO
TABLE 6-2. PRINCIPLE COEFFICIENTS
Description Value
Maximum Growth Rate 2.10
Arrhenius Temperature Coefficient 1.08
for Growth
Saturating Light Intensity 125
Carbon to Chlorophyll Ratio 50
Nitrogen to Chlorophyll Ratio 12.5
Phosphorus to Chlorophyll Ratio 0.5
Half-Saturation Coefficient for 0.5
P Limited Growth
Biomass Loss Rate due to 0.03
Endogenous Respiration
Maximum Biornass Loss Rate Due to 0.3
Half—Saturation Coefficient for 500
Microbial Biornass Loss
Arrhenius Temperature Coefficient 1.08
for Biomass Loss
Available Fraction of Respired 0.6
Phytopi ankton
Nutrient Mineralization Rate 0.03
Arrhenius Temperature Coefficient 1.08
for Mineralization
Half-Saturation Coefficient for 8.0
Mineralization
Settling Rate for all Particulates 0.2
langleys/day
pg—C/ .ig-ch 1—a
ig—N/iig-ch 1-a
.ig—P/ ig—ch 1-a
pg —P/9.
days’
days-’
1 g—ch1-a day/2.
none
none
Units
days 1
none
KC
KT
K MR
SVEL
days
none
pg—chl-a/2,
rn/day
26

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plankton species, nutrient limitation status, external nurient concentra-
tions, and past population history. For a thorough discussion of these in-
fluences and their incorporation in a phytoplankton model see Bierman et
al. (1981). In general, large ratios correspond to excess nutrients and
small ratios to a limiting nutrient situation. The stoichionietry chosen
should therefore reflect the phosphorus limited conditions of Lake Michigan.
The calibrated nutrient to chlorophyll ratios in Table 6-2 suggest a C:N:P
ratio of 100:25:1. Literature values of phytoplankton stoichiometry, re-
ported in Table 6—3, provide a standard guideline for which the calibrated
nutrient ratios can be compared. The C/dry wt. ratio of 0.39 reflected a
range of phytoplankton functional groups and therefore should reflect a
mixed field population. An expected Chl/dry wt. ratio is calculated by
dividing the C/dry wt. ratio by the calibrated C/Chl ratio. This calcula-
tion yields 0.0078 as the expected Chl/dry wt. ratio and is within the
range reported in Table 6—3. Furthermore, the product of this Chl/dry it.
ratio and the calibrated P/Chl ratio (0.5) provides a P/dry wt. ratio of
.004, again within the range of observed data. A check on the external con-
sistency of nutrient ratios calibrated for similar models (Thornann et al.
1978; DiToro and Connolly 1980; DiToro and Matystik 1980) does not yield a
consistent result. Their C/Chl ratio of 100 suggests a Chl/dry wt. ratioof
.0039 and a P/Chl ratio of 0.002. Both ratios are at or below the extreme
minimum reported in Table 6—3.
p vdtopl tkton D coniposition Coefficients: Equation 1 in Section 5
represents a sub-model describing the decomposition of phytoplankton. This
decomposition sub-model represented the observation that nutrients recycle
more rapidly when the trophic status of a system increases. The first order
decay rate was pararneterized in a saturation function which is proportional
to an indicator of trophic status and inversely proportional to the physio-
logical state of the phytoplankton. MICH1 uses this proposed sub—model and
the required coefficients, as calibrated, are also reported in Table 6—2.
The calibration of these coefficients should be considered provisional. Re-
finements in deterministic models which are made for rendering that model
acceptable to lakes of various trophic status are best calibrated when
applied to multiple systems. A single system like Lake Michigan is not
diverse enough to test the performance of this type of sub—model.
27

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TABLE 6-3 REPORTED PHYTOPLANKTON STOICHIOMETRY
Ratio Description
Value Range
Reference
Carbon
0.15—0.67
Bierman (1981)
Dry .
(Q .3 9)*
Ch1oro y11—a
0.005-0.015
(0.01)
Dolan et al. (1978),
Rodgers (1979)
Dry wt.
Phosohorus
0.002—0.050
Sawyer (1973),
Dry wt.
(0.006)
Rodgers (1979),
MacKenthun et al. (1978)
Nitrogen
4—80
Rhee and Gotham (1981)
Phosphorus
(10—40)
*Typjcal value.
The calibrated coefficients, if accurate, do have ecological signi-
ficance. The endogenous respiration rate, Ke of 0.03 day is appli-
cable to the phytoplankton community without bacterial mediation. This loss
is a result of normal cell maintenance requirements. However, Kmax repre-
sents that loss due to microbial activity and is an order of magnitude
higher. AlthOU9h Kmax is only realized under the worse conditions of cell
maintenance. The half—saturation coefficient (k) which characterizes the
controlling saturation function is of particular interest. Its calibrated
value means that as long as the ratio of chlorophyll biomass (A) to growth
rate ( .i) is less than 500 the phytoplankton decomposition rate is a linear
function. Most useful lakes exhibit chlorophyll concentrations between 1
and 50 .ig-chl/2. and the growth rate of algae in natural settings is commonly
between 0.05 and 0.5 days . Therefore, the A/u ratio frequently ranges
from 2 to 1000. Even when this ratio is at its upper range only two-thirds
of the maximum decay rate is operative. For non—eutrophic lake conditions
and during active growth periods the specific decay rate is about 20 per
cent or less of the maximum rate, Kmax• Temperatures less than 20°C would
additionally impair the magnitude of the specific decay rate.
28

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6.3 CAL. BRATION RESULTS AND DISCUSSION
esz L s: The coefficients presented and discussed in Section4. 2-
were calibrated by observing their abi1it ’ to simulate the field data of
1976 and guided by knowledge of lake processes. The results of this sirnula-
tion, in its totality, would reflect the time dependent behavior of nine
state variables as well as observing the concurrent behavior of model func-
tions. The two macor state variables for the purpose of this research, are
phytoplankton bicmass (chlorobhyll—a) and total phosphorus. The model out-
put for chlorophyll-a fcr the four segments of the laka is :resented cra hi—
cally in Figure 6-. This figure plots the model output as a continuous
line over the observed data. The solid squares denota the arithmetic mean
of data collected for a particular cruise within a lake segment. These
means are each bounded by one standard deviation. Similar plots are output
by each run of the mcdel f or each state variable of interest. The model
does simulate chlorophyll-a within the ncre biologically active epiliTnion
Figure 6-3. Model calibration results for chlorophyll—a during 1976.
29
EPILIMNION
SOUTHERN 8ASIN
HYPOLIMNION
-J
-J
>-
I
0
0
0
-J
I
L)
NORTHERN BASIN

-------
EPI LI MN ION
SOUTHERN BASIN
20
20
9:
J’F 1 M T A 1 M J J ‘A’S’O’N 1 D
NORTHERN
16
12
8
4
HYPOLIMNION
0
BASIN
C
a
=
-J
4
GD
Figure 6-4. Model calibration results for total phosphorus during 1976.
both in respect to trend and magnitude. The model produces the observed
peak in phytoplankton as reflected by chlorophyll—a in late NAay to late
June. The peak in the North lags somewhat behind that of the Southern Basin
due to greater dispersion and colder ambient temperatures. The model does
not simulate the chlorophyll-a concentrations of the hypolimnion segments
quite as effectively.
The calibration to the 1976 data for total phosphorus is presented
in Figure 6—4. It is evident that the model simulates total phosphorus as
relatively non-dynamic over short periods. Tnis is to be expected in a lake
having a detention tine of 69-100 years. This output of total phosphorus
results is a representative simulation throughout most of the lake. How-
ever, the output for the hypolimnion of the Southern Basin fails to simulate
the dyr amic increase observed in the late sumer and early fall. If these
data are accurate then the model would have to account for approximately
J ‘F 1 A’M 1 J J ‘A
30

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TABLE 6-4. 1976 CALIBRATION STATISTICS
SeQment Grouping
Epi limnion
Hypolimnion
Whole Lake
Chloride
1.1/80*
1.1/100
1.1/90
Combined Inorganic
Nitrogen
29.7/56
9.5/45
4.6/89
Total P
6.1/100
19.8/89
16.9/89
Chlorophyll—a
19.3/100
42.5/78
28.4/67
Herbivorous Zooplan
kton
42.3/80
AA
*Relatjve Error/T-test Score.
No field data available.
6,800 metric tonnes of temporary phosphorus influx during low flow months to
produce an accurate fit.
Statistical analysis of model output compared to 1976 field data
provided an objective judgement of the model s simulation. The T—test and
relative error analyses yield a standard quantitative comparison (Thorriann
et al. 1979) and the resulting statistical scores for select state variables
are reported in Table 6-4. The higher the T-test scores the more often the
model output lies within plus or minus one standard error of the cruise
mean. This evaluation ascribes the same error flexibility to the model as
that calculated for the mean of each data point. The relative error score
is an indication of model adequacy and ideally should approach zero. Rela-
tive error evaluation has a number of problems associated with its interpre-
tation. The error in the data mean is not taken into account. The evalua-
tion is poor at relatively low data values when there are large differences
in model output and data values. This statistical technique, however, is
used in model comparison and in fine tuning of coefficients.
Discussion of CaLibration: When evaluating the calibration of a
deterministic model there exists a myriad of relevant considerations. Cer-
tainly, it is fundamental that the model simulate the state variables within
desired limits both in time and space. In achieving that goal, an equally
31

-------
important concern is the model’s accurate representation of dominant pro-
cesses. This representation should reflect the goals of the model as well
as the state of the art knowledge. The final calibration results do not re-
present a best fit to field data, but instead reflect a most appropriate
fit. When model output deviates from available field data or calibrated co-
efficients appear not to lie within reported ranges then a re—evaluation of
either available knowledge or of the modeling framework may be appropriate.
A model must maintain this flexibility in order to interact with current
thought and approach new problems.
The problem encountered in Figure 6-3 where the model does not ac-
curately simulate the mean chlorophyll in the hypolimnion may be due to the
existence of deep chlorophyll layers (DCL). The phenomenon of DCL is well
documented as observed high concentration layers of chlorophyll in the
vicinity of or just below the thermocline (Fee 1976, Tailing 1966, Ichimura
et al. 1978, Steele and Yentsch 1960). Fee (1976) concluded that the DCL
reflected a species specific light adaptive mechanism for growth. The in-
ability of the present modeling framework to consistently simulate DCL has
previously been noted (DiToro and Matystik 1980).
Although light adaptation may be a partial explanation for the DCL,
especially when the species composition of these layers are unique to the
water column, there exists two other processes which undoubtedly influence
the occurrence of DCL. Steele and Yentsch (1960) concluded that the DCL
near the compensation depth in the Atlantic Ocean was controlled by de-
creased sinking rates. There is little doubt that during stratified condi-
tions the thermocline would reduce the apparent settling of phytoplankton
originating in the upper waters (Hutchinson 1967) and thereby result in ob-
served deep layers of biomass. Another explanation for DCL recognizes the
variability in the ratio between ch1orophyl1— and other biomass indicators
(Dolan et al. 1978). Tailing (1966) demonstrated variability in chlorophyll
content when he found a range between 0.8 and 2.0 my of chlorophyll-a per
10 Asterionelia cells, the higher values clearly associated with samples
from deeper layers. To a large extent this variability is probably due to a
concurrent change in the physiological state of the phytoplankton. Chloro-
phyll—a content per cell generally increases with Increasing growth rates
32

-------
(Rhee 1981, Rodgers 1979), yet is comparably high for very low growth rates
(Rodgers 1979) and for cells grown at low light illurninance (Steemann
Nielson 1962). These observations probably reflect a physiological response
to stress conditions and may be referred to as chlorophyll compensation.
Recall that during late sunTner and early fall of 1976 the field
data, evident in Figure 6-4, indicated an increase in total phosphorus con-
centration in the hypolimnion of the Southern Basin which the model output
failed to simulate. The question arises as to where and by what means does
this total phosphorus enter the hypolimnion during this time period. Three
potential sources of this hypolimnetic total phosphorus are 1) Vertical re-
suspension of sediment phosphorus; 2) Sedimentation of epilimnetic phos-
phorus; and 3) Horizontal transport of phosphorus which had been resuspended
in the nearshore zone. Resuspension of a sufficient amount of sediment
phosphorus to account for the observed increase in phosphorus mass seems un-
likely in a lake having a mean depth of approximately 92 meters. The energy
sources required to create the stress necessary to accomplish resuspension
diminish exponentially with lake depth (Sheng and Lick 1979). As a result,
resuspension of in-lake sediments can be considered minimal. The hypothesis
that the observed mass of phosphorus could have originated from epilimnetic
waters appears even more unlikely. The entire mass of total phosphorus pre-
sent in the Southern Basin s epilimnion constitutes only about one—third of
the mass required to produce the concentration increase in the hypolinniofl.
The location and timing of this increase in total phosphorus con-
centrations may indicate that fts origin was from nearshore zones. The
sediment distribution in Lake Michigan indicates that there has been non-
homogeneous deposition of sediments and that the southeastern sector has
served as a sediment sink over the long term (Edgington and Robbins 1976).
The source of these sediment deposits are not only the particulates gen-
erated in the overlying water column, but most likely reflect sediment
transfer from adjacent segments and from the nearshore zone. The nearshore
zones of Southern Lake Michigan have substantial resuspension and erosion
activity. Chesters and Delfino (1978) characterized Lake Michigan’s near-
shore resuspension as having the highest mean number of potential days of
resuspension conditions for all the Great Lakes and ranked it a close second
33

-------
behind Lake Superior for amount resuspended on a nearshore areal basis. In
fact, the southeastern nearshore area of Lake Michigan proved to have the
highest areal resuspension potential of any of the Great Lakes’ twenty—
eight nearshore zones studied. In addition, Lake Michigan has also been
identified as having the highest erosion rate per kilometer of shoreline of
the Great Lakes (Sonzogni et al. 1979). The combined processes of nearshore
resuspension and shoreline erosion suspend large masses of sediment and
associated nutrients into the water column of Lake Michigan. The high sea-
sonal winds may succeed in mixing sortie of these sediments horizontally.
Lower layer velocities of 3-7 cm/sec (Kizlauskas and Katz 1973) would be
sufficient for the timely transfer of nearshore sediments to in—lake hypo—
limnetic stations. Turbulence created by thermocline oscillation would
assist in prolonging suspension of these sediments and their associated
nutrients. The turbidity in the southern hypolimnion also doubled during
this time period and may support the contention of horizontal transfer of
nearshore sediments. The absence of similar observations in the epilimnion
could be a result of its depth being less, resulting in particle retention
being several times shorter than in the hypolirnnion. The sediment dynamics
may therefore result in a loss of sediments from the epilimnion by the time
in—lake locations are reached by horizontal mixing.
The inability of present models to track sediment movement and to
include nearshore resuspension and shoreline erosion may not be of equal
biological importance when compared to present model sources because of
questions involving biological availability of associated nutrients (Lee et
al. 1980, DePinto et al. 1980). However, these sediments r io doubt play
important roles in nearshore zones and quantification of their transport and
biological role remains a research need.
34

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SECTION 7
MODEL APPLICATION TO 1977 DATA
7.1 APPROACH AND RESULTS
The data gathered in 1977 indicated a substantial loss of total
phosphorus from the Southern Basin when compared to the results of the 1976
survey (observed in Figure 4—2). Initially there may have been a temptation
to attribute the improvement in water quality to active remedial programs.
However, since the hydraulic detention of Lake Michigan approaches a cen-
tury, and since our present understanding of long term sediment rates would
suggest a loading response time on the order of years, then alternative loss
mechanisms must be responsible for such a rapid depletion in total phos-
phorus. The main challenge in applying MICH1 to the 1977 data was to sug-
gest a process by which such a rapid loss of total phosphorus could occur.
The approach to applying MICH1 to the 1977 Lake Michigan data was
guided by the above realization. Initially, MICH1 would be run from 1976
through 1977 only changing the values of certain forcing functions as the
model progressed into 1977. This included changing phosphorus loadings,
flows, and ambient temperatures. If the model simulation failed to demon-
strate the observed depletion of total phosphorus then the model structure
would be inspected for the absence of a mechanism not included which might
have been operative in Lake Michigan during the survey period.
Rest lts To run MICH1 for 1977 it was only necessary to link the
initial conditions to the final output for 1976 and at the same time change
the appropriate forcing functions. This attempt at direct verification, as
seen in Figure 7—1, failed to simulate the substantial decrease in mean
total phosphorus within the water column of the Southern Basin. The model
responded to the 2000 metric ton decrease in phosphorus load with a maximum
0.36 pg—P/i loss in concentration instead of the 3.1 1 jg—P/2 . loss necessary
35

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1
EPILIMNION HYPOLIMNION
SOUTHERN BASIN
20 20—
16 16
12- 12k-
01
8 ______ __ __________
4 4- 1
JlFIMIAJMIjJAlSICJN Q 0 J F’M A’M’J T J 1 A S 1 O 1 N’D
..-.
01
I
L)
Figure 7-1. MICH1 application to 1977 data for total phosphcrus and
chlorophyll -a.
- Calibrated motel using 1977 -— Model incorporating changes
loads. Initial conditions in forcing functions for re-
linked to Final output for presenting ice cover effec:s.
1976. No change in settling rate
coeffi ci ent.
to simulate the field data observed in the Southern Basin. Even thougn the
phosphorus fit was awry the chlorophyll-a fit to the limited data was rea-
sonable (Figure 7-1), which may suggest a possible inconsistency between the
phosphorus data and the concurrent chlorophyll-a data. Although such an ob-
servation may also indicate that the biologically available phosphorus in
the epilimnion was not radically affected by the dynamic total phosphorus
depletion.
7.2 CONSIDERATiON OF ICE COVER EFFECTS
As suggested previously, an explanation for not simulating the ob-
served phosphorus loss is the absence of a particular loss mechanism not
originally incorporated in the model structure which might have been opera-
tive in Lake Michigan. The extreme ice cover during the winter of 1976—77
(Quinn et al. 1978) presented a potential phenomenon that might be substan-
2TTTftF
36

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tial enough to enhance the loss of phosphorus from the water column. The
ice cover would have isolated the lake from normal mixing and turbulence-d.ue
to wind driven forces. This mixing would otherwise act to inhibit particles
and associated nutrients from sinking out of suspension. Such a severe cli-
matic induction of an accelerated loss, if operative, would be rare and
temporal in nature.
The structure of MICH1 was examined for ways of simulating the ef-
fect of the ice cover upon phosphorus dynamics. Vertical dispersion, inci-
dent light, and water temperature were adjusted with respect to per cent ice
cover, available data, and expected effects. P n ice cover was assumed to
reduce wind induced mixing proportional to per cent ce cover for weekly
periods. Estimating changes in transmission of photosynthetically active
radiation was somewhat more complicated due to the observed effect of ice
type on light transmission (Bolsenga 1978). However, its total attenuation
is also influenced by per cent ice cover. These changes in the model struc-
ture represent an attempt to simulate a unique and significant climatic
event without altering the calibrated coefficients or the structure of
MICH1. Since this approach was based on deductive estimates, rather than
actual data, the accuracy of the representation is subject to continued im—
provernent based on measurement of pertinent parameters. The results of this
approach are represented by the dashed line in Figure 7—1. The most in-
fluential change was the reduction in vertical dispersion, since vertical
dispersion acts as a competitive parallel process to particulate sinking.
Therefore, its reduction results in an increase in net (or apparent)
sinking, thereby increasing the losses from the water column. By the end of
the simulation year, this adjusted model exhibits a slight improvement but
still fails to simulate the large phosphorus loss. Equally important is the
observation that the response did not progress rapidly enough to simulate
the total phosphorus concentration observed on the first cruise. In addi-
tion, the chlorophyll-a response to these dynamics did not fit the field
data as well as it had previously.
The calibrated settling rate used in MICH1, and in many eutrophica-
tion models, reflects the net forces affecting the long term loss of parti-
culate matter from the water column. Wind driven resuspension and intra—
37

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segment mixing no doubt affect this calibrated “apparent” settling rate.
The present model structure cannot account directly for these component
forces which may have been influenced by the ice cover. However, if it is
assumed that the ice cover decreased these forces then net settling would
have been further enhanced during this period. MICH1 was run while in-
creasing the settling rate during ice cover until the model output simulated
the first cruise total phosphorus concentration. The necessary settling
rate proved to be 1.6 m/day, eight times the value from the 1976 calibra-
tion. After the ice cover receded significantly, the settling rate was re-
turned to its previous calibrated value. The results of this approach can
be seen in Figure 7—2 for total phosphorus, and in Figure 7-3 for chloro-
phyll-a simulations.
7.3 DISCUSSION OF 1977 SIMULATION
There are a number of potential explanations for the model and data
not coinciding when 1977 was initially linked to the 1976 final conditions.
For example, the phosphorus samples were stored up to 90 days (Rockwell et
al. 1980), which exceeds the E.P.A. recormiendation of a maximum storage time
of 24 hours (U.S. E.P.A. 1974). Whether this storage practice influenced
the analytical evaluation of the samples is difficult to ascertain. Also,
the incomplete coverage in data collection in 1977, both in spatial coverage
and cruise frequency, makes a thorough analysis additionally difficult.
This research approach accepted the validity of the data and exa-
mined the modeling framework for methods of simulating the potential in-
fluence of an extreme ice cover upon the dynamics of the particulates re-
siding in the water column. When the initial attempt to simulate the 1977
data by simply altering the phosphorus load and certain other forcing func-
tions failed there were two approaches devised for representing the in-
fluence of ice cover.
The first approach did not alter model structure but instead looked
at present model inputs which might have been altered by a substantial ice
cover. Model components which were changed included vertical dispersion and
incident light. These components are normally time variable and, therefore,
their adjustment required only assumptions in regard to the influence that
38

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Figure 7-2.
Two ‘fear
eight fold increase in apparent
ice cover per od (between
incorporating an
net settl ng during the
dashed lines).
1976 I 1977
Figure 7-3. Two year chlorophyll-a simulation incorporating an
eight fold increase in apparent net settling during the
ice cover period (between dashed lines).
total phosphorus simulation
EPILIMNION
(UPPER LAYER
C
-J
I
a.
0
0
-J
I
HYPOLIMNION
(LOWER LAYER
4,0
10
1.0
39

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an extensive ice cover might have had. When this approach proved to fail at
mediating a sufficient loss the alternative mechanism that net sedimentation
is enhanced directly by the ice cover reducing wind induced intra—segment
mixing, turbulence, and resuspension was then explored.
Analysis of the attempts to adjust the modeling framework to simu—
late the ice cover event suggests that if the phosphorus data is accurate
then the net settling during ice cover is altered substantially. In order
to fit the total phosphorus data and the chlorophyll-a data simultaneously
it was necessary to make extensive alterations in the settling coefficient
and the vertical dispersion between segment layers. This meant decreasing
vertical dispersion and increasing the “apparent” settling rate during the
period of ice cover. This final approach succeeded in simulating both the
phosphorus and chlorophyll-a dynamics. Its implication is that the
“apparent” settling rate, whose value is normally determined over the long
term, can change dramatically in the short term due to rare and extreme cli-
matic conditions. What role such climatic influences may have in long term
responses to nutrient loading alternatives is a subject yet to be addressed.
Perhaps the solution to such a problem lies in representing the frequency of
occurrences on a statistical basis. These observations indicate that a more
thorough analysis of ice cover events would be in order.
40

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SECTION 8
LONG TERM SIMULATIONS
8.1 RATIONALE AND APPROACH
Hindcasting or historical simulations, when successful, add credi—
b’lity to the model structure. Through this exercise the behavior of the
model for prolonged periods can be observed and the ability of the model to
“predict’ present conditions, given historical loadings, can be tested. To
aid the historical simulation, a surmiary of historical loading estimates was
gathered from a variety of sources and were graphically presented in Figure
4-3. Forecasting fulfills a primary motive of model development, the
ability to make scientific cause and effect .judgements to aid present
management decisions concerned with resource preservation. Simulating lake
response given the nature of a remedial program along with estimating the
time necessary for that response is a valuable model application.
In Section 5—1 three models besides MICH1 were briefly described
and in Table 5—1 a model requirement sun nary for all four models was pre-
sented. The time variable total phosphorus model (TPM) was the only model
applied for historical simulation. 1PM was chosen for this task because the
loads during the simulation period (1800—1980) were variable, therefore a
non-steady-state model was required. Secondly, the model requirements for
running TPM during the historical period were considerably less than what
would have been required by MICH1. All models were applied for forecasting
simulations of steady—state loading scenarios.
8.2 HISTORICAL SIMULATION RESULTS
The historical loads resulting from Chapra’s (1977) loading model,
as presented in Figure 4—3, were used as an input to 1PM from 1800 through
1960. Thereafter, an interpolation of the estimated loads were used through
41

-------
10
S
6
4
2
0
a.
U,
C
-r
C-
U,
0
I
a.
-J
4
0
TIME ( years)
Figure 8—i. 1PM historical simulation output for Lake Michigan
for the years 1800 —i980.
— Southern Basin —— Northern Basin
1980. Using this recreation of historical loads produced the TMP results
evident in Figure 8-1. Note that the maximum total phosphorus concentra-
tions, 9.5 and 10.6 1 .ig-P/9.. in the Southern and Northern basins, respec-
tively, were during the early—l960 s. These concentrations are within the
range of values reported through the U.S. Department of the Interior (1966,
1968) and by Risley and Fuller (1965) for the years 1962-63. This entire
range of 6.5 - 22.8 .ig -P/Z is large due to the inclusion of nearshore
stations, but the few in-lake stations appear to vary between 6.5 and 13.1
j.jg—P/2 . The 1976 concentration resulting from this historical s muiation
are 7.8 1 .ig-P/i in the south and 8.9 pg-P/Z in the north. This horizontally
segmented total phosphorus model predicts slightly higher concentrations in
the Northern Basin due to its shorter detention time and the loading of
phosphorus this basin receives from the Southern Basin.
Recall that the loadings used in this historical simulation were
primarily obtained from a loading model based on cultural activity and the
0
1800 1829 j34( isse 88a 1900 1929 1949 1.960 i s
42

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physical characteristics of the drainage basin (Chapra 1977). These
loadings were r ver verified due to a lack of appropriate data. TPM re-
flected the input loadings in a consistent manner and reflects the 1976 re-
sults within the error 0 f the field data (compare with the values evident in
Figure 6-4). The results do favor the high side of the data but the loads
for the preceding years may be somewhat high. Even though the TPM model
says nothing about the response in the biological corrriunity during this his-
torical period its performance in regarc’ to total phosDhorus renders the
model suitable for limited comparison with MICH1 forecasting results.
8.3 FORECASTING RESULTS
The three loads presented in Table 4—3 and noted in Figure 4—3 were
utilized in applying the models for forecasting purposes. Case 1 reflects
the high flow, high load condition of 1976. Case 2 is the value recommended
by Task Group III (Vallentyne and Thomas 1978). At the lower end of the
load spectrum, Case 3 represents the extreme low flow, low load condition of
1977.
The Vollenweider model (1975) makes use of an empirical observa-
tion. When the areal loading of many lakes are plotted versus their over-
flow rate, lakes classified as eutrophic generally group separately from the
oligotrophic lakes. In the area in between these two groups reside meso—
trophic lakes and some lakes from each category. Using whole lake loading
and morphornetry measurements the Vollenweider model suggests that Lake
Michigan would fall within the mesotrophic range if long term loads equiva-
lent to Case 1 are assumed. Application of this sort of model does not per-
mit specific phosphorus concentrations to be obtained. Also, this loading
plot model” cannot indicate response times to load changes. A similar
application, using Cases 2 and 3, reveals that these load reductions are
barely sufficient to enable Lake Michigan to be within “permissable” loading
limits and to reside in the oligotrophic zone.
These loading scenarios were applied to MICH1 (as calibrated to
1976), TPM and the Dillon and Rigler empirical model. Except for MICH1,
forecasting was performed on a whole lake basis as well as for the two basin
scheme. The input to these models assume, for the purpose of illustration,
43

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TABLE 8-1. MODEL COMPARISONS OF FORECASTING RESULTS FOR
STEADY-STATE TOTAL PHOSPHORUS CONCENTRATION ( ig/2 .)
Loading Case* MICH1
TPM --
Dillon & Rigler
Whole Lake
1
2
3
-
-
-
(10
7.7
6.4
5.4
yrs.)
12.7
10.6
8.8
(29 yrs.)
Southern Basin
1
2
3
7.4
6.6
5.5
(7 yrs.)
(8
7.3
6.1
5.1
yrs.)
12.0
10.1
8.4
(25 yrs.)
Northern Basin
1
2
3
9.0
7.4
6.7
(14 yrs.)
(14
8.2
6.9
5.8
yrs.)
13.4
11.1
9.3
(30 yrs.)
*Whole lake loadings reported in Table 1.
Response time for reaching > 95% steady—state.
a step change starting in 1978. Table 8-1 surrrnarizes the results for easy
comparison of the steady—state concentration of total phosphorus and the re-
sponse time for each of the three models. Reference to Figure 4-2 provides
a baseline comparison to the 1976 and 1977 observed concentrations.
For the most part these forecasting results produced similar
loading responses. The Northern Basin consistently reaches steady—state
concentrations for non-conservative substances which are somewhat higher
than those in the Southern Basin. This concentration gradient may not be as
evident in the actual case due to sedimentation in Green Bay of particulate
phosphorus that is not represented in the models. However, since the
Southern Basin receives the higher phosphorus load, these modeling fore-
casts suggest that the Southern Basin serves as a loading source to the
Northern Basin. In a similar way, Lake Erie has been noted for being a
loading source to Lake Ontario (Chapra 1977). In Lake Michigan, MICH1 finds
that even the chloride concentration in the North, 12.7 mg/ Q at steady—
44

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state, would only be 4.7 mg/p. were it not for the load from the Southern
Basin. The shorter residence time in the Northern Basin also influences the
model results from non-conservative state variables. Note that the whole
lake responses are intermediate to the two basin results.
The Dillon and Rigler empirical model consistently predicts higher
phosphorus concentration responses to the loading scenarios. The explana-
tion for this deviation may lie in that model’s loss term. Unfortunately,
this loss term is very difficult to measure and, therefore, is normally
estimated via data from many lakes (Kirchner and Dillon 1975) or from gener-
alized assumptions derived from lake morphometry (Dillon and Rigier 1975).
The value utilized for this loss term was 12.3 rn/yr. after estimates made
by Sonzogni et al. (1979). The uncertainty in this loss term and its in-
accuracy in depicting a highly kinetic environment results in an equal un-
certainty in results, especially when applied to a lake not used in the ori-
ginal empirical data base. Although the magnitude in the steady—state re—
suits for the Dillon and Rigler model are higher than the other two models,
the general trends noted previously are similar for all model forecasts.
The response times, also indicated in Table 8—1, were obtained for
the time variable models by observing the elapsed time required for greater
than 95% equilibration. Conservative substances in Lake Michigan would be
expected to have a response time of three times the hydraulic detention time
of approximately 100 years. The net loss of total phosphorus to the sedi-
ments provides the mechanism for the predicted response times being con-
siderably shorter. Due to the hydrology of the lake, the Northern Basin
lags behind the response of the Southern Basin. The fourteen year response
time in the north includes the seven to eight year response in the south.
For the main lake portion to respond in eight to fourteen years in the kine-
tic models compares favorably with the estimate made by Chapra (1977) of
sixteen years for the entire lake. A more optimistic response time of five
years has been estimated and reported by Sonzogni et al. (1979). These re-
sponse times should be regarded with caution because they assume well de—
fined steady—state conditions and no resuspension events of sediments out-
side that included in the long term net settling rate.
45

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Special note regarding the MICH1 forecasts should be made. These
results indicate that if Lake Michigan were to receive a long term phos-
phorus load equivalent to the 1976 load (Case 1) then the in—lake concentra-
tion of total phosphorus would exceed the GLISP goal of 7.0 jg—P/Z for Lake
Michigan. Even when a 1 mg/2 treatment standard is applied to this load
(i.e., Case 2) the Northern Basin is forecast to exceed the goal by 0.4
‘ug—P/2.. However, on a whole lake basis Case 2 loading does result in phos-
phorus concentrations very close to the GLISP goal. These loading scenarios
do not include probable increases in wastewater volume in the basin due to
expected population growth.
Unlike the total phosphorus model, MICH1 can predict concurrent re-
sponses in chlorophyll-a when forecasting. The calibrated 1976 sirnulat on
of chlorophyll—a indicated a peak concentration of 2.8 jig/Z in the Southern
Basin and 2.9 ug/9. in the Northern Basin, although the annual productivity
is greater in the south due to a longer growing season. The forecast based
on Case 1 loading only sees less than a 0.5 pg/Z increase in peak chloro-
phyll in the south and nearly a 1 .ig/.Z increase in the north. A 0.3
decrease in peak chlorophyll-a for the south is predicted by the GLISP re—
conrended phosphorus load, represented in Case 2. This same scenario finds
a very slight increase in the north. Case 3 loading, on the other hand,
would result in decreases in peak chlorophyll—a in both basins, 0.9 ig/2. in
the south and 0.4 pg/9 in the north, when compared to the 1976 values. None
of the forecast loadings results in dramatic shifts in chlorophyll-a. Ob-
viously these concentrations of in—lake chlorophyll-a do not envision Lake
Michigan as exhibiting eutrophic responses to these loading examples. How-
ever, Green Bay and the nearshore zones may indeed display such undesirable
water quality problems.
46

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SECTION 9
SUMMARY
The intensive surveys of 1976 and 1977 provided the data necessary
for calibrating MICH1, a nutrient and phytoplankton model. These data also
indicated a substantial total phosphorus decrease in 1977, when compared to
1976. A reflex explanation that short term remedial programs were respon-
sible could not be accepted in light of known loss mechanisms and lake
hydrology. In fact, because the flow decreased by 66% in 1977 compared to
the high flow year of 1976 it is not clear that remedial programs affected
the load decrease appreciably during these survey years.
MICH1 was first calibrated to the 1976 field data and then applied
to the 1977 data. This application of the calibrated model overestimated
the 1977 total phosphorus. In order to suggest an explanation for the ob-
served phosphorus loss, a careful examination of the meteorological condi-
tions separating the surveys was made. The winter of 1976—77 was the fifth
coldest in 200 years. Record breaking low temperatures from mid—October to
mid—February resulted in an extraordinary ice cover over the entire Great
Lakes. The maximum extent of ice cover in Lake Michigan was over 90% (Quinn
et al. 1978). This ice cover would have isolated the lake from wind induced
mixing and resuspension. The result being enhanced sedimentation and loss
of phosphorus from the water column. Based on this scenario of events, re-
finements were made to the MICH1 forcing functions to account for the ex-
pected effects of the observed ice cover. The final results of the 1977 re—
finement efforts indicated that the apparent settling rate would had to have
been increased eight-fold during the ice cover to affect the loss in phos-
phorus mass observed. This increase in net apparent settling is in addition
to reduced vertical dispersion, incident light, and ambient temperatures.
47

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The application of MICH1 and the implicit incorporation of possible
physical effects due to ice cover does not close the case on the validity of
the survey data. However, it does suggest a possible loss mechanism not
normally incorporated in long term ecological models. In addition, such a
model application demonstrates how a modeling framework can be utilized in
the difficult assessment of remedial programs, especially when such an
evaluation is made difficult by concurrent physical and biological pheno-
mena of a complex nature. The combined influence of dispersion, particle
settling and resuspension is a major factor in determining the fate of
particulates and associated parameters. The predicament encountered in
interpreting the 1977 data is a strong case for at least limited winter
sampling.
There are important cautions in considering the observed phosphorus
loss of 1977. If indeed a loss of this magnitude did occur there is no
doubt that a short term reduction in load was not responsible for the bulk
of the loss. Secondly, if resuspension of sediments or sediment transfer
are important mechanisms in Lake Michigan then such a loss should not be
considered entirely permanent, but rather as a phosphorus rich deposition
available for subequent resuspension.
The Fifth—Year Review of Canada — United States Great Lakes Water
Quality Agreement (Vallentyne and Thomas 1978) has recomended an annual
load of 5553 metric tonnes of phosphorus as a target load for Lake Michigan.
This load, reflected by Case 2, was considered achievable through a 1 mgJ2.
effluent standard and was projected at the time to result in approximately
7 ug-PIQ. MICH1 results indicate that the target load may result in
slightly higher concentrations than the projections in the Northern Basin,
but overall this work reaffirms their projections. Whether the target load
can be maintained in light of population and industrial growth in the drain-
age basin under only a point source standard is open to question. The ques-
tion of phosphorus availability of the high erosion inputs may also affect
the attainability of the effective target load and resulting water quality.
48

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REFERENCES
Ayers, J.C. 1970. Lake Michigan Environmental Survei . Univ. Michigan,
Great Lakes Res. Div., Spec. Rep. No. 49, 97 pp.
Bartone, C.R., and Scheiske, C.L. 1980. Limnological conditions in Lake
Michigan based on analysis of 1976 surveillance data, submitted for
pub., J. of Great Lakes Res .
Bierman, V.J., Jr., Stoermer, E.F. and Smith, V.E. 1980. The development
and calibration of a soatially simplified multi-class ph p1ankton
model for Saqinaw Bay, Lake Huron . A Great Lakes Environmental Planning
Study (GLEPS) Report, Contribution No. 33.
Bolsenga, S.J. 1978. Photosynthetically active radiation transmission
through ice . NOM Technical Memorandum, ERL GLERL-18.
Chapra, S.C. 1977; Total Phosphorus Model for the Great Lakes. J. of
the Env. Eng. Div . 103: 147-161.
Chesters, G. and Delfino, J.J. 1978. Freguence and Extent of Wind-Induced
Resuspensin of Bottom Material in the U.S. Great Lakes Nearshore
Waters. PLURG Technical Report, U.S. Task 0, IJC, G.L.N.P.0., Windsor ,
Ontario, 111 p.
DePinto, J.V., Young, T.C. and Martin, S.C. 1980. Bioassay determination
of algal—available phosphorus in suspended sediments of Great Lakes
tributaries. Progress Report for EPA Grant #807155 .
DiToro, D.M. and Connolly, J.P. 1980. Mathematical models of water quality
in large lakes, Part 2: Lake Erie . EPA—600/3-80-065.
DiToro, D.M. and Matystik, W.F., Jr. 1979. Phosphorus recycle and chloro-
phyll in the Great Lakes. J. of Great Lakes Res . 5(3-4): 233-245.
DiToro, D.M. and Matystik, W.F., Jr. 1980. Mathematical models of water
quality in large lakes, Part 1: Lake Huron and Saginaw Bay. EPA-600/3 -
80-056.
Dillon, P.J. and Rigler, F.H. 1975. A simple method for predicting the
capacity of a lake for development based on lake trophic status. J.
Fish. Res. Board Can . 32(9): 1519-1531.
49

-------
Dolan, D.M., Bierman, V.3., Jr., Dipert, M.H., Geist, R.D. 1978. Statisti-
cal analysis of the spatial and temporal variability of ratio chloro-
phyll-a to phytoplankton cell volume in Saginaw Bay, Lake Huron. 3. of
Great Lakes Res . 4(1): 7 —83.
Dolan, D.M., Bierman, V.3., Jr., Gonzales, P. and Paddy, B. 1980. Analysis
of the effect of total phosphorus load reductions on phosphorus concen-
trations in Saginaw Bay. A paper presented at the 23rd Conference on
Great Lakes Res. , Kingston, Ont.
Dolan, D.M. and Clark, J.L. 1981. Analysis of the tributary phosphorus
loading decrease to Saginaw Bay, Lake Huron and the associated by re-
sponse. In Proc. of Envirometrics 81, Wash., D.C .
Edgington, 0.N. and Robbins, J.A. 1976. Records of lead deposition in Lake
Michigan sediments since 1800. Environ. Sci. Technol . 10(3): 266-274.
Eisenreich, S.J., Effxnling, P.3. and Beeton, A.M. 1977. Atmospheric loading
of phosphorus and other chemicals to Lake Michigan. 3. Great Lakes Res .
3: 291-304.
Fee, E.J. 1976. The vertical and seasonal distribution of chlorophyll in
lakes of the Experimental Lakes Area, Northwestern Ontario: Implica-
tions for primary production estimates. Limnol. Oceanog r . 21(6): 767-
783.
Great Lakes Water Quality Board. 1974. Great Lakes Water Quality, Second
Annual Report to the International 3oint Comission . IJC, Windsor, Ont.
Hutchinson, G.E. 1967. A Treatise on Limnology, Vol. 2 . New York: John
Wiley and Sons.
Ichimura, S., Nagasawa, S. and Tanaka, T. 1968. On the oxygen and chloro-
phyll maxima found in the metal imnion of a mesotrophic lake. Bot. Mag.
Tokyo . 81: 1-10.
International Joint Coninittee. 1976. Great Lakes Water Quality, Fourth
Annual Report, Appendix B, Surveillance Subcomittee Report. IJC ,
Windsor, Ont.
International Joint Comission. 1978. Great Lakes Water Quality, Sixth
Annual Report, Appendix 8, Surveillance Subcoriinittee Report . IJC,
Windsor, Ont.
Kirchner, W.B. and Dillon, P.3. 1975. An empirical method of estimating
the retention of phosphorus in lakes. Water Resour. Res . 11: 182-183.
Kizlauskas, A.G. and Katz, P.L. 1973. A two—layer finite difference model
for flows in thermally stratified Lake Michigan. In: Proc. Sixteenth
Conf. Great Lakes Res. , pp. 743—753. mt. Assoc. Great Lakes Res.
50

-------
Lee, G.F. 1974. Phosphorus, water quality, arid eutrophication of Lake
Michigan. In Conf. in the matter of pollution of Lake Michigan and its
tributary basin in the states of Wisconsin, Illinois, Indiana, and
Michigan, 4th session, Chicago, 111., 19-21 September 1972, VoL 1 .
USEPA, U.S. Government Printing Office.
Lee, G.F., Jones, R.A. and Rast, W. 1980. Availability of phosphorus to
phytoplankton and its implications for phosphorus management stra-
tegies. In Phosphorus Management Strategies for Lakes , ed. R.C. Loehr,
C.S. Martin, W. Rast, pp. 259-310. Ann Arbor Science Pubi.
Lorenzen, M.W., Smith, D.J. and Kinii el, L.V. 1976. A long-term phosphorus
model for lakes: Application to Lake Washington. In Modeling Bio-
chemical Processes in Aquatic Ecosystems , ed. R.P. Canale, pp. 75-92.
Ann Arbor Science Pubi.
MacKenthun, K.M., Keop, L.E. and Stewart, R.K. 1968. Nutrients and algae
in Lake Sebasticock, Maine. J. Water Pollut. Control Fed . 40(2): R72-
R81.
Monteith, T.J. and Sonzogni, W.C. 1976. U.S. Great Lakes shoreline erosion
loadings . PLUA Tech. Report, IJC, GLNOP, Windsor, Ont.
Patalas, K. 1972. Crustacean plankton and the eutrophication of St.
Laurentian Great Lakes. 3. Fish. Res. Board Can . 29: 1451-1462.
Phillips, D.W. and McCulloch, J.A.W. 1972. The climate of the Great Lakes
Basin, from climatological studies . Number 20, Environment Canada,
Toronto.
PLUA G, Pollution From Land Use Activities Reference Group. 1978. Environ-
mental management strategy for the Great Lakes system . I 1 JC, Windsor,
Ont.
Quinn, F.H., Assel, R.A., Boyce, D.E., Leshkevich, G.A., Snider, C.R. and
Weisnet, 0. 1978. Suniiiary of Great Lakes weather and ice conditions,
winter 1976—77 . NOM Technical Memorandum, ERL GLERL-20.
Quinn, F.H. 1977. Annual and seasonal f1o i variations through the Straits
of Mackinac. Water Resour. Res . 13(1): 137-144.
Rast, W. and Lee, G.F. 1978. Surirnary analysis of the North American OECD
Eutrophication Project: Nutrient loading-lake response relationshios and
trophic status indices . EPA—600/3—T8-008.
Rhee, C. and Gothani, 1.3. 1981. Effects of environmental factors and their
interactions on nutrient kinetics of Great Lakes phytoplankton . Manu-
script for publication.
Risley, C., Jr. and Fuller, F.D. 1965. Chemical characteristic of Lake
Michiaan . Proc. 8th Conference on Great Lakes Research. Great Lakes
Research Div., Institute of Science and Tech., Univ. Michigan. Pub.
#13, 168-174.
51

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Rockwell, D.C., Marion, C.V., Palmer, M.F., DeVault, D.S. and Bowden, R.J.
1980. Environmental trends in Lake Michigan. In Phosphorus Management
Strategies for Lakes , ed. R.C. Loehr, C.S. Martin, and W. Rast, pp. 91-
132. Ann Arbor Science Pubi.
Rodgers, P.W. 1979. Kinetic studies of phytoplankton decomposition. Ph.D.
dissertation, Univ. of Michigan Publ., Ann Arbor, Michigan.
Rousar, D.C. and Beeton, A.M. 1973. Distribution of phosphorus, silica,
chlorophyll—a, and conductivity in Lake Michigan and Green Bay.
Wis. Acad. of Sciences, Arts, and Letters . 61: 117—140.
Rumer, R.R. 1978. Methodology for evaluating in-lake effect resulting
from ohosohorus management in the Lake Erie drainage basin. Prepared
for LEnIIS, U.S. Army Engr. District, Buffalo, N.Y.
Sawyer, C.N. 1973. Phosphorus and ecology. In Environmental Phosphorus
Handbook , ed. E.J. Griffith, et al., pp. 633-648. New York: J. Wiley
and Sons.
Schelske, C.L. 1974. Nutrient inputs and their relationship to accele-
rated eutrophication in Lake Michigan. In Biological Effects in the
Hydrobiological Cycle , ed. E.J. Monke, pp. 59-81. Proc. 3rd Inter-
national Syiiiposiuni for Hydrology Professors, Purdue Univ., Dept. Agric.
Eng.
Schelske, C.L. and Stoerrner, E.F. 1971. Eutrophication, silica deple-
tion, and predicted changes in algal quality in Lake Michigan. Science
173: 423—424.
Schelske, C.L., Rothnian, E.D., Stoermer, E.F. and Santiago, M.A. 1974.
Responses of phosphorus—limited lake Michigan phytoplankton to fac-
torial enrichments with nitrogen and phosphorus. Limnol. Oceanogr .
19(3): 409—419.
Sheng, Y.P. and Lick, W. 1979. The transport and resuspension of sediments
in a shal1 i lake. J. of Geophysical Res . 84(C4): 1809—1826.
Sonzogni, W.C., Monteith, T.J., Skimin, W.E., and Chapra, S.C. 1979.
Critical assessment of U.S. land derived pollutant loadings to the Great
Lakes, a sumary U.S. Task 0 . PLUARG, IJC, Windsor, Ont.
Sonzogni, WE., Monteith, T.J., Bach, W.N. and Hughes, V.G. 1978. U.S.
Great Lakes tributary loadings . Great Lakes Basin Conmission for 1JC,
Windsor, Ont.
Steele, J.H. and Yentsch, C.S. 1960. The vertical distribution of chloro-
phyll. J. Mar. Biol. Assoc. U.K . 39: 217-226.
Steeman Nielsen, E. 1962. Inactivation of the photochernical mechanism in
photosynthesis as a means to protect the cells against too high light
intensities. Physiol. Plant 15: 161-171
52

-------
Stoerrner, E.F. and Tuchman, M.L. 1980. Conservative ion effect on phyto—
plankton . A proposal to the USEPA, Great Lakes Res. Div., Ann Arbor,
Michigan.
Surveillance Subcoriiiiittee Report. 1978. Great Lakes water quality 1977-
Appendix B . IJC, Windsor, Ont.
Tailing, J.F. 1966. The annual cycle of stratification and phytoplankton
growth in Lake Victoria (East Africa). mt. Rev. Hydrobiol . 51: 545-
621.
Thomann, R.V., Diloro, D.M., Winfield, R.P. and O’Connor, D.J. 1975.
Mathematical modeling of hytoolankton in Lake Ontario, 1. Model
development and verification . EPA-660/3-75-005.
Thomann, R.V., Winfield, R.P. and Segna, J.J. 1979. Verification analysis
of Lake Ontario and Rochester embayment three dimensional eutrophica-
tion models . EPA-600/3-79-094.
U.S. Dept. HEW. 1953. Great Lakes—Illinois River Basins Project, Part 1
Text, Report on the Illinois River System, Water Quality Condition .
A report by the Public Health Service, Division of Water Supply and
Pollution Control.
U.S. Dept. Interior. 1966. FWPCA. Comprehensive Water Pollution Control
Program . Lake Michigan Basin, Milwaukee Area.
U.S. Dept. Interior. 1968. FWPCA. Physical and chemical quality condi-
tions . Water Quality Investigations, Lake Michigan Basin. 81 p.
U.S. EPA. 1974. Methods for chemical analysis of water and wastes . EPA-
625/6-74-003, p. xi.
Vallentyne, J.R. and Thomas, N.A. 1978. Fifth year review of Canada-United
States Great Lakes Water Quality Agreement . Report of Task Group III,
a technical group to review phosphorus loadings, IJC, Windsor, Ont.
Vollenweider, R.A. 1975. Input - output models with special reference to
the phosphorus loading concept in limnology, Schwizer. Z. Hydrol . 37:
53-84.
Vollenweider, R.A. 1976. Advances in defining critical loading levels for
phosphorus in lake eutrophication. Mern. 1st. Ital. Idrobiol . 33: 53-
83.
Yui, A.K. 1978. The VWA data base at the LLRS . System manual, Grosse lie,
MI.
Zar, H. 1974. Report of the Phosphorus Technical Coninittee to the Lake
Michigan Enforcement Conf. In Conf. in the matter of pollution of Lake
Michigan and its tributary basin in the states of Wisconsin, Illinois,
Indiana and Michigan, 4th session, Chicago, Illinois, 19-21 September
1972, Vol. 1. U.S. EPA, U.S. Govt. Printing Office.
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