EPA-600/3-77-126b
November 1977
GREAT LAKES ENVIRONMENTAL PLANNING USING
LIMNOLOGICAL SYSTEMS ANALYSIS:
PHASE I - PRELIMINARY MODEL DESIGN
by
Hydroscience, Inc.
363 Old Hook Road,
Westwood, New Jersey
07675
prepared for
Great Lakes Basin Commission
Ann Arbor, Michigan
48106
Contract Number: DACW-35-71-C0030
and
ENVIRONMENTAL RESEARCH LABORATORY - DULUTH
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
DULUTH, MINNESOTA 55804
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DISCLAIMER
This report has been reviewed by the Office of Research
and Development, U.S. Environmental Protection Agency,
and approved for publication. Approval does not signify
that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor
does mention of trade names or commercial products con-
stitute endorsement or recommendation for use.
11
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FOREWORD
Man and his environment must be protected..from the adverse
effects of pesticides, radiation, noise, and ;other forms
of pollution, and the unwise management of solid waste.
Efforts to protect the environment requires a focus that
recognizes the interplay between the components of our
physical environmentair, water, and land. The Office
of Research and Development contributes to this multidisci-
plinary focus through programs engaged in
studies on the effects of environmental contaminants
on the biosphere, and . . '
e a search for ways to prevent contamination and to
recycle valuable resources. . .
This report assesses the technical feasibility and economic
practicality of developing mathematical models to assist in
defining and making selections among alternative management
strategies and structural solutions proposed [for solving
water resource problems of the Great Lakes.'- ;The deliberate
decision-making process reported is a milestone in preappli-
cation analysis of modeling for natural resource management
purposes. :
iii
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ABSTRACT
The report documents the deliberate decision making process used
by the Great Lakes Basin Commission in concluding that rational modeling
methodologies could be used to evaluate the effect of different planning
alternatives on the Great Lakes and that planning for specific problems
affecting the Great Lakes system can- be technically and economically
supported through mathematical modeling and systems analysis. It assesses
the technical and economical feasibility of developing mathematical models
to assist in making selections from among alternative management strate-
gies and structural solutions proposed for solving water resource problems
of the Great Lakes. The study reviews, evaluates and categorized present
and future water resources problems, presently available data, problem-
oriented mathematical models and the state of models; and model synthesis
for large lakes. A demonstration modeling framework for planning is devel-
oped and applied to western Lake Erie and the Great Lakes system. The
report evaluates four widely ranging alternatives for future modeling ef-
forts in the Great Lakes and recommends the modeling, level most feasible
to answer planning questions on scales ranging from the Great Lakes to
regional areas. Also discussed is a proposed Commission study which will
apply limnological systems analysis to the planning process.
The report consists of three volumes: :/
a. Summary .''
b. Phase I - Preliminary Model Design.
c. Model Specifications
iv
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CONTENTS . ., ;
Foreword iii
Abstract iv
Figures .viii
Tables .. . :. .xv
Abbreviations and Symbols .xviii
Acknowledgment .xxxii
I. Summary and Conclusions 1
II. Recommendations 7
III. Introduction 9
Purpose and Orientation 9
Methodology. ...'.. 10
Description of Limnological System . 13
IV. Water Resource Problems and Variables ...19
Water Resource Uses and Problems 19
Variables and Planning Activities 35
References 47
V. Existing Data 49
Introduction .. 49
Physical Data ...;.. 49
Chemical Data 59
Biological Data '. 83
Special Data 83
Summary 84
VI. Problem Oriented Models 87
Introduction 87
Mathematical Models. 89
Administrative Problem Definition .'. . 90
Model Development .,....... 91
Evaluation Process and Model Status 92
VII. Available Models - State Of The Art ;. . 99
Hydrological Balance Models 99
References 113
Ice and Lake Wide Temperature Models ......115
References 125
Thermal Models 127
References 134
v
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CONTENTS
VII. (continued)
Lake Circulation and Mixing Models 137
References 168
Erosion and Sediment Models. 175
References 181
Chemical Models 183
References 200
Eutrophication Models 203
References 225
Dissolved Oxygen Models 229
References 239
Pathogens and Indicator Bacteria Models 241
References 253
Fishery Models 255
References 268
Ecological and Food Chain Models 271
References 293
VIII. Model Synthesis for Planning Needs 297
Summary of Evaluation of Model Status 297
References 311
IX. Demonstration Model 3^3
Introduction 313
Model of Chloride and Total Dissolved Solids 318
Lake Erie Western Basin Chlorides and Coliform Models..327
Coliform Model Development and Verification 333
Lake Eutrophication Model . 337
Data Sources ;'. 354
The Exogeneous Variables ' 359
A Food Chain Model of Cadmiuin in Western Lake Erie 405
Summary 427
References , 429
VI
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CONTENTS
Recommended Phase II Study 433
Problems Proposed for Study in Phase II 433
Alternate Programs 438
. Recommended Phase II Study 449
yil
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FIGURES
Number ; Page
1 Methodology for Great Lakes Limnological Systems
Analysis 11
2 Great Lakes Basin Drainage Boundaries 14
3 Components of Water Resource Problem 20
4 Chloride Concentrations In Lake Michigan. . 23
5 Location of Phytoplankton Growth 25
I
6 Location of Dissolved Oxygen Problems .. 27
7 Shore Erosion and Silting .' 30
8 Location of Areas Affected By Ice Jan,s 32
9 Location of Water Level Gaging Stations « 51
10 Location of Gaged Surface Runoff Areas 55
11 Location of First and Second Order J
Meteorological Data Stations 56
12 Location of Solar Radiation and Pan
Evaporation Data Stations '.'' 57
13 Location of Upper Air/Wind Data Stations ' 58
14 Determination of Model Status 1 93
15 Role of Hydrodynamic Modeling Output. ....... 138
16 Comparison of Computed and Observed Current
Measurements 147
17 Comparision of Computed and Observed Current
Measurements 148
viii
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FIGURES ' . . .
f
Number '..-.'.' ' - . Page
18 Progress of the Thermal Bar From Winter to
Full Summer Stratification.. ......' 152
19 Observed and Computed Buffalo Minus Toledo
Set-Up . 155
20 Comparison of Observed Versus Calculated '
Solubility Products .....' 194
i
21 Phytoplankton Growth Rate Interactions...' .' ..211
22 Phytoplankton Death Rate, Zooplankton .'
Growth and Death Rates, Interactions. ...' ." 213
23 Verification of Riley's Phytoplankton and
Zooplankton Models 216
24 Vertical Distribution - Verification.....; 219
25 Antioch Verification, 1966 .: 222
26 Areas Where Problems Associated With High
Bacterial Concentrations Exist. ........' 242
27 Bacterial Densities in Lake Michigan. ,...'.' 243
28 Bacteriological Data at Big Bay Beach ' ...
Whitefish Bay, Wisconsin '.... 245
29 Coordinate System for Discharge of Bacteria
Into a Lake . 248
30 Comparison of Observed and Computed Values
for Bacteria in Lake Michigan Vicinity
Indiana Harbor . .'. 249
31 Major Sub-Systems of Fishery Modeling i
Framework 256
ix
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FIGURES
Number . . Page
32 Catch and Effort Data for Northern Green Bay....; 258
33 Simulation for Lake Trout 'of Lake Michigan...../ 261
34 Sardine Anchovy Model 265
35 A Ten Compartment Model 274
36 A Ten Compartment Model With Spatial Defintipn 275
37 A Food Chain Model . ..' 276
38 Interactions Among Six Compartments 278
39 Geometrical Presentation of Equilibrium . /
Solution and Deviations 282
40 Uncertainty in Linear and Non-Linear Models..... 288
41 Summary of Model Status ..;. 299
!
42 Steps in Model Synthesis ......' 301
43 Example of Model Synthesis ,:.' 303
44 Compartment Calculation Times ; 307
45 Time to Compute One Year Simulation '...'. 308
46 Time to Compute One Year Simulation at Five
Levels in Depth for Various Horizontal
Spacings 310
47 Demonstration Model Framework. J 314
48 Primary Input - Output Variables . '
Demonstration Model '. 315
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FIGURE
Number Page
49 Hydrological Balance 320
50 Computed Versus Observed 'Chlorides 323
51 Source Components for Lakes Erie and Ontario 324
52 Projected Total Dissolved Solids Concentrations
for Great Lakes 325
53 Projected Total Dissolved Solids Concentrations
for Lake Erie with In-Basin Control Measures 326
54 Comparison of Measured and Predicted Velocities
at Four Locations in Western Lake Erie 328
55 Vertically Integrated Net Circulation in
Western Lake Erie 329
56 Txco-Dimensional 88 Compartment Model of
Western Lake Erie 331
57 Chloride Verification Comparison of Model
Results and Observed Data 334
58 Coliform Bacteria Verification 336
59 Projected Distribution of Coliform Bacteria .
Under a Hypothetical Treatment Policy ". 338
60 Circulation Pattern in Western Lake Erie
Showing Prevailing Current Directions 343
61 Chloride Concentrations in Western Lake Erie 344
62 Steady-State Transport for Seven Compartment
Western Lake Erie Model 345
63 Kinetic Pathways of the Endogenous Variables .355
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FIGURE
Number Page
64 Water Quality Monitoring Locations in Western
Lake Erie 356
65 .Water Temperature Variables in Western Lake
Erie - April Through October, 1970 360
66 Variation of Photoperiod and Solar Radiation
for Western Lake Erie 362
67 Western Basin Secchi Disk - 1970 363
68 Variation of Extinction Coefficient in Two
Compartments of the Western Lake Erie Model 364
69 Lateral Distribution of Nutrients at the
. Mouth of the Detroit River 365
70 Chlorophyll Concentrations of Tributary Streams 366
71 Inorganic Phosphorus Concentrations of Tributary
Streams. 367
72 Organic Phosphorus Concentrations of Tributary
Streams 368
73 Organic Nitrogen Concentrations of Tributary
Streams 369
74 Ammonia Nitrogen Concentrations of Tributary
Streams 370
75 Nitrate Nitrogen Concentrations of Tributary
Streams 371
76 Relationship Between Total and Algal Cell
. Counts and Total Chlorophyll Measurements
.in Western Lake Erie 374
xii
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FIGURES -...
Number ' , Page
77 Chlorophyll Verification 378
!
78 Chlorophyll Relationships in Compartment
Number 7 379
79 The Zooplankton System Model Results 381
80 Comparison of Historical Zooplankton Counts
Observed in Western Lake Erie 382
81 Organic Nitrogen Verification 383
82 Ammonia Nitrogen Verification. 384
83 Nitrate Nitrogen Verification 385
84 Total Nitrogen and Phosphorus in Western
Lake Erie . .;. 387
85 Inorganic Phosphorus Verification 388
86 Verification of the Total Phosphorus System 389
87 Chlorophyll Hindcast to 1930 391
88 Zooplankton Hindcast to 1930. 392
89 Organic Nitrogen Hindcast to 1930. 393
90 Ammonia Nitrogen Hindcast to 1930. 394
91 Nitrate Nitrogen Hindcast to 1930. 395
92 Total Phosphorus Hindcast to 1930........ 396
93 Inorganic Phosphorus Hindcast to 1930...V. 397
94 Historical Trends in Western Basin
Eutrophication 399
xiii
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FIGURES ' .
Number .
95 Influence of Phytoplankton Growth on Lake' .
Erie Phytoplankton Concentrations 402
96 Phytoplankton Concentrations Versus. Time
for Phosphorus Removal Policies 403
97 Phytoplankton Concentrations Versus Time
for Nitrogen and Phosphorus Removal Policy 404
98 Interactions of Eutrophication and Food ;
Chain Models 1 408
99 Food Chain Model Configuration 419
100 Comparison of Food Chain Model Output with'
Some Observed Data in Western Lake Erie.. '. 422
101 Computed Cadmium Concentration Along South!
Shore of Western Lake Erie '..''. 425
\
102 Computed Cadmium Concentration Factors Along
South Shore of Western Lake Erie 426
103 Water Resource Problems and Mathematical .;
Models Included in Phase II Program '. 451
xiv
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TABLES '. " - . :
Number .: Page
1 General Great Lakes Information ........... ..... ....... 15
i
2 Water Resource Problems . . .' ..... ............... . ........ 36
3 Kindred Variable Grouping ............... . . . . . .'; ........ 40
4 Planning and Management Functions Related to
Model Input Variable Groupings ....... ....... . ........ ^5
5 Planning and Management Fundtions Related to . '
Model Output Variable Groupings ....... ..... .......... 46
6 Summary of Water Level Gaging Stations in ;
the Great Lakes Basin .................... ... ......... 50
7 Lake Circulation Data ....................... . .. ; ........ 53
8 Great Lakes Water Sampling Data Summary ........ ' ........ 60
' l
9 Summary of Published Waste Inputs to the . .
Great Lakes ........................... . ...... ! ........ 76
10 Summary of Available State and Provincial.
Waste Input Data ............... . ...... . . ..... ' ........ 77
11 Characteristics of Thermal Models.
12 Computed and Observed Periods of the First;.,.
Five Modes of Longitudinal Free Oscillations;
of Lake Michigan. ..... . ..... . . ______ ....... ..". . ........ 156
13 Summary of Some Horizontal Dispersion . ':
Coefficients in the Great Lakes ...... ........ ........
14 Mineral Dissolution. ..... ............ ... . .'.. ............ 192
15 Illustrative Reconcentration Factors ...... . ; . . ........ 285
xv
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TABLES
Number Page
16 Ranking of Modeling Frameworks 298
17 Problem Categories and Related Modeling
Frameworks 304
18 Lake Parameters 321
19 Eutrophication Sub-Model Variables 340
20 The Nitrogen System 352
21 The Phosphorus System 353
22 Data Sources 357
23 Maumee River Mass Discharges 373
24 Kinetic Parameters 376
25 Population Projections for Lake Erie Basin 400
26 Illustrative Application of the Phase I
Limnological Systems Analysis Demonstration
Model 406
27 Summary of Observed Cadmium Data for Western
Lake Erie ., 410
x
28 Assumed Average Biomass Concentrations for
Four Trophic Levels. 420
29 Percent of Mass of Cadmium by Spatial Segment
and System Level as Calculation for Food
Chain Model 424
xvi
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TABLES
Number . Page
30 Relation of Model Problems 435
31 -Summary of Funding Levels 447
* !
32 Problem Time and Space Scale for Recommended
Applications 454
33 Estimated Costs of Recommended Applications 455
xvii
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LIST OF ABBREVIATIONS AND SYMBOLS'
From Section VII '
Hydrological Balance Models . ... ;
CL
D
E
GP
HB
I
NBS
0
P
Q
R
U
AS
Ice
e
a
o
~w
Fh
= Lake Erie level at Cleveland, in feet
= artificial diversions into or out. of the lake
= evaporation from the lake surface1
= Lake St. Clair level at Cross Point Yacht Club
= Lake Michigan-Huron level at Harbor Beach
= inflow from upstream lake ' . . /
= net basin supply ' ' .
= outflow from lake through its . natural outlet
= precipitation on lake surface. .:
= flow rate :
= runoff from the lake drainage basin
= ground water contribution 1
= change in volume of water stored :in lake
and Lake Wide Temperature Models .
= partial pressure of water vapor in air
= vapor pressure at water surface '".'
= reaction force of the structure under pressure
Page
107
100
100
107
107
100
103
100
100
107
100
100
100
117
117
122
xviii
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.^
: Page
ice weight force '. 122
F = wind force on ice surface : '; 122
m . . ;
F = froude number 120
F = shore resistance force 122
o . '
F = frictional force of water on ice. 122
w ,
g = acceleration due to gravity . : 120
k, = bending coefficient . 122
k = crushing coefficient : 122
k = k, + k R /R, + k R /P, ! 122
s b sr sr D c cf D
k = shearing coefficient / '/ 122
3 r ^ ',.'
P = atmospheric pressure i 117
3. ..'''
Q = net gain or loss of heat ..: 116
Q, = effective back radiation . ' i 116
Q = heat gain by condensation , 116
O
QQ = heat loss owing to evaporation ' 116
Q, = heat conduction across interface ' 116
i 1 .
Q = reflected radiation . ' .: 116
Q = insolation heat source . 116
3 .
R = Bowen ratio 117
R, = ultimate strength of ice in bending 122
R = ultimate strength of ice in crushing 122
o
R = ultimate strength of ice in shearing 122
O X.
xix
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Page
t = thickness of the upstream edge at equilibrium 120
T = air temperature ' . ' 117
Cl ~~ - I
T = water temperature ; 117
V = velocity of upstream edge ; 120
W = wind speed 118
y = water depth in front of upstream edge 120
E, = porosity 120
p,pi = specific masses of water and solid icei 120
Thermal Models .
A(z,t)= cross sectional area .; 128
E(z,t)= vertical dispersion coefficient 128
Q(z,t)= vertical net flow rate i 128
S. = inputs of thermal energy : 128
S = outputs of thermal energy I. 128
t = time , 128
T(z,t)= water temperature . ' 128
z = depth ' . . ; 128
Lake Circulation and Mixing Models ; '
A,, = coefficient of vertical eddy viscosity 144
f = coriolis parameter ' 140
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Page
F = force in x direction 140
jV
F = force in y direction, 140
F = force in z direction . 140
2
^
g = acceleration of gravity 140
h = bottom depth . 144
H = bottom depth 145
K = x component of the heat dispersion coefficient 141
X.
K = y component of the heat dispersion coefficient 141
K = z component of the heat dispersion coefficient 141
LJ
p = pressure . 140
Qrp = net heat input 141
t = time 140
T = water temperature 141
u = x component of the velocity 140
U = depth averaged velocity in x direction 145
v = y components of the velocity 140
V = depth averaged velocity in y direction 145
w = z components of the velocity 140
x = spatial coordinate 140
y = spatial coordinate 140
z = spatial coordinate 140
xxi
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': Page
p = '.fluid density 140
n = . '.height of the free surface 144
T = :. x; component of the wind stress 144
X ,
T = y component of the wind stress 144
T, =. x'comDonent of bottom frictional stress 145
bx . . .
T, = y,component of bottom frictional stress 145
by : c
T = . x component of surface wind stress 145
sx
T = y component of surface wind stress 145
Erosion and Sediment Models
H = peak to valley wave height 176
M = 'beach slope . . 178
R =. maximum wave run-up 176
T = . ''wave period 176
a = .- beach slope 176
Chemical Models
t ~'
a. = number of models of element e contained in 185
' component i
A. = molecular formula of i1"' chemical component 186
b = total mole fraction concentration of element e 185
e
E = number of elements 185
XXll
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Page
G = Gibbs free energy , 185
[H] = molar concentrations of H ; .. 186
[HC03]= molar concentrations of HCOa" 186
[H2COa]= molar concentrations of H2COs 186
[i] = activity of component i . 185
K = solubility product for condensed -species 187
C ; '
K. = equilibrium coefficient . : 188
In = natural logarithm . 185
n. = mole fraction concentration of. component i 185
N = number of components ' .. 185
R = universal gas constant ;' 185
T = temperature in °K 185
v. = stoichiometric coefficient , 186
y. = chemical potential | 185
.'
y.° = standard free energy ; ' 186
i
Eutrophication Models ;
A = zooplankton grov;th rate , 215
C = carnivore predation rate 215
D = natural death rate . . 215
g = predation rate/unit zooplankton concentration 218
xxiii
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G
H
Ki
K2
Ks
K6
M
N
NB' =
P
Ph =
R
R
P
V
z =
* Dissolved
B
c =
Co =
cs =
zooplankton grazing rate ...
zooplankton biomass ..'
growth rate/unit nutrient concentration
respiration rate ','..-.
phytoplankton uptake rate . :
regeneration rate ' :
exchange rate
nutrient concentration
nutrient concentration in hypolimnion
phytoplankton bioinass . . ;'
phytosynthesis rate
respiration rate ' :
respiration rate -; i
L. _ - . .
sinking velocity . ' . '
vertical spatial coordinate ';' -'
Oxygen Models
benthic uptake rate
concentration of dissolved oxygen
dissolved oxygen concentration at z = o
saturation concentration of dissolved oxygen
Page
214
215
218
218
218
218
218
218
218
214
214
214
217
217
217
234
232
234
234
XXIV
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Page
E = diagonal matrix of dispersion coefficients 232
E. = dispersion coefficient at z = h : 234
E = dispersion coefficient at z = o 234
E = dispersion coefficient in z direction 233
Z ,
K = temperature dependent reaction rate ' 233
KT = surface transfer rate ' . ' 234
-Li " ' .. - .
L(z,t)= concentration of dissolved organic matter 233
P(z,t)= rate of photosynthetic contribution of dissolved 233
oxygen .
R(z,t)= rate of respiratory sink of dissolved oxygen 233
+ = velocity vector - i 232
£.S. = sum of all sources and sinks of dissolved oxygen 232
. . I 232
''
Pathogens and Indicator Bacteria Models . : .
/ >.
c, = ' concentration of bacteria ' 246
b .-..'.
. K, = rate of die-off of the bacteria 246
W, = direct discharge of bacteria , 246
Fishery Models
a. . = interaction constant between i and j fish 262
species
XXV
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b. = growth constant for i fish species 262
c = ratio of F to x 259
th
c. = fishing intensity for the i i fish species 262
F = fishing mortality rate 259
g = growth rate 260
k = logistic model constant 259
K = empirical coefficient 260
L = asymptotic length of fish 260
M = rate of natural mortality 259
n = effect of external environment 259
N = fish numbers 260
(N) = vector of numbers of fish in the year classes 264
p = fish biomass 259
p. = population of the i fish species 262
P = asympotic equilibrium fish population 259
P. = fraction of year class i that survives from 264
1 t to t + 1
r = rate of recruitment 259
R = number of recruits 260
R. = fraction of year class i that is newborn at 264
1 t + 1
XXVI
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Page
t = age of fish retained by fishing gear 260
t = : time zero 260
t = ';' age of fish entering exploitation area 260
W ' = . fish weight 260
x = . fishing'effort 259
x. = ..fishing intensity of the i . species 262
y = .yield 259
5 '= empirical coefficient 260
Ecological .and Food Chain Models
A = matrix of competition coefficients a.. 290
B. . =. ..niche breath of specie i 289
c = .concentration of tracer in the organism 283
c1 = .. concentration of tracer in the water 283
C =. mn x 1 vector of concentrations ^, 281
C. .= '- . concentration of variable i at location r 277
D, ... = niche diversity of environment h 289
f., = proportion of individuals of species i in 289
1 environment h
F. = 'bulk transport of variable i from location r to 277
'. location s
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Page
g = vector of sources ' 281
g. = source of variable i at location r 277
[K] = ran x mn matrix of interaction coefficients 281
K = column vectors of carrying capacities K. 290
K. = equilibrium population of specie .i 289
K.. = causal transformation of variable;i to variable 277
^ ' j at location r
P.., = proportion of specie i in environment h 289
Q = flow rate ! 284
r = growth rate of specie i . ' 289
V = single homogeneous volume j ' 284
W = mass input rate ;, 284
X = column vectors of species X. 290
X. = i specie concentration : 289
a.. = competition coefficient between species i and j 290
-J s'
X = half-life (base e) \ 284
From Section IX i
Introduction
C = concentration 318
Q = parameters 319
t = detention time 318
xxviii
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V
V
n
W
W
n
Lake
c .
Ev
Qkj
W.
°kj
8kj
Lake
ai
azp
c
P
Cg(T)
= lake volume
= volume of n lake ..
= wastewater input
= n wastewater input
Erie Western Basin Chlorides and Cbliform Models
= concentration of the water1 quality variable in
segment j
= bulk dispersion coefficient between segments k
and j . ;
= net advective flow from segment "k to segment j
= mass input rate to segment j . ''',
- weighting factor for the finite- difference
approximation used
1 - a, . ''.:
Kj
Eutronhication Model
= conversion efficiency of zooplanktdn
= carbon/chlorophyll ratio - . zooplankton
= inorganic phosphorus
= temperature dependent grazing rate of the
Page
318
318
318
319
332
332
332
332
332
332
349
349
348
341
total inorganic nitrogen . 348
XXIX
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Page
D . = death rate - zooplankton 349
Z]
D = phytoplankton death rate 346
D_ = zooplankton death rate 346
Lt
e = 2.718 347
f = photoperiod 347
G = phytoplankton growth.rate 346
G^ = zooplankton growth rate 349
u "
H = depth of segment 347
I = light intensity 346
I_ = mean daily light intensity . . 347
ct
I = optimal light intensity : ; 346
h3 ' ,' .
I = surface light intensity 346
K = extinction coefficient ' 346
e '.
K ... = half-saturation constant - total inorganic 348
mN . , . 3
nitrogen ...'
s
/
K = half-saturation constant - total inorganic 348
phosphorus
Ki» = empirical mortality constant 350
K2(T)= temperature dependent grazing rate of the zoo- 341
plankton biomass
Ks(T)= temperature dependent endogenous respiration 350
rate .
P = phytoplankton chlorophyll - 346
^ . a
XXX
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Page
r = time averaged growth rate reduction factor . 347
S., . = the k source or sink of substance i in 341
"-' segment j
V. = segment volume 341
z = depth 346
Z = zooplankton biomass concentration 349
A Food Chain Model of Cadmium in Western Lake Erie
[A(d/dt)]. = n x n matrix 413
C = concentration of toxicant in the phyto- 415
p plankton
C = concentration of toxicant in the water 414
column
C7 = concentration of toxicant in the zoo- 415
plankton
K... . . = toxicant production from i - 1 to i 412
x 'x'3 trophic level at location j
[K. .. .V] = n x n diagonal matrix "' 413
il, i
tM = mass trophic level/volume water 411
N = mass toxicant/mass trophic level 411
(N.M.) = n x 1 vector of the tracer material 413
T. = i trophic level mass 413
xxxi
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ACKNOWLEDGEMENTS
The information and results presented in this report are an
outgrowth of contributions by numerous individuals interested
in the Great Lakes water resource problems and management.
Foremost among those who contributed to this project are Mr.
Frederick 0. Rouse, Chairman of the Great Lakes Basin
Commission; Mr. Leonard T. Crook and Mr. David C.N. Robb,
staff members of the Commission.
In addition, significant inputs to the study were provided by
the Board, of Technical Advisors convened by the Great Lakes
Basin Commission. This board provided technical input and
project'review periodically during the study. The members
of the board, Dr. John M. Armstrong, Dr. Alfred M. Beeton,
Dr. G.E. Birchfield, Dr. Carl W. Chen, Dr. Leo J. Hetling,
Dr. Norbert Jaworski, Mr. Edwin L. Johnson, Dr. Ronald T.
McLaughlin, . Dr. Arthur P. Pinsak, Mr. Howard L. Potter, and
Dr. Sam. B. ' Upchurch contributed in their areas of technical
speciality with a candor and generosity that is greatly
appreciated.
The Plan and Program Formulation Committee composed of
staff members from the various federal agencies and states
represented-, on the Commission furnished valuable input
and review,,particularly with respect to definition of
administrative and planning problems in the Great Lakes
Basin. The encouragement of this group assisted in insuring
that the study results were directed towards^solution of
planning problems on the Great Lakes.
.,. Battelle Northwest performed subcontracting services within
the project; for problem definition and state of the art
technical evaluation and analysis in the areas of hydrological
balance, ice and lake-wide temperature, and erosion-sediment.
Hydroscience's Board of Technical Consultants consisting of
Dr. Donald R.F. Harleman, Dr. James R. Kramer, Dr. Clifford
H. Mortimer:, Dr. Gerald A. Rohlich, and Dr. George W. Saunders
provided guidance and initial input to the study. Their
contribution is both appreciated and acknowledged.
xxxn
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Several individual consultants gave assistance in specialized
technological areas. In particular,' Drs. Bernard C. Patten,
Gerald J. Paulik, and G.T. Csanady provided valuable
contributions in the areas of ecological, fisheries, and
hydrodynamic modeling. Dr. Raymond Canale;joined our staff
on a temporary basis and provided significant assistance in
development and application of demonstration models. Dr.
R.T. Gedney kindly supplied us with detailed hydrodynamic
calculations for the demonstration model.
Members of the Canada Centre for Inland Waters, in particular,
Dr. James P. Bruce, were most helpful, in making Western Lake
Erie water quality data available for use in the Demonstration
Model effort. Their assistance is sincerely appreciated.
Members of the Hydroscience staff who participated in this
study are: Dr. Robert V. Thomann, Dr. Dominic M. Di Toro,
Dr. John A. Mueller, Mr. Daniel S. Szumski, Mr. Henry J.
Salas, Mr. Joseph A. Nusser, Mr. James J. Fitzpatrick, Mr.
William F. Lederle, Miss Viola J. Whartsnby, and Mrs. Leslie
A. Fitzpatrick. Their contributions.to the project were
enormous and are sincerely appreciated. .Special acknowledgement
is expressed to Mrs. Anne Detroyer-for her patient and
considerate efforts in synthesizing and .editing the final
project report. . '. :
The cooperation and input of all the .above individuals and
the assistance and cooperation of innumerable federal, state,
and university personnel involved in Great Lakes Water
Management is acknowledged with sincere thanks.
XXXlll
-------
SECTION I
SUMMARY AND CONCLUSIONS
The purpose of this report is to present an: assessment of the
feasibility of applying a Liranological Systems Analysis (LSA)
to the water resource problems of the Great Lakes. A
methodology that proceeds along two parallel lines in order
to evaluate the feasibility of the LimnologdLcal Systems
Analysis is established. The first line of; analysis
evaluates the present and future water resource problems and
water use interferences with their associated water resource
variables. The second line of analysis evaluates presently
available data, problem oriented mathematical models, and
present state of the art of models and model building which
are required for a Liranological Systems Analysis. The two
lines of analysis are synthesized into a problem and model
ranking of priority from which feasibility^recommendations
are drawn. In order to illustrate the Limnological Systems
Analysis in several problem contexts, a demonstration modeling
framework was constructed. ;
Water resource problems in the Great Lakes-were identified
and grouped into seven problem categories as follows:
1. Monthly Lake Water Levels arid Flows
2. Erosion, Sediment
3. Ice :
4. Toxic and Harmful Substances
5. Water Quality ' ' /'
6. Eutrophication, Fishery '
7. Public Health
For each problem category a detailed review was made of
associated water uses and water variables, to provide the link
to the available models. In order to address these problems
a number of disciplines and specialties are required and are
brought together in a systems context in the modeling
framework. A central requirement for framework modeling is
the data available for its development and use.
-------
The review of water resource data in the Great Lakes region
followed five broad classifications: physical,; chemical,
biological, and specialized data types. Contact was made
with all of the major data storage and retrieval centers in
the Great Lakes area and the data were then generally
reviexved for geographical and' variable coverage- incorporating
in the review the data needs of the available models. From
the large amount of information uncovered during the study,
it is concluded that sufficient data presently exists for
preliminary model development for many of the water resource
problems of the Great Lakes.
A review was also made of the available models that may be
useful for a Limnological Systems Analysis.and a convenient
grouping of eleven modeling frameworks was obtained. The
frameworks are:
1. Kydrological balance
2. Ice and lake wide temperature
3. Thermal - ' . . ;
4. Lake circulation and mixing '
5. Erosion and sediment ' , .
6. Chemical .'.' :
7. Eutrophication . '. -\
8. Dissolved oxygen . '
9. Pathogens and Indicator bacteria
10. Fishery .' '. -', ,
11. Ecological and food chain ;
Each of the modeling frameworks was reviewed and analyzed in
depth following an evaluation process to determine the
present status of the framework as applied to water resource
problems. The major considerations in determining model
status are: 1) basic understanding and knowledge, 2) data
availability, 3) degree of model verification, and 4) degree
of model application. Numerical weights were assigned to
each of several steps in the evaluation process.
As a result of this review it is concluded that the
hydrological balance and lake circulation and mixing
modeling frameworks are sufficiently developed to address
-------
certain water resource planning problems of the Great Lakes.
The status of two other modeling frameworks, a) ice and
temperature and b) ecological models is poor; and
considerable expenditure and research effort are required
to bring these models to the point of useful application in
water resource planning. The remaining seven modeling
frameworks fall in a marginal" status where some key variables
or phenomena may be lacking but a sufficient base has been
laid for some preliminary applications of the models to
planning questions. It is also concluded from the analysis
that there is a pressing need for model synthesis, because
many efforts in the past have been fragmented and directed
to rather narrowly conceived aspects of planning problems.
A demonstration modeling framework was constructed to
illustrate this process of synthesis and to demonstrate
the feasibility of the application of existing modeling
technology to real planning problems in the Great Lakes.
The demonstration model framework includes models of:
1. Long term trends on the Great Lakes
scale of conservative water quality
variables such as total dissolved
solids and chlorides.
2. Regional models of Western Lake Erie
for chlorides and bacteria.
3. Eutrophication model of Western Lake
Erie.
s
4. Food chain model of Western Lake Erie.
The primary emphasis in the demonstration model effort is
placed on the eutrophication model. This model is structured
so as to maximize its ability to respond to several planning
alternatives. The model includes effects of both biological
and chemical reactions with the primary variable being
phytoplankton biomass. Forty-nine simultaneous nonlinear
time dependent equations are solved numerically in order to
compute the phytoplankton, zooplankton, and nutrient
distributions to be expected from various planning alternatives
-------
Model verification using data from cruises in 1967-1970 and
some earlier data is considered satisfactory for evaluating
effects of: planning activities.
A variety of applications of the demonstration model
framework to Type II planning questions were carried out.
It is concluded on the basis 'of the results of these
applications that the models provide new and important
insights into the consequences of proposed control actions,
insights, that would ordinarily not be obvious without the
application of quantitative modeling and system analysis
techniques.
In evaluating and ranking the problem categories to provide
a basis for recommendations in any further Phase II study,
four criteria were used: 1) existing modeling efforts, 2)
ranking of the modeling framework, 3) data availability, and
4) the degree to which the problem can be considered a Type
II planning problem.
Of the seven problem areas, it is concluded that the ice
category and a portion of the public health category (near
shore pathogen problems) are generally not Type II planning
problems. ' It is also concluded that Great Lakes problems
associated with a) lake levels and b) erosion and sediment
are being analyzed and are adequately modeled in various
ways for present needs. The ranking of the four remaining
Type II planning problems which was subjectively established
in lieu of being objectively determined is:
'1. Eutrophication
:2. Water Quality
3. Public Health (regional and lake wide
. : scale)
;4. Concentrations of toxic or harmful
' ' substances
-------
It is concluded that it is feasible to construct a Limnological
Systems Analysis for these categories using the existing
available data, although the degree of detail and specificity
of the Limnological Systems Analysis would vary with the
problem category.
A range of alternate Limnological Systems Analysis programs
were evaluated in order to explore varying levels of effort
and cost for a Phase II study. ;
1. Level 1: This alternate is estimated
to cost $0.7 million with a two year
completion time and represents the
lowest level at which a meaningful
Limnological Systems Analysis can be
carried out.
2. Level 2: This level is estimated at a
$2 million cost with a three year
completion time and represents a
favorable balance between problem
contexts that can be approached rapidly,
given the present modeling ..status, and
those problem categories which have
high priority but for which.-modeling
frameworks must be significantly advanced.
3. Level 3: The cost of this level is
estimated at $3.9 million.with a three
year completion time .and represents a
more intensive effort than Level 2.
Level 3 funding is felt to be the
maximum amount that can be prudently
spent for a Phase II study of the use
of a Limnological Systems Analysis
for the Great Lakes. ;
The overall conclusions of this Phase I study can be summarized
as follows:
-------
1. It is feasible to .construct.a Limnological
System Analysis for certain Type II water
resource problems in the Great Lakes.
2. Mathematical modeling and system analysis
techniques can provide important preliminary
quantitative estimates of the effects of
certain proposed water resource control
actions. .
3. Sufficient data presently exist for the
immediate implementation of :a Limnological
Systems Analysis although this does not
preclude the need for further extensive
field efforts on the Lakes.
4. Feasible funding ranges for a Phase II
Limnological Systems.Analysis are from
SO.7 million to $3.9 million.
-------
SECTION II
RECOMMENDATIONS
It is recommended that a Phase II Liranological Systems Analysis
study be funded at the $2.0 million level with a three-year
completion time.
Within this level, it is recommended that:
1. Existing subsystem models, parameter
values, and inputs be gathered into
interactive modeling frameworks..;
2. Generalized computer programs be
developed and modifications be .made
to existing models to accomodatei-
recently evolved numerical and j
software techniques.
3. Applications be made of existing;
systems technology to those problem
categories for which a reasonable
degree of.success for the application
is assured. !
The following specific problem contexts are recommended for
inclusion in the Phase II study: . s '
1. Water Quality Problems .' >
a) Dissolved oxygen j
b) Chemical interactions . .'
2. Public health ' '
3. Eutrophication - biomass problems
4. Food chain toxicant problems :
-------
It is recommended that the Phase II study be directed toward
three spatial scales:
1. Comprehensive Great Lakes
scale
2. Lake wide scale
3. Regional scale
- All lakes interconnected
- Lakes Erie and Ontario
- Duluth, Minnesota area,
Southern Lake Michigan,
Green Bay,
Saginaw Bay,
Lake St. Clair.
-------
SECTION III
INTRODUCTION
' Purpose and-Orientation
The purpose of this report is to present an assessment of the
technical feasibility and the economic practicality of applying
a Limnological Systems Analysis (LSA) to water resource problems
of the Great Lakes. Specific attention is directed to an
evaluation.of the state of the art of modeling as it applies
to these interrelated problems. The overall purpose.of the
study is to indicate the degree of understanding of limnological
phenomena as affected by both nature and man's activities.
Equally important, if not more so, its purpose is to evaluate
the degree to which these processes can be expressed in a valid
mathematical form within a system analysis framework. Such a
framework comprises two essential elements the mathematical
forms or models and the predictive techniques.
The greater our ability to express these processes in a
mathematical form within a system analysis framework, the
better the .basis for selection among the alternate plans
control and management of the system. Systems analysis is
thus one important tool available to the administrator in his
decision making role as environmental planner and manager.
Systems analysis.has been applied in various ways to both
natural and technological systems. Natural systems comprise
those phenomena whose structures have been determined without
man's influence whereas technological systems have been
"directly designed by man to meet various objectives. Although
our fundamental knowledge of both systems is approximately of
the same order, the application of modeling to technological
systems, such as communications, transportation, energy, and
industrial production has progressed to a further degree than
has the application to natural systems, such as biological
and chemical cycles in natural waters and hydrological and
meteorological phenomena. The reason lies in the fact that
many systems in the former category were understood and, in
some cases, were created in terms of mathematical models
which preceded their development. The second component of
-------
systems analysis the predictive methodologies incorporated
in the general field of operations research - has been applied
to technological systernsv to a greater extent. The majority
of these techniques which are presently available have been
developed within the framework of technological rather than
natural systems, many of which originated, or at least
significantly advanced, during and since the second World
War. One of the general directions to be taken in the future
is the transformation and application of these techniques to
natural systems. i
This report, which is primarily concerned.with the modeling
element, summarizes the models which describe natural
limnological systems, both those significantly modified
by man and those substantially unaffected by man, and
indicates the utility of models in seeking and assessing
alternate solutions to the problems arising.from multiple uses
of the water resource. In the case of the Great Lakes, as
in many other natural, settings, each use. with its associated
effects potentially or actually influences another use. It
is one of the purposes of this report to demonstrate the
application of modeling and to delineate and. evaluate these
interactive effects.
Although emphasis in this report is placed on the state of
mathematical modeling, its predictive capability is not
overlooked. Without the former, the latter is impossible,
and without the latter, the former is useless within the
context of this project. The models reviewed are those which
have been specifically applied to Great Lakes problems, those
which have been developed for other areas but,-do not have
application in the region, and lastly, those'which can be
constructed within the time frame of the planning activity.
These models are to be evaluated not only from the viewpoint
of their internal validity, but also from their utility in
planning and predicting.
Methodology
Figure 1 presents the overall methodology followed in the
Limnological Systems Analysis of the. Great Lakes. Two
10
-------
PLAINING a
ADMINISTRATIVE
ANALYSIS
SCIENTIFIC 3
ENGINEERING
AM ALT'SIS.
IDENTIFICATION OF
//ATER HESOJRCE
USES 3 PROBLEMS
(SECTION., H)
1
1
1
1
1
1
|
1
|
1
1
1
DEPICTION
OF
M n n F i
BY "PROBLEMS'-
(SECTION ET) '.
1 .
1 '"
r *
OEFINITION OF
V/.hlABLF.S
1 i-.OF.LEI.1."
(SECTION ]:!
1 "
1
i
AVAILABLE
MODELS
STATE OF AM"
REVIEW
(SECTION T) . - :
1
.- - ,
--
»
r'*
-
'
DETERMINATIOfJ OF
PROBLEM
PRIORITY
(SECTION VHI)
EXTENT AND
AVAILABILITY OF
(SECTION m)
1
1
i
- |
1
*
MODEL
EVALUATION
SYNTHESIS
(SECTION VT
' 1
"1 '
*
1
DELI ME A
PROE
CATEGC
FC
PH-AS
(SEC1IO
\ i
DESCfi
0
ALTEF
PROG
(SECTIO
RECOMK
PHAS
DEI/I Of! ST RAT 10 N
(SECTION SOT- .".HPEfl
I.10DKL
vrai
PhOGRAM
MO DELS
' APPLICATIONS
FUNDING
TIMING
(SECTION vmi
FIGURE I
METHODOLOGY FOR GREAT LAKES LIMNOLOGICAL SYSTEMS ANALYSIS
-------
parallel paths are followed. One path analyzes aspects of
the Limnological Systems Analysis concerned with planning
and administrative functions simultaneously..The second
path explores the scientific and engineering features of the
Limnological Systems Analysis.
The first step in the planning and administrative analysis
is the identification of Great Lakes water resource uses and
associated problems, both present and anticipated. This
identification is followed by a definition and grouping of
water resource variables identified with the resource
problems. These two steps are discussed in Section IV.
The extent and availability of data is an important evaluation
that provides input information for several steps in the
methodological framework. This step in presented in Section V.
The scientific and engineering analysis.begins in Section VI
with a description of the basic principles of modeling and a
methodology for evaluating model status. The array of models
is scanned and a grouping of the models using problem categories
is prepared as part of this step. Eleven modeling frameworks
result from the analysis. . . .'';'
Section VII reviews the state of the art of the eleven
modeling frameworks. The problem context, theory, extent
of verification, and application are explored in detail.
The first indication of the degree of feasibility of an
Limnological Systems Analysis are given in this step.
The evaluation and synthesis of the eleven, modeling frameworks
are given in Section VIII. An analysis is also provided of
the computational feasibility of interactive synthesized
modeling structures.
The demonstration model which is used as .an illustration of
many of the steps in the overall methodology is presented in
Section IX. The demonstration modeling framework consisting
of several integrated submodels also provides, input to the
question of feasibility of an Limnological Systems Analysis.
Section X begins with an analysis of the problem categories
examining each of the categories in the light of several
12
-------
priority criteria. The interaction of a subjective assessment
of problem priority, available data, and modeling status, in
essence, sets a level of possibility. The problem categories
for Phase II are then discussed and a series of four alternative
programs with funding is presented. Section X closes with a
recommended Phase II program chosen and shaped from the
alternative programs.
Before beginning the detailed review of each of these steps,
it is well to provide a brief description of the Great Lakes
System so that the report is placed in its proper geographical
and limnological setting.
Description of Limnological System
Extending from the heartland of North America, the Great Lakes
St. Lawrence River system constitutes one of the continent's
most magnificient natural resources. Great population centers
have developed on these shores and an economically diverse
society has evolved through the effective management of the
raw materials that the basin provides. The water system
represented by the lakes provides the people of the United
States and Canada with economic recreation and aesthetic water
uses of unmeasurable value.
In geological terms the lakes are young. Their present forms
were created during the Pleistocene era by glaciers that moved
across the North American continent. Glacial advances and
retreats over millions of years caused numerous morphological
changes which about 2,500 years ago resulted in the Great
Lakes system that we know today.
The Great Lakes system is composed of five major drainage
basins covering an area of 295,800 square miles; 173,470
square miles of the region is in the United States with the
remaining 122,330 square miles being located within the
Province of Ontario, Canada. Figure 2 shows the location
of the basins, and pertinent characteristics are given in
Table 1. Nearly one-third of the basin constituting 94,680
square miles is lake surface. The system forms a natural
waterway 2,300 miles long extending from the head waters of
13
-------
..
-,. .- ' \
LEGE_ND.
- Greal Lakes Basin Drainage Boundaries
- Subbosms
FIGURE 2
GREAT LAKES BASIN DRAINAGE BOUNDARIES
-------
Description
Low Water Datum (LWD) Elevation
in feet IGLD (1955)
Dimensions in miles:
Length
Breadth
Shoreline including islands .
Areas in square miles:'
Drainage basin in U.S.
Drainage basin in Canada
Total drainage basin (land &
water
Water Surface in U.S.
Water Surface in Canada
Total Water Surface
Volume of water in cubic miles:1
Depths of water in feet: l
Average over lake
Maximum observed
Outlet river or channel St
Length in miles
Average flow in cfs (1860-1969)
TABLE 1
GENERAL GREAT LAKES INFORMATION
Lake Lake Lake Lake
Superior Michigan Huron St. Clair
600.0
350
2
37
43
81
20
11
31
2
\
1
160
,980
,500
,500
,000
,600
',100
,700
,935
489
,333
. Mary ' s
74
70
,500 .
576.8
307
1
67
67
22
22
1
118
,660
,900
0
,900
, 300
0
, 300
,180
279
923
Mackinac
52
-
,000
576.8
206
3
25
49
74
9
13
23
183
,180
,300
,500
,800
,100
,900
,000
849
195
750
St. Clair
187
27
,000
571.7
26
24
169
2, 370
4,150
6,520
162
268
430
1
10
212
Detroit
32
130,000
Lake
Erie
568.6
241
57
856
\
23,600
9,880
33,500
4,980
4,930
9,910
116
62
210
Niagara
37
202,000
Lake
Ontario
Total
242.8
193
16,
15,
32,
3,
3,
7,
53
726
800
300 .
100
460
880
340
393
283
802
9,571
173,470
122,330
295,800
60,602
34,078
94,680
5,474
St. Lawrence
. 239,
502
000.
'Lake level at Low Water Datum Elevation.
2Maximum natural depth.
LWD is a reference elevation for nautical charts and projects.
-------
TABLE 1
(continued)
GENERAL GREAT LAKES
Description
Monthly Elevations " in feet5
Average (1860-1969)
Maximum
Minimum
Average-winter low to summer high
Maximum-winter low to summer high
Minimum-winter low to summer high
tj Annual precipitation in inches
(1900-1969)
Average on basin (land & water)
Average on lake surface
Runoff (cfs/miles squared)
Detention time (years)
Lake
Superior
600-. 38
602.06
598.23
1.1
1.9
0.4
29.4
30
1.00
191
Lake
Michigan
578. 683
581.94
575.35
1.1
2.2
0.1
31.2
30
0.86
99.1
INFORMATION
Lake
Huron
578. 683
581.94
575.35
1.1
2.2
0.1
31.2
31
1.05
22.6
Lake
St. Clair
573.01"
575.70
569.86
1.6
3.3
0.9
-
-
-
~
Lake
Erie
570.37
572.76
567.49
1.5
2.7
0.5
\
34.0
33
0.79
2.6
Lake
Ontario Total
244.77
248.06
241.45
1.8
3.5
0.7
24.3
33
1.30
7.9
3The Straits of Mackinac between Lakes Michigan and Huron is so wide and deep that the difference in
monthly mean levels of the lakes is not measurable.
''Lake St. Clair elevations are available only for the period 1898 to date.
5Lake elevations are as recorded at Marquette (L. Superior) _,_ Harbor Beach (L. Michigan-Huron, Grosse
Pointe Shores (L. St. Clair), Cleveland (L. Erie) and Oswego (L. Ontario). Recorded elevations are
affected by man-made changes such as regulation of outflows from Lake Superior (1-921) and Lake Ontario
(1960); diversions of water from Hudson Bay basin into Lake Superior (1939) and from Lake Michigan basin
into Mississippi basin at Chicago (before 1860); and regimen changes in the natural outlet channels
from the lakes throughout the period of record.
.NOTE; Area data shown above were prepared by the Coordinating Committee on Great Lakes Basin Hydraulic
and Hydrologic Data. Total basin areas do not necessarily equal the sum of their component parts
because of rounding.
-------
Lakes Superior and Michigan through Lakes Huron, St. Glair,
Erie, and Ontario into the St. Lawrence River and finally
into the Atlantic Ocean. The economic value of this waterway.
has been enhanced by the construction of deep-water navigation
channels and canal systems between the lakes.
Lake Superior is the largest 'and deepest of the lakes having
a surface area of 31,700 square miles and a maximum depth of
1,333 feet. Because of its size and relatively small inflow,
it also has the largest displacement time of 191 years. By
contrast Lake Erie, which is the shallowest of the lakes, has'
the smallest volume and an associated displacement time of
2.6 years. Lake Ontario has the smallest surface area of the
major lakes. ''';.
The tributary streams of the Great Lakes basin are generally
short with relatively small drainage basins. They range in
size from drainage areas of a few square miles to the size of
the Maumee River and Grand River basins which are 6,600 and
5,600 square miles, respectively. The Great Lakes basin is
also characterized by thousands of small upland lakes.
On the basis of data taken at land based stations, the average
annual precipitation over the basins is estimated to be about.
31.5 inches, while the average annual runoff of the rivers
within the region varies from 9 to 38 inches.
In 1960 there were "31,780,000 people living in the Great Lakes :
region. Over 80 percent of this population was living in the ;
United States. Economic development in the basin has proceeded
from the highly agricultural economy of the late 19th Century to'
the present degree of development characterised by a high degree;
of urbanization and industrialization. In 1963, manufacturing .
exceeded 40 billion dollars, almost one-fourth of the nation's
total. Annual investments in industries which are dependent
on the Great Lakes water resource are in excess of 1.6 billion
dollars. Present United States commercial shipping on the
lakes is in excess of 200 million net tons annually.
The Great Lakes constitute a major source of municipal,
industrial, and agricultural water supply for the basin's ;
population. The 18 million people who rely on water supplied
by the lakes utilize 4 billion gallons per day while present
industrial supply is double that figure.
17
-------
Forests and woodlands concentrated primarily in northern
Minnesota, Michigan, Wisconsin, and New York constitute
48 percent of the land in the region; and 39 percent of the
remaining land is covered by cropland and pastures located
primarily in Wisconsin, southern Michigan, northern Indiana,
and Ohio. The remaining 13 percent of the land area is
non-agricultural and includes the urban centers, commercial,
transportation, and industrial developments as well as
farmsteads, idle land, and park and recreation areas.
18
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SECTION IV
WATER RESOURCE PROBLEMS AND VARIABLES
Water Resource Uses and Problems
Public policy objectives and their associated standards are
fundamental to the definition of water resource problems.
Actual or potential failure to meet a standard or objective
identifies a water resource problem. Water resource problems
therefore are generally associated with a comparison of the
level or magnitude of a variable in the water environment
and the desirable or required level, as specified by a
standard or public policy objective. In addition, standard
and policy objectives can be identified on the basis of
interference with a desirable water use or environmental
status. Therefore, as shown in Figure 3, water resource
problem definitions contain two major parts: the first deals
with variables in the water body and implies a comparison
with a standard or norm; the second identifies water use or
environmental status. This latter component of problem
definition generally indicates the time and space scale in
which the problem must be viewed. In addition to the time
and space iscale, the significance of the problem or the
problem priority is also important.
In the first interim report of this Study [1], a variety of
Great Lakes water resource uses and problems are identified
and referenced in detail. Specific localities experiencing
various water resource problems are listed in Reference 1,
Appendix A. A brief description of the major water uses
and problems is given here.
Water Supply
This water use encompasses water supplies for domestic,
municipal, industrial, and agricultural purposes. The
population of the Great Lakes basin is expected to grow to
60 million over the next fifty years from a present level
of over 30 million.
19
-------
WATER
RESOURCE
VARIABLE
WATER
RESOURCE
PROBLEM
PRIORITY
FIGURE 3
COMPONENTS OF WATER RESOURCE PROBLEM
-------
The entire population is not served by water supply drawn
from the lakes; but most of the large population centers do
use the lake as a water supply source. The total United
States and Canadian withdrawals from Lakes Erie and Ontario
are estimated at 685 MGD (United States) and 419 MGD (United
States), respectively [2],
The major consideration associated with water supply in the
Great Lakes is the quality of raw water obtained from the
lake. Public health considerations, such as contamination
of raw water by bacteria, virus, and toxic or harmful
substances are of primary concern. The majority of water
intakes within the Great Lakes are presently located to yield
relatively high quality waters. As population and economic
growth continue around the Great Lakes Basin, it will be
necessary to insure that the influence of wastewaters
discharged from treatment plants or urban and other runoff .
do not contaminate water intakes with increased bacterial
and viral concentrations. There have been no reported
outbreaks of viral disease related to water obtained from
well-operated water treatment plants in the Great Lakes Basin.
Thus it may be inferred that water borne viruses have been
controlled in public water supplies. There is, however,
little or no direct evidence or data on viral concentrations
within the Great Lakes or on the number of viruses present
in water supplies after treatment.
A second broad area of concern in the water supply is the
quality of finished water and the cost of water treatment
plant operation. Specific problems have been experienced
with Great Lakes water supplies in terms of taste, odor, and
color problems and with clogging of intake screens, reduced
filter runs and increased chemical costs [3,4]. Municipal
.supplies in Milwaukee, Chicago, Cleveland, and Toledo have
also been affected. These problems have been associated
with cladophora growths and phytoplankton blooms, and
periodically have been ascribed to the residual effects of
chemicals discharged in industrial and municipal wastes.
These water supply problems can result in increased water .
treatment and supply costs together with reductions in
finished water quality. The available supply of treated
water may be temporarily reduced if water treatment plant
capacity is significantly curtailed and adequate additional
21
-------
facilities are not available. Many of the taste, odor, color,
and clogging problems are encountered in the summer period
when water supply demands approach a maximum.. Thus the
maximum demand periods occur when problems tend to increase
operating costs and reduce the effectiveness of installed
treatment plant capacities.
A potential long range water supply problem is associated
with a possible buildup of total dissolved solids (TDS),
chlorides, hardness, and other dissolved chemicals in the
lakes. These water supply problems are not significant at
the present time, but future population and economic growth
could accelerate the buildup of these materials. Beeton
[5,6] and O'Connor and Mueller [7] have explored some of
these problems in detail. Figure 4 shows the chloride
concentrations in Lake Michigan and the components that
contribute to the total concentration as estimated by Mueller
and O'Connor. Present TDS in Lakes Erie and Ontario are in
the order of 180-200 mg/1 which presently meets water quality
criteria. Increased population and industrial growth will
result in increased mass discharges of TDS to the system.
These increases coupled with increased water consumption may
result in future levels of TDS which will violate acceptable
criteria. This problem is explored in the Demonstration
Model discussed in Section IX of this reoort.
Recreation and the Aquatic Ecosvstem
This category of water usage is considered in both an active
and passive sense. Active recreational water use includes
water contact sports such as swimming, boating, scuba diving,
and water skiing as well as recreational boating and fishing.
It is estimated that there are nearly one million recreational
boats registered in the United States region of the Great Lakes
basin with some 65 more boats moored in the Great Lakes proper.
Included also is the broad area of aesthetic appeal of the
water for picnicking, comtemplative relaxation, and scenic
beauty. In addition, this water usage category has been
broadened to include passive aesthetic appeal thus reflecting
the conservationist viewpoint that a legitimate natural state
of the environment should be maintained with a balanced
relationship existing at all trophic levels.
22
-------
2 0
Natural Concentration
1900
1900
1920 1940
YEAR
I (_
1920 1940 I960
Road Salt
I960
Municipal
I960
10
<
a:
UJ
8
O 1900 1920 1940
H YEAR
I960
FIGURE 4
CHLORIDE CONCENTRATIONS IN LAKE MICHIGAN
(AFTER O'CONNOR a MUELLER (7)
-------
Potential public health problems have been identified on the
Great Lakes specifically with respect to bacterial pollution
of beaches and associated permanent or temporary beach
closings. Appendix A of Reference [1] lists forty-six
beaches on the Great Lakes which have been reported closed
because of bacterial pollutidn.
Degradation of local waters in the Great Lakes from an
aesthetic viewpoint has been reported at twenty-one locations.
There are a number of phenomena which can result in loss of
aesthetic appeal. Rooted aquatic plants, specifically
cladophora, have been washed up onto beaches and picnic
areas causing unsightly conditions and local odor problems.
Massive alewife dieoffs have resulted in accumulation of
these fish on beaches with potential health and odor problems.
Other potential problems which could interfere with direct
usage and aesthetic appeal are large inshore photoplankton
blooms and accidential spills of oils, floatables, and other
chemicals.
Buildup of toxic and harmful substances has also been reported
in the Great Lakes. Potentially harmful materials can build
up in concentrations in the water column, in the benthos, and
through the various trophic levels of the food web. These
accumulations can result in rendering fish unfit to eat and
may cause undesirable alterations and changes in the structure
of the food web. Mercury and DDT have been identified with
specific problems in this type of water and terrestial
environment [2], This phenomenon can infringe directly on
active water usage and on the passive aesthetic concept of
legitimate state of the environment.
The problem of eutrophication in the Great Lakes is perhaps
the most significant. It is manifested in part by increased
biological productivity especially at the phytoplankton level
and undesirable changes in species composition at one or more
trophic levels in the water column or the benthos. Increased
productivity in the Great Lakes has usually been associated
with the major nutrients (phosphorus, nitrogen, and carbon)
discharged in wastes. Figure 5 shows the general location
of excessive phytoplankton growth in the Great Lakes.
24
-------
LEGETJD
GreaJ Lakes Basin Drainage Boundaries
SubDosms
1.
AREftS OF EXCESSIVE NUISANEF
ALGAE GROWTHS
FIGURE 5
LOCATION OF PHYTOPLANKTOIM GROWTH
-------
The low dissolved oxygen levels in the hypolimnion of the
central basin of Lake Erie are apparently related to the
eutrohpication process. Figure 6 displays those areas
experiencing dissolved oxygen problems. The shore local
areas, such as Milwaukee Harbor are generally associated
with discharge of organic wastes.
Changes in the composition of the benthos have been reported
in various areas of the Great Lakes. These changes can be
considered to represent a perturbation of existing aquatic
balances and have been attributed to wastewaters entering
the lake. The alterations in bottom fauna have been
associated with low dissolved oxygen levels, chemical
compounds of wastes, and physical settling of both organic
and inorganic solids. The impact of changes in the benthos
is not fully understood with regard to its effect on the
overall aquatic balance. The premise has been offered that
the observed changes in benthos permeate the food web, with
influences ranging from destruction of fish habitat to changes
in growth rate of phytoplankton and zooplankton.
The influence of the lake levels on recreational water usage
can be considered in terms of possible changes in accessibility
and aesthetic appeal of beaches, swimming, and picnicking
areas. In addition, boat launching sites and fishing areas
can also be sensitive to the levels of the Great Lakes. Lake
levels can have an impact on the extent of the littoral zone
and wildlife habitat availability in shallow and near shore
reaches. Erosion and incoming sediment, which are related
in part to the water levels in the Great Lakes, can reduce
benthos population, increase turbidity, and cover fish
spawning bends.
Shoreline and Harbors
The use of private, public, and commercial waterfront property
is considered in this category. Recreational use of the
shoreline is particularly significant in this regard. Use of
shoreline property can be directly affected by variations in
26
-------
Great LoVes Basin Drainage Boundaries
Subbasms
AREAS EXPERIENCING DISSOLVED
OXYGEN PROBLEMS
FIGURE 6
LOCATION OF DISSOLVED OXYGEN PROBLEMS
-------
lake water levels through erosion, reduction of beach width,
exposure of aesthetically unappealing areas, interference
with boat launching facilities, approach channels, and
fishing areas.
Lake water levels can have a significant impact on shoreline
and harbor usage. This impact results from the several
components which influence the average and instantaneous
lake levels. These factors are:
a. Man-made changes in lake levels
..resulting from regulation of the
flow basin or flow diversions into
or out of the basin. These changes
may be direct, such as the influence
of regulation at the Sault Ste. Marie
control works on Lake Superior or
indirect such as the influence of
Lake Superior regulation on the
unregulated Lakes Michigan, Huron,
and Erie.
b. Annual variations in precipitation
and outflow capacity which can
result in seasonal, monthly, and
long term fluctuation in lake levels.
c. Fluctuations in lake levels caused
by seiches, storm surges, and wind
waves.
Lake level fluctuations associated with the second and third
components have been cited as being responsible for the severe
damage caused to shore property during the high lake level
period of 1951-1952. At that time innundation and accelerated
shoreline erosion resulted. During the low lake levels of
1964 some shore installations, such as marinas, became less
convenient to use and there were instances when they became
unusable during ;very low water periods. However, certain
recreational areas (where the sand beach is normally narrow)
had the advantages of wider beaches during the 1964 low water
oeriod.
28
-------
LEGEND
Great Lakes Bosin Drainage Boundaries
Suboosms
1,
AREAS EXPERIENCING SHORE EROSION
PROBLEMS
AREAS EXPERIENCING SILTING OF HARBOR!
AND CHANNELS
FIGURE 7
SHORE EROSION AND SILTING
-------
Specific locations [8,9] have been reported to have shoreline
erosion problems or local flooding by lake waters. Figure 7
shows those areas experiencing erosion problems or silting
of harbors and channels.
Fishing
The species composition of the Great Lakes fishery has varied
significantly over several decades [10], although the average
annual total weight of fish caught has been stable, fluctuating
between 60 and.80 million pounds per year from 1920.
It has been suggested that intensive exploitation and
environmental factors are responsible for the changes in the
species composition of the catch. In addition, the invasion
of the sea lamprey and the successful establishment of the
alewife in the upper Great Lakes are also responsible for the
changes. The sea lamprey apparently selectively preys on the
lake trout and the burbot, both deep water predators,
depleting these species. This depletion coupled with
intensive harvesting of chubs allows the establishment and
explosive growth of alewife populations in Lakes Michigan and
Huron. This postulated sequence of events points out the
impact of predation and exploitation on the fishery resource.
Contamination of the fishery resource by potentially toxic
and harmful materials, such as mercury, DDT, or deldrin has
been a problem on the Great Lakes. Mercury concentrations
above the maximum permissible level have been found in fish
caught from Lake St. Clair, western'Lake Erie, and the Detroit
and St. Clair Rivers. As an illustration of the difficulty
that has been encountered with the build-up of DDT, 28,000
pounds of coho salmon were ordered seized in 1969, because
the DDT concentration limit had been exceeded. Therefore, a
significant problem exists in the contamination of fish by
potentially toxic and harmful Substances. This contamination
can occur through the food chain or through direct ingestion
and concentration bv the fish themselves.
30
-------
The near shore area is of extreme importance in the maintenance
of adequate fishery resources. Discharge of waters from power
plants which have been used for cooling can significantly
influence local areas of the littoral zone. Thermal shocks and
the possible physical destruction of fish fry and eggs at the
water intake structure are possible consequences. Temperature
changes in the zone surrounding the discharge may either
damage or enhance the food available for fish depending on
the design of the discharge facility.
\
The influence of the lake level changes on the fishery resource
occurs in the littoral zone or shallow fish spawning and
growing areas. /
Navigation
Navigation on the Great Lakes is primarily influenced by
low lake levels and ice formation [11], During periods of
extremely low lake levels, the capacity of the Great Lakes
commercial fleet can be substantially reduced as; a result
of decreased available channel water depths. With regard to
recreational boating the effectiveness of launching facilities
and marinas can be impaired or made unusable by low water
levels. ;
Low lake levels of 1964 caused adverse effects on commercial
navigation and restricted to some extent the areas where
recreational craft could be operated. During the 1964
navigation season when the levels of Lakes Michigan and Huron
were about one foot below datum and the available channel
depths correspondingly lessened, the cargo carrying capacity
of the Great Lakes fleet was reported to have been materially
reduced [11] .
New United States commercial navigation traffic^on the Great
Lakes has been estimated at 222 million tons in 1968 [11].
Commercial navigation is seasonal on the Great Lakes. Ice
formation in the connecting waterways, harbors, and in
portions of the open lake system impede navigation. Figure
8 indicates problem areas associated with this phenomenon.
31
-------
LEGEND
Great Lakes Basin Drainage Boundaries
Subbjsins
AREAS SUBJECT TO FLOODING OR
IMPAIRMENT OF NAVIGATIONAL USE
DUE TO ICE JAMS
FIGURE 8
LOCATION OF AREAS AFFECTED BY ICE JAMS
-------
Considerable attention is currently directed towards
exploration of methods of extending the navigation season,
predicting time of ice formation, and the time for the
lake navigation system opening in the spring. A 90-day
forecast ability for navigation seems to be required to
satisfy overseas,shipping interest on the Great Lakes while
a 30.to 60-day forecast is apparently satisfactory to
interlake shippers.
Navigational use of the Great Lakes can impact two other *
water resource problem areas. The first of these is
concerned with spills of harmful or toxic materials due to
shipping accidents in transit or during loading activities.
The second major potential area of concern is disposal of
dredge spoils. Extensive studies of this latter problem
have resulted in.the development of a number of pilot programs
to evaluate alternative methods of dredge spoil disposal on
the Great Lakes.
Power Generation: .
Power generation" includes hydroelectric power generation,
nuclear power generation, and fossil fuel power generation.
It also encompasses pump storage projects and the disposal
of heat from the;generation of power by fossil or nuclear
fuels.
In 1965r 25 million kilowatts of installed generation capacity
was in the basin. 'In 1970, approximately 4,070 megawatts of
hydroelectric generation capacity was available with
approximately 2,100 megawatts of pumped-storage capacity
either installed or under construction. It has been estimated
that by the yeari2020, 467 million kilowatts of installed
generation capacity will be required to insure the
self-sufficiency'of the power region [12]. The major
increases in power generation are expected to be associated
with nuclear facilities by the year 2000.
Hydroelectric generation on the Great Lakes is influenced
significantly by., fluctuations in lake levels and. the quantity
of available water. Low lake levels and reduced outflow have
33
-------
resulted in substantial reductions in the power which can be
generated by hydroelectric facilities on the Great Lakes. For
example, the Niagara River flow available for power production
in 1964 was approximately two-thirds of the long term average
amounts available. Conversely, high lake levels and increased
available outflow can result in increased electrical generation
by hydroelectric facilities within the basin.
Power generation and cooling water disposal can contribute to
Great Lakes water resource problems. Damage to the local
aquatic balance may be associated with excessive heat disposal
in the immediate vicinity of power plant discharges. Power
plant locations' and sitings may reduce aesthetic appeal of
the surrounding area. Fish spawning and habitat areas as well
as wildlife propagation areas may be impaired or destroyed in
the vicinity of pump intakes and discharges. Alternatively,
proper management and planning may enable excess heat from
power generation to be employed to obtain desirable increased
lake productivity and recreational and fishing opportunities.
There is a possibility of radiological contamination from
nuclear installations. Finally, the proposed solution to
some of the thermal pollution problems requires increased
consumption of water through cooling towers at power
installations.' This consumptive use of water will influence
lake levels and outflow and will tend to increase the build
up of dissolved.materials in the Great Lakes.
Given the preceding brief review of water uses, there are a
variety of ways to stratify the various water use problem
contexts. The definitions of problems discussed at some
length in Reference [1] were grouped by categories composed
of similar classes of associated variables'and/or standards.
Seven problem.categories resulted, each of which has various
associated water uses. The seven problem categories are:
1.
2.
Water Level and Flow Rates of Great Lakes
Erosion-Sediment
3. ,Ice
4. ; .Toxic Substances
5. ;.Organic and Inorganic Chemicals
6. Eutrophication
7. Publid Health
34
-------
Table 2 expands on these categories and shows the associated
affected water use of each category. Note that the first
three categories generally deal with physical phenomena:
flow, temperature, sediment, and precipitation. The last
four categories are related to the general quality of the
Great Lakes system, its water plants and animals.
Variables and Planning Activities
The problem categories shown in Table 2 involve numerous water
resource variables. Some of these variables are requisites
for several of the problem categories. An example is the
water circulation patterns of the Great Lakes which are
obviously important constituents in many of the problem
categories, depending on the time and space scale under
investigation.
Variables are part of the water resource problem definitions
which measure the status of the environment. In this sense, the
level of a variable can be considered as output from modeling
or other analysis efforts which a planning institution
compares to an environmental standard or norm. In addition,
some variables can be directly influenced by planning
alternatives which change the mass (weight) or the time and
space distribution of inputs or withdrawals from the system.
In this latter sense, particular variables can be considered
as inputs to a modeling or other analysis effort. The most
obvious example of variables which may have external controls
is the class of variables associated with wastewater inputs.
Applications of various levels of waste removed will result
in differing levels of an input variable such as metals.
Finally, there are input variables which are not of direct
interest to the administrator but are required in the modeling
or analysis effort. These are'inputs over which there is
generally no possible environmental control, such as the lake
circulation or wind field.
The water resource variables associated with each of the seven
problem categories are listed and then classified into twenty
kindred variable groupings.
35
-------
TABLE 2
WATER RESOURCE PROBLEMS
Problem Category
Kindred Variable Groupings/
Standards
1. Mean monthly water level
and flow rates of the
Great Lakes ,
2. Erosion-sediment
3. Ice
Concentrations of toxic or
harmful substances per
unit weight of mass of
biomass in the benthos and
in the water column
Water Use
A. Available channel depths for
navigation ;
B. Available flows for hydro-
electric power generation
and water diversions
C. Accessibility and useability
of marinas, beaches, and
lakeside parks
D. Changes in the extent and
character of fish and
wildlife habitat
A. Lakeshore erosion with
reductions in property values
and utility
B. Flooding of lakeshore areas
C. Channel dredging require-
ments for commercial and
recreational 'craft
D. Changes in the extent and
character of -fish and
wildlife
A. Opening and closing of the
navigation season on the
Great Lakes :. . ,
A. Accumulation'of toxic or
harmful materials in the
food chain which result in
changes in the aquatic
balance or destruction of a
portion of the.chain or web
36
-------
TABLE 2
(continued)
WATER RESOURCE PROBLEMS
Problem Category
Kindred Variable Groupings/
Standards
A. Heavy Metals
B. Persistent: organics
C. Radionuclides
D. Other substances
Water Use
5. Concentrations of organic
and inorganic chemicals
which exceed present and
projected water quality
standards .'"
A. Dissolved pxygen
concentration
B. pH j ;'
C. Substances influencing
visual appeal
D. Nutrients : .
E. Other Substances
6. Eutrophication.; Concen-
tration level of.biomass,
species distribution, and
diversity inseach of the
trophic levels .
A. Biomass i. ? '
B. Species Distribution
C. DiversityIndicies
B. Accumulation of materials in
higher life forms which
render them unsafe or un->
desirable for human use
C. Unsafe or undesirable water
as a source of municipal,
agricultural, or industrial
water supply
A. Changes in water quality of
fish and wildlife habitat
B. Reductions in the aesthetic
appeal of the water
C. Changes in the aquatic
balance of the biological
system (eutrophication)
D. Destruction of portions of
the food web
E. Increased costs for operation
of water supply facilities
A. Changes in the aquatic
balance of the biological
system
B. Changes in fish and wildlife
habitat
C. Destruction of a portion of
the food web
D. Reduction in aesthetic appeal
of the water
E. Increased cost for operation
of water supply facilities
F. Management of commercial
and recreation fishery
57
-------
TABLE 2
(continued)
.WATER RESOURCE PROBLEMS
Problem Category
Kindred Variable Groupings/
Standards
7. Public Health:,Bacterial
and virus concentrations
in the water body
Water Use
G. Management of fish and
wildlife habitat
A. Water unsafe or undesirable
for use as a domestic,
agricultural, or industrial
water supply
B. Water unsafe or undesirable
for use in bathing and
contact water sports
C. Contamination of fish and
wildlife habitat
38
-------
Table 3 presents a detailed listing of the twenty variable
groupings used in this study and specific examples of
variables in each grouping. This table also contains an
indication of the types of function variables within a
variable grouping.generally served in terms of model input
or model output.
The specific water resource variable and the variable
grouping provide the formal linkage between the planning
and administrative activities and the technical modeling
efforts.
ts
A part of the planning function consists in formulating
alternative management strategies (structural and
non-structural) for obtaining desired objectives. These
alternatives will influence the status and quality of the
environment of the Great Lakes by changes in the inputs and
withdrawals from the system. Communication between the
planning function and the lake based models requires that
variables which are affected by the proposed planning
alternative be identified, potential water resource problems
specified, and the level of the variable in the inputs or
withdrawals associated with the planning alternative be
quantified.
Table 4 indicates the variable groupings potentially affected
by major planning activity in the Great Lakes Basin. These
are the model input variables to which the lake based models
respond. '
Table 5 presents a matrix linking planning and management
activities in the Great Lakes to the output from the modeling
effort. Thus .the planner considers altered levels of the
model input variables indicated in Table 4 and analyzes the
influence of this change by comparison of the model output
variables from Table 5 with a goal or standard.
39
-------
TABLE 3
KINDRED VARIABLE GROUPING
Primary Variable
Function
model model
output input
1. Meteorological
a) Precipitation (over lake) - X
b) Evaporation (over lake)
c) Wind speed and direction
d) Atmospheric pressure gradients
e) Solar radiation
f) Air temperature and humidity
2. Geomorphological
a) Water depth
b) Water surface area
c) Shore slope
d) Shoreline soil type
3. Hydrodynamic
a) Water currents (circulation patterns)
b) Dispersion coefficients
c) Wave heights
d) Wave energy at shoreline
4. Flow X
a) River and water import flows
. b) Connecting channel flows
c) Consumptive water use (flow rates)
5. Lake Level X
a) Mean monthly lake level
b) Mean any period (i.e., weekly, sea-
sonal, et.al.) lake level
c) Water surface tilt
d) Wave run-up
6. Sediment-Erosion X
a) Erosion rate (ft/yrs tons/yr)
b) Accumulation rate and location of
deposited sediment
c) Turbidity of water-light penetration
d) Sediment concentration (suspended
solids .
40
-------
TABLE 3
(continued) :
KINDRED VARIABLE GROUPING
Primary Variable
Function
model model
output input
7. Ice l X
a) Time of ice formation and breakup :
b) Percent'ice cover :
c) Ice thickness
8. Thermal i X X
a) Water temperature and temperature
profiles '
9. Heavy Metals 'X X
a) Arsenic
b) Chromium .'
c) Copper i
d) Lead j
e) Zinc ' ... '
f) Mercury ;
g) Cadmium . :.
h) Selenium !
10. Persistent or harmful organic con- :
.... A A
taminants
a) Pesticides
b) Carbon chloroform extractables and :
other measures of refractory
organics ' '
c) NTA '
d) MB AS
e) Toxic units - .
f) Other organic toxins
11. Radionuclides i ,X X
a) Gross beta radiation ; . .
b) Radium - 226 :
c) Strontium : .
d) Other radionuclides '
41
-------
TABLE 3
(continued)
KINDRED VARIABLE GROUPING
Primary Variable
Function
model model
output input
12. Dissolved oxygen levels X -
a) Dissolved .oxygen
b) BOD-TOC-COD
c) Nitrogenous oxygen demand
d) Bottom oxygen demand
e) Oxygen production rate by photosyn-
thesis :
f) Oxygen utilization rate by phyto-
plankton and rooted plants
13. pH ] X
a) pH ;
b) Carbonates
c) Bicarbonates
d) Acidity : '.
e) Alkalinity .
f) Chemicals or other buffer systems
14. Nutrients (free and combined) - X
a) Nitrogeniseries
1) organic.'
2) ammonia
3) nitrite
4) nitrate:
b) Phosphate series
1) .ortho!
2) -total; ,
c) Apatite iron complexes
d) C02 and other forms of'carbon
e) Silica ].
f) Trace nutrients
15. Biomass
a) Chlorophyll (phytoplankton) X
b) Carbon (zooplankton)
c) Area measures (periphyton)
d) Carbon (fish)
42
-------
TABLE 3
(continued)
..KINDRED VARIABLE GROUPING
'-.-., Primary Variable
:: Function
1 : model model
output input
.. ~ ^
16. Species ! X
a) Individual species populations
1) Phytoplankton
2) Zooplankton
3) Periphyton
4) Bottom organisms (vertibrate
and invertibrate)
5) Fish ! ,
6} Wildlife
b) Allowable fish catch, per year by
species J;
17. Diversity . X
a) Diversity index (taxonomic and other)
1) Phytoplankton
2) .Zooplankton
3) Bottom organisms (vertibrate and
invertebrate)
4) Fish ;''..
5) Wildlife.
b) Niche
1) Breadth (total or trophic level)
2) Carrying capacity (total or
trophic level)
18. Bacteria and Virus X X
a) Indicator organisms
1) Total .coliform
2) Fecal 1coliform
b) Pathogenic bacteria
c) Other bacteria .
d) Virus ''...'..
-------
. :. TABLE 3
(continued)
; KINDRED VARIABLE GROUPING
: . Primary Variable
Function
model model
output input
19. Substances-'influencing visual appeal X -
a) Floating solids
b) Settleable solids
c) Debris
d) Oils and greases
20. Other substances X X
a) Barium
b) Boron
c) Fluorides
d) Iron
e) Cyani'de
f) Chlorides
g) Sulfates
h) Total' dissolved solids
i) Salinity
j) Magnesium.
k) Manganese
1) Color, units
m)' Taste test units
n) Odor 'test units
o) Hardness
p) Phenols
44
-------
TABLE 4
PLANNING AND MANAGEMENT FUNCTIONS
RELATED TO MODEL INPUT
VARIABLE GROUPINGS
NOTE: *Cargo Dependent
1.
2.
3.
4.
.
6.
.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
/
Meteorological
Geomorphological
Kydrodynamic
Flow
Lake Level
Sediment
T ^-. /-*
ice
Thermal
Heavy Metals
Persistent and harmful
organics
Radionuclides
Dissolved Oxygen
pH
Nutrients
Biomass
Species
Diversity Index
Bacteria
Visual appeal (variables)
Other Substances
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r^ CD
cn Ai
rH f^j
&4 h3
- -
- -
X -
X -
X -
- -
-
- X
- X
X -
X -
cn
C
O
H
cn
H
o
0)
'd
CD
>
C -H
O 4J
H td
4-> rH
10 CO
O -H
H CT>
4-1 0)
H rH
T3
0 t3
g C
(0
)_l
CD >i
£ 0
4-> -H
-------
TABLE 5
PLANNING AND MANAGMENT FUNCTIONS
RELATED TO MODEL OUTPUT
VARIABLE GROUPINGS
NOTE: *Cargo Dependent
4J
G
i
CU
tn
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
'
Meteorological
Geomorphological
Hydrodynamic
Flow
Lake Level
Erosion
Ice
Thermal
Heavy Metals
Persistent or Harmful
organics
Radionuclides
Dissolved Oxvgen
pH
Nutrients
Biomass
Species
Diversity Index
Bacteria and virus
Visual appeal (variables)
Other Substances
c
rd
g
cu
4-)
CO
id
^
r£j
C
(0
^
CU
4-1
3:
X
X
X
-
X
X
X
X
X
X
X
X
X
X
X
X
X
plains management 1
river modification '
i
»
T3 CO
0 4J
O C
rH CU
m E
"3
13 G
C 3
rd O
ft
CU g
W -H
3
»
fO en
C
n3 fo
rJ Q
X X
- X
X X
- -
- -
X X
X X
- _
- -
- -
X X
X X
X X
X X
- -
- -
X X
CU
rH
CU
X!
c
H
CU
O
XI
CO
cu
C 0
O -H
4-J
tn o
CU rd
H >-t
4-> fl.
-H
> rH
-H (0
-P M
U 3
(0 4J
H
tn d
C O
H -H
C M
H tn
S <
- X
- -
X X
- -
- -
X X
- X
- -
- -
_ _
- X
- X
- X
- X
- -
X -
X X
1
ction and analysis '
cu
rH
rH
o
o
rd
4J
13
tn £
C U
H >M
£7* fd
T) CU
cu tn
>-l Q)
Q &
- X
- X
X X
- X
- X
- X
X X
X X
X X
X X
X X
X X
X X
X X
X X
- X
X X
X X
1
1
and boating* 1
tn
C1'
-H
G ft'
O ft
H -HI
4-> x;.'
rC CO '.
5-1
cu fQ
G CU
cu en.
C7> (0|
O:
s-i i ;
CU CU;
O "3
CM 1-3
- -:'
;
X -'
X X-
- -'
X X
X -
V1-
- X
X X
- -
- X
- -! '
X -
x -
X -
- -
- X
- X
'-. - . . " -.V ''-..' 1
cting channel flows '
i
cu
:4J C
C C
CU ,O
g 0
tn «i
rO
G tn
rd H
g cu
>i 0)
U H
.CU
x; cu
tn ^4
H rd
frl (-4
'.
'.- X
. X X
X -
V - = X
\'.x -
' x -
X -
X -
X -
v _
X -
X X
.'x x
X X
X -
"'- -
.
. 1
ive decisions 1
O 4->
H fO
4-> rH
rd tn
O -H
-H tn
M-l CU
-H rH
i3
O t)
g G
CO
)*l
CU >,
X! 0
4-1 -H
rd rH
CU O
12 CM
X X
. - -
X X
X X
x x
X X
- X
- X
- X
- X
- X
- X
- X
X X
X X
X X
. - X
- X
. - x
c
o
H
4J
o
CU
4-)
o
ft
CU
c
H
H
CU
l-l
o
x;
en
-
'
-
X
X
X
-
-
>
-
-
-
-
X
X
X
-
-
-
4->
c
CU
g
tn
rd
C
rd
g
CU
H
i )
t3
rH
H
;s
-
-
X
X
X
-
X
X
X
X
X
X
X
X
X
X
X
-
-
1
ation & economic growth
rH
3
ft
O
ft
m
0
c
0
-H
4->
fD
^j
rH
rd
J>
W
-
-
X
X
X
-
X
X
X
X
X
X
X
X
X
X
X
X
X
46
-------
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Limnological Systems Analysis for Great Lakes - Phase !_,
Preliminary Model Design, Progress Report, Prepared by
Hydroscience, Inc., Westwood, New Jersey for Great Lakes
Basin Commission, Ann Arbor, Michigan, Contract No. DACW-
35-71-C-0030, p 105 and Appendix, (August 1971).
Pollution of Lake Erie, Lake Ontario, and the International
Section o_f the. Saint Lawrence River, International Lake
Erie Water Pollution Board and the International Lake
Ontario - Saint Lawrence River Water Pollution Board,
Volume 1 (1969).
Lake Michigan Water Quality Investigations - Biology,
United States Department of the Interior, Federal Water
Pollution Control Administration, Great Lakes Region,
Chicago, Illinois, (January 1968).
Lake Erie Report - A Plan for Water Pollution Control,
United States department of the Interior, Federal Water
Pollution Control Administration, Great Lakes Region,
Chicago, Illinois, -(August 1968).
Beeton, A.M., | "Environmental Changes in Lake Erie," Trans-
action of the -American Fish Society, 90(2) :153-159 (1961) .
Beeton, A.M., "Eutrophication of the Saint Lawrence River
Great Lakes," iLimnological Oceanography, 10:240-254 (1965).
O'Connor, D. J;,. Mueller, J.A., "A Water Quality Model of
Chlorides in Great Lakes," Journal ASCE, Sanitary Engin-
eering Division., Volume 96, -No. SA4 (August 1970).
[8],,
Limnology of"Lakes and Embayments," Great Lakes Basin
Framework Study, Appendix 4, Draft No"! I fNovember 1970).
47
-------
REFERENCES
(continued)
r 91 .-
Great Lakes Water Use Map, Prepared by CCIW, Resources
Research Centre, Policy Research and Coordination Branch,
Department of. Fisheries and Forestry, No. JN 359.
i
"Fisheries," Great Lakes Basin Framework Study, Appen-
dix 4, Draft:No. 1 (April 14, 1971).
mi .' '
1 "Navigation'," Great Lakes Basin Framework Study, Appen-
dix 9, Draft'-No. 1, Volumes 1 and 2(December 1970).
Lake Michigan.Water Quality Investigations - Physical
and Chemical- Quality Conditions, United States Depart-
ment of Interior, Federal Water Pollution Control Ad-
ministration; Great Lakes Region, Chicago, Illinois
(January 1968) .
48
-------
SECTION V
EXISTING DATA
Introduction
Many significant elements in the development and application
of models for water resource management require the use of
observed data. ' Analysis and review of such observations
provide a chronology of the history and development of water
resource problems. These data also provide a basis to develop
a scientific understanding of the phenomena involved. One
of the most important functions, particularly within the scope
of this study, is to provide the necessary information for
verification of the various models required in the analyses
of water resource problems. Finally, historical data,, when
evaluated in conjunction with data from ongoing collection
and monitoring...programs, can provide a measure of the
effectiveness!of management efforts.
Several classes of data are required for an understanding of
the water resource and its proper management. These may be
grouped under!the following broad classifications: physical,
chemical, biological, and special categories.
Physical Data
Data in this category relate to the geomorphology, meteorology,
hydrology, and hydrodynamics of the systems, and have been
accumulated for we'll over a century. The structure, bathymetry
and pertinent dimensions are well known. Maps showing the
soundings in the lakes and tha connecting waterways are
available from the United States Lake Survey Center, NOAA.
Lake levels have been monitored as early as 1819 in Lake Erie
(Table 6). Additional gages were added to the monitoring
system over the.years so that now a complete U.S.-Canadian
network circumscribes all the lakes (Figure 9). All gages
have continuous recorders and data are available on an hourly,
49
-------
TABLE 6
SUMMARY OF WATER LEVEL GAGING STATIONS
IN THE GREAT LAKES BASIN**
Lake Basin
Number of Gages
Earliest Year of Record
/
Superior
Michigan
Huron
Erie
Ontario
Connecting River
St. Mary's
St. Clair
Detroit
Niagara
St. Lawrence*
U.S.
6
8
6
3
4
Number
U.S.
2
7
4
8
2
Canada
4
-
6
5
5
of Gages
Canada
4
2
4
5
4
U.S.
1860
1859
1874
1819
1837
Earliest
U.S.
1867
1919
1897
1930
1916
Canada
1907
-
1906
1860
1861
Year of Record
Canada
1908
1927
1925
1919 .
1919
* 15 additional gages operated in connection with the St.
Lawrence River Power Project by Ontario and New York
(earliest year of record 1954).
**"Levels and Flows," Great Lakes Basin Framework S_tudy_,
Appendix 11, Draft No. 2 (January 1971).
50
-------
GRAND
TWO HARBORS,
DULUTH
150
THUNDER BAY
MARAIS
LAKE SUPERIOR
TOBERMORY
LAKE
HARRISVILLEf. HURON
iGOENSBURG
CAPE VINCEN"
MILWAUKEE
CALUMET(
HARBOR
OSWEGO
FERMI
: TOLEDO
MARBLEHEAD
KINGSVILLE
RIFBII \
KltAU \PORT
CLEVELAND
ROCHESTER
iLCOTT
BUFFALO
TURGEON BAY
PORT COLBORNE
ARCELONA
PORT DOVER
ERIE
FIGURE 9
LOCATION OF WATER LEVEL GAGING STATIONS
-------
monthly, or annual basis from the United States Lake Survey
Center and the Canadian Department of the Environment, Water
Levels.Division. 'All lake levels reported by the above
agencies are referred to the International Great Lakes
Datum (1955) , as agreed upon by Canada and the United States.
A comprehensive historic record of the United States gaging
stations is available in the United States Lake Survey Center
publication, Great Lakes Water Levels, 1960-1970.
Ever since Harrington released drift bottles in the Great
Lakes prior to the turn of the century, work has proceeded *
on establishing representative net circulation patterns in
the lakes. Most of the data have been obtained for the
surface current by means of floating objects such as drift
cards, drift bottles, and drogues (Table 7). In recent
investigations, however, current meters have been used for
general inplace currents and their temporal variations. Thus
far, comprehensive', surveys utilizing current meters have been
conducted on Lakes Michigan and Erie by the F.W.P.C.A. In
these surveys, data were obtained at several depths and a
number of meters were monitored under both summer and winter
conditions. A similar large scale survey of Lake Ontario is
scheduled to be conducted in the summer of 1972 under joint
United States-Canadian sponsorship.
Data on the surface water entering the Great Lakes are
available from the United States Geological Survey, Department.
of the Interior in the form of Water Supply Papers and from
the Canadian Inland. Waters Branch, Department of Environment
as Surface Water Data, Ontario. These flow measurements are
tabulated by water years on a daily basis. All regularly
operated gages are.rated as to probable accuracy of measurement
for periods of both'.high and low flows. The period of gaging
records varies; the earliest information available is from the
United States streams in 1884 and Canadian streams in 1906.
The coverage of gaged streams was approximately 50 percent of
the drainage area in the 1930's and has increased to 64 percent
at present. Estimates for the .individual lakes are:
Lake . Drainage Area Gaged
Superior 53 percent
Michigan 71 percent
Huron . 66 percent
Erie 67 percent
Ontario ' 63 percent
' '' . 52
-------
TABLC 7
LAKE CIRCULATION DATA
Lake . Year(s)
Superior 1953
Michigan 1931-32
1954-55
1955
1962-63
1963
ui Huron 1954
-w 1956
1962-63
1964
Erie 1928
1948-49
1964-65
1964-65
Ontario 1963-68
1970
.' Extent
Eastern Portion
Entire Lake
Entire Lake
Entire Lake
Entire Lake
Five Harbors
Entire Lake
Saginaw Bay
Douglas Point
Daie du Dore
Western Basin
Western Basin
Eastern and
Central Basin
Entire Lake
Nearshore
Type
' Drift cards
Drift Bottles
Drift Bottles and Envelopes
Drift Bottles
Current Meters
Drogues and Current meters
Drift Bottles
Drift Bottles
Drift. Cards
Drogues
Drift Bottles
Drift Cards
Current Meters
Current Meters
Drift Cards
Current Meters
Remarks
4470 released, 8% recovered
745 released, 70% recovered
3000 released, 60% recovered
1297 released, max. 26% rec.
44 stations, several depths.
summer and winter
830 released, 93% recovered
1 station several depths
93 released, 54 recovered
14 stations, several depths,
summer and some winter
34 stations, several depths,
summer and some winter
5 stations
Agency*
'.USFWS
USFWS
USFWS
GLRD
FWPCA
GLRD
GLRD
USFWS
GLRD
GLI
USFWS
ODNR
IJC
FWPCA
IJC
CCIW
*Collecting (Reporting). See Legend of Table 8.
-------
The areas where streamflow is gaged are shown in Figure 10.
In preparing this graphical summary, two publications were
especially useful. The first is Catalog of Information on
Water Data - Index to Surface Water Section", together with
station location map₯, prepared by the Office of Water Data
Coordination (OWDC); United States Geological Survey. This
publication lists thousands of stations which collect water
data and gives the location, period or record, type of data
storage, drainage area, frequency of measurement, types of
data collected,, and agency reporting the data. Similar
information on Canadian streams is available in Surface
Water Data Reference Index, Ontario which also includes
station location maps. The Canadian stations are listed
in downstream order and the list of United States stations
can be obtained in similar form upon request to the Office
of Water Data Coordination.
In the Great Lakes region, meteorological data are available
from the United States National Weather Service (NWS) and
the Canadian Meteorological Branch, Department of Transport.
The data are collected primarily from shore-based stations
although a few.;:stations on islands and on light ships are
maintained. First order stations provide hourly weather
observations such as sky conditions, ceiling, pressure, air
temperature, humidity, wind direction, and speed. Second
order NWS stations are primarily operated by the Federal
Aviation Administration (FAA) and maintain hourly records
although many'do not operate twenty-four hours a day. These
first and second .order stations provide coverage for the
entire Great Lakes Basin, as seen in Figure 11. The above
system is supplemented in both countries by a large number
of cooperative.observers who provide daily observations
of air temperature and precipitation.
Additional data,.such as rate of rainfall, soil and water
temperature, upper air and wind condition, sunshine and solar
radiation, and;pan evaporation are available. The locations
of current United States and Ca'nadian stations obtaining
solar radiation,, pan evaporation, and upper air/wind data
are shown in Figures 12 and 13.
-------
t_n
Oi
BOUNDARY OF GREAT LAKES
FDRAINAGE BASIN
NOTE:GAGED AREAS
CROSS HATCHED
ARE
SCALE
- MILES
1 (-
0 25 50 75 100
FIGURE IO
LOCATION OF GAGED SURFACE RUNOFF AREAS
-------
50°
1ST ORDER STATIONS
2ND ORDER STATIONS
100 2OO
FIGURE II
LOCATION OF FIRST 8 SECOND ORDER
METEOROLOGICAL DATA STATfONS
-------
01
SOLAR RADIATION
O PAN EVAPORATION
FIGURE 12
LOCATION OF SOLAR RADIATION S PAN EVAPORATION DATA STATIONS
-------
Ui
oo
FIGURE 13
LOCATION OF UPPER AIR/WIND DATA STATIONS
-------
NWS data for a particular station are available in the form
of the monthly publication, Local Climatological Data, from
the NWS Records Center, Ashville, North Carolina. A national
monthly summary, Climatological Data, which includes daily
averages of upper air/wind data as well as solar radiation
data is also available. Comparable Canadian data are
available in the Monthly Record - Meteorological Observations
in Canada, Monthly Radiation Summary and Monthly Bulletin -
Canadian Upper Air Data from the Queen's Printer, Ottawa.
Chemical Data
In evaluating the availability of past and present water
quality data for.the lakes, attention was focused on those
sources whose data were collected over large areas of the
lake or whose records extended over long periods of time.
These sources are listed chronologically by lake in Table 8
together with an indication of the spatial and temporal
extent of the surveys and a list of variables measured.
The data that .are available cover most chemical and biological
parameters of-: interest although they are for varying times
and locations. .Full synoptic cruises on which significant
variables were all collected are rare. Often the cruises are
scheduled for specific purposes, such as trace metals
determinations..'. The present International Field Year effort
on Lake Ontario is designed to gather all pertinent
information during a given year. The coverage therefore
spans lake-wide surveys conducted during different times of
the year to a specific one hundred year record at a water
intake in Lake Michigan. Ranked according to the number of
major surveys, Lake Erie is first with twenty-eight entries,
Lake Michigan next with thirteen entries, followed by Lake
Huron with twelve, Lake Superior with ten, and Lake Ontario
with seven.
As may be seen from the table,-United States and Canadian
federal agencies are the prime collectors of data, supplemented
by state agencies and educational institutions. At the present
time, the Canada Centre for Inland Waters (CCIW) and the Lake
Survey of the National Oceanic and Atmospheric Administration
59
-------
o
Time
Period
08/13/52-
08/27/52
05/03/53-
10/25/53
12/11/61
07/18/64-
12/08/64
08/00/68
05/00/68-
11/00/68
07/02/69-
07/09/69
CHEAT LAKES W.
Ho. Of
Sampling Geographical Sampling
Periodicity Extent Stations
Grab Entire Lake 35
Irregular Entire Lake 105
East & NE Max. 32
Portion Min . 4
\
Irregular Entire Lake 86
Grab Entire Lake 86
., ., . Eastern -,-,
Monthly ^ , . i£
irortion
_ , Southern __
ur ao _., £ £
Shore
TABLE 8
.VPIJR SAMPLING DATA SUMMARY*
Variables Measured
l.AKH SUPERIOR
tamp , pll ,spec. cond. ,DO, tot.alk. ,all
for several depths
temp, Ca, Ma, S iO 2 , tot.alk. , tot .P. ,
spec. cond. ,pH,DO ,Mg,N (dis) .
temp. ,conduct. (limited secchi, color
and pii)
temp, cond, turb,pH,alk (phenol and to-
tal) ,00
sGcclu. , color , temp , turb , spec. cond. ,
TDS,pll,T Alk,DO,T PO,,,SO,,F,Cl,SiC2,
hard,Ca,Mg,K,Na,Chloro a, tot. coli. ,
ft: c . eo i i. .
temp, trans, pH, Eh, T Alk,TC Alk,C,Cl,
spec. cond. , DO, Tot .coli. , sedi . chem.
macro fauna, solar rad.
secchi disk, carb. fix. ,SO,, ,N03-N,NH3-
N,Ortho P0i,,all at surf and bottom
Type of Collecting/
Data Reporting
Storage Agency
P USBCF
P USBCF
P,C GLI
P,C GLI
C,P CCIW
C NOAA
GLRD
* See Legend at end of Table.
-------
TABLE 8
(continued)
GREAT LAKES WATKR SAMPLING DATA SUMMARY*
Time
Period
05/00/69-
11/00/69
Sampling
Periodicity
Monthly
Geographical
Extent
Western
Portion
Ho. oE
Sampling
Stations
51
\
Variables Measured
LAKE SUPERIOR
tCMiip, trans ,pH, Eh, T Alk,TC alk,Cl,
spec. cond. , DO, tot. col i. ,sedi.chem. ,
Type of
Data
Storage
C
Collecting/
Reporting
Agency
NOAA
11/00/69
04/00/70-
11/00/70
seechi,color , temp,turb,spec.cond. ,
TC Alk.,HCO3,DO,SO.,,Cl,hard,Ca,Mg,
K ,Na,Ch.loro a
secchi,color,temp,turb,spec. cond. ,
pll,TG Alk,HC03,DO,TPO^,Ortho PCK,
Nil 3 ,N03,Org N,SCK ,C1,Si02,Cd,Ca,Cr,
Co,Cu,Fe,Pb,Mg,Mn,Hg,Mo,Ni,K,Na,V,
2n,ChIoro a
CCIW
CCIW
*See Legend at end of Table.
-------
. .Time
Period.
1860-1970
1930-1932
05/06/54-
12/15/54
07/30/54-
07/31/54
01/24/55-
11/12/55
06/28/55-
08/10/55
04/24/62-
12/06/62
GREA
Sampling ... Geographical
Periodicity Extent
. ' South West
Water Intake
Entire Lake
Irregular Southern & -
^ v Central Part
Grab Grand Trav"
erse Bay
Irregular Northern and
^ Central Part
Grab (4) Entire Lake
1 to 3 Grab _ _. T .
,, , T Entire Lake
Samples , Ir.
TABLE 8
(continued)
T LAKUS WATER SAMPLING DATA SUMMARY*
Mo. of \ Type of
.Sampliny Variables Measured Data
Stations . . . Storage,
LAKE MICHIGAN ' '
C1~,SO,, P
277 temperature vs. depth P
temp, pH, spec. cond. , DO, Ca,Mg,Na, Tot.
P,Si02,(all for several depths)
... teinp,secchi ,Mg,Si02 , (all for several _
JJ depths)
q ,, temp, pH, spec. cond. , DO, Ca,Mg,Na, Tot. p
P,Si02,(all for several depths)
Max. 46 ternp,secchi ,Ca,Na,Mg,Si02 , (all for p
Min. '10 several depths)
NH 3-N,sol. PO^,SiO2,DO,phenols,MBAS,
DOD,pH,TSS ,NO3 ,Na,K,Ca, spec. cond. ,
12. to JO alk. ,Mg,SOM ,Cl,Cu,Cd,Ni,Zn,Pb,Cr, '
phy topi. ,benthic fauna
Collecting/
Reporting
Agency
CDW&S
USBCF
USCBF
GLRI
USBCF
GLRI
GLIRBP(HEW)
* See Legend at end of Table.
-------
Time
. . Period
04/24/64-
11/07/64
01/00/68-
12/00/68
04/07/69-
2 11/14/69
07/22/69-
08/23/69
08/23/69-
06/11/70
05/00/70-
11/00/70
. . Sampling
Periodicity
' Approx. '
Monthly
Monthly
\
Biweekly
Grab
Grab (3)
Bi-monthly
GREAT LAKES- l«
No. of
Geographical Sampling
Extent ..Stations
Entire Lake 15
SW Part, 111. 5 2
Water Intakes
SW Part, 111. 4f)
Beaches
South and ,
North Parts
Entire Lake 50
North 62
Portion
TAfiLE 8
(continued)
VTER SAMPLING DATA SUMMARY*
Type of
Variables Measured Data
,-.'. ' . . Storage
"LAKE MICHIGAN . ' .
organic N P
tot . coli. fee. coli . , turb,odor ,pH, tot.
PO ,, ,01,30,, ,radioac. ,phytop. , macro- P
invert.
tr.ot .coli ., fee. coli . ,turb , temp, pH,
NH 3-N,MBAS , tot. PO,, , plankton
secchi,C-f ixation,Si02 ,NO 3-N ,NH ,-N
ortho POi.-Pjfall at surf and bottom)
radioactivity in water sedi. , benthos ,
zooplankton , phy toplankton , f ish , trace P
elements analysis
temp, trans ,pH,Eh,T Alk. ,TC,alk . ,C1,
spec.cond. , DO , tot . coli . sediment C
chemistry
Collecting/
Reporting
Agency
GLRD
ISWB
ISWB
GLRD
GLRD
NOAA
*See Legend at end of Table.
-------
.Time
Period
1946-1948
06/28/54-
08/28/54
06/05/56-
10/27/56
06/07/56-
10/30/56
04/28/61-
12/19/61
04/29/61-
12/11/61
04/00/64-
12/00/64
05/00/64-
12/00/64
.
Sampling
Periodicity
Grab
Bimonthly v
Grab
Approx.
Monthly
Approx.
Monthly
Monthly
Monthly
GKBAr
Geographical-'
Extent . ' -
Southern Tip
Entire Lake
South-Central
Portion
Saginaw Bay
Entire Lake
Georgian Bay
Entire Lake
Georgian Bay
[' LAKES WA'l
Mo., oil ''
S a ill pi inq
Stations
A'/
90
23
56
Max. 80
Min. 37
66
6.1
60
TABLE 8
(continued)
.'iilli SAMPLING DATA SUMMARY*
Variables Measured
J.AKC HURON
tot. coli. ,C1, phenols, chloro.dem. ,
HO, BOD 5, turb. TS, TVS
terao,Ca,Mg ,Si ,cond (several depths)
te!iip,Ma,K,Ca,Cl,SO^ ,SiO2/ spec. cond. ,
DO , pll
tOMip,Ma,Ca,SO 5,conduct,K,Mg,P,Tot.
alk. ,Cl,DO,pH
transp, color , temp, DO,pH,alk . ,cond. ,
phenol , tot . coli . , solar radiation
transp, color ,temp, DO ,pH,alk. ,cond. ,
phenol , tot . coli . , solar radiation
temp, secchi , cond. , turb .pH, alk . ,DO;
above at 2 or more depths
temp, secchi ,cond. , turb,pH,alk. ,DO;
above at 2 or more depths
Type .o'f
Data
Storage
P
P
P
P
P,C
P,C
P
P
Collecting/
Reporting
Agency
IJC
ODLF
USBCF
USBCF
GLI
GLI
GLI
GLI
*See Legend at end of Table.
-------
TABLE 8
(continued)
GREAT I,AKi:S IVA'iT; K SAMPLING DATA SUMMARY*
Un
Time
Period
Sampling
Periodicity
No. tit-
Geographical Sampiiny
Extent Station:;
05/00/66-
11/00/66
Monthly
08/00/68 Grab
10/00/69-
12/00/69
05/00/70-
10/00/70
Entire Lake
Entire Lake
76
100
Variables Measured
Type of Collecting/
Data Reporting
Storage Agency
1,-MCi-: HURON
t'.:!'..[>, solar rad. , trans . ,pH ,Eh ,T.alk. ,
Cl-, spec. cond. ,DO
secchi,color,temp,turb,spec.cond. ,
TDS,pllrT.alk. ,DO,T POi,,Sol. PO^,N03,
SO,, ,F,Cl,SiO2 ,hard,Ca,Mg,K,Na,Chlor
a, tot.coli.,fec.coli.
£;ecclii , color, temp, turb , spec. cond. ,
TC ,-j.l.k. ,IICO3,T P0^,ortho PO^,NH3,N03,
SiOi,SOi, ,C1 ,hard,Ca,Mg,Ca,K,Na,Chlor
a,Lot.coli.,fec.coli.
sec;chi., color, temp, turb ,spec. cond. ,
TC alk.,Org,C,HC03,DO,T P0^,ortho
PO,, ,MII 3,NO 3 ,org N ,30,, ,Cl,Si02 ,Cd,
Ca,Cr,Co,Cu,Fe,Pb,Mg,Ma,Hg,Mo,Ni ,
K,Zn,Chloro. a,tot.coli.,fec.coli.
C,P
NOAA
CCIW
CCIW
CCIW
*See Legend at end of Table.
-------
TABLE 8
(continued)
GREAT LAKES WATER SAMPLING DATA SUMMARY*
No. of Type of Collecting/
Time Sampling Geographical Sampling Variables Measured Data Reporting
Period Periodicity Extent Stations Storage Agency
LAKE ST. CLAIR
1946-1948 ' Fntirp Lake 112 tot.colif,Cl, phenols,MH3,chlor dem. ,
ly46 194b Entire Lake 112 temp,BOD5,turb,TS.TVS P IJC
12/09/64~ Monthly Lake" °f 5 temp.cond, turb ,pH, t alk. ' P GLI
7 total coliform P MWRC
*See legend at end of Table.
-------
TABLE 8
(continued)
GREAT LAKES WATER SAMPLING DATA SUMMARY*
. . No. of
Time
' Period
01/1910-
02/1957
01/1920-
12/1956
6/15/28-
9/15/28
06/07/29-
09/19/29
04/29-
10/29
04/30-
10/30
1946-1948
. Sampling
Periodicity
Daily
Daily v
Monthly
Monthly
Irregular
Irregular
Geographical: .''-'Sampling;
.Extent - Stations
Water intake
at Lorain, 1
Ohio
Water intake ^
at Erie, Pa.
Eastern 2^
Portion
Eastern and ,2
Central Basin
Western
Portion
142
'_..- . Variables Measured'
LAKE ERIE'
temp, Ts, HO 3F,C1,SO, ,HCO 3,Na+K ,.Mg,Ca,
Fe,SiO 2 ,Alk , monthly av.are reported
for each year
temp , TS , NO 3 , C 1 , SO ,_ , HCO 3 , Na+K , Mg , Ca ,
Fe,Si02,Alk ., monthly av. are repor-
ted for each year
temp, alb. N,NH 3,NO 3 , R coli.
DO, CO,, a Ik . ,pH,Cl,Turb. , temp, transp,
microplankton ,macrop lank ton
temp,Cl,NH3 , a Ik, Nil 3 , M0i ,NO 3 ,DO,CO 2 ,
Alk. ,pH,phy top lank ton ,zooplankton
bottom organisms
tot. coli. ,C1 , phenols , NH 3-N,chloro.
dem. , temp, DO, BOD 5 , turb,alk.TS,TVS
Type of Collecting/
. Data Reporting.
Storage Agency .
P GLRI
P GLRI
P USBCF
P USBCF
P USBCF
P IJC
*See legend at end of Table.
-------
oo
TABLE 3
(continued)
. Time
Period
1947-1953
16/00/50-
09/00/51
06/28/55-
09/15/55
09/04/59-
09/05/59
06/20/60-
11/15/60
08/30/60-
08/31/60
Sampling
Periodicity
Irregular
Irregular ,
Irregular
Grab
Monthly
Grab
GREAT LAKliS WAT'ICR S
."' "."; ."NO". ofT" ~ ' ""
' Geographical Sampl.i.iKi . .
Extent Stations
Central 14,
Portion
Nearshore,
Ohio
Entire Lake 12U
Western and __
Central Basin
Entire Lake 60
Entire Lake 168
i.,/..r.
AMP LING D7^TA SUMMARY*
Variables Measured
E ERIE
tor.ii,, DO, C02,alk. ,pH, secchi, all at 4
or more depths
ttimo
SCO,
F , MO
temp
temp
chi
to nip
towp
sevc
da ta
, tot. coli . , DO, color ,pH, spec. cond.
,Fe,Cu,Cr,Ca,Mg,Na+K,HCO 3,SO,,,C1,
, ,TDS , hard , bottom fauna
(several depths)
, DO (generally at 3 depths ),sec-
, 00, cond ., (surf ace and bottom)
, 120 ,alk ,pH,spec. cond. , (all for
ral depths) , secchi , some hourly
Type of
Data .
Storage
P
r
p
p
p
p
p
Collecting/
Reporting.
Agency
GLRI
ODNR
ODLF
USBCF
ODLF
USBCF
*See legend at end of Table.
-------
TABLE 8 .
(continued)
GREAT LAKES WATER SAMPLING DATA SUMMARY*
. ' Time.
Period
07/25/60-
09/22/60
04/13/61-
09/22/61
05/01/61-
10/05/61
06/00/63
1963-1964
04/23/64-
12/11/64
07/00/65-
11/00/65
Sampling
Periodicity
Grab
Irregular
Monthly
Irregular
Irregular
Approx.
Monthly
Monthly
Geographical
Extent
Entire Lake
Western
Basin
Entire Lake
Western
Basin
Entire Lake
Entire Lake
Entire Lake
Ho. of - . . - . ....'
Sampling '. . -Variables Measured'
Stations; . - -'
LAKE ERIE
60 temp, pH, Eh, a Ik. ,Ca,Mg,Na,K,DO,Cl,SO ^
44 temp, D0,alk., (several depths)
60 secchi , color , temp, DO,pH,alk. ,cond. ,
phenols , tot . coli . , solar radiation
24 ternp, DO, (several depths)
temp, DO, COD, BOD, cond. ,DS,TS,T alk. ,
p!I,Cl,SO,,,Ca,Mg,Na,SiO ,Sol PO^tot
158 N,H1I .,-N,6'rg-N, NO 3-N,ABS, phenols, Zn,
Cu,Cd,Ni,Pb,Cr ,bot. sedi. ,chemi. ,ben-
thi.c pop. ,phytop. , tot. coli . fee. coli.
83 (max) secchi , temp , cond, turb,pH, alk ., DO
63 temp,colar rad. , transp. ,pH,Eh,alk. ,
Cl, spec. cond. , DO
Type of Collecting/
Data Reporting
Storage Agency
P UWO
P USBCF
P,C GLI
P USBCF
P FWPCA
P GLI
C NOAA
*See legend at end of Table.
-------
Time
Period
06/00/66-
09/00/66
08/00/66
06/00/67-
-u 10/00/67
O
04/00/67-
11/00/67
04/00/67-
08/00/67
05/00/67-
01/00/68
TABLE 8
(con tinued )
GREAT LAKES WATER SAMPLING DATA SUMMARY*
No. of Type of
Sampling Geographical Samnlinq Variables Measured Data
Periodicity Extent Stations \ Storage
LAKE ERIE
Irregular shorelin 4° '-f-'t.a'l. coli. (Michigan Beaches) P
seech i. , temp , turb , spec, cond. , pH,alk . ,
105 BOD, DO, PO ,,, NO 2, Cl, hard, phenols, tot. C
col. i .
seech i , color , temp, turb, spec. cond. ,pH,
Bi-weeJOv ' Entire Lake Max" 192 alk ' ' DOD' D0 ' SO" 'C1' Si°2 'hard'Cd 'Ca' c P
Bi weekly Entire Lake Min> 77 Cr/Co,Cu,Fe , Pb,Li,Mg,Mn,Ni,K,Na,Sr , C'P
Zn, tot . col. i . , fee. coli . ,TCS,ortho POM
. temp, solar rad., trans, pH, Eh, alk., Cl,
Grab Lntire Lake o3 spec. cond, CO , tot. coli .sedi .cherai. C
Western temp, spec. cond. ,C1, phenol, DO , Tot P,
Basin sol P , NO 3 ,NH 3 ,org-N , tot. coli . ,SS ,SOi,
secchi , temp, alk. ,spec. cond. , DO, BOD 5
COD,pH,Eh,TS,TDS,Cl,NH3,N03,org-N,
Mia-i.aKe Sol p/Tot P , si02 , turb,chlor a,seston, L'r
phy topi . sedi . chemi . ,raacro-inverte.
Collecting/
Reporting
Agency
MWRC
CCIW
CCIW
MOAA
FWPCA
FWPCA
*See legend at end of Table.
-------
Time
Period
TABLE 8
(continued)
. GREAT LAKES ','ATi'R SAMPLING DATA SUMMARY*
Sampling
Periodicity
Geographical
Extent
No. of
Sampling
Stations
Variables Measured
Type of Collecting/
Data Reporting
Storage Agency
LAKE ERIE
05/00/68-
11/00/68
02/00/69-
12/00/69
04/00/70-
12/00/70
Monthly
Entire Lake
Max.
Min.
85
59
sGcchi,color,temp,spec.cond.,pH,alk.,
87 DO,tot POn,ortho PCK ,NHs ,MO 3,30", ,F,
33 Cl,SiOj,hard,Ca,Mg,Na,chlor a,tot.
coli.,Eec.coli.
secchi,color,temp,spec.cond.,alk. ,
IICO] , DO,SO<, ,Cl,hard,Ca,Mg,K,Na,tot.
coli.,fee.coli.
secchi,temp,turb,spec.cond.,pH,alk.,
ilC03,DO,Tot POt,ortho POi»,NH3 ,N03,SOi.,
TFN,Cl,SIOz,Cd,Ca,Cr,Co,Cu,Fe,Pb,Li,
:Ig,Mn,Mp,Ni,K,Na,V,Zn,chlor a,bact.
C,P CCIW
C CCIW
C CCIW
*See .Legend at end of Table
-------
TABLE 3
(continued)
GREAT LAKES WATER SAMPLING DATA SUMMARY*
Time
Period
Sampling
Periodicity
Geographical
Extent '
llo. of , . . x Type of Collecting/
.Sampling . ' Variables Measured . . . Data . Reporting
Stations "". .' Storage Agency
08/10/59-
11/13/59
01/06/64-
12/19/64
09/08/64-
04/18/64
06/00/66-
10/00/66
06/00/67-
11/00/67
Irregular
Grab
Approx.
Monthly
Mid-Lake Wes-
tern Portion
Irregular Entire Lake Max. 60
Entire Lake 106
Irregular Entire Lake
Entire Lake
LAKE ONTARIO ' ' '"
temp,pi I,Eh,a Ik . ,Ca,Mg,Na,K,(all gen-
17 erally at several depths): sedi.,temp,
pH,Kh
secchl,temp,cond.,turb,pH,T aIk.,DO,
(all at 2 or more depths)
temp,DO,spec.cond.Ph,TC alk.,T alk.,
tla , K,C'a,SiO 2 (many sta. sampled at
several depths)phyto.,ben.macrofauna
secchi , ternp , turb ,spec .cond. ,pH,T.alk. ,
47 BOD,DO,Ortho P0^,MO3,N02,C1,hard,phe-
nol ,tot.coli .
secchi., color , temp, turb, spec. cond. , TDS
pH,T alk.,TC alk.,BOD,DO,POM,NH3,N03,
62 NO2,TKJ-N,Org-H,SO,,,Cl,Si02,hard,Cd,Ca,
Cr,Co,Cu,Fe,Pb,Li,Mg,Mn,Ni,K,Na,Sr,Zn,
phenols,ohlor a,tot.coli.,fee.coli.
P UWO
P GLI
P GLFC
C,P CCIW
C,P CCIW
*See Legend at end of Table.
-------
TABLE 8
(continued)
GREAT LAKES WATER SAMPLING DATA SUMMARY*
Time
Period
. Sampling
Periodicity.
No. of
Geographical Sampling
... .Extent . . . Stations..
Variables Measured
Type of Collecting/
Data Reporting
Storage.. Agency..
05/00/68-
11/00/68
02/00/69-
12/00/69
04/00/70-
12/00/70
Monthly
Entire Lake
Max. 87
Min. 33
85
59
LAKE ERIE .'
seechi ,color, temp, spec.cond. ,pll,alk. ,
DO, tot PCK,ortho .PCU , Nil 3, HO 3 ,SO^,F,
Cl,Si02,hard,Ca,Mg,Na,chlor a,tot.
coli.,fec.coli.
secchi,color,temp,spec.cond.,alk.,
HCOs, DO,SO>,,Cl,hard,Ca,Mg,K,Na,tot.
coli.,fee.coli.
C,P CCIW
C CCIW
C CCIW
*See Legend at end of Table
-------
TABLE 8
LEGEND
Time Period: First and last date of sampling.
Sampling Periodicity: Approximate time between sampling.
Geographical Extent: General area coverage of sampling
No. of Sampling 'Stations: Representative number of sampling
stations for time period.
Variables measured: Physical, chemical, biological sediment,
bacteriological
Type of Data Storage: P = published, C = computerized
Collecting/Reporting Agency:
USBCF ;U.S.. Bureau of Commercial Fisheries
GLI ; Great Lakes Institute, University of Toronto
CCIW ! Canada Centre for Inland Waters
NOAA :.National Oceanic and Atmospheric Administration
" Lake Survey
GLRD .Great Lakes Research Division, University of
Michigan (GLRI prior to I960)
CDW&S ; Chicago Department of Water and Sewers
GLIRBP Great Lakes - Illinois River Basin Project, U.S.
; Department of Health, Education, and Welfare
ISWB Illinois Sanitary Water Board
IJC International Joint Commission
MWRC . Michigan Water Resources Commission
ODNR Ohio Department of Natural Resources
UWO : University of Western Ontario
FWPCA ; Federal Water Pollution Control Administration
GLFC : Great Lakes Fishery Commission
ODLF 'Ontario Department of Lands and Forests
74
-------
(NOAA) are the primary organizations having historical
continuing lakewide data collection programs. Other
.significant sources of recent water quality data include
state agencies (Ohio Department of Natural Resources and
Illinois Sanitary Water Board) and the educational institutions
(University of Michigan - Great Lakes Research Division and
Sea Grant Program, University of Wisconsin, University of
Toronto - Great Lakes Institute, University of Western Ontario)
A wealth of historical water quality data as well as general
lake environmental information is located in the Van Oosten ^
Library of the Bureau of Sport Fisheries and Wildlife, Great
Lakes Fishery Laboratory, Ann Arbor, Michigan. Although not
probed in depth--, it is felt that much more data of a localized
nature is available, such as from cities having water intakes
in the lakes and from power plants on the lakes.
Prior to the mid-sixties, data were generally available in
the form of data reports or cruise summaries. These proved
extremely useful to this project in determining the scope of
the surveys. At present, much of the data are stored in
computerized data banks. Based on the experience accumulated
to date, it is difficult to obtain summaries in meaningful
or concise forms from the computerized data banks servicing
the Great Lakes. The specific data can be readily obtained
with time averages and values of the parameters measured as
well as sorae statistical analysis. However, the appropriate
qualifications and methods of analyses are difficult to
retrieve. Summaries, currently being developed by NOAA
personnel and made available to this project, should be most
helpful to future investigators.
To understand the water quality data, the quantity of waste
inputs of all chemical parameters are required. The current
literature contains few summaries of waste inputs to the
lake. Examples of published data are shown in Table 9
where it is seen that the data are sparse and only available
for downstream lakes. To supplement this information, a
survey of the state and provincial agencies responsible for
water pollution control was conducted as part of this project.
The results of this survey (Table 10) indicate that a
considerable body of information concerning waste inputs
from tributary streams, direct municipal STP discharges, and
direct industrial discharges is available from the state/
provincial agencies.
75
-------
Lake
Michigan
Erie
Erie
Erie
Ontario
Ontario
SUMMARY OF PUBL
Time Period Frequency Type
1963-1964 Trib.
Trib.
10/50-9/51 (in
Ohio)
Mun i.e.
1966-1967 Trib.
Indus I .
Trib.
02/15/67- D. . , along
01/29/68 Bi-weekly gQut(!
shore
01/10/64- k Ssi-r'o
Munic.
1966-1967 Trib.
- . Indus t.
ISHEIJ
NO
19
12
30
26
27
13
1
31
45
53-
TABLE 9
WASTE INPUTS TO THE GREAT LAKES
Extent
Flow
(MGD)
10536
257
4468
4700
416
489
19,700
Variables Measured
NH 3,NO 3,Org-N,PO ^SiO ,TDS ,TSS ,Ca,Cl
SO^NajKjMg.MBASjCUjNl.Zn
tot.coli. ,DO,BOD 5, (av. flows and av.
values of following parameters given
temp, BOD, color ,pH,cond. ,SiO ,Fe,Cu,
Cr,Ca,Mg,Na+K,HCO 3,SO ,,,C1,F ,NO 3-N ,
DS , h ard , CN , phenols )
flow , BOD 5 , TS , SS ,TM , TP , Cl ( limited Fe ,
SO ^ , COD ,CN , phenols , heat , oj. 1 , Zn , pH ,
Ca,Mi,Cu for industries)
flows , temp , TS , C 1 , TP
flow, temp, pH,PO,, ,tot-N,ABS
f low, BOD, TS,SS,Tn,TP,Cl ; Indus trial
only: Fe,SO^ , SO 3 , ether solubles , COD,
phenols and limited Cr ,alk . ,Fe, Zn,
sulphide, Cu,Pb,Na,U-2 38, As, Co, Mg,Ni
Collecting
(Reporting)
Agency *
, USPHS
(GLRD)
ODNR
(IJC)
FWPCA
Syracuse U.
(GLRD)
(IJC)
*See Legend at end of Table 10.
-------
TABLE 10
SUMMARY OF AVAILABLE STATE AMD PROVINCIAL WASTE INPUT DATA*
Province/ Waste -. . -''. ' . -' - ' . Sampling
" State . Type %.' Known . .. Parameters Monitored Frequency Yr. of Rec.
Illinois Trib. " 100 DO , turb, spec .cond . ,C1, SO., , COD, alk , hard, monthly 6
NO 3 -N , NH 3 -N , To t . PO i, , pH , MB AS , F , Fe , ph enol ,
CN ,fec.coli ,radiactivity
Mun. 100 BOD,SS ,pH, fee. coli ; monthly 6
(7 ea.) Cl,TDS,tot.PO^,HH3-N (irreg. sampled)
-~j Ind. 100 varies with industry; heavy metals, SS; monthly 6
~-J (2 eav. ) TDS , BOD, complete records available
Indiana Trib. TAlk,Cl ,NOs-N ,pH ,spec. cond. , hardness , 2 week 15
color, turbid, SS, VSS , sol POt , BOD, DO , ABS ,
tot .coli, temp; flow; plankton algae;
radioactivity
Mun. There are no direct municipal discharges.
Ind. Data on file
Source
Illinois
Environmental
Protection
Agency
Indiana
State
Board
of
Health
*See Legend at end of Table.
-------
oo
.Province/
State
Michigan
Minnesota
TABLE 10
(continued)
SUMMARY OF AVAILABLE STATE AND PROVINCIAL WASTE INPUT DATA*
Waste'' . ^ ' '.'- ; . Sampling .. . . -
Type % Known . Pa'rameters Monitored Frequency Yr. of-Rec. : Source
Trib. 85 Temp, pH,DO ,BOD 5 , cond ,Hl'l 3-tJ ,MO 3-N,SS ,SVS , monthly 9
' DS,Ortho-OR;,,hard.ea,Na,T,Mg,C,C02,alk, '
tot.coli . , fec.coli . , trub, color, totPO ,,,Si,
SO,,
Michigan
Trib. phenol, NiCH ,Cr, As, Cu ,F, Zn , Cd,Pb,Hg, Ag,Fe, quarterly 5 Department of
Mn . 5 Natural
radioactivity 17 Resources
pesticides 2
Mun. 100 temp, flow, pH,BOD5 ,SS ,SVfl , tot ,p,coli . daily 21
Ind. 70 varies irreg. 1
Trib. temp, tot.coli . , fec.coli. ,TS , TVS ,SS,SVS, monthly 19
turb, color, hard, alk. ,C1, DO ,BCD,TotP . ,NH ,
NO 3 ,N02 , &Org-N,MBAS , , cond . , Cu,Cd,Ni , Zn,Pb, Minnesota
Fe, Mn,Hg, As ,Se, radioactivity , pesticide ' Pollution
fecal strep, Cr, CM , phenol, B ,!Ja,K, SI ,,, F,Ag, yearly 19 Control
Si . , SO 3 ,Mg ,Ca,Ba,oil&grease Agency
Mun. tot.coli. fec.coli. DO, BOD, setteable solids, daily
TSS ,SVS,tot-P,Kjeld-N
Ind. BOD, SS, temp, pH, (plus others)
*See Legend at end of Table.
-------
TABLE 10
(con Linued)
SUMMARY OF -AVAILABLE' STATE "ANIJ" PROVINCIAL WASTE "INPUT DATA*'
Province/ . Waste
State Type % Known
Parameters Monitored
Sampling
Frequency Yr. of Rec.
Source
New York
Ohio
Ontario
Trib.
- Mun .
Ind.
Trib.
Mun .
Ind.
Trib.
Mun.
Ind.
Data on file
Data on file
Data on file
20 spec.cond. ,pH,DO,tenip,SO,, ,C1,MO 3,NO2 ,NH3, contin.
totP ,OrthoP ,PO,, , phenol, TS , hard alk., color, to 2
turb , radioactivity, pesticides months
100 pH,DO,SS ,BOD5 ,tot.coli. ,sorae fecal coli . daily to
weekly
Data on file.
f low, tot. coli .temp, DO, BOD, TS ,SS , turb. , monthly
cond. ,totPO^,sil,PO^ ,WH j-N , Kjel-N ,N02-N,
N03-N,C1, Hard, alk. , tot. Fe, pli , phenol, ABS ,
As,COD,Cr,Cu,CN,ether solubles ,F1 , SO ,, ,
Hi,Pb,An
New York State
Department of
Environmental
Conservation
Ohio
Department
26 of
Health
8
Ontario
Water
Resources
Commission
*See Legend at end of Table.
-------
co
o
TABLE 10
(continued)
SUMMARY OF AVAILABLE STATE AND PROVINCIAL WASTE, INPUT DATA*
Province/ Waste
State Type % Known Parameters Monitored
Pa. Trib.
Mun. 100 pH,BOD,POn ,SS ,settleable solids ,NH3-N
Ind. 100 . pH, acidity, alk. ,PO,, , BOD, (others such as
heavy metals,DS)
Wisconsin Trib. 90 Alk , tot . coli , BODS ,C1 , color , hardness ,TS,
TVS ,SS , VSS,DO, temp, & radioactivity
Org-N,NH3-N,N03-N; tot&sol P
heavy metals
Mun. 75 BOD 5 ,TS ,SS ; heavy metals,
Org-N,NH 3-H , NO 3-N , tot&sol P
Ind. BOD5,SS
heavy metals
pH,BODs , solids (pulp & paper mills)
Sampling
Frequency
irregular
3 to 6 mo.
3 to 6 mo.
monthly
quarterly
quarterly
5 year
irreg.
5 year
irreg.
yearly
Yr. of Rec.
varies
varies
11
11
3
22
3
22
42
Source
Pennsylvania
Department of
Environmental
Resources
Wisconsin
Department of
Natural
Resources
*See Legend at end of Table.
-------
TABLE 10
LEGEND
Province/State: Origin of waste input
Waste - Type: ,-Trib. = tributary stream input
Mun. = direct municipal discharge to a lake
Ind. = direct industrial discharge to a lake
Waste: % Known
Parmeters Monitored:
Sampling Frequency
and Years of Record:
Estimate of percent of flow, (or waste
input) known to "source". Blank col-
umns indicate that estimates were not
available. : :
List of all parameters monitored during
years or record. "Data on file" indi-
cates that some form of data is avail-
able from the "source".
Approximate periodicity of observations
and number of years of record
Source: State or Provincial Office which complete survey forms
requesting information for this table.
81
-------
Although generally not in published form, the data could be.
obtained by visiting the particular agency - as project
personnel were invited to do by several agencies.
Specific data on the water quality of United States streams
tributary to the Great Lakes are available from the U.S.G.S.
publication Quality of_ Surface Waters in the United States.
Physical and chemical concentrations are tabulated and,In
several cases, suspended sediment concentrations and discharges
(tons/day) are presented. Several state agencies issue
periodic reports on tributary water quality. Examples include
the Periodic Report of the Water Quality Surveillance Network
1965-1967 Water Years by the New York State Department of
Environmental Conservation and the Report of the Water
Pollution Control in the Michigan Portion of the Lake Michigan
Basin and its Tributaries prepared by the Michigan Water
Resources Commission and the Michigan Department of Health
in 1968. A listing of the locations of water quality sampling
stations in the United States is found in the Catalogue of
Information on Water Data, Index to Water Quality Section,
published by the; USGS Office of Water Data Coordination.
Physical, chemical, and bacteriological data of Canadian
streams tributary to the Great Lakes are available in the
Ontario Water Resources Commission annual publication, Water
Quality Data for the Ontario Lakes and S treams. In general,
concentration data are available and, in a limited number of
cases, yearly average discharges (kilotons/year) are given.
Daily suspended sediment concentration and discharges (tons/
day) of several Canadian streams tributary to Lakes Erie and
Ontario are given in the Sediment Data for Canadian Rivers,
published by the Water Survey of Canada.
As has been indicated above, there is much data on the quality
of streams tributary to the Great Lakes, but, in most cases,
these data have not.been correlated with flows. Consequently,
the mass discharge rates are generally not readily available;
but the proper order of magnitude of these can be estimated.
For major U.S. streams tributary to the Great Lakes, the mass
rates are available.from the EPA Storet computer system for
some parameters.'
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Biological Data
Bacteriological surveys of the lakes have generally been part
of more comprehensive limnological surveys in recent years.
All the lakes have been sampled for total and fecal coliform
bacteria, primarily in the shore areas. Early surveys by the
U.S.P.H.S. International Joint Commission and the United
States Bureau of Commercial Fisheries (U.S.B.C.F.) are helpful.
Present conditions can be adequately assessed from the ongoing
surveys of the water quality by the CCIW.
Phytoplankton measurements in the form of chlorophyll or
species counts are available for all the lakes for present
conditions and historical surveys are also available for
western Lake Erie. Table 9 shows stations where such
measurements are made. Zooplankton data are less readily
available, although specific locations are well documented.
Benthic animal surveys have been conducted for isolated
locations.
Commercial fish production records are maintained by the
U.S.B.C.F., and the Ontario Department of Lakes and Forests.
Effort and catch per unit effort are tabulated. The Great
Lakes Fishery Commission has compiled an historical record of
catch by species and by lake for the period 1867-1960 for
both United States and Canadian catches. Data on year classes
for various species are recorded. An extensive collection of
fish scales (used to determine age of fish) as well as a
large amount of historical data on the Great Lakes fishes,
fish research publications, and general basin environmental
information is located in the Great Lakes Fishery Laboratory,
Bureau of Sport Fisheries and Wildlife. Data on predator-prey
relationships, assimilation of contaminants, toxicity
thresholds for various chemicals, effects of temperature,
and dissolved oxygen are also available.
Special Data
Other data for a variety of areas are available for use on
the Great Lakes. Sediment bearing characteristics of
tributary streams are available in the Water Supply Papers
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of the United States Geological Survey and in the Water Survey
of Canada publication, Sediment Data for Canadian Rivers.
Chemical analyses of the bottom sediments have been performed
for all the lakes. An extensive study of radioactivity in
the water, sediment, benthos, plankton, and fish of Lake
Michigan is available, together with estimates of the
radiological wastes entering the lake. The United States
Public Health Service has also accumulated data on the
radioactivity of tributary streams as well as for some near k
shore sampling locations. Waste input data such as oils and
heat have been measured.
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Summary
From the large amount of information uncovered during the
investigation, it is apparent that sufficient data presently
exist for preliminary model development for many of the
water resource problems of the Great Lakes. The resources
expended on data collection programs on the Great Lakes are
proportionately greater than the effort devoted to analysis
of these data. Preliminary modeling will therefore tend to
use the available data and increase the impact of this
information on the decision making process.
The available data have been collected by numerous agencies
and investigators. It should be anticipated, therefore,
that difficulties will be encountered in the use of these
data for any proposed Phase II program. Data gaps will
undoubtedly exist and difficulties in interpretation of the'
information and translation of the data will occur. In spite
of anticipated problems and the shortcomings of the existing
data base, it is concluded that the available information is
sufficient to support "first cut" modeling effort. This
will result in analysis of the existing data. In addition,
the knowledge and understanding gained from modeling can be
employed to guide ongoing data collection programs by
providing indications of the spatial and temporal scales on
which data should be collected.
Based on the analysis of available data, a need exists for
continuation and possible expansion of ongoing data
collection programs, particularly with respect to broad
scale programs such as the International Field Year on the
Great Lakes. Other data collection programs carried out
in recent years by CCIW, NOAA, EPA, and other organizations
should be coordinated with standardized sampling locations,
measurements, procedures and data reporting formats.
A number of questions have been raised suring this study
with regard to the need or desirability for central data
storage facilities for the Great Lakes. It is possible that
an assessment of the total needs within the basin will
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provide sufficient justification for development of central
data storage facilities. It is concluded that the needs
for data in the proposed Phase II study can be adequately
met from the existing scattered data base. Consolidation of
the existing data base in a central storage facility can
not be justified solely by the benefits to be obtained for
the proposed Phase II study. .
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SECTION VI
PROBLEM ORIENTED MODELS
Introduction
In the field of water resources modeling, there are a few
basic principles from which all modeling efforts are evolved^
or developed. These principles are discussed below.
Conservation Principle
This principle allows the establishment of the basic balances
of mass and energy within a specific volume of a natural
water system by accounting for the inputs and outflows of
the particular constituent and its various sources and sinks.
The net rate of change of these factors results in either
an accumulation or fdecrease of the substance within the
volume or in no change, i.e., an equilibrium condition exists
if the inflows, outflows, and sources and sinks are in
balance. It is pertinent to note that the principle may be
applied to living (biological and biochemical) systems as
well as inanimate (physicaland chemical) systems. With
respect to.mass balances, the principle applies to the water
budget itself and to constituents contained in the water
body. The energy balances, on the other hand, are applied
primarily to thermal regimes and temperature conditions
throughout the lakes. Thus, this principle provides the
basis for the framework of the hydrological and temperature
models as well as the eutrophication, dissolved oxygen, and
bacterial models. Furthermore, it plays an important role
in the sediment, chemical, and fisheries models.
Momentum Principle
This scientific law (Newton's Second Law of Motion) allows the
description of the various hydrodynamic factors of concern in
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natural water systems. It is specifically applied to an
evaluation of the velocity regimes and wave patterns due
to the various forcing functions found in nature such as
winds and storms. It is also fundamental to the description
of transport of dissolved and suspended materials as well
as the erosion of shorelines. Its primary application is
in the evaluation of velocity and dispersion fields of
various spatial and temporal scales throughout the system.
It is fundamentally the principle which underlies the
hydrodynamic modeling. v
Thermodynamic Principles
These principles (the first and second law of thermodynamics)
can be used to provide a general description of the chemical
state of the system with 'respect to the equilibrium condition
of its constituents. They specify the necessary relationships
between the Gibbs Free Energy and the chemical composition
of a system. They also permit the application of thermodynamics
to the calculation of chemical and thermal regimes in natural
water systems and are the essential basis for the chemical
models. One of the primary applications is the computation
of chemical or thermal equilibrium levels for actual or
assumed conditions of practical concern.
Ecological Principles
These principles refer to the more qualitative, but equally
fundamental, aspects of both terrestial and aquatic resources
which have been discovered to be important in the understanding
of these biological systems, such as principles which provide
the framework for the understanding of food chains and webs
of the life-death processes of the biological organisms in
the lake system. As such, they encompass or utilize in its
application one or many of the previous fundamentals. This
analytical framework of the ecological model which has been
constructed using these principles permits definition of the
transport and accumulation of critical substances through
the system and its elements.
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These principles may be and frequently are expressed in
mathematical forms which are succinct, precise, and very
general. These expressions usually take the form of
differential equations which describe the rates of change
of the phenomena in time and/or space and relate these
changes to natural fundamental concepts. Because these
relationships are so fundamental, they are also very
general. Thus the continuity equation applies equally to a
mass balance as well as an energy balance and to any natural
water body, regardless of its specific characteristics. v
Furthermore, as specific phenomena are addressed within the
Great Lakes settings, the mathematical structure may include
one or more of these principles, e.g., the hydrodynamic
equations of motion encompass both the continuity as well as
the momentum principles. The physical setting is usually
incorporated in the boundary conditions of these equations.
Thus the fundamental principles take on a greater specificity
as they are applied in greater detail to the analysis of
certain phenomena within the natural environment of any
water system. These equations are then further specified as
they are applied in a lake system. The final set of working
equations, addressing a particular problem within the Great
Lakes setting, is the mathematical model of the system.
Mathematical Models
The mathematical model of a system is developed to answer a
given problem in a natural system. As described above, the
development of the model utilizes one or more of the principles
and their associated equations. This step results in the
formation of a specific set. of equations which may be algebraic,
differential, either ordinary or partial, or integral. Further,
they may be either deterministic or probabilistic, or contain
elements of each depending on the state of knowledge of the
causality chains. The equations contain constants,
coefficients, or functions, which characterize the components
of the system in a quantitative fashion. If the principles
upon which the model is based are fundamental, and the
constants or coefficients are well established, the model
will accurately describe the real world. If, on the other
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hand, assumptions are made either about the specific
applicability of the principles or the coefficients, the
less certain is the ability of the model to reproduce
observed phenomena. In the vast majority of applications
of systems analysis, including limnological systems, there
is a broad spectrum of models ranging from those based on
scientific principles to those qualitative relations which
are primarily empirical in nature. This condition is .
characteristic of the field of water resources.
Administrative Problem Definition
The basic requirement of the Limnological Systems Analysis is
that it be directed to and responsive to planning needs of
the Basin. This condition implies that water use and problems
associated with or resulting from the uses can be sufficiently
described by administrators and planners, so that an accurate
technical and scientific translation of the problem may be
made with respect to the variables of significance. This
problem definition is the primary step in the application of
water resource models and systems analysis techniques to the
planning process. The process must contain three basic
elements:
1. Specification of the water use to which
the problem is related.
2. Specification of the variables of concern
in sufficient detail to distinguish
between possible overlaying classes of
variables and effects.
3. Specification of the apparent extent of
the water use interference (spatial scale)
and the period of time over which the
interference occurs (temporal scale).
This procedure, described in Section IV, is followed in
defining the problems and the related variables of the Great
Lakes. For each of the problems and their variables presented
in Table 3 of Section IV, one or more models are required
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for their analysis. A review was made of the many models
that would be required for these problems. Out of this
review, it was determined that eleven modeling frameworks
could be grouped together. These eleven modeling frameworks
are required to address the problems of the Great Lakes
system:
1. Hydrological balance
2. Ice arid lake wide temperature
3. Thermal
4. Lake circulation and mixing
5. Erosion-sediment
6: Chemical
7. Eutrophication
8. Dissolved oxygen
9. Pathogens and Indicator bacteria
10. Fishery
11. Ecological
Model Development
Given the problem definition by the administrator and having
specified the variable or variables associated with the
problems, the basic steps in the required model structure
and evaluation may be initiated.
The first step involves a more detailed technical assessment
of the dependent (endogenous) and output variable following
the rather qualitative assessment made in the administrative
definition of the previous step. Part of this step involves
the specification of the appropriate time and space scale for
the model which may be, and usually is, different from the
time-space scale implied by the problem.
The next step involves the selection of the necessary inputs,
forcing functions, variables, and parameters the endogenous
variables which relate to the problem now more specifically
defined. The key element in executing this step is relevance,
i.e., only those variables that are important to the problem
context are introduced to the model structure.
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The third step is to provide a basis or a norm for determining
the status of model structures available to deal with the
specified problem. The output from the previous step is used
to formulate suggested model structures along three broad
lines:
1. Definitive equations with specified
functional relationships and
interactions.
^
2. Equations with only general
functional relationships and
-interactions.
3. Qualitative descriptions of a model
structure.
The basis for this classification lies essentially in the
degree to which scientific knowledge, data, and model
specifications and applications are available.
Evaluation Process and Model Status
Figure 14 shows the sequence of steps to be used in evaluating
the status of model structures available to solve specified
problems. It may be noted that the major considerations in
determining model status are:
1. Basic understanding and knowledge
2. Data availability
3. Degree of model verification
4. Degree of model application
In order to provide a basis for ranking each of the modeling
frameworks, numerical weights are associated with each step
as shown in Figure 14.
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A. DETERMINATION
AVAILABILITY
BIBLIOGRAPHIC
SEARCH
(0-50) i ^)
SOME MODELS AVAILABLE 7 NO MODELS AVAILABLE
A I
B. DETERMINATION F. DETERMINATION
(Ql^) OF DATA OF LACK OF
AVAILABILITY BASIC KNOWLEDGE
t
BASIC SOME (^rj^ipN
KNOWLEDGE UNDERSTAND!NGV-C_>/
f LACKING AVAILABLE 1
C:' DETERMINATION G. DETERMINATION H. DETERMINATION
OF DEGREE OF COHO^ OF DEGREE OF OF DATA
Monc, v,cD,c,r1-r,nM EFFORT REQUIRED TO AVAILABILITY
MODEL VERIFICATION OBTAIN KNOWLEDGE FOR GREAT LAKES
SOME ,
VERIFICATION \
G
1
i
'NO VERIFICATION
I
D. DETERMINATION
-, OF SERIOUSNESS
jHOx OF LACK OF
VERIFICATION
i
E. DETERMINATION
(t}HO"\! OF DEGREE OF
^- -1 MODEL APPLICATION IN
PLANNING ACTIVITIES
(~ ^WEIGHTS OF
COMPONENT
- 1
(0-2d) \
I
[.DETERMINATION
OF DEGREE OF
(0^\Q* DIFFICULTY IN
v ^ FORMULATION
8 VERIFICATION
I
J. DETERMINATION
f^TT^ OF SOFTWARE a
Viil!> COMPUTER
AVAILABILITY
i i I
K. DETERMINATION
OF OVERALL STATUS
OF MODEL STRUCTUR
E
STATUS
"S 1
FIGURE 14
DETERMINATION OF MODEL STATUS
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Determination of Model Availability (Weight, 0-30)
This step requires an analysis of work that has been done in
structuring models for the given problem. A bibliographic
computer search has been implemented to aid in this step.
A considerable number of references dealing with the Great
Lakes have been put into the retrieval system. A search,
using key words, can then be made of the reference file to
determine what relevant progress has been made in structuring
applicable models for the given problem context.
s
Determination of Data Availability (Weight, 0-40)
Major data sources and data banks are evaluated in this step
to determine: a) where data are collected, b) time of year,
c) frequency of sampling, and d) variables that are analyzed.
Compilations are analyzed by lake and region to determine
degree of overall coverage and to highlight data gaps, if
any. The overall data structure can then be interrogated at
this step to determine the available data specific to the
time-space scales and problem variables defined previously.
Determination of Degree of Model Verification (Weight, 0-20)
This.step is one of the more important evaluations in
determining the status of a model structure. Consideration
is given to whether the model has been verified at all and,
if so, the number of independent verifications that have
been conducted.
In all cases, an evaluation is made of the degree of success
of the verification which governs, to some extent, the
confidence that can be placed in the use of the model for
planning purposes. Some models are only crudely verified
in the sense that output conforms generally to what one
expects. Other models attempt through a series of independent
data analysis to verify the model by hindsight. This type of
verification increases the degree of confidence in model use
for predictions.
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Determination of Seriousness of Lack of Verification (Weight,
0-10) . . .
If a model has not been verified, this step evaluates the
consequences of the lack of such verification. For some
model structures the lack of detailed verification analyses
may not be critical. This may be so if the problem context
has been dealt with successfully in other geographical areas-
or other natural water systems.
On the other hand, if a model consists of a series of
hypothesized equations with little follow-through, and ,the
problem context is new, then the lack of verification could
seriously affect the utility of the model. An example would
be the formulation of equations of complex ecological systems
which have not been tested against real data. This step,
then/ evaluates the impact of the lack of verification or the
usefulness of the modeling structure for application and
prediction. : ; .
Determination of Degree of Model Application (Weight,. 0-10)
In addition to model verification an important consideration
in evaluating model status is the extent of the Iapplication
of the model in planning or predictive situations. This step
evaluates the existing models in order to determine the
degree, if any, of application of the model. Items such as
the success of the analytical tools in predicting future
courses of events or the degree to which they have proved
useful in the planning process are evaluated. i-
}
Determination of Reasons for Lack of Models (Weight, 0-10)
As shown in Figure 14 this step is initiated when it has been
determined that no models are available for the. given problem
specifications. If models do not exist, this step examines
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the reasons for the deficiency. For some problem contexts,
basic scientific,knowledge may be lacking as to the
mechanisms and pathways that are operative in a particular
phenomenon. Hypotheses may be available, but for a variety
of reasons models have not been structured for planning or
predictive purposes. This step evaluates each problem for
a determination of the reasons for a lack of modeling
structure. I
;' I
Determination of'Degree of Effort Required to Obtain
Knowledge (Weight, 0-10)
If the determination has been made that basic scientific
knowledge is lacking for a modeling structure, then the
effort that is required to obtain that understanding must
be estimated. The estimation includes such considerations
as the necessary scientific research work in the laboratory,
research work in; the field, and analysis of results. Each
incurs a cost and requires time for accomplishment. This
step estimates the cost and time required to obtain necessary
basic knowledge for each problem contect.
!
Determination of. Data Availability (Weight, 0-20)
This step is similar to the Determination of Data Availability
step in the parallel path except with weight, 0-20.
Determination of Degree of Difficulty in Formulation and
Verification (Weight, 0-10)
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If some understanding is available but model structure has
not yet been constructed, a determination must be made of the
degree of difficulty in formulating a model structure and its
subsequent verification. Estimates are made of data needs
for verification and the degree of complexity of required
model development. :
Determination of Software and Computer Program Availability
(Weight, 0-10)
In conjunction'with formulation and verification, analyses are
made of the availability of computer programs and hardware
to deal with given model structures. Substantial efforts in
terms of program development may be required to implement a
given model. \
The procedure, then, for evaluation of model status is to
apply the preceding ten steps to each of the eleven modeling
frameworks, determine the numerical weight of each framework,
and rank the results.
Three development
Development Stage I
Development Stage II
Development State .III
.stages are considered:
Good model status - planning
applications are direct.
Marginal model status - key
variables or phenomenon is
lacking, conceptual framework
may be untested.
Poor model status - considerable
expenditure and research effort
will be required.
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A summary of the available models is given in the next Section
follov/ed by a summary of the ranking of model status in Section
VIII.
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SECTION VII
AVAILABLE MODELS - STATE OF THE ART
Hydrological Balance Models
Problems and Scope
The hydrological or water balance of the Great Lakes is
concerned with the overall supply, storage, and withdrawal
of water from the Great Lakes system as a whole and also
with the interrelations between the various mechanisms
which influence the inflows and other inputs, storage, and
outflows and other losses of Great Lakes water.
The primary variables of concern in the hydrological balance
of the Great Lakes are the levels of the lakes and the flows
between the lakes. The water resource problems are related
to lake levels and connecting channel flows and include:
availability of channel depths for navigation and dredging
requirements; availability of flows for hydroelectric power
generation and water diversions; accessibility and usability
of marinas, beaches, and lake side parks; changes in the
extent and character of fish and wildlife habitat; lakeshore
erosion with reductions in property values and usefulness;
and flooding of lakeshore areas.
The planning and management functions most directly impacted
by the hydrological balance are concerned with navigation,
power, and shoreline protection. A number of modeling
efforts are currently being carried out in the Great Lakes
which address the hydrological balance and several aspects
of the associated water resource problems and planning needs.
Modeling Frameworks
A water budget for each lake is the framework employed in the
hydrological balance models. In equation form, the water
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budget can be expressed as follows:
I-.0±D
(1)
where:
AS = change in the volume of water
stored in lake , .
P = precipitation on lake surface
R = runoff from the lake drainage
basin
U = ground water contribution
E = evaporation from the lake
surface
I = inflow from upstream lake
t
0 = outflow from lake through its
natural outlet ;
D = artificial diversions into or
out of the lake '
Precipitation and Runoff. The independent variables,
precipitation, P, and evaporation, E, in Equation (1) are
related to overlake meteorological conditions. A number
of studies [1,2,3,4,5,6] have indicated that overlake
meteorological conditions can differ from those observed at
shorebased stations. The differences between shorebased
and overlake precipitation have been estimated [6,7] on an
average annual basis to range between 6 percent and 11 percent.
This is equivalent to a constant flow rate of about 3,000
cfs or 1.9 inches in net lake level. The seasonal variation
in the difference between onshore and overlake precipitation
is even more marked. It has been estimated that; average
overlake precipitation in Lake Michigan may be 14 percent
lower in the summer and 4 percent higher in the winter than
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onshore values. Equivalent differences have been reported
[5,6,7] in evaporation rates and other meteorological
conditions.
The dependent variable, runoff, R, in Equation (1) is related
to onshore meteorological phenomena as well as the specific
character and conditions of the tributary drainage area.
Gaging records for tributary streams of the Great Lakes
covered approximately 50 percent of the drainage area in the
1930's and has increased to 64 percent at present. Estimates
for the individual lakes are given below [7]:
Lake Drainage Area Gaged
Superior ' 53 percent
Michigan 71 percent
Huron 66 percent
Erie 67 percent
Ontario 63 percent
One potential difficulty in estimating the runoff, R, is that
extrapolations to; the. total drainage area are required. In
general, the ungaged .areas are regions near the lakes whose
meteorology is influenced by the proximity of the lake.
Further, the characteristics of the near-lake portions of
the drainage basin .can be significantly different from
upstream conditions because of the geological history of
the area and because of man's activities such as the creation
of urban and agricultural areas. When significant changes in
runoff are not expected to be associated with alternative
plans under study, the historical information may be used to
obtain estimates .of the runoff. If, however, future
conditions are projected to differ significantly, it may be
necessary to consider a shorebased hydrological balance
model as an"adjunct.to the lake hydrological model.
>
";
A. number of model's have been proposed in the past for the
computation of runoff from precipitation for small time
intervals and for small tributary areas. This includes a
large number of linear models, many based on the concept of
the unit hydrograph. . A number of methods have also been
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developed which permit the computation of .the unit hydrograph
from records of rainfall and runoff; and computer programs
for routine application are available from many sources, such
as the Hydrologic'Center of the Corps of Engineers.
The unit hydrograph method is still used widely, although it
is generally acknowledged that the relationship between
precipitation andirunoff is not linear. A promising
extension of the unit hydrograph approach is the use of a
functional series'of progressively higher order integrals,
thus attempting to', account for the nonlinearity of the
process. '
-------
Lake Level Model. The lake level models that have been
proposed to date are structured to compute average monthly
horizontal lake levels using a water balance equation of
the type:
AS = NBS + I - O (2)
The variables P, R, E, and U in Equation (1) have been
grouped together into a term called the Net Basin Supply
(NBS) as shown in Equation (3):
NBS = P + R+U-E (3)
Various efforts are in progress on the Great Lakes to
compute the components of the historic and real time NBS
considering both hydrologic and meteorologic processes.
For example, 'Witherspoon [10] has developed a regional
hydrologic response model for Lake Ontario considering
evaporation, !soil moisture, and snow melt to compute runoff
to the lake from the surrounding drainage basin.
An attempt is being made by Meredith and Jones [11] to
compute tha components of the net basin supply (NBS) for
each lake. Jones is computing lake precipitation and
evaporation,and Meredith is computing land runoff. Ground
water interactions with the lakes are neglected. Monthly
records of NBS for the years 1946-1965 are being used for
this analysis. Runoff, precipitation, and evaporation are
determined from the existing records; then the computed NBS
is compared with the NBS values published by the Lake Survey.
Precipitation over land is determined from the existing
United States and Canadian precipitation gages using
weighting factors and considerable extrapolation to obtain
overlake precipitation. Isohyets of monthly precipitation
for the recorded years are drawn for each month.
Evaporation from each lake is computed using the Richards
Irbe procedure. [12] which is a modified method based on
the Lake Hefner studies. This method requires knowledge of
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water temperatures of the lakes. The Canadian Meteorologic
Service has been conducting infrared flights once a month
over all lakes except Lake Michigan, since 1950. The flights
are conducted in criss-cross patterns, so that a good
sampling of lake surface water temperatures is obtained for
the time of the flight. An average lake temperature is
computed for the entire flight. This average is used by
Jones to compute lake evaporation. Little is known,
however, about the temperature change during the rest of the
month, and this knowledge would be required for more *
accurate evaporation computations. There is a need to have
corresponding infrared flights over Lake Michigan. Some
flights have been conducted for special purposes over limited
areas, for example, last year, a flight was made over Green
Bay near the University of Michigan. Actual lake water
temperature measurements are spotty and do not cover many
years. Some records are also available from lake steamers.
Some regressions have been attempted between lake water
temperatures and land air temperatures and wind, which
includes their current and previous monthly values. However,
these attempts are limited by the lack of data. Meredith
plots isopleths for each month of the years used for the
analysis to determine monthly runoff to each lake. The
number of stations used for each month varies depending on
the records available for each month.
Preliminary 'computations for two years for Lake Superior and
Lake Ontario show good agreement of the computed and actual
NBS for Lake Ontario, but large errors exist for Lake Superior.
This seems to be the result of haying many fewer precipitation
stations around Lake Superior and also a higher water-to-land
ratio requiring more extrapolation of land precipitation
records to cover the lake precipitation for Lake Superior.
To date these efforts are greatly limited by the lack of
data on over-the-lake precipitation and lake temperature
distributions. Difficulties are also caused by the high
variation in data density between the lower lakes and Lake
Superior.
The results of the hydrological balance are sensitive to the
measurements of connecting channel flows as represented by
variables, inflow, I, and outflow, 0. By way of illustration,
the average flow in the Detroit River is on the order of
200,000 cfs. Therefore, every one percent error in flow
measurement represents an error of ± 2,000 cfs.
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Planning functions and management activities can influence
the individual variables grouped in the net basin supply
(NBS) term by alterations of meteorological conditions or
the runoff characteristics of the drainage area. The
remaining terms, input, I, outflow, O and diversion, D, in
Equation (1) are those variables which are most likely to
be changed by various planning functions and management
activities.
State of the Art
There are two lake level models currently available for the
Great Lakes. Both models employ the basic water balance
Equation (1) for Lakes Michigan, Huron, and Erie and use
existing operating rules for Lakes Superior and Ontario.
Each model contains semi-empirical equations which are
developed by using regression analysis for calculations of
connecting channel flows. The basic difference in the two
models is found in the manner in which the net basin supply,
Equation (3), is considered. The Corps of Engineers model
[13,14,15] employs NBS without attempting to subdivide the
individual components. In the model developed by Quinn [16]
evaluation of the individual components which make up net
basin supply, NBS, as indicated in Equation (3), is attempted.
The model equation currently used by the United States Corps
of Engineers is:
AS = NBS + I - 0 ± D
where:
(4)
AS = change in volume of water stored
in lake !
t
NBS = net basin supply : '
I = inflow from upstream lake
105
-------
0
outflow from lake through
its natural outlet
artificial diversions into
or out of the lake
The net basin supply in Equation (4) can be calculated from
historical records.of lake levels, flow in the connecting
channels, and diversions. Thus, knowledge of the magnitude
of its separate components is not required for the
application of the model involving historical conditions.
s' '
This model has several versions, each used for a specific
purpose. All versions use the same routing algorithm based
on change of storage equals.inflow minus outflow. Basically,
two main versions exist:
(1) the forecasting model used to forecast
lake levels in real time six months
ahead
(2)
the regulation model used to test
various lake level regulation schemes
and which employs either of two sources
for input to NBS:
a.1 .the historic net basin supply
values
b.
Each of these two
regulation schemes
between the lakes
possible regulation
Rivers.
simulated (Markov chain) values
of net basin supply [13].
versions (2a and 2b) can run with different
for the flow in the connecting channels
and proposed operating rules, including
of the flows of the St. Clair and Detroit
The forecasting model uses only the existing rules for Lake
Superior and Lake
Ontario regulation. The regulation model
uses either historic or simulated values of NBS. The
simulated values are based on the statistical properties of
106
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the historic values using a simple linear single lag
autoregressive Markov chain model.
For forecasting purposes, the NBS is estimated by two steps.
For the end of the.first month forecast, regression equations
are used relating the NBS of that month with precipitation
and air temperature forecasts for that month and recorded
precipitation and air temperature of the preceding month. A
separate equation is developed for each lake from historical
records. For the remaining five months of the six month
forecast the statistical properties of the NBS are used
based on historical records and adjusted for recent trends.
All computations are based on present day conditions; that
is, historic records are adjusted to represent present day
conditions. Constant values are used and no seasonal or
other adjustments are made (for the major diversions (in or
out of the lakes). A total of 680 years is simulated which
is ten times the.historical record on which it was based.
No attempt is made to estimate any possible future changes
in the hydrologic and hydraulic regime of the lakes.
f
All computations:result in monthly averages for flows and
end-of-month values for water levels in the lakes. However,
smaller time steps are used to route the flows through the
connecting channels (10 equal time steps for a constant
30-day month for--all months of the year on upper lakes, 10
equal time steps:for each quarter of a constant 30-day month
on lower lakes)..
The channel routing is accomplished using a two stage
discharge relationship derived from using regression analysis
from historical records. The following equations are
employed: !
St. Clair River:- .
Q = .173515 (.5 HB + GP -.540.84)2 (HB - GP)1/2
Detroit River:
Q = yi7729 (GP - 547.95) 2 (GP - CL) 1//2
107
-------
where:
HB .= ' ' Lake Michigan-Huron level at
Harbor Beach
GP '.=' Lake St. Clair level at Cross
Point Yacht Club
CL .= . Lake Erie level at Cleveland,
.in feet, referenced to the
;" .. IGLD (International Great Lakes
Datum).
Only two of the coefficients for each equation have been
determined by regression in each equation; the others,
including the exponents, have been held fixed. These
equations are based on the record for the 1962-1968
hydraulic regimes of these rivers. For the other outflows
(Lakes Superior -and Ontario), the existing rule curves are
incorporated into the programs.
During the winter, flow retardation values are incorporated
in the computations of the flows in the connecting channels,
based on conditions in each channel for the first month of
the forecasting. For this purpose, the St. Glair-Detroit
Rivers are broken into shorter subreaches to determine the
restricting reach. Average retardation values are used for
each month for{the regulation studies based on historical
records.
There is also some flow retardation in the summer due to
weed growth in!Lake St. Clair, but the model neglects this
at present. However, the .computations of the lake level
models are sufficiently accurate for the computation of
average monthly' flows in the connecting channels and their
effects on the;lake levels.
The Lake level'model as used for planning employs the
historical data, for calculation of NBS. Thus, the model
is not verified in the sense used in this report. In view
108
-------
of the use of the Corps model in near term planning, however,
this lack of verification does not appear to be a significant
impediment.
For the real time prediction purposes, the accuracy of the
Corps model deteriorates rapidly with successive months [13],
The deterioration appears to be primarily a result of present
difficulties in accurately predicting climatological
conditions. Thus, a deterministic model using predicted
precipitation and air temperatures is used only for the first
month's prediction, while statistical properties of past *
records are considered for predictions during the following
months.
.-
Using the models described above, the Corps of Engineers has
developed new rules for the regulation of Great Lakes levels.
These include regulating the presently unregulated St. Clair
and Detroit Rivers, which would increase economic benefits
compared to the existing rules. These results are developed
considering monthly historical records spanning 68 years and
adjusted for present development. The new rules are devised
to consider the hydraulic interrelationships of the lakes,
while the existing rules are based on considering each lake
separately. Using the Markov chain model, the new rules have
been tested against monthly simulated values spanning 680
years.
A systematic mathematical optimization technique has been
developed by Su and Deininger [17] to determine the optimum
regulation of Great Lakes levels considering economic factors,
A periodic Markov chain decision model computes monthly lake
releases from each lake which maximizes long-range economic
benefits rather than determining fixed rule curves.
It is significant to note that with respect to planning
activities related to lake based variables (lakes, levels,
and flows) on the Great Lakes, the existing Corps of
Engineers model appears adequate for the present needs and
in fact represents one of the few available illustrations
of successful model application to Great Lakes problem
analysis and planning needs.
109
-------
The major shortcoming, with respect to lake based variables,
is the loss of accuracy in real time prediction of lake level.
This is an example of the situation wherein a model meets
planning needs but does not meet operating and real time
management and prediction needs. This latter shortcoming is
associated with the inability to predict meteorological
phenomena. :
Modifications of the appro'ach which would tend in the direction
of improving accuracy from the modeling standpoint would
depend on improved treatment of NBS, retardation, and
hydraulic gradients in channel portions of the system. The
model proposed by Quinn [16] is a step in this -direction.
The model calculates the values of the individual component
variables of NBS rather than using the aggregate variable.
It, therefore, can readily include any improvements in
ability to independently measure or calculate any of these
components. Both ice and weed retardation in the connecting
channels have been evaluated. In addition, a model for the
Detroit and St. Clair Rivers which routes unsteady flows
through these connecting channels has been developed. However,
the hydrodynamic routing model is not a part of the basic
hydrologic balance model. \
This calculation procedure should also facilitate evaluation
of any changes which would influence the individual component
variables of the NBS. As an example, weather modification
and/or predicted long-term climatological changes could be
considered in this computational framework. In addition,
changes in runoff characteristics of the drainage area could
also be considered directly. This could be a significant
feature if large increases in urban development are to be
investigated or if proposed waste disposal practices include
diversion of waters from the lake for on land disposal or
basic export. :
An error or sensitivity analysis of this lake level model has
also been presented and it should be consulted with respect
to allocation of funds for improved scientific measurements
between runoff, evaporation, precipitation; and connecting
channel flows. :.
110
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Evaluation of Model Status
Model Availability. A number of hydrological balance models
are available for;the Great Lakes. These models are presently
operational and are being actively employed for evaluation of
Water Resource planning alternative by agencies involved in
management activites on the lakes.
^
Data Availability. The amount of information and data
available for use;in modeling of the hydrological balance of
the Great Lakes-"is in excess of that available for any
other aspect of the limnological system. There are several
specific areas where increases in measurement accuracy
and/or collection'of more information would be of value
scientifically. These are:
i
(1) Improved accuracy in measurement of
connecting channel flows.
(2) Increased gaging of the drainage area
adjacent to the lakes.
(3) Improved information on overlake
meteorological processes such as
winds, precipitation, and evaporation.
The hydrological balance models are not significantly
constrained by lack of data in meeting present planning
needs on the Great Lakes.
Model Verification. Hydrological balance models for the
Great Lakes have generally employed the observed data in the
basic modeling effort. Independent verification of the models
has not been carried out. This lack of verification is not
a significant impediment in the"application of existing models
to meet present planning needs. -
"i
Model Application in Planning. As indicated above, the
hydrological balance models are presently being employed to
examine planning alternatives on the Great Lakes. They
111
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represent one of the few examples of successful application
of models to planning problems and they are regarded as
adequate for present needs.
112
-------
REFERENCES
^ Bruce, J.P., and Rodgers, G.K., Water Balance of The Great
Lakes Systems, Great Lakes Basin, Research Pub. No. 71,
AAAS, pp 40-69 (1962).
F21 '
1 Lemire, F., Winds on the Great Lakes, Canada Dept of Trans-
port Met.'Branch, CIR-3560-TEC-380 (1961).
Richards,JT.L., and Loewen, P., Preliminary Investigations
o_f Solar Radiation over the Great Lakes as_ Compared to
Adjacent Land Areas, University of Michigan, Great Lakes
Res. Division, Pub. No. 13, pp 278-282 (1965).
F 41 :
Richards, T.L., Bragert, H., and Mclntyre, D.R., "The In-
fluence of Atmospheric Stability and Over-Water Fetch on
Winds over the Great Lakes," Monthly Weather Rev., 95:5,
pp 448-453 (1966) .
Kresege, R.E., Blust, F.A., and Roper, G.E., "A Comparison
of Shore and Lake Precipitation Observations for Northern
Lake Michigan," Lake Erosion, Precipitation, Hydrometry,
Soil Moisture, I.A.S.H. Pub. No. 65~, pp 311-323 (1963).
^Changnon,;S.A., "Precipitation Contrast Between the
Chicago Urban Area and Offshore Stations in Southern Lake
Michigan," Bull. Amer. Met. Soc., 42:1, pp 1-10 (1961).
j
"Limnology of Lakes and Embayments," Great Lakes Basin
Framework;Study, Appendix 4, Draft NoTI[November 1970).
r Q I "' '
Amorocho,; J., and Brandstetter, A., "Determination of Non-
linear Fuhctional Response Functions in Rainfall-Runoff
Processes'," Water Resources Research, Volume 7, No. 5,
' pp 1087-1117 (19717T~^
r 91 '
JCrawford,' N.H., and Linsley, R.K., Digital Simulation in
Hydrology:; Stanford Watershed Model IV, Technical Report,
No. 39, Stanford University (July 1966).
113
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REFERENCES
(continued)
" Witherspoon, D.F., A Hydro logical Model of_ the Lake On-
tario Local Drainage Basin, Technical Bulletin No. 31,
Inland Waters Branch Dept. of Energy, Mines, Resources,
pp 1-13 (1970).
" JMeredith, D.D., and Jones, D.L. , Work in Progress, Jan-
uary, 1972 - private communications to Battelle Pacific
Northwest Laboratories.
n 91
11 Richards, T.L., and Irbe, J.S., "Estimates of Monthly
Evaporation Losses From the Great Lakes, 1950-1968, Based
on Mass Transfer Techniques," Proc. 12th Conf. Great Lakes
Research, Int. Assoc. for Great Lakes Research, pp 469-
487 (1969).
* ^DeCooke, B.D., and Megarian, E., "Forecasting the Levels
of the Great Lakes," Water Resource Research, Volume 3,
No. 2, pp 397-403 (September 1967).
ri4i
L JDeCooke, B.D., "Regulations of Great Lakes Levels and
Flows," XI, Pan American Consultation on Cartography (1970)
Megerian, E., and Pentland, R.L., "Simulation of Great
Lakes Basin Water Supplies," Water Resource Research,
Volume 4, No. 1, pp 11-97 (March 1968).
Quinn, F.H., "Quantative Dynamic Mathematical Models for
Great Lakes Research," Ph.D. dissertation, University of
Michigan (1971).
Su, Shiau, Y. , and Deininge-r, R.A. , Optimal Operating
Policies For the Great Lakes. System, The University of
Michigan, Ann Arbor, Michigan, UIRICH-ENUSA-71-3, pp 1-
189 (June 1971) .
114
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Ice and Lake Wide Temperature Models
Problems and Scope
The basic water resource problem associated with temperature
balances and ice on the Great Lakes is the opening and closing
of the navigation season on the Great Lakes. Overall heat
balance calculations in the lakes are possible, but carrying
these to the point of prediction for the opening,and closing *
of the navigation season appears beyond the present state of
the 'art. It shpuld be noted that most of the problems in
this regard are, under most circumstances, beyond the scope
of Type II planning. For example, the ice problem associated
with the navigation season opening and closing is primarily
a reflection of an operational need for real time predictions.
Modeling Frameworks and State of the Art ;
Lake Wide Heat Budget Model. The heat budget calculation is
an energy balance which considers the sources and sinks of
heat energy such as heat transfer at the air-water interface,
the heat transfer at the bottom of the water body, and heat
generated by biochemical reactions if they are shown to be
significant. The terms generally considered for heat transfer
at the airwater interface are shortwave solar radiation, long
wave atmospheric radiation, reflected solar and atmospheric
radiation, longwave back radiation, evaporation,, and conduction,
Many studies have been conducted to evaluate these factors
from easily measured meteorologic parameters, if direct
measurements are not possible or not available. , The best
known investigations were conducted at Lake Hefner:, Lake Mead,
and the Salton Sea; and the relationships developed during
these studies have been widely used.
There are a number of processes .acting across the air-water
interface'to change the temperature of the water. .Short and
longwave radiation, evaporation, condensation, and sensible
heat conduction act to produce absolute heat changes, whereas
convective and turbulent mixing generate a redistribution of
the thermal structure. By computing the contribution of each
115
-------
of these terms to obtain a net heat gain or loss, it is
possible to estimate the changes to the thermal structure.
The following air-water interface processes are jointly
referred to as the heat budget and can be represented by
the equation:
where:
Q = Q +Q - Q, - Q -Q - Q,
. ws c b e wr h
Q =. net gain or loss of heat
,-'
Q = ' . insolation
Q = heat gain by condensation
C_»
Q, =. effective back radiation
Q =. heat loss owing to evaporation
Q =; reflected radiation
Q, = heat conduction across interface
Precipitation may cause local temperature changes. There are
also heat changes, that result from heat flow through the lake
bottom, the dissipation of wind and tidal energy, and heat
bound or released by chemical processes; but these changes
are insignificant for short term predictions.
Heat budget formulations usually require a knowledge of both
air and water temperature, particularly for the evaluation of
evaporation and its effect on heat transfer.
Because of the lack of information on the eddy conductivity,
it is general practice to relate sensible heat transfer to
evaporation. Assuming that evaporation and conduction of
specific heat energy are similar processes, Bowen [1] derived
a ratio for the two processes:
(1)
116
-------
Q T T P
h _ _ ( w a) . a
_ _
(e - e ) 1,000
w a '
where: '
R = ; Bowen ratio
P = [: atmospheric pressure
cl
constant
and T , T , e , and e are water temperature, air temperature,
vaporwprefsur₯ at wattir surface, and partial pressure of water
vapor in air, respectively.
The handling of the radiative terms has received extensive
analysis. Battelle [2] has found that it is hazardous to the
accuracy of predictions to use computed values of input solar
radiation for making verification simulations. The use of
statistically treated point measurement data more accurately
reflects the input energy than any mathematical treatment
proposed to date.' This is essentially the same conclusion
reached by Anderson, et.al.[3]. This variable is closely
related to the atmospheric opacity as affected by air
pollution in metropolitan areas. Consequently, for predictive
work, close attention needs to be placed on accuracy in the
forecasting of radiative inputs.
The longwave radiation exchange terms are only important in
the wintertime. Errors in computation of back radiation are
introduced by two, problems. Usually, summer conditions
are used for heat; budget studies, but the Bowen ratio is
apparently considerably different in the deep of winter when
boundary conditions modify the evaporation/conduction ratios
widely. Estimates of radiation exchange are also modified
in winter. Additional research is needed in order to obtain
more evaluations of thermal transfer in the winter months.
117
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Formulae for computing evaporation vary from simple
expressions relating evaporation to the wind and vapor
pressure difference alone to complex considerations involving
aerodynamic surfaces, occurrence of spray, and vertical
profile of wind and vapor pressure. The Lake Hefner studies
described by Marciano and Harbeck [4] include comparison of
evaporation as computed with the equations developed by a
number of authors (Sverdrup, Millar, Norris, Button) to
measurements;of evaporation based on water budget calculations.
The complicated equations of Sverdrup and Sutton give
satisfactory comparisons, but a simple empirical equation
was devised that also gives good agreement, although the
only inputs are wind speed and the difference in water vapor
pressures at two levels. A similar equation developed by
Rohwer [5] and slightly modified by Laevastu [6] gives
comparable values and is considered more realistic for
ocean evaporation. Rohwer [5] presented a comprehensive
investigation of evaporation involving evaporation
measurements;under both laboratory and natural conditions.
Observations,were made with various types of equipment and
procedures and.included measurements in still air, in natural
air flow, air under various controlled wind speeds, over a
heated surface, from an ice surface, and at different
altitudes. From data gathered over a six year period, Rohwer
concluded that one formula has general application. Laevastu
modified this formula slightly to compensate for the wind
profile over the sea. This formula for calculating
evaporation is:
where:
|Q '.= 2.46 (0.26 + 0.04W) (e - e ) (3)
e i .= saturated vapor pressure at sea
surface temp., mb
dry bulb vapor pressure, mb
W > = wind speed, knots
118
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For inland lakes, the Bowen ratio R is 0.61 under normal
atmospheric conditions, but it can vary between 0.58 and
0.66. Although originally conceived for molecular diffusion
pressures, Bowen's ratio has been shown to apply to
nonlaminar flow also. Some authors have suggested theoretical
modifications to Bowen's ratio, but observations have
generally supported his concept. Anderson [3] found from
the exhaustive Lake Hefner observations that the Bowen ratio
is generally valid. Tabata [7] and Gaul and Elder [8]
reviewed methods of computing sensible heat transfer and ^
concluded that Bowen's ratio is satisfactory.
Neglecting the pressure term, which has only a small effect,
and substiting for Q in the above equation, the transfer
of sensible heat can be found from:
Q, = 0.83 (0.26 + 0.04W) (T - T ) (4)
n w a
This equation is applicable for surface cooling where colder
air overlies warmer water. The wind is important in that the
warmed air is rapidly removed by atmospheric convection. The
reverse situation, where warm air lies over colder water,
produces surface heating of the water. Here the stabilizing
effect of the air's being cooled from below reduces the
transfer of heat. To reduce the rate of surface heating,
the above equation is modified in accordance with Laevastu's
[6] proposed reduction of the constants so that:
Qh = 0.036W (Tw - Ta) (5)
Roughness of the lake surface has been extensively studied
and has some relation to the changes in effective transfer
coefficient, however, the extension of studies to swiftly
flowing rivers produces relatively dramatic deviations from
the classic concept. In these cases, sensible transfer of
from three to five times that predicted by the Bowen ratio
occurs. Jaske [9] has attempted to compute the sensible
heat exchange coefficient variation as a function of stream
surface velocity, but the work is incomplete and requires
additional research.
119
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Ice Models. Ice transport and the estimation of forces and
the hydraulic modifications related to ice accumulation are
difficult to model. A number of excellent techniques are
available for the estimation of ice forces and rates of
accumulation in flowing rivers, such as the Detroit River,
Lake St. Clair. reach, and St. Clair River. Aerial surveys
of ice are also conducted, and the results are published
monthly by the Lake Survey. ;
t
Correlations are principally based on the use of Kivisild's
theorem, which states [10] that the accumulation of .ice is
related to critical values of the Froude number ranging from
0.6 to 0.8. In 1955, Michel tested the Kivisild criterion
in a number of cases and found it applicable. In this
method, the relation of the equilibrium of the upstream edge
of the cover fed by ice flows can be estimated from the
following:
I
where:
F = -^ = /2P " Pl (1 - g) * (1 - t) I (6)
r gy p y y' s v '
F = Froude number of the flow in :
front of upstream edge '
V = velocity in feet per second ;
in front of upstream edge
y = depth of water in feet, in front
of upstream edge * j
P,pi = specific masses of water and :
solid ice :'
.porosity of -the accumulation
thickness of the upstream edge,
in feet, at equilibrium
120
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Porosity plays a major role in the progression of ice covers
and is also a very difficult quantity to estimate. An ice
cover may consist, of frazzle flocks of very high porosity, of
solid flows of low porosity, or a combination of both [11].
The situation with respect to the initial movement of pack
ice under wind or current movement is less well developed.
Ice booming .is successfully carried out in bays with small
reaches, and in some instances, such as the booming of hydro^
facilities on the St. Lawrence, some success has been noted.
The reduction of this practice to numerical analysis is very
difficult and, a:t best, essentially empirical in that the
information needed for the solution of complex theoretical
expressions is not available.
The Russian literature has much useful information on the
modeling of ice movement. A paper by Panfilov [12] contains
the following relationships which appear to be useful in
defining a first '.approach to the deterministic modeling of
ice forces involved in pack ice movement. These forces can
be divided into active and reactive forces. The active
forces promote ice movement in the direction of the wind or
the current flow ,and include: (a) the frictional forces F
of water on ice acting on the lower surface of the pack,
or alternatively .F , the forces due to wind on the ice
surface, and (b^ ;tiae component F. ^ of the ice weight in the
direction of net movement. The pressure exerted on the
upstream rim of the ice field is grouped with the active
forces, but is ambiguous in some cases because of internal
bridging. Reactive forces oppose the movement and comprise
the shore resistance F and the reaction F, of the structure
under pressure. :
At any moment, the ,ice condition is in dynamic equilibrium
with the basic forces. As unbalance occurs because of
temperature rises, flow changes, ice expansion, or other
active factors, modifications o'f the dynamic balance occur
rapidly. As a result, deformation of the edge of the ice
pack and reductions in the thickness and strength of the
ice occur. The resistance offered by the shore and shore
based structures ;.decreases and the forces associated with
active pressuresiincrease. This occurs until the active
121
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forces exceed the total reaction of the structures and the
shore, and the ice sheet begins to move.
The condition for limiting equilibrium of the ice sheet can
be mathematically: .stated as follows:,
Fic - Fs - Fh=
In order to use this approach, a number of simplifying
assumptions are necessary: principally that relatively
straight edges are presented by the pack and that the
thicknesses are uniform enough to be represented by a mean
thickness. '
The resistance exerted by the structure against ice movement
is related to the configuration and resiliance of the shore
line structure; to the nature of the contact between shore,
structure and ice; and to the thickness and strength of the
ice itself., As these factors are indefinite and depend on
rapidly varying local conditions under some critical stages,
a rigorous quantitative evaluation of shore reaction force
is very difficult [13].
It is also well known that because of the nature of ice
itself, sheet movements are accompanied by ice pile-ups on
the shore. These, are particularly heavy at constricted
entrances to bays, and harbors . The pile-ups occur as a
result of the disruption of the continuity of the pack at
points of contact with the shore structure and involve
internal forces of bending, shearing, and crushing.
Consequently, the total shore- resistance force can be
expressed as :
Fs =
where k =. k, + k R /R, + k R /R, . The coefficients k
s b .sr sr' D c c' JD
represent each type,of deformation, and R, , R and R are
D S IT C
the ultimate strengths of the ice, respectively, in bending,
shearing, and crushing.
122
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Similarly, the other forces can be evaluated in terms of
coupling coefficients, momentum transport to the ice from
wind, and the differential movement of the pack under applied
forces. The numerical summation of the forces balance
equation is solved to permit a first approximation of the net
forces involved.
Other detailed modeling problems might be encountered in
fine detail as a number of shoreline factors are taken into
consideration. These are the impacts of ice flows on ^
structures. However, most of these transport problems are
more directly related to the engineering design of individual
protective works- and probably need not be considered for Type
II planning. :If such consideration is necessary, for example,
in the determination of the extra cost of protection for year
round harbor operation on a large and widely distributed
scale, the basic formulations for estimation are presently
available.
Research on ice mechanics indicates that as the rate of
loading on ice is increased, the strength of ice increases
rapidly until'a maximum static compressive strength of
approximately 400 psi is reached at a load rate of 1,000
psi/minute. Beyond this value, the strength decreases and a
value of 160 is about average for first approximation of
collapse stress. When ice collides with a vertical
obstruction, the leading edge v/ill be progressively crushed.
A state of progressive failure is maintained. If the
structure is massive, a maximum force equivalent to the
brittle strength .of ice at the highest rate of loading is
applicable. ; .
Ice impacts are accompanied by dynamic oscillations which
are functionally related to the thickness and condition of
the ice. Measured oscillations with periods on the order
of 3 to 10 seconds can be expected with appropriate resonant
coupling to the response spectra of the structure itself.
However, the determination of mass ice movement from wind
forces or the., estimation of ice breakup by deterministic
means remains1in a relatively unknown state. A number of
investigations .have shown promise of the creation of open
123
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passage for navigation or structures using bubbler systems;
however, the closing of these relatively vulnerable passages
can occur promptly with massive destructive forces. The
booming of large ice masses has been attempted by the various
agencies involved in the St. Lawrence Seaway, but to date no
deterministic results have been reported. It appears safe to
assume that in the absence of an approach, no method can be
recommended without extensive additional investigation. Such
an investigation is now underway by the United States Army
Corps of Engineers. <-
Evaluation of Mo'del Status
Model Availability. The models for prediction of the opening
and closing of the navigation season require prediction of
thirty to ninety-day meteorological conditions and the
formation of ice in open lake areas, connecting channels, and
harbors. In addition, lake wide temperature modeling would
also be required. The former prediction requirements are
beyond the scope of present technology. Lake wide temperature
modeling, given meteorological data, is within available
technological capabilities.
Data Availability. Data on historical meteorological conditions
are adequate for shore stations around the Great Lakes. Over
lake meteorological data are inadequate. Information allowing
conversions of shore meteorological data to overlake data
requires substantial additional investigations. Data on ice
cover closing and opening dates and lake temperatures appear
adequate for a first-cut analysis effort.
Model Verification. In view of the need to predict
meteorological conditions and ice and temperature conditions
on a lake-wide and local (harbor, connecting channel) scale,
the problem formulation and verification would be difficult.
Software and Computer Availability. Present generation
computers appear adequate to support a first cut modeling
effort.
124
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REFERENCES .': .
" Bowen, I.S., "The Ratio of Heat Losses by Conduction and
Evaporation from any Water Surface," Phvs. Rev., Sev. 2,
Vol. 27, pp 779-787 (1926).
r 21
1 Jaske, R.T., and Spurgeon, J.L., "Thermal Digital Simula-
tion of Waste Heat Discharge," Water Research, Pergamon
Press, Volume 2, S-777-802 (1968TT:
* Anderson, E.'R., "Energy Budget Studies," Water-Loss Inves-
tigations ; Volume 1, Lake Hefner Studies, U.S. Navy Elec-
tronics Lab. Tech. Report 327, pp 71-119 (1952).
F 41 !
Marciano, J.J., Jr., and Herbeck, G., "Mass Transfer Stud-
ies ," Water Loss Inves tigations Volume _!> Lake Hefner
Studies, U.S. Navy Electronics Lab. Tech. Report 327, pp
46-70 (1952).
Rohwer, C., "Evaporation From Free Water Surfaces," Tech.
Bull. U.S. Dept. Agric., p 271 (1931).
Laevastu, T., "Factors Affecting the Temperature of the
Surface Layers of the Sea," Commentat. Physico-Math.,
Volume 26, pp 1-136 (1960). r
m i'
1 Tabata, S., and Giovando. L.F., Prediction ofiTransient
Temperature Structure in the Surface Layers of_ the Ocean!
Fishery Res. Bd. of Canada, Manuscript Report: (Ocean),
NO. 132 (1962) . j ,
i
F 81
Gaul, R.D., and Elder, R.B., A Critical Summary of Sea
Surface Heat Exchange Equations, IMR 0-40-62,,U.S . Naval
Oceanographic Office (1959). ;
F91 ..;-.
1 Jaske, R.T., An Evaluation of the Use of Selective Dis-
charges from Lake Roosevelt to Cool the Columbia River,
Battell Northwest Report, BNWL-208, pp 1-87 (1966).
125
-------
REFERENCES
(continued)
Michel, B. , and Deslaurieries , "Kivisild's Criteria for
Ice Movements and Accumulation in River Described in Re-
view Papers," Proc. of ci Conf . held at Laval University ,
Quebec (November 196(TF.
, L.W., "Elastic and Strength Properties of Fresh-
Water Ice," National Research Council of Canada, Conf.
on Ice Pressure Against Structures, Quebec (1966).
F121
1 Panfilov, D.F., "Ice-Flow Conditions Upstream of Hydro-
stations," Tranlated from Gidrotechnickeskow Stoitel
Studies , No. 5,. pp 33-36 (1971).
[ ^Xivisild, H.R., Ice Impact on Marine Structures, (1969).
126
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.Thermal Models
Problems and Scope .
The scope of problems considered in this grouping deals with
the fate of waste, heat discharged to the Great Lakes and
the influence of 'the natural heat sources ori the thermal and
transport regimes of the Great Lakes. The spatial scale of
these phenomena span the range from the local thermal
distribution, which is affected by a particular discharge
with a particular diffuser configuration, to harbor and
region-wide thermal patterns, to the lake-wide thermal
distributions characterized by phenomena such as the thermal
bar and the thermocline. Although the detailed temperature
distribution and dilution characteristics of a specific
diffuser are not directly Type II planning questions and are
therefore not pertinent to this discussion, the effect of a
series of discharges on lake temperature is of concern.
Thermal inputs to the Great Lakes are primarily of natural
origin and the effect of these inputs is clearly seen in the
development of the vertical temperature distribution which
prevails during the summer months in the Great Lakes and is
characterized by /the thermocline. The importance of the
thermocline and the thermal bar is in their effect on the
lake circulation and mixing and the effect of the differing
temperatures on biological and chemical phenomena. Thus
the interest in the large spatial scale thermal phenomena
is centered on these effects; and if data is available which
specifies the temperature behavior of the lakes at this
spatial scale, it would be equivalent to having a model
which calculates:the temperature distributions.
This is not the case, however, for the problem associated
with thermal effluents. The primary sources of man-made
thermal inputs are .fossil fuel 'and nuclear power plants.
The quantity of waste heat to be. disposed of under projected
industrial development around the shores of the Great Lakes
is substantial. ;The problems associated with this disposal
are of concern; and the first requirement for an assessment
of these problems is a method of calculating the expected
temperature distribution, i.e., a model.
127
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Modelina Framework and State of the Art
The state of the art of modeling these phenomena can be
conveniently addressed in terms of the spatial scale
implicated. On the lake-wide scale, seasonal development
of the temperature distribution and associated thermocline
is the major manifestation of the natural inputs and outputs
of heat energy. v
As incident solar radiation and other direct inputs of heat
energy exceed .the heat energy being lost, lake surface layers
begin to warm .relative to the deeper layers. Above 4°C, the
density of water decreases, as its temperature increases so
that the warmer- surface layers are buoyant relative to the
deeper layers. This buoyant force competes with the vertical
turbulent mixing; and if the mixing is sufficiently weak,
the buoyant forces prevail and a temperature stratification
develops in the vertical direction. This stratification is
characterized, in. most cases, by a depth at which there is
a sharp temperature change that separates the warmer surface
waters from the colder deep water layers. This region of
rapid temperature change is the thermocline. Examples of
this rapid temperature variation for Central Lake Erie are
given in the Project Hypo report [1] .
Models which address this phenomenon directly have been
developed over a period of years and their behavior is
reasonably well understood. The classical formulation
considers only the variation of temperature in the vertical
direction and'1; the governing equation is conservation of
energy averaged horizontally. That is:
If
where T(z,t) is the horizontal average temperature, A(z) is
the cross sectional area at depth z, Q(z,t) is the vertical
flow rate, E(z,t) is the vertical dispersion coefficient.
128
-------
S. and S are the inputs and outputs, or sources and sinks,
respectively, of thermal energy.
Orlob [2], Dake [3], Dake and Harleman [4] , Huber and
Harleman [5], and Sundaram [6] discuss the basic equation of
heat conservation for a lake. The solution of the above
equation requires specification of the velocity field, the
dispersion coefficient, and the distribution of heat sources
The references quoted above bring out the following points:
The temperature structure in lakes is likely
to be---very homogeneous horizontally. This
is a consequence of the tendency for the
temperature pattern to approach a stable
state relatively rapidly with respect to
seasonal changes. Under these conditions,
the horizontal variations can be neglected.
Horizontal inputs of heat may be accounted
for in the source terra. At certain times
during the year a horizontal stratification
called the thermal bar is set up in several
of the Great Lakes. This phenomenon does
not persist for more than a few weeks and
the associated current structure is of
negligible magnitude. An analytical model
which reproduces some of the features of the
thermal bar is given by Brooks [7].
The vertical diffusion coefficient, E ,
is in general a function of the inputs of
energy by wind stress on the water surface
and of the local stability of the
temperature distribution [8,9], Near the
water surface, the vertical diffusion
coefficient, E, is large because of wind
action, and a well mixed surface layer is
found in most lakes. 'The thermocline is
a consequence of the gravitational stability
damping out wind induced turbulence.
However, during periods of heat loss from
the water surface, unstable temperature
distributions may generate mixing and result
in thermocline erosion or overturning of the
lake as in the late fall.
129
-------
c. The heat source, S.f is usually composed of
the following components:
a) solar radiation absorbed at the '
water surface ,
b) solar radiation absorbed within
the water body :
c) lateral inputs of heated or colored
water, either natural or man-made
(usually power plant discharges)..
s
In summary, thermocline formation is at a reasonably well
developed stage with a variety of analytical and:numerical
models available as summarized in Table 11. To date, most
applications have been made to small lakes. The!models
depend on observed data to establish the vertical dispersion
coefficient, although some progress has been made to relate
the vertical dispersion coefficient to wind and lake physical
characteristics. Typically the horizontal variations are
neglected, and only the temperature distribution; as a
function of depth and time is the object of the analysis.
The seasonal time scale is usually considered, although a
diurnal model has been investigated [10]. The seasonal
models have been verified in a number of cases for reservoirs
and small lakes, but no detailed Great Lakes data has been
analyzed.
The thermal bar phenomenon, which is peculiar to 'large lakes,
has been observed to occur and last for a few weeks [11].
During this time it has an effect on the horizontal mass
transport near the shoreline. It is essentially1 a vertical
thermocline which then merges with the normal thermocline.
An analytical model has been proposed [7,12,13] which exhibits
the features of the thermal bar; and realistic models of near
shore transport which are conce'rned with weekly variations
during the period of the thermal, bar should consider this
phenomenon. No Great Lakes applications have yet been
attempted. <
130
-------
' , TABLE 11
CHARACTERISTICS OF THERMAL MODELS
Investigators
Harleman,et.al.
[3,4,5,15,16,17]
Analytical
Numerical
Wind Stress
Variable E >\.
Mixed Surface Layer
Arbitrary Geometry .
Arbitrary Heating'.
Absorbed Radiation
Lateral Inflows '
Power Plant'Dynamics
Verifications
x
X
X
X
X
X
X
Orlob,
et.al.
[2,21]
x
x
x
x
x
x
X
Sundaram,et.al,
[6,18,19,20]
x
X
x
X
131
-------
Thermal discharges entering the lakes constitute an input of
heat, which may substantially affect the thermal regime of
the near shore. Models for temperature distributions in
lakes have been proposed, and in some cases, verified [14],
The development of .'thermal models can be either
straightforward or very difficult depending on whether the
thermal discharge being considered substantially modifies
the velocity and dispersion characteristics of the water
body. The local velocities and dispersion are surely
modified, but whether a substantial modification occurs at
larger spatial scales is the key issue. If not, and this
is the conventional assumption, models can be and have been
constructed based on conservation of energy. If so, only
complex numerical1'models which are currently being
constructed offer:hope for a solution. As discussed in the
hydrodynamics modeling review, models of this sort have been
constructed for oceanic circulation and are currently being
contemplated for Great Lakes applications during the
International Field Year on the Great Lakes.
Evaluation of Model Status
Model Availabilityi'. Models are available for seasonal
thermal phenomenon.although they have been applied primarily
to small lakes and reservoirs. The vertical distribution of
temperature has been the primary concern since in this case
the buoyant forces are a significant factor. The physics of
this phenomenon is well understood although details of the
turbulent structures are still a matter of investigation.
Models for the distribution of waste heat have been proposed
and applied, although not to a Great Lakes situation directly.
Comprehensive models which include the equations of fluid
motion as well as' conservation of heat energy are in the
process of development.
Data Availability. Temperature data for detailed modeling
of thermocline development in the Great Lakes is available
for each of the lakes to some degree. Extensive data for
132
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Lake Erie has been collected during Project Hypo and is being
collected during the International Field Year on the Great
Lakes for Lake Ontario. Temperature distributions which
result from individual waste heat inputs are also available
as part of surveillance monitoring which is currently being
conducted.
Model Verification. Vertical thermocline models have been
verified in smaller lakes and reservoirs, but no Great Lakes
applications are yet available. Horizontal temperature >
distribution models have also been verified in non-Great
Lakes applications.
Model Application in Planning. Great Lakes applications are
lacking; however, applications elsewhere have been made in
the design of 'detailed diffuser devices and in the assessment
of their effect on the receiving water [22].
133
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REFERENCES
Burns, N.M., Ross, C., Project Hypo, CCIW (February 1972).
Orlob, G.T., Development of_ a_ Mathematical Model for Pre-
diction of Temperatures in Deep Reservoir, Water Resource
Engineers~7 Walnut Creek, California (1966).
?.
Dake, J.M.K., and Harleman, D.R.F., An Analytical and Ex-
.perimental Investigation of Thermal Stratification in Lakes
and Ponds, M.I.T., Department of Civil Engineering, Ralph
M. Parsons Laboratory for Water Resources and Hydrodynamics,
Technical Report, No. 99 (September 1966).
F41
Dake, J.M.K., and Harleman, D.R.F., "Thermal Stratification
in Lakes - Analytical and Laboratory Studies," Jour. Water
Resources Research, Vol. 5, No. 2 (April 1969).
* Huber, W.C., and Harleman, D.R.F., Laboratory and Analyti-
cal Studies of_ the Thermal Stratification of_ Reservoirs,
M.I.T., Department of Civil Engineering, Ralph M. Parsons
Laboratory for Water Resources and Hydrodynamics, Technical
Report No. 112 (October 1970).
" Sundaram, T.R., et.al., An Investigation of the Physical
Effects of Thermal Discharges into Cayuga Lake, Cornell
Aeronautical Laboratory, CA: No. VT-2616-0-2 (November
1969). " '
* Brooks, I., and Lick, W., "Lake'Currents Associated with
the Thermal Bar," Proc. 14th Conference Great Lakes Re-
search (1971) .
r 81
1 Li, Ting Y., "Formation of Tfrermocline in Great Lakes,"
Proc. 13th Conference Great Lakes Research (1970).
r g -I
Li, Ting Y., "Maintenance of Thermocline in a Stratified
Lake," Proc. 14th Conference for Great Lakes Research,
University of Toronto, Toronto, Canada (1971).
134
-------
REFERENCES
(continued)
Foster, Theodore, D., "A Convective Model for the Diurnal
Cycle in the Upper Ocean," J_._ Geophysical Research (76)3
(January 1971) .
j
Rodgers, G.K., "The Thermal Bar in the Laurentian Great
Lakes," Proc. 8th Conference Great Lakes Research (1965)<
n 21 ;
L JElliot, G.fXElliot, J., "Small-Scale Model of, the Ther-
mal Bar, Proc. 12th Conference Great Lakes Research,
Great Lakes Research Division (1969).
-"Elliot, G., Elliot, J., "Laboratory Studies on the Ther-
mal Bar," Proc. 13th Conference Great Lakes Research,
Great Lakes Research Division, Part 1 (1970).
f 141 '
Csanady, G., "Waste Heat Disposal in the Great Lakes,"
Proc. 13th Conference Great Lakes Research, Great Lakes
Research Division, Part 1 (1970).
i
Markofsky, M., and Harleman, D.R.F., A Predictive Model
for Thermal Stratification and Water Quality in Reser-
voirs ," M.I.T., Department of Civil Engineering, Ralph M.
Parsons Laboratory for Water Resource and Hydrodynamics,
Technical Report No. 134 (January 1971).
Ryan, P.J., and Harleman, D.R.F., Prediction p_f the An-
nual Cycle of^ Temperature Changes in a Stratified Lake
or Reservoir"7 M. I.T., Department of~cTvil Engineering,
Ralph M. Parsons Laboratory for Water Resources and Hy-
drodynamics, Technical Report, No. 137 (April; 1971).
r 171
Huber, W.C., Harleman, D.R.F., and Ryan, P.J., "Temper-
ature Prediction in Stratified Reservoirs," J1. Hydraulics
Division, Am. Soc. Civil Engineers, 98(HYA) p 645 (April
1972). | : . / .
135
-------
REFERENCES
(continued)
f 181
Sundaram, T.R.', and Rehm, R.G., "Formation and Mainten-
ance of Thermoclines in Stratified Lakes Including the
Effects of Power Plant Thermal Discharges," AIAA, 8th
Aerospace Sciences Meeting, N.Y. (January 19-21, 1970).
rig i
L Sundaram, T.R., and Rehm, R.G., "The Effects of Thermal
Discharges on the Stratification Cycle of Lakes," AIAA
9th Aerospace Sciences Meeting (January 1971).
Sundaram, T.R., Rehm, R.G., Rudinger, G., and Meritt,
G.E., A Study of_ Some Problems cm the Physical Aspects
of Thermal Pollution, Cornell Aeronautical Laboratory,
CAL No. VT-2790-A-1 (June 1970).
Or lab, G. T., Development of_ a Mathematical Model for
Prediction of Temperatures in Deep Reservoirs, Water
Resources Engrs., Walnut Creek, California (1966).
f221 :
Harleman, D.R.F., Stolzenback, K.D., and Jirka, G., A
Study of Submerged Multi-port Diffusers with Applications
to the~Shoreham Nuclear Power Station, M.I.T., Depart-
ment of Civil Engineering, Technical Report (June 1971).
136
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Lake Circulation and Mixing Models
Problems and Scope
This modeling section presents a portion of the overall
hydrodynaraic system and includes the general circulation of
the Lakes (both steady and time variable), transient motions
leading to variable lake levels, and the random and smaller
scale motions resulting in lake mixing or dispersion. The ^
general hydrological system including water balances, lake
level forecasting, and climatological effects are considered
in a preceding subsection. Lake circulation is assumed to
incorporate the mean, i.e., the relatively large-scale
(lake-wide), approximately organized motions that generally
vary seasonally. ;Mixing and dispersion are considered as
the results of random movements of smaller spatial-temporal
scales.
The importance of;understanding and predicting water movements
in the Great Lakes is expressed in two fundamental ways.
First, water movements and lake level fluctuations directly
impact such problem contexts as flooding, shore line erosion,
and harbor and channel improvements. Second, the general
circulation and changes in water level are important input
information for many other aspects of the limnological
systems, such as water quality, eutrophication, and general
ecological models. These interactions occur principally
through circulation, mass transport of water, and lake mixing
and dispersion processes. The overall role and the importance
of the hydrodynamic modeling framework are schematically
depicted in Figure 15.
There are a variety of time and space scales associated with
the general interactive scheme shown in Figure 15. The direct
impact of the hydrodynamic modeling framework on water resource
problems is concerned with shoirt term transient phenomena such
as wind setup and; wave action during storms. Such transient
forcing functions; .also play important roles in the general
lake circulation.: Seasonal variability in circulation coupled
with variable density effects is an important time scale in
the interaction of circulation models and other limnological
137
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PROBLEMS
U!
CD
, .- . ...
HYDRODYNAMIC
MODELING
FRAMEWORK
LAKE
LEVEL
- FLUCTUATIONS
LAKE
CIRCULATION
LAKE MIXING
&
DISPERSION
i
i
INPUT
FL(
SH
CH
HA
DODING
ORE LINE EROSION
ANNELIZATION
RBOR CHANGES
MODELS
CHEMICAL
EUTROPHICATION
ECOLOGICAL
WATER QUALITY
FIGURE 15
ROLE OF HYDRODYNAMIC MODELING OUTPUT
-------
systems. Finally, quasi-steady-state circulation and mixing
patterns, usually thought of as occurring within a seasonal
time frame, can also be significant inputs to subsequent
limnological models.
Space scales of interest extend from general lake-wide
circulation scales to scales characteristic of the nearshore
area to harbor circulation or regional water movements. As
with other modeling frameworks, the problem context often
dictates the time-space scale of importance. However, as
discussed further below, the time-space grid of some
hydrodynamic modeling efforts may be at a considerably finer
scale than that' required or even possible for the other
limnological modeling. Such fine grids are often occasioned
by computational necessity rather than by the nature of the
problem under consideration.
In contrast to some other modeling contexts discussed in
this section, the subject of water movement and Great Lakes
circulation has been the subject of a considerable amount of
scientific literature over the years. The subsections which
follow are intended as an overview of the state of the art
followed by an evaluation of the status of circulation
modeling.
Modeling Framework
There are two primary forcing functions leading to water
movement in the Great Lakes: (a) wind stress on the water
surface and (b) density differences resulting from heat
transfer through the water surface. The motions resulting
from these inputs are further modified, depending on the
time-space scale, by the rotation of the earth, bottom
topography, shoreline configuration, and river inflows.
Field observation and analytical and numerical modeling
studies have permitted a general" description of the lake
circulation. The wind as the primary forcing function sets
up large-scale mass movements in the Great Lakes in all
seasons. The character of these motions varies strongly
with the density distribution in the lake, so that there are
pronounced seasonal differences in flow regimes. Early in
139
-------
the spring, the lakes are typically homogeneous and their
motions are dominated by seiches as modified appropriately
by friction. During the spring warm-up period, a warm ring
of water surrounds a cold core with a primary circulation
in geostrophic equilibrium (a balance between Coriolis and
pressure forces) , a secondary flow with sinking near the
4°C isotherm, and seiches and internal oscillations of the
spring thermocline superimposed on this pattern. ' In the
summer, the baroclinic motions (resulting from intersecting
isobaric and density surfaces) give rise to strong coastal
jets accompanied by upwelling or downwelling near shore.
There are also a number of near-inertial oscillations (which
dominate curren^ velocities at midlake) , while seiche
movements are present during other seasons. The irregular
topography of the lakes and fluid and boundary friction
complicate the picture even further: topography controlled
gyres are presumably present under certain conditions,
although there is no permanent steady-state current pattern
(of appreciable amplitude) present. A complete and wholly
satisfactory synthesis of the lake movements does not yet
exist. However, within the framework of the general fluid
flow equations, various portions of the problem have been
explored in detail. All, however, begin from the generalized
equations of motion. ; .
One form of the equations for the general hydrodynamic
modeling framework, which is sufficient for a starting point
in this discussion, is: > '
Z" + u^± + v^ + w^ = _i ^Ji + f v + p (1)
dt ox dy dz P dx :X
3v 3v 3v 3u _ 1 3p ,. -p
Tt ?>c ^v 3~z p 3v v
9w , 8w 3w , 3w 1 3p , ' ,_.
Tt-7- + u^j + v-,r + w-^ = Tr-^+g + F.. (3)
3 1 ox. dy dz- pdz.^ z
140
-------
+ QT (5,
P = f(T, p) (6)
where x, y, and z are the spatial coordinates (z positive
downward), t is time, u, v, and w are the x, y, and z
components of the velocity, p is the pressure, p is the fluid
density T, is water temperature, g is acceleration of gravity,
f is the Coriolis parameter, K , K , and K , are components
' j>> y^ iLt
of the heat dispersion coefficients, and F , and F , and
F represent other forces in x, y, and z directions and
incorporate eddy.viscosity and wind stress components.
Equations (1), (2), and (3) express the conservation of
momentum, Equations (4) and (5) are the continuity (mass
balance) equations for the fluid and temperature,
respectively, and Equation (6) is an equation of state
relating the density, temperature, and pressure fields.
Even though Equations (1) through (6) do not include all
possible effects land associated mathematical terms, they are
still difficult to. deal with numerically and impossible to
handle analytically. The framework is, therefore, often
reduced considerably in complexity by a series of assumptions
depending on the.problem context.
Further, the frictional terms are considered at several
levels of complexity ranging from simple linear friction to
more complicated non-linear.forms or by assuming that
friction is proportional to the horizontal Laplacian of the
velocity. Density effects are either ignored (homogeneous
water body) or incorporated indirectly. Some large models
attempt to compute the density-field simultaneously with the
velocity field. ; The handling of boundary conditions at the
lake surface, the. bottom sides, and islands also bears
heavily on the final form of the complete equations and
available methods of,solution. It is clear, then, that
while one can write the equations that theoretically
represent the flow, field.under any conditions, the actual
141
-------
implementation of the equations is not direct, and various
simplifying assumptions must often be made. In the
historical development of Great Lake circulation models,
therefore, the first efforts began with.simplified forms
of the Equations >' (1) through (6) which could be studied
analytically. The analytical studies continue to increase
understanding of:lake circulation and have also provided
information as to which terms in the governing equations
need to be retained and how the solutions may best be
obtained numerically.
Although Equations (1) through (6), in theory, permit the
description of all.fluid movements in time and space, and
hence should produce output that directly reflects
dispersion effects, this is generally not possible in
practice. Therefore the handling of mixing and dispersion
of water has generally been through externally supplied
sets of dispersion coefficients, as in Equation (5), rather
than through attempts to compute such effects internally.
Some recent models,, however, do carry out such internal
computation.
State of the Art;
As indicated above, one can proceed in many directions from
the basic.Equations (1) through (6). In the Great Lakes the
progression has generally been from the analytical formulation
and solution to the numerical simulation, the latter usually
incorporating moire non-linear and topographic effects. In
order to summarize the work that has been done to date, it
is convenient to! group the efforts as follows:
A) Steady-state
B) Transient
1) Homogeneous
2) Stratified
1) Homogeneous
2) Stratified
Within these four categories, the work can be further divided
into three sub-categories:
142
-------
a) theoretical (analytical) studies,
usually based on a linearized theory
and simple lake models
b) numerical computer modeling
c) laboratory model simulation of entire
lake basins or of isolated phenomena
In addition, as often mentioned throughout this report, it
is important to review the field observations available for
each category to show to what degree evidence exists to
support conclusions resulting from the above modeling efforts.
Steady-state Homogeneous Models. Extensive literature exists,
especially in. the oceanographic field, on steady-state
circulation models. Much of the earlier literature did not
concern itself with lateral boundary problems. The models
proceeded from the simplest geostrophic case to more complex
numerical models. Thus, if in Equations (1) through (6),
assumptions of. a homogeneous density, non-accelerated,
fri'ctionless,. -linearized situation are made, the resulting
equations are simply:
fv
- 1 3D _
0 = TH- - fu
This approach
of magnitude
0 =-FTt
The horizontal motion resulting from these equations is the
simple geostrophic flow. By incorporation of the hydrostatic
equation, a very crude estimate of the fluid velocity can be
made if the density (temperature-pressure) field is known.
has been used by Avers [1,2,3] to deduce orders
(7)
of velocity and transport. It should be stressed,
of course, that the geostrophic estimates of transport are only
143
-------
grossly approximate. For example, Ayers [1] estimated a
transport of 473,000 ft3 per second across a section of
Lake Huron compared to an outflow of 216,000 ft3 per second
of the St. Clair River. This is about the order of
verification that can be expected, although, as discussed
below, other attempts to correlate geostrophic currents to
measured current in certain lake areas have been somewhat
more successful. Noble [4] has provided some evidence for
geostrophic circulation in Lake Michigan. It is generally
recognized, however, that models based solely on the
geostrophic approximation can be subject to large errors.
For any really serious modeling effort on lake circulation,
therefore, one must incorporate other effects into the
modeling framework which more realistically reflect the
prototype situations.
A more reasonable steady-state model incorporates wind stress
at the surface and places a bottom in the lake. Friction and
density effects are ignored. The equations then become [5]:
g = A
:)3x zo 2
= A
32v
fv
- ru
(8)
where the free surface is z = n(x,y) , the bottom is at z =
-h (x,y) and A is the coefficient of vertical eddy viscosity.
The boundary conditions are:
at
- o
at z -
(9)
u = 0 ; v = 0 at z = -h
where T and T are the components of the wind stress acting
on the lake surface. Analytical solutions exist for this set
of equations and permit evaluation of the behavior of the
144
-------
fluid field and surface under different wind stress
conditions. Some of the approaches used to obtain analytical
solutions are quite ingenious. For example, Welander [5] in
dealing with Equation (9) temporarily assumes 3n/3n as known,
obtains solutions for u and v in terms of 3n/3n,
-------
and H = H(x,y). H is the depth of water, T and T are
;" SX ^*jf
x and y components of surface wind stress and T, and T.
are the x and y components of bottom frictional stress. The
surface stresses are used as the forcing functions while the
bottom stresses are assumed to be linearly proportional to
volume transport. .Murthy and Rao applied this numerical
model to Lakes Erie, Huron, Michigan, and Superior. Grid
sizes varied from about 5 km across Lake Erie to 15 km in
Lake Huron.
Gedney and Lick [10,11] have constructed a steady-state
numerical model of Lake Erie assuming homogeneous conditions.
The approach is similar to that of Welander's [5] which is
discussed above. The vertical eddy viscosity is independent
of depth. Since Lake Erie is stratified during the summer,
the results are considered to apply only during fall, spring,
and non-ice winter conditions. Island geometry is
incorporated. A single equation for the stream function is
obtained from the vertically integrated continuity equation
and equation of motion. With the stream function calculated
numerically, velocity components and water levels can be
computed. In the; island region, a grid size of 0.3 km (about
2800 grid points):was used while outside the region, a 3.2 km
(about 2250 grid points) grid, was employed.
The Gedney-Lick study also represents one of the few attempts
to directly compare the velocity output from the model to
observed current information. Some current data on Lake
Erie were available from the Environmental Protection Agency
during spring and fall of 1964. Figures 16 and 17 show some
of these comparisons which, in general, agree qualitatively
and approximately quantitatively. In addition, for this
Feasibility Study, net velocity field in the Western Basin
of Lake Erie was computed from the Gedney-Lick output and
used in a chloride demonstration model. The results of this
computation, utilizing chlorides as a tracer which acts as
a verification of- the flow field", are quite good. The
analyses and results are discussed in detail in the
Demonstration Model. The results from these models show
large topography-controlled gyres, which are presumably
present in the lakes during months of nearly homogeneous
density distributions.
146
-------
Distance
. Current
magnitude
20 tO Miles
=&
0 -- 30 ~60 Kilometers
cm/sec
Current meter measurements
>fr 5/24/64
10/25/64
I cX S ^
SSS^^
Horizontal velocities at a constant 9.9 M(32.8 ft)from surface. Wind direction, W50S; wind magnitude,
10.1 meters per second(22.7mph); friction depth,27.4meters(90.0ft)-,rivers= Detroit, Niagara.
AFTER GEDNEY8LICK (II)
FIGURE 16
COMPARISON OF COMPUTED AND OBSERVED CURRENT MEASUREMENTS
-------
oo
Wind
40 Miles
60 Kilometers
0 20
Distance
0 30
Current O} fl/sec
magnitude f^ cm/sec
Current meter measurements
5/24/64
10/25/64
Horizontal velocities at a constant 14.9 M(49.2 ft )from surface. Wind direction,W50S-, wind magnitude,
10.1 meters per second (2-2.7mph);friction depth,27.4 meters(90.0ft);rivers:Detroit, Niagara.
AFTER GEDNEY 8 LICK (II)
FIGURE 17
COMPARISON OF COMPUTED AND OBSERVED CURRENT MEASUREMENTS
-------
Other numerical models of steady homogeneous circulation in
lakes have been constructed by Cheng and Tung [13] and Cheng
[14] using a finite element method of solution. This
computational approach has a distinct advantage over more
traditional methods of finite differencing in the handling
of boundary conditions. Thus, complicated lateral boundaries
or islands in the lake are readily incorporated. Numerical
results for transport in Lake Erie are qualitatively similar
to other work although no detailed verification is attempted.
V
Hydraulic models have also been constructed, and they provide
a means for estimating circulation in homogeneous water.
Rumer [15] has Constructed models of Lake Erie and recently
of Lake Ontario. The Lake Erie model has a horizontal length
scale of 1:200,000 and a vertical scale of 1:500. These
models again show the effects of topography similar to those
exhibited by the numerical models and also the effects of
river inflow and outflow. *
Field observations following periods of relatively steady
winds under homogeneous conditions indeed indicate gyres of
the kind predicted by numerical and physical laboratory
models, although the evidence is not quite conclusive. The
presence of opposite Ekman drifts in the surface and bottom
layers of Lake Erie has been shown by drift cards and bottom
drifter observations. Rumer's hydraulic model shows that
the inflow from the Detroit and Niagara Rivers tends to follow
the south shores of Lakes Erie and Ontario, respectively [16].
Verification of the numerical models has been generally
supported by observed surface current directions from drift
cards and bottles. Murthy and Rao [9] report good qualitative
agreement of their numerical circulation pattern with observed
drifts in Lakes Erie, Michigan, and Superior. For Lake Huron,
the authors consider the general circulation pattern agreement
remarkable. It should, of course, be added that most
observed motions in the Great Lakes are unsteady and the lakes
during important times of the year, from a limnological point
of view, are not homogeneous.
Steady-State Stratified Models. Analytical studies of steady
..state'circulation in stratified lakes have been published by
Csanady [17,18] and Huang [19].
149
-------
For example, Csanady [18] developed an analytical model based
on geostrophic flow along the shore in the warmer regions
during spring, which also conserves potential vorticity. By
dividing the nearshore region into two density regimes, the
basic features of observed phenomena are indicated by this
frictionless steady linear model. The analytical models,
therefore, predict baroclinic motions with a velocity maximum
close to shore (coastal jets). ;
i
During the early part of the season, only the nearshore >>
regions contain warm water; the inclined spring thermocline
separates this part from the rest of the lake. Baroclinic
motions of appreciable amplitude are predicted to ;be confined
to these nearshore regions by the theory. Later in the season
the thermocline is continuous across the lake except that it
may tip up or down near the shores where the coastal jets
are located. The water transport arriving by Ekman drift in
the shore zone is removed horizontally by the coastal jets.
The observed facts of a spring thermal regime in Lake Ontario
consisting of a thermocline surface of wedge or lens shape
in the shore zone and a summer regime characterized by tilting
of the across-lake thermocline are generally explained by some
of the above analytical models. Additional discussion of the
nearshore circulation is given below. ;.
A numerical model of flow in stratified bodies of water has
been constructed by Bennett [20]: a model lake consisting of
an infinitely long rotating channel in which all variables
are assumed independent of the long axis. A constant slope
region and a flat interior region are used.. The results are
similar to those obtained by the analytical models: an
inclined thermocline accompanied by a geostrophic current
near shore.
Laboratory studies by Elliot and Elliot [21,22] have shown a
friction-dominated circulation to be set up by surface heating
in a shore zone of a physical model of constant slope. This
is associated with a thermal structure similar to'< that
observed during the spring warming period (the thermal' bar) .
The circulation which results is essentially perpendicular
to the shore and involves sinking of water in the;neighborhood
of the spring thermocline and upwelling at mid-lake and near
the shores.
150
-------
From the point of' view of verification analyses, many of the
features of the modeling effort have been observed in the
Great Lakes. For example, Rodgers [23,24] has studied and
observed in great detail the motion of the thermal bar
during the spring. Figure 18 shows some of the field
results. The steady-state stratified models generally
provide similar results to those observed. A direct
comparison between observed currents and currents estimated
by a simple geostrophic calculation was made by Smith and
Ragotzkie [25] off the Keeweenaw Pensinsula in Lake Superior.5"
Computed current velocities reached 15 cm per second but were
generally less ;than 10 cm/sec. The normal component of the
measured currents was often 30 cm/sec in some parts of the
cross-section; and significant speeds extended down to 60 m,
the assumed level of "no motion" used in the geostrophic
calculations. While this work indicates the non-verification
of the simple geostrophic current, in this case it does
provide direct observation of the coastal jets predicted by
the above models..
j
A similar analysis of the coastal current of the south shore
of Lake Ontario has been made by Scott, et.al. [26]. For this
case, comparison ;of computed (geostrophic) and observed current
indicated good agreement. Average measured transport was 2.35
(km3/dav) compared to an average comouted transport of 2.26
(km3/day) . ,;
It appears that the circulation observed by Elliot and Elliot
[21] is also present in the real lakes, in the manner of a
secondary flow. ^Parallel to the thermocline surface there.
are geostrophic motions of considerable intensity, as may be
expected from theory, although the details are by no means
easy to interpret. Ragotzkie and Bratnick [27] have
demonstrated the prolonged existence of slow upwelling during
the summer in the middle of Lake Superior (which remains in
a "spring regime1' essentially all summer) . A detailed study
of flow in the coastal zone near Oshawa, Ontario has also
turned up a number of coastal jets [28].
While many of the observed features of lake circulation agree
with theoretical predictions of steady-state baroclinic models,
it should be noted that none of the above observed motions are
in fact steady. :
151
-------
SURFACE TEMP£«ATuneS
-S TEMPERATURE SECTIONS
FIGURE 18
PROGRESS OF THE THERMAL BAR FROM WINTER
TO FULL SUMMER STRATIFICATION
AFTER RODGERS (23)
152
-------
Time Variable Homogeneous Models. Transient motions of a
homogeneouslake(seiches)have been the subject of a large
number of analytical studies. One outstanding investigation
is that of Platzman [29] who studied wind tides of Lake
Erie. In basins the size of the Great Lakes, the effects
of rotation are noticeable in that high water rotates around
the basin counter-clockwise. Apart from this distortion,
seiches are mass-movements of water from one end of the lake
to the other. . One should add that the same seiches occur
also when the lake is stratified, only then they are
accompanied by other motions. There are an infinite number
of modes which seiches may take (depending on how they are
excited, i.e., what distribution of wind stress causes them)
but only the few lowest frequencies are of practical
importance. The periods of these are of the order of 10
hours in most of the lakes [30],
Platzman's work provides a great degree of analytical insight
to the behavior of transient motions and wind set-up in Lake
Erie. His model is essentially the classical Ekman wind
driven circulation model and incorporates vertical eddy
viscosity, Coriolis forces, pressure gradients, surface wind
stress, and bottom friction. A numerical differencing scheme
is used to compute model results for Lake Erie conditions.
Platzman also carries out an extansive verification analysis
of his model; as discussed below.
Other numerical and analytical studies of unsteady motions
in homogeneous .closed basins have also been carried out with
reference to' unsteady motions resulting from unsteady wind
stress. For, example, Paskavsky [31] has developed a numerical
model of Lake'.Ontario under a uniform density regime. His
model incorporates the non-linear field acceleration terms
such as: i .' .' -
:' '.-:" ' 2U L 3U
, . U-2 + VTT
x dy
bottom and lateral f.riction, and topographic and Coriolis
effects. '. ....
Simulations are conducted under transient wind fields starting
as a cyclonic, disturbance passing across the lake in an east
153
-------
to west direction in one day. Simulation results indicate
that during the early part of the storm passage, the direction
of the flow near the southern lake boundary becomes westerly
and later changes back to easterly. No verifications are
presented in this analysis.
Simple laboratory models with and without rotation have been
used extensively for demonstrating seiches. Physical models
of Lakes Erie, Ontario, and Superior have been used for this
purpose.
In terms of general verification of transient motions in
homogeneous bodies of water, the results appear quite good
especially with respect to comparison of observed and
computational water level data. For example, Figure 19 shows
a set of verifications from Platzman's work [29]. As
indicated, for this case, agreement is quite good. Indeed,
as noted by Platzman, the average coefficient of correlation
between computed and observed setup for all cases is 0.9.
Limitation on use of the dynamic prediction method rests
largely on the inability to accurately forecast the wind
fields.
A number of careful experimental studies have been made of
seiche periods; and such studies confirm theoretical results
by hydrodynamic calculations very well. For example, Table
12 shows some comparisons by Rockwell [30].
It is safe to say then, that the free barotrophic oscillations
in the Great Lakes are quite satisfactorily understood.
However, verification analyses need to be done on the general
time variable current structure in the lakes during times of
homogeneous density.
Time Variable Stratified Models. Transient motions in simple
stratified lake models have been studied analytically by
Csanady [32,33,34], Birchfield - [35], and Johnson and Mortimer
[36]. A sudden burst of wind sets up a series of long
baroclinic waves of two kinds: Poincare waves which have a
frequency barely above the inertial frequency and Kelvin
waves which are much slower. The Poincare waves occupy the
whole basin and cause particle motions essentially in
inertial circles. Kelvin waves are shorebound and produce
154
-------
i _t i _e^ »
. Gc'CiHfl
1) 20
y o
.3
22 }}
lO
s
KO
-1
IS 1C 1) II IS
20 21 22
Ul
Ln
f 28
IT IB
>i :o 21 22 21
- 3/
:!^3f:x
n
ksTsTl
13
1_
I11S
Till
.... i .
I (hc.lvy ctirvc-i) anrl coinp;itc.l
in Cases' 30 ar.vl -tO inJ
ClSf 10
20 |l 22
.n'rvvi) ll.ii(7.il(,.|iiH1u<.*r(.!oiIo iO(-«;i. Dotlcd pottioiis of clj-XTvcd !^t-up curves
nl luliluiir-ii o.' d.ii.i .11 Mour.'C for mtusnij Toledo J.Ka.
FIGURE 19
OBSERVED AND COMPUTED BUFFALO MINUS TOLEDO SET UP
AFTER PLATZMAN (29) "-
-------
; . TABLE 12
COMPUTED AND OBSERVED PERIODS OF THE
FIRST:FIVE MODES OF LONGITUDINAL FREE
..OSCILLATION OF LAKE MICHIGAN
X
'(Adapted from Rockwell [30])
Mode Computed (hours) Observed (hours) Error %
1 8.83 9.0 - 1.9
2 4.87 5.2 - 6.3
I
3 3. S3.. 3.7 " -4.6
4 2.85 3.1 - 8.1
i
5 2.39 2.5 - 4.4
156
-------
a flow structure practically indistinguishable from the
coastal jets of the steady-state models, except that they
have a wave-like amplitude distribution along the basin
perimeter. One should note again that these baroclinic
motions associated with intersecting density and pressure
surface occur side by side with barotrophic seiches (where
density and pressure surfaces remain parallel) producing a
quite complex total response in a stratified lake. One
important practical conclusion is that a stratified lake
extracts much more energy from the wind than a homogeneous
one.
Large numerical' models of unsteady motion in stratified
waters have been constructed by oceanographers. For example,
West [37] has developed a two-layered prognostic model of
the circulation in the Gulf of Mexico. Each layer includes
horizontal and vertical momentum exchange, Coriolis effect,
and non-linear advection of momentum. Bottom topography is
included but wind effects are excluded, the primary function
being the inflow through the Yucatan Strait. Surface and
internal gravity waves are filtered out by several
approximations. The model is spun up to a steady-state
which is then used as an initial condition. A one year
prediction is then made of the baroclinic and barotrophic
modes of circulation in the Gulf using a seasonally varying
input flow., The spin-up process takes about 3 hours of
CDO6500 CPU time while the 360-day prediction takes 10 hours
which "explains why a parametric study was not pursued..."
[37]. The spatial grid used in this study was 20 km on a
model size of 1420 x 800 km or a total of about 2800 grid
points. The time;step is approximately 1.5 hours, the
circulation predicted by the baroclinic model has the same
basic features as the observed data in the Gulf of Mexico.
The barotrophic mode of the circulation could not be
verified because of a.lack of data. ' Similar models have
been constructed of the North Pacific Ocean [38], the Indian
Ocean (which includes monsoon effects), and the North
Atlantic [39].
A rigid three-dimensional finite difference grid was used
by Friedrich [39] .who developed a 14-layer non-steady model
of ocean circulation,' including temperature and salinity
157
-------
effects, based.on the work by Bryan [40], and tested in the
North Atlantic Ocean. A period of 80 years was simulated
using a 5° grid, followed by 70 years using a 3° grid. A
time step of 2.22 hours is used for the 3° grid computations.
A grid of 26 x 37 horizontal cells and 14 vertical layers
(a total of 13,468 cells) requires nine seconds .of computer
time per time step on the UNIVAC 1108. Consequently, more
than 10 hours of computer time are required to simulate one
year of real time. This points out the present limitations
of three-dimensional models, in general. These limitations
make it extremely expensive to test such models and to perform
sensitivity analyses to evaluate the importance of various
parameters.
For the Great Lakes area, Simons [41] has formulated a three
dimensional solution of the hydrodynamic equations, based
on vertically .integrated equations for each layer. The model
is being tested at present in Lake Ontario, initially using
a 5 km horizontal grid. A time setup of one minute is used.
It is interesting to note that Simons concludes from his
initial work with a homogeneous model that the effects of
non-linear acceleration terms do not seem to be significant
enough to justify their inclusion in tns model.
From a verification viewpoint, detailed comparisons between
model output and observation has generally not been possible.
As indicated several times above, however, numerous features
generated by the models such as coastal jets, tilting of
thermoclines,- and approximate order of magnitude of current
speeds and directions are observed in the prototype.
There is extensive evidence for the existence of Poincare
waves during summer condition in the Great Lakes. Mortimer
[42,43] has reviewed this evidence and interpreted it in
terms of the theoretical concepts. Away from the shores,
currents are produced mostly by Poincare waves during the
summer, while close to shore more persistent velocities
occur. The temperature structure of Lake Michigan, in
particular, shows the presence o'f both Poincare and Kelvin
waves quite clearly. Similar conclusions follow from the
Lake Ontario observations of Csanady [28]. The latter study
also shows the presence of near-inertial oscillations during
the spring period with the thermal bar present.
158
-------
Near-Shore Circulation. The primary reason for singling out
the nearshore zone for special attention is, of course, the
concentration of human activity with the associated waste
residuals. However, there is also a scientific reason as
discussed above. The shore zone is a singular region on
several counts: the Ekman drift arriving from midlake has
to accommodate itself to the presence of the shores, while
the depth of water reduces gradually to zero. Under summer
and spring conditions, it has already been indicated that a >>
peculiar thermocline structure develops in the shore zone
(see Figure 18) which may be accompanied by coastal jets.
Thus one may legitimately describe the coastal zone (of some
10 km width) as a boundary layer of greater than usual
complexity. The relatively small width of this layer also
means that inertial forces cannot be neglected in it (linear
theory is not applicable except as a crude approximation).
All the forces: wind stress, Coriolis force, pressure
gradient, friction, and inertial forces play an important
role. An additional complication is caused by surface waves
arriving from midlake, usually at an oblique angle against
the shore. Their momentum parallel to the shore causes
longshore currents in a beach-zone (of at most a few hundred
meters width).
It is possible to focus on phenomena in a shore zone, ignoring
the lake-wide circulation, except insofar as it causes an
inflow of mass (Ekman drift) or of momentum into the shore
zone. A well known theory of this type is that of edge-waves
along a sloping shore [44]. In a shore-zone model of
constant slope (usually of order 10 2 to 10 3), wave-like
modes of motion are found to exist. These are trapped at
the shores in the sense that they decay exponentially with
distance from shore.
The baroclinic Kelvin wave, which was discussed above in the
lake wide context, is also such a trapped wave in a basin
with vertical boundaries. In a more realistic shore-zone
model containing a sloping beach", many baroclinic Kelvin type
waves are possible [34]. These all have long wave-lengths
(comparable to basin dimensions) and their frequency is quite
low, a small fraction of the inertial frequency.
159
-------
Thus, given the otherwise rapid variation of flow structures,
their velocities are nearly in geostrophic equilibrium.
Kelvin waves in the Great Lakes are not possible if the water
is homogeneous because the basins are too small or, putting
it another way, the propagation speed of surface.seiches are
too fast.
Edge waves and Kelvin waves are both transient motions even
if the latter appears steady. Strictly steady baroclinic'
currents (coastal jets) have also been found in theoretical ^
studies of shore zones [34]. These are similar to the
coastal jets in basins with vertical shores, but are displaced
shoreward. Their driving mechanism is the influx of water
from midlake.
All the above theoretical conclusions were derived from
linearized theory. However, the Rossby number based on the
width-scale of shorebound currents is often in the order of
unity, which means that inertial forces are not negligible.
The physical mechanism involved is quite simple: when water
drifts from midlake into a strong coastal current, some
considerable convective accelerations are exerted. .
Bottom friction must play an important role, at least in the
shallower parts of the coastal zone. These effects have
already been referred to in connection with some( lakewide
theoretical models involving friction (a frictional
boundary layer). Elliot's [21] laboratory model also shows
a frictionally controlled (thermally induced) circulation.
There has been, however, no theoretical (analytical).attempt
to describe the structure of coastal currents subject to
friction in a sloping shore zone.
The theory of longshore currents in a beach zone, generated
by incident wave-trains, has been treated recently by Longuet-
Higgins [45] and others. The component of the momentum
transport by the waves parallel to the shore causes a radiation
stress in the same direction, which maintains a longshore
current against the "force of friction. The current is
concentrated on the inshore side of the breaker .line and its
velocity is proportional to wave orbital velocities (but is
about one order of magnitude less). Under conditions typical
of the wave climatology of the Great Lakes, namely, during
160
-------
major storms when wave heights are of the order of 5 meters,
the longshore currents are only rarely comparable to other
lake currents (10 cm/sec or more). Also, these currents
are confined to a smaller inner portion (order 100 m width)
of the coastal zone. The mass transport they cause is
nevertheless very important from the point of view of
sediment movement and presumably also for the initial
transport of pollutants from small sources offshore or of
any pools of effluent trapped along the shore.
h
Most experimental studies of shore zone currents are based
on continuous records of one or a few moored current meters.
Statistical analysis of long records obtained in this manner
provides some valid data on current climatology, but gives
very little information on nearshore circulation patterns.
A good recent study of this kind is that of Birchfield and
Davidson [46] which shows the considerable differences
between nearshore and offshore currents. Some more detailed
studies have been reported by Smith and Ragotzkie [25] and
Csanady [28] from'Lake Superior and Lake Ontario, respectively.
The Lake Ontario.; data in particular shows clearly the
existence of a distinct shore zone of approximately 7 km
width, in which the water movements are more nearly persistent
(current like) than wave-like. Their complex structure could
be interpreted as the combined result of wind stress, Coriolis,
and non-linear accelerations as well as pressure and friction
forces. One important practical conclusion is that records
of one, or'even a few, moored current meters would be quite
inadequate to elucidate the details of the complex shore
current structure and could lead to some deceptive conclusions.
Summarizing this'discussion briefly, theory suggests that
there is a special nature in nearshore circulations where
a coastal boundary layer of rather complex characteristics
develops. Inflow of mass and momentum into this boundary
zone forces the circulation there, while several free modes
of motion (edge waves, Kelvin waves) are also possible. In
a narrow zone radiation., stress of surface waves sets up
longshore .currents over beaches.- Experimental data confirm
the complexity and.special nature of shore zone circulations
and demonstrate the inadequacy of point measurements of
currents.
161
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Mixing and Dispersion. The above discussion has centered
primarily around the regular, somewhat deterministic,
structure of water movements in the Great Lakes. For
certain applications, however, notably, attempts to describe
the paths and distribution of pollutants, attention must
also be focused on the random smaller scale oscillations
in fluid flow. These oscillations give rise to a mixing
and dispersion of.material discharged into the lakes. In
addition to tempo.ral changes in flow, spatial gradients
also contribute to the dispersive phenomena. As indicated
in the previous subsection, currents in the Great Lakes tend
to be concentrated in narrow bands around the boundary so
that there are strong velocity gradients at these locations.
Within the Ekmanlayer at the surface or at the bottom,
velocity varies both in magnitude and direction.
Another kind of mass transport by (nearly) steady motions
is that caused by.secondary flow of the type associated with
the spring thermocline. As indicated above, a confluence
(sinking) occurs'near the 4° isotherm. The cells of
secondary circulation inshore and offshore of this confluence
effectively produce large scale mixing. Semi-permanent
confluences have , been observed in the Great Lakes in other
places and other!times; all are, presumably, evidence of
secondary circulation of various sorts which produce mixing.
In wave-like motions,- particle paths are almost closed
curves. There is a second-order effect giving rise to a
net mass transport velocity (Stokes Velocity). This
residual velocity in surface waves has been studied in
detail, but not in Poincare waves, edge waves, or other long
waves common in the Great Lakes. Such wave-like motions
dominate the flow at least during the summer and outside the
shore zone where,.there is neither theoretical nor experimental
information on mass transport velocities.
The importance of wave-like motions in causing dispersion
is demonstrated by a' recent study of Ahrnsbrak and Ragotzkie
[47]. A simple diffusion-advection model is used to compute
the effective eddy diffusivities (or dispersion coefficients)
in Green Bay. Values ranges from 0.25-105 cm2/sec at the
southernmost end; of the Bay to about -3«106 cm2/sec at a
distance of 30 km. Northward, diffusivities decreased to
about 0.7-105 cm2/sec.
162
-------
The authors continue their analyses by using the output from
a numerical model of Green Bay circulation to independently
check the observed dispersion coefficients. The model used
takes into account wind stress, free oscillation in the Bay,
and a forcing function at the mouth of the Bay which is due
to the seiching of Lake Michigan. The eddy diffusivity is
assigned equal''.to the product of the root mean square
velocity residuals (due to seiche activity) and a time scale
(taken as one-half, the free period of the Bay) . Agreement
between diffusivities predicted from the model and the ^
observed results is quite good. The results, therefore, show
that seiche movements in Green Bay are responsible for the
observed decay of Fox River water concentration along the
axis of the bay. Seiche movements at this location are of
relatively large amplitude, and there is, of course, a
considerable variation of velocity between the bottom of the
bay and the surface. It appears that this velocity gradient,
coupled with vertical diffusion and the temporal variation of
seiche velocities, produces the relatively high longitudinal
diffusion.
The direct effects of turbulence in causing dispersion have
been studied experimentally and related to the classical theory
of turbulent diffusion in connection with dye plume and patch
observations [49,50], The problem is very similar to oceanic
diffusion in that the apparent diffusivity increases as the
size of the cloud grows, due to the increasing range of flow
nonuniformities encountered. For example, Murthy [50] found
that the 4/3 law. resulting from the similarity theory of
turbulence is.;suggested by dye diffusion studies in Lake
Ontario. His-results indicate that the_horizontal dispersion
coefficient (K). is given by K = (6 x 10 ^L1*'3 where K is in
cm2/sec and L:: in cm. A summary of some horizontal dispersion
coefficients obtained by different workers in the Great Lakes
is given in Table 13.
Vertical mixing in the Great Lakes has been found to be
generally quite small (2-3 orde'rs of magnitude less than
horizontal dispersion, i.e., approximately 1*102 cm2per
second) except;when there is strong momentum flux into the
water and/or heat flux into the air at the free surface.
Strong mechanical and/or thermal turbulence develops in the
latter cases and mixes the surface layer down to a sharp
thermocline. :Mixing across the thermocline also occurs (as
163
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TABLE 13
SUMMARY OF SOME HORIZONTAL DISPERSION
COEFFICIENTS IN THE GREAT LAKES
Area
Method
Approximate Range
(cm2/sec)*
Reference
Green Bay
Lake Michigan,
Lake Erie
Lake Erie,
Lake Huron
Tracer and
Circulation
Model
Drogues
Dye
100 - 200 10
3 - 5.5 10
3-4
10'
,05 - .03 10
47
48
49
Lake Ontario
Little Traverse
Bay
Lake Erie
Dye
Dye
Current
Meters
0.1 101* (100 m scale) 50
10 10* (10 km scale
.02 10" 51
.02 - 4.0 104 52
*10'* cm2/sec = .033 square miles/day
164
-------
demonstrated by the gradual sinking of the thermocline during
the season, mainly in September/October), but the exact
mechanism of this is not well understood. Some preliminary
diffusion experiments involving dye release below the
thermocline [53] have shown no measurable upward.diffusion.
Evaluation of Model Status
Model Availability. It is clear from the preceding discussion
that a great variety of models exists to describe circulation
and mixing in the Great Lakes. The models extend- from steady
state representations of the general circulation to numerical
analyses of time variable motions and include specific models
of near shore boundary phenomena under variable density
regimes. Models of water movement and dispersion in the
Great Lakes are in more plentiful supply than any other
component of the limnological systems and there is little lack
of fundamental knowledge. :
Data Availability. Relatively speaking, more is known about
circulation in the Great Lakes than many of the other
components in the limnological systems. This is the result
of measurements of all types (drift bottles cards,. bottom
drifters, current speed and and direction, temperature) made
over a period of many years, some work extending over 80 years,
From the many direct and indirect measurements (primarily of
surface currents), a broad picture of the general circulation
pattern during different seasons has emerged. It is true,
then, that for most long-term planning purposes,^ the general
lake circulation has been observed and is continuing to be
observed at a level sufficient for many limnological problem
contexts. .
There are data gaps, however, primarily in more 'local
transient situations. For example, reliable current
measurements in the Lakes have 'yet to be made on any large
scale of the coastal, jet effect and the nearshore (0-10 km)
circulation during thermal bar conditions. Also, although
some comprehensive current measurement programs (e.g., on
Lake Michigan) have been carried out from fixed buoy stations,
the data are not readily available. Measured current data
165
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of this type would be of significant value in verification
studies associated with simulation models. The present
International Field .Year on the Great Lakes effort will
provide valuable data for verification of hydrodynamic
models. '
Model Verification. In general, the models of circulation
and mixing have been compared to observed data, summaries of
data, or general qualitative descriptions. The comparisons
have indicated a reasonable degree of model veracity,
sufficient for many planning purposes. In some cases, the
verification analysis has been extensive (i.e., Platzman's
work), while in other cases only general features are
compared. For some modeling situations, its quite difficult
to obtain information that would verify model output due to
the physical difficulties of measuring current regimes in
large bodies of water. Also, some modeling structures
analyze only certain features of water movement (e.g.,
motions due to transient storms). A meaningful comparison
between model output and observed data would require an
extensive and intensive sampling program coupled with data
analysis to provide observed movement that could be compared
to model output. In general, however, verification of
hydrodynamic model output has been good to excellent and
many of the models can presently provide a strong basis for
limnological planning.
Model Application' in Planning. For planning purposes, models
of lake water movements have been applied primarily in lake
level forecasting; during storm surges. There apparently has
been little.direct incorporation of circulation modeling in
models of chemical and/or eutrophication problem contexts.
The demonstration* model discussed in this report shows an
example of the necessity of a verified circulation model
for planning problems associated with water quality and
eutrophication. It should be recognized, however, that
fluid flow calculation in almost all cases can be decoupled
from modeling activities of limnological problems. Thus,
although hydrodynamrc model output is often not included
explicity in the water problem contexts, it invariably
has been incorporated as sets of exogenous input generated
by other analyses..
166
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Finally, it should be.noted that additional significant
advances in hydrodynamic modeling are in the offing and
rely on the complete use of large computers for successful
implementation. .These advances will most likely be of
sufficient 'extent to answer many of the remaining loose ends
of circulation modeling, certainly with respect to planning
activities of the limnological systems. For example, within
a few years, it is entirely conceivable that a realistic,
synthesized model of lake circulation will be available and
will incorporate such features as: a) time variable wind
stress, b) realistic lake geometry including a nearshore
zone, probably on denser network of grid points, and c)
time variable density effects.
In conclusion, the present modeling structures for lake
circulation and mixing are well developed for planning
purposes. Furthermore, the historical interest in lake
water movements, coupled with a firm physical basis for
understanding the phenomena, has generated a momentum among
researchers' and modelers in the Great Lakes Basin. Such
momentum is probably sufficient to develop as complete a
modeling structure as would be desirable or necessary for
planning purposes for the next several years.
167
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REFERENCES
" Ayers, J.'C., "A Dynamic Height Method for the Determina-
tion of Currents in Deep Lakes," Limnology and Oceano-
graphy , Vol. No. 3 (July 1956) .
f21 ;
Ayers, J.C. et.al., Currents and Water Masses of Lake
Huron, Great Lakes Research Division, University of
Michigan, Pub. No. 1 (February 1956).
Ayers, J.°C.', et.al., Currents and Water Masses of Lake
Michigan, Great Lakes Research Divison, University of
Michigan, Pub. No. 3, p 169 (1958).
F41
1 Noble, V.E., "Evidences of Geostrophically Defined Cir-
culation in. Lake Michigan," Proc. 10th Conf., Great Lakes
Research, pp 289-298 (1967).
* Welander, P:., "Wind Action on a Shallow Sea: Some Gen-
eralization- of Ekman's Theory," Tellus, Vol. IX, pp 45-
52 (1957);.. !
" Birchfield. G. £., "Wind-Driven Currents in a Long Ro-
tating Channel," Tellus, Vol. 19, pp 243-249 (1967).
Birchfield, G. E., Wind-Driven Currents i_n a. Large Lake
2JL £ Small- Ocean, Report 70-6, Series in~Applied Mathe-
matics, Northwestern University (1971).
F 81 '
Janowitz, G.S., "The Coastal Layers of a Lake When Horizon-
tal and Vertical Ekman Numbers are of Different Orders of
Magnitude," Proc. 14th Conf. IAGLR (1971).
f 9 1 ': '
Murty, T.S-,,' and' Rao, D.R., "Wind Generated Circulation
in Lake Erie,. Huron, Michigan, and Ontario," Proc. 13th
Conf. IAGLR, pp 927-941 (1970).
168
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REFERENCES
(continued)
Gedney, R., and Lick, W., "Numerical Calculations of the
Steady-State Wind Drive Currents in Lake Erie," Proc.
13th Conf. IAGLR, pp 829-838 (1970).
* Gedney, R., and Lick, W. , "Numerical Calculations of the
Wind-Driven Currents in Lake Erie and Comparison with ^
Measurements," NASA Tech. Memo. X-67804, p 19 and figures
(April 1971).
f 12 1
Simons, T.J., "Development of Numerical Models of Lake
Ontario," Proc. 14th Conf. IAGLR (1971).
" Cheng, R.T., and Tung, C., "Wind-Driven Lake Circulation
by the Finite Element Method," Proc. 13th Conf. IAGLR,
pp 891-903 (1970).
f 141
Cheng, R.T., "Numerical Investigation of Lake Circulation
Around Islands by the Finite Element Method," To appear
in Int. J. for Numerical Methods in. Engineering, p 16 and
figures.
Rumer, R.R., and Robson, L., "Circulation Studies in a
Rotating Model of Lake Erie," Proc. llth Conf. IAGLR,
pp 487-495 (1968).
Howel, J., Riser, K., and Rumer, R., "Circulation Patterns
and a Predictive Model for Pollutants Distribution in Lake
Erie," Proc. 13th Conf. IAGLR, pp 434-443 (1970).
Csanady, G.T., "Wind-Driven Summer Circulation in the
Great Lakes," J. Geophys. Res_. , Vol. 73, pp 2579-2589
(1968).
"Csanady, G.T., "On the Equilibrium Shape of the Thermocline
in a Shore Zone," J. Phys. Oceanog., Vol. 1, p 92-104 (1971)
169
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REFERENCES
(continued)
r 191
1 JHuang, J.C.K., "The Thermal Current in Lake Michigan,"
J. Phys. Oceanog., Vol. 1, pp 105-122 (1971).
Bennett, J.R., "A Numerical Simulation of the Thermal
Bar," Proc. 14th Conf. IAGLR (1971).
Elliot, G.H., and Elliot, J.A., "A Small Scale 'Model of
the Thermal' Bay," Proc. 12th Conf. IAGLR, pp 553-557
(1969).
^22]Elliot, G.H., "A Mathematical Study of the Thermal Bar,"
Proc. 14th Conf. IAGLR (1971).
F231
L JRodgers, G.K., "The Thermal Bar in Lake Ontario, Spring,
1965 and Winter, 1965-1966," Proc. 9th Conf. IAGLR, Uni-
versity of Michigan, pp 369-374 (1966).
P41
l~ Rodgers, G.K., and Sato, G.K., "Factors Affecting the
Progress of the Thermal Bar of Spring in Lake Ontario,"
Proc. 13th Conf. IAGLR, pp 942-950 (1970). ;
[251 '
Smith, N.P. and Ragotzkie, R.A., "A Comparison of Com-
puted and Measured Currents in Lake Superior," Proc.
13th Conf. IAGLR, pp 967-977 (1970). -; .
r 261
Scott, H.T., Jekel, P., 'and Fenlon, M., "Transport in
the Coastal Current Near the South Shore of Lake Ontario
in Early Summer," Proc. 14th Conf. IAGLR (1971).
* Ragotskie, R.A., and Bratnick, M. , "Inferred Temperature
Patterns on Lake' Superior and Inferred Vertical Motions,"
Proc. 8th Conf. IAGLR University of Michigan,pp 349-357
(1965) .
170
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REFERENCES
(continued)
f 2 81 '
Csanady, G.T., Coastal Current Regimes in Lake Ontario,
to be published.
1291 ; '
Platzman, G.W., "The Dynamical Prediction of Wind Tides
on Lake Erie," Meteorological Monograph, Volume 26, p 44
(1963). ;
Rockwell, D.C., "Theoretical Free Oscillations of the
Great Lakes," Proc. 9th Conf. IAGLR, University of Michi-
gan, pp 352-368 (1966).
^Paskavsky, D.F., "Winter Circulation in Lake Ontario,"
Proc. 14th Conf. IAGLR, p 20 and figures (1971).
Csanadv, G.T'i. , "Large-Scale Motion in the Great Lakes,"
J. Geophys. Res.', pp 4151-4162 (1967) .
Csanady, G.T;. > "Motions in a Model Great Lake Due To a
Suddenlv Improved Wind," J_. Geophys. Res., 72, pp 6435-
6447 (1968)".
f 341
Csanady, G.Ty,, "Baroclinic Boundary Currents and Long-
Edge Waves in'Basins With Sloping Shores," J. Phys.
Oceanog., Vol. 1, p 92-104.
Birchfield, G.E., "Response of a Circulation Model Great
Lakes to a Suddenly Improved Wind Stress," J_. Geophys.
Res. 74_, pp 5547-5554 (1969).
°JJohnson, M.A., and Mortimer, C.H., Theory of Internal
Waves in Large Basins with Particular Application to
Lake Michigan, Spec. Report, Centre for Great Lakes
Studies, University of Wisconsin, Milwaukee (1971).
171
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REFERENCES
(continued)
[37] : .
West, R.T., "A Baroclinic Prognostic Numerical Model of
the Circulation in the Gulf of Mexico," Ph.D. Disserta-
tion, Texas A&M^University, p 66 and ix (May 1970).
^
[38]
O'Brien, J.J., "A Two Dimensional Model of the Wind-Driven
North Pacific,'" Investigation Pesquera, Vol. 35 (1) ,
Barcelona, pp 331-349 (February 1971) .
[39]
Friedrich, H.J., Preliminary Results from a Numerical
Multilayer Model for the Circulation in the North Atlantic,
UDC, 551.465.45, pp 145-164 (1969).
Bryan, K., "A Numerical Method for the Study of Ocean
Circulation," Jour, of Computational Fhys., Vol. 4, pp 347-
367 (1969). ;
[41]
Simons, T.J., "Development of Numerical Models of Lake
Ontario," Prcc.i 14th Conf. IAGLR (1971).
[42]
Mortimer, C.H.,!"Frontiers of Physical Limnology with
Particular Reference to Long Waves in Rotating Basins,"
Proc. 6th Conf.',. IAGLR, University of Michigan, pp 9-42
TT963) . | .
[4-1]
Mortimer, C.K./. Large-Scale Oscillating Motions and
Seasonal Temperature Changes' in Lake MjTchigan and Lake
Ontario7 Special Report No. 12, Center for Great Lake
Studies, University of Wisconsin, Milwaukee (1971).
172
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REFERENCES
(continued)
[44]
Reid, R.O., "Effects of Coriolis Force on Edge-Waves,"
J. Marine Res., Vol. 16, pp 109-144 (1958).
[45]
Longuet-Higgins, M.S., "Longshore Currents Generated By
Obliquidy Incident Sea Waves," J. Geophys. Res., Vol. 75,
pp 6778-6801 '(1967) .
\
[46] '."
Birchfield, .G.E. , and Davidson, D.R., "A Case Study on
Coastal Currents in Lake Michigan," Proc. 10th Conf.
IAGLR, pp 26.4-273 (1967) .
j
[47] >
Ahrnsbrak, W.F., and Ragotzkie, R.A., "Mixing Processes
in Green Bay," Proc. 13th Conf. IAGLR, pp 880-890 (1970).
Okubo, A., and Farlow, J.S., "Analysis of Some Great Lake
Drccue Studies," Proc. 10th Conf. IAGLR, pa 299-307
(1967) ;' , '
[49]
Csanady, G.T., "Turbulence and Diffusion in the Great
Lakes," Proc. 7th Conf. IAGLR, University of Michigan,
pp 326-339 (1964).
Murthy, C.Rl, "An Experimental Study of Horizontal Dif-
fusion in Lake Ontario," Proc. 13th Conf. IAGLR, pp 477-
489 (1970) . ''..-.:
Noble, V.E. > ..Measurements of Horizontal Diffusion in the
Great Lakes," Proc. 4th Conf. IAGLR, University of Michi-
gan, pp 85-95 (1961).
17.3
-------
REFERENCES
(continued)
[521
Palmer, M.D., and Izatt, J.B., "Lakeshore Two Dimensional
Dispersion," Proc. 13th Conf. IAGLR, pp 495-507 (1970).
Murthy, C.R., and Csanady, G.T., "Outfall Simulation Ex-
periment in Lake Ontario," Water Research, in press (1971)
174
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Erosion and Sediment Models
Problems and Scope
The water resource problems associated with erosion and
sediment-related phenomena on the Great Lakes include:
lakeshore erosion with reductions in property values and
utility, flooding of lakeshore areas, channel dredging
requirements for commercial and recreational craft, and
changes in the extent and character of fish and wildlife
habitat. In addition, there are problems associated with
channel dredging requirements and the impact of the dredged
sediment on habitat, which, while significant, are generally
associated with local conditions and are therefore not
considered in Type II planning activities.
The major lake-wide problems are associated with shoreline
erosion and local flooding. The Corps of Engineers is in
the process of studying the economic impact of lake level
regulation on flooding and erosion. This study utilizes
a model for ultimate water level calculations which is
described below.
Modeling Frameworks and State of the Art
Erosion. Prediction of wave .heights is a critical factor in
the evaluation of erosion and the design of facilities and
protective works. A great deal of research, centered in
Holland, has been performed .in the field. The size, shape,
and frequency spectrum of waves is a function of; the
induced wind turbulence, the duration of exposur'e, the
length of the exposure path or fetch, and the shape of
beach as it determines reflective energy additions. The
term "setup" is used to identify the incremental wave
height related to tilting of the lake surface from extended
exposure to low atmospheric pressure associated with storms.
Lake Erie, which is shallower than the other Great Lakes,
is more responsive to storm surges, and has been extensively
studied. :
175
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The classical calculation for storm surges on the Great
Lakes has been described by Platzman [1,2,3]. These dynamic
models are used by a number of agencies for safety analysis,
and are accepted by the United States Atomic Energy
Commission for'analysis of storm surges for nuclear plant
safety analysis. , Keulegan [4] has also made extensive
contributions to the analysis of drag forces involved in
determining the coefficient of wind stress and sea
roughness over Lake Erie. The United States Weather Bureau
currently uses;a regression method based on the work of *
Harris and Angelo [5] and described by Richardson and Pore
[6], The computer simulation using the statistical approach
is preferred by the Weather Bureau for operational reasons
which are principally related to inputs during stormm
conditions.
The state of the art in the analysis and prediction of beach
erosion, littoral drift, dune formation, and the development
of engineered structures which influence and control these
effects has been presented by the Corps of Engineers [7].
This compilation has been obtained from the worldwide
experience of the Corps in the development and management
of shorelines. It represents the basis for ths modeling of
beach conditions-with respect to water and wave motion.
Most of the established principles have been embraced by a
majority of investigators and, where exceptions exist, the
literature has; ample contributions from the Dutch and other
European sources which permit sophisticated modeling. A
number of studies [8,9,10,11] are available in the Great
Lakes which contain data that can or have been used for
initial model development and verification of shoreline
processes. :
A number of investigators, including the Beach Erosion Board
of the Corps of Engineers, have confirmed the use of Hunts'
empirical relation for application to a natural beach [12]:
;';' R = 2.3 T H tan a (1)
where:
R ': .= maximum'wave run-up
176
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T = wave period
H = peak to valley wave height
a = beach slope
The work of Battjes [13] has extended and confirmed the
application of Hunts' rule to various wave forms ranging
from steep sided to swell waves. In his summary of the
work, distributions of run-up of breaking waves are derived
by assigning to.'individual waves in an irregular wave train
a run-up value according to Hunts' formula. Explicit
expressions for the run-up are obtained for waves of which
the squares of heights and periods have a bivariate Rayleigh
distribution. The extremes of this distribution are
limiting cases for a young sea and a fully developed sea.
The actual transport of materials in an eroding shore
requires additional steps beyond the physical description
of wave form, run-up, and energy input information. Methods
for the estimation of beach transport have been made by a
large number of investigators as well as by the Corps of
Engineers who summarized the techniques [7]. A criticism
by some foreign investigators of the methods used to date is
that they are largely empirical and take into account
neither longshore currants nor the material size and slope
of the beach.
Bijker [14] has published the results of intensive
investigations to determine if longshore current and bed
roughness are related to the longshore transport. His work
represents the state of the art in the description of long-
shore transport.
Despite the large amount of dynamic and statistical modeling
of the details of beach and shore erosion, ultimate reliance
on the statistics of. shoreline regression is still required.
Mo general approach has been found having satisfactory
predictive capability for the many varying conditions
involved in shoreline erosion on the Great Lakes. In
general, where regular beach conditions prevail, excellent
177
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dynamic prediction of both physical run-up and transport are
possible. When irregular land formations and overhanging
cliffsides are involved, there are no known techniques to
predict undercutting and toppling of such features other
than long term statistics. In the latter case, observations
of Great Lakes shoreline contours have been under extensive
investigation for a long period of time, and the inventory
of beach regression information appears adequate to handle
most problems during the near term.
i,
Flooding. The term "ultimate water level" has been adopted
in the Great Lakes to designate an extreme water level
associated with'a storm on the lakes. The ultimate water
level calculation considers three phenomena. The undisturbed
water level which is a result of the hydrological balance
for the lake makes up one of the components of the ultimate
water level. This undisturbed water level is either a
measured value or it may be calculated employing one of the
lake level models described previously. Winds associated
with storms on the lakes cause the water surface of the lake
to tilt in the direction of the wind, lowering the water
level along the up-wind shore and raising the water level on
the down-wind shore. The third component of the ultimate
water level is the maximum vertical height of waves which
reach the shore and runup the beach.
The Corps of Engineers [15] has calculated ultimate water
levels for thirty-six significant reaches of the Great Lakes.
The ultimate water levels for a reach allows for average
conditions and actual levels may vary locally. Data from
fifteen water level gaging stations and sixteen weather
stations are used to determine storm water levels for
corresponding wind speeds and directions. The maximum
instantaneous lake level observations each month are adjusted
to constant conditions of water diversion and flow. The lake
surface tilt is then determined from analysis of the observed
information.
Wave run-up is calculated employing Equation (2):
R = 2.3 M T H~°'5 (2)
178
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where:
R = wave run-up
M = beach slope
H = wave height
The wave periods and wave heights are obtained employing
hourly wind data and equivalent fetch lengths in conjunction
with available deep water wave curves [7], Average wind
speed and direction are computed from hourly wind data at
each weather station for periods of one to twenty-four hours
duration before the time each storm water level is recorded.
Land station wind speeds are increased by a factor of 1.2 to
adjust the wind for overlake conditions. The Corps of
Engineers' calculations for wave height thus obtained
are compared to the maximum height of a wave that can be
sustained at the storm water level and water depth. The
lesser of the wave heights is used in Equation (2) to
calculate wave run-up.
The Corps of Engineers' calculation procedure (or model)
discussed above is used for a comparison of alternative lake
regulation systems and planning activities. There are a
number of limitations associated with the approach: short
period surges from squalls are not included in the analysis;
and in general, local phenomena, the amplitudes of which are
dependent upon local beach and shoreline configurations, are
not included in the model.
The Corps of Engineers' model for calculation of ultimate
water level has been used in the comparison of lake
regulation plans. This model employs observed data on the
Great Lakes in conjunction with empirical curves developed
for marine conditions. There has been no independent
verification of the -model reported to date. The Corps'
model deals with broad scale regional conditions. The lack
of verification has been recognized in application of this
model; however, the model is employed primarily to develop
comparisons between alternative regulation schemes. The
179
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absolute output from the model in terms of ultimate water .
levels should, as indicated by the Corps, be used with
extreme caution. This is because of the lack of verification
and the fact that the model does not include the effect of
short period surges and local phenomena.
In spite of the limitations that are associated with the
existing ultimate water level model, it represents one of
the few applications of models and computational procedures
to planning and problem evaluation on the Great Lakes. The T.
lake level model and the ultimate water level model are used
together in this planning process, and they are both
adequate to meet present planning needs in the Great Lakes.
Evaluation of Model Status
Model Availability. The shoreline erosion process has not
been modeled in detail on the Great Lakes. However, the
Corps of Engineers has developed a very broad scale shore-
line erosion model which enables examination of the :economic
impact of alternative lake level regulation plans on lake
shore erosion. :. . .
Data Availability. Some data are available on shore line
erosion and could provide a beginning data base for a more
detailed analysis of this problem. Significant additional
data collection would ba required for an adequate, formulation
and verification of detailed erosion models.
Degree of Verification. The existing model is'not-verified
from the standpoint of direct physical measures of erosion.
However, the model does use available physical data and
economic information. Because of the broad scale nature of
the existing modeling effort, lack of verification does not
appear to be a significant impediment.
Planning Application-. The existing modeling effort appears
to adequately meet present broad scale Type II planning needs,
180
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REFERENCES
Platzman, G.W., "A Numerical Computation of the Surge of
26 June 1954 on Lake Michigan," J. Geophys. Res., Vol. 6,
pp 407-438 (1958).
F21
1 Platzman, G.W., "A Procedure for Operational Prediction
of Wind Set-up on Lake Erie," Report No. 11, University
of Chicago, ESSA Contract E-91-67.
Platzman, G.W., "The Dynamic Production of Wind Tides on
Lake Erie," Meteorological Monographs, Volume 4, No. 26,
p 44 (1963) .
F41
1 Keulegan, G.H., "Hydrodynamic Effect of Gales on Lake
Erie," Journal of_ Res., U.S. Nat. Bureau of Standards,
Volume 50, No. 2, pp 99-109 (1953).
Harris, D.L., and Angelo, A., "A Regression Model for
Storm Surge Productions," Monthly Weather Review, Volume
91, Nos. 10 to 12 (1963) .
" Richardson, W.S., and Pore, N.A. , "A Lake Erie Storm Surge
Forecasting Technique," ESSA, Tech. Memo. WBTM, TDL 24
(1964).
U.S. Army Corps of Engineers, Technical Report No. 4,
Beach Erosion Board (3.966) .
r si
Fox, W.T., and Davis, R.A., "Profile of a Storm Wind, Waves
and Erosion on the Southeastern Shore of Lake Michigan,"
Proc. 13th Conf. IAGLR, pp 233-241 (1970).
rg i
1 JBajournas, L., and Duane, D.B., "Shifting Offshore Bars
and Harbor Shoaling," Journal of_ Geophysical Res., Volume
72, No. 24 (1967).
181
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REFERENCES
(continued)
JBerg, D., and Duane, D.B., "Effects of Particle Size
Distribution on Stability of Artifically Filled Beaches,
Presque Isle, Peninsula," Proc. llth Conf. IAGLR, p 161
(1968).
* ^Coakley, J. , "Natural and Artifical Sediment Tracer Ex- ,,
periments in Lake Ontario," P roc. 13th Conf. IAGLR,
p 181 (1970).
ri21
JU.S. Army Corps of Engineers, "Water Levels on the Great
Lakes - Report on Lake Regulation," Appendix C, pp 6-12
(1965) .
Battjes, J.A., "Run up Distributions of Waves Breaking
on Slopes," Jour. Waterways, Harbors, and Coastal Engin-
eering Div., ASCE (February 1971).
T14 1
Bijker, E.W., "Littoral Drift as Function of Waves and
Currents," Proc. llth Conf. Coastal Eng., Volume 1, Part
1 and 2, Chapter 26, Volume II, Part 3 and 4, ASCE pp
415-432 (1968).
U.S. Army Corps of Engineers, "Levels and Flows," Great
Lakes Basin Framework Study, Appendix H, Draft 2, Vol-
ume 1 and 2 (January 1971) .
182
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Chemical Models
Problems and Scope
Chemical models which are of practical use for planning needs
are concerned with the reactions that may occur among the
various aqueous chemical species in natural waters. Problems
which are specifically chemical in nature include the effects-
of direct discharges of substances to the lakes, such as
strong acids and bases, dissolved solids, heavy metals, and
other toxic ions and gases. In addition, discharges of dredge
spoils, mine tailings, and other solids can appreciably affect
the lake chemistry through dissolution reactions. Interaction
between the chemical and biological regimes is the second
major class of chemical effects which impact planning
alternatives. Examples of biological consequences are the
phytoplankton populations and their nutrient supply, the
bacteria populations and their oxidation reduction reactions,
and the effects of toxic chemical species on these forms as
well as on other flora and fauna such as fish and wildlife.
Two general classes of chemical models have been developed.
The first considers only the steady-state or equilibrium
configuration of a chemical system and is based entirely on
chemical thermodynamic principles. Given the total
concentration of the components being considered (e.g.,
cations such as calcium and magnesium, and anions such as
carbonate and sulfate) and the temperature, it is possible to
calculate the steady-state concentration of the various
aqueous chemical complexes and condensed species (gases and
solids) which are included in the model. Calculations of this
sort have been pursued for the major ion chemistry at the
Great Lakes spatial scale with quite encouraging results. An
example of the application of equilibrium chemical models to
planning problems is a recent calculation on a lake wide
scale of the probable effect of NTA discharges on Lake Ontario
water chemistry, specifically, its effect caused by forming
heavy metal complexes. In addition, the development of large
scale computer models with the capacity to include tens of
components and hundreds of possible complexes and solids is
now in progress.
183
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The second class of chemical models which have been formulated
are concerned with the kinetic behavior of chemical reactions,
i.e., the transient approach to steady-state. Unlike
equilibrium models, there is no general workable theory for
the aqueous chemical reactions which are of interest. The
available models are specific for certain reactions such as
the rate of hydration of carbon dioxide. The rates can also
be affected by the presence of certain other components, such
as the rate of oxidation of Fe(II) in the presence of silica.
These models can be included in problem contexts if their
importance is suspected. For example, oxidation-reduction
reactions, which tend to occur at slow rates, would be
included in chemical models associated with hypolimnetic
dissolved oxygen calculations. However, if a class of
reactions are known to attain equilibrium rapidly with
respect to the time scale of the problem being considered,
their detailed kinetic behavior is of little concern and the
well developed equilibrium models can be used.
Thus chemical models are required for the analysis of
problems that are explicitly chemical and also as submodels
for inclusion in larger modeling frameworks.
Modeling Framework
The principle which underlies all chemical equilibrium models
proposed to date is derived from two fundamental thermodynamic
principles: the first and second laws' of thermodynamics [1].
These laws state, respectively, that for a closed isolated
system, energy is conserved; and that the equilibrium
composition of the system is reached at maximum entropy.
An equivalent statement of the second law is that all
permissible processes result in an increase in the entropy
of the system. For systems of variable composition (e.g.,
chemical systems) in which the-reactions occur at constant
temperature and pressure, the relevant state function which
corresponds to the entropy in an isolated system is the Gibbs
free energy G = Ey.n.. At constant temperature and pressure,
the criterion for equilibrium is that the Gibbs free energy
is minimum at the equilibrium configuration of the system.
184
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This condition and the equations of mass balance which
insure that all the elements present are conserved are the
bases for all chemical equilibrium models which have been
proposed.
Gibbs Free Energy and Chemical Potential. To make the Gibbs
Free Energy specific, it is necessary to obtain an expression
for the chemical potential y.. Under certain idealized
assumptions, the chemical potential for the i dissolved
species is given by the equation:
s
y = y? + RT In [i] (1)
/ -L X
* ,
where R is the universal gas constant, T is the temperature
in °K, [i] is the activity of,component i, and y? is the
standard free energy of the i component. For dilute
solutions the activity is approximately equal to the mole
fraction or the concentration of the dissolved species so
that the Gibbs free energy can be given explicitly in terms
of the mole fraction concentration, n., and the standard
free energy values, y?, i.e.:
G = Z n^y? + RT In (n±) ] (2)
The mass balance equations have the general form:
2 aie ni = be; e = 1,...,E (3)
where a. is the number of moles of element e contained in
component i and b is the total mole fraction concentration
of element e. There are as many of these equations as their
are elements in the system being considered. One additional
set of equations which guarantees uniqueness and constrains
the solution to be physically meaningful is:
n * 0; i = 1,...,N (4)
185
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which states that all concentrations at equilibrium must be
non-negative. Thus the equilibrium concentrations, n.f are
uniquely given by the conditions that G, given by Equation
(2) be minimum subject to the conditions of Equations (3) and
(4). And in order to calculate the equilibrium composition
of a chemical system all that is required is the standard
Gibbs free energies, y?, which, for most well understood
chemical reactions, are available.
Mass Action Equations. Although the above approach is " v
completely general, it is not the conventional formulation
for the equations of chemical equilibrium. However the
conventional eq-uations, commonly referred to as the equations
of Mass Action, are directly derivable from the above
conditions. As an example consider the single reaction given
by the chemical equation:
I v .A. J Z v .A.
i 1 1 j 3 D
where v. is the stoichiometric coefficient and A. is the
molecular formula of the i a chemical component. The
condition for equilibrium is given by a minimum value of the
Gibbs Free energy G. It can be shown that this results in
the condition:
Ev.y.Ev.y. lr.
i i i = j D D (6)
An example of such an equation which corresponds to the
carbon dioxide-bicarbonate equilibrium reaction is:
\
[H] [HC03]/[H2C03] = K (7)
where [H], [HCOa], and [KaCOs] are respectively the molar
concentrations of the reactants H , HCOs", and HaCOs. This
result can be generalized to include many reactions, all
occurring simultaneously. The resulting equilibrium equations
are all of the form of Equation (6). In addition to these
186
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equilibrium equations the elemental mass balance equations
(Equation (3)) and the positivity conditions (Equation (4))
must also be satisfied.
Condensed Species - Dissolution and Precipitation. In the
preceding section the equations presented apply to dissolved
ions and complexes in the aqueous phase. However under
certain conditions it is possible for condensed species (e.g.,
minerals) to form or, conversely, for these minerals to
dissolve. In order to include this possibility within the
framework presented, the chemical potential for a condensed,
species is needed. For the c condensed species the
chemical potential is given by:
(8)
This equation states that the chemical potential for the c
species is independent of the concentration of the species
as long as it is present in abundance. This is also the
assumption made concerning the water in which the reactions
occur. The condensed species are then included in the
formula for the Gibbs free energy and in the elemental mass
balances, and the formulation is as previously given.
Condensed species may also be included in the mass action
equation formulation. For this case the mass action equation
is given as an inequality, i.e.:
« Kc (9)
where, as before, v. are the stoichiometric coefficients of
the condensed species and K is the solubility product. The
procedure for incorporating this equation into the calculation
is somewhat different from the one used when the Gibbs free
energy equation is employed. If the condensed species is
known to exist, then Equation (9) is treated as an equality
and the elemental mass associated with the mineral is
incorporated into the mass conservation laws. On the other
187
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hand, if there is a possiblity that the condensed species
represented by Equation (9) may form, the calculation is
done assuming it is not present and the final concentrations
are compared to Equation (9). If this inequality is
satisfied then the mineral does not precipitate; if the
inequality is violated then precipitation will occur and the
inequality becomes an equality.
.Computational Methods. The computational methods which are
currently available for solving chemical equilibrium problems
are based on the two sets:of formulations possible for the
chemical equilibrium problem. The equations based on the
Gibbs free energy are: ;.
G = Z n. [u°' + RT In n.J + Ey° n (10a)
i 1 i1 . 1 c c c
2 a. n'. + E a n = b (lOb)
ie i ce c e
n. VO; n £ 0 (lOc)
.1» ' . >-*
where the problem is to minimize the Gibbs free energy given
by Equation (lOa) subject, .to the elemental mass balance
conditions, Equation (lOb), and the positivity conditions,
Equation (lOc). This approach to chemical equilibrium
calculations was initiated by White, et.al. [2], who
formulated the problem as, a non-linear convex programming
problem. It is interesting to note that if no dissolved
species are present, and .only condensed species are 'being
considered, then the problem is a classical linear programming
problem. With the additibn of the dissolved species, however,
the problem becomes.a non-linear programming problem,
specifically a convex programming problem, for which
algorithms have been and are be.ing developed. Perhaps the
most readily available implementation of these algorithms
is described in the-.series of memoranda issued by the Rand
Corporation [10]. ' !
Methods of computation ba;s'ed on the mass action equation have
a longer history. In fact, the first proposed numerical
methods dealt with the equations in this form. The problem,
stated mathematically, is. to solve the following equations:
188
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E v^ In n± = K.. (lla)
v In n. * K. (lib)
1C 1 J
JS a n± + Z a n = b , (lie)
1 i c
; . n. > 0, n ;* 0 (lid)
These simultaneous non-linear equations are difficult to solve
analytically except for simple situations in which the problem
reduces, essentially, to finding the roots of an algebraic
equation. The inclusion of condensed species represented by
Equation (lib) adds an additional difficulty to the
formulation since'! this equation is an inequality. However,
methods are being; developed which can satisfactorily cope
with this added complexity.
An excellent summary of the currently available chemical
equilibrium computation with the emphasis primarily on
gaseous systems is.available [3], and the literature
relating to the application of these techniques to aqueous
systems is currently growing. Thus the computational aspects
of large scale chemical equilibrium models are well in hand,
although they do require rather extensive numerical
calculations that, can only be implemented on a computing
machine. . <
Restrictions. There are some inherent difficulties with
equilibrium.thermodynamic models as they are classically
formulated when directly applying these models to natural
water systems such as the Great Lakes. As expressed by Stumm
and Morgan [4] they include the facts that:
189
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A. Natural systems are continuous flowing
systems. That is, they exchange mass
; with their surroundings and, therefore,
; are not necessarily at thermodynamic
equilibrium, although they may be at
a temporal steady-state.
B.'. Pertinent chemical equilibria may have
been ignored or important solid or
: aqueous species left out of the
formulation.
C. The thermodynamic data upon which
calculation is based may be incorrect.
Temperature and activity corrections
may be necessary.
t>. There may be inadequate chemical
'". characterization of the species
involved. For example, dissolved
; versus suspended components may not
; be properly measured.
E. . Although certain reactions are
' thermodynamically possible, they may
' in fact occur at very slow rates so
that if an equilibrium is calculated
based only on thermodynamic
'{ considerations, the resulting
equilibrium configuration may represent
a configuration which will occur only
in the distant future and may not be
representative of the time scale within
which the problem is being formulated.
An example of such a slow reaction is
the dissolution,or precipitation of
quartz.
190
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State of the Art
Mineral Dissolution Models. The use of therraodynamic
equilibrium models which are based on the assumption that
lake waters are in thermodynamic equilibrium with certain
minerals has been pursued and applied to the Great Lakes
in a series of important papers by Kramer [5,6]. The models
all share a common basis in addition to their being all
equilibrium models. A group of minerals are assumed to exist
and to be in chemical equilibrium with the overlying lake
waters. The partial pressure carbon dioxide, temperature,
and perhaps ionic strength (which is directly correlated to
total dissolved solids) are specified. Then, depending upon
the minerals chosen, the resulting equilibrium concentration
of the output variables are calculated. The number and type
of minerals included within the model determine the chemical
ions which are included in the calculation.
Perhaps the most straightforward of these models is the
calcite model applied by Kramer [5] to the Great Lakes.
The assumptions are that the lake waters are saturated with
respect to carbon dioxide and calcite. In addition, the TDS
concentration is used to calculate the ionic strength of the
medium. The results of the calculations are the pH of the
overlying \vater, the calcium concentration, and the
alkalinity. For 5°G and atmospheric saturation of carbon
dioxide, the results are pH = 8.38, Ca =33 ppm, and
alkalinity (CaCOs) = 81 ppm. These results compare
reasonably well to lake wide average pH, calcium, and
alkalinity concentrations in the carbonate Great Lakes
(Michigan, Erie, and Ontario).
The more complex mineral dissolution models proposed by
Kramer and his students all follow the pattern of the
calcite model. The major structural features of these
models are outlined in Table 14. The minerals considered,
the assumptions made, the input constants, the input
variables, and the outputs are listed. In general, the
variables considered cover the major cations and anions in
the lake water, as well as the pH, phosphate, and fluoride
concentrations. The input constants are usually the carbon
dioxide concentration, the temperature, the chloride +
sulphate concentrations, and the total phosphate concentration,
191
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vD
IO
Reference Assumptions
CO 2 , saturation
5 Calcite Satura-
tion
CO 2 saturation
5 all minerals
saturated
CO asaturated,
6 all minerals
saturated
Calcite, dolo-
6 mite, satura-
tion
OH-apatite sat-
uration, pH set
6,7 by carbonate
Input
Constants
Temperature
Temperature
Cl + 2SO.,
Temperature
Cl + 230.,
Ca, Mg,
Alkalinity
Ca, Mg, P,
PH
TABLE 14
MINERAL DISSOLUTION
Input
Variables Minerals Considered
Calcite
Calcite, H-illite, Mg-illite,
K-feldspar, Na-feldspar,
quartz, kaolinite, OH-apatite,
F-apatite
Calcite, colomite, K-feldspar,
Na-feldspar, kaolmite, gibb-
site, OH-apatite
Temperature Calcite, dolomite
Temperature. OH-apatite
Output
Variables
pH , HCO 3 , CO 3 ,
Ca
pH , HCO 3 , CO 3 ,
Ca, Mg, Na, K,
S iO k , PO i. , F
ph , HCO 3 , CO 3 ,
Ca, Mg, Na, K,
SiOi,, P
apparent solu-
bility of cal-
cite & dolomite
apparent solu-
bility of OH-
P, is fixed
apatite
-------
A notable feature.of these models is that the calculations
which result are ^compared to observed measurement in the
Great Lakes as shown in Figure 20. (See also Figures 5, 6,
and 7, reference ; [6] ; Table 3, reference [5], Figure 5,
reference [7]) . :Although the models are not verified in
every detail and they include measured observations as part
of their input constants, they do represent the major
features of the aquatic chemistry of the variables
considered. In addition, since the models are based on well
understood theoretical foundations, they can be incorporated"1
into larger modeling frameworks. In particular they can be
joined to biological models. The obvious importance of the
carbon dioxide "concentration in establishing the equilibria
that are observed and the possibility of either phosphate
dissolution or precipitation due to the apatite minerals
provide an important biological aspect of these models.
Calculations of similar types have been explored and applied
to oceanic settings by a variety of investigators, among them
Silien, GarreIs and Thompson, Kramer, and others [4] in an
attempt to construct model oceans.
Aqueous Chemical Equilibria Models. A second class of
chemical equilibrium models which have been presented by the
various authors,iand for which an application to a Great
Lakes problem has been made, is a calculation presented by
Childs [8] to assess the effect of discharging NTA, a
proposed substitute for phosphate in detergents, on Great
Lakes water chemistry. These models consider only the
aqueous ions and complexes and generally do not consider the
possibility of mineral precipitation and dissolution. The
inputs to such a model are the total concentrations of the
various metal ions and ligands which make up the chemical
species being considered in the model. For the calculation
presented by Childs the metals and ligands considered are
presented below:;
' Metals (M) ' Ligands (L)
Ca2"r Cd2 Cu2 NTA3~
+ '"!'+' +
Co2' Fe2 Fes PO 3
Pb^"1" Ni2' Zn2 CO 3~
+ ' '+ + "* -
Mn2 Ba2 Mg2 SO 3
Na+ Sr2 + Hg2+ Cl~
193
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LEGEND. ;.
DATA BOUNDARY. ' .
CALCULATED SOLUBILITY
FOR INDICATED CO,
CONCENTRATION
(a) CALCITE
. 9
10 15 20 25
temperature t'C.)
(b) DOLOMIT
5 .1 10 . 15 20 25
j tem'ptrolurt I'C.)
(c) OH-APATITE
120
7- 116
108
10 15 20
lemperotute l'C.1
25
FIGURE 20
COMPARISON OF-OBSERVED VS CALCULATED SOLUBILITY PRODUCTS
(a) CALCITE (b) DOLOMITE (c) OH-APATiTE
: ''.-' AFTER KRAMER (5)
194
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Three general classes of reactions are considered: ligand
protonations which have the form:
a(L) + 3(H) =
where L is
proton and
metal
hydrolys
the ligand in question and H represents the
a and $ are the stoichiometric coefficients;
is reactions which have the form:
and metal ligand complexations which are either of the form:
or of the form:
(12)
a(M) + 3(OH) = (MaOHg)
(13)
a(M) + 3(L) + y(K) =
(14a)
a(M) = B(L)
Y(OH) =
(MaLgOH
(I4b)
Childs considers 8 protonation reactions, 20 hydrolysis
reactions, and 71 complexation reactions for a total of 99
chemical reactions. The equilibrium constants for these
reactions are obtained mainly from the published literature.
The calculations are performed using a modification of the
algorithm proposed by Perrin [9]. Two kinds of calculations
are presented by Childs, The first involves the speciation
to be expected in normal lake water containing no NTA. The
results indicate that, for no NTA addition, over a range
from pH 6 to .pH 9, the metals included in the model appear
primarily as.free ions with the exception of copper (II),
iron (III),jlead (II), and iron (II), which appear as
carbonates or hydroxides. Only a small amount of phosphate
and carbonate and no chloride ion is complexed. The second
calculation:involves the addition of NTA to normal lake water.
195
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Childs calculates that for a 1 micromole/liter concentration
of NTA and pH 8, 50 percent of the copper ion is complexed
and 20 percent of the lead ion is complexed with the NTA ion.
This is a marked change from the speciation in normal lake
water where the copper is primarily copper carbonate and the
lead is a free ion, lead hydroxide, and lead carbonate. In
addition, all of the added NTA is complexed with one or another
of the metals.and no free NTA concentration is calculated.
This change in the heavy metal speciation may have important
biological effects. Another possible avenue that such a v
calculation points to is the possibility that NTA in aqueous
systems may cause liberation of heavy metals which are bound
in the sediment's. If, as is indicated in the calculations,
the complexing ability of NTA is sufficiently active, then it
is possible that heavy metals, which exist as stable minerals
or are bound in the organic sediment, would be resoluabilized
and would enter the aqueous phase as NTA complexes.
Large Aqueous - Solids Equilibrium Calculations. There has
occurred recently the development of efficient computational
algorithms for large chemical equilibrium calculations for
both solid and aqueous species. The older and more limited
program has been under development by the Rand Corporation
for some time [10]. Although it does not appear to have been
applied to problems in a natural waters setting as yet, the
capabilities of the program are adequate for at least initial
applications. A recent described chemical equilibrium program
by Morel and Morgan [11] has the largest capacity of any
program available to date. Their published example
calculations include 20 metals, 31 ligands, 730 complexes,
and 64 possible solids, almost an order of magnitude larger
than those preceding it. Thus the computational aspects of
equilibrium chemical models are well in hand.
Nonequilibrium Chemical Models. A number of the restrictions
discussed above are directly related to the principle
assumptions underlying chemical equilibria models, namely
that of thermodynamic equilibrium. For many chemical
reactions this is an excellent assumption. However for
some important reactions, especially those mediated by
bacterial action, the rate at which the reaction occurs can
be important depending on the time scale of the problem
being considered. Unfortunately there is no general,
196
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workable theory from which the reaction kinetcs for anything
but the simplest reaction can be calculated. For reactions
of interest in natural water systems, it is necessary to use
empirical reaction kinetics formulations based on' laboratory
data. For example the oxidation of Fe(II) has been found
to follow the kinetic law [12]:
2+ 2 ;
^I||1 = -k [Fe +] [02] [OH-]2 : (15)
oxidation-reduction reactions have been studied and
some kinetic results are available [4], In particular,
nitrification reactions can be adequately described in some
cases by simple linear kinetic models [13]. ;
Processes at the Air-lake and Lake-bottom Interfaces. The
chemical processes and reactions that occur in the Great
Lakes are influenced by transport processes which exchange
dissolved gases between the atmosphere and the lake water
and between the lake water and the lake bottom or benthos.
In addition, processes and reactions occuring in [the
sediments themselves can have an impact on lake water
chemistry. .Of the two interfaces, the air-lake interface
is better understood and reasonable models are available to
describe the transport phenomena [14]. Although these
models have been developed and applied primarily .to rivers
and estuaries, the problems involved in these applications
to a.lake setting are understood and suitable approximations
can be proposed.
This situation with respect to the sediment-water interface
is less well understood. A quantity of qualitative and
quantitative information is available [15] and speculations
concerning mechanisms which control transport and reaction
are available; however, the modeling effort is in its
infancy.
197
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Evaluation of Model Status
Model Availability. A number of chemical equilibria models
are available for. both the major ion chemistry and some of
the heavy metals.: The framework is well understood, since
it is the basis of. aquatic chemistry; and the computational
tools are available for application to Great Lakes problem
settings. For those applications which require
non-equilibrium calculations, the availability depends on
the particular reactions .of concern. Computational
difficulties can occur if the reaction rates are fast with
respect to the other.rates in the problems. Airwater
interface transfer of gases is reasonably well understood
in streams and estuaries although no applications to lakes
have been uncovered. Models of sediment-water interface
phenomena are not .as yet available.
Data Availability* . Open water data for verification of
chemical equilibrium models of the major ions is in plentiful
supply. Some of :ithe earliest data available for the Great
Lakes are measurements of the concentrations of the major
ionic constituents.- Heavy metals data are only currently
becoming available due in part to the growing concern
regarding their introduction and accumulation in the Great
Lakes. Sedimentjdata and experimental results are
available, although they appear to be scattered and sketchy.
One problem is that the relevant variables and modeling
framework are not available to assess the utility of the
data that are available.
i
Model Verification. Only the major ion-mineral dissolution
models have been :yerified and these to order-of-magnitude in
some cases and to lake wide averages in other. However, the
verifications are .quite encouraging. Models of heavy metal
complexes and models of biologically active species such as
phosphate are not verified per'se, although in the latter
case, they provide some basis for comparison with observed
data. "> ::.
198
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Model Application. Only the simplest chemical model, that
for which there is no chemical reactions considered (the
chloride demonstration submodel), has been used for
planning applications. No other chemical models have been
used in this way.
199
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REFERENCES
Lewis, G.N., Randall, M., Thermodynamics, 2nd Edition,
Revised, Pitzer, K.S., Brewer, L., McGraw Hill, New York
(1961) .
[2] :i
White, W.B>, Johnson, S.M., Dantzig, G.B., "Chemical Equi-
librium in Complex Mixtures," J. Chem. Phys., 28, pp 751-
75 (1958).:
[3] ''
Van Zeggeren, F., Storey, S.H., The Computation of Chem-
cal Equilibria, Cambridge University Press (1970).
[4] ;
Stumiri, W.,; Morgan, J.J., Aquatic Chemistry, Wiley-Inter-
science, New York (1970).
[5] !
Kramer, J.R., "Theoretical Model for the Chemical Composi-
tion of Fresh Water with Application to the Great Lakes,"
Pub. No. 11, Great Lakes Research Division, p 147 (1964).
!
[61 ='
Kramer, J.R., "Equilibrium Models and Composition of the
Great Lakes in Equilibrium Concepts in Natural Water Sys-
tems," Advances in Chemistry, Series No. 67 Am. Chem. Soc.,
Washington D.C. (1967) .
"i
Sutherland, J.C., Kramer, J.R., Nichols, L., Kurtz, T.D.,
"Mineral-Water Equilibria, Great Lakes: Silica and Phos-
phorus," Pub. No. 15, Great Lakes Research Division, p 439
(1966). :j.
200
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REFERENCES
(continued)
[8]
Childs, C.W., "Chemical Equilibrium Models for Lake Water
which contains Nitrilo triacetate and for Normal Lake
Waters," Proc. 14th Conf. IAGLR (1971).
[9]
Perin, D.D., Sayce, J.S., "Computer Calculation of Equili-
brium Concentration in Mixtures of Metal-ions and Complex-
ing Species," Talanta, 14, p 833 (1967).
[10 ]
Shapley, M., Cutler, L., "Rand's Chemical Composition
Program: A Manual," R-495-PR, Rand Corporation, Santa
Monica, California (June 1970).
fill
Morel, F., and Morgan J.J., "A Numerical Method for
Computing Equilibria in Aqueous Chemical Systems,"En-
vironmental Science and Technology, 6(1) p 58 (January
1972).
[12]
Stumm, W., Lee, G.F., "Oxygenation of Ferrous Iron," Ind.
Engr. Chem. Volume 53, p 143 (1961).
* Thomann, R.V., O'Connor, D.J., DiToro, D.M., "The Effects
of Nitrification on the Dissolved Oxygen in Streams and
Estuaries," Technical Report, Environmental Engineering
and Science Program, Manhattan College, New York (1971).
O'Connor, D.J., Dobbins, W.E., "Mechanism of Reaeration
in Natural Streams," Journal Sanitary Engineering Division,
ASCE, Process paper 1115 (December 1956).
201
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REFERENCES
(continued)
Mortimer, C.H., "Chemical Exchanges between Sediments and
Water in the Great Lakes - Speculations on Probable Regu-
latory Mechanisms," Limnology and Oceanography, ;16(2) ,
p 387 (March 1971).
202
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Eutrophication Models
Problems and Scope
t
Problems that are classed as eutrophication problems have in
common an excessive growth of either microscopic' or
macroscopic species of aquatic plant life. Accompanying
this excessive growth is usually a predominance of species
which are in some way less desirable than those which had
predominanted before eutrophication had occurred. The usual
chain of events.-starts with an increasing quantity of
inorganic nutrients being discharged to the body of water
as a consequence of increasing population and industrial
growth. The increased available nutrients, in conjunction
with other factors, enhance the growth of aquatic plant
life. The changes which make up the eutrophication problem
spring from this enhanced growth.
In particular, the microscopic plant life of a lake, the
phytoplankton, can reach population densities which are in
themselves detrimental to water use. Such changes can occur
either lake-wide ;or basin-wide, such as in the western basin
of Lake Erie or in smaller regions, such as harbors or
embayments. If conditions are suitable, macroscopic aquatic
plants, primarily', .of the rooted variety, can proliferate
along the shoreline. Excessive cladophora growth in Lake
Erie and Ontario ;is an example. These phenomena tend to
occur on a seasonal time scale. With increasing fertilization
phenomena characterized by shorter time scales such as patch
blooms are also in evidence. Surface scums of phytoplankton
and their resultant accumulations on shorelines as well as
the formation of .'rooted aquatic windrows are a serious
consequence of severe eutrophication.
In addition to the general increase in population densities
as measured by the biomass of phytoplankton, observed changes
in species predominance can also occur. Less desirable forms
of phytoplankton,, .particularly blue-green algae, can also
be a consequence :iof overf ertilization. These forms can
cause taste and odor problems in water supplies and'their
decomposition on''shorelines gives rise to noxious odors.
203
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In addition to directly phytoplankton-related problems,
interactions occur between the increased biomass and the
other water quality variables. In particular, the
phytoplankton cause a dissolved oxygen variation and affect
the major nutrients required for phytoplankton growth
(inorganic carbon, nitrogen, and phosphorus). The
utilization of dissolved carbon dioxide can have important
consequences on the carbonate balance, pH, and the attendant^
chemical systems.
The excessive phytoplankton which are produced eventually
settle to the bottom of the lakes and can seriously
interfere with benthic organisms. Also, the decaying
phytoplankton exert a demand on the dissolved oxygen
resources and release organic forms of carbon, nitrogen,
and phosphorus. ;The water transparency suffers at high
phytoplankton biomass concentrations, and this condition
hampers those predator which depend upon visual identification
of their prey. 1
The increased phytoplankton and possible species changes can
influence the overall production of zooplankton and their
species distribution. This can have an effect upon the higher
order carnivores'such as fry or adult fish which rely either
upon phytoplankton'or zooplankton as their primary food
sources. The competitive structure of fish predator-prey
relationships can.'also be altered.
i . *
Accordingly, large scale changes in the population structure
of the phytoplankton, which are the primary producers of
organic material'in lakes, can be expected to have wide-
range effects. Therefore, the quantitative description of
phytoplankton and zooplankton population distribution is of
primary importance in the successful formulation of a
limnological systems analysis. Without such a quantitative
description it is unlikely thai: successful analyses and
predictions of the probable effects of remedial actions
directed at water quality modifications can be successfully
accomplished. ; .';.
The basis of such .a modeling effort is available within the
scientific discipline of limnology which is concerned with
the cause and effect interactions that govern the behavior
204
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of aquatic species in.lakes. An impressive amount of
qualitative information has been assembled regarding the
various phytoplankton species, zooplankton species, and
their interactions. However, only recently has substantial
quantitative '.information become available. In the absence
of detailed quantitative descriptions of phytoplankton
behavior, the problem of eutrophication has been addressed
in several empirical fashions. Perhaps the first attempt
to set quantitative relationships between the quantity of w
nutrients, which must be present in order that eutrophication
problems do not occur, was attempted by Sawyer [1]. More
detailed empirical relationships have been suggested since
then. However, the predictive value of empirical correlation
is open to question, and thus more detailed cause and effect
structures have been attempted. These formulations will be
discussed subsequently.
The formulations which have proven most successful to date
deal with the phytoplankton and zooplankton populations
characteristized solely in terms of the biomass concentrations,
Although a large amount of qualitative and some quantitative
information is available with regard to individual species
or genera of > both phytoplankton and zooplankton, this
information has not as yet been utilized in the construction
of model structures. Thus the problems which are related to
subtle shifts in species compositions of the population
cannot as yet be addressed. However, the success of biomass
calculations; indicate that successful models can be developed
to this level of detail. It is likely that similar models
can be successfully developed for rooted aquatics and perhaps
benthi'c algal species. The rooted aquatic plants are a-
significant problem in Great Lake eutrophication-and some
projected work for development of such models has been
scheduled during the International Field Year on the Great
Lakes '(IFYGL.)..
Modelina Frameworks
Empirical Relationships. As is common in the development of
most engineering-scientific disciplines, the initial attempts
205
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to understand phenomena are based on observed correlations
between controllable variables and the variables which are
associated with the problem of concern.. An initial attempt
to formulate an empirical relationship between the inorganic
nitrogen and inorganic phosphorus concentrations, which
were required for eutrophication problems not to occur, was
formulated by Sawyer [1] based on his experiences in the
Wisconsin lakes.
Although it is apparent with hindsight that this formulation
is a vast oversimplification, considering all the factors
which can contribute to excessive phytoplankton biomass
growth, it has the advantages of being a simple description.
In particular, Sawyer suggests that if, before the spring,
development of phytoplankton concentrations of inorganic
nitrogen and phosphorus is below 0.30 mg/1 nitrogen and 0.015
mg/1 phosphorus, then it is probable that eutrophication will
not occur during the spring, summer, and fall months.
A more sophisticated version of such correlation has been
developed by Vollenweider [2J. He suggests that the primary
important variables are the areal discharge rate of
phosphorus and the average depth of the lake. Shallow lakes
with excessive nutrient inputs tend to be eutrophic. His
contention is supported by a series of observed conditions
in many lakes. As with all empirical correlations, the
primary difficulty with such a formulation is the uncertainty
as to the underlying cause and effect relationships and the
range over which prediction is possible, based on such a
correlation.
Attempts to structure phytoplankton models based on more
fundamental relationships have been attempted. The
structures have become increasingly more complex but their
construction is based on generally accepted ideas concerning
the growth and death of phytoplankton and zooplankton
populations and the effect of environmental parameters on
these processes.
Principles of Kinetically Structured Models. The point of
view adopted in the construction of the models discussed
below has been frequently advocated as a basis for the
development of a mathematical biology. As expressed by
206
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Lotka [3] in his Elements of Mathematical Biology, the method
of approach is as follows: :
It now behooves us to establish, with respect
to the problem of evolution [in the sense of the
time history of a biological system, either .over
short or long time spans], a viewpoint, a . .
perspective, a method of approach, which has
hitherto received its principal development and
application outside the boundaries of biological
science.
x
This 'perspective is that which contemplates
an evolving system as an aggregation of numbered
or measured components of several specified kinds,
and which observes and enregisters the history of
that system as a record of progressive changes
taking place in the distribution, among those
components, of the material of which the system
is built up. | ..
It is thus that physical chemistry views .the
progressive changes in a system comprising several
chemical species, that is to say elements, compounds
phases, etc. It describes the system by enumerating
these components, by stating their character ."-and
extent (mass) ; and by further indicating the .values
of certain quantities or parameters, such as volume
or pressure, temperature, etc., which, together
with the masses of the components, are found
experimentally to be both necessary and sufficient,
for the purposes in view, to define the state of
the system. With the instantaneous state of the
system thus defined, physical chemistry investigates
by observation and by deductive reasoning (theory)
the history, the evolution of the system, and gives
analytical expression to that history, by
establishing relations, of equations, between the
variations defining these states (after the 'manner
set forth above), and the time. ;
It is commonly found that these fundamental
equations assume the simplest, the most perspicuous
form, when they are written relative to rates of
207
-------
change of the state of the systems, rather than
relative to this state itself... . In the
language ofthe calculus, the differential
equations display a certain simplicity in form,
and are therefore, in the handling of the theory
at least, taken as the starting point, from
which the equations relating to the progressive
states themselves, as functions of time, are then
derived by integration.
With the outlook gained in our preceding
reflections, we envisage the life-bearing systems,
in the progress of evolution, as an assembly of
a number ofcomponents: biological species;
collections or aggregations of certain inorganic
materials such as water, oxygen, carbon dioxide,
nitrogen, free and in various combinations,
phosphorus , , sulfur, etc.
These components are placed in various
relations of mutual interaction under specific
conditions of area, topography, climate, etc.
Under these: conditions each may grow, decay, or
maintain equilibrium. In general the rate of
growth, dX/dt, of any one of these components
will depend! upon, will be a function of, the
abundance in 'which it and each of the others is
presented; this rate of grov/th will also be a
function of, the topography, climate, etc. If
these latter features are defined in terms of a
set of parameters PiP2...P^, we may write:
dXi,
~5t = Fi (Xi,X2,. ..Xn; Pi,P2...P.)
dXz1
-j£' = Fa (Xi ,Xa,. .'.Xn; Pi,P2...P.)
dX
(Xi,X2,...Xn; PifP2...Pj)
208
-------
Thus Lotka envisioned the formulation of a mathematical
theory of biological growth and change (what he called
evolution) in terms of sets of differential equations
specifying the rates of change of the dependent variables
X. as functions of the dependent variables X., and the
environmental parameters, PI,...P..
These equations, which are most commonly associated with
chemical kinetics,. form the basis of the kinetic interaction^
among the dependent species being considered. In addition
to the interactions among the species, the second principle
on which phy top'lank ton biomass models are based is the
principle of conservation of mass. This principle simply
states that the mass of each species being considered must
be accounted for in one way or another. For the models
being considered ;herein, the primary mechanisms associated
with this principle are the transport mechanisms which serve
to advect and disperse the various components being
considered. The 'function of the hydrodynamic and transport
models is to provide the quantitative description of these
transport phenomena. The primary"emphasis of this discussion
will, therefore, :center on the kinetic interactions which
appear to be the -primary controlling mechanisms for the
development of phytoplankton biomass.
Phytoplankton Growth Kinetics. The behavior of a natural
assemblage of phytoplankton is a complicated function of the
species of phytoplankton present and their differing
reactions to the;environmental variables which affect their
development. For simplified models, which consider only
the biomass of the phytoplankton, the primary variables
which have been investigated are temperature, solar
radiation intensity, and nutrient concentrations. The
complex data pertinent to this problem have been reviewed
by Hutchinson [4], Strickland [5], Lund [6], and Raymont [7].
A review of pertinent Great Lakes literature is contained
in the Framework'Study [8]. The detailed references for the
kinetic behavior!as described below is available [9].
The influence of i.temperature on the growth rate of
phytoplankton has been experimentally investigated by a
number of researchers. It has been found that at optimum
209
-------
conditions of light and nutrients the growth rate varies
approximately linearly with respect to temperature and
indicates an .approximate doubling of the growth rate for
an approximate doubling of the temperature over the
temperature range from 10° to 20°C. Observed growth rates
at 20°C lie in the range from 1.5 to 2.5 per day (base e).
The growth rates observed under optimal conditions are not
directly applicable to the natural setting in a lake where
the light intensity and nutrient concentrations are not
optimal. The effect of varying light intensity on the
growth rate of the population is that at low light
intensities, .the growth rate increases approximately linearly
with respect ;to incident light intensity and as the intensity
increases the rate reaches the maximum and then decreases
as higher intensities are encountered. This effect, coupled
with the decrease of light intensity as a function of depth
in natural waters (as measured by the extinction coefficient)
reduces growth rate of the natural population.
Similar effects have been demonstrated with respect to the
concentration of the macronutrients required for
phytoplanktongrowth (carbon, nitrogen, phosphorus, silica
for diatoms) .' At a low concentration of the specific
nutrient, the -growth rate appears to be linearly proportional
to the nutrient concentration available; and as the nutrient
concentration is increased, the growth rate eventually
reaches the value specified by the available light intensity
and temperature.
These effects'are graphically presented in Figure 21.
Figure 21A represents the growth rate as a function of
temperature at optimal conditions. Figures 21B and 21C
indicate the ;.effeet of incident light intensity as a
function of depth. Thus, at a particular depth a specific
light intensity occurs which results in the growth rate to
be expected at that temperature. Figure 21D, a graph of
the Michaelis Menton function, shows a hypothesized
functional form 'for the behavior of the growth rate as a
function of a required nutrient concentration. It has been
further hypothesized [9] that these effects are multiplicative
and that the-; resulting growth rate is a function of the
product of the reduction due to nutrient limitations and
non-optimal light intensities.
210
-------
PHYTOPLANKTON
GROWTH RATE'
A. TEMPERATURE
EFFECT
GROWTH
RATE
TEMPERATURE
B. SOLAR RADIATION
EFFECT
C. EXTINCTION
EFFECT
GROWTH
RATE
DEPTH
i LIGHT INTENSITY
I
I LIGHT INTENSITY
I
D. NUTRIENT
EFFECT
GROWTH
" RATE
NUTRIENT CONCENTRATION
FIGURE 2f
PHYTOPLANKTON GROWTH RATE INTERACTIONS
211
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Phytoplankton Death Rate. In addition to the grow'th of
phytoplankton, an additional series of phenonema causes a
loss of phytoplankton population biomass. Endogenous
respiration, the rate at which phytoplankton lose; biomass
because of their metabolic energy requirements, is a primary
mechanism. Experimental information has shown that the
respiration rate is also approximately linear with respect
to temperature, again exhibiting a doubling in rate for a
twofold increase in temperature. Reported respiration
rates at 20°C are on the order of 0.1 per day (base ej.
Thus at optimal conditions the growth rate of a phytoplankton
population is on the order of 10 to 20 times its .respiration
rate. ;
Phytoplankton are the primary producers of organic material
in aquatic systems and form the base of the food chain for
all aquatic animals. Thus an important contribution to the
rate at which phytoplankton population biomass is .removed
is the rate of predation by the microscopic animals in the
next level of the food chain, the zooplankton. Experiments
have indicated that the rate of phytoplankton removal by
zooplankton grazing is approximately proportional to the
zooplankton concentration and increases as a function of
temperature. Figure 22 presents a graphical illustration of
these relationships. i
Zooplankton Growth and Death Rates. Since the zooplankton
form an essential part of the mechanism by which ;phytoplankton
populations are influenced, it is important' thatithe kinetics
of zooplankton growth and death be -formulated. !. .
Zooplankton growth occurs because the zooplankton .graze on
phytoplankton and, in some cases, on smaller zooplankton
forms and particulate organic material that may be present.
For that portion of the zooplankton (herbivorous) which
grazes primarily on phytoplankton, the rate at which the
zooplankton grow is directly related to the concentration
of their primary food, the phytoplankton. A graphical
presentation of the relationships that have> been,observed
is presented in Figure 22. The growth rate of zooplankton
is linearly proportional to the phytoplankton population
present at low phytoplankton population, but becomes
independent of phytoplankton concentration at large
concentrations. This effect is similar to the phytoplankton
212
-------
PHYTOPLANKTON
D.EATH RATE ='
A. RESPIRATION
TEMPERATURE ;
EFFECT
DEATH
RATE
TEMPERATURE
B. ZOOPLANKTON .
GRAZING EFFECT
ZOOPLANKTON
GROWTH ia DEATH RATES
c. ASSIMILATION,
EFFECT '
DEATH
RATE
3ROWTH
RATE
INCREASING
TEMPERATURE
ZOOPLANKTON
CONCENTRATION
INCREASING
TEMPERATURE
PHYTOPLANKTON
CONCENTRATION
D. RESPIRATION.!
TEMPERATURE!
EFFECT -
RESPIRATION
DEATH
RATE
TEMPERATURE
FIGURE 22
PHYTOPLANKTON DEATH RATE,ZOOPLANKTON
GROWTH AND DEATH RATES , INTERACTIONS
213
-------
nutrient relationships given in Figure 22D. In addition, a
temperature effect has been observed, which increases the
grazing rate as a.function of temperature.
Zooplankton death rates are functions of the population's
respiration which -appears to increase as a function of
temperature and predation on the zooplankton by higher
forms. The mechanisms which control the zooplankton
population are less well understood than the phytoplankton
population so that the functional forms of the mechanisms
and, indeed, the proper biomass variables to be utilized
for trophic levels above the herbivorous zooplankton are
as yet unclear.,--'However, the major outlines of the kinetic
interactions of phytoplankton and zooplankton with respect
to the environmental variables temperature, solar radiation,
and the important nutrients are reasonably well understood.
State of the Art
Seasonal Phytoplankton Model. The first phytoplankton
biomass model which incorporates major features that
influence phytoplankton population kinetics was proposed by
Riley [10]. This model followed the prescription given by
Lotka in establishing the differential equation which
relates the growth of phytoplankton biomass, P, to the
mechanism of growth (phytosynthesis), P. ; respiration, R;
and zooplankton grazing, G. Riley proposed the equation:
where:
r'P
1=
-------
The inputs to the model are temperature, T, solar radiation,
I ; the extinction coefficient of the water body, K ; depth
or the euphoric zone, z ; nutrient concentration (in this
case phosphate), N; andezooplankton biomass concentration, H.
The parameters which govern the biological rates in Equations
(2) , (3), and (4), are the growth rates, p; the death rate
and its temperature coefficient n,rz; the grazing coefficient,
G; and a nutrient reduction constant, M. For a given set of
inputs, the parameters are chosen either from experimental ^
information or to fit the observed data, and the resulting
phytoplankton ^biomass concentration is compared against
observed data. 'xTwo verifications [11,12] are shown in Figure
23, Part A and B. The resulting agreement, considering the
simplified nature of the model, indicates that the major
environmental relationships appear to be correctly formulated.
Seasonal Zooplankton Model. Following the structure of the
seasonal phytoplankton model discussed above, Riley [13]
presented a seasonal zooplankton model. The mechanisms
included in the kinetic structure of the model are the
zooplankton assimilation and grazing of available
phytoplankton,'''A; respiration, R; carnivore predation, C;
and natural death, D. The equation which he developed is:
g|=(A-R-C-D)H (5)
A =
'
where:
: R = ri e*Ai (7)
' C = cS (8)
The inputs to the model are the observed temperature, T; the
observed, phytoplankton concentration, P; and the carnivore
biomass concentration, S. The parameters that specify the
behavior of the population are the grazing coefficient, G;
215
-------
A. GEORGES BANK
LEGEND
CALCULATED
-OBSERVED
I-
<
0-
o
X
Q.
40
30
20
10
S' O' N1 D ! J ' F ' M ' A^M ' J
B.
P T,
400
5 M. 300|
5 o
a" -S 200
I I ,.
J- O
HUSAN HARBOR
'J'J'A'S'O'N' 0! J ' F'W A1 .SV -J ' J' A' S'' 0 ' N ' 0
IS32 '933
c.
GEORGES BANK
0 =
FIGURE 23
VERIFICATIONS OF RILEY'S PHYTOPLANKTON
AND
ZOOPLANKTON MODELS
AFTER RILEY (II 812)
216
-------
the maximum growth'rate, A ; the respiration coefficients,
rl , ri; the carnivore grazing rate, c; and the rate of
natural death, D. The resulting model was applied to the
observed zooplankton population for Georges Bank' and the
result is shown in Figure 23, Part C. Again, the reasonable
agreement between observed populations and predicted results
indicates substantial agreement.
Steady-state Vertical Distribution of Phytoplankton and
Nutrients. In an important contribution to the modeling of x
phytoplankton population and their interactions, Riley,
Stommel, and Bumpus [14] presented a phytoplankton model
which includes 'the transport mechanisms that characterize the
vertical transport in offshore oceanic waters. In addition,
the phytoplankton and nutrient equations are coupled so that
their solutions are interdependent. Thus the reliance on
observed nutrient concentration is dropped from 'the modeling
framework and instead a more advanced attempt to model both
phytoplankton and nutrient concentration as a function of
depth is attempted. The equations for phytoplankton and
nutrient concentrations which were used are:
0 =
0 =
3P
at
3N
at
(P. - R - GH)P
h p
o
£"z"
np
- V
L'h
(9)
(10)
In addition, a vertically integrated zooplankton equation is
included:
0 = = (GP -
- cs)
.(11)
The kinetic structure of the phytoplankton and zooplankton
equations are similar to those previously used. ; The
nutrient equation includes the effect of nutrient uptake
by phytoplankton, -a P, ; and the nutrient excretion by
plankton, a R , and by zooplankton a , R,
These ' equations
represent the first interacting model for phytoplankton
217
-------
populations to have been formulated and, in addition, they
take into account the vertical transport structure. These
are two important; improvements over the previous modeling
attempts. A number of comparisons were made between
observed data and; the resulting theoretical predictions.
These are illustrated in Figure 24 for two months using data
from Georges Bank.
Although there are differences between the observed data
and the calculated distributions, it is clear that the
resulting calculations indicate the approximate shape and
levels of phytoplankton biomass as measured by chlorophyll
and nutrient as measured by phosphate concentrations.
In an attempt to further incorporate the interactive
structure of phytoplankton, zooplankton, and nutrient
concentrations, a; model was developed by Steele [15] which
utilizes a series of differential equations expressing the
kinetic, interaction and, in addition, utilizes a simple
two layer approximation for the effect of spatial
distribution in depth. The two layers were taken to
represent the epilimnion and hypolimnion of a lake. The
equations as given by Steel and shown below follow the
structure of the previous models for phytoplankton and
nutrients and incorporate a more empirical formulation for
zooplankton: I. ,
-vKiN .- K2 - gH - H )P
Growth Resp. Pred. Exchange
= K3P - K^H2 (13)
Empirical
-( K5N - K6 )P + M(Nn - N)
' B (14)
i Uptake Regener- Exchange
':' ation
218
-------
GEORGES BANK
MAY 1940
TEMPERATURE
-O .2 .4
PHOSPHATE
.6 .8 1.0 1.2
en
tr
25
50
i r
. . ' PHYTOPLANKTON
0 '. 2000 4000 6000 8000 IQOOO 12000
Q--
LU
' >-«- '
25
50
JUNE i940
PHOSPHATE
0=
i.O 1.2
T r
cr
Ld-
50
H.
a
r, PHYTOPLANKTON
.0 '! 2000 4000 6000 8000 10000
251-
50!
.'". . FIGURE 24
VERTICAL DISTRIBUTION - VERIFICATIONS
' ' AFTER RILEYII4)
219
-------
Calculations employing these equations and numerical
integration.techniques suitable for computer use were
performed. The predicted variation of the populations are
in accord with reasonable behavior and, in particular, show
the effect of varying the rate of exchange between the
epilinnion and hypoliranion.
Seasonal Variations of Phytoplankton, Zooplankton, and
Nutrients. . The incorporation of seasonal effects as well
as direct interactions of the phytoplankton, zooplankton, ;,
and a single nutrient was investigated by Davidson and
Clymer [16]:with further calculations presented by Cole [17].
The equations utilized are similar to those discussed above,
but they explicitly include the seasonal variation of
temperature and solar radiation in the phytoplankton growth
rate. Although the simulation is hypothetical, it exhibits
the behavior characteristic of the spring bloom.
A more detailed model of the seasonal phytoplankton
distribution which includes a predator of the zooplankton
in addition?to the phytoplankton, zooplankton, and phosphate
has been presented by Parker [181. This model is not just
hypothetical,' but the computed results are compared to data
from Kootenay Lake. The general patterns are approximately
reproduced for the initial growth of phytoplankton and .
zooplankton, although the subsequent behavior is not
properly reproduced, and the details of the temperature
dependence of the phytoplankton growth rate are questionable.
Interactive; models which consider a wider range of mechanisms
than those presented above have also been developed. A
hypothetical eutrophication model with interactions between
dissolved and suspended organic matter, a sediment layer,
and attache'd plants as well as phytoplankton, herbivores,
fish, and dissolved nutrients has been structured by Brezonik
[19]. This/model is an example of the general class of
linear ecological models which are discussed in a subsequent
subsection i(Ecological Models).' The major drawback of such
a model is .the. lack of realistic formulations for the
interaction mechanisms. For example, instead of the
non-linear ;coupling, which is characteristic of the
p'nytoplanktori-nutrient interactions, a simple linear coupling
is used. This framework is further analyzed in the
Demonstration Model section, and its drawbacks are detailed.
220
-------
An interactive model with nonlinear kinetic coupling which
also attempts to include a wider range of mechanisms and
variables in the formulation has been presented by Chen [20].
Two groups of phytoplankton, differentiated by their growth
rate-nutrient dependence; zooplankton; inorganic nitrogen;
phosphorus; and organic detritus are included in this
formulation. The transport regime considered is a one
dimensional stream, and the calculations presented are
hypothetical. However, further applications of this model
which include verification attempts are underway.
/
A phytoplankton, zooplankton nutrient model has been
developed by Di Toro, O'Connor, and Thomann [9] and applied
to the Sacramento-San Joaquin Bay Delta estuary in
California. An example of the verification achieved is
shown in Figure 25. Since an extension of this effort
comprises the eutrophication sub-model of the demonstration
model, its description is included in a later section. The
primary thrust of this effort is to derive the phytoplankton
growth and death rates from available laboratory and field
data, and to incorporate a realistic vertically integrated
representation1 of the interaction of'the incident solar
radiation, extinction coefficient, and growth rate-light
dependency of the phytoplankton.
Models which emphasize other aspects of the eutrophication
phenomena have also been formulated. A detailed, though
hypothetical, model of the rotifer life cycle has been
presented by King and Paulik [21]. The influence of the
stoichiometric composition of algae and bacteria on
predicted seasonal variations has been investigated by
Verhoff, et.al.[23]. Inorganic chemical effects have been
incorporated within a lake eutrophication model [23], which
includes the vertical transport structure, algae and
bacteria, but not zooplankton. Efforts are underway to
apply this model to the Lake Er'ie Time Study data. The
influence of upwelling phenomena on phytoplankton growth
in coastal waters is being investigated along the line
described above [24], with nitrogen as the primary nutrient.
Comparison to- observed data is being used to verify the
simulation.
221
-------
40
S t 30
c i
o -*
cr co
Q 5
2°
10
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT ; NOV- DEC
.20.
.10
JA.M FE3 MAR APR MAY JUM JUL AUG SEP CCT ; NOV OEC
JAM FE8 MAR APR MAY JUN JUL AUG SEP OCT.-NOV DEC
FIGURE 25
ANTIOCH VERIFICATION , 1966
Al rtR Dl TORO eta I (9)
222
-------
Evaluation of Model Status
Model Availability. The previous section has reviewed the
models and modeling framework available for use in assessing
the eutrophication phenomena. All models to date have
concentrated on aspects of the seasonal distribution of
biomass, primarily phytoplankton and zooplankton, and the
effects of the major nutrients, nitrogen and phosphorus.
This is a promising first step because some eutrophication *
problems are directly related to the excess biomass produced
by overfertilization. However, other problems are related
more to the detailed biological changes which accompany this
increased biomass: for example, species changes in the
biomass composition with bluegreen algae becoming predominant.
Also, the nutrient recycling accomplished in the benthos has
not been considered in a convincing way. Links to the food
chain above the zooplankton may be required as well as more
detail in the predation effect of zooplankton grazing and
the influence of iparticulate organic detritus. Thus,
although models are available they do not address- the full
range of eutrophication problems, nor do they include all
the known interaction mechanisms which may influence
eutrophication in the Great Lakes.
Data Availability. .Data surveys which include the requisite
variables for the construction of first cut biomass
eutrophication model are available for each of the Great
Lakes. Although.the data is not complete, either spatially
or temporally, arid there are gaps which may prove trouble-
some, the construction and verification of biomass model
can proceed through initial verification. Detailed data
is available on Lake Erie and Lake Ontario. The latter
will be greatly augmented by the International Field Year
on the Great Lakes effort.
i
Model Verification. The model verification efforts to date
have been restricted to only a few applications. However,
the general agreement achieved has been encouraging and
indicates that the major features of the phenomena are
understood. There are, of course, many questions of detailed
mechanisms and pathways which are still only hypotheses. One
drawback is the lack of Great Lakes verifications, although
223
-------
the eutrophication submodel of the demonstration model adds
weight to the applicability of eutrophication biomass models
to Great Lakes settings. Thus, some model verifications
are available. ./..
Model Application .in Planning. Direct planning applications
of eutrophication models to the Great Lakes are lacking,
and only preliminary planning results have been produced
elsewhere. This ,.is primarily due to a lack of verifications
of the model in sufficient degree to warrant detailed
planning investigations. However, the structure of the
models is such that the models lend themselves to answering
planning questions'. This is also illustrated using the
demonstration model.
224
-------
REFERENCES
Sawyer, C^N., "Fertilization of Lakes by Agricultural and
Urban Drainage," J«N_.E. Water Works Association, 61(109) ,
(1947). See.also Sawyer, C.N., "Basic Concepts of Eutrophi-
cation," J. Water Pollution Control Federation, 38(5),
p 737 (May 1966).
: " : ^
f 21 '
Vollenweider, R.A., "Scientific Fundamentals of the Eutro-
phication of,Lakes and Flowing Waters," Organization for
Economic * Cooperation and Development Directorate for Scien-
tific Affairs (OECD), Paris, France (1963).
Lotka, A.J.,. Elements of_ Mathematical Biology, Reprint,
Dover, New York (1956).
r 4 i : '
Hutchinson, G.E., A Treatise on Limnology Volume II, In-
troduction to Lake Biology and the Limnoplankton, J. Wiley
and Sons, New York (1967).
rsi ' ''
Strickland,. J.D.H., "Production of Organic Matter in the
Primary Stages of the Marine Food Chain," Chemical
Oceanography, Volume I, (ed.) J.P. Riley and G. Skivow,
Academic: Press (1965).
Lund, J.W.G., "The Ecology of the Freshwater Phytoplaukton,"
Biol. Res_....40, pp 231-293 (1965).
Raymont,! J.E.G., Plankton and Productivity in_ the Oceans,
Pergamon: .Press (1963).
r O I
L Great Lakes Basin Framework-Study, Draft No. 1, (April 1971).
rQ i '
Di Toro, D.M., O'Connor, D.J., Thomann, R.V., "A Dynamic
Model of the Phytoplankton Population in the Sacramento-
San Joaquiri Delta," in Nonequilibrium Systems in Natural
Water Chemistry, Adv. in Chem. Series 106, Am. Chemical
Soc., Washington, D.C., pp 131-180 (1971).
225
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REFERENCES
(continued)
Riley, G.A., "Factors Controlling Phytoplankton Populations
on Georges Bank," J. Marine Res., 6(1), pp 54-73 (1946).
Riley, G.A., "Seasonal Fluctuations of the Phytoplankton
Populations in New England Coastal Waters," J. Marine Res.
6(2), pp 114-125 (1947).
ri21
Riley, G.A., and Von Arx, R. , "Theoretical Analysis of
Seasonal Changes in the Phytoplankton of Husan Harbor,
Korea," J. Marine Res., 8(1), pp 60-72 (1949).
Riley, G.A., "A Theoretical Analysis of the Zooplankton
Population of Georges Bank," J. Marine Res., 6(2), pp 104-
113 (1947).
ri4i
Riley, G.A., Stommel, H., Bumpus, D.F., "Quantitative
Ecology of the Plankton of the Western North Atlantic,"
Bull. Bingham Oceanog. Coll. 12(3), pp 1-169 (1969).
* 'steele, J.H., "Plant Production on Fladen Ground," J.
Marine Res. 3'iol. Assoc. , United Kingdom, 35, pp 1-33
(1956).
Davidson, R.S., and Clyraer, A.B., "The Desirability and
Applicability of Simulating Ecosystems," Annals, N.Y.
Acad. of S_ci. , 128(3), pp 790-794 (1966).
Cole, C.R., A Look at Simulation Through a. Study on
Plankton Population Dynamics, Report BNWL-485, Battelle
Northwest Laboratory, Richland, Washington (1967).
r I q 1
"Parker, R.A., "Simulation of an Aquatic Ecosystem,"
Biometrics, 24(4), pp 803-822 (1968).
riQ i
Brezonik, P.L., "Application of Mathematical Models to
the Eutrophication Process," Proc. llth Conference,
G.L.R.D. p 16 (1968).
226
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REFERENCES
(continued)
Chen, C.W., "Concepts and Utilities of an Ecologic Model,"
J. San. Engr. Div., Proc. A.S.C.E., Vol. 96, No.SAS,
pp 1085-1097 (October 1970).
" King, C.E., Paulik, G.J., "Dynamic Models and the Simula-*-
tion of Ecological Systems," J. Theoret. Biol. 16, pp 251-
267 (1967) .
/
s
F221
L Verhoff, F.H., Echelberger, W.F., Tenny, M.W., Singer,
P.C., Cordeiro, C.F., "Lake Water Quality Prediction
Through Systems Modeling," Environmental Health Engr.,
University of Notre Dame, Indiana, 46556. ;
[231
Prober, R., Haimes, Y., Teraguchi, M., Moss, W.., "An
Ecosystem Model of Lake Algae Blooms," Symposium on
Biol. Kinetics and Ecological Modeling, A.I.Ch.E., 69th
National Meeting, Cinncinati, Ohio (May 1971).
F241
Walsh, J.J., "Simulation Analysis of Trophic Interaction
in an Upwelling Ecosysterr,," Proc. Summer Computer Simula-
tion Conference, Boston, Massachusetts (1971).
227
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Oxygen Models
Problems and Scope
The concentration of dissolved oxygen is one of the most
significant water quality parameters in all natural water
systems. Its presence is usually associated with high water
quality conditions, which deteriorate as the concentration
of dissolved oxygen decreases to a level of degradation
when the water is devoid of the gas. It takes on particular
significance in-lakes, especially those undergoing
eutrophication in which the concentration in the hypolimnion,
at times during the annual cycle, is greatly reduced and,
under certain conditions, reduced to levels that are barely
measureable.
Dissolved oxygen; is a controlling factor in many biological
and chemical processes. It is of utmost importance to many
forms of aquatic1- life. Fish, in all stages of their
development - egg, larvae, young, and adult - depend on
oxygen. It is furthermore highly related to the chemical
process of oxidation and reduction, and the level of its
concentration is; critical in the precipitation and release
of many chemicals. It could well be the controlling factor
in the recycling of nutrients and minerals.
Under aerobic conditions and at proper pH levels, iron and
manganese in their oxidized form are relatively insoluble
and usually complexed with other compounds such as phosphate
and organic substances.' These complexes precipitate and
are subject to settling under conditions commonly encountered
in lakes. They accumulate and remain in the bed material,
provided an aerobic condition is maintained in the
hypolimnetic waters overlying the bed and the surface of the
benthos contains^, dissolved oxygen. The interface between
oxidizing and reducing conditions is found a short distance
(1 cm) below the benthal surface. If the dissolved oxygen is
depleted in the hypolimnion, the interfacial layer is reduced
and the iron and manganese are solubilized and phosphate is
released. Furthermore, the gaseous end products of anaerobic
decomposition diffuse to the bed surface and are introduced
228
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to the overlying water. The concentration of dissolved
oxygen is thus critical, not only to recycling of minerals
but also to nutrients that enter the biological food chain
and ultimately lead to the problem of eutrophication.
Although many physical and chemical factors come into play
in the oxygen balance of lakes as indicated by the examples
above, the processes involving the utilization of dissolved
oxygen are primarily biologically and biochemically oxidative
in nature. They are usually the result of the bacterial and.
enzymatic breakdown of organic matter and the respiration
of a variety of aquatic organisms, notably the phytoplankton.
The most significant factors initiating or controlling these
reactions are the thermal regime and circulation patterns
for the specific geomorphological structure and the amount
and concentration of oxidizable substances and nutrients in
the system. The organic materials are oxidized by bacterial
activity while the inorganic nutrients are predominantly
assimilated by the phytoplankton. Both these metabolic
processes may occ\ir in the overlying water or at the
interface with the benthos, the relative importance depending
on the nature of the inputs and the structure of the lake.
The upper epiliminion, in general contrast to lower
hypolimnion, is usually characterized by higher
concentrations of; dissolved oxygen, higher temperatures
during the spring' to fall period, and more intense mixing
and circulation, iThese conditions are more conducive to
greater metabolic, .activity of both bacteria and phytoplankton,
The end-products of these processes, such as dead or dying
cells and partially.or totally oxidized residues settle
through the upper' into the lower zone where further oxidation
at a slower rate takes place. Ultimately these substances
settle to the bottom where they accumulate, and the final
stages of oxidation take place provided oxygen is present
and available. If oxygen is depleted by these processes,
nutrients and minerals are reduced, released, and recycled
as described above.
In addition to the factors which utilize oxygen, account
must be taken of
two: atmospheric
The atmosphere in
the mechanisms which replenish it. These are
reaeration and photosynthetic production.
contact with the lake surface is the
229
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ultimate source of oxygen for reaeration. The rate at which
it passes from the atmosphere through the air-sea interface
into solution depends on the deficit created by the sinks
of dissolved oxygen described above and by the condition
of the water surface. The greater the surface renewal as
determined primarily by winds and waves, the greater the
rate of transfer. Oxygen is also derived from photosynthetic
activity of .rooted plants and phytoplankton as a by-product
of carbon synthesis. The latter source is obviously limited
in time to the daylight hours and in space by the vertical ,.
limit of light transmission in the euphotic zone. This zone
occupies a more significant portion of the water depth in
the near shore .areas than it does in the mid-lake regions.
The transport of dissolved oxygen both horizontally and
vertically is brought about by the velocity field with its
fluctuations and gradients. These regimes are primarily
the result of wind action on the lake surface and of density
differences .between different layers and zones and the lake.
These in turn are created by the meteorlogical conditions
and their interplay with the earth and water surfaces,
particularly by differentials in pressure and temperature.
Ultimately the predictability of the velocity field is tied
to weather prediction techniques which yield, relatively
speaking, only reasonable short-term projections. Thus,
verification'of, transport and constituent models may be
accomplished a posteriori with knowledge of the wind
patterns; but long-term projection must be based on
probabilistic analysis.
In describing the overall oxygen balance of a lake, account
must be taken not only of the biological and chemical
reactions, but also of the amount of organic material and
nutritive substances which are introduced into, stored in,
and flow from the system by natural phenomena and man's
activities.; These are the factors in the mass balance over
which there;exists some control for planning purposes, in
contrast to;chemical and physical reactions over which
minimal control can be exercised. The analysis must
therefore incorporate the inputs and outflows of the system
as well as -j:he various mechanisms involved in the reactions.
The degree to which the thermal regimes and hydrodynamic
effects must be included depend on the nature and scale of
the problems, specifically on the time and space scales.
230
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The time scale associated with a significant problem of
dissolved oxygen is seasonal, from spring through fall.
During this period the dissolved oxygen can be markedly
depressed in hypolimnion reaching a maximum and possibly a
steady state during the summer. The analysis of vertical
distribution therefore may be approached practically from
two bases: a steady-state analysis during the most severe
period and a time variable analysis directed to the seasonal
variation. This analysis may extend from spring, when the
concentrations are reasonably uniform over the vertical
plane, to the fall when thermal and circulation conditions
again produce uniformity. The space scale for these
problems may be conveniently divided into near shore and
mid-lake regions initially, with subsequent modeling
frameworks incorporating an overall spatial analysis.
The second significant problem area relates to the dissolved
oxygen depression in shore regions receiving the discharge of
polluted rivers and/or the effluents from municipal and
industrial waste treatment plants. This analysis may be
developed on a steady-state two dimensional horizontal scale.
Consideration may be given to the transient problems arising
from short term discharges, such as storm water overflow.
Lastly, the long term projections, in which elements of a
simplified completely mixed system approach may be
incorporated, should be considered.
Modeling Framework
The basis for construction of dissolved oxygen models is the
principle of conservation of mass as expressed by the three
dimensional advective-diffusion equation:
+ V *[-E Vc + Uc] = Z Si (1)
i
231
-------
where c is the concentration of dissolved oxygen,, E is the
diagonal matrix of diffusion coefficients, U is the velocity
vector, and £S. is the sum of all the sources and' sinks
of dissolved oxygen. The sources, as discussed previously,
include atmospheric reaeration (which appears as a boundary
condition at the lake surface) and photosynthetic, productions
The sinks include all the chemical and biological reactions
which utilize oxygen. Reactions which occur at the lake
bottom are included as a boundary condition at the lake
bottom.
The general three dimensional equation is too complex and
general to be solved directly in practical applications.
Usually at least one spatial dimension may be suppressed by
averaging (e.g., over depth for a shallow water body).
Sometimes two dimensions may be suppressed by considering
only depth variations and taking horizontal averages.
State of the Art
Although limited applications of the basic equations have
been reported on the water quality analysis of lakes [1],
it is believed that the basic understanding of the phenomena
and the general experience gained in other natural 'bodies of
water is sufficient to warrant a presentation of ;what the
state of the art may be in the immediate future. .; 'As has
been stated by a number of limnologists (e.g., [2]), the
distribution of oxygen in a stratified lake has been studied
more than many other aspects of limnology. Coupling this
with experience from other natural systems and the advances
made in the modeling of these phenomena, there is every
reason to assume that sufficient progress can be.made over
the short term to justify its inclusion in this section of
the report.
Vertical Distribution. Assuming initially that the horizontal
transport is not significant in the formation of;the vertical
profile of temperature and dissolved oxygen, the:problem
be analyzed as follows: . :
f? = fe (Ezfi1) " K L
-------
The time rate of change of dissolved oxygen is the result of
two factors. The first term is the transport due to vertical
dispersion. The second is the oxidation of dissolved organic
matter, with concentration L(z,t), which is acting as a sink
of dissolved oxygen. The coefficient, K, is the temperature
function and varies over the season. It may also vary over
depth as does the dispersion coefficient, E . The last two
terms, P and R, represent the photosynthetic contribution
and respiratory sink of dissolved oxygen which is due to the
phytoplankton. Both terms are functions of temperature and,
in addition, the photosynthetic source is a function of light
and nutrient concentration. These parameters may be assigned
from measurement on background data or calculated by using
the phytoplankton-eutrophication model. The analysis may be
envisioned as a two layered model with an interfacial
resistance at the; thermocline or as a series of vertical
segments iri.which the coefficients and parameters may vary
from element to element over the total depth and, in time,
over the season or year. In any case, the boundary conditions
are the oxygen transfer at the surface and oxygen utilization
at the bed: : '
.: Eo If = KL Ccs - Co] at z = 0 (3)
r
i Eh |£ = B at z = h (4)
The solution of these equations is a straightforward matter
and should yield :a preliminary analysis of some value. The
most important step in this analysis is the development of a
relationship between the concentration of organic matter, L,
and the benthal uptake, B; and a relationship between the
phytoplankton parameters, P and R, and the inputs of organic
matter and nutrients. The most extreme condition is a short
term steady-state in mid or late summer at maximum temperature
and minimum dispersion . that period of maximum stability and
greatest utilization of oxygen. This steady-state is a more
simplistic view, yet it may provide sufficient information,
233
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even on a preliminary basis, to use for planning needs,
again provided some correlation can be made between the
inputs and the dissolved organic and benthal demands.
Sufficient data should be available for the preliminary
analysis but efforts will have to be made to extend the data
collection, both .spatially and temporally, for the next
modeling step. !
Horizontal Distribution of Oxygen. This problem is associated
with the near shore distribution of organic and chemical s
pollutants in the vicinity of river outlets and waste
treatment effluents. It is a common problem in all the Great
Lakes and has b.een frequently reported. These substances
cause a reduction in dissolved oxygen in the large scale
plumes within which oxidation is taking place. The resulting
oxygen distribution, taking into account the various sources
and additional sinks, is suggested as follows:
- K L(x'y> - B + Ka'cs -
The origin of the axis is the river mouth at the shoreline
or the location of' the discharge diffusor. The x and y
coordinates refer to the axis in the horizontal plane with
its dispersion components, E. and ET . The x coordinate
arbitrarily represents the major advective direction, with
velocity U, the term, KL, is the sink due to oxidation of
the organic matter, whose concentration is L and reaction
coefficient, K. ; This may be the output of another model
which links the mass emission rates to the dissolved oxygen
concentration. It would be appropriate to classify this
input in accordance with its carbonaceous and nitrogenous
components and thus carry two subsystems instead of one as
indicated by the single term, L. This has practical planning
implications since separate control may be exercised over
these components! in some cases,' and since cost and technology
factors also come into play. The benthal uptake, if present,
is represented by B and the atmospheric reaeration by the
last term, in which c is the saturation value of dissolved
oxygen at the prevailing temperature, and K is the oxygen
transfer coefficient.
234
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The analysis assumes vertical uniformity of oxygen over the
area of concern, which may be a realistic assumption in the
relatively shallow shore waters. If however, a vertical
profile exists, the vertical dispersion term is introduced
and replaces the surface transfer and benthal uptake terms
which enter as boundary conditions, as described above.
;
The first three terms of Equation (5) represent the transport
field which may be the output of the hydrodynamic model or
may be obtained from measurement and specified in terms of
the dispersion and advective coefficients as shown in the
equation. ;
s
If the phytoplankton contribution is significant in the
dissolved oxygen analysis, the photosynthetic and respiratory
terms must be'added in Equation (5). In areas of severe
depression of'dissolved oxygen, these terms may not be
significant, but farther from the shoreline and in high
quality shoreareas, they may be. The individual situation
would indicate the importance of these factors, in any case,
it wpuld have!to be taken into account in any projections
to analyze controls which would affect water quality
improvements .';''
If these factors are integrated and averaged over the depth,
and this procedure is valid in some circumstances, the
dissolved oxygen equation is simply Equation (5) with the
additional P and R terms. If, on the other hand, significant
variations over. the depth exist, it may be more appropriate
to introduce this variation in the fundamental equation
which then becomes:
Tt
E -r1) + -5-CE -P1) - V-(U c) - 4-(U c) -
voy 3z zoz 3x x 3z z
(6)
L(x,y,z,t) - R(x,y,z,t) + P(x,y,z,t)
which is Equation (1) in component form. The oxygen exchange
at the air-water interface and the uptake at the lake bottom
are used as boundary conditions. The solution of the equation
235
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is more complicated due to the three dimensional aspects
of the problem and the uncertainties associated with the
vertical variations of phytoplankton. It is, however, a
problem of some significance and should be regarded as one
of the required models for practical planning in the
immediate future.
Large Scale Completely Mixed Systems. Long term analysis of
dissolved oxygen conditions(more than 10-20 years) may be
approached on this relatively simple basis as a preliminary
step. Each lake may be segmented in 3 or 4 spatial elements5"
and the time interval of the analysis may be taken as
one-quarter to ^one year in length. Interactions between
lakes could be examined as well as individual lakes on the
segmented basis. Critical to this analysis would be the
overall nutrient and organic balances and the correlations
between these inputs and the commonly measured parameters
in water quality. In any case, it is a recommended step for
planning purposes on a long-range scale.
Evaluation of Model Status
Model Availability. Conceptual frameworks exist for dissolved
oxygen balance models and the significant sources and sinks
are known. However, direct applications to the Great Lakes is
lacking. The importance of phytoplankton photosynthesis and
respiration as well as the influence of benthic processes,
both bacterially mediated and algal related, are the major
sources of uncertainty. A less severe difficulty, because
some information is available [3,4,5], relates to the surface
reaeration coefficient which must also be quantified for Great
Lakes application. In addition, the aqueous reactions related
to bacterial oxidation of organic carbon and ammonia must be
included.
236
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Model Verification and Data Availability. As indicated above,
because little application of modeling has been performed on
lake systems, model verification is likewise lacking. Assuming
that approaches described above are in the appropriate
direction, the major emphasis in the next phase is the
application and the verification of these models within the
framework of a specific location and problem. There are a
number of locations in the Great Lakes which lend themselves
to the type of analysis described above. Furthermore, from
the point of view of a preliminary analysis, sufficient
data are presently available to justify this step. Data
availability varies markedly from area to area where this
problem exists,'but, in general it is sufficient for present
purposes. In particular, Lake Erie data are readily
available as a result of Project Hypo [6]. Based on these
analyses, recommendations would be forthcoming for additional
data, if required. Similarly, application of dissolved
oxygen modeling to planning needs has not been conducted in
lake systems. As indicated above, dissolved oxygen modeling
has been applied to many river and estuarine systems and this
experience should provide an excellent basis for;translation
to the lake system. To date, however, there does not appear
to have been any significant area of application'to planning
needs. i
Model Application in Planning ';
In view of the above, it is felt that a reasonable basis
exists for a useful modeling framework for certain
relatively simple problems, and additional efforts are
required for some more advanced problems in dissolved oxygen
analysis. Sufficient data appear to be available -for
verification purposes; whatever is required for preliminary
analysis could be collected without great difficulty and
expense. Additional efforts should be directed to measuring
237
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number of locations in the Great Lakes which lend themselves
to the type of analysis described above. Furthermore, from
the point of view of a preliminary analysis, sufficient
data are presently, available to justify this step. Data
availability varies markedly from area to area where this
problem exists, but, in general it is sufficient for present
purposes. In particular, Lake Erie data are readily
available as a result of Project Hypo [6]. Based on these
analyses, recommendations would be forthcoming for additional
data, if required. Similarly, application of dissolved
oxygen modeling to planning needs has not been conducted in
lake systems. As'indicated above, dissolved oxygen modeling
has been applied to. many river and estuarine systems and this
experience should'provide an excellent basis for translation
to the lake system. To date, however, there does not appear
to have been any significant area of application to planning
needs.
Model Application;in Planning
i
In view of .the above, it is felt that a reasonable basis
exists for a useful modeling framework for certain
relatively simple , problems, and additional efforts are
required for some'more advanced problems in dissolved oxygen
analysis. Sufficient data appear to be available for
verification purposes; whatever is required for preliminary
analysis could be;collected without great difficulty and
expense. Additional efforts should be directed to measuring
the organic and nutrient inputs to the lake system. Although
preliminary planning results have been produced elsewhere,
direct planning applications of eutrophication models to
the Great Lakes are minimal. The reason is that there is
not a sufficient degree of model verification to warrant
detailed planning: investigations. However, the structure
of the models enables the analyst to answer planning
questions.
238
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the organic and nutrient inputs to the lake system. Although
preliminary planning results have been produced elsewhere,
direct planning applications of eutrophication models to
the Great Lakes are .minimal. The reason is that there is
not a sufficient degree of model verification to warrant
detailed planning investigations. Hov/ever, the structure
of the models enables the analyst to answer planning
questions. .
239
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REFERENCES
Bella, D.Q., "Dissolved Oxygen Variations in Stratified
Lakes," J. Sanit. Div. A.S.C.E., 96(SA5), p 1129 (October
1970).
r 21
Hutchinson, G.E., A Treatise on Limnology, J. Wiley and
Sons, New York, pp 575-652 (19577"!
O'Connor D.J-i, Dobbins, W.E., "Mechanism of Reaeration in
Natural Streams," Trans. A.S.C.E., 123, p 641 (1958).
F41 '
Churchill, M.A., Buckingham, R.A., and Elmore, H.L., "The
Prediction of Stream Reaeration Rates," Tennessee Valley
Authority, Chattanooga, (1962).
'Owens, M., Edwards, R., and Gibbs, J., "Some Reaeration
Studies in Streams," Int. J. Air Water Pollution, Perga-
mon Press',: Volume 8, pp 469-496 (1964) .
Burns, N.M., Ross, C., "Project Hypo," Canada Centre for
Inland Waters, Burlington, Canada, U.S. Environmental
Protection Agency, Fairview Park. Ohio, (February 1972).
240
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Pathogens and Indicator Bacteria Models
Problems and Scone
The presence of pathogenic and other indicator bacteria in
waters to be used for water supply or recreational purposes
is a direct reflection of sewage pollution and is of general
public health concern. Although incidences of waterborne
communicable diseases have decreased rapidly in recent
years, continual awareness of the potential problem must be
maintained, especially as water use and contact with
possibly contaminated water increases.
The variables concerned in this class of problems include
such pathogens as Salmonella; indicator bacteria such as the
coliform, fecal coliform, and fecal streptoccoci groups; and
viruses. Specific pathogens and viruses have been isolated
from sewage effluents and are known to survive for varying
periods in water. The isolation of such specific organisms
is generally difficult and time consuming. As a result,
groups of bacteria are often used as indicators of known
pollution, although it should be stressed that the absence
of such indicators does not assure absence of pathogens.
In the Great Lakas, the problems associated with bacterial and
viral discharges are primarily confined to a relatively small
space scale. Thus, the bacterial quality of open lake water
is excellent in all of the Great Lakes. Concern with bacterial
contamination is evident in the near shore (0-10 miles) and
harbor areas and tributary rivers and streams which are most
heavily used for water based recreation and municipal water
supply. For example, as indicated previously in this report,
forty-six beaches on the Great Lakes have been reported closed
because of bacterial pollution. This is reflected in the fact
that about one-third of the U.S. Lake Erie shore is affected
either continuously or intermittently by bacterial contamination
[1]. Figures 26 and 27 show the overall spatial scale of the
problem which is generally confined to the shoreline
241
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Great Lakes Bof.in Drainage Boundaries
Suhbosuis
NJ
-P-
FIGURE 26
AREAS WHERE PROBLEMS ASSOCIATED WITH HIGH BACTERIAL CONCENTRATIONS EXIST
-------
; V-I-2Q
Coliform densities in 10-mile zone alone west shore of Lake Michigan.
j 7-1-2 b
Colil'ornt densities in 10-mile zone aion^ t-:ast shore of LaJ\c .Michigan.
; FIGURE 27
BACTERIAL DENSITIES IN LAKE MICHIGAN
.'' ' AFTER SCARCE (2)
243
-------
regions and harbor areas. (Note difference in coliform
concentrations between the one mile and ten mile stations
in Figure 27). Along the shoreline, however, the problem
may extend for twenty to thirty miles or more indicating
a general area-wide bacterial contamination due to urban
and suburban development. The contrast between the west
and east shores of Lake Michigan, as shown in Figure 27,
illustrates the point.
Pathogens have been isolated in Great Lakes waters and are
present in tributaries to the Great Lakes ([3], [4], and
[5]). No specific data have been reported on the isolation
of viruses in the near-shore area or tributary stream.
The time scale associated with the above space scale ranges
from steady-state, and seasonal scales to short term hour
scales. The former time frame is related to the general
level of urban development (see Figure 27). The latter time
scale is associated with tne transient discharges of combined
and separate sewer overflows which emit high concentrations
of bacteria, but .only for a short duration of time during and
after periods of rainfall. In the city of Milwaukee, for
example, beaches on -Lake Michigan are closed for variable
periods of time after a storm to allow bacterial
concentrations to return to the levels required for swimming.
Figure 28 shows some results for Big Bay Beach in Milwaukee
[6] and illustrates the transient nature of the bacterial
problem.
Also, a variety of the scales ranging from daily to seasonal
is of importance .in bacterial levels at water supply intakes
throughout the Great Lakes. Bennett [7] has investigated the
daily and weekly changes of bacteria concentration in the
intake of two water treatment plants on Lake Ontario near
Toronto. A wide range of variability was found, depending on
short term meteorological effects and longer term seasonal
trends. '.
In summary, the time-space scales,for the pathogen and
indicator bacteria sub-system range from 0-10 miles in
the near shore and harbor areas, and from steady-state to
short term transient problems as a result of combined and
separate storm sewer overflows.
244
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MEDIAN STANDARD
LAKE MICHIGAN
-BEACHES
AUGUST 1964
FIGURE 28
BACTERIOLOGICAL DATA AT BIG BAY BEACH,
WHITE FISH BAY, WISCONSIN
AFTER ERNEST16)
245
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Modeling Frameworks
The basis for the modeling of the bacteria systems is the
dispersion-advection equation:
3c
5-^ + V [-E Vcb + Ucb] = -Kb(x,y,z,t)cb + Wb(x,y,z,t) (1)
t>
where c, is the concentration of bacteria, K, is the rate of
die-off of the .bacteria, and W, is the direct discharge of
bacteria (other terms have been previously defined). The
reaction kinetics in Equation (1) are usually assumed to
be first order, but they are in fact generally complex
functions of space and time through other exogenous variables.
Specification of K, is then central to the application of the
modeling framework.
It should also be noted that the form of Equation (1) does
not result in an aftergrowth of bacteria, a phenomenon also
observed, especially after chlorination. For example, Scarce
et.al. [3] observed increases in bacteria of 200 - 300 percent
after one day in chlorinated samples, the aftergrowth effect
generally lasting about one to two days.
State of the Art
Steady-State. The one-dimensional steady-state form of
Equation (1) has been applied extensively in analyses of
bacterial distributions in rivers and estuaries. Applications
to distributions of bacteria in lakes has been limited.
O'Connor [9] obtained solutions to a two-dimensional version
of Equation (1) given by:
0 = E(- + -) - K. c (2)
v v b
246
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The justification for the use of this equation is that in
the absence of a well defined steady-state current pattern
and variable wind speeds and directions, the effects of the
resulting variable current movements can be incorporated in
the constant dispersion coefficient. An advective velocity
can also be incorporated if it exists. Figure 29 shows the
orientation of axes after transformation of Equation (2)
to polar form and assuming C is constant within 45° in
either side of a given radius. The solution is in terms
of Bessel functions. Some early data are available for the
distribution of coliform bacteria in Lake Michigan in the
vicinity of the Indiana Harbor. The results of comparing
the analytical "solution to observed data are shown.in
Figure 30. The interesting point to note is that a.
simplified version of the complete equation does quite well
in verifying the order of magnitude of the observed data.
More complex situations involving complicated geometry or
circulation patterns require a finite-difference form of
Equation (1), Under steady-state, then, such modeling
contexts involve sets of algebraic equations. The
application of such models to a finite grid in Western Lake
Erie is presented in the Demonstration Model section.
Applications of steady-state multi-dimensional models have
not been made for pathogens or viruses.
Non-Steady-State. The transient bacterial problem is related
principally to overflows from combined and separate sewers.
Thus, the forcing function, W (t) , has a probabilistic
component and depends largely on the random occurrences of
rainfall of variable amounts. The modeling framework for
the combined sewer overflow problem is therefore simple
in principle but quite difficult to apply in practice. In
a dispersion-advection situation the bacterial density can
be readily calculated by numerical integration of the
finite-difference form of Equation (1). The difficulty lies
in obtaining reliable information on the transient bacterial
inputs. For some planning purposes, however, it may be
sufficient to construct a simulation using past records of
rainfall, drainage characteristics, and typical values of
bacterial concentrations in both combined and separate over-
flows. There are few instances available where a' transient
bacterial model has been verified, although the difficulty
247
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ro
.£>
CO
RIVER
SHORE
LAKE
FIGURE 29
COORDINATE SYSTEM FOR DISCHARGE OF BACTERIA INTO A LAKE
AFTER 0 CONNOR (9)
-------
100
100
or
O
I
2
O
IT
o
z:
O
o
Cd
ill
O
<
m
0.01
0.001
246
DISTANCE- MILES
LEGEND
C JUNE AVG.
© MAY 20,1925
O JULY 14,1925
JULY 15,1925
E-0.0063 sq. mi/day
- 6.0mi/day
K=0.50/day
\ \--K=3.00/day
\ \
E = 1.00 sq. mi/day \ \
U = 6.0 mi/day \ \
I
l\
246
DISTANCE- MILES
THREE MONTH AVERAGES
NO ADVECTIVE VELOCITY
DAILY AND MONTHLY AVERAGES
WITH ADVECTIVE VELOCITY
FIGURE 3O-
COMPARISON OF OBSERVED AND COMPUTED VALUES (SOLID LINES)
FOR BACTERIA IN LAKE MICHIGAN VICINITY INDIANA HARBOR
O'CONNOR O) *
-------
is often.not with the modeling framework as much as with the
proper determination of the inputs. With the exception of
present ongoing work in Milwaukee River and Harbor, a detailed
modeling analsyis of transient coliform bacteria has not yet
been conducted on the Great Lakes, although efforts in this
direction are underway [10].
Evaluation of Model Status
Model Availability. The conceptual modeling framework for
indicator groups is quite simple and consists of the
dispersion-advection equation with a first order die-away of
the bacteria. The modeling structure is therefore available
and sufficient for most planning questions. A model of this
type is presently being applied in the Great Lakes [11].
Attempts have not yet been made to structure modeling
frameworks for specific pathogens or viruses, although, on
the surface', there does not appear to be any strong reasons
to doubt that a first order die-away model might also apply
to these situations. It should also be noted that the model
of Equation' (1) does not include the aftergrowth phenomenon
or the possible interaction of phytoplankton populations
and the dea'th rate of bacteria and pathogens. Hedrick [12]
has, for example, indicated an apparent toxicity effect of
algae on the population of Shigella. In the presence of a
natural assemblage of lake phytoplankton, the rate of die-away
is about 15/day or a one percent survival after approximately
seven hours1. From a planning point of view, however,
incorporation of this type of interaction may not be warranted,
because results using lower die-away rates will be conservative
estimates and algal toxicity can be considered as a type of
safety factor. In summary, then, models of indicator bacteria,
and in some cases, pathogens, are readily available and have
proved useful in a number of water resource planning problems,
but have not yet been applied in the Great Lakes setting,
although efforts are currently-being made in this direction.
i '
Data Availability. A review of the data sources for indicator
bacteria shows a considerable amount of available data suitable
for modeling purposes. Information is also generally available
on the inputs, waste discharges, and tributary inflows; and an
250
-------
increasing amount of information is being generated on the
typical bacteria and pathogenic characteristics of combined
and separate sewer overflows. Data are generally lacking on
virus distribution, but this is a situation common to almost
all water bodies, and is a subject of continuing research.
Model Verification. Where steady-state models of bacteria
distribution have been tested in rivers, estuaries, and
harbors; verification has generally been adequate for
planning purposes. It should be recognized that a
verification of bacterial data is generally considered
adequate when comparisons between observed and computed data
agree within an-order of magnitude. The data are generally
quite variable and subject to substantial variation because
of sampling and measurement errors, so that refinement of
the model is generally not warranted.
Attempts at verifying time variable bacterial or pathogen
data resulting from combined sewer overflows have not
generally been made. Leendertse and Gritton [14] have
compared some computed transient bacterial profiles in
Jamaica Bay (subject to considerable loading from combined
sewer overflows) to average bacterial data collected in
the Bay. Results were reasonably good, although the
verification was not with tiine variable data.
In general, for most purposes, verification of bacterial
models has been adequate. Although specific verifications
have not been carried out for the transient case, the high
die-off rates and generally dominant advective flow regime
indicate a favorable prognosis for such verifications. This
lack of verification, therefore, for combined sewer overflow
problem setting is not considered serious. Indeed, the
difficulty lies essentially in determining reliable input
data (e.g., overflow loads and rainfall) rather than in the
modeling structure itself.
Degree of Application to Plannrng. As mentioned above,
existing models of indicator bacteria distribution have
generally not been applied to the Great Lakes setting to
answer planning questions. In fact, it is surprising that
even the simple modeling framework describing bacteria in
natural waters, coupled with generally good data on the
251
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near shore area of the Lakes, has not been used to answer
some of the planning problems associated with beach
closings on the Great Lakes. Where such models have been
applied elsewhere, the results have contributed in a
meaningful way to the decision making process, especially
with regard to the order of priority and effectiveness of
various environmental control schemes.
252
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REFERENCES
Lake Erie Report, A Plan for Water Pollution Control,
United States Department of Interior, F.W.P.C.A., Great
Lakes Reg., p 107 (August 1968).
* Scarce, L.E., "The Distribution of Bacterial Densities in
Lake Michigan," Proc. Eighth Conference, G. L.R., Univer-
sity of Michigan, pp 182-196 (1965).
Clemente, J.", and Christensen, R.G., "Results of a Recent
Salmonella Survey of Some Michigan Waters Flowing Into
Lake Huron and Lake Erie," Proc. 10th Conf. IAGLR,
pp 1-11 (1967) .
F41
Petersen, J.L., "The Occurrence of Salmonella in Streams
Draining Lake Erie Basin," Proc. 10th Conf., IAGLR, pp 79-
87 (1967).
Dutka, B.N., Poplow, M.J., and Yurack, V., "Salmonellae
Isolation from Surface Waters," Proc. llth Conf. IAGLR,
pp 531-537 (1968).
Ernest, L.A., "Effects of Storm Water on Bathing Beaches
in Separate and Combined Sewer Areas," Report presented
at 38;th Mtg. , Central States W.P.C.A. , Albert Lea, Min-
'nesota, p 19 (June 1965) .
Bennett, E.A., "Investigations of Daily Variations in
Chemical, Bacteriological, and Biological Parameters at
Two Lake Ontario Stations Near Toronto Part II - Bacter-
iology," Proc. 12th Conf., IAGLR, pp 21-38 (1969).
r si '
Scarce, L.E., Rubenstein, S.H., Nad Megregian, S., "Sur-
vival' of Indicator Bacteria in Receiving Waters Under
Various Conditions," Proc. 7th Conf., GLRD, University
of Michigan, pp 130-139 (1964).
253
-------
REFERENCES
(continued)
[91
O'Connor D.J., "The Bacterial Distribution in a Lake in
the Vicinity of a River Discharge," Proc., Second Indus-
trial Waste Conference, Texas Water Pollution Control
Federation, p 6 (June 1962).
Hydroscience, Inc., "Time Variable Analysis of the Mil-
waukee River and Harbor," in progress.
Canale, R., University of Michigan, in progress.
Hedrick, L.R., Meyer, R., and Kossoy, M., "Survival of
Salmonella, Shigella, and Coliforms in Lake Michigan
Water," G.L.R.D., University of Michigan, Publication
No. 9, pp 159-171 (1962).
Leendertse, J.J., and Gritton, B.C., "A Water Quality
Simulation Model for Well Mixed Estuaries and Coastal
Seas: Volume III, Jamaica Bay Simulation," N.Y.C. Rand
Institute, N.Y., N.Y., R-709-NYC, p 73 (July 1971).
254
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Fishery Models
Problems and Scope
The fisheries problem in the Great Lakes incorporates the
following aspects: changes in species composition, a decline
in value of commercial catch, a rapidly rising demand for a
viable sport fishery, and conflicting claims over the impact
of environmental changes and commercial effort.
The full dimensions of the problem are explored in detail in
the Framework Study [1] and are not repeated here. Extensive
catch and effort data exist [2] for previous years and
provide specific information which documents species shifts
and apparent population changes. Eleven species of fish
assumed important roles prior to 1950. Three species either
invaded or were introduced to the Great Lakes region, and
five species have been or will be introduced in the near
future. The changing species composition associated with
market demands for certain species (e.g., lake whitefish) has
resulted in a general decline in dollar value of the total
catch. The volume of commercial fish catches has remained
at about 75 million pounds annually since 1920. During 1967,
about 40 percent of the total catch was from Lake Erie and
46 percent (including alewives) from Lake Michigan [3]. As
commercial valuation of the catch has declined, there has
been a general increase in sport fishing pressure. Fish
stocking for sport is assuming increased importance as
evidenced by early successes in planting of coho salmon.
In 1967, sport fishermen harvested 55,000 fish in 232,000
man-days of effort, representing approximately a $3,700,000
effort [4]. The sport fishery is therefore extensive and,
although generally confined to the near-shore area, sport
fishing pressure is expected to exert a continuing influence
on species population.
There are several sub-systems that interact with the Great
Lakes fisheries sometimes in subtle and, as yet, poorly
understood ways. Figure 31 outlines the major sub-systems
which are known to influence species numbers and
composition. The relative degree of impact has not yet been
adequately quantified, although evidence indicates that
255
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NAVIGATION
(INTRO. OF NEW
SPECIES)
LAKE LEVELS
(NURSERY
GROUND EFFECT)
HYDROELECTRIC
POWER PRODUCT
EXTERNAL MARKET
DEMANDS & PREFERENCES
COMMERCIAL &
SPORT FISHING
EFFORT
FISHERY
SPEC. I US, POPULATION
LOCATION
NATURAL
PREDATION
FISH
STOCKING
NATURAL GROWTH
&
DEATH
FIGURE 31
MAJOR SUB - SYSTEMS OF
FISHERY MODELING FRAMEWORK
-------
commercial fishing, water quality, and unplanned introduction
of new species play fundamental roles. The purpose of a
systems analysis of the Great Lakes fishery is to develop
a structure which incorporates the interactions shown in
Figure 31 in a manner sufficient to aid future management
schemes.
Modeling Framework and State of the Art
Population Data. One of the major difficulties in
structuring a fishery model is the uncertain nature of the
data on population distribution. Classically, catch
statistics and fishing intensity are utilized as measures
of population and predation, respectively. Often the catch
and effort xJata are expressed in relative terms. Thus, let
p = percent abundance above some base period (where p = 100
is the average pounds caught per fishing intensity during
base period), and x = percent fishing intensity during base
period. Then data on catch and effort can be displayed and
analyzed in relative terms. Figure 32 (from [5]) shows some
data of thisjtype for northern Green Bay. It is: obvious
that care must be taken in interpreting data such as are
shown in Figure 32. Abundance data are only a crude measure
of population dynamics and are never a substitute for actual
intensive sampling of the population. In the absence of
such data gathering efforts, abundance data afford at least
a first approximation of the population data needed to
develop a modeling structure of fish population .'dynamics.
The lake herring (Figure 32A) show a typical predator-prey
relationship, while lake whitefish (Figure 32B) appear to
display some transient modes that are not readily explainable
by simple.predator-prey interactions. .
Yield Models. The yield of a fishery has assumed an
important historical role, because the early impetus for
modeling fisheries came from ar desire to exploit a fishery
at a maximum level. Yield is considered in production
terms, i.e., pounds of fish produced from a fishery. Early
models looked toward describing yield as a function of
various properties of the fish and fishery and are being
used extensively in the West Coast salmonoid fisheries,
257
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A $
; ! / \i
FIGURE 32-C
GREEN BAY-v/ALLEYE
FIC-URE 32-3
L;REEM BAY-uAKE WHITEFISH
FIGURE 32 A
GREEN DAY-LAKE HERRING
FIGURE 32
CATCH AND EFFORT DATA FOR NORTHERN GREEN BAY
AFTER //ALTER 3 HOOKAH (!>)
258
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Worth Sea, and North Pacific fisheries, among other
locations. Yield models have apparently not been
extensively applied to the Great Lakes. A general review
of yield models is given in [6] and [7]. The analysis
generally begins by writing a growth equation for a species
as [6] :
= r(p)
g(p) ~ M(p) " F(X)
n
(1)
where p = fish biomass; r, g, and M are rates of recruitment,
growth, and mortality, respectively; F = fishing mortality,
x = a function of fishing effort, and n represents external
environmental conditions. Most models to date have ignored
the external environmental conditions and have considered
the fishery over some average environmental regime.
Under steady state, dp/dt = 0, and introducing yield y =
F(x)p, one obtains (ignoring environmental effects):
y = F(x)p = [r(p) + g(p) - M(p)]p
(2)
Beverton and Holt [8] attempt to explicitly account for the
individual terms in (2), while Schaefer [9]' chooses a
logistic functional form for the fishery growth and a
linear relationship between fishing mortality and fishing
effort, i.e., F = ex. Therefore, Schaefer1s model is:
ex = kCP - p)
(3)
where P is the asymptotic equilibrium population.
The Beverton-Holt model begins by examining the number of
recruits, R, at age t entering an exploitation area, but
not retained by the size of the gear until age t . Natural
mortality only operates during this period.
The yield is:
259
-------
= F(t)N(t)W(t) (4)
where W = fish weight. The Beverton and Holt model is given
by:
- M(t - t ) - (F+M) (t - t ) -K(t-t )
= (F) (R) [e c re c][gLS(l-e °)] (5)
where W(t) is given in the last term in brackets, L =
asymptotic length of fish, and K, q, and 6 are known
coefficients from empirical data.
Computations are often carried in relative terms, because
estimates of the absolute number of recruits may not be at
hand. One can then make estimates of Y/R, the yield per
recruit to the fishery. A fishery manager is then in a
position to estimate the magnitude and direction of the
effect of a change in fishing intensity or gear. Equation
(5) is integrated over a fishable life span to get the total
yield of a fishery. Response surface analysis can then be
carried out to determine appropriate optimal yield conditions
[8,9]. Numerous applications of the basic yield models have
been developed [10,11,12] and utilized extensively for fishery
management.
Silliman [12] describes the application of a simple yield
model with variable coefficients. The model was implemented
on an analog computer and applied to a variety of fish
situations including the lake trout of Lake Michigan. His
results are shown in Figure 33 and indicate that the
simulation was good from 1929 to 1944. After that date,
actual catches of lake trout were always below calculated
catches, indicating some other influence was operative. The
parasitic sea lamprey was assumed as one of the causes of
this decline in actual catch.
A generalized computer program has also been developed for
equilibrium yield calculations [13]. Walters [14] has
developed a more general simulation model for yield studies.
260
-------
125
100
X 75
LJ
O
UJ
- 50
25
i I l I I
1930 1932 1934 1936 1938 1940 1942 1944 1946 1948
FIGURE 33
SIMULATION FOR LAKE TROUT OF LAKE MICHIGAN
( AFTER SILI.IMAN) (12)
-------
The model uses age-specific natural mortality rates, growth
rates, and relative fecundities. Any stock-recruitment
relationships can be used. One interesting result from
this work is the great differences in a fifty-year yield
computation using the Beverton-Holt equation assuming
constant recruitment and the computer model using variable
coefficients. The Beverton-Holt equation predicted maximum
yield for high fishing rates and low entry ages to the
fishery. The computer model predicted maximum yield at low
fishing rate and high age at entry.
Deterministic-Statistical Models. Recently, a species
specific model -has been proposed which attempts to describe
species interactions in the Great Lakes [5]. The growth
equation for each species is given by:
± i "h a r> r-v
T, u ci * * u u A .
p.^ dt i 11*1 i i
where p. = population (abundance! of the i fish species,
and x. = fishing intensity of i species and a.., b.1, and
c. are constants. In the form of Equation (6),1the relative
growth term is expressed as the sum of growth (b), death, or
self-species interaction (a..p.) and predation.by fishing
(c.x.). If other species interact with the i species,
then the interactions are included as product interactions.
Therefore for n interactive species:
," - = bi - aiipi - .ai2p2 .. . - ai p - cixi
" "" "!^i."~ ~ -D 2 3-2lpl ""* 3-22M2 "" 9-2 P "~ C2^2
pa at n n
dp
.. n = b - a ip i - a 2p2 ... - a p -ex
n dn n n *n n ^ nn^n n n
n
262
-------
The relative growth rate is estimated from abundance data by
a a difference approximation. Stepwise multiple regression
techniques are then used to find the constants a.., b., and
c. for a complete set of abundance and fishing intensity data
for each species (see, for example, Figure 32). Time lags
are introduced by regressing relative growth rates of species
i with population of species j at some earlier time.
Goodness-of-fit data on the outcome of the regression
analysis, however, are not given.
The model was applied to data in Northern Green Bay and
included analysis of eight fish species and one predator (sea
lamprey). The results show that there was little effect of
fishing intensity on relative growth rates which is somewhat
surprising, as the authors themselves indicate. For example,
casual inspection of Figure 32 indicates an apparent
correlation of lake herring with fishing intensity and a
lag of about four to six years.
Attempts were not made to use the regression model obtained
to generate the actual population (abundance) data that were
used. It should be noted again that the regression model
fits relative growth rates and not the actual abundance data.
Stochastic Models - Leslie Matrices. Year class behavior
and species interaction can be examined by stochastic models
using the basic principles of Markov chains and formulating
the problem in a Leslie matrix form [15]. If:
P. = fraction of year class i that survives from t to t + 1
R. = fraction of year class i that is new born at t + 1
N. = number of fish in year class i
Then the population at t = 1 is:
263
-------
No
Ni
N
mi
=
Ro
Po
0
o
Ri
0
Pi
R
m
o
o
m
No
Ni
Na
N
m
(8)
or:
(N) i = [M] (N)
o i
(9)
where [M] in the form given is known as a Leslie matrix.
population at time t is therefore:
The
(N). = n
(10)
or, for a constant Leslie matrix:
(N)
(11)
More generally, one can consider (N) as a vector of biomass
measures of several categories of animals (year, class,
species, competitors, etc.). The maxtrix [M]._, . is then
viewed as the probabilities of transition from one category
to another category during the interval i-l,i. [M] is
therefore referred to as a transition matrix. Equation (10)
is then called a non-stationary Markov chain, while Equation
(11) is a stationary Markov chain.
This approach has been explored and applied in detail by
Riffenburg [16] to a sardine-anchovy model. The interactions
are shown in Figure 34. Nine categories were used (including
biomass lost from system). An encouraging feature of this work
264
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FISHERY
SARDINE
ADULTS
SARDINE
LARVAE
FIGURE 34
SARDINE .ANCHOVY MODEL
(AFTER RIFFENBURGH) (16!
265
-------
is the verification analysis using data collected during
1950-1959. The results of comparisons between predictions
and observations are good and permit the generation of
projections with at least some degree of confidence. Also,
Pella [17] has developed a Poisson process representation of
searching for schooling fish combined with empirical
estimates of factors such as fishing density and weather.
Simulation Models. In this category, there are a number of ,
models which do not necessairily attempt to incorporate
detailed physiological mechanisms in analytical form, but
rather include phenomena in a decision-rule context. Thus
the models are built up from a series of simple rules, e.g.,
for population i, it takes twelve days to pass through
region y and an average of 60 percent of the fish are caught
with a standard deviation of 20 percent from a normal
distribution. The difficulty with these models is the lack
of generality, i.ei, basic underlying theory and principles
that interact with, apparently differing phenomena can be
masked by the simulation procedure. On the other hand,
simulation models permit easy inclusion of complex
interactions and: spatial detail, are readily constructed,
and, most important, tend to be more easily understood by
decision makers.^ Some simulation models are given in [18]
[19], and [20]. j ,
Evaluation of Model Status
Model Availability.' The previous subsection has indicated
the variety of models of fisheries resource that are
available. The models range from single species exploitation
(yield) models to more complex interactive species models
including large .simulation models that have been used
extensively in management decisions relating to maximum
fishery yields. ! ".
! -
Thus there does -not appear to be any fundamental lack of
basic knowledge which would hamper the construction and
application of existing models to the Great Lakes fishery.
It should be recognized, however, that all of the existing
models really deal with a present biological structure and
are not structured in an ecological predictive sense. The
266
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existing fishery models have little external environmental
effects built iinto them. For example, the models do not
permit the prediction of the effects of long term depletion
of oxygen in the hypolimnion in the fisheries resource.
Data Availability. In terms of the type of data available
for fisheries :model construction, there is ample data
available on the Great Lakes. As mentioned previously,
good records of catch and effort exist for the major
species and for major geographic areas. Of course, as with
all fishery data, information on actual numbers of
population is 'minimal. Planned work as part of the
International 'Field Year of the Great Lakes effort on Lake
Ontario will hopefully provide estimates of the population
of major species in that lake.
Model Verification. Where attempted, verification of catch
data with a fishery model has generally been satisfactory.
This is true solely within the context of the utilization
of model results. Output from fishery models is used most
often to indicate direction of changes and not, necessarily,
absolute magnitude of population changes.
Model Application and Planning. In terms of the Great Lakes
fisheries problem, two major additions must be made to the
more traditional modeling structure: a) more detailed
incorporationiof species interactions, possibly in predator-
prey and competition modeling frameworks, and b) incorporation
of external environmental effects of fish reproduction,
behavior, and'survival. These additions do not produce
any conceptual difficulties, because much is already known
about the physiological mechanisms of the major species, and
effects of environmental water quality on fish are also well
documented. .;
267
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REFERENCES
Great Lakes Basin Framework Study, Appendix No. 8, Fish,
Draft No. 1, (April 1971).
f 21
"Commercial Fish Production in.the Great Lakes 1867-
1960," Great Lakes Fishery Commission, Technical Report,
No. 3, Ann Arbor, Michigan, p 166 (July 1962).
* NacNish, C.,,,-and Lawhead, H.G., "History of the Develop-
ment of Use of the Great Lakes and Present Problems," in
Proc. of Great Lakes Water Resource Conference, Toronto,
.Canada, sponsored by EOC and ASCE, pp 3-48 (1968).
f 41
Cain, S.A., "Conflicts of Recreation and Other Uses of
the Great Lakes," in Proc. of_ Great Lakes Resources Con-
ference, Toronto, Canada, sponsored by EIC and ASCE,
pp 123-153 (1968).
" Walter, G., Hooman,M., "Mathematical Models for Estimating
Changes in Fish Populations with Applications to Green
Bay," Conference £52, Conference for Great Lakes Studies,
University of Wisconsin, Milwaukee, Wisconsin (1971).
JSchaefer, M.G., and Beverton, R.J.H., "Fishery Dynamics
- Their Analysis and Interpretation," The Sea, Volume
II, Hill, M. , (ed.), J. Wiley and Sons, New York, New
York, pp 464-483 (1960).
Gushing, D.H., Fisheries Biology, A Study _In Population
Dynamics, University of Wisconsin Press, Madison, Wis-
consin, p 200 (1968).
r n 1
JBeverton, R.r and Holt, S., On The Dynamics of Exploited
Fish Populations, Agricultural and Fish Investigations,
Section 2, p 533 (1957).
268
-------
REFERENCES
(continued)
T91
Schaefer, M.B. "Some Aspects of the Dynamics, of Popula-
tions Important to the Management of Commercial Marine
Fisheries," Bull. Inter-American Trop. Tuna Commission,
1, pp 26-56 (1954).
Paulick, G.J., and Gales, L.E., "Allometric Growth and
the Beverton and Holt Yield Equations," Trans. American
Fish Soc., Volume 43, No. 4, (October 1964).
Ricker, W.E., Handbook o_f Computations for Biological
Statistics of Fish Populations, Fish. Res. Bd. Canada,
Bulletin No. 119, p 300(1958). ;
F121 '
Silliman, R.P., "Analog Computer Simulation and Catch
Forecasting in Commercially Fished Populations," Trans.
America Fish Soc., No. 3, pp 560-569 (1969).'
" JPaulik, G.J., and Bayliff, W.H., "A Generalised Computer
Program for the Ricker Model of Equilibrium Yield Per
Recruitment," J. Fish. Res. Bd., Canada, 24(2), pp 249-
259 (1967).
ri4i -''
Walters, C.H., "A Generalized Computer Simulation Model
for Fish Populations Studies," Trans. Amer. Fish. Soc.,
No. 3, pp 505-512 (196.9). . | .
i
Pielou, E.G., An Introduction to Mathematical' Ecology,
Wiley Interscience, New York, New York, p 286. (1969).
'16-'Riffenburgh, R.H., "A Stochastic Model of Interpolation
Dynamics in Marine Ecology," Journal Fish. Res. Bd.,
Canada, Vol. 26, No. 11, 2, 843-2, p 880 (1969).
i '
r i 71 '
1 JPeall, J.J., "A Stochastic Model for Purse Seining In
a Two-Species Fishery," J. Theoret. Biol., Volume 22,
pp 209-226 (1969) . .. .
269
-------
REFERENCES
(continued)
r 181
Royce, et.al., Salmon Gear Limitations in Northern
Washington Waters, University of Washington, Volume
II, No. 1, Cut No. 145, (February 1963).
Olsen, J.C., "Steelhead Trout Growth and Production in
Fern Lake, Washington Determined by Sampling and a
Simulation Model," pH.D. Thesis, University of Washing-
ton, College of Fisheries, p 194 (1969).
Paulik, G.J., and Greenough, J.W., Management Analysis
for a. Salmon Resource in Systems Analysis in Ecology,
K.E.F. Watt (Ed.), Academic Press, New York, New York,
pp 215-252 (1966).
270
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Ecoloqical and Food Chain Models
Problems and Scope
Ecological models'.in the context of this subsection are
considered to be "analytical structures of broad segments of
the aquatic ecosystem. Several trophic levels are generally
included and the models attempt to analyze behavior and «.
interactions of riumerous ecological variables. The so-called
compartment models and models of trophic level concentration
of chemicals (fo'c-d chain models) are included in this
category. Models directly related to lake enrichment and
eutrophication are treated separately in a preceding
subsection. j .
:)
The substantial difficulty in constructing models of the
ecological system is primarily related to the lack of a
basic scientific feet--of laws which describe biological
behavior. This can be seen when one contrasts the state of
the art of modeling hydrodynamic phenomena as opposed to
biological phenomena. In the former case, the Navier-Stokes
equations, together with well known and tested energy
balance and continuity equations, comprise the foundation
for predicting water movements. This is not intended to
minimize the difficulty of implementing these basic
equations in any jspecific problem setting; rather, the
observation is intended to form a contrast to the ecological
problem area for ;which, such a basic starting set of equations
simply does.not exist, nor is there any hope in the
foreseeable future for constructing such equations. Aside
from continuity statements, rigorous deterministic equations
for prediction of biological behavior at all trophic levels
are generally not available, and indeed, such behavior is
characterized as 'much by its stochastic properties as by its
deterministic structure.
'j
Nevertheless, ecdlogical models have been constructed along
several lines. These models include (a) descriptions of
portions of the Biological setting called compartment models;
(b) closely related food chain models of 'concentration of
chemicals and radioactive substances through various trophic
271
-------
levels; (c) detailed models replete with complex interactions
attempting to describe the details of trophic level behavior;
and (d)' classification models (e.g., niche analysis) coupled
to sets of deterministic equations.
The basic difficulty of these analyses (aside from problems
of verification and data availability, discussed more fully
below) lies in the difficulty of predicting a sequence of
biological events. Thus the models do not generally attempt,
nor in fact are they claimed to do so by their creators, toi-
predict, for! example, the evolutionary patterns of specific
species under a variety of environmental conditions. Rather,
the models are-xlargely descriptive in nature and the degree
to which they can be perturbed from existing conditions is
generally no't known.
Modeling Framework and State of the Art
The subsections previous to this have discussed the details
of the prese'nt state of the art' of a series of water resource
models. The nature of these models indicates the separate
and often disparate lines of inquiry from which they are drawn.
In order to Irespond to today's planning problems, the need to
synthesize -the apparently separate sub-models into a unified
system must ;be satisfied. Ecological models to date have not
generally responded to this need, but rather have retained a
type of descriptive character of specific phenomenon.
Attainment of a goal of interactive sub-systems at the
present time is not without its difficulties and dimensions
of infeasibility-
I
In discussing the structure of complex interactive ecological
models, it is useful to define an elemental component which
can act as a type of building block for comparing differing
levels of analysis. The notion of a "compartment" is useful
for this purpose. A compartment is considered as any x\/ater
resource or lecological variable, suitably located in space.
Positioning Jin time will be governed by the problem context.
The concept^of a compartment arises, on the one hand, from
the finite difference approximation of partial differential
equations which will express mass balances. Continuous space
is therefore- replaced by discrete finite elements or spatial
272
-------
compartments within which are located (usually uniformly
distributed) the variable of interest. On the other hand,
the concept of a cqmpartment arises from quantitative
ecological models where the continuum of the environment
is also replaced by finite, discrete, interacting trophic
levels. Physical volume in the spatial domain corresponds
to mass of the ecological variable in the trophic level or
state domain. Other analogies also apply; for example,
residence time in spatial compartments correspond to mean
ages in state compartments.
Figures 35, 36, and 37 diagramatically depict a ten
compartment model with no spatial definition, a ten
compartment model with spatial definition, and a seven
compartment food chain model.
The species of each compartment need not be expressed in
detail; therefore, a black box concept is used. Internal
mechanisms which are probably of a non-linear nature are
not examined. Rather, the compartments are defined in a
manner consistent with the type of problem under examination.
The model building ecologist therefore carries out a type of
free-body analysis before beginning construction of his
model. Attention is usually directed to a portion of the
ecosystem, the degree of specificity of compartments
depending heavily on the aims of the investigator. Thus,
one investigator describes compartments including shore
birds of various maturity, their food source compartments,
and their nesting compartments. Only passing attention is
given to other ecological compartments, such as carnivorous
fish, because the investigation context is shore birds. The
ecological concepts of this type of first analysis have been
reviewed adequately by Watt [1], Dale [2], Patten [3,4], and
Mankin and Brooks [5]. A bibliography of modeling in ecology
has also been prepared [6]. Much of the more recent work
has been conducted as part of the International Biological
Program.
Mathematical Structure. With the general notion of a
compartment in mind, one can define C. as the i * variable
uh ir
located in the r spatial position. Interactions between
variables can be considered as linkages, such linkages
including, for example, physical transport of a variable
from location r to location s. Alternately, one can consider
273
-------
FIGURE 35
A TEN COMPARTMENT MODEL
-------
AGRICULTURAL
RUNOFF
SHORE BIRDS
(V
LAKE LEVEL
NUTRIEfgT EPILIMNION
PHYTO. ^_
I EPILIMNION |
©
-14
H
NUTRIENT HYPOLIMNION
©
PHYTO.
HYPCLIMNION I
H-
I S N
JJ
NUTRIENT SEDIMENT
FIGURE 36
A TEN COMPARTMENT MODEL
WITH SPATIAL DEFINITION
-------
j
i
"^
1
'' ,
i
i
i
1
,'
'
i
i
h
TOP
CARNIVORE
t
1
SECOND
CARNIVORE
i
FIRST
CARNIVORE
i
HERBIVORES
1 1
AQUATIC
PLANTS
t,
_ INPUT
FIGURE '?-7
A FOOD CHAIN MODEL
276
-------
causal linkages which transform variable i to variable j.
The linkages may be complex functions of the compartments
that are interacting (as, for example, nutrient limited
growth kinetics in a phytoplankton compartment) or may be
independentiof .the compartments, as in fluid flow transport
between spatial compartments of the same variable.
From these notions of compartments and linkages, a variety of
model structures can be considered. A simple model of six
compartments consisting of three variables positioned at two
spatial locations can be considered as a starting point. *>
Diagramatically, the six compartments can be displayed as in
Figure 38. :
1 ,'
As shown, the variables Ci, C2, and Ca are each found in
two spatial;compartments. The double subscript in Figure 38
therefore indicates the variable and its location. Thus,
Cz\ is the second variable located at the first position.
The interaction between compartment #1 and #4 is possible
only through compartment #2. That is, variable Ci must be
physically transported from location 1 to location 2, before
it can causally interact with variable Cz. Note that at this
stage, the analytical nature of the links is not specified;
it may be linear or non-linear or constant or time variable.
Further, the., link may be empirical, probabilistic, or
deterministic functions of characteristics of the compartment
or contiguous compartment.
In general,;one can consider a link as K.. , which represents
the causal transformation of variable i to1'variable j at
location r.: It is convenient to distinguish further the mass
transport links as F. , which represents the bulk transport
of variable: i from location r to location s. Let K*C
symbolically' represent a causal transformation operation and
F'C represent a mass transport operation. (Note that for
some compartment realizations as between #8 and #9 in Figure
36, the transport need not be passive, but might involve
active transport as in the self-mobility of fish). With this
notation, any output variable can be written as:
Cis ± Kij,r*Cjr+ *ir(t) .
-------
SPATIAL DIMENSION
1
2
3
.]
1 2
©
_ TRANSPORT LINK _
C|2
©
' t . t
KINETIC
1 LINK
* *
C2,
CD
TRANSPORT LINK
*"
c22
©
t t
KINETIC
LINK
7 1
r~
©
TRANSPORT LINK
C32
©
CAUSAL
DIMENSION
i
FIGURE 38
INTERACTIONS AMONG SIX COMPARTMENTS
278
-------
where g. (t) represents an input forcing function of
variable'i at location r. This expression really represents
a discrete version of a mass balance around the i
compartment, and is composed of transport over all .s
spatial compartments bordering on r, plus the causal
transformation of all j variables linked to i, all located
.at the r position.
For a total of m variables and n spatial locations, there >>
are mn compartments which represent mn differential equations
to be solved. Under steady state, there are mn algebraic
equations to bexsolved. For example consider twenty-five
resource or ecological variables that are interactive in
complex ways, i.e., none of the twenty-five variables can
be analyzed separately or sequentially. For some lake wide
problems, a spatial grid size of 200 compartments might be
reasonable. For Lake Michigan, this represents a,resolution
of horizontal gradients on the order of miles, with no
vertical definition. Thus 5,000 possibly non-linear and time
variable equations must be solved, which is not an
inconsiderable number. ;
i
If one attempts to construct compartment models on the same
spatial scale as the usual hydrodynamic grid size, the size
of the problem increases substantially. For example, for
Lake Erie the number of spatial compartments for some
hydrodynamic models is about 5,000. For the same twenty-five
variables, this results in a total of 125,000 equations.
Except for large scale numerical weather forecasting,
implementation and operation of problem sizes of this
magnitude have not been accomplished. This issue.of
computability is further addressed in a later section.
Nevertheless, the framing of a limnological problem in the
broad context of compartment analysis has significant utility
in describing the nature of the^ problem to be investigated.
Notwithstanding the computational difficulties of;large num-
bers of equations, it is useful to attempt to construct at
least the broad outlines of a meaningful ecological model,
which through compartmentalized structure can respond to
a variety of problems.
279
-------
Linear Compartment-Analysis. A special case of the general
mathematical compartment structure as given by Equation (1)
is to consider all compartment interactions as linear [7].
A large number of; ecological and food chain models have been
constructed under this assumption. It is generally made
because of two basic reasons. First, it is difficult, if
not impossible, to.specify in non-linear detail all the
complex mechanisms that may exist in a given problem context.
Further, it is not necessarily clear that such a detailed'
specification is -l-o "1 = 1 J' -I * ' i
In this time variable form, .the coefficients may still be
temporally variable. This may not produce difficulty with
regard to the transport links, but the specification of
time variable kinetic links is usually not accomplished
independently of.;
the data at ha'nd. For many applications
(e.g. [8], [9], [10], [11]), 'a steady state approximation is
made initially to aid in determining the order of the
kinetic interaction.coefficients. In the case of steady
state, the resulting vector equation can be written as:
280
-------
[K] (C) = (g) (3)
where [K] is an mn x ran matrix of interactions, (C) is an run
x 1 vector arranged in such a way that the first n elements
represent the distribution of C. (r = 1 ... n) , the second
set of n elements represents therdistribution of Ca (r=l...n)
and so on. The vector (g) is interpreted similarlyrfor the
input forcing functions.
There are two interpretations that can be placed on Equation
(3). First, the! set of equations can be viewed as representing
an equilibrium "situation. In this case, it is necessary to
have all elements of (C) positive for physically realistic
results. That is, the problem would lose its meaning if after
solution of (C) it was discovered that the phytoplankton
compartment became negative. It can then be shown that all
terms off the main diagonal of [K] must be negative for an
all^-positive vector (C) . The major ecological consequence of
this restriction; is that direct inclusion of predation or
other similar effects is not possible. Mathematically, this
means that K.. Vj^i, must be positive in Equation (2). If
Equation (3) """^^interpreted as an absolute steady state
equation, then the preceding restrictions must be met.
The alternate interpretation of Equation (3) is to consider
the solution to be a deviation from some equilibrium level.
The two interpretations are shown schematically in Figure 39.
Reexpressing Equation (3) to delineate this interpretation
gives: -,
'( . '
\ [K] (6C) = (6g) (4)
)
where
-------
EQUILIBRIUM
SOLUTION
4-DEVIATIONS FROM
-EQUILIBRIUM
FIGURE 39
GEOMETRICAL PRESENTATION OF EQUILIBRIUM
' SOLUTION AND DEVIATIONS
282
-------
perturbation is one which does not result in a physically
unrealizable result and mathematically describes a solution
trajectory along the same solution path as would be
generated with a more realistic non-linear model. It is not
possible to know these paths and degree of physical
realizability a_ priori. Indeed, if they were known, it
would not be ne~cessary to carry out the linear analysis.
For food chain models, i.e., the transfer of radionuclides
or pesticides through various trophic levels, a similar
compartment procedure is followed [12], [13], [14], and [15]
In this case, however, the mass balance is now taken around
the trophic level and fluxes are computed into and out of
the given level located at a specific physical place. The
emphasis in Equation (2) is then on the second term on the
righthand side, namely, the transfer of material between
causal compartments.
Food chain models have been extensively applied to study the
movement of radioactive substances in the environment. The
capacity of an organism to accumulate radioactive substances
is expressed by the ratio of its radioactivity to that of the
aqueous medium or preceding food link. This ratio is called
the concentration factor and is defined as:
K = c/c1 (5)
where c is the concentration in the organism and c1 is the
concentration in the water.
Concentration factors are generally based on the wet weight
of the organism. The concentration factors are constant for
a very wide range of concentration values in the water and
are usually the same for both the radionuclide and the stable
form for most elements. It has been found that pH, light,
and CO2 can influence the concentration factor K, for Sr and
Zn in plants. Concentration factors are often reported for
equilibrium conditions.
283
-------
Concentration factors within freshwater, terrestrial, and
marine ecosystems are well known. The kinetics of
concentration factor changes also seem to be well; defined.
Some results are from laboratory experiments, some from
controlled field tests, and others are measured directly in
natural waters. Table 15 after Ayres [16] lists ...
concentration factors, phytoplankton, zooplankton, and
benthos for several elements in Lake Michigan.
Gustafson [17] has used a simple model to predict future
levels of tritium in the Great Lakes from nuclear power
production. Tritium is an important component of the wastes
discharged by stich installations and is produced during the
routine operation of a reactor. Apparently, the movement
of tritium through food chains involves no trophi:c level
effect or reconcentration along the food chains leading to
human consumption. Therefore, a mathematical model need
not consider such phenomena. As a result, it is possible
to write a continuity equation based on a single homogeneous
volume, V, that is:
r
V = W - QC - VC/X
where W is the mass input rate, Q is the flow rate, and A is
the half-life of tritium (12.4 years). The mass
(6)
inputs result
from natural sources, weapons tests, and nuclear power plants
The author estimates each of these loadings for each of the
Great Lakes. The equilibrium concentration of tritium for
each Lake is then calculated assuming uniform mixing. In each
case, the equilibrium concentration is well below.the maximum
permissible concentration for tritium'in drinking water, which
is 3,000 pci/ml. i
However, the uniform mixing assumption may result in an over
optimistic estimate of future tritium levels. As an example,
a large nuclear power plant (2,000 MW) can be expected to
discharge approximately 2,000 curies/year. If such a plant
were to locate near Traverse City on the west arm .of Grand
Traverse Bay, significantly higher tritium levels would be
expected. Indeed, the calculation indicates that for the
size and detention time of Grand Traverse Bay, the equilibrium
value is about twenty times the value estimated for complete
mixing through the Lake.
284
-------
j TABLE 15
ILLUSTRATIVE RECONCENTRATION FACTORS
Element
Ca
Fe
Mn
Zn
Co
Mg
Ba
K
Na
V
Br
As
Al
Phytoplankton
Lightly
Contaminated
-'' 1 161
36,000
14,100
;2,710
v 207
.' 85
\- 937
;8,950
;2,030
J2,200
;4,730
is, 200
Zooplankton
Lightly
Contaminated
795
26,800
11,900
3,550
123
194
473
6,360
1,275
860
6,630
3,510
6,700
[16]
Benthos
Lightly-
Contaminated
600
20,100
31,000
3,670
109
145
985
10,250
1,900
<1,000
5,000
9,700
285
-------
Linear models have been constructed by ecologists largely for
descriptive purposes, i.e., to better understand the observed
data. Transfer coefficients are usually obtained from the
data directly, thereby weakening the utility of the model
framework for prediction purposes. Thus, verification of the
models in the sense of attempting to independently evaluate
the analysis is usually not done. This is explored more
fully below in Evaluation of Model Status.
' i>
Non-linear Analysis. The basic structure is given by Equation
(l) .Attempts are. made throughout the analysis to incorporate
those phenomena "which are known to be non-linear. For example/
in the linear model, nutrient uptake must be incorporated in
the self-decay coefficient of the nutrient balance equation.
In the non-linear modeling framework, nutrient uptake can be
explicitly incorporated in the nutrient balance equation in a
manner that more closely reflects the phenomenon.
A variety of computer codes now exist to aid the analyst in
structuring his model of a selected portion of the ecosystem.
For example, a Continuous System Simulator (CSS) [18] has
been developed for ecologists as part of the IBP. This
program incorporates features that ecologists are most
likely to use and can be contrasted to more general simulation
languages, such as CSMP (Continuous Systems Modeling Program,
IBM)' and MIMIC (C'DC) . One of the obvious advantages for the
ecologist using the program is that the language is somewhat
more familiar. For example, the following transfers between
compartments are .jincorporated in CSS:
a); linear flow
b).' . product interactions
c)! proportional to input
dj!.." Michaelis-Menton
e)i proportions'! to product of
'!. input and compartment
f)' logistic
286
-------
These programs tend to be limited in scope and are generally
useful for exploratory model building only. Spatial detail
is usually not included explicitly, and considerations of
verification of the model are not discussed.
O'Neill [19] has conducted an error analysis of ecological
models aimed toward determining the degree to which
introduction of nonlinearities results in a more reliable
model. By examining several modeling levels, O'Neill was
able to test the hypothesis that a more complex model is a
more accurate model. The total uncertainty accompanying a
model prediction is analyzed and is observed to consist of
two components (Figure 40): system uncertainty, high at the
linear level; and measurement uncertainty of the parameters
which tends to increase with the introduction of-more
complex phenomena in the non-linear models. The degree to
which these errors propagate through the system and result
in an uncertain prediction may not be intuitively clear.
It is interesting to note that in a comparison of relative
error between a simple three compartment linear model and a
similar non-linear version, the linear model was calculated
to be more accurate over a wide range (±50 percent of the
equilibrium model. The nonr-linear model was more accurate
outside this limit.
Niche Analysis. The above modeling framework deals
exclusively with deterministic sets of equations. There is
an obvious limit to the extent of determinism that one can
build into an ecological structure. Predation and
competition efforts among numerous biological species are
difficult to analyze explicitly and some other means should
be at hand for characterizing biological systems. The
niche concept represents an attempt to analyze species
interactions and community structure.
Basically, the niche represents the ecological requirements
for the existence of a specie. More specifically, Levins [20]
has defined the niche as a measure of fitness in environmental
space. Two important measures of niche are considered; the
niche breadth and the niche dimension. One can arrange
relative frequencies of species in given environments
287
-------
SYSTEM
"UNCERTAINTY
cc
UJ
o
I-
Q
UJ
CC
Q.
MEASUREMENT
UNCERTAINTY
LINEAR
MODELS
INCREASING
COMPLEXITY
NON-
LINEAR
MODELS
MODEL COMPLEXITY
FIGURE 40
UNCERTAINTY IN LINEAR AND NON-LINEAR MODELS
288
-------
in a matrix form, with elements P-^> where the subscript i
represents the specie and subscript h represents the
environment. The quantity P., therefore represents the
proportion of species i in environment h of the total number
of species in all environments. The 'niche breadth is then
defined as: '.' '
B. = 1/Z P.,
1 h lh
(7)
which is a measure of the spread of specie i over ;all
environments. Abundant species therefore have broader
niches, i.e., B tends to be larger.
The niche dimension or diversity is computed for a fixed
environment over all species. Therefore, let f., be
proportion of individuals of species i in environment h of
all individuals in the same environment h. The niche
diversity is therefore: ;
Dh - - f
fih
(8)
The dimensionality of the niche therefore dependson the
degree to which the species divide the total environment
among themselves. Levins [20] also structures the.
competition structure between species by estimating the
probability that two species will interact. These interaction
coefficients are thqn used in growth-death equations of the
species. Thus, the equations for specie i is given'by:
where X^ is
equilibrium
dX.
dt
=
riX
K.
i (K
the i specie,
population (the
i
Xi
r is the
"carrying
E d. .
V
growth rate,
capacity" ) ,
(9)
K.is the
and the a.
are [20]:
289
-------
a. . = Ep,, P ., (B.)
13 ih jn i
(10)
The coefficients a.. are known as the competition coefficients,
Transport terms have, of course,,been dropped from Equation
(10). Under steady state, the i equilibrium community is:
or, in matrix form:
K. = X. +
11
(11)
[A] (X) = (K)
(12)
where (X) and (K)\are column vectors of species and carrying
capacities, respectively, and the community matrix is:
[A] =
OM 2 Oil 3
Equation (12) can;be solved -for (K) if present species numbers
a. .'s are known. 1 The carrying capacity vector (K) is
tne'refore a useful measure of the degree which a specie has
filled the environment. Lane and McNaught [21] and Lane [22]
have applied these analyses to zooplankton communities in Lake
Michigan. The analyses permit the determination that habitat
selection, rather! than resource allocation, is operative in
the zooplankton structure. The habitat selection is accomplished
though diel vertical migration.
290
-------
It should be- noted that the theory of the niche is still in
its infancy. As a consequence, there is still a large
measure of subjectivity associated with the theory. This
is particularly true for the determination of the environment
groupings. No a_ priori objective selection of environments
can yet be made7 and it is obvious from the above that such
selections can influence results markedly. Moreover, the
theory does not yet result in a predictive framework, but
rather has aided .in further understanding and recasting of
observed data. i .
Evaluation of Model: Status
Model Availability. As indicated above, there are a variety
of ecological models available, most are in a linearlized
compartment form.- Although gaps exist in the detailed
knowledge of species interaction, a considerable body of
knowledge exists on which to base a meaningful framework.
Unfortunately, su'ch a framework to date has relied
exclusively on tire observed data and very little prediction
of the consequences of environmental actions has been
attempted. ']
Data Availability. The extent of data availability
specifically related to transfers between ecological
compartments is not very great. Isolated regional studies
have been conducted but there has not generally been'any
Great Lakes-wide .attempt at ecological modeling. Data that
exists from other sources may be applicable to the Great
Lakes Limnological Systems Analysis. For example, O'Neil
[23] has compiled a variety of transfer matrices that may
be useful in line'ar compartment analysis.
r
The distribution Sof radioactivity within the food web in the
Great Lakes has been -studied only to a limited extent. Risley
and Abbott [24] have described gross beta levels in plankton
and sediments for .Lake Erie, and Risley [25] for Lake
Michigan. The Michigan Water Resources Commission has
measured the distribution of radioactivity in Lake Michigan
and tributary streams as well as in the plankton, periphyton,
291
-------
filamentous ialgae, crayfish, and minnows in the immediate
area of the ;Big Rock Nuclear Power Plant. During 1969 and
1970, Ayres '..[.16'] conducted an extensive survey of the
distribution of radionuclides in Lake Michigan. The work
was supported by several power companies and was conducted
to evaluate and forecast the damages that would result from
the expansion of nuclear fuel plants on Lake Michigan.
Radiological' analyses were performed on the water, benthos,
phytoplankton, zooplankton, sediment, and fish. Concentrations
of Cs-137, Zn-65, K-40, Ra-226, and gross beta activity were^
obtained. j .
Model Verification. As noted above, ecological models to
date are almost totally descriptive in nature and have not
been verified in the usual sense. That is, the transfer
coefficients between compartments have not been used to
verify model output' against observed data. The capacity of
ecological models for predicting environmental changes is,
therefore, not known.
;
This lack of verification is generally serious. As stated,
it implies a reduced utility of the models in answering
planning questions. Nevertheless, for the first time,
attempts are being made to provide some structure to the
complex nature of the ecological systems. At the very
least, then, although ecological modeling is in its infancy,
it provides some basis for elucidating interactive variables,
tha degree of interactive variables, and the degree of
interaction;and importance of the various ecological
variables. 3
Model Application in Planning. Ecological models have
generally not been applied in a limnological planning context.
This is duel primarily to the largely descriptive nature of
the present!state of the art. However, once an ecological
model is constructed as outlined above it may provide a
useful basis .for planning purposes. This would be
especially so if the ecological modeling framework were
imbedded inf or attached to portions of the Limnological
Systems Analysis that are better understood.
292
-------
REFERENCES
1 Watt, K.E.F., Ecology and Resource Management: A Qualita-
tive Approach, McGraw-Hill Book Company, Inc., New York,
New York, p 450 (1968).
T21
Dale, M.G., Systems Analysis and Ecology, Ecology Volume
51, No. 1, pp 1-16 (1970).
" Patten, B.C., "Ecological Systems Analysis and Water Qual-
ity," Proc. 3rd Annual Symp. on Water Resources Research,
Ohio State, p 37 (1967).
f 41
Patten, B.C., Editory, Systems Analysis and Simulation in
Ecology, Academic Press, New York, p 607 (1971).
* Mankin, J.B., and Brooks, A.A. , Numerical Methods for Eco-
system Analysis, ORNLIBP 71-1, Oak Ridge National Labora-
tory, Oak Ridge, Tennessee, p 99 (June 1971).
* O'Neill, R.B., et.al., A Preliminary Bibliography or_ Mathe-
matical Modeling i_n Ecology, ORNL-IBP-70-3, Oak Ridge Na-
tional Laboratory, Oak Ridge, Tennessee, p 97 (October 1970),
Funderlic, R.E., and Heath, M.T., Linear Compartmental Anal-
ysis o_£ Ecosystem, ORNLIBP714, Oak Ridge National Lab-
oratory, Oak Ridge, Tennessee, p 50 (August 1971).
r o I
Williams, R.B., "Computer Simulation of Energy Flow in
Cedar Bog Lake, Minnesota Based on the Classical Studies
of Lindeman," in Systems Analysis and Simulation in
Ecology, B.C. Patten, Ed., Volume I, Academic Press, pp
543-582.
F91
Eberhardt, L.L., "Similarity, Allometry, and Food Chains,"
J. Theor. Biol., 24:43-55, (1969).
293
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REFERENCES
(continued)
FlO 1
Bledsow, L.H., and Van Dyne, G. , "A Compartment Model
Simulation of Secondary Succession," in Systems 'Analysis
and Simulation in Ecology, B.C. Patten, Ed., Volume I,
Academic Press pp 480-485 (1971). ;
J Bloom S . G . , et . al . , Mathematical Simulation of Ecosystem
- A Preliminary Model Applied to a Lotic Freshwater
Environment, Battell Memorial Institute, Columbus Labora-
tory, Columbus, Ohio, p 32 (1969).
Eberhardt, L.L., et.al., "Food Chain Model . for DDT Kinetics
in a Freshwater Marsh," Nature, Volume 230, pp 60-62 (March
1971) . .> .
Harrison, et.al., "Systems Studies of. DDT Transport,"
Science, Volume 170, (October 1970) . \
Kaye, S.V., and Ball, S.J., "Systems Analysis of a Coupled
Compartment Model for Radionuclide Transfer in a Tropical
Environment," Proc. 2nd National Symposium on Radiology,
Ann Arbor, Michigan pp 731-779 (1967).
Riley, G.A., "Theory of Food-Chain Relations in
in The Sea, (M.W. Hill, Ed.) Volume 2 pp 438-463 (1963).
r -. ^- 1
Ayers, J.C., Lake Michigan Environmental Survey
Report No. 49, G.L.R.D., University of Michigan
the Sea,"
Special
(1970).
294
-------
REFERENCES
(continued)
" JGustafson, "Future Levels of Tritium in the Great Lakes
from Nuclear Power Production," Proc. 13th Conf. G.L.R.D
Part 2, p 839 :;(1970) .
r 181
Sollins, P., .CSS; A Computer Program for Modeling Ecologi-
cal Systems, ORNL-IBP-71-5, Oak Ridge National Laboratory,
Oak Ridge, Tennessee p 96 (August 1971).
T191 '
LJO'Neill, R.V.,'. Error Analysis of Ecological Models, Decid.
Forst Brochure, Memo Report 171-15, Oak Ridge National
Laboratory, Oak Ridge, Tennessee, p 31 (September 1971).
*-" -"Levins, R. , Evaluation in. Changing Environments, Princeton
University Press, Princeton, New Jersey, p 120 (1968).
foi 1
1 JLane, P,A., and McNaught, D.C., "A Mathematical Analysis
of the Niches,.'of Lake Michigan Zooplankton," Proc. 13th
. Conf. IAGLR, pp.47-57 (1970) .
[22]
1 JLane, P.A., "A Comparative Study of the Structure of Zoo-
plankton Communities," pH.D. Thesis, State University of
New York, Albany, New York p 202 (Unpublished).
r 9 -51 . | ' '
LJO'Neill, R.V., .Examples of Ecological Transfer Matrices,
ORNL-IBP-71-3;. Oak Ridge National Laboratory, Oak Ridge,
Tennessee, p 2,6. (June 1971).
t
[24^Risley, C., Jr., Abbott, W.L., "Radioactivity in Lake
Erie and its Tributaries," Proc. 9th.Conf. GLRD, (1966).
295
-------
REFERENCES
(continued)
[25]
Risley, C., Jr., "Radioactivity in Lake Michigan and its
Tributaries," Proc. 8th Conf. GLRD, (1965).
296
-------
VIII. MODEL SYNTHESIS FOR PLANNING NEEDS
As indicated in Section VI, the main thrust of the Limnological
Systems Analysis is the application of problem oriented models
to specific'planning situations. The preceding review of the
state-of the art of available models indicates that a variety
of models and submodels have been developed in various degrees.
In general,, the modeling frameworks tend to be concerned
with specialized areas. There is a notable absence of
integrated and synthesized modeling frameworks aimed at Great
Lakes planning "problems. The purposes of this section are
to summarize the existing model status, describe the process
of model synthesis, and examine the level of computational
feasibility; of interactive modeling frameworks.
:; Summary of Evaluation of Model Status
The ranking' of each of the preceding eleven modeling frameworks
is summarized in Table 16 and Figure 41. It should be recalled
that this ranking was performed by using the relative weights
of key aspects in the evaluation of model status, as shown in
Figure 14, Section VI. Further, although cost is not explicitly
included in; the above individual analyses, it is included
implicitly in the evaluation, i.e., a relatively low score
reflects, among other things, the difficulty of bringing a
specific modeling framework, to a point where it can be useful
as a planning tool.
As indicated previously, each of the eleven modeling frameworks
includes, in varying degrees, submodels of component phenomena.
Thus, the eutrophication modeling framework includes a submodel
of nutrient; flow in the water column which in turn includes a
model of the water circulation.. In addition, the ranking
shewn in Table 16 represents a type of average ranking over
all the lakes. Although geographical differences do occur in
some of the' modeling frameworks, the ranking is an attempt to
present an overall picture of relative modeling status.
-297
-------
00
1.
2.
4.
5.
6.
7.
8.
9.
10.
11.
3.
Model Frameworks
Hydrological Balance
Thermal Balance
Lake Circulation and
Mixing
Sediment-Erosion
Chemical
Eutrophi cation
Dissolved Oxygen
Pathogens and Virus
Indicator Bacteria
Fishery
Ecological and Food Chain
Ice and Lake-wide
RANKIH
Available
Models
(0-30)
25
18
'24
18
15
18
20
25
18
9
Extent
of
Knowledge
(0-10)
5
TABLE 16
G OF MODELING
Available
Data
(0-40)
25
20
24
10
14
20
20
14
16
6
Available
Data
(0-20)
12
FRAMEWORKS
Model
Verification
(0-20)
7
7
15
4
5
5
10
10
10
5
Verification
Difficulty
(0-10)
8
Planning
Application
(0-10)
8
5
3
7
5
5
0
5
2
0
Software
Availability
(0-10)
5
Total Score
65
50
66
39
39
48
50
54
46
20
Total Score
30
Temperature Models
-------
VO
PROBLEM AND
MODEL CONTEXT
1 HYDROLOGICAL
2 THERMAL BALANCE
3 ICE8LAKE WIDE TEMP
LAKE CIRCULATION
A f>J Pi M 1 Y I W ft
5 SEDIMENT-EROSION
6 CHEMICAL
7 EUTROPHICATION
8 DISSOLVED OXYGEN
pATHnrsFNic; A VIRII^
INDICATOR BACTERIA
10 FISHERY
ECOLOGICAL AND
FOOD CHAIN
' ' - .. . - . - (D.(
. . ' (2)
(3)
SUMMARY OF MODEL STATUS
DEVELOPMENT STAGE III DEVELOPMENT STAGE U DEVELOPMENT STAGE I
MODEL STATUS POOR"' MODEL STATUS MARGINAL^) MODEL STATUS GOOD (3)
i,0 2(0 3,0 . 40 50 60 7p Qfj Bp
I 1 l 1 111
xxxxxx*xxxxyxxxxxxxxxxx*xxxxxi
xxxx>oo<>i
XXXXXXXXXXX 'xxxxx
xx>oocx^^
>6sO.':<:\xyx-./X;.rxj
xx;xxxxx'x\ocx'xxxj
xxxxxxxxxxxx>rxxxxxxx>oi
X>,>C>OC>^C>\XXxXXXXXJ
X>XXXXXXXXXXXvX'X>:.X>3
x^!
xxxxxxxxXxl
JONSIDERABLE EXPENDITURE AND RESEARCH EFFORT REQUIRED. NO PRESENTLY VIABLE MODELING FRAMEWORK.
SOME KEY VARIABLES OR PHENOMENA LACKING. MARGINAL VERIFICATION AND/OR APPLICATION.
:ONCEPTUAL FRAMEWORK MAY BE. UNTESTED.
PLANNING APPLICATIONS DIRECT. SOME ADDITIONAL EFFORT REQUIRED FOR GREAT LAKES PROBLEMS.
FIGURE 41
SUMMARY OF MODEL STATUS
-------
The ranking as shown in Figure 41 indicates that two modeling
frameworks are in the upper level of a marginal status:
hydrological balance and lake circulation and mixing. This
reflects the longstanding scientific and planning interest
in the problems associated with these areas. At the other
end of the scale,1two models are in the poor to poor-to-
marginal category: ice and temperature, specifically the
modeling of ice buildup and breakup phenomena, and general
ecological and food chain models. The latter represents the^
lowest modeling development status of the eleven analyzed
models and reflects the relative recent interest in
constructing models related to the aquatic ecosystem. The
low score is primarily a result of little available data and
no verification analysis of the ecological models. The
remaining seven groups fall in the intermediate category
representing, as indicated, the fact that some key variables
or subproblem contexts have not been adequately modeled. No
model framework fell in the advanced development stage,
primarily because; some subproblems have not been modeled in
sufficient detail: for planning applications.
Model Synthesis
The essence of the process of model synthesis is to
interrelate individual submodeling frameworks into a
structure that is:; aimed at a particular planning problem.
The steps followed in model synthesis in this study are
shown in Figure 42.
As indicated, seven general categories of water resource
problems are identified. These categories are listed in
Table 2, Section ^IV, together with the associated water use
interferences. The eleven modeling frameworks shown in
Figure 42 are identified with the frameworks analyzed in
Section VII and are ranked in Figure 41. For each problem
category, selections were made .from the individual eleven
modeling areas to provide a synthesized modeling structure.
The overall rank of the modeling structure is the arithmetic
average of the ranks of the component models. The
computational feasibility of implementing each modeling
300
-------
VKQBl.EM C.vrEGOHt"
SPECIFICATION
1.
Hydrologicol
2.
Theimol
Bolor.ce .
MODELING FRAMEWORK SELECTION
3
Ice a
Lake Wide
Temperature
4.
Lake
Circulation
a Mi xing
5.
Sediment-
Erosion
Cr.err.icul
\
7
Eutrophi-
coiion
6
Dissolved
Oxygen
9.
Pothogens
a Indicator
Organisms
10.
Fishery
II.
Ecological
a Food
Cham
RJ^:K OF
SYNTHESIZED
MODEL STRUCTURE
f'EASIBILirV OF
SYHIHEiliEO
MODEL. STRUCTURE
FIGURE -42
STEPS IN MODEL SYNTHESIS
-------
structure was then analyzed in terms.of the total number of
equations to be solved simultaneously. This step is
discussed more fully below. The results of the model
synthesis for each problem category then provide an important
input to the.formulation of Alternative Phase II plans as
presented in Section X.
An example of the process of model synthesis is shown in
Figure 43. The three component modeling frameworks for
problem category #4, toxic and harmful substances, are #4
Lake Circulation and Mixing, #6 Chemical, and #11 Ecologicals
and Food Chain. The average ranking of this synthesized
modeling structure is 42, placing the structure in Development
Stage II.
The results .of the application of the process of model
synthesis to each of the seven problem categories are given
in Table 17.
It should be noted that if a modeling context is in a
specific developmental stage it does not necessarily imply
an accompanying need for action in that area. Thus,
although the ice and temperature modeling sector has a poor
status, this., .does not imply that effort should necessarily
be expended lin. a Phase II study to improve the status of
that modeling framework. The priority of the problems must
be interacted with the models and the model status to
determine candidates for inclusion in further study. This
interaction ;requires the specification of problem priorities.
The subjective' establishment of such priorities as part of
this study is given in a subsequent section.
With respect to the state of model development, it is
concluded from the above analysis that several frameworks
are at a stage where certain planning problems can be
approached on the Great Lakes. Other dimensions of planning
problems, however, will require significant additional
effort to bring the modeling to- a point useful for planning.
The analysis also indicates the need for model synthesis
because so many efforts in the past have been fragmented
and directed to more narrowly-conceived aspects of planning
problems. .
302
-------
-PROBLEM-
H 4-Toxic a Harmful
Substances
(Table H-A-I)
MODELING FRAMEWORK SELECTION
LO
O
U)
RANK OF SYNTHESIZED
MODEL STRUCTURE
* 4-Toxic a Harmful
Substances = (42)
FIGURE T43
EXAMPLE OF MODEL SYNTHESIS
-------
TABLE 17 <
PROBLEM CATEGORIES AND RELATED MODELING FRAMEWORKS
Problem Categories
(See Table 2)
Average
Component Modeling Frameworks Rank
1. Mean monthly water
levels and flows
2. Erosion, sediment
3. Ice
4. Toxic and harmful
substances
5. Water quality
6. Eutrophication
7. Public Health
Hydrological Balance ;
Sediment-Erosion, circulation
and mixing .
Ica and Lake Wide Temperature
!
Ecological and food chain,;
chemical, circulation and mixing
i
Hydrological balance, chemical,
dissolved oxygen, ecological and
food chain, thermal, circulation
and mixing ' }
Hydrological balance, eutrpphi-
cation, fishery, dissolved, oxy-
gen, ecological and food chain,
circulation and mixing j
65
52
30
42
45
45
Pathogens, circulation and mixing 60
304
-------
Determination of Computational Feasibility
The construction of large, interactive Limnological Systems
Analysis requires"not only that the component models be
available, but that they can be easily interfaced. Furthermore,
it is highly desirable that as many models as possible be
implemented using ' the same modeling framework and computer
programs. That this may be the case is suggested by the
fact that the majority of the models are based on the
principle of conservation of mass or energy (See Section VI).
The exceptions .are hydrodynamic equations which conserve
momentum and mass;and the equilibrium chemical relations
which, in addition to mass conservation, also are constrained
by a free energy minimum condition. The equations which are
based on the conservation principle are quite similar in
their mathematical expressions and their modeling structures.
This fact leads to a number of simplifications which can be
exploited in the synthesis of individual models into larger
frameworks and ini the design of generalized computer programs
for their implementation. Each conservation lav/ is expressed
as a partial differential equation in time and space
variables. In the 'numerical solution of these equations, the
spatial domain is ;.considered to be a grid, and the equations
are written in terms of finite differences. For steady-state
conditions, the result is a set of simultaneous algebraic
equations. If the. equations are also linear, their solution
is straightforward. For non-steady-state models (linear or
nonlinear), the result in explicit finite difference equations
specifies the manner in which the solution evolves in time.
Again the solution of such sets of equations is straightforward.
Thus, if computer; programs (software) are designed which can
solve both the steady-state linear equations and the non-steady
state equations, ponsiderable savings in development effort
can be effected. \ Furthermore, if the softx^are is designed to
be flexible, so that it can be "used to structure the
appropriate'equation sets for each planning model as required,
additional advantage is gained. These observations lead to
the recommended computer program development: the available
models can all be. developed using the same computer programs,
the exceptions being the hydrodynamic and the equilibrium
305
-------
chemical models. ! Although the hydrodynamic model is indeed
based on the conservation principle, specialized software has
already been developed by many scientists and engineers for
its solution. For the chemical model, the resulting
mathematical problem is equivalent to a set of non-linear
algebraic equations with special properties, for which special
solution techniques and software are also available. The only
remaining problem is one of interfacing, which can be easily
resolved in view of theoretical similarities discussed above.
In order to gauge, the complexity of an integrated model, the
notation of .a compartment has been evolved. A compartment
is defined as one dependent variable at one grid point. The
dependent variable could be the magnitude of a velocity, the
concentration of ia substance, or the number of organisms;
and the grid point is a specific location in any of the three
dimensions in the lake. Thus, a series of five dependent
variables at 500 horizontal locations and at two depths in
the lake constitute a 5,000 compartment model. In the
eutrophication mo'del discussed in the next section, seven
variables are modeled in seven spatial segments. This
represents a forty-nine compartment model. Data have been
obtained on the computational running times of a variety of
models, principally in atmospheric and hydrospheric simulations
The number of compartments was determined in each case. Some
results are shown in Figure 44, which indicate there is a
tendency for the .>larger machines to be more efficient in the
evaluation of a compartment step.
The utility of the concept steins from the fact that over a
wide range of model -compartment types, the total time
required to execute a computation on similar third generation
computers is approximately proportional to the number of
compartments in the model. Using this relationship, it is
possible to estimate the execution time of a model based on
the number of compartments involved, the time step used in the
simulation, and the total real time of computation. Thus, for
a one year simulation with a computational time step of 0.1
days, the relationship between number of compartments and
central processing unit (CPU) time required for execution is
that which is given in Figure 45. The upper solid line
corresponds to the large third generation computers, the
lower solid linefto the newly developed pipeline or parallel
306
-------
6.0
QMINTZ(6)
IBM 7090
UJ
te
cc
<
O.
O
O
a
'g
w
WASP
A ONONDAGA(I)
CDC 6600
WASP(I)
POTOMAC
CDC 6 600
WEST(2)
X NCAR (3)
©FREDRICH (4)
Q.
O
UCLA (5)
IBM 360/91
.01
10
100
1,000 COMPARTMENTS 10,000
100,000
1,000,000
FIGURE 44
COMPARTMENT CALCULATION TIMES
-------
100,000
UJ
3
O
\-
<
(-
O
Q_
5
5
- -I DAY
"-IOHR
10,000
-3HR
1,000
ICO
1NFEASIBLE
RANGE
/'
/ c? j
/ ^ ?' /
/ fr /
/ + /
/ *y /
/ / /
10
I
10
100 1,000 10,000 100,000 1,000,000
COMPARTMENTS
FIGURE 45
TIME TO COMPUTE ONE YEAR SIMULATION
At =0.1 DAY
(CPU TIME)
308
-------
processors. The execution time for a seasonal simulation of
50,000 compartments (3-10 hours) appears to be the. feasible
limit. Most current large numerical meteorological and
hydrodynamic models appear to have this range as their upper
limit of execution time per run.
Figure 45 also contains the probable upper limit of
computational power that appears to be technically, feasible
today, the dashed lines representing the ultimate computer x
[7], For such a machine, 1,000,000 compartments and beyond
become feasible..
Figure 46 is another representation of computation complexity
versus execution time. For various grid sizes, the
computational time required for a given number of dependent
variables is indicated for two lake sizes. For this figure,
it is again assumed that the simulation is for one year at
a time of t = 0.1 day. In addition, it is assumed that a
five layer model is contemplated with the various 'horizontal
spacings indicated. Based on the surface area of :each of the
Great Lakes, the number of compartments required for a given
number of water quality variables is calculated. ';The number
in parenthesis is the number of spatial compartments based on
the horizontal spacing and the five levels assumed.
Assuming the feasible limit at ten hours of execution time,
5-10 variables would be the feasible limit for a five km
spacing; 15-40 variables for a ten km spacing; and'16-150
variables for a twenty km spacing. For development
purposes, it is reasonable to use an order of magnitude below
the limits so that the number of variables allowed decreases
accordingly. For this condition, a five km model is
infeasible; a ten km model with 1-4 variables andja twenty
km model with 6-15 variables are the feasible development
models.
309
-------
100,000
AX=5km
AX- 10km
AX-20km
10 HR-
3HR
10,000
IHR
o
!,000
'-'0
100
10
10 100
NUMBER OF VARIABLES
NUMBER OF SPATIAL COMPARTMENTS FOR INDICATED GRID SIZE
5km
Okm
20km
1,000
FIGURE 46
TIME TO COMPUTE. ONE YEAR SIMULATION AT FIVE LEVELS IN DEPTH
'.FOR VARIOUS HORIZONTAL SPACINGS
At =0.1 DAY
310
-------
REFERENCES
O'Connor, D.J., Thomann, R.V., DiToro, D.M., "Dynamic
Water Quality Forecasting and Control," Environmental
Engineering and Science Program, Manhattan College,
(1972) .
[2]
West, R.T., "A
the Circulation
Baroclinic Prognostic Numerical Model of
in Gulf of Mexico," Ph.D. Dis., Texas A&M
University, p 66 and ix (May 1970).
Kasahara, A., ".Computer Experiments in the Global Circu-
lation of the Earth's Atmosphere," Fall Joint Computer
Conf., 1968, AFJIPS, Vol. 33, Thompson Book Company, Wash-
ington, D.C. (1968).
[41 '
Friedrich, H.J.?,' "Preliminary Results from a Numerical
Multilayer Model for the Circulation in the North Atlantic,"
UDC, 553.. 465.45,. pp 145-164 (1969).
[51 ' " '
Langlois, W.E./.'.'Digital Simulation of the General Atmos-
pheric Circulation Using a Very Dense Grid," Fall Joint
Computer Conf.; 1971, AFIPS Press, Montvale, New Jersey,
pp 97-103 (1971).
Mintz, V., "The General Circulation and Long Range Pre-
diction," Advances in Numerical Weather Prediction 1965-
1966 Progress Report, Travelers Research Center, Hartford,
Conn.
311
-------
REFERENCES
(continued)
[7]
',
Ware, W.H.,: "The Ultimate Computer," IEEE Spectrum pp 84'
91 (March 1972).
312
-------
SECTION IX
DEMONSTRATION MODEL
Introduction
In order to illustrate the steps of model construction,
synthesis, verification, and application to planning
problems, an example - a demonstration model - is presented
in this section... The modeling structures are formulated to
illustrate a range of time-space scales as well as a range
of significant limnological planning and problem settings.
The primary emphasis in the demonstration model is directed
toward the high priority problem of lake eutrophication and
the interaction of other water resource variables within
this problem context. The spatial scales included in the
demonstration models are the entire Great Lakes, considered
as completely mixed systems, and Western Lake Erie with a
spatial scale from 5 to 40 km. The time scales considered
includa decades which are associated with Great Lakes wide
space scales, seasonal variations of water resource
variables in Western Lake Erie, and steady-state distributions,
Figure "47 illustrates the . separate submodels of the overall
demonstration model. The input and output variables
associated with the framework are listed in Figure 48. As
indicated, five submodels are formulated and analyzed with
major emphasis on the eutrophication model. The models and
the associated problem structure are:
1. Total dissolved solids (TDS) and
chloride model - Great Lakes scale:
this submodel permits estimation of
long range buildup of dissolved solids
due to such factors as municipal and
industrial discharges as well as the
secondary effects of urban growth,
such as the use of salt for deicing.
High concentrations of TDS affect
the quality of .water for municipal
and industrial water supply purposes
and can have secondary effects on the
chemical balances of the lakes.
313
-------
T.D.S -CHLORIDE
_ M_pDEL_ _
TS: DECADES
SS: W. LAKE ERIE
CHLqR|D_E_M_OpEL
TS: STEADY STATE
SS: W. LAKE ERIE
BACTERIA MODEL
TS: STEADY STATE
SS: W. LAKE ERIE
EUT_ROPHICAJ JO_N_MODE L
ZOOPLANKTON
PHYTOPLANKTON
NITROGEN FORMS
PHOSP_HO_RUS_ _FORMS
TS: SEASONAL
SS: V/ESTERN LAKE ERIE
TS: STEADY STATE
SS: W. LAKE ERIE
|
'* TS'---TIME SCALE ;
SS = SPACE SCALE
FIGURE 47 \
DEMONSTRATION MODEL FRAMEWORK !
-------
INPUT VARIABLES
I
LAKE LEVEL
TRIBUTARY INFLOW
WASTE DISCHARGES
MUNICIPAL I
AGRICULTURAL |
INDUSTRIAL I
DEMOf.'fJRATION
MODELING
R AM E WORK
I
OUTPUT VARIABLES
1
-H
I TDS -CHLORIDES
BACTERIA
ZOOPLANKTON BIOMASS
PHYTOPLANKTON BIOMASS
I NITROGEN
| PHOSPHORUS
i CADMIUM
FIGURE 48
PRIMARY INPUT - OUTPUT VARIABLES
DEMONSTRATION
MODEL
-------
2. Chloride model for Western Lake Erie:
this submodel provides a means for
determining a valid steady-state
water circulation pattern for Western
Lake Erie using chloride as a tracer.
In-addition, with output from the
previous submodel, estimates can be
made of the long term effects of
increased TDS and solids on the
municipal water supplies of the local
regions in the Western Lake Erie.
.** '
3. Bacteria model: the coliform bacteria
demonstration model is constructed
to' highlight its role in comprehensive
planning. The problem addressed
relates to the water quality of bathing
areas. Attention is directed toward
the Western Lake Erie region. The
submodel uses the water circulation
pattern determined from the chloride
submodel.
4. Su'trophication model for Western Lake
Erie: primary attention is directed
toward construction of this non-linear,
non-steady-state model of lake
eutrophication. The motivation for
this effort is the high priority
assessment associated with problems of
increased lake fertilization. The
model draws on the chloride submodel
output which verifies a water circulation
pattern for Western Lake Erie. The
primary input variables include the
rates of discharge of nutrients from
municipal, industrial, and agricultural
sources. The primary output variables
include phytoplankton and zooplankton
biomass and nutrient concentrations.
The:structure illustrates the utility
316
-------
of such models in the planning of large
, scale nutrient removal programs and
; assesses the interactions which exist
; with other water resource variables,
: such as lake levels and river inflow.
: Food chain model: this submodel is
!.constructed to illustrate the methods
employed and restrictions implied in
; the construction of linear food chain
: models which relate to problems of the
:' concentration of potentially toxic
,' substances in aquatic ecosystems.
; Cadmium is selected as the toxic
: substances for this example. Steady-
i state conditions are analyzed for
seven segments in Western Lake Erie.
\ The growth characteristics of the
I .phytoplankton and zooplankton
i generated by the eutrophication model
ara used. Cadmium is traced through
i-'-the water, phytoplankton, zooplankton,
! fish, and lake birds sections of the
i:'aquatic ecosystem. The model
I .illustrates the linking of non-linear
;' and linear submodels as well as the
' difficulty of verifying food chain
; .models.
The framework', of the entire demonstration model illustrates
the importance of model synthesis - the process of
formulating an interactive model structure from a number of
available submodels. In terms of compartments, a total
of eighty-five interactive compartments are formulated in
the eutrophiqation and food chain models. An additional
one hundred eighty compartments, are analyzed, although they
are not interactive simultaneously.
In the development of the demonstration model, emphasis is
placed on the three major steps of limnological systems
analysis: (a)1 .model construction based on known phenomena
and laws, (b) model verification using whatever observed data
is available, and .(c) model application to real problem
settings.
317
-------
Model of Chloride and Total Dissolved Solids
An increase in the concentration of conservative substances,
such as chlorides and total dissolved solids, has been
observed in the Great Lakes over the past 100 years [1].
That change, both as observed in the past and projected into
the future, may be analyzed on the basis of assuming the
Great Lakes to be a chain of completely mixed bodies of
water in which the concentration of the constituent is
considered to be uniform spatially within the time scale
of the analysis. The model is used to illustrate an
application to both the assessment of future water quality
conditions and the evaluation of present water quality
standards [2,3].
Basis of Analysis
Consider a lake, the volume of which is V, receiving fresh
water flow, R, from the rivers in the drainage basin and, in
some cases, an inflow, I, from the upstream lake. The mass
rate of waste discharged from the population and industrial
sources is W, which may be composed of a number of individual
components. It is clear that both the flows and the volume
(R, I, V,) are variable in time, yet considering the time
scale in question, these variations are assumed to have a
minimal effect. The long term pattern of flow and volume is
characterized by constant values upon which are superimposed
cyclic or random variations. A mass balance is constructed
taking into account the inflow and outflow and the various
sources and sinks of material. The differential equation
which expresses this mass balance is:
dc c _. w(t)
dt ~ ~~
where c(t) is the annual average concentration. The
wastewater discharge, W, is a time variable quantity and
the flows and volume are assumed constant in accordance
with the above analysis. The parameter, t , is the detention
time, V/Q, in which Q is the flow out of tfie lake.
318
-------
In order to evaluate the effect of inputs to upstream lakes
on water quality in downstream lakes, it is convenient to
consider a series of completely mixed bodies. The output
from one acts as an input to the downstream lake/ which in
turn feeds the next. Identifying the lakes from,1 (the
first.upstream) to n (the most downstream) the equation for
the n lake is: .'.'''
Vn
(2,
' '
where the input from the upstream lake is Q , c ,
n-l n-1.
Verification
In order to apply the above equations in a quantitative
fashion, it is necessary to assign values to the;various
parameters, V and Q , and the inputs, W . These.values are
abstracted from references [4,5,6], The major components
of the water balance of the lakes are the inflows and
outflows, runoff, and precipitation and evaporation, the
magnitudes of which vary considerably from year to year.
A water balance is shown in Figure 49 which Indicates the
average values of all components for the period 1900-1960.
The volumes, flow rates, and detention times are presented
in Table 18.
The magnitude of the chloride inputs are derived from
municipal, industrial, and road deicing sources, which are
superimposed on a background concentration due to natural
sources within the hydrologic structure [7,8,9].. The time
variable nature of the problem 'is due to the increase over
the century of the population and the associated' industrial
growth. These data are taken from the above references
and amplified, by additional data and analysis, based on the
historical increase of chlorides and total dissolved solids
in the lakes.
319
-------
u>
tvj
O
R-43. 2
P = 69.0
lE-45
Superior
P=53.0
ST. Marys
River
Chicago
Diversion
3.1
Michigan
Mackinoc
Straits
fE-35.5
P=5I.5
Huron
175.4
Sr. Clair River
LAKE
ST.CLAIRf
R-2.8
!78.2Detroit River
194.0
Niagara River
7.0
LEGEND'
(R) Basin Runoff
(P ) Precipitai ion on Lake
(E) Evaporation from Lake
Values= 1000 c fs
Welland Canal
-22.6
R=35.4
238.0
St. Lawrence River
E=I7.4
= I9.0
FIGURE 49
HYDROLOGICAL BALANCE
-------
TABLE 18
I
\ LAKE PARAMETERS
1 *,
Volume Mean flow Detention Time
Lake cubic miles cubic feet/second in years
Superior 2,940 71,800 191
Michigan 1,170 55,000 99.1
Huron
Erie
850 175,400 22.6
113 201,000 2.6
Ontario ; 404 238,000 7.9
321
-------
The computed concentration in accordance with the model is
shown in Figure 50 with various sats of observations for
the five lakes. The contribution of each of the components
is shown in Figure 51 for Lakes Erie and Ontario. An
equivalence between the chloride and total dissolved solids
exists and a comparable analysis of the total dissolved
solids may also be performed.
Application
The calculated TDS mass discharge rates in each basin for
1970 were extrapolated from the growth projections
provided by the Great Lakes Basin Commission Staff. For
the Regional Development Objective (DEV), the National
Economic Development Objective (NED), and the Environmental
Quality Objective (ENV), the projected mass discharges of
total dissolved solids are inputed to the TDS Great Lakes
model. .This -step is an illustration of the need to convert
alternative management strategies, in this case rates
of population and economic growth, into discharges to the
Great Lakes system. The model output is shown in Figure 52
for the period 1970 to 2000. Also shown is the IJC and
U.S.P.H.S. standard for the lake. This is an example of the
comparison of model output to a standard or policy objective.
It is evident from this figure that either control .
requirements jfor TDS removal or a more rigorous evaluation
of standards :will be needed for the future. The output can
also provide !an indication of tha time horizon required for
action. ; y
i
The model has also been applied to illustrate the methods
of testing alternative control policies. Under the NED
population projections, the effect of estimated municipal
and industrial consumptive and evaporative losses proved
to be minimal as did the effect of fifty percent diversion
of out-of-basin .municipal flows". However, the results of
fifty percent removal of in-basin TDS loads into Lake
Michigan andjLake Erie, which is equivalent total industrial
control in these two basins, had a significant effect as
demonstrated:for Lake Erie in Figure 53. In this example,
compliance with the existing IJC standard is obtained for
approximately forty years by the control alternative.
322
-------
10
Superior
-o-o-
-oa
1900 10 20 30 40 50 60 1900 10 20 30 40 50 60
YEARS YEARS
cc
1900 10 20 30 40 50 60
YEARS
Legend-
o Observed
Colculaed
UJ
O
O
O
UJ
O
1900 10 20 30 40 50 60 1900 10 20 30 40
YEARS YEARS
50 60
FIGURE 50
COMPUTED Vs. OBSERVED CHLORIDES
FIVE LAKES
323
-------
1900 10 20 30 40 50 60
.. YEARS- - - - - -
30
25
20
15
10
ONTARIO
INDUSTRIAL
I
NATURAL.
I I I
1900 10 20 30 40
YEARS .- -
I
50 60
FIGURE 51
SOURCE COMPONENTS FOR LAKES ERIE 8 ONTARIO
-------
300
200 -
100 -
SUPERIOR
1970 8O 90 : 2000 10. 20
300
200-
100 -
Q
O
o
UJ
J
Q
HURON
I97O 80 9O i 2OOO 10 2O
600
_i 50O '
i-
o
40O -
300-
20l
!CO
ERIE
!J S.r H S.
I
1970 80 90 2000 10 2O
300
200 -
100-
600
500 --
400-
300 -
200 -
ONTARIO
1970 80 90 2000 10 20
U.S.P.H.S.
I.J.C.
IS7Q 80 yo 2000 10 20
FIGURE 52
PROJECTED TOTAL DISSOLVED SOLIDS CONCENTRATION
FOR GREAT LAKES
325
-------
300
- 250
CO
Q
U 200
o
to
0
LJ
O
CO
CO
!50
100
LAKE ERIE
NED POPULATION PROJECTIONS
BASED ON GROWTH
OVER PREVIOUS
DECADES
5O% REMOVAL OF iN-BASIN DISCHARGE
L TO LAKE MICHIGAN 8 LAKE ERIE
EQUIVALENT TO INDUSTRIAL CONTROL)
I
I
1970 ' ' I960 1990 2000
;' YEAR
2010
2020
... FIGURE 53
PROJECTED TOTAL DISSOLVED SOLIDS CONCENTRATIONS
FOR LAKE ERIE WITH IN-BASIN CONTROL MEASURES
326
-------
Lake Erie Western Basin Chlorides and Coliform Models
A successful Limnological Systems Analysis must deal with a
variety of problems and associated variables which are
characterized'by various time and space scales. The purpose
of this demonstration model is to illustrate the techniques
and principles which are available to construct models that
have a relatively small spatial scale and for which the
assumption of temporal steady-state can be made. An
illustration is also provided of the techniques whereby
hydrodynamic modeling results can be successfully used in
the specification of the transport regime. The resulting
transport structure can then be used to calculate the
distribution of water quality variables.
Hydrodynamic Model
The hydrodynamic model of Lake Erie developed by R.T. Gedney
[10] for1 calculation of wind driven currents in Lake Erie
is used. This model is described in Section VII of this
report. Model results were obtained detailing the horizontal
currents produced -in the Western Basin of Lake Erie for a
given wind condition at a series of depths. The magnitude
and direction' of these predicted currents compare favorably
with observed'Current information [11] as shown in Figure 54.
This comparison was undertaken because the Gedney model was
verified only for main lake circulation. The resulting
agreement is Jquite encouraging because the data used for the
comparison were not available during the hydrodynamic model
construction ;and the precise wind conditions which correspond
to the observations were not used for the model calculations.
i
In order to use the calculated three dimensional velocities
for a two dimensional water quality model it is necessary to
calculate the depth averaged velocities. The resulting
depth averaged, net horizontal circulation pattern is shown
schematically in Figure 55. Average velocities range from
less than 0.1 ft/sec to 0.5 ft/sec near the mouth of the
Detroit River.
32"
-------
STATION'. P-6-7
DATE:7-3Q-67
T! MEM 315 HOURS 35 FT
BOTTOM
Wlf.'^SW IOMFH
:URFACE
2CFT
THERMOCLINE AT 30 FT
PELEE °ASSAGE OUTFLOW
S7ATION-P-4-2
DATE : 7-26-67
TIME: 1345 HOURS
WINO^SSWS-IOMPH
10 FT
-OBSERVED
-CflLCULATEO
FIGURE 54
COMPARISON OF MEASURED AND PREDICTED VELOCITIES
AT FOUR LOCATIONS IN WESTERN LAKE ERIE
328
-------
ro
vo
63°-30' NOTE: NOT ALL VECTORS SHOWN
i
FIGURE 55 -.
VERTICALLY INTEGRATED NET CIRCULATION IN WESTERN LAKE ERIE
-------
The basic principle utilized in the mathematical modeling of
water quality parameters is that of conservation mass, that
is, the mass in a system must be accounted for by the various
sources and sinks,. Such a calculation is effectively
accomplished by subdividing the study area into a series of
interactive volumes which are chosen on the basis of geometric
characteristics. -The segmentation adopted for the Western
Basin is shown in Figure 56: a series of eighty-eight two-
dimensional segments.
Segmentations of this sort are based on a knowledge of the
location of thexsignificant gradients of the water quality
variables of concern. Thus the region near the Detroit and
Maumee Rivers is ^divided into segments smaller than the
regions further removed from the main sources of the variables
of interest. This procedure results in a model which has
greater spatial resolution in the areas of interest for a
fixed total number of segments. Because the computation time
for solution of a steady-state model increases proportionally
to the total number of segments to a power of between two
and three, there ',is an effective upper limit to the size of
such models. Although the computational limit of present day
computers is well beyond the number of segments employed for
this demonstration model, the principle is well illustrated
by this example. -! A similar reduction in segment size is
employed in the hydrodynainic model [10] , for which the
Western Basin grid size is one-half that of the remainder of
the lake. ,'
Having defined the physical characteristics of the system, it
is possible to formulate a series of mass balance equations
for each finite segment and solve for resulting steady-state
equations for the-concentration of the water quality variable
of concern. The!steady-state mass balance equation for
segment j, for a conservative substance, is:
Ekj (ck -
330
-------
63°-30'
~42°-00'
TOLEDO,
83°-30'
LAKE ERIE
WESTERN BASIN
83°-00
PELEE PT,.
42°-00'-
82«30'
FIGURE 56
TWO DIMENSIONAL-88 COMPARTMENT MODEL OF WESTERN LAKE ERIE
-------
where:
c . ' = concentration of the water quality
^ ; variable in segment j
Q, . ; = net advective flow from segment k
^ to segment j
a . .= weighting factor for the finite
^ ' . difference approximation used
s
E ' . : = bulk dispersion coefficient between
^ r . segments k and j
W. \ . mass input rate to segment j
In order to establish a value for the dispersive mass
transport coefficients, E ' , and to further verify the net
circulation pattern employed, it is desirable to compare
the concentration calculated for a conservative quantity
with observation' of that variable.
j
j
Chloride Concentration Verification
The Western Basin of Lake Erie is characterized by sharp
gradients of chloride concentrations due to the lateral
stratification .of the chloride concentration of the Detroit
River. The relatively low concentrations in the central
portion by contrast to the higher concentrations at the
edges produces a. central core of relatively low chloride
concentration which persists in the central portion of the
basin. The magnitude of these differences and the resulting
shape of the plume are the basis for establishing the
magnitude of the dispersion coefficient and assessing the
validity of the calculated hydrodynamic circulation.
The circulation pattern utilized for the chloride comparison
is that which.results for a wind velocity of 11.8 mi/hr
332
-------
directed at W67°S as shown in Figure 55, the choice being
dictated by the availability of the hydrodynamic modal
output. This appears to be a reasonable choice for the
prevailing wind direction for the summer period considered.
The influence of changing wind directions on the net
circulation was not investigated. The chloride concentrations
for the incoming Detroit River are obtained from the IJC
sampling stations [12] and FWPCA survey data [13]. The
total inflowing chloride mass is 1.8 x 107 Ib/day for a
Detroit River flow of 193,000 cfs. Of secondary importance (i
is the Portage River contribution of 4.5 x 101* Ib/day at a
flow of 400 cfs., which is included for completeness since
the hydrodynamic model flow calculation includes the Portage.
The horizontal, depth averaged, dispersion coefficient
utilized for the calculations is 1.0 mi2/day, a value which
appears reasonable for the Western Basin.
The comparison between observed data and the calculated
profile is shown in Figure 57. The observed data are for
the period June-July 1967 [13], The resulting agreement
is quite satisfactory; the calculated profile has the
appropriate shape and magnitude with the central core of
lower concentrations clearly delineated.
The successful verification of the observed chloride profile
indicates that the major features of the transport structure
of the Western Basin are known in a quantitative fashion,
and this information can now be used to analyze other water
quality variables, in this case, the coliform distribution.
Coliform Model Development and Verification
The modeling of the distribution of coliform bacteria and
the effects to be expected from proposed remedial actions
are an example of an analysis which is quite complex in
principle. However, for preliminary planning purposes, an
order of magnitude analysis is relatively straightforward.
The complexity arises from the requirement that the growth
and mortality kinetics of the coliform group of bacteria
must be established in order to characterize their behavior
in natural waters and these kinetics are likely to be
333
-------
OJ
-EN
61°-30'
-42°-00'
82°-30'
TOLEDO,
. LAKE ERIE
WESTERN BASIC,
(~J FVV'PCA 1967
..
26 MODEL "RESULTS
83°-30'
PELEE PT.
82030'
I
42°-00'-
4I°-30'-
FIGURE 57
CHLORIDE VERIFICATION
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
complex. However:, for the purposes of order of magnitude
calculations which are the common first step in preliminary
plans, these complications are not significant because it
has been found that an adequate description of their kinetics
is available using a first order reaction with a rate
coefficient that is dependent on temperature and the salinity
of the receiving water (See Section VII).
;
Employing first order kinetics the conservation of mass
equation which describes the concentration of coliform
bacteria, c., in the j segment is:
0 = E [-Q
k
(a.
+ E
(c, - c.) ] - V.K.c. 4-
k ' 3
W
(4)
where K. is the reaction rate for coliform bacteria in the
segment^ This equation, therefore, is identical to Equation
(3) with the exception of the reaction kinetic term which
indicates that the substance being considered is
non-conservative "and follows a first order reaction. The
assumption of temporal steady-state has also been made as
in the case.of the chloride verification.
The reaction rate coefficient for coliform bacteria in the
Western Basin is :not known; thus it is necessary to use
actual observations to establish its value. Figure 58
presents a comparison between the June-July 1967 FWPCA
survey [13] mentioned previously and other sources [14] and
the model output, using a reaction rate of 1.0/day, a common
value for fresh waters. The quantity of coliforms
discharged into the Western Basin is established from
observed data in;the.Detroit, Maumee, Raisin, and Portage
Rivers as reported by the IJC. The resulting comparison is
judged to be acceptable if the variability of coliform
count data which is due to measurement uncertainties is
kept in mind. ' .
.th
335
-------
LO
OJ
ON
63°- 30'
-42°-00'
DETROIT
RiVER
I'
82°-30'
-4I°-3O'
83°-30
j OBSERVED DATA
-CALCULATED CONTOURS
(WPr.'/IOOML)
82°30'
4I°-30'
FIGURE 58
COLIFORM BACTERIA VERIFICATION
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
Planning Application
As a simple example of the type of application that can be
made using this model, a calculation is presented in Figure
59 for a hypothetical planning alternative which establishes
a treatment procedure that removes 99.9 percent of the
coliform bacteria entering the Western Basin from the Maumee
River. The -resulting effect is quite localized: the region
around the Maumee is noticeably improved with projected
concentrations between 10 and 100 MPN/100 ml; yet the majority
of the basin is ..unaffected. The coliform which remain,
hoxvever, are. due not only to the residual Maumee River source
but also to the effect of the other sources. Thus with such
a model it is possible to quantify not only the extent to
which narrowly conceived treatment alternatives can be
expected to iimprove conditions throughout the basin, but
also the extent to which there are interactions among the
various sources of coliform bacteria in producing observed
coliform distributions.
The eutrophication model is a small scale test of the
operational .feasibility of Limnological Systems Analysis. Its
construction was undertaken to illustrate the principles and
techniques employed and to demonstrate the utility of such
an analysis, once it is available. The water resource
problem addressed is eutrophication. The choice is dictated
primarily by .the complexity and interactive nature of the
biological, -physical, and chemical mechanisms which underlie.
the phenomena, and by the conflicting testimony of experts
in various scientific disciplines - which appears to be a
reflection of this complexity - as to the causes and possible
cures of eutrophication in the -Great Lakes. In addition,
a eutrophication model is a necessary component of a successful
Limnological Systems Analysis. Finally, the model as it now
stands can be used in a preliminary investigation of the
possible consequences of certain planning alternatives.
337
-------
to
oo
83°-30'
-42°-00'
TOLEDO,
tlEIKOIT
83°-30'
82°-30'
<*2°-00'~
PELEE PT.
62030'
4I°-30'
FIGURE 59
PROJECTED DISTRIBUTION OF COLIFORM BACTERIA
UNDER A HYPOTHETICAL TREATMENT POLICY
-------
Model Construction - Spatial and Temporal Scales
As a compromise between a lake-wide model and a small model
on the scale of a harbor, a regional model is chosen. Data
availability and the extent to which eutrophication has
progressed suggests the choice of the Western Basin of Lake
Erie as the location for the eutrophication submodel
construction and verification. : .
i
The seasonal variation of biomass is the relevant time scale."
This is generally the period for which eutrophication models
have been developed previously and it is the time scale which
characterizes a significant portion of the eutrophication
problem. The spatial scale of the model is in the order of
the characteristic lengths of the Western Basin, and the
approximate length of the spatial segments is chosen to be
approximately 40 km. The rationale for this choice and its
justification are discussed subsequently.
Model Structure - Variables and Equations
The eutrophication model is structured so as to maximize its
ability to respond to planning alternatives. The major
variable groupings - physical, chemical, and biological -
that are incorporated in the model are listed in'Table 19.
The exogenous variables are supplied externally and the
endogenous variables are computed internally. The planning
alternatives that can be addressed are determined by the
exogenous variables and the effects that can be elucidated
are determined by the endogenous variables. \
The basis of the model is a series of conservation of mass
equations which relate the endogeneous variables' to each
other and also interrelate the exogenous and endogenous
variables. The model is an extension of previously proposed
phytoplankton biomass models (see Section VII) and it includes
the effects of biological phenomena (predator-prey relations),
chemical reactions (nitrification), and the other attendant
interactions which provide the nutrients necessary for
phytoplankton growth.
339
-------
TABLE 19
'EUTROPHICATION SUB-MODEL VARIABLES
Exogenous ;
Physical Variables
Temperature Lake Level
Solar Radia-tion Detroit River Inflow
Photoperiod Water Clarity
Chemical Variables
Detroit.River Chemical Quality
Maumee River Chemical Quality
Biological; Variables
Detroit; River phytoplankton and zooplankton biomass
Maumee River phytoplankton and zooplankton biomass
Enaoaenous
Physical Variables
Extinction coefficient (euphotic zone depth)
Chemical Variable
Organic, Nitrogen Organic Phosphorus
Ammonia Nitrogen Orthophosphate
Nitrate; Nitrogen
Biological Variables
Phytoplankton biomass (chlorophyll)
Zooplankton biomass (carbon)
340
-------
A typical conservation of mass equation used in the model
for concentration c. . of substance i (i = !,...?) in segment
j has the general form:
- ctj>
V . is the segment volume, S. ., is the k source (+) or sink
(-) of substance i in segment j ; EJ . is the bulk rate of
3
transport of c.f into and c. . out of segment j for all segments
IK 1 ~^
k adjacent to segment j , and Q, . is the net advective flow
rate between segments k and j . -^Numerical integration of
these equations gives the seasonal distribution of the
endogenous variables in each of the seven spatial segments
of the model. Thus a total of forty-nine compartments are
considered.
Model Construction - Transport Reaimes
A basic requirement for a modeling effort based on conservation
of mass is an adequate representation of the mass transport
mechanisms in the Western Basin. The representation chosen
for the demonstration models is based on the advection-
dispersion formulation of mass transport. Advective mass
'transport is accomplished by the average unidirectional net
motions of the water. Dispersive mass transport is
accomplished by the mixing motions of the water body such
as the smaller scale circulations. The mass conservation
equation which results from this formulation is a partial
differential equation in the time and space variables as
discussed in Section VII. In order to implement the solution
of such an equation on a computer it is convenient to express
the equation in terms of finite differences. For the spatial
variables this corresponds to dividing the water body into
a series of segments or cells which are chosen so that the
assumption of^spatial homogeneity within each segment is
reasonable. Seven segments are chosen as a compromise between
the requirements of homogeneous concentrations and
computational complexity.
341
-------
With the number of spatial segments chosen it remains to
choose their locations and size. This is dictated primarily
by the requirement that the shallower coastal regions, which
are the productive regions for phytoplankton, be delineated
from the deeper central portions.
For the spatial scale and segmentation chosen, the advective
flows are established primarily by the Detroit River inflow
and its passage through the Western basin into the central
basin. The assignment of these flows for the demonstration x
model is made primarily on the basis of observed and computed'
flow patterns as discussed in the detailed Western Basin
steady-state model. Figure 60 presents such a circulation
pattern [12] with the prevailing directions of flow also
indicated.
In addition to the advective flow, it is necessary to assess
the magnitude of the mixing flows between adjacent segments.
This is accomplished in an indirect way by the use of a
conservative tracer, in this case, chloride concentration.
The procedure is to establish the mixing or exchange flows
in such a. way that the observed tracer concentration
distribution is matched by that calculated by the model.
A result of such a comparison is shown in Figure 61. This
comparison is judged to be adequate within the spatial
and temporal scale adopted for the demonstration model.
Figure 62 specifies both the exchange and advective flows
which are used for this comparison.
Model Construction - The Kinetic Structure of the Endogenous
Variables
The endogenous variables which are considered in the
eutrophication demonstration model are listed in Table 19.
In order to construct a model which includes these variables
it is necessary to specify quantitatively the variable
interactions among themselves and with the exogenous variables,
This is accomplished below beginning with the biological
variables.
342
-------
FIGURE 6O
CIRCULATION PATTERN IN WESTERN LAKE ERIE
SHOWING PREVAILING CURRENT DIRECTIONS
-------
OJ
-p-
-O
22.0 CHLORIDES COMPUTED
20.0 CHLORIDES OBSERVED
JULY 1967- FWPCA- DETROIT,
CLEVELAND PROGRAM OFFICES
FIGURE 61
CHLORIDE CONCENTRATIONS IN WESTERN LAKE ERIE
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
SPATIAL COMPARTMENT NUMBER
A 1970 C.C.I.W STATIONS
EXCHANGE FLOW-I09 Ft3/Day
FIGURE 62
STEADY STATE TRANSPORT FOR SEVEN COMPARTMENT
WESTERN LAKE ERIE MODEL
-------
The Phytoplankton System. The basis of the phytoplankton
equation is the principle of conservation of phytoplankton
biomass which relates the rate of change of biomass, measured
in this demonstration model as chlorophyll concentration,
to the rates of growth and death of the population, and to
the transport structure. Thus if P. is the chlorophyll
concentration in segment j, then: ^
V dPi
3 -£ = I Qkj pk + I Ekj (pk - pj> + (GPJ - DPJ> pj vj
where EA . and Q, . are the transport coefficients discussed
KJ K3
previously. G . is the phytoplankton growth rate and D . is
^ th ^
the phytoplankton death rate in the j segment.
The formulation of the phytoplankton growth rate for a
depth-averaged model is based on the following reasoning
[15]: At optimal conditions of light availability and
nutrient concentration the growth rate of a population is
dependent on temperature only, and for moderate temperature
ranges, it is directly proportional. The effect of
non-optimal light intensity is to reduce the growth rate.
If I is the optimal or saturating light intensity, then
it has been proposed [16] that the reduction in growth rate
due to an intensity I is given by:
F(I) = ~ exp [- ^- + 1] (7)
s s
In the natural environment the light available at any depth
I(z) , varies inversely with depth according to the equation:
where z is the depth (positive downward) , I is the surface
light intensity, and K is the extinction coefficient. In
(8)
346
-------
addition, the surface light intensity varies throughout the
day. For the time scale of this model, however, it is
adequately represented as a constant I , the mean daily
incident solar radiation, which is incident on the basin for
fraction of a day, the photoperiod.
For a model which is depth averaged and with a time scale
on the order of a week, it is appropriate to use a depth
averaged, time averaged growth rate reduction factor, r,
due to non-optimal light. The result, using Equation (7)
and (8) , is [15]-:
r = ^| [e"1 - e ~\ (9)
where:
I -K H
cu = _1 = e e (10)
s
ao = ^ (11)
ana:
H = depth of the segment
f = photoperiod
K = extinction coefficient
e
I = optimal light intensity
o
I = mean daily light intensity
rf
a
e = 2.718...
The effect of non-optimal nutrient concentrations is to
further reduce the growth rate. The form of the reduction
347
-------
factor chosen is the same as that adopted by Monod for
bacterial growth, namely, the Michaelis-Menton expression:
N/(K + N), where N is the nutrient concentration and K
is tRe Michaelis or half-saturation constant for that
nutrient [17]. Based on the available data and theoretical
formulations the two nutrients considered are total
inorganic nitrogen: c, (NH3 + NO3, assuming NO2 concentrations
are negligible) and orthophosphorus: c (POi*) . Based on an
analysis of a set of laboratory experiments [18], and for lack
of a better assumption, it is assumed that the growth rate v
reduction due to low nutrient concentrations is expressable
as a product of/two Michaelis-Menton expressions: CNC /(K +
c^T) (K + c )) where K .T and K are the half-saturation
N mp p mN mp
constants for total inorganic nitrogen and orthophosphorus
respectively. The growth rate expression is then assumed
to be the product of these reduction factors:
G = Ki(T) r =, ? = £ . (12)
P KmN " °N Kmp T Cp
where Ki(T) is the temperature dependent saturated growth
rate.
The formulation of the phytoplankton death rate follows a
previous analysis [15]. It is assumed that the phytoplankton
biomass is reduced by its endogenous respiration, which is
assumed to be proportional to the temperature, and by the
grazing of the zooplankton population, which is assumed to
be proportional to the zooplankton biomass concentration Z.
Thus the death rate expression is given by:
where:
Dp = K2 (T) + C (T) Z (13)
Ka (T) = temperature- dependent endo-
genous respiration rate
constants
348
-------
C (T) = temperature dependent grazing
" rate of the zooplankton
biomass
Thus equations (12) and (13) specify the growth and death
rates of the phytoplankton and, therefore, also specify
the behavior of the phytoplankton population's interaction
with temperature, light, extinction coefficient, depth,
nutrient concentrations, and zooplankton predation.
The Zooplankton System. The conservation of zooplankton
biomass equation is analogous in form to that of the
phytoplankton (Equation (6)):
zk + £ Ekj (zk - V + (Gzi - V zj vj
where G_ . and D- . are the growth and death rates of the
L-] L~}
zooplankton population whose biomass concentration, Z, is
expressed as its equivalent organic carbon concentration.
Assuming that there is sufficient phytoplankton biomass to
provide the food source for the zooplankton which affect the
phytoplankton (i.e., the herbivorous zooplankton which are
the zooplankton of concern) then their growth rate is directly
related to their grazing of the phytoplankton which can be
formulated as [15] :
Gz = a> azp rrnr VT) p
where:
ai = the conversion efficiency of
zooplankton
K = the half-saturation constant for
TnP
the phytoplankton biomass grazed
a = a conversion factor, in this case
the carbon/chlorophyll ratio of
the phytoplankton population
349
-------
The formulation of the zooplankton death rate presents
somewhat of a problem, because in addition to their
endogenous respiration rate the zooplankton are being
preyed upon by the upper levels of the food chain. In
order to simplify the model framework it is necessary to
introduce this effect empirically as an additional death
rate constant. Thus the zooplankton death rate is
expressed as:
where:
DZ = K3 (T) + KI, (16)
Ka(T) = the temperature dependent
endogenous respiration rate
KI, = empirical mortality constant
The Nitrogen System. The major components of the nitrogen
system included in this demonstration model are non-living
organic nitrogen, ca; ammonia nitrogen, ci*; and nitrate
nitrogen, cs. In natural waters there is a step-wise
transformation, mediated by bacteria, of the organic nitrogen
to ammonia nitrogen which itself is subsequently transformed
to nitrite and then to nitrate nitrogen. The first of these
steps can be an important source of inorganic nitrogen for
phytoplankton growth, which is the reason: for its inclusion,
whereas the second step, referred -to as nitrification, can
have important consequences in the dissolved oxygen balance
of lakes (Section VII). The kinetics of these transformations
are assumed to be first order reactions with temperature
dependent rate coefficients.
Two sources of detrital organic nitrogen are considered:
(1) the organic nitrogen produced by phytoplankton and
zooplankton endogenous respiration (the assumption being that
only organic forms of nitrogen result from this process) and
(2) the organic nitrogen equivalent of the grazed but not
350
-------
metabolized phytoplankton excreted by the zooplankton. The
nitrogen that results from these processes is not completely
recycled into the nonliving organic nitrogen system because,
as is shown in the verification section, the data indicate
a substantial loss of total nitrogen from the Western Basin.
It is hypothesized that this loss is due to settling of the
particulate fraction of the total nitrogen. In order to
incorporate this effect into a depth averaged formulation,
only a fraction, (3, of the nonliving organic nitrogen source
due to phytoplankton and zooplankton processes is recycled;
the remainder is assumed to be removed, presumably by settling.
The other sink of organic nitrogen included in the formulation
is the transformation of organic nitrogen to ammonia nitrogen
and, as discussed above, this is assumed to be described
by first order kinetics.
The primary kinetic source of inorganic nitrogen is via
the organic nitrogen transformation into ammonia nitrogen.
It is assumed that there are no direct kinetic pathways from
organic nitrogen to nitrate nitrogen. The primary sink of
the inorganic nitrogen forms is the phytoplankton uptake.
In order to conform with the suspicion that ammonia nitrogen
is preferentially used by phytoplankton, a praference
coefficient is introduced: a = Ci»/(K v + cO which specifies
that tha form of inorganic nitrogen utilized by growing
phytoplankton is ammonia (cO until its concentration reaches
the vicinity of the inorganic nitrogen half saturation
constant, at which point the nitrogen source shifts to
nitrate (cs). The algebraic forms used for these kinetic
interactions are shown in Table 20, and the conservation
equations are versions of Equation (6) and (14) with Table 20
indicating which sources and sinks are 'included in each
equation.
The Phosphorus System. The formulation of the phosphorus
conservation of mass equations is somewhat simpler than the
nitrogen equations because only two forms of phosphorus
are considered: nonliving organic phosphorus, CG; and
orthophosphorus, c?. The mechanisms which are included
parallel those for the nitrogen systems with the exception
of nitrification, for which it appears there is no phosphorus
counterpart. The sources and sinks which result are shown
in Table 21 and the conservation equation follows Equations
(6) and (14) in form.
351
-------
TABLE 21
THE PHOSPHORUS SYSTEM
Sources ( + ) , Sinks (-)
c& c?
Process (Org-P) (PO^-P)
Organic Phosphorus - -K67(T) c6 K67(T) c7
Orthophosphorus Transformation
Phytoplankton Uptake v -a Gp P
Ui
w Phytoplankton Endogenous Respiration Ba. K2(T) P
Zooplankton Endogenous Respiration Ba Ks(T) Z
Zooplankton Excretion . B(a C (T) ZP - a G7 Z)
pjr y pZi Zj
-------
The complete kinetic interactions of the endogenous variables
are shown in Figure 63. The cyclical structure of.the
pathways is apparent: the primary production which converts
inorganic nutrients to the phytoplankton; the secondary
production of zooplankton accomplished by their grazing on
phytoplankton; the mortality and excretion pathways which
release organic material in detrital and soluble form; the
deposition pathway which accounts for whatever settling of
the particulate fraction of the organic material occurs;
and the regeneration pathways which convert organic forms >
into inorganic forms that are then available for the primary
production pathway.
Data Sources
The limnological data base for the eutrophication* demonstration
model has been derived primarily from the survey data collected
by two groups:
1. Canadian Centre for Inland Waters ;
(CCIW) ', ' . '
i
2. Environmental Protection Agency (EPA)
The data encompasses the bulk of the data used in' the model
verification. The spatial distribution of the monitoring
stations is shown in Figure 64. In general, CCIW-- sampling
locations were visited eight times each year and the EPA
stations were visited four times during 1967-1968. Additional
observed data were reviewed from numerous sources; including
those listed in Table 22. i .
\
Observed data were retrieved from the available sources and
each data set was then analyzed for its compatabi.lity with
other comparable data sets and 'its applicability 'to' the
modeling effort. The resulting data base was then subdivided
into three data types:
354
-------
U)
Ul
01
-If- PRIMARY PRODUCTION
~t-»- -SECONDARY PRODUCTION
,f, -MORTALITY, EXCRETION
t*- -REGENERATION, NITRIFICATION
-f f--*- -DEPOSITION BY SETTLING
FIGURE 63
KINETIC PATHWAYS OF THE ENDOGENOUS VARIABLES
-------
OJ
i-n
ON
BASIN
RIVER IAT L. ERIE)
/ (19GB-69 Only)
TOLEDO OHIO WATER\JTAKE 73
WE030I
A CCI.W MONITOR CRUISE ST/i
NEARSHCRE, TRIBUTARY, AND
WATER INTAKES SAMPLING LOCATIONS
IN THE STUDY AREA.
PORT Cl INIOfl.OiUO
WAIi f< I
I: COVO-1
SANDUSKY70HIO
V/ATER INTAKE
A C.C.I.W. MONITOR CRUISE STATION-I970
HURON, OHIO
WATER INTAKE
it. . -. -^. o9
FIGURE 64
WATER QUALITY MONITORING LOCATIONS IN WESTERN LAKE ERIE
-------
TABLE 22
DATA SOURCES
Agency
Data
1. National Ocean and Atmos-
pheric Administration, Lake
Survey Center
2. United States Geological
Surveys, .
3. Great Lakes Research Di-
vision^ University of
Michigan
4. Michigan Water Resource
Commissiion
5. International Joint Coin-
mission
6. Great Lak'es Study Center
University of Buffalo
7. Frans Theodore Stone Lim-
nology Laboratory, Ohio
State University
8. U.S. Bureau of Commercial
Fisheries
9. Great Lakes Institute, Uni-
versity of Toronto
temp, transparency, pH, Eh,
alkalinity, Cl, spec.cond.,
tox.col., sediment chem., N
series, t.phos., ortho. p.
tributary flows
limnological data
phosphorus data - Detroit R.
lake level information,
coliform data
transport data
limnological data
temp, NH 3 , alk., N, NO 2,
phytoplankton,zooplankton
limnological data, solar
radiation data
357
-------
1. Open water limnological data
2. Tributary stream influent data
3. Physical, meteorological, and
hydrological data
Canadian Centre for Inland Waters Cruise Data
Since 1967, CCIW has been involved in data collection
activities on Lake Erie. Each year a series of cruises is
conducted for the purpose of monitoring a broad base of
limnological variables. These cruises normally take place
on a monthly schedule, beginning immediately following the
ice breakup and concluding some time in November. On each
cruise, 60 to 80 limnological sampling stations are visited
of which approximately 10 percent are in the Western Basin
of Lake Erie. At each station, samples are collected at
the surface and at three meter intervals to the bottom.
These samples are then analyzed for their chemical, physical,
and biological properties according to the schedule presented
in the Data Availability Section of this report. The CCIW
data base for Lake Erie was made available for the purpose
of this analysis. Data that had been collected in the
Western Basin were then separated for a detailed analysis
of its spatial and temporal variations.
The Federal WaterPollution Control Administration -
Cleveland and Detroit Program Office Limnological Data
A large body of limnological and tributary data is available
through the Environmental Protection Agency STORET system.
The availability of these data -is summarized in the data
section of this report. In 1967-1963 the Detroit Office of
the EPA conducted four extensive surveys of Lake Erie's
Western Basin. During the same period the Cleveland Program
Office collected samples on four midlake cruises which began
at Toledo Harbor and terminated at Buffalo, New York. The
358
-------
overall spatial coverage in the basin totaled 38 sampling
stations each of which was monitored at surface, mid-depth
and bottom. These data as well as data collected by the
EPA during 1965-1966 were retrieved from STORET. i
Tributary information is available through STORET for most
rivers discharging to Lake Erie. The two that are of
primary importance in the modeling effort are the Detroit
River and the Maumee River. Both rivers are sampled on a
regular basis.
Since 1913, the International Joint Commission has maintained
a water quality surveillance network at the mouth-of the
Detroit River. 'Monitoring stations are located at 500 feet
intervals across the width of the river. Each of.the fifteen
stations is visited monthly. A complete record of the IJC
network data collected since 1965 is included in the STORET
system. !
In addition, STORET is also a repository of data collected at
Water Pollution Surveillance Systems network stations by the
U.S. Department of Health, Education, and Welfare. Two of
these stations, one on the Detroit River below Trenton,
Michigan, and the other at the mouth of the Maumee, provided
pertinent biological data inputs for the modeling effort.
The Exogenous Variables :
The exogenous variables which are supplied to the; .demonstration
model are of two types: CD the variables which characterize
conditions within the Western Basin, in this case, water
temperature, solar radiation intensity and photoperiod,
lake level, and light extinction coefficient; and (2) the
variables which characterize the conditions at the boundary
of the model which in this instance are required for the
seven biological and chemical endogenous variable's being
considered. I'
The variation of water temperature from April through October
1970, the period chosen for the verification, is shown in
Figure 65. The data shown are from the 1970 CCIW cruises.
For each model segment the variation indicated is that used
in the subseauent calculations.
359
-------
LJ
C*
O
A M J J A 5 0
25 r-
UN ITS -"C
STUDY AREA
FIGURE 65
WATER TEMPERATURE VARIATION IN WESTERN LAKE ERIE
APRIL THROUGH OCTOBER,1970
-------
The photoperiod and solar radiation variation used for the
period of concern.in shown in Figure 66. The data indicated
are for 1961 [19]. It is assumed that the data are
representative of: 1970 conditions. The seasonal variation
of both temperature and solar radiation are major
contributions to the seasonal variations of the phytoplankton'
growth rate during the period of non-nutrient limited growth.
The variation of extinction coefficient as a function of time
also contributes substantial variations to the phytoplankton1
growth rate. The: variations observed in secchi depth are
shown in Figure,67. Secchi depth is converted to extinction
coefficient using the relationship [20]:
'._ Ke = 1.9/secchi depth (17)
which corresponds* to the assumption that the secchi depth
is the 15 percent', light penetration depth. The variations
assumed for two segments of the model are shown in Figure
68. ;:-"/
The boundary conditions employed for the modeling calculations
are obtained from two sources. The open water boundaries at
segments 4, 5, and 6 are obtained directly from the nearest
available CCIW sampling stations outside the Western Basin.
The Detroit River inflow concentrations are obtained from
the available IJC; data, an example of which is shown in
Figure 69. j
It is significant; .to-note the marked lateral variation of
concentrations adross the Detroit River, with the central
section concentrations being a factor of at least two lower
than the shoreline region. This lateral variation is a
major reason for the two shoreline regions and the central
region entering separate segments as shown in boundary condition
Figures 70 through 75. The Maumee River inflow quality is
set using the observed variations obtained from STORET. The
locations and identification of the sampling stations are
shov/n in Figure 64. The temporal variations of the boundary
condition used for the 1970 verification calculation are
shown in Figures ;70 through 75 with the exception of the
361
-------
22-
a , .Ntf- 4 N
Aoril
Moy June July August September Octooer
FIGURE 66
VARIATION OF PHOTOPERIOD AND SOLAR RADIATION
FOR
WESTERN LAKE ERIE
362
-------
5.00
X-DATA
A-DATA AVERAGE
4.00
LLl
h-
UJ
«>
I
X
I
Q.
LD
Q
X
o
CJ
3.00
I.CO
X X
X
X
X X
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
FIGURE 67
WESTERN BASIN
SECCHI DISK DEPTH (Meters)-1970
363
-------
Z
UJ
o
o
o
X
UJ
0.5:
0.7
1.0
2.0
100
EXTINCTION COEFFICIENT (KE) IN TWO
AREAS OF WESTERN LAKE ERIE
Apr;!
May
June July
August
September October Novemcer
FIGURE 68 /; -.
VARIATION OF EXTINCTION COEFFICIENT IN TWO COMPARTMENTS
OF THE WESTERN LAKE ERIE MODEL
364
-------
DISSOLVED ; S
PHOSPHORUS
FIGURE 69
LATERAL DISTRIBUTION OF NUTRIENTS AT
THE MOUTH OF THE DETROIT RIVER
. . 365
-------
OJ
tr>
cr.
25
20
Ib
10
5
...0 .
'25
20
15
iO
5
0
A M J, J A -S 0
- '
-
-
, l_l 1 l_l 1 1
A M J J A SO
NOTE: SCALE CHANGE
UNITS: /xgm CHLQ/L
STUDY AREA
FIGURE 70
CHLOROPHYLL CONCENTRATIONS OF TRIBUTARY STREAMS
CHLOROPHYLL BOUNDARY CONDITIONS
-------
10
GB
Ob
'J J A S 0
' ' .
-I J 1 ...._!.. -.1 . J '.
10
(-u
uc
0
A M J J A S
.
I. i.^__i I ' -I
.10
.06
.06
. .01
.02
0
A M j . J ^ A S 0
*
.
L-llL-i.-JiJ
A M J J A S 0
NOTE: SCALE CHANGE
UNIT: mg PHOSPHORUS/L
.10
.08
0G
.01
.02
0
AM J J . A S 0
.10
.08
.06
.04
02
A M J J A S 0
-
-
Lj^^^xH
STUDY AREA
FIGURE 71
INORGANIC PHOSPHORUS CONCENTRATIONS OF TRIBUTARY STREAMS
INORGANIC PHOSPHORUS BOUNDARY CONCENTRATIONS
-------
00
C5
.04
.02
.02
01
0
A M J J A S 0
.05
.04
O3
.02
.Ol
0
A M J J A S 0
-
-
-
-
i I I i i t j
.35
.2
.15
- .1
.05
0
A M J J A SO
NOTE: SCALE CHANGE
UNIT'S- mg Phosphorus/L
i I I.... ]
A M J J A S 0
03
ft?
01
0
-
_J (__J_1_.J 1 I \
STUDY AREA
FIGURE 72
ORGANIC PHOSPHORUS CONCENTRATIONS OF TRIBUTARY STREAMS
ORGANIC PHOSPHORUS BOUNDARY CONCENTRATIONS
-------
-NOTE: SCALE CHANGE ..
UNITS: mg NITROGEN/L
FIGURE 73
ORGANIC NITROGEN CONCENTRATIONS OF TRIBUTARY-STREAMS
ORGANIC NITROGEN BOUNDARY CONCENTRATIONS '
-------
CO
^1
o
A M J ' J A S 0
__)_ L I
I
A M J J A S 0
i I I I I I I
A-.M J J A S 0
.25
.2
15
.1
05
0
A M J J A 13 0
NOTE: SCALE CHANGE
UNITS ir.g liitrogtn/L
A M J J A S 0
.5
.4
.3
.2
.1
~
-
-
-
V-r^-r^rr ,
.5
.4
.3
.2
.1
0
AM J J A S 0
.' '
-
-
S x^
i i i r*'^ i ^i i
.5
.4
.3
.2
.1
0
A M J J A S 0
-
-
-
-
l""*"^ ', | | | |
STUDY AREA
FIGURE 74
AMMONIA NITROGEN CONCENTRATIONS OF TRIBUTARY STREAMS
AMMONIA NITROGEN BOUNDARY CONCENTRATIONS
-------
UNITS: mg NMTROGEN/L
1.25
1.0
75
.5
25
A M J J AS 0
-
-
\
I T 1 1 1 '1 1
1.25
in
.75
.5
35
A M J J A S 0
-
~
-
V-T^r- ^_
FIGURE 75
NITRATE NITROGEN CONCENTRATIONS OF TRIBUTARY STREAMS
NITRATE NITROGEN BOUNDARY CONCENTRATIONS
-------
zooplankton; boundaries which were set at constant values
for both the Detroit River (0.02 mg Carbon/1) and the western
boundary (0.. 4 mg Carbon/1) as estimated from the available
data. .( ' .
The Maumee River inflow contributions are treated as direct
mass inputs: because of the seasonal variation of the river
flow. The values used are listed in Table 23.
In order to; establish the Maumee River phytoplankton boundary
condition i.t is necessary to have a relationship between
the two measurements of phytoplankton biomass available:
chlorophyll: concentration and total phytoplankton cell
counts. Since both these measurements are available in the
Western Basin for the EPA cruises, a linear regression
relating the .two measurements, constrained to have zero
intercept, was performed with a resulting correlation
coefficient! of 0.82. The regression equation is:
m ^ - -'^v,i v. 11 / /i v n°« of cells/milliliter ,,_.
Totai .Chlorophyll (yg/1) - ~ (18)
j
which corresponds to the line indicated on Figure 76, a plot
of the total chlorophyll versus the counts data for the EPA
Western Lakie Erie surveillance data, 1967-1968. The ratio
of chlorophyll to total chlorophvll is assumed to be 0.75.
a "*
,1
Verificatio'ri Procedure
With the boundary conditions and exogenous variables
established as in the previous sections, the effect of
external variations of the variables of concern on the
Western Bas'in are specified. It remains to establish the
parameters iwhich specify the internal kinetics of the seven
dependent variables. The structure of the kinetics have
been -presented in Tables 20 and 21; the constants and their
temperature dependence are required in order to complete
the model. .This is done by initially using whatever
laboratory 'experimental data are available to set the probable
range of the constants [15], Then detailed comparisons are
372
-------
TABLE
23
MAUMEE RIVER MASS DISCHARGES
(thousand pounds/day)
Month
April
May
June
July
August
Sept.
Oct.
Nov.
Phy top lank ton
Chlorophyll
3.
.53
.66
1.2
.35
.20
.73
.53
.27
Zoop lank ton
Carbon
28.
18.
9.4
7.3
\
8.1
7.3
11.
5.3
Organic
Nitrogen
4.2
1.8
3. 3
5.5
5.5
5.6
0.3
0.3
Ammonia
Nitrogen
47.
44.
4.6
6.0
4.0
1.0
2.0
3.0
Nitrate
Nitrogen
28.
11.
0.5
3.7
7.7
0.08
0.56
0.6
Organic
Phos .
9.4
4.8
4.0
1.4
2.2
0.3
0.75
2.5
Inorganic
Phos.
4.0
3.0
1.5
1.0
2.0
0.1
.0.3
1.0
-------
4,000
3,500 -
3,000 -
2 2,500
3
z.
t-
i 2,000
o
o
_J
-------
made between the observed data in the Western Basin and the
computations of the model in order to fine tune the values.
The result of this exercise, if successful, is a set of
parameter values which is compatible with the observed
behavior of the phytoplankton, zooplankton, and nutrients..
The kinetic parameters which result from the verification
procedure are listed in Table 24. Comparisons with
available experimental information and other modeling studies
[21,22] indicate that for those parameters which have been
investigated, the|values tabulated are in the range of
reported values and temperature dependencies. However, these
kinetic parameters are not necessarily the unique set which
gives the best verification. A computational procedure to
find this set, though desirable, is beyond present
capabilities for a model of this complexity and the quantity
of data available.
In order to strengthen the model verification it is advisable
to compare the model to a situation which was not considered
in the initial verification. For this demonstration model
such a comparison: has been made using a composite set of data
from the years 1928-1930.
Verification Results
Fhytoplankton Chlorophyll. The comparison of the model
calculations and the 1970 CCIW survey data for chlorophyll
are shown in Figure 77. The magnitudes and shapes of the a
calculated curves' are in reasonable agreement with the
observations, although some systematic deviations are present.
In order to appreciate the importance of the kinetic
transformations, a calculation has been made assuming that
chlorophyll is a: conservative substance. The result for
segment 7 together with the verification calculation and
the available CCIW data for 1967 and 1970 is shown in Figure
78. An equilibrium concentration of less than 10 yg chl /I
results, as compared to peak concentrations of 30 yg chl /I
for the verification,, which indicates the importance of a
the kinetic interactions. That is, chlorophyll would behave
as a conservative; variable if the net growth rate (G - D )
375
-------
Phytoplankton
Saturated Growth Rate
Optimum Light Int
TABLE 24
KINETIC PARAMETERS
= 0.1 + 0.06 T ( /day)
ensity I = 350. (ly/day)
Inorganic Nitrogen
Michaelis Constant
i
i
Orthophosphorus
Michaelis Constant
N/l)
K
mP
Endogenous Respiration (T) = 0_Q04 T ( /(Jay)
Grazing Rate
Zoonlankton
Assimilation Efficiency a1 = 0.65 (rag C/mg C)
aVT. = 50. (mg C/mg Chi )
Carbon - Chlorophyll
Ratio
Constant
Empirical Mortality
Constant
C (T) = 0.012 + 0.021 T (1/mg C-day)
S"°r?Sy11 Michaelis K D = 60 (pg Chi /I)
mP
Endogenous Respiration = 0>OQ07 ( 2 ( /d }
Rate "
K
4 = 0.015 ( /day)
376
-------
TABLE 24
KINETIC PARAMETERS
(continued)
Nitrogen
Organic Nitrogen-
Ammonia Rate
Nitrification Rate
Nitrogen - Chlorophyll
Ratio .;
Nitrogen -; Zooplankton
Carbon Ratio
Fraction Recycled
Phosphorus:
Organic Phbsphorus-
Orthophosphorus Rate
K34(T) = 0.002 T ( /day)
K4S(T) = 0.002 + 0.0025 T ( /day)
aNp = 7 (mg N/mg Chl&)
aNZ =0.14 (mg N/mg C)
3 = 0.3 (mg N/mg M)
K67(T) = 0.02 T ( /day)
Phosphorus-; - -Chlorophyll -, , ,
Ratio ; * apP = l' (mg P/mg
Phosphorus;- Zooplankton
Carbon Ratio
Fraction Recycled
a =0.02 (mg p/mg C)
pz
= 0.3 (mg p/mg p)
377
-------
OJ
-J
co
50
40
30
20
10
0
A M J J A
50
40
30
20
IO
0
A M J J A S 0
50
40
30
20
10
0
A M J J A S 0
UNITS: /xgm Chla/l
x-1970 CCIW DATA
-I968 CCIW DATA
A M J J A S 0
i i i'
50
40
30
20
10
0
A M J J A S 0
50
40
30
2O
10
0
ft M J J A S O
X
X
* XK___^
-^£?~ T »'\-^_*
i i i i i i i
^
STUDY AREA
FIGURE 77
CHLOROPHYLL VERIFICATION
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
40.0
30.0
o
a.
i
o
Q-
O
CC
O
20.0
I 0.0
A 1970 DATA
n 1969 DATA.
O 1968 DATA
A 1967 DATA
CONSERVATIVE
VERIFICATION
I
I
I
I
April May June July August Sept. October . Nov.
CHLOROPHYLL IN SEGMENT No:7 !
FIGURE 78
CHLOROPHYLL RELATIONSHIPS IN COMPARTMENT NUMBER 7
COMPARISON OF MODEL RESULTS AND OBSERVED .DATA
379
-------
were everywhere zero. Under such a situation less than 10 ug
chl /I is predicted whereas actual observations are in the
range from 10 to 30 yg chl /I.
cl
Zooplankton. The ; zooplankton biomass calculated for 1970 is
shown in Figure 79. Unfortunately the CCIW zooplankton data
for this period are not available at this time, therefore a
direct comparison is not possible. However, an estimate of
the population biomass can be made using historical data [23].
Zooplankton population counts reported by various workers
are shown on Figure 80. The more recent data indicate a
population of between 500 and 1000 individuals/1. If an
organic carbon content of 1.5 yg C/individual is used as an
average between adult and juvenile forms, the observations
exceed the peak zooplankton carbon concentrations calculated.
Also it appears that the shapes of the calculated zooplankton
biomass concentrations are somewhat different from that
observed. This suggests that another food source such as
detrital organic material is an important component of the
zooplankton -nutrient source.
.] ;
Nitrogen. The verification results for the three forms of
nitrogen considered are shown in Figures 81 to 83. The
organic nitrogen data is a filtered measurement and therefore
comparable to the'Soluble fraction of the nonliving organic
nitrogen. Because the particulate fraction of the organic
nitrogen is not directly available from the model calculations,
this comparison is not precise. However, within the limited
amount of available data the results are encouraging.
The ammonia and nitrate nitrogen comparisons are direct since
the computed variables and the measurements correspond. The
agreement between:the calculations and the data is quite
good, with the major features of the data being reproduced.
The significant kinetic features of the nitrogen system
which are included in this model are phytoplankton uptake,
organic-inorganic* conversion, nitrification, and settling.
The first two effects can be separated from the last since
only settling removes, nitrogen from the water column whereas
the others are transformations for which total nitrogen
is conserved. Thus for a situation where no settling occurs,
380
-------
OJ
CO
FIGURE 79
THE ZOOPLANKTON SYSTEM
MODEL RESULTS
-------
I.OOO
500
< 100
Q
50
i:
z
Q.
O
o
N
10
EzV
1930 - WRIGHT -ISLAND REGION
O 1930-WRIGHT-MAUMEE BAY
A 1938 - 39- CHANDLER
I950-5I-OAVIS
T 1956 - 57-DAVIS
X 1962 - U. OF TORONTO (COPE POD 8 CLADOCERA ONLY)
I
Jon.
Feb Mar Apr May June July Auq Sept Oct Nov Dec
FIGURE 80
COMPARISON OF HISTORICAL ZOOPLANKTON COUNTS
. ' .OBSERVED IN WESTERN LAKE ERIE (23)
382
-------
00
OJ
.25
.2
15
.1
.06
0
25
.2
.IE
.1
.05
0
A^M J^J A S 0
^X_^ s
^- --
It
-
-
1 ! 1 1 1 | J
25
.2
.15
.1
05
0
A M J J A S 0
UNITS mg f-Jitrogcn/L
STUDY AREA
FIGURE 81
ORGANIC NITROGEN VERIFICATION
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
,. A M J J A S 0
UNIT-nig -'NITROGEN /L -";---
.25
.2
.15
.1
05
0
A M J J A S 0
-
-
rX
* \
h . \X n -*-"
r "V? * ^ , ,
STUDY AREA
FIGURE 82
AMMONIA NITROGEN VERIFICATION
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
CO
03
Ul
UNITS; mg Nitrogen /L
STUDY AREA
FIGURE 83
NITRATE NITROGEN VERIFICATION
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
total nitrogen, defined as the sum of organic, ammonia, and
nitrate nitrogen, is a conservative variable. If settling
is not allowed in the model, the result for total phosphorus
as well as total nitrogen is as shown in Figure 84. The data
are the appropriate sums from all 1970 Western Basin CCIW
cruises; the theoretical curves are the volume average total
nitrogen and total phosphorus concentrations computed for
no settling and based on the 1970 boundary conditions.
The discrepancy indicates a removal mechanism and the likely
candidate is settling. With settling included, the results
are as indicated on Figure 84. v
Phosphorus. The verification results for the two forms of
phosphorus considered are shown in Figures 85 and 86.
Total phosphorus data and the computed total phosphorus,
the sum of the nonliving phosphorus (ce) , orthophosphorus
(c?) , and the phosphorus equivalents of the phytoplankton
(a ^P) and zooplankton (a ^Z), are compared in Figure 86.
P~ " P^
The relative lack:of change in total phosphorus is a result
of its being a conservative variable, with the exception of
the settling of the nonliving fraction. The behavior of
the orthophosphorus is directly a result of phytoplankton
uptake. The apparent discrepancy at the low phosphorus
concentration (<20 ug PCK-P/1) is probably due to the
difficulty of accurately measuring orthophosphorus at these
low concentration levels.
Hindcast and Verification
A hindcast to the; year 1930 was employed to determine the
effectiveness of the phytoplankton model in predicting the
environmental effects of a set of conditions that are completely
different from those employed in the verification task. The
year 1930 was chosen for txvo reasons: first, there is a
significant base of observed data collected by Wright, et.al.,
[24] of the U.S. Department of'Interior, Fish, and Wildlife
Service during the period 1928-1930, and second, conditions
that existed in 1930 are far enough removed from the 1970
limnological conditions in the basin that a significantly
different set of events could be modeled. Data collected
386
-------
_J
CL
i
CO
02
cc
o
I
Q.
CO
O O.I
X
a.
<
b
April
Aorii
TOTAL NITROGEN
+ 1970 C.C.I.W. DATA
August
September October
TOTAL PHOSPHORUS
+ 1970 C.C.I.W. DATA
May
June
July
August
September October
i FIGURE 84
TOTAL NITROGEN AND PHOSPHORUS IN WESTERN LAKE ERIE
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
387
-------
CO
00
UNITS: mg PHOSPHORUS/L
STUDY AREA
FIGURE 85
INORGANIC PHOSPHORUS VERIFICATION
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
UJ
CO
.25
.2
.15
.1
05
0
A M J J A S O
* « » > « < n.
_i_ I I i i _1 J
AM J J A S O
f T fr... T *i
.25
.2
.15
I
05
0
A M J J A S 0
_
*
^r~~, ^
*
i ; i i i t i
25
.2
J5
.1
.05
0
A M J J A SO
-
-
/" »^_ *
% ' ".:- "it ».
>. »
i i i i i i ]
.UNITS: mq PHOSPHORUS/L
.25
.2
.15
.1
.05
0
A M J J A S 0
-
-
_ ^^
f /^>---^_i__*--i
i i i i i i i
STUDY AREA
FIGURE 86
VERIFICATION OF THE TOTAL PHOSPHORUS SYSTEM
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
in 1930 consists of algal cell counts, crustacean zooplankton
counts, albuminoid nitrogen, free ammonia, nitrate and nitrite.
No phosphorus measurements were made. A bi-weekly sampling
program was conducted at 16 stations located in the Western
Basin during the summers of 1928 through 1930.
These data were analyzed in the same manner as the verification
data base. Temporal plots of all variables were prepared for
each model segment. Tributary influent information for
phytoplankton, zooplankton, and nitrogen are available for
the Maumee River.: These data were used in estimating total
mass discharges to the system. In addition, comparisons
were made with expected per capita waste inputs and land
drainage inputs'. , A favorable comparison results.
Because phosphorus discharge information was not available
for the survey period, phosphorus inputs were established on
the following basis: 1) phosphorus detergent use was
insignificant during the survey period, 2) an approximation
of the phosphorus; mass input rate can be achieved by multiplying
the total nitrogen mass input rate by an appropriate
physiological phosphorus to nitrogen ratio. This ratio,
assumed to be 1 mg'Phosphorus/7 ing Nitrogen, was applied to
the total inorganic nitrogen mass inputs to estimate the
phosphorus mass input.
The absence of ob'servecl data with regard to sunlight and the
light extinction ''properties of the water column necessitates
using the values 'for the 1970 verification. All reaction
rates and transport phenomena employed in the 1970
verification are -employed in the hindcast. The results of
the 1928-1930 hindcast are presented in Figures 87 through
93. The total phytoplankton counts data are converted to
equivalent chlorophyll concentration using Equation (18). A
reasonable.agreement with observed data results for all
systems. However, there is some discrepancy in the crustacean
zooplankton concentrations along the western shore of the
basin. The data jindicate higher concentrations than are.
calculated. This ;..could be due to the existence of higher
zooplankton concentration at the mouths of the two tributaries,
the Maumee and the -Rasin Rivers, where these samples were
collected, as well as an inadequate modeling of the
zooplankton food -sources as discussed previously.
.390
-------
UNITS:/igm CHLOROPHYLLa/L
STUDY AREA
FIGURE 87
CHLOROPHYLL HINDCAST TO 1930
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
MD
1-0
50
40
30
20
10
A M J J A S 0
_
-
x x\^--
""-
STUDY AREA
FIGURE 88
ZOOPLANKTON HINDCAST TO 1930
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
LO
-------
' UNITS= tTi'g Nitfogen/L
^x'
.^i-jj-
25
..15
.1
,O5
0
A M J J A S 0
-
N^
_j_S==fc«=tertrrli
.25
.2
.15
1
05
0
_AMJJASO
-
\
i T V..T ' 'T *i ^i
FIGURE 9O
AMMONIA NITROGEN HINDCAST TO 1930
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
OJ
VO
Ul
FIGURE 91
NITRATE NITROGEN HINDCAST TO 1930
COMPARISON OF MODEL RESULTS AND OBSERVED DATA
-------
LJ
MD
A M J J A S 0
.2
15
.1
.05
O
.25
.2
.15
-.1 .
.05
0
.A M ' J J. A S O
i i i
UNITS:mg PHOSPHORUS/L
.25
.2
.15
.1
.05
0
A M J J A SO
-
. ~-^___ _
I I 1 i I I J
.25
.2
.15
.1
.OS
0
AM J J AS 0
-
-
-
^ ___
II II 1 I J
A M J J A S 0
.25
.2
.15
.1
.05
O
-
-
_
1 II I III
,
.25
.2
.15
.1
05
0
A M J J A S 0
-
-
-
- -_^_
1 1 I 1 1 i f
STUDY AREA
FIGURE 92
TOTAL PHOSPHORUS HINDCAST TO 1930
MODEL RESULTS
-------
u>
vo
\STUDY AREA
FIGURE 93
INORGANIC PHOSPHORUS HINDCAST TO 1930
MODEL RESULTS
-------
Hindcasting is a valuable tool in systems analysis because
it provides a means of checking the creditability of the
model. A model that is able to reproduce an historic set
of conditions that are far removed from the verification
conditions has greater reliability and can be used with more
confidence to predict water quality conditions in a future
situation. The results of the 1928-1930 hindcast provide
an encouraging test of the Western Basin eutrophication
model.
Applications to Planning
The primary purpose for constructing a Limnological Systems
Analysis is to have available a method for assessing the
effects of planning alternatives. The demonstration model is
a small scale example of such a planning tool and it is the
purpose of this section to demonstrate some of the types of
planning questions for which the eutrophication model can
provide guidance. However, these applications are not intended
to represent absolute projections o_f_ future conditions; they
are presented for illustrative purpose's" only.
The increase in the eutrophication of the Western Basin over
the past fifty years is well documented, as shown in Figure 94
[25]. To form a basis for developing plans to control this
v/ater quality problem it is necessary to estimate the effect
of the projected increases in human population and their
effect on eutrophication. Three population projections are
available for the region: The Regional Development Objective
(DEV) for relatively rapid growth, the National Development
Objective (NED) which projects relatively moderate growth,
and the Environmental Quality Objectives (ENV) for a
relatively slower growth during the planning period [26].
These population projections are shown in Table 25. The
exogenous variables of the demonstration are adjusted to
reflect these projections as follows: The nutrient inputs to
the Western Basin are computed based on the projected increase
of urban runoff and municipal and industrial contribution in
398
-------
2500 -
FIGURE 94
HISTORICAL TRENDS IN WESTERN BASIN EUTROPHICAT10N
AFTER DAVIS (2'51
399
-------
; TABLE 25
POPULATION PROJECTIONS FOR LAKE ERIE BASIN [26]
(in millions)
Growth
Projection
ENV1
NED2
DEV3
1980
; 12.2
! . 13.3
;;.'.;i4.6
1990
12.
14.
17.
8
8
5
2000
13.
16.
20.
4
8
8
2010
14.
19.
25.
0
0
5
2020
14.
21.
33.
6
3
0
NOTE: Wes-tern Basin Population is 57 percent of basin total,
Environmental ; .
2National Economic Development growth
i
3 Developmental '<
400
-------
accordance with the population increase on a per capita basis.
Agricultural runoff is assumed to be constant for the period.
Thus it is assumed that no nutrient removal programs are
instituted during the projection period. All other exogenous
variables are held at 1970 values. The results of these
projections are shown in Figure 95. The chlorophyll
concentration shown is the summer average for model segment 7,
adjacent to the Maumee River. The increases are, of course,
more pronounced for the rapid growth projected by the Regional
Development Objectives than for the more modest growth
envisioned by the Environmental Quality Objectives. Such
projected increases, and indeed current phytoplankton population
levels, are cause :for concern so that it is necessary to
investigate possible control measures. The currently favored
control policy is ,aimed at removal of the phosphorus entering
the basin. Projected conditions for both an 80 percent
removal policy and a 95 percent removal policy in addition
to a total ban on detergent phosphorus are shown in Figure 96.
The moderate National Development Objective population
projections are used for these calculations. If it is assumed
that the 1930 level of population is the desired standard,
then until 1990 the standard will be achieved and by 2010
the standard will ibe exceeded by both control policies. It
is important to note that the level of removal assumed for
the more stringent.control policy may not be presently
technologically feasible.
An alternate policy that appears to be feasible using
presently available technology is to remove 80 percent of
the phosphorus and 50 percent of the nitrogen being directly
discharged to theibasin. The projected result is shown in
Figure 97. It appears that for such a policy it is possible
to attain the assumed standard through 2010.
Thus a direct use;for.a eutrophication model is made in
assessing the efficacy of control policies specifically
designed to alleviate eutrophication. In addition, other
planning alternatives can be investigated, such as the
effect of lake level changes on eutrophication (a shallower
body of water is more productive than a deeper one, all
elsa being the same) or an agricultural land use policy
which results in a 50 percent decrease in the phosphorus
content of the agricultural runoff. The projected results
401
-------
1930
1950
1970
1990
YEAR
2010
2030
FIGURE 95
INFLUENCE _OF POPULATION GROWTH
ON' LAKE ERIE PHYTOPLANKTON CONCENTRATIONS
( No Eutrophication Control Policy)
402
-------
30 -
CL
O
a:
o
o
to
o
1-
a_
a
\-
(J OBSERVED DATA (NO REMOVAL)
AACALCULATED VALUES
WESTERN LAKE ERIE
MODEL SECTION No.7
& 30% REMOVAL
/ ^A NO DET. + 95% REMOVAL
/ ASSUMED STANDARD
1930 I950
1970 1990 2010
YEAR
2030
FIGURE 96
PHYTOPLANKTON CONCENTRATIONS Vs. TIME
FOR PHOSPHORUS REMOVAL POLICIES
(NED- Population Growth Used)
403
-------
_J
\
* 30
o
0-
§ 25
0
en
20
2iT
O
r
S 15
h-
51
in
O OBSERVED DATA (NO REMOVAL)
+ CALCULATED VALUES
WESTERN LAKE ERIE '
,' MODEL SECTION No. 7 '
1
Cl 80% P -t- 50% N
/\ REMOVAL
/ * :
/ \ i-
- / \
/ \
/ \ '
~/ !930 LEVEL ^ ^ ASSUMED STANDARD
\s \ /
\ /
\ /
V
! 1 T 1 1 1
1930 1950 1970 1990 2010 2030
YEAR
FIGURE 97
PHYTOPLANKTON CONCENTRATIONS Vs. TIME
FOR NITROGEN AND PHOSPHORUS REMOVAL POLICY
(NED- Population Growth Used)
404
-------
are shown in Table 26 which also summarizes the calculations
previously described. These two planning interactions have
no more than a 10 percent effect on the projected phytoplankton
populations for 1970 conditions. These variations are within
the probable error of the projections so that the precise
magnitude of the effect is in doubt, although it is likely to
be small.
The types of planning interactions that can be investigated
are limited only by the exogenous variables incorporated in
the model. The effects that can be projected are limited by ^
the endogenous variables and the realism and verification
of the model. Thus on a relative basis, the projected
phytoplankton changes are more reliable than the projected
zooplankton population changes because the data available
for verification for the latter are weaker. Also it should
be reemphasized that all the projections made above are in
the nature of a demonstration of the utility of a
eutrophication model and are not projections of future
events.
A Food Chain Model of Cadmium in Western Lake Erie
Introduction
The build-up of certain substances, such as heavy metals in the
ecological food chain, has been the subject of considerable
study in recent years. Ecologists have attempted to analyze
the flow of such 'material into various sectors of the
ecosystem. Planners and environmental managers have attempted
to control the release of such substances, often with little
guidance on the expected environmental response to various
levels of control actions. A mathematical model of the transfer
of material in the food chain would provide a means for
generating some information to jguide the environmental manager
on the consequences of differing policies.
The ourposes of the model, therefore, are to:
405
-------
TABLE 26
ILLUSTRATIVE APPLICATION OF THE PHASE I
LIMNOLOGICAL SYSTEMS ANALYSIS DEMONSTRATION MODEL"
Year Observed3
1930 15 yg/1
1970 25 yg/1
1990
° 20.10
Pop .
Accelerated
Growth
~
-
37 yg/1
42 'yg/1
Pop.
Moderate
Growth
-
-
30 yg/1
35 yg/1
Pop. J
Limited
Growth
-
_
26 yg/1
28 yg/1
2' Lake
Level ''
Change
-
A 2 yg/15
-
-
Phos.
Removal
50% Agr.
-
Al to 2
yg/i5
-
-
Phos.
Removal
95%+Deterg.
-
10-15 yg/12
15-20 yg/12
80% P1
-
-
15 yg/1
20 yg/1
NOTES:
'These levels are for the moderate growth population levels.
2The same algae levels can be obtained with an 80% phosphate removal policy plus 1990-25%
Nitrogen removal and 2010-50% Nitrogen removal.
3Values are micrograrns/liter of chlorophyll for Western Lake Erie in Section VII of the
Demonstration Model (near the Maumee River)
"*The information presented should be considered as an illustration of the type of results
obtainable from application of eutrophication model to analysis of planning problems
rather than a projection of future conditions.
5Change in chlorophyll levels from 1970 conditions.
-------
1. Examine the structure of the build-up
of potentially toxic substances in the
food chain.
2. Determine what data would be required
for a verification of the model.
3. Determine the utility and applicability
of linear food chain models in broad
scale ecosystem planning.
4. Demonstrate the interfacing of nonlinear
and linear modeling frameworks.
This modeling effort is directed specifically toward food
chain modeling within the context of the phytoplankton-
zooplankton model of Western Lake Erie. A seven spatial
compartment, five system steady-state model was constructed
for this purpose. Figure 98 illustrates the basic structure
of the system.
As shown, the ecosystem is considered on five levels: the
water column, phytoplankton, zcoplankton, fish, and lake
birds. The last two compartments are included as
illustrations of higher trophic levels which can act as
additional concentrators of the tracer substance. As such,
they are not necessarily realistic representations and the
results calculated should not be interpreted literally.
The geographical setting is Western Lake Erie which is
divided into seven spatial compartments as shown in Figure
98. The basic model structure is linear - discussed more
fully below - with a link from a more complex nonlinear
eutrophication model.
Identification of a Tracer Substance. Identification of a
suitable tracer substance is predicated on the following
conditions:
1. The tracer must be a substance that
concentrates in plant and animal tissue
in measureable quantities.
407
-------
; DETROIT RIVER
o
co
EUTROPHICATION
MODEL
FIGURE 98
INTERFACING OF EUTROPHICATION AND FOOD CHAIN MODELS
-------
2. It should be significant to the public
health or welfare of man.
3. It should be, preferably, a substance
for which concentration factors or
bioraass concentrations have been .
determined. ,
On this basis, cadmium is selected as a tracer element in
the food chain model. Cadmium occurs in combined forms in
nature. No important ores of cadmium are known, but it
invariably occurs as an impurity in zinc ores in a ratio
of about 1 part-'cadmium to 200 parts zinc. It is typically
a by-product of the zinc industry and is therefore
prevalent in waste discharges associated with zinc plating
processes.
Cadmium has a high toxic potential when ingested by humans.
At concentrations of greater than 0.1 mg/1, it accumulates
in soft body tissue resulting in anemia, poor metabolism,
possible adverse arterial changes in the liver, and at
high concentrations, death. The Public Health Service
Drinking Water Standard for cadmium is 0.01 rag/1; for
domestic supplies [27] . .; .
Relatively few studies have been made of cadmium concentrations
and toxicities in the aquatic environment, but studies of
mammals and fish have shown a considerable cumulative effect
in the biomass. Concentrations of a few mg/1 in. food
supplies have been known to cause sickness in man .[28].
Some cadmium data for Western Lake Erie are summarized in
Table 27. It should be noted that the lake water samples are
representative of nearshore conditions whereas offshore
samples have lower concentrations. Cadmium samples analyzed
by the Canadian Centre for Inland Waters at offshore stations
in Western Lake Erie confirm this as shown in Table 27. All
fish samples for the data shown were collected from East
Harbor, near Sandusky, Ohio. : '
409
-------
TABLE 27
SUMMARY OF OBSERVED CADMIUM DATA (yG/L)
FOR WESTERN LAKE ERIE
Number of
Ref.
Tributaries :
a) Detroit River
b) Maumee River
Lake Erie (offshore)
Lake Erie (nearshore)
a) Sandusky, 0.
water intake/
b) Toledo, O.
water intake
c) Huron, Mich.
water intake
d) Port Clinton, 0.
water intake
Fish;
a) Spottail shiner*
b) Gold Fish'
c) White Sass+
d) Yellow Perch"'"
e) Walleye
Average in
Tributaries
Average in
Lake Water
w^
5.55 34. N.D.
12.50 34. 5
N.D. N.D. N.D.
1.76 10. N.D.
1.18 10. N.D.
.59 10. N.D.
.59 10. N.D.
100.
30
1400.
1100
200.
60
200.
8.34 34. N.D.
.6 10 . N.D.
JO U- -L VCIL.XU11D
140 [29]
47 [29]
111 [30]
17 [29]
17 [29]
17 [29]
17 [29]
[31]
[31]
[31]
[31]
[31]
187
68
NOTES :
*
Whole Fish analysis (yg Cd/gm tissue)
^Fish liver analysis (yg Cd/gm tissue)
N.D. Not Detectable
A10
-------
Theorv
A discussion of ecological and food chain modeling is given
in Section VII, together with a review of the literature.
A discussion of the generalized notion of a compartment in
both physical and ecological space is presented. In general,
the biological world is discretized into a series of trophic
levels. A one dimensional trophic system can be considered
in which each level is affected only by those levels above orb
below. A food web is then a logical extension of the one
dimensional case for which interactions are more widespread
among the trophic levels.
The equations of the theory are mass balances around each
discrete trophic level positioned at some location in physical
space. The relevant measure of toxicant mass in a trophic
level is mg toxicant per unit biomass at that level. For
example, for the phytoplankton, the measure is mg cadmium
per mg chlorophyll while for fish, the measure might be mg
cadmium per mg of fish carbon. Let:
_ . mass toxicant >
" ij ~ mass trophic leva'l i
(19)
at location j and
_ .mass trophic level i»
ij ~ volume of water
(20)
at location j. Then N..M.. = C.. is the mass of toxicant
relative to volume of water at location j.
In one-dimensional trophic space for volume of water V.,
the rate of change of the mass -of toxicant is given by?
d N..M.
V.
JVJ
+ Advection + Dispersion + Sources - Sinks
(21)
411
-------
where K. , . . represents the rate of production of the toxicant
1""J- i ! I D
in trophic level i due to the transfer from trophic level i - 1,
all located at position j in geographical space and K..
represents the transfer out of trophic level i. Note1all K
values have dimensions [1/T].
The advection terms between the j location and all surrounding
k locations will have the form:
(C. . + C., )
- £ Q,k -^ (22)
k D* 2
for a central finite difference operator where Q, . is the
mass flow advected from k to j for positive outward flow.
The dispersion terms will be of the form:
E E' (C., - C. .) (23)
k ]k ik i]'
where E' is the bulk dispersion [L3/T] between j and all
surrounding k segments.
The complete mass balance equation for the mass of the tracer
substance in trophic leval i at location j is given by:
Q
(N. .M. . + N..M.,)
- L Q ., 1] 1J , 1K 1K + Z E \. (N ., M -, - N . . M. . ) + W . .
k D^ 2 k Dk 1:J 1:) 1]
for i = 1 ... m trophic levels, j = 1 ... n spatial segments
and W.. = direct input of tracer substance into trophic level
13
i at location j. The first term in Equation (24) represents
the flux of material from trophic level i-1 to level i while
(24)
412
-------
the second term represents the flux out of level i; where
the flux in Equation (24) is only "up the,food chain." If
other trophic levels interact with the i level, this
effect is a direct extension of Equation (24).
Most linear compartment models proceed by assuming a constant
trophic level mass. It is interesting to explore this special
case to draw some parallels to linear water quality models.
For constant trophic level mass in space and time and a single
volume (completely mixed), then Equation (24) becomes:
VM. dN. = S. , .N. . - S..N. + W. (25)
,1 i i-l,i i-l 11 i i
dt
where S. , . = (K. , .M. ,V) and S.. = K..M.V and no
i-l,i i-l,i i-l 11 11 i
significant inflow or outflow of water is considered. The
flux quantities, S, have dimensions of trophic level mass .
transfered per unit time. The quantity M.V has units of
trophic level mass and is designated r, tften:
F. dN. = S. , . N. , - S..N-. -i- W. (26)
1 1 1-1,1 1-1 11 1 1 '
dt
This equation is identical to the mass balance equation which
results for a water quality variable in physical space. In
the case of Equation (26), however, physical space is replaced
by trophic space. Therefore Ti represents the volume of
the i trophic level, i.e., the mass of that level available
for dilution of a toxicant, N, discharged into that i level.
The quantity S. .. . is analogous to the physical flow
i1,1
transport of water. It is clear, then, that in Equation (26)
the size of the trophic level in terms of its mass is
analogous to the size of a water body expressed in volumetric
units.
Returning to Equation (24), one can show after some
simplification that:
[A(d/dt)]. (N.M. ) = [K. V] (N. M. ,) (27)
1 1 -L J_~~ JL f j_ I*" J_ J_~" J_
413
-------
where [A(d/dt)]. represents an n x n matrix with a derivative
operator on the1main diagonal and with elements representing
the spatial transport and dispersion of material, (N.M.) is
i -U -* ^-
an n x 1 vector of the tracer material in the i * trophic
level, [&_-, -V] is an n x n diagonal matrix of transport
between the i - 1s and i trophic levels and (N. ,M. ,) is
an n x 1 vector of tracer in the i-ls level. Under steady-
state conditions, the operator d/dt is equal to zero and
the matrix equation given by (27) represents a set of linear *
algebraic equations. An example will illustrate the model
structure. ,
Consider the aquatic ecosystem as composed of three systems:
water, phytoplankton, and zooplankton; and consider a direct
input of the tracer substance into the water column. The
steady-state matrix equations are then:
Water: [A] (C ) = (W) .
w w i
Phytoplankton: [A]p (NpMp) -
Zooplankton: [A] z (N^) = tKv^pZ (NpMp)
Note that for the water column equations, the product term
N.M. does not appear and C represents the concentration of
tiie1 toxicant in the water column. The solution for the
phytoplankton system is then:
(Np) = [Mp]" [Alp" [KV]wp (Cw) (29)
where [?!_]" = diag (1/M,..., 1/M ) the inverse of the
phytoplankton biomass concentrations for the n spatial
segments. The concept of the trophic level mass acting as
a diluting volume is indicated by this matrix.
If there is feedba.ck between trophic levels or parallel
interactions (food webs) , the matrix equation is a general
extension of Equation (27) :
414
-------
[A(d/dt)]i (N^) = z [RkivJ (NkMk}i' k = ! n (30)
The summation on the right hand side of the equation expresses
all possible feedforward, feedback interactions. Under steady-
state, Equation (30) represents a set of mn simultaneous linear
equation which are readily solved.
*
In order to examine the behavior of a system such as Equations
(28) and (30) , gonsider a steady-state situation, a single
spatial volume 'and a feedback loop from the phytoplankton
and zooplankton to the water phase. The equations then are
simply:
lCw + K21CP + K31CZ = W
° = K12 Cw - K22 CP
r\ "f /° TT c*
u - .23 Cp - A33 Cz
where CD and C7 represent the concentration of toxicant in
the phvtoplankfeon and zooplankton per liter of water. Note
that if all mass is conserved, then K.. = ^.K... The ratio
of the zooplankton toxicant concentration to the concentration
in the next lowest trophic level is:
33
or the mass of toxicant per mass of trophic level is given by
N M_ K
. .
N M K
P 1Z K3
415
-------
The ratio of the concentration of toxicant in one trophic
level to the preceding level is therefore inversely
proportional to the mass of the levels and directly
proportional to the ratio of the rates at which the toxicant
is fed forward to a given level and the rate at which it
leaves that level.
The Western Lake Erie Model
As indicated in Figure 98, a five system, seven spatial
segment model has been constructed for Western Lake Erie,
which results in a set of 35 simultaneous linear equations.
This model accepts input from a nonlinear, non-steady-state
eutrophication model. The system is assumed to be at
temporal steady-state and all kinetic reactions are first
order. The concentration of toxicant in the phytoplankton,
zooplankton, fish, and lake bird systems is dependent on the
selection of feedforward or growth coefficients, K. , .,
1 -L , 1
from the previous trophic level. Likewise, decay of material
is accomplished via self-decay terms, K... 3y permitting
the feedback coefficients to be some fraction of the
difference (K. . - K. ,-,)/ the model permits resolubilizing
1,1 i, 1+1 ^_,^
of trace materials present in the i ' trophic level. In
the case inhere the sum of the feedforv;ard and feedbackward
rates does not eaual the svstein decay rate, K. ., allowances
1 1,1
can be made for deposition of materials outside the influence
of the water column.
The theoretical development of the food chain model given
above indicates that estimates of both biomass and tracer
substance concentration should be available in order to
compute the theoretical concentrations of the tracer in a
trophic level.
A significant feature of the eutrophication model is that it
estimates the growth coefficients and biomass for phytoplankton
and zooplankton systems. Since the time constants for the
highest two trophic levels are appreciably longer than that of
the phytoplankton and zooplankton, a steady-state assumption
for these trophic levels is reasonable. Steady-state biomass
concentrations for phytoplankton and zooplankton are obtained
416
-------
by conducting a simulation ;for. the entire year of 1970, and
average biomass data as well as average growth and death
coefficient are extracted from the non-linear model output.
The average annual system kinetics are incorporated into a
linearized form of the eutrophication model to check for
marked deviations in the biomass calculations, and no
significant deviation is observed.
The phytoplankton-zooplankton eutrophication model is composed
of two trophic levels and a water system. Thus it cannot be
used to make estimates of the fish or lake bird biomass.
In addition, there is a lack of available data on the magnitude
of these populations. An absolute lower bound on the fish
population is considered to be the annual commercial catch.
Estimates of the lake bird.biomass are made on the basis of
bird populations in Lakes Huron and Michigan. Although the
final biomass estimates are constructed on tenuous grounds,
they are considered reasonable. Future investigations can
provide a better framework within which to make this type of
biomass estimate. Again it should be recalled that the lake
fish and lake bird trophic.levels are included for
illustrative purposes only; .
As pointed out previously, it is possible to estimate average
phytoplankton and zooplanktoh kinetics from the output of
the nonlinear eutrophication model. The two higher trophic
levels are considerably more difficult to define in terms
of kinetic interactions. The populations are large and very
diverse, necessitating an all inclusive definition of their
behavior. Very limited data are available in this regard;
therefore assumptions have'been made to arrive at best
estimates of the reaction rates K 3 >», Ki*4, Kifs, and KSS.
Studies on the growth rates of guppy populations, when
converted to organic carbon, yield results comparable to
those usad in the food chain model. Although these rates
do vary from species
-------
Figure 99 summarizes the kinetic reaction rates and the
distribution of the net lake flows used for Western Lake Erie.
As indicated previously, the kinetic rates for the fish and
lake bird trophic levels are included solely as illustrated
values to demonstrate the build-up of a tracer in higher
trophic levels. ;The validity of the values can be estimated
only by having data available on the tracer concentration in
the biomass of the given trophic level.
Determination of Biomass Estimates. The food chain modeling.
results are most adequately interpreted when the concentration
of the tracer substance can be quantified in terms of a
biomass measurement common .to each trophic level. Organic
carbon has been selected as that basis. Physiological
factors defining ythe carbon content of various trophic levels
are readily available in the literature. For purposes of
this model, the carbon content of the phytoplankton and
zooplankton systems is taken as 50 percent of their dry weight.
The carbon content of the fish and lake bird systems is
considered to be 4 percent of the total weight.
Carbon concentrations of the phytoplankton and zooplankton
are available from -the average summer concentrations computed
in the nonlinear .-eutrophication model and are tabulated in
Table 23. For fish biomass, it was assumed that the carbon
content would be .-'approximately one twentieth of the
phytoplankton biomass, i.e., 0.05 mg carbon/1. Total biomass
of fish in all ofLake Erie on the basis of this carbon
content is computed to be 1.25 x 109 pounds. The reported
annual commercial.catch for the lake is approximately 3.5
percent of this figure. Limited data are available on fish
population of the.' Great Lakes, however, virtually no adequate
measurements of Lake. Erie's populations have been determined
to date. For demonstration purposes, 1.25 x 109 pounds of
total fish biomass as wet weight may be considered a reasonable
number, although isubject to possible order of magnitude
variations. ' '... .
For demonstration purposes, the bird populations are specified
as 0.01 |ig C/l of Lake Erie water. This figure is estimated
on the basis of bird populations for Lake Huron and Lake
Michigan [32]. The total biomass associated with these
populations is about 0.2 - 0.5 billion pounds (wet weight).
418
-------
LAKE ERIE FOOD CHAIN MODEL
v KINETIC REACTION RATES
DATP
KAI L
K II
KI2
K22
K2I
K23
K33
K3I
K34
K44
K4I
K45
K55
K5I
COMPARTMENT
1
0.130
0.130
O.lll
0.082
0.028
0.100
0.020
0.060
0.020
0.002
0.000018
0.000002
.0000002
2
0.121
0.121
0.116
0.083
0.033
0.100
0.020
0.060
0.020
0.002
0.000018
0.000002
.0000002
3
0.253
0.253
0.147
0.098
0.047
0.100
0.020
0.060
0.020
0.002
0.000018
OO00002
.0000002
4
0.117
0.117
0.197
O.I2O
0.076
0.100
0.020
0.060
0.020
0.002
0.000018
0.000002
.0000002
5
0.130
0.130
0.240
0.146
0.093
0.100
0.020
0.060
0.020
O.O02
0.000018
0.000002
.0000002
6
O.I95
0.195
0.304
0.175
O.I28
0.100
0.020
0.060
0.080
0.002
0.000018
O.OOO002
.OO00002
7
OJ85
0.185
0.192
O.I2O
0.07O
O.IOO
0.02O
0.06O
0.08O
OOO2
O.OOOOI8
0.000002
OOOOOO2
DETROIT RIVER
7 COMPARTMENT MODEL
OF WESTERN LAKE ERIE
14.4*
229.6*
MAUMEE RIVER
) COMPARTMENT NUMBER
- FLOW IN 1,000 CFS
EXCHANGE FLOW
NOT SHOWN
FIGURE 99
FOOD CHAIN MODEL CONFIGURATION
-------
TABLE 28
ASSUMED AVERAGE BIOMASS CONCENTRATIONS
FOR FOUR TROPHIC LEVELS IN
mg CARBON/LITER - SPRING 1970
WESTERN LAKE ERIE
System Spatial Segment (See Figure 2)
1234567
NOTES :
Average Values Spring 1970; Source - non- linear
phytoplankton-zooplankton model.
2Estimates of Average Annual Concentrations
Phytoplankton1 0.95 0.90 1.45 1.00 0.65 0.95 1.55
Zooplankton1 0.10 0.10 0.10 0.10 0.20 0.40 0.10
Lake Fish2 0.05 0.05 0.05 0.05 0.05 0.05 0.05
Lake Birds2 .01 .01 .01 .01 .01 .01 .01
420
-------
Concentrations of tracer substance are presented as the
concentration in the water column in mg/1 corresponding to
Ci' = Ni'Mi' in Equation (21).
The distribution of flows is shown in Figure 99 and is
obtained from other hydrodynamic information and: a'-verification
of a chloride tracer model which also provides estimates of
E' as discussed previously. With the transport structure,
kinetics, and biomass estimates at hand, the solution of thev
thirty-five equations provides the distribution of cadmium
in trophic and physical space.
Model Results
Figure 100 summaries the results of the application of the
model to Western Lake Erie. The general increase in
concentration as the cadmium proceeds up the food chain
results from two factors: the decrease in total biomass ,at
higher trophic levels and the decrease in uptake-irate. Note
that under the conditions assumed in Figure 99 and'.Table 28,
the concentration of cadmium in the fish trophic-level is
about 20 - 30 ug Cd/mg carbon which compares favorably with
the reported data as indicated on Figure 100. Also, for
the reaction rates indicated in Figure 99, the cadmium
concentration in the water phase does correspond to the order
of magnitude of observed concentrations.
If cadmium had been considered as a conservative' variable,
and therefore'not subject to uptake by the,biological system,
a value of about 5 yg/1 cadmium in the water column is
calculated due to the input loads of the Detroit, and Maumee
Rivers (see Table 27). This is 1 to 2 orders of magnitude
greater than that calculated by the food chain model. It
is also interesting to note that 5 yg/1 is1 50 percent of the
U.S. Public Health Service standard. At least from the point
of view of drinking v/ater quality, it is the biological
uptake phenomenon which has kept the cadmium concentrations
low in the water phase. .';'
421
-------
ZOQf
1970 CONDITIONS
IOQ-
50.-
.^,
£
PUBLIC HEALTH SERVICE ORINKING. WATER STANDARD
____^
RANGE
OF
NEAR
SHORE
DATA
o
1
cf
Z 34567
12 3456 7
SPATIAL
r- SEGMENTS
VSEEFIG.I)
U2 34567
I 234567
I 234567
WATER [, PHYTOPLANKTON
ZOOPLANKTON
FISH
LAKE BIRDS
FIGURE 100
COMPARISON OF FOOD CHAIN MODEL OUTPUT
WITH SOME OBSERVED DATA IN WESTERN LAKE ERIE
422
-------
It is also informative to examine the distribution of the
mass of cadmium over the seven spatial segments and over
the five systems. ; The.results of the total mass computations
appear in Table 29. As shown, about 54 percent of the
cadmium resides iri .the three upper trophic levels, the
remainder being distributed in the water and a separate
bottom or sediment compartment. The values in the latter
compartment were not computed directly but obtained by
difference. ' It should be stressed again that the results
apply only to the ;set of uptake coefficients used in the
model. The percent mass distribution in the spatial segments
reflects the effect of the flow transport in the structure.
It should be recognized, however, that the concentrations
will vary depending on the volume of the spatial segment.
Figures 101 and 102 show the model results as a function of
distance along the south shore, i.e., along segments 3, 7,
and 6. A smooth curve has been drawn between the three
concentrations (see Figure 100 for the actual levels). It
can be seen that the concentration in the water decreases
rapidly with distance because of the uptake by the aquatic
ecosystem. The degree of uptake depends on hov; long the
water takes to travel along the south shore, i.e., how long
the water is exposed to the predatory effect of the
phy top lank ton. '
\ '
This residence time-spatial effect can also be seen by
examining Figure 102 which shows concentration factors
(relative to phytoplankton) of each of the upper trophic
levels. Note that by being in an interactive phase longer,
i.e., by traveling, through segments 3, 7, and 6, the
concentration factors.increase by about one order of
magnitude. : '
The simple food chain model illustrated here could prove
useful in large scale planning applications provided
additional data are collected on the various trophic levels.
The model demonstrates the increase in concentration of
potentially.toxic1 substances, such as cadmium, as one proceeds
up the food chain'. The food chain demonstration model also
illustrates how interactive modeling between complex nonlinear
and linear compartment models can be accomplished.
423
-------
Segment No.
(See Figure
1
2
3
4
5
6
7
: ' TABLE
PERCENT OF MASS OF
. SPATIAL SEGMENT AND
29
CADMIUM BY
SYSTEM LEVEL
AS CALCULATED FOR FOOD CHAIN MODEL
% Total
1 Cadmium
98) Mass
' , 2
23
3
-: 16
: 44
7
3
- . loo
System
(See Figure 98)
1 - Water
2 - Phyto.
3 - Zoo.
4 - Lake Fish
5 - Lake Birds
Bottom
% Total
Cadmium
Mass
37
24
13
15
1
10
100
-------
200.
100.
70.
50.
40.
= 30.
T3 ''
O
0.20.
< IQ
LU I.
O
O
O
d
c_>
1970
Units for water= /ig cd/l
Units for other systems^/.
cd/mgC
J
2.
X
/
o
o:
>
CL
z
(/)
1
cc
UJ
<
2
,t ,t
0 10 20 30 40 50 60 70 80 90 100
DISTANCE FROM DETROIT RIVER KILOMETERS
FIGURE 101
COMPUTED CADMIUM CONCENTRATION ALONG SOUTH SHORE
OF WESTERN LAKE ERIE
425
-------
200.
100.
70.
-"50.
40.
O
£20.
Z
O
a: ,n
LJ
O
2
1-3.
o
2.
1.0
1970
PHYTOPLANKTON (C.F= 1.0)
cc
UJ
o
(E
cc
a: ^J
UJ >
cc
i
, I
0 10 20 30 40 50 60 70 80 90 100
DISTANCE FROM DETROIT RIVER-KILOMETERS
FIGURE 102 :
COMPUTED CADMIUM CONCENTRATION FACTORS ALONG SOUTH SHORE
OF WESTERN LAKE ERIE
426
-------
Summary
The demonstration modeling framework illustrates the processes
of model selection, synthesis, verification, and application
of mathematical models to various Great Lakes water resource
problems. The Great' Lakes basin-wide model of chlorides and
Total Dissolved Solids demonstrates the utility of such
analysis for larg.e space scale and long time scale problems.
The regional analyses as exemplified by the models of Western
Lake Erie indicate,the applicability of systems analysis
techniques to a/variety of important water resource problems.
The coliform bacteria model for Western Lake Erie indicates
the role that the hydrodynamic transport structure plays and
illustrates the use of chlorides as a tracer for verification
purposes. A model of a non-conservative variable, such as
coliform bacteria, can be used to evaluate a variety of
wastewater control actions.
The eutrophicatibn model of Western Lake Erie demonstrates
the feasibility of constructing a model that approximately
verifies observed data. The validity of the basic model
structure is further enhanced by a favorable hindcast using
1930 data. The eutrohpication model, in its preliminary form
given in the demonstration modeling framework, illustrates
the major interactions that exist in the eutrophication
phenomenon. . Although some applications of the model are
given for projected future conditions, additional detailed
analyses are required before firm conclusions could be drawn
on future water quality levels.
j
Tha food chain model illustrates the interaction between
the eutrophication model and a model of the build-up of
potentially toxic substances. Problems of verification and
data availability are demonstrated by the food chain model.
This model is an;'example of a modeling structure that is
still in an early .-stage of development and is in need of
additional'research, and development effort before it can be
utilised in a planning context.
The overall demonstration modeling framework, therefore,
illustrates the various levels of model availability and
427
-------
feasibility. It.is concluded, in general, that the use of
mathematical models in a Limnological Systems Analysis is
feasible and can, at the present state of the art, provide
important quantitative information for the decision-making
and planning processes.
428
-------
REFERENCES
rn !
Beeton, A.M., "Eutrophication of the St. Lawrence Great
Lakes," Limnology and Oceanography, Volume 10, No. 2,
(April 1965).
f 21
LJO'Connor,:D.F., Mueller, J.A., "A Water Quality Model of
Chlorides .in Great Lakes," Journal of the Sanitary Engi-
neering Division, A.3.C.E., Volume 96, No. SA4, pp 955-975
(August, 1970).
Rainey, R.H.y "Natural Displacement of Pollution from the
Great Lakes," Science, Volume.155, No. 3767 (March 10,
1967). ,|
T41
Brunk, I.W., "Hydrology of Lakes Erie and Ontario," Proc.
8th Conf.jGreat Lakes Research, Publication No. 11, GLRD,
University of Michigan (1964).
Carlson, G.T., and Persoage, N.P., "Development and Coor-
dination of Basic Hydrolo'gic Data for International Joint
Commission Study of the Great Lakes," Proc. 10th Conf. on
Great Lakes' Research (1967).
JDeCooke, 3.G., "Regulation of Great Lakes Levels and Flows,"
Proc. of_ the Great Lakes Water Resources Conf. , Toronto,
Canada (June 1968) .
Ownbey, C.E., and Kee, D.A., "Chlorides in Lake Erie,"
Proc.'10th Conf. Great Lakes Research (1967).
r R i :
U.S. Department of Health, Education, and Welfare, Public
Health Service, Division of Water Supply and Pollution
Control, "Report on Pollution of Lake Erie and its Tribu-
taries, Part'l, Lake Erie," (July 1965).
r 91
L JU.S. Department of Health, Education, and Welfare, Public
Health Control, "Great Lakes Illinois River Basins Com-
prehensive./Study, Interim Report Illinois River Basin,"
'(August 1961) .
429
-------
REFERENCES
(continued)
" Gedney, R.T., "Numerical Calculations of the Wind-Driven
Currents in Lake Erie," Ph.D. Thesis, Department of Fluid,
Thermal, and Aerospace Sciences, Case Western Reserve
University (June 1971).
Herdendorf, C.E., "Lake Erie Physical Limnology Cruise, %
Midsummer 1967," State of Ohio, Department of Natural
Resources, Division of Geological Survey, Columbus, Ohio
(1967) .
International Joint Commission, Report on the Pollution
of Lake Erie, Lake Ontario, and the International Section
of the St. Lawrence River, Volumes l^O(1969).
n "31
LJFederal Water Pollution Control Administration, Lake Erie
Surveillance Data Summary 196 7-196S, U.S. Department of
the Interior, Great Lakes Region, Cleveland Program Of~
fice (May 1968).
Federal Water Pollution Control Administration, Report
2H Water Pollution rn the Lake Erie Basin Maumee River
Area, U.S. Department of the Interior, Great Lakes, Ill-
inois River Basin Project, Cleveland Ohio (August 1966).
DiToro, D.M., O'Connor, D.J., Thomann, R.V., "A Dynamic
Model of the Phytoplankton Population in the Sacramento-
San Joaquin Delta," Advances in Chemistry Series, No. 106,
Nonequiibrium Systems iri Natural Water Chemistry, American
Chemical Society (1971).
Steele, J.K., "Notes on Some Theoretical Problems in Pro-
duction Ecology," Primary Production in Aquatic Environ-
ments , C.R. Goldman, Ed., Mem. Inst. Idrobiol., University
of California Press, Berkeley, p 383-398 (1965).
430
-------
REFERENCES
(continued)
" ^Eppley, R.W., Rogers, J.N., McCarthy, J.J., "Half Satura-
tion Constants for Uptake of Nitrate and Ammonium by
Marine P hy top lank ton," Limnol. Qceanog. 14 (6) pp 912-920
(1969).
r 181
1 Ketchum, B.H., "The Absorption of Phosphate and Nitrate -
by Illuminated Cultures of Nitzschia closterium," Am.
J. Botany, p 26 (June 1939). ;
119 1 :
Great Lakes Institute, University of Toronto, Data Report
(1962). " j
Beeton, A.M., "Relationship Between Secchi Disc Readings
and Light Penetration in Lake Huron," Am. Fish. Soc.
Trans., 87, pp 73-79 (1958).
O'Connor, D.J., DiToro, D.M., Mancini, J.L.,
Model of Phytoplankton Dynamics in the .Sacramento-San
Joaquin Bay Delta," Preliminary Report, Hvdroscience, Inc.,
(1972).
"A Preliminary
Potomac Es-
"1
Thomann, R.V., DiToro, D.M., O'Connor, D.J.,
Model of Phytoplankton Dynamics in the Upper
tuary," Manhattan College, in press (19,72).
r 931
l~ Skock, E.J., "The Biology of Upland Lakes," Great Lakes
Basin Commission Framework Study, Preliminary Draft.
"Mathematical
S., Tiffany, L.H. , Tidd, W.M. , "Limn'ological
Survey of Western Lake Erie," U.S. Department of In-
terior, Fish and Wildlife Service, Special Scientific
Report: Fisheries No. 139, Washington D.C. (1955).
r 2 5 1 '
Davis, C.C., "Evidence for the Eutrophication of Lake
Erie from Phytoplankton Records," Limnology and Ocean
ography , 9 ( 3 ) ( 19 6 4 ) .
431
-------
REFERENCES
(continued)
Great Lakes Basin Commission Framework Study, personal
communication.
[27]U.S. Department of Health, Education, and Welfare, Public
Health Service Drinking Water Standards Revised, Publica-
tion No. 956, U.S. Government Printing Office, p 61, (1969)
r 2 g ]
Water Quality.Criteria, Report of National Technology
Advisory Committee, to Secretary of the Interior, F.W.P.
C.A., Washington, D.C., (April 1968).
F291
"Environmental Protection Agency, "STOPET Data Inventor-
ies," Washington D.C..
Canadian Centre for Inland Waters, Limnological Data
Reports, Lake! .Erie, Canadian Oceanographyic Data Centre,
Burlington, Ontario.
^ Lucas, H.F., Edgington, D.N., Colby, P., "Concentrations
of Trace Elements in Great Lakes Fishes," Jour. Fishery
Res. Bd. of Canada, Volume 27, No. 4, pp 677-684 (1970).
Ludwig ,. J.P. ,.. "Herring and Ring-Billed Bull Populations
of the Great Lakes, 1960-1965," Proc. 9th Conf. G.L.R.D.,
University or Michigan, Publication No. 15, pp 80-88
(1966). " ;
432
-------
:' - SECTION x
RECOMMENDED PHASE II STUDY
Problems Proposed for Study in Phase II
In order to arrive at a recommended course of action in
Phase II of the Limnological Systems Analysis, the procedure
presented in Figure 1 was followed. The methodology
generally consists 'of two broad areas of evaluation and
analysis: first,'; the administrative determination of problems,
water uses, and associated variables; and second, the
scientific engineering analysis of modeling frameworks
associated with these problem areas. The alternate programs
are essentially based on a synthesis of these factors, a
product of the priority of the problems, and the status of
the associated modeling area. This section carries the
analysis to the point of delineation of the general problem
categories which: 'are to be considered for inclusion in Phase
The procedure shown, in Figure 1 consists of developing a list
of categories which cover the general water resource
problems of the Great Lakes. These problems basically arise
from the various water uses of the area and are summarized
in Table 2. For each of the problem areas, pertinent water
variables are identified (Table 3) . The step of assigning
a priority to each of these problem areas is the essential
one in the administrative definition of the project.
An identification of the various modeling areas, as they
apply generally to water resource problems, was simultaneously
and independently performed. These areas were then grouped
into eleven modeling frameworks which were determined by the
problems and variables enumerated in the above-mentioned
steps relating to the administrative definition. This step
was followed by an. evaluation and a ranking of the various
modeling frameworks, as summarized in Figure 41.
An interactive analysis of the eleven modeling frameworks
and seven problem categories led to the listing shown in
Table 17 and discussed in Section VIII.
433
-------
Of the seven'problem categories, those to be included in the
Phase II study-were selected on the basis of the following
criteria: :.
1.. Existing models and programs directly
:: related to or operational on Great
Lakes problems would not be duplicated.
2. Problem categories included in the
, 'Phase II effort would deal with
broad scale interactive Type II
; \-planning, not x^ith local problems or
: operational control of specific
; problems.
3...' Adequate technical knowledge should
. be available for development and
;. application of preliminary models.
Adequate data and information on
system conditions and inputs should
be available to provide at least
minimum verification of models
.proposed for Phase II.
A summary of1 this step is presented in Table 30. For each
problem category, this table includes a general assessment
of the modeling status and of the previous modeling efforts
on the Great.Lakes. In addition, an evaluation of the data
availability and the extent to which the category fits a
Type II planning problem are indicated.
The first criterion indicates that existing models for water
balance, erosion, and lake circulation should be used in the
Phase II study. Funds should be allocated to interfacing
with these existing models but should not be expended to
duplicate them. Major planning efforts associated with lake
levels and erosion would therefore be retained by the Corps
of Engineers. Interfacing of the results of these ongoing
planning activities with other water resource areas would be
part of the Phase II study.
434
-------
1.
2.
3.
Problem Category
Mean monthly water
levels and flow rates
of the Great Lakes
Erosion-sediment
Ice
RRt.ATIO.-!
Existing Modeling
Effort on the
Great Lakes
Adequate for plan-
ning and model
interaction needs
Meets near term
planning needs
None for planning
TABLU 30
OF MOUKL PROBLEMS
General State
of knowledge
and modeling
Wall advanced
(70)
Generally em-
pirical (58)
Inadequate for
Kiodaling (not
Data Availability
Adequate for plan-
ning needs
Inadequate for
model verification
Available
Type II
Planning
Problem
Generally
yes
Yes
Generally
no
4. Concentrations of
toxic or harmful
substances
5. Concentrations of
organic and inorganic
chemicals which exceed
water quality standards
6. Eutrophication
7. Bacteria and virus
concentrations in
the water body
None for planning
None for planning
None for planning
None for planning
(except in near
shore area)
Type II plan-
ning problems)
(35)
Adequate for
1.'.;t cut model-
ing (47)
Adequate for
Ist cut model-
ing (50)
Adequate for
1st cut model-
ing (50)
Adequate for
ls_t cut model-
ing" (68)
Adequate for 1st
cut modeling needs
Adequate for 1st
cut modeling needs
Adequate for 1st
modeling needs in
problem areas of
the lakes
Inadequate for
model verification
Yes
Yes
Yes
No near
shore local
Yes, lake
zone
NOTE: Numbers in brackets are average for modeling frameworks associated with each problem category.
-------
Application of the second criterion, which requires broad
scale interactive Type II planning, eliminates local water
resource modeling and predictive models for specific
operational problems. Therefore Phase II funds should not
be devoted to either modeling of ice formation for prediction
of the opening and closing of the navigation season or
improvement of lake level forecasting models for the six month
projections. These two modeling efforts, while important in
the Great Lakes, are essentially associated with operation
and management of a specific element of the system. In
addition, beach closings and harbor pollution, which are
generally of a,-local nature, do not conform to the criteria
of broad interactive water resource problems. These water
resource problems, while significant, are therefore excluded
from the Phase II study. ;
Application of the first and second criteria has therefore
resulted in elimination of water levels and flows, erosion-
sediment, ice, and local aspects of the Public Health problem
categories from consideration in Phase II. The four problem
areas which should be considered for inclusion in. the Phase
II effort are: ; .
1. Eutrophication
2. Water quality (excluding harbor scale
problems) ;
3. Public Health (excluding local beach
scale problems) ;
4. Accumulation of harmful or toxic I
substances in the food chain. ; :
Examination of these remaining- problem categories"-'Is made
based on the third and fourth criteria: namely, the levels
of modeling knowledge and data availability. With .respect
to problems of accumulation of toxic and harmful 'substances
in the food chain, the available information and knowledge
are only marginally adequate for modeling in this area. The
436
-------
problem priority, ^ox'/ever, appears to be reasonably high and
it is anticipated that the general public and governmental
agencies will tend, to increase the priority given to this
problem category in the future. It is therefore recommended
that the Phase II 'study address this problem. The lack of
scientific understanding and data indicates that this area
should have a relatively modest funding level in the Phase
II study, sufficient to provide a preliminary step in analysis,
This recommendation is made acknowledging the possible risks
of not obtaining reliable model output which will be useful
in planning and decision making processes.
The remaining problem categories all have an adequate data
base and model status to satisfy the third and fourth
criteria. The water resource problems associated with
pathogens and other indicator bacteria have low priority
when the local beach scale is excluded from consideration.
It is therefore recommended that only moderate funding or
regional scale modeling of the pathogen problem be included
in the Phase II study.
;! . *
The remaining problem categories of eutrophication and water
quality are interrelated. Based on discussions with agency,
state, and commission staffs, coupled with the general
public awareness of-the water resource problems, it is
concluded that eutrophication has a slightly higher problem
priority in the Great Lakes than do large scale water
quality problems.' However, the assessment is not sufficient
to justify a difference in allocation of funds and, since
the two areas are:closely related, it is recommended that
each receives approximately equal funding in the Phase II
Limnological Systems Analysis.
There are two additional benefits which may be derived from
the four modeling; frameworks recommended in the Phase II
study. The output may be used in the process of establishing
standards for these water resource problem categories. The
insight and knowledge'gained from modeling should be used
to guide data collection problems in terms of variables
to be measured with their associated spatial and temporal
scales. This modeling effort may be employed to increase
the effectiveness: of ongoing sampling and data collection
programs in the Great Lakes.
437
-------
Finally, it is recognized that landbased regional and
metropolitan activities have a profound impact on the four
problem areas delineated above. Consequently, planning
alternatives of this nature must be interfaced with the
proposed Phase II effort. It is anticipated that these
planning efforts '.will be a part of the continuing Great
Lakes programs and no funds have been proposed in the Phase
II Limnological Systems Analysis program for these activities.
In summary, the problem categories and models recommended
for inclusion in-the. Phase II study are based on a
qualitative estimate of the product of problem priorities,
the available data, and modeling status. Problem priorities
have not, as of the writing of this report, been assigned
by authorities in the Great Lakes region to the extent that
the Phase II study can be directed by priorities. It is
possible and desirable for representatives of the public
to establish problem priorities to which the Phase II study
could directly respond. Modifications in the specific models,
problems, and funding level of the Phase II study may then
be made to insure that the study is responsive to public
needs. ! '
AIternate Programs
A range of approaches to the overall Limnological System
Analysis is explored in this section. The alternate
programs are used as a basis for the selection of the
recommended program for the Phase II study. Four alternates
are presented which vary in philosophy and structure with
respect to the direction of the Phase II program.
The following factors are considered in developing these
alternates: : '..
The model evaluation results, summarized
in Section VIII and presented in Figure
41, which include an evaluation of the
basic knowledge and understanding
of the phenomena involved, the level of
previous models and their verification,
arid the degree of successful application
438
-------
A subjective evaluation of the relative
importance of each water resource
problem
The extent of availability of trained
personnel to carry out the Limnological
Systems Analysis
The common1 basic assumptions underlying the alternate programs
are:
University and other government sponsored
research and data collection on the Great
Lakes will continue at approximately
present levels.
The International Field Year on the
Great Lakes (IFYGL) will provide increased
understanding of laka processes and will
act as a stimulus, at least through 1975,
for research and field effort in Lake
Ontario.
Hydrodynamic circulation models and
output will be available from existing
ongoing programs. No effort in this
direction (except for provision for
suitable interfacing) is therefore
included in the alternates.
Alternate A
This alternate is predicated on. the assumptions that
understanding of many biological, chemical, and physical
phenomena with respect to water resource problems in the
Great Lakes is far from complete and requires substantially
more effort. Field observations have generally been
insufficient to describe adequately the changes which are
439
-------
apparently taking place so that meaningful predictions cannot
be made. These assumptions are coupled with the fact that
the development or application of a limnological systems
analysis approach in the Great Lakes area has been extremely
limited, specifically with respect to those problem contexts
which have been modeled elsewhere and are known to be
adaptable to the Great Lakes setting. A clear distinction
is drawn between the ability to construct equations of
phenomena and the existence of reliable meaningful predictive
tools for answering planning questions. This alternate thus,
reflects the position that much more must be done to
understand the interactions in the limnological system and
that more effort in data analysis and model verification is
required.
There are, however, several selected problem contexts which
can be modeled to produce useful results. The methodology
proposed for this alternate is to select the most competent
individual specialists available in each problem area and to
define a series of special studies for the purpose of verifying
existing or readily developed models for which sufficient
data are available. For those areas where this is not the
case, an estimate should be made of what can and should be
done with further data and model development.
Given a reasonable assessment of the problems and their
interactions, funds should be allocated to a specific
organization to coordinate and interact the models produced
by the individual specialties. Having thus initiated the
framework for a limnological systems analysis, in cooperation
with' the individual projects mentioned, the basis for
completion of this analysis would be established.
Accordingly, this alternate highlights the development of
necessary information, verification of available models, and
the extension of useful predictions which relate to
meaningful problems in conjunction with the initial steps in
the development of an overall Analysis. The applications
proposed, therefore, for Alternate A are directed to those
problems that are both practical and can be modeled with
existing analyses. Primary among these are the water quality
and eutrophication problems of the lakes which are given
high priority in the alternate.
440
-------
Alternate B
This alternate retains substantial reservations about the
feasibility and utility of constructing limnological models
for certain problem contexts, as for example, the;
construction of models of the broad scale ecological impact
of water resources activities.. However, in contrast to
Alternate A, this alternate begins with a specific
centralized activity devoted to the development of
computational software with applications to specific
problems. The applications suggested in this alternate
generally include those of Alternate A. Furthermore,
recognizing the need for interactive model development, the
initiation of such a development is recommended at a
restricted level of funding.
A generalized linear steady-state feedback system'would be
programmed under this alternate to address problems such as
water quality analysis, food chain, and broad scale ecological
models. The program would have provision for about 2,000
spatial compartments; and programming effort would be devoted
to development of computational efficiency. :
j
A generalized non-linear, non-steady-state system;is also
suggested. It should have provision for about 1,000
compartments and should be expandable so that 4,000 to
10,000 compartments can be considered to address such
problems as seasonal eutrophication, food chain, and broad
scale ecological modeling. Significant programming effort
would be devoted to development of computational efficiency.
A detailed user's manual (of both the linear and non-linear
programs) which addresses the program and the problems which
are to be analyzed would be prepared. The programming effort
devoted to the input-output would be minimized with card,
disk, or tape input and output, and digital graphical displays
as options. The program would be constructed to facilitate
significant future expansion and embellishment of input-
output routines and options as well as interlinking of
this program with the other programs, such as lake level,
chemical equilibrium, and hydrodynamic models.
441
-------
The applications in this alternate generally include those
of Alternate A and are expanded to include some applications
on the impact of consumptive use of water and a beginning
effort in the development of an interactive ecological
model. In addition,-supporting output from existing models
is to be provided.' Specifically, lake level models and
hydrodynamic models would be operated by other agencies and
individuals, and the results would provide input to the above
activities.
Alternate C
This alternate is centered around a broad scale interactive
planning model of .limnological systems, and is based on
the notion that'the implementing agency is not concerned
primarily with the. detailed solutions of problems but with
exposing the ramifications of proposed actions and in the
planning of water resource projects. The nature of the
applications in;.;this alternate is concerned more with broadly
interactive problems, rather than the detailed applications
suggested in Alternate B. The planning model itself consists
of two major sections a linear steady-state compartment
model and a non-linear, non-steady-state-model. The essence
of the alternate .lies in the belief that suitable information
exists today to;provide at least a first basis for estimating
the impact of various proposed water resource projects.
Thus, the approach in this alternate is to gather existing
subsystem mechanistic models, parameter values, and input
forcing function.levels into a broad interactive modeling
framework capable of accommodating new information as it is
developed from ongoing research effort in other areas.
All environmental .mechanisms may not be understood; indeed,
some may be quite poorly understood, while other systems
may be understood in detail. In this alternate, the fact
that a mechanism-, or phenomenon is poorly understood does not
preclude its entry into the modeling framework at the level
of known information. .This feature necessarily introduces
an unknown level of risk into the system framework, a risk
that at any given -point in time may produce a planning
result that is subsequently shown to be wrong in some sense.
442
-------
The essence of Alternate C is the willingness to take the
risks necessary to answer long range planning problems.
The development of computational software at this level is
similar to Alternate B and consists of synthesizing linear
and non-linear modeling frameworks. The application of this
alternate, hox^ever', has a direction different from that in
Alternates A and B. The emphasis in the applications is
on the broad scale limnological effects of water resource
activities, yet with some applications devoted to regional
and local problems.
Alternate D
This alternate consisting of a large interactive Limnological
Systems Analysis recognizes that an essential component for
successful long term Type II planning is the ability to
identify the consequences of alternate planning decisions.
The interactive nature of the processes which control the
water resources of the Great Lakes makes the elucidation of
these consequences a difficult exercise. However, this
alternate, like Alternate C, assumes that the amount of
scientific laws and". information available for the construction
of a Limnological Systems Analysis which can respond to a
large class of planning problems is sufficient to warrant a
concerted effort at synthesis in the form of large computer
models. j '. .
To perform these calculations on a lake-wide basis using
a three-dimensional grid with a density of grid points
sufficient to resolve medium scale phenomena is a task which
strains even the largest currently available third
generation computers. (See for example the discussion given
in Section VIII).1. With large computations of this sort,
the amount of output generated requires graphical display
for interpretations of the result. Interactive computation
can be of enormous aid in the construction, verification,
and understanding.'phase of model building.
443
-------
The observations indicate that development of an interactive
Liranological Systems Analysis computer capability, which can
utilize the .power of currently available third generation
computers (and soon to be available fourth generation
computers), is a necessary adjunct to the construction of
lake-wide or. regional models with both reasonable spatial
detail and '.a sufficient number of physical, biological, and
chemical variables to achieve the capability of exposing
subtle and .unexpected consequences of planning decisions.
>
The applications envisioned in this alternative are those
proposed in Alternate C. The major difference in approach
is that significant effort will be expended to achieve
efficient and flexible software which produces output that
is useful both for planning purposes and for model
understanding and verification. The larger computational
capacity available in this alternative (50,000 to perhaps
100,000 compartments), the flexibility of input-output,
model, structuring, and model linking will enable the
addressing,; of a wide series of planning and modeling
questions.;
It is estimated that this alternate will require a minimum
of five years for completion. This alternate strongly
supports the approach to a sequential development of a large
computer structure, rather than the immediately beginning
development of a 100,000 compartment framework.
In the development and design of this alternate, three steps
are Proposed:
Initially, emphasis would be on the bulk
of the numerical algorithms and
programming, together with preparation
of rudimentary input and output facilities
for a 5,000 compartment capacity. This
would occur during the first year of
effort; and output from this activity
would be used early to aid in solutions
of some of the problem applications
indicated for alternate C.
444
-------
2. During the second-third year of the
Phase II work, effort would be devoted
toward improvement of execution speed
and the increase of system capacity to
20,000 compartments. This would include
a major effort at achievement of
flexibility of model structuring and
interactive capabilities.
3. The fourth and fifth years would involve
evaluation of the ultimate capability
of a 50,000-100,000 compartment modeling
^structure. External efforts would be
directed toward interactive computational
models via cathode ray tube terminals.
Interaction would take place directly
with planning personnel and large scale
planning questions; and a variety of
interactions would be addressed with the
computational framework. Coincident
with the effort would be the final
applications of Alternate C.
The four preceding alternates present a range of viewpoints of
the nature of a Phase II study for Limnological Systems
Analysis. In summary, Alternate A generally considers large
scala interactive modeling as marginally feasible. Alternate
B exhibits an increasing trend toward feasibility of large
scale systems analysis, but with substantial reservations
about the actual utility of the results, while Alternate C
assumes that sufficient information is available to construct
useful limnological models. Alternate D extends the concept
of Alternate C on a larger scale particularly with respect
to computer software and input-output developments. It can
also be noted that there is a variety of views expressed in
the alternates regarding the priorities of the various
problems.
The recommended alternate which is aimed at extracting the
best elements of the four described above within certain
445
-------
funding levels, in essence, combines Alternates B and C.
Alternate A is rejected on the grounds that in spite of
certain risks, the Great Lakes region cannot afford to wait
any longer in structuring a framework that can respond to
broad planning problems. On the other hand, there are a
sufficient number of poorly understood phenomena to warrant
a negative vote on Alternate D, which would probably result
in only marginal advances for significant greater
expenditures.
Funding Levels .
Based on the above analysis and discussion, three,levels of
funding can be identified (see Table 31): !
Level 1. The cost at this level is $0.7 million; and a two
year completion time is reasonable. This funding represents
the lowest level at which a meaningful Limnological Systems
Analysis can be carried out and provides the basis for future
expansion to a broad scale interactive Limnological.Systems
Analysis effort. It is proposed that at this level of
funding, the eutrophication model be developed to;the fullest
practical extent. This level is therefore associated
primarily with Alternate B and, to a limited degree, with
Alternate A. This effort would include the development of
necessary non-linear non-steady-state computer programs, .
verification analysis, and application all specifically
directed to Lake Erie. The development of an LSA;is not
considered feasible below the $0.7 million level.; :The most
useful results of funding below this level can be;obtained
through support of existing efforts in individual,problem
and modeling contexts as represented in Alternate: A.
Level 2. The cost at this level is estimated at $2.0 million
with a three year completion time. The level represents a
favorable balance between the priority problem contexts that
can be approached, rapidly, given present modeling-status, and
those which have high priority, but for which modeling
frame-works must be significantly advanced. This level is
therefore associated with Alternates B and C. It is proposed
that this level of funding cover spatial scales oh a basin-
wide lake and regional basis and investigate the effects
of various uses on water quality, chemical levels, and food
chains. -..'.
446
-------
TABLE 31
SUMMARY OF FUNDING LEVELS
Description
Computer Program Development
!
a. Linear system development
b. Non-linear system development
c. Input preparation
d. Hydrodynamic and chemical
subsystein interfacing
Subtotal - .computer program
development
Estimated Costs
(millions of dollars)
Funding Level
I II III
0.2
0.1
0.3
0.1
0.2
0.1
0.2
0.6
0.-2
0.5
0.2
0.2
1.1
Applications
a. Great Lakes Scale
Consumptive use of water, chemical
levels and compositions, lake fer-
tilization
b. Lake Wide Scale
1. Seasonal Eutrophication
2. Water quality effects of pollu-
tants;, seasonal changes, in
.biomass and chemical levels,
food-chain model development
3. Water quality effects of pollu-
tants;, as in funding level 2,
with 'expansion to include 2-3
additional problem areas, sea-
sonal change in biomass and
chemical levels as above, food
chain model development, includ-
ing links to chemical and eco-
logical models
0.4
0.25
0.6
0.3
1.3
447
-------
TABLE 31
(continued)
SUMMARY OF FUNDING LEVELS
Estimated Costs
(millions of dollars)
Funding Level
I II III
c. Regional Scale
Water quality (bacterial and dis-
solved oxygen distributions) and
eutrophication. As in funding
level 2, with additional problem
areas included - 0.55 0.7
d. Other lake wide and regional appli-
cations, fishery model development,
links to other sub-models, erosion
sediment model development, develop-
ment of ice formation, and movement
forecasting model - - 0.5
Applications subtotal 0.4 1.4 2.8
Funding Level Total 0.7 2.0 3.9
443
-------
Level 3. In addition to the problem addressed in Level 2,
problem areas of lower priority are also included. This
level is estimated at $3.9 million, with a three year
completion time. Level 3 therefore represents a more
intensive effort than Level 2. It is felt that this level
of funding is the maximum amount that could be prudently
spent for Phase II of the Limnological Systems Analysis. It
is proposed that this level cover the elements of funding
Level 2 and, in addition, a broader range of water resource
problems, such as fisheries, erosion and sediment, and an
increased effort in the food chain modeling.
s
A summary of these funding levels is presented in Table 31
These estimates include only modeling studies using readily
available existing and anticipated data on the Great Lakes.
The estimates further assume that the agency or organization
staff performing the analysis for Phase II represents an
experienced group well-versed in the techniques of mathematical
modeling and the specific applications to the aquatic
limnological setting. They do not include provision for
field data collection, program, administration, agency or
program coordination, or data retrieval facilities.
Recommended Phase II Study
It is recommended that the Commission fund Phase II efforts
at the $2.0 million level.
At this funding level, a balance is obtained by taking an
initial step to develop and apply broad scale interactive
models providing a framework for testing the adequacy of
technical knowledge, evolving an administrative structure,
and training technical personnel in the Great Lakes problem-
oriented setting.
On the basis of the analysis given in Section VIII, it is
concluded that the Phase II program be specifically directed
to the four priority problem categories of (1) Eutrophication,
(2) Water Quality, (3) Public Health, and (4) Toxic and
Harmful Substances. The results of the model synthesis step
449
-------
in the overall methodology were given in Table 17 which
relates each problem category to synthesized model
frameworks. Inspection of this table indicates that seven
modeling structures are associated in varying degrees with
the four high priority problem categories.
Therefore the formal modeling structure proposed for Phase II
is composed of a broad scale framework consisting of seven
integrated modeling subsystems: water balance, lake
circulation and mixing, chemical, eutrophication, dissolved
oxygen, pathogens and ecological as shown in Figure 103.
These modeling frameworks are divided into two major
components by virtue of their common computational frameworks:
(1) linear steady-state systems, and (2) non-linear non-
steady-state systems.
Three broad activities are suggested for the implementation
of the Phase II program:
1. Generalized computer program development
and modifications to accommodate recently
evolved numerical and software techniques.
2. Application of existing systems technology
to those classes of problems for which the
model evaluation ranking indicates that a
reasonable degree of "success" for the
application is assured.
3. Gathering of existing sub-system models,
parameter values, and inputs to a broad
interactive modeling framework capable
of accommodating new information as it is
developed from ongoing research in other
areas.
The last step incorporates the fact that if a mechanism or
phenomenon is poorly understood, its entry into the modeling
framework is not precluded, but incorporated at the level
of known information. The models to be developed, tested,
and applied under the third activity are those that have not
450
-------
Eutrophication
V/ater
Quality
Water
Balance
Lake
Circula-
tion &
Mixing
1
Cheniicc
Public
Health
Toxic &
Harmful
Substances
PHASE II PROGRAM
Computer Program
Development
Planning Applications
a. Great Lakes Scale
b. Lake-wide Scale
c. Regional Scale
Eutrophi-
cation
~l
_xygen..
Pathogens
& Virus
Indicator
Bacteria
Ecological
&
Food
- -Chain
MATHEMATICAL MODULING FRAMEWORKS
FOR PHASi: II
FIGURE IO3
WATER RESOURCE PROBLEMS AND MATHEMATICAL MODELS
INCLUDED IN PHASE I PROGRAM
-------
generally been successfully applied to problem analysis and
prediction of future conditions. The ecological and food
chain modeling framework is an example of this situation.
No data collection program in addition to those already in
existence is proposed; the feasibility analysis indicates
that sufficient data are available for Phase II effort and,
in addition, it is difficult to determine additional data
requirements until that which is presently available is
thoroughly and adequately analyzed.
Applications for Recommended Program
In choosing applications for inclusion in the recommended
Phase II program, consideration is given to the points
outlined earlier, especially the priority of the problem
and the model status. The applications at this funding
level reflect the problem priorities that are weighted in
the direction of the effects of man's activities on the
chemical and biological quality of the lakes. At the end of
the three year effort, it is estimated that a modeling
framework will be available that can answer a broad array
of planning problems. During the Phase II study, of course,
some planning associated with the various problem areas
will be directly addressed.
Three space scales are included in the computer program
development (Great Lakes scale, lake wide, and regional).
Each scale is then applied to each problem context, together
with the nature of the modeling framework (i.e., linear and
non-linear, non-steady-state). It is further assumed that
the results of ongoing land based regional planning activities
will provide the information on systems inputs associated
with various planning alternatives, levels of population,
and industrial growth.
The three levels of spatial detail that are recommended for
incorporation in the Limnological Systems Analysis are
therefore:
452
-------
1. Great Lakes wide scale (.approximately
100-500 spatial compartments)
2. Lake wide scale (250-1,000 spatial
compartments)
3. Regional scale (250-1,000 spatial
compartments)
For each of these spatial scales, approximately 5-20
interactive variables would be considered, leading to a
maximum number pf compartments of approximately 5,000. As
discussed previously, it is not considered feasible at this
time to structure an LSA for a number of compartments
greater than 50,000. Since the present state of the art of
Limnological Systems Analysis is at a considerably lower
level (on the order of 500 to 1,000 compartments), this
appears to be a prudent level for Phase II effort.
The applications and associated costs are summarized in Table
32 and Table 33. On a Great Lakes spaca scale, two broad
areas of application assume particular importance. The first
area includes the effects on the liinnological system of the
direct use of water from the lakes for municipal, industrial,
and other related activities. Specifically, applications to
be considered are: basin wide use of evaporative cooling
control methods; water diversions for municipal and industrial
water supply; and other uses of water such as diversion of
wastewater for land reclamation projects. In each of these
cases, the linear systems framework appears appropriate. Both
time variable and steady-state analyses would be conducted.
The applications would consider the effect of the various
components of water use on concentrations of indicator
conservative constituents, such as chlorides and total
dissolved solids, changes in lake level, and associated
changes in overall quality of the lake. The time scale would
be years to decades.
The second area of application on the Great Lakes space scale
is concerned with the problem of water quality and effects
of increased lake fertilization. Therefore, this grouping
of applications deals with changes, on a Great Lakes scale,
453
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TABLE 32
PROBLCM TIME ,'VMD Sl'hCK SCAUiS FOR RECOMMENDED APPLICATIONS
Ln
-P-
Lake Wide Scale
Regional Scale
DuluthSuperior
Great Lakes Lake Area of Lake Saginaw Lake
Problem Category Scale Lake Erie Ontario Superior Michigan Bay Green Bay St. Clair
I. Water Quality
a. Dissolved
Oxygen
b. Chemical
annual
decade2
II. Public Health
III. Eutrophication
a. Biomass annual2
IV. Food Chain
seasonal'1
annuall
weekly"
seasonal1 seasonal1
monthly1 monthly1 monthly1
v;eekly2 weekly2
annual'
annual
Steady-state model application
2Time variable model application
-------
Ul
UT
TABLE 33
ESTIMATED COSTS OF RECOMMENDED APPLICATIONS
Lake Wide
Scale Regional Scale
Great Oulutli Southern
Lakes Lak-e Lake Area of Lake Saginaw Green Lake
Problem Category Scale Erie Ontario Suporior .Michigan Say Bay St. Clair
I. VJater Quality
a. Dissolved - 0.15 - 0.05 .05
Oxygen
b. Chemical v 0.15 0.10 - - - - -
II. Public Health - - - - 0.05 0.05 0.10
III. Eutrohpication
a. Biomass 0.10 0.25 - 0.05 0.15 -
IV. Food Chain - - 0.10 - - - - 0.05
NOTE: All Costs reported in millions of dollars.
Total Estimated cost of applications
Total Cost
0.25
0.25
0.20
0.55
0.15
.. .$ 1.40
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in nutrient levels and plant biomass. The modeling
framework is generally non-linear and non-steady-state,
although linear sectors can be included. A non-linear
chemical equilibrium model would be included, as well as a
seasonal and yearly non-linear model of algal biomass as
developed in the Demonstration Model.
On the lake wide and regional scale, primary emphasis is
given to the effects on water quality and the general
ecosystem of present and future discharges of municipal
and industrial wastes, agricultural runoff, and other
natural and man-made pollutants. Both linear and non-linear
model framework's are employed, and the time scale is
generally seasonal or steady-state. Problem variables
would include biomass and chemical, biochemical, and
bacterial indicators of water quality.
Geographically, emphasis on the lake wide scale is directed
toward Lake Erie, an area associated with water quality and
eutrophication problems. In addition, it is recommendedd
that the results of the International Field Year on the
Great Lakes effort on Lake Ontario be used on a lake-wide
basis as input data for an analysis of the ecological and
food chain problem category for that lake. Therefore, it
is suggested that a broadly based interactive model be
developed which would provide a basis for decision making
on the planned or inadvertent introduction of food chain
accumulants such as pesticides and heavy metals.
On a regional scale, as shown in Tables 32 and 33, five
areas are recommended for problem analysis and model
application:
1. Duluth area of. Lake Superior
2. Southern Lake Michigan
3. Saginaw Bay
4. Green Bay
5. Lake St. Glair
456
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The applications thus cover a wide geographical area and
span problem locations in all Great Lakes.
The applications as described are approximately evenly
distributed between specific problem contexts that have a
reasonable degree of assurance of being successfully
analyzed by the Limnological Systems Analysis and problem
contexts that are more vaguely stated and require
incorporation of less well-understood phenomena. It is
believed that pursuit of the Phase II program as outlined
above will provide a meaningful structure to the decision
making processes on the water resources of the Great Lakes,
457
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing}
1. REPORT NO,
EPA-600/3-77-126b
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Great Lakes Environmental Planning Using Limnological
Systems Analysis: Phase I - Preliminary Model Design
5. REPORT DATE
November 1977 issuing date
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Hydroscience, Inc., 363 Old Hook Road, Westwood, New
Jersey 07675
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
prepared for the Great Lakes Basin Commission
P. 0. Box 999
3475 Plymouth Road
Ann Arbor, Michigan 48106
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
DACW-35-71-C0030
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Research Laboratory-Duluth, MN
Office of Research and Development
U.S. Environmental Prptection Agency
Duluth, MN 55804
55804
13. T_YP£ OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA-600/03
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The report documents the deliberate decision making process used by the Great Lakes
Basin Commission in concluding that rational modeling methodologies could be used
to evaluate the effect of different planning alternatives on the Great Lakes and
that planning for specific problems affecting the Great Lakes system can be technical-
ly and economically supported through mathematical modeling and systems analysis. It
assesses the technical and economical feasibility of developing mathematical models
to assist in making selections from among alternative management strategies and
structural solutions proposed for solving water resource problems of the Great Lakes.
The study reviews, evaluates and categorizes present and future water resources
problems, presently available data, problem-oriented mathematical models and the
state of models and model synthesis for large lakes. A demonstration modeling frame-
work for planning is developed and applied to western Lake Erie and the Great Lakes
system. The report evaluates four widely ranging alternatives for future modeling
efforts in the Great Lakes and recommends the modeling level most feasible to answer
planning questions on scales ranging from the Great Lakes to regional areas. Also
discussed is a proposed Commission study which will apply limnological systems
analysis to the planning process.
17.
KEY WORDS ANfD DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
COSATl field/Group
Limnology, Systems, Mathematical Models,
Water Resources, Planning, Hydrology,
Ecology
systems analysis, Great
Lakes, ecosystems, long
term planning,
environmental effects,
large lakes
08 H
13 B
'.8. DISTRIBUTION STATEMENT
Release Unlimited
19. SECURITY CLASS (This Kepon)
Unclassified
21. NO. OF PAGES
491
20. SECURITY CLASS (This page I
Unclassified
22. PRICE
EPA Form 2270-1 (Rev. 4-77)
PREVIOUS EDITION IS OBSOLETE
458
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