Lake Currents
Lake Michigan Basin
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CONTENTS
Chapter Page
Foreword xi
1 SUMMARY 1
2 PHYSICAL SETTING
Location and Description 4
Previous Studies 6
Geology 7
Physiography and Sediments 11
Hydrology 12
Lake Levels 15
O 3 INTRODUCTION TO LAKE CURRENT STUDIES
o
General Considerations 17
Diffusion 18
, Turbulent Mixing 18
Advection 21
, Meteorology 22
1 Possible Fate of Pollutants 23
'•) Previous Studies 2U-
Procedures 25
Temperature Studies 26
Tracer Methods 26
Fixed-Position Current Metering 26
Equipment Testing 28
Description of Test Studies 28
Results of Test Studies 28
Reliability 30
Mooring Characteristics 31
Operational Characteristics 31
Flow Characteristics 37
Winds and Currents 37
Correlation Between Meters at one Station 38
Significance of Findings kk
Summary of Test Studies kk
k METHODS FOR MOORINGS, INSTRUMENT CHECKS, FILM
PROCESSING AND FILM CONVERSION
Introduction k6
Mooring Systems k6
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CUNTUU'S (Continued)
Chapter Page
4 METHODS FOR MOORINGS, INSTRUMENT CHECKS, FILM
PROCESSING AND FILM CONVERSION (Continued)
Film Processing 66
Format for Fila Reading 75
Tape Data Format 76
5 CURRENT METER FILM PROCESSING
Specifications 78
Initial Processing 80
First Pass Program..... 82
Second Pass Programs 8k-
Six-Hour Averages 84
Histograms 85
Envelopes => 85
Spectral Analysis 88
Formulas 90
Cross Spectrum 91
Graphing 92
Third Pass Program 93
Trajectory Programs 93
Maps 93
Temperature Data 93
Drogue Surveys 96
6 CURRENT STUDIES
Introduction 101
Data Compilation 102
Net Flows 110
General Circulation Patterns - Surface 120
General Circulation Patterns - Subsurface 127
Spectral Analysis 135
Summary. 173
Monthly Histograms 17^
Six-Hour Averages 176
Two-Hour Envelopes 178
Flow at Straits of Mackinac 179
Summary of Lake Currents 179
ii
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CONTENTS (Continued)
Chapter Page
7 TEMPERATURE STUDIES
Introduction 183
Definitions 183
Previous Studies iQk
Methods of Study 186
Instruments 186
Bathythermograph Surveys 189
Temperature Recorder Data 21?
Results - BT Surveys 217
Fall, 1961 217
Winter, 1961 217
Spring, 1962 220
Summer and Fall, 1962 220
Spring, 1963 221
Summer, 1963 221
Discussion 221
Results - Temperature Recorder Data 22 3
Internal Waves 223
Analog Records 230
Summary 230
8 DROGUE STUDIES
Introduction 234
Equipment 23*4-
Field Methods 238
Analysis Methods 2kO
Description of Experimental Results 2kO
Characteristics of Diffusion 25^
Theoretical Models of Pollutant Diffusion from
Continuous Sources 28l
Prediction of Pollution Distribution 28k
Discussion 295
Summary 295
9 METEOROLOGICAL STUDIES
Introduction » 297
Instrumentation and Collection of Data 297
Climatology of Surface Pressures and Winds 307
Data Analysis and Discussion. 308
Lake Breeze Phenomenon 314
iii
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CONTENTS (Continued)
Chapter
9 METEOROLOGICAL STUDIES (Continued)
A Comparison of Lake Wind to Land Wind 314
Wind Spectra 320
Summary 324
10 CORRELATION OP WIND, CURRENT, AND TEMPERATURE
IN SUMMER 325
11 RELATIONSHIP TO WATER USE AREAS
Introduction 351
Water Use Areas Along Shore 352
Water Use Areas in the Lake 353
Significant Factors 354
ACKNOWLEDGMENTS 356
REFERENCES 357
iv
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TABLES
Number Title
2-1 Tributary Inflows 13
2-2 Water Budget for Lake Michigan 14
2-3 Computed Periods of the First Five Modes 16
3-1 Current Meter Readings in Each Quadrant 43
4-1 Specifications of Metering Equipment. 65
4-2 Specifications of Mooring Materials 65
4-3 16 mm Film Data Identification Sheet and Log 67
4-4a Inspection Sheet-Current Meters Tear-Down 68
4-4b Inspection Sheet-Current Meters Build-Up 69
4-5a Inspection Sheet-Temperature Recorder Tear-Down 70
4-5b Inspection Sheet-Temperature Recorder Build-Up 71
4-6a Inspection Sheet-Wind Recorder Tear-Down 72
4-6b Inspection Sheet-Wind Recorder Build-Up 73
3-1 Format Six-Hour Averages 86
5-2 Sample Format of Histogram... 87
6-1 Timing Accuracy of Clocks 101
6-2 Current Meter Records 105
6-3 Current Meter and Wind Recorder. , Ill
6-4 Questionnaire.............. 113
6-5 Conversion Factors 114
6-6 Drogue Variations. 115
6-7 Current Spectra Data 165
6-8 Histogram 175
6-9 Six-Hour Average Winds 177
6-10 Cross Section of the Straits of Mackinac 180
6-11 Average Speed and Direction in the Straits 180
7-1 Degree of Accuracy of Instruments 189
7-2 Temperature Data and Station Location of Cruises 214
7-3 Schedule of Cruises 216
8-1 General Information on Experimental Runs 245
8-2 Values of Characteristics of Diffusion 264
9-1 Lake Michigan Wind Data 299
9-2 Ratio of Buoy and Ship Wind Speeds 311
9-3 Average Deviation of Buoy and Ship Wind Directions... 311
9-4 Histogram of Winds - Station 5 312
9-5 Wind Spectra Data 322
10-1 Position of Stations 335
10-2 Correlation Table of Standing Poincare Waves 348
10-3 Correlation Between Temperature 'Waves' and Currents.
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FIGURES
Number Title
2-1 Drainage Basin 5
2-2 Geologic Map 8
2-3 Bathymetric and Physiographic Map 9
2-4 Bottom Sediments 10
3-1 Telemetry Current Meter Locations 29
3-2 95 Percent Confidence Limits 32
3-3 Speeds at 18 and 27 Meters 33
3-4 Current Meter Speeds................... 34
3-5 Direction at 18 and 27 Meters 35
3-6 Direction at 27 and 36 Meters 36
3-7 Histogram of Speed at Three Levels 39
3-8 Savonius Rotor Calibration 40
3-9 Polar Diagram - 18 m kl
3-10 Polar Diagram - 27 m 42
4-1 Station Diagram - Summer 47
4-2 Typical Current Station 48
4-3 Recovery Buoy System 50
4-4 Link and Line Storage Case. 51
4-5 Typical Current Station - Winter 52
4-6 Subsurface Buoy 53
4-7 Temperature Recorder. 54
4-8 Current Meter 55
4-9 Anchors 56
4-10 Instrument Line Components 57
4-11 Rigid Bridle 58
4-12 Navigation Light 59
4-13 Wind Recorder 60
4-l4 Heavy Duty Anemometer. 6l
4-15 Instrument Buoy 62
4-16 Buoy and Float 63
4-17 Camera Loading Diagram 74
5-1 Compass and Vane Angle Deflection. 82
5-2 Major Axis of Positive Angles 83
5-3 Inertia! Type Rotation ;.... 89
5-4 Format of Trajectory Program 94
5-5 Format of Mapping Program 95
6-1 Histogram of Blurring 103
6-2 Lake Michigan Current Meter Station Locations 104
6-3 Current Direction Phase Shift - Station 8 117
6-4 Winter Circulation, N-NW Winds 121
6-5 Winter Circulation, S-SW Winds 122
6-6 Summer Circulation, N-NE Winds 123
6-7 Summer Circulation, S-SW Winds 124
vi
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FIGURES (Continued)
Number Title Page
6-8 Subsurface Net Flows, 60 Meters 128
6-9 Subsurface Net Flows, 90 Meters 129
6-10 Subsurface Net Flows, 120 Meters 130
6-11 Subsurface Net Flows, 150 Meters 131
6-12 Subsurface Net Flows, 180 Meters 132
6-13 Subsurface Net Flows, 210 Meters 133
6-14 Subsurface Net Flows, 240 Meters 134
6-15 Winter Current Spectra - Lake Michigan 136
6-16 Summer Current Spectra - Lake Michigan 137
6-17 Spectra of Components, Sta. 9, 15 m 138
6-18 Spectra of Components, Sta. 9, 30 m 139
6-19 Spectra of Components, Sta. 9, 90 m 140
6-20 Spectra of Components, Sta. 10, 10 m 141
6-21 Spectra of Components, Sta. 10, 15 m 142
6-22 Spectra of Components, Sta. 13, 10 m................. 143
6-23 Spectra of Components, Sta. 13, 30 m 144
6-24 Spectra of Components, Sta. 13, 60 m 145
6-25 Spectra of Components, Sta. 17, 10 m 146
6-26 Spectra of Components, Sta. 20, 15 m 147
6-27 Spectra of Components, Sta. 20, 90 m 148
6-28 Spectra of Components, Sta. 29, 15 m 149
6-29 Spectra of Components, Sta. 29, 60 m 150
6-30 Spectra of Components, Sta. 31, 10 m 151
6-31 Spectra of Components, Sta. 31, 15 m 152
6-32 Spectra of Components, Sta. 31, 22 m 153
6-33 Spectra of Components, Sta. 31, 30 m 154
6-34 Spectra of Components, Sta. 40, 60 m 155
6-35 Spectra of Components, Sta. 41, 10 m 156
6-36 Spectra of Components, Sta. 41, 90 m. 157
6-37 Spectra of Components, Sta. 41, 120 m 158
6-38 Spectra of Components, Sta. 54, 10 m 159
6-39 Spectra of Components, Sta. 54, 22 m 160
6-40 Spectra of Components, Sta. 54, 30 m l6l
6-41 Spectra of Components, Sta. 6l, 10 m 162
6-42 Spectra of Components, Sta. 6l, 15 m 163
6-43 Spectra of Components, Sta. 6l, 22 m 164
6-44 Flows at Straits of Mackinac l8l
7-1 Density of Fresh Water 185
7-2 Bathythermograph 187
7-3 Temperature Recorder 188
7-4 Lake Michigan Cruise No. 1 190
7-5 Lake Michigan Cruise No. 2 191
7-6 Lake Michigan Cruise No. 3 192
7-7 Lake Michigan Cruise No. 4 193
vii
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FIGURES (Continued)
Number Title
7-8 Lake Michigan Cruise No. 5 194
7-9 Lake Michigan Cruise No. 6 195
7-10 Lake Michigan Cruise No. 6 196
7-11 Lake Michigan Cruise No. 6 197
7-12 Lake Michigan Cruise No. 6 198
7-13 Lake Michigan Cruise No. 7 199
7-14 Lake Michigan Cruise No. 8 200
7-15 Lake Michigan Cruise No. 10 201
7-16 Lake Michigan Cruise No. 11 202
7-17 Lake Michigan Cruise No. 12 203
7-18 Lake Michigan Cruise No. 13 20k
7-19 Lake Michigan Cruise No. 13 205
7-20 Lake Michigan Cruise No. Ik 206
7-21 Lake Michigan Cruise No. 15 207
7-22 Lake Michigan Cruise No. 16 208
7-23 Lake Michigan Cruise No. 17 209
7-24 Lake Michigan Cruise No. 18 210
7-25 Station Locations, Cruise No. 50 211
7-26 Station Locations, Cruise No. 51 212
7-27 Station Locations, Cruise No. 52 213
7-28 Lake Michigan Temperature Recorder Locations 218
7-29 Formation of the Thermocline 224
7-30 Internal Waves at Station 9, 15 m 225
7-31 Spectra of Temperature Records - 1963, Sta. 31 and kl 227
7-32 Spectra of Temperature Records - 1963, Sta. 8 and 11. 228
7-33 Spectra of Temperature Records - 1963, Sta. k and 20. 229
7-34 Temperature Changes at Station 8 231
8-1 Drogue 235
8-2 Drogue Surface Floats 237
8-3 Reference Marker 239
8-4 Map - Runs 1 and 2 24l
8-5 Map - Runs 3 and k 242
8-6 Map - Runs 5 and 6 244
8-7 Drogue Positions (Run l) 246
8-8 Drogue Positions (Run 2) 247
8-9 Drogue Positions (Run 3) 248
8-10 Drogue Positions (Run 5) 249
8-11 Drogue Positions (Run 6) 250
8-12 Time Variation (Runs 1 and 2) 251
8-13 Time Variation (Run 3) 252
8-14 Time Variation (Runs 5 and 6) 253
8-15 Movement of Drogues and Wind Track (Run l) 255
8-l6 Movement of Drogues and Wind Track (Run 2) 256
viii
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FIGURES (Continued)
Number Title
8-17 Movement of Drogues and Wind Track (Run 3) 257
8-18 Movement of Drogues and Wind Track (Run 5) 258
8-19 Movement of Drogues and Wind Track (Run 6) 259
8-20 Standard Deviation of Drogues to Initial Position
(Runs 1 and 2) 26l
8-21 Standard Deviation of Drogues to Initial Position
(Run 3) 262
8-22 Standard Deviation of Drogues to Initial Position
(Runs 5 and 6) 263
8-23 Mean Separation (Runs 1 and 2) 266
8-21* Mean Separation (Runs 2 and 3) 267
8-25 Mean Separation (Runs 3 and 5) 268
8-26 Mean Separation (Run 6) 269
8-27 Mean Square Separation Versus Time (Runs 1 and 2).... 271
8-28 Mean Square Separation Versus Time (Runs 2 and 3).... 272
8-29 Mean Square Separation Versus Time (Runs 3 and 5).... 273
8-30 Mean Square Separation Versus Time (Run 6) 27^
8-31 Standard Deviation-Pair Versus Time (Run l) 276
8-32 Standard Deviation-Pair Versus Time (Run 2) 277
8-33 Standard Deviation-Pair Versus Time (Run 3) 278
8-3*4. Standard Deviation-Pair Versus Time (Run 5) 279
8-35 Standard Deviation-Pair Versus Time (Run 6) 280
8-36 Steady-State Distribution of Concentration
("1 = 0.2) 287
8-37 Steady-State Distribution of Concentration
(WL = O.I*) 288
8-38 Relative Concentration (y^ = 0) 289
8-39 Relative Concentration (y^ = 2) 290
8-1*0 Relative Concentration (y^ * k) 291
8-1*1 Non-Steady Distribution (y, = 0(0.2)) 292
8-1*2 Non-Steady Distribution (yx = 0(0.1*)) 293
8-1*3 Relative Concentration 29!*
9-1 Network Stations 298
9-2 Calibration 302
9-3 Instrument Buoy 303
9-1* 6-Hour Averages - Station 5 305
9-5 2-Hour Envelope 306
9-6 Lake Michigan Printout 309
9-7 Current Trajectories 313
9-8 Weather Map 12C, August 20, 1963 315
9-9 Weather Map 12C, August 21, 1963 316
9-10 2-Hour Envelope - Station 8 317
9-11 2-Hour Envelope - Station 18 318
ix
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FIGURES (Continued)
Number Title
9-12 Lake Michigan Versus Shore Wind Direction 319
9-13 Lake Michigan Versus Shore Wind Speed 321
9-14 Spectra, Station 13 323
10-1 Temperature Distribution Between Milwaukee and
Muskegon 326
10-2 Distribution of 10° Isotherm, Milwaukee to Muskegon.. 328
10-3 Qualitative Representation of Kelvin and Sverdrup
Waves 329
10-4 Transverse Standing, Kelvin, Sverdrup and Poincare'
Waves 330
10-5 Comparison of Lake and Land Wind Speeds 331
10-6 Comparison of Lake and Land Wind Speeds 332
10-7 Wind, Temperature, and Currents - Station 15 336
10-8 Wind, Temperature, and Currents - Station 15 337
10-9 Wind, Temperature, and Currents - Station 17 338
10-10 Wind, Temperature, and Currents - Station 17 339
10-11 Wind, Temperature, and Currents - Station 17 340
10-12 Wind, Temperature, and Currents - Station 20 341
10-13 Wind, Temperature, and Currents - Station 20 342
10-14 Wind, Temperature, and Currents - Station 20 343
10-15 Sections Across a Uninodal and a Trinodal Wave 344
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FOREWORD
In I960 the Federal Government undertook the task of determining
the sources of wastes responsible for degrading the quality of Great
Lakes waters, evaluating the effects of such wastes on the quality and
uses of the receiving waters, and developing comprehensive water pollu-
tion control programs to enhance and protect their quality. To better
understand the physical mechanisms by which pollution-laden waters mix
with and are transported by lake currents, an extensive study of these
phenomena was incorporated into the investigations. An account of part
of this monumental task — relating to circulation, diffusion, and
seasonal changes in physical parameters in Lake Michigan — is given in
the report which follows.
In view of the oceanographic scale of the study, instruments and
data processing techniques recently developed for ocean investigations
were utilized. A lake-wide deployment of recording instruments produced
a long series of records of current and water temperature at several
depths from more than 30 stations covering «•!! of Lake Michigan. Wind
was also recorded at some of the stations. This is the first occasion
on which physical events and processes in so large a natural water body,
fresh or marine, have been monitored for an interval of nearly 2 years
with so close a network of recorders.
While the need to solve immediate practical problems provided
the impetus for the investigation, the invested effort has yielded much
new information of scientific interest, and this provides yet another
example of the advantages to be gained by close association between
applied and so-called pure research.
Practical questions of great urgency concerning the fate of the
Great Lakes await answers; and it is in the light of these concerns
that the appearance of this report must chiefly be welcomed. Its find-
ings — on such matters as the dominant summer and winter circulation
patterns, the differences between inshore and offshore current regimes,
and the rates of turbulent dispersal — will have important bearing on
the interpretations to be placed on water quality changes. There can be
no doubt that this and subsequent reports by the Great Lakes-Illinois
River Basins Project will be indispensable source books for future
water planning in the Great Lakes region and for other scientific and
engineering studies.
Clifford H. Mortimer, D.Sc., F.R.S.
Director, Center for Great Lakes Studies
University of Wisconsin-Milwaukee
xi
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CHAPTER 1
SUM4ART
Lake Michigan is the third largest of the Great Lakes and the
only one lying wholly within the United States. It has a surface area
of 58,016 square kilometers, an average depth of 8k meters, and a total
volume of £,878 cubic kilometers. In general, the Lake is oriented
along the north-south axis, the northern part of the Lake curving
gently to the northeast. The Lake is divided into two basins by two
parallel ridges running in an easterly direction from Milwaukee to
Grand Haven. The southern basin is smaller and shallower than the
northern basin with a nuyylnnnB depth of l60 meters. The northern basin
is longer and narrower. In it is located the deepest point in the Lake,
281 meters.
The energy Inputs into the Lake responsible for mixing and move-
ment of its waters are derived almost exclusively from meteorological
disturbances. Whereas in small lakes the transfer of energy through
wind stress tends to drive the surface water out, in Lake Michigan this
process is complicated by such factors as the Corlolls effect of the
earth's rotation, nonuniformity of wind stress, and by the variation in
atmospheric pressure on the water surface from the progression of high
and low barometric pressure areas passing over the Lake. Although there
are an infinite variety and frequent changes in both direction and mag-
nitude of energy input, certain patterns of water movement have been
observed. These patterns result from the fact that seasonally there is
a dominance of winds from one general direction.
Both water movements and rate of mixing are materially influ-
enced by the formation of thermoclines, or zones of temperature tran-
sition between two layers of water which differ in temperature and
density. Once stabilized at depths which prevent storm turbulence
interruption, summer thermoclines effectively prevent mixing of waters
of the epilimnion (upper layer) with those of the hypollmnion (bottom
waters). Reverse thermoclines, involving very small density changes,
are found in winter but usually at greater depths than in summer
because they offer less resistance to wind mixing.
Thermal bars, phenomena resulting from a difference in tempera-
ture between adjacent waters along a vertical plane, occur both in the
spring and in the fall in shallow waters parallel to the shoreline.
Like the thermocline, a thermal bar prevents mixing between the shal-
low waters along the shore and the deeper Lake waters.
Temperature records from many of the stations showed that
internal waves were almost always present on the thermocline. Spectral
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analysis of the teaperature clearly established several frequencies
for these waves, the most dominant being in the 16 to 18-hour fre-
quency. This corresponds closely to the inertial period for the lati-
tude. The inertial period is related to the rotation of the earth,
being 2k hours at 30° latitude and varying as the sine of the latitude.
Four basic patterns of water movements occur in the upper
layers, two la winter and two in summer. Each current pattern is soste-
vhat modified by the nearshore currents. The shore currents appear to
be dominated by the prevailing or net winds. One winter pattern shows
the influence of north-northwest winds. The currents generally move
southerly along the east shore and northerly along the west shore.
There is a rotation in the southern basin with some of the northerly
flow moving eastward in the general area of Milwaukee and joining the
southerly flov along the east side below Grand Haven. A similar gyre,
elongated in shape, exists in the northern basin. It extends from an
area north of Milwaukee to the Straits of Mackinac and also circulates
in a clockwise direction. This pattern may be expected during 25 to 30
percent of the year.
The other winter pattern occurs only 20 to 25 percent of the
year, principally between January and April. In this pattern the gyres
in the northern and southern basins are reversed and rotate counter-
clockwise with principal flows north along the east shore and south
along the west shore.
The dominant summer pattern is created by south-southwest winds
occurring nearly 40 percent of the year. Mich obscured by rotating
currents associated with internal waves, the picture of general circu-
lation may be defined roughly as follows: In the southern basin the
counterclockwise gyre exists, but inshore currents on both the east
and west shores are northward. The northerly flov along the west shore
is weaker and undoubtedly fed by westerly flows In the deeper waters.
In the northern basin, the dominant flow is southward in the center of
the Lake. This southward flow splits above Milwaukee, one part moving
east and north along the east shore, and the other moving west and
north along the western shore.
When under the occasional dominance of north-northeast winds,
the southern basin gyre continues in its previous counterclockwise di-
rection, but the inshore currents along both the east and west shores
then move southward. This pattern, again obscured by rotating currents
associated with internal waves, occurs about 10 percent of the year. At
such times, southward currents also prevail along both shores in the
northern basin, and there is a narrow current south in the central part
of the northern basin. This splits above Milwaukee to feed narrow cur-
rents running northward on both sides of the central southern movement
and between the southerly currents along both shores.
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Drogues were used to track water Basses in the following diffu-
sion studies: In southern Lake Michigan, at the mouth of the Detroit
River in Lake Brie and near Cleveland, Ohio in Lake Erie. A special
study was also conducted in Lake Michigan in September 1961, following
the release of a large mass of polluted water into the Lake from the
Chicago River mouth. This latter study did not use drogues; instead, a
grid of ssjspling points was established in the area and the water Move-
ment and mixing were established on the basis of coliform analyses.
Based on the diffusion studies it was concluded that mixing in
shallow shore waters with steady wind velocities in the range of 300 to
400 cm/sec is relatively slow. Under such conditions pollutants dis-
charged into the Lake can travel several miles relatively undiluted.
Although the extent of mixing can be calculated, the duration of winds
having the particular direction and velocity to produce maximum effects
at a particular water use point is less certain.
The complexity of the Interplay of forces providing energy
inputs Into Lake Michigan has prevented the development of mathematical
models describing the relationship between the direction and velocity
of winds over land with the associated water movements. Xevertheless,
knowledge of the current patterns described herein should be helpful in
the site selection and design of water intakes and waste outlet instal-
lations. Additional more specific data are available where such a site
is near a current meter station. However, special studies or investi-
gations should be undertaken to confirm the validity of the data at the
chosen site, since most of the current metering stations were set In
deeper waters and would not necessarily reflect the local effects of
Irregularities along the shoreline; nor would they detect the presence
of a thermal bar which could prevent the ••» y» ffg of nearshore with off-
shore waters.
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CHAPTER 2
PHYSICAL SETTING
Location and Description
Lake Michigan is the only one of the Great Lakes that lies
wholly within the boundaries of the United States, but it is so large
and extends so far into the United States that it forma a small inte-
rior sea. The Lake has a -surface area of 58,016 square kilometers
(km?), which is equal in area to the combined States of New Hampshire,
Massachusetts, Connecticut, and Rhode Island. It has an average depth
of 8k meters (m) and a maximum depth of 281 m. The deepest portion of
the Lake is 105 » below sea level. Its length is k?k km and its width
is 190 km; the total length of shoreline is 2,673 km and the total vol-
ume of water is 4,878 cubic kilometers (km3). The mean-water surface
elevation of Lake Michigan is 176.5 m above sea level. The range of
monthly mean elevation is 2 m and the average seasonal fluctuation is
0.30 m.
The States bordering Lake Michigan are Illinois, Indiana, Michi-
gan, and Wisconsin. Major cities located on the Lake are Chicago,
Illinois; Gary, Indiana; Baclne, Wisconsin; Milwaukee, Wisconsin; and
Muskegon, Michigan. The 1960 population of the basin was approximately
5*7 million, about 3.2 percent of the United States. These figures do
not Include the Chicago region which is located in the Illinois River
Basin, Figure 2-1.
The climate of the Lake Michigan Region is typical humid conti-
nental with severe winters and warm summers. Temperatures increase
from north to south. The greatest extremes occur during the winter
months. The January means for Chicago and Green Bay, respectively, are
5.5° and -9-8°C. The July means for Chicago and Green Bay, respectively
are 22.5° and 21.7°C. The mean annual temperature of Chicago is 9«5°C,
whereas to the north at Green Bay it is 6.6°C.
The mean annual precipitation for the region is approximately
77*2 centimeters (cm), and is higher between April and September than
between October and March (USLS, 8l). The east side of Lake Michigan
receives more precipitation than the western side. Precipitation
increases with ground elevation In the basin and averages approximate-
ly 10 percent higher over upland areas than over the lakes which are a
hundred meters lower (Day, 2*0.
Intralake shipping on the Great Lakes ceases around December 1
each year because of Ice conditions. Lake Michigan does not usually
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GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
DRAINAGE BASIN
of
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Great La^es Region Chicago,Illinois
FIGURE Z-\
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freeze over, except during severe winters, but ice conditions in such
areas as the Straits of Mackinac, eastern Lake Erie, the Welland Canal,
and the St. Lawrence River close passage to all ships. Winter naviga-
tion on Lake Michigan consists of car-ferries and fuel vessels operat-
ing regularly between the major ports. The ice builds up from shore and
later may break off and becoaie drift ice. During severe winters, Lake
Michigan has been known to freeze completely over, for instance during
February 1963. Upon breakup, drifting ice usually piles up, in con-
stricted areas, into ridges and windrows as high as 10 m and 13 or more
m in depth.
The opening date of navigation is usually early April, but has
been as late as early May.
Previous Studies
The first study of currents in Lake Michigan was conducted by
Harrington in 1895 (36). Field work for his report was carried out
from 1892 to 1894. Harrington released approximately 1,500 drift bot-
tles at various points in the Lake and recovered 203 of them at their
points of stranding on the shores. From these returns, a chart was made
showing the surface currents. This chart showed two counterclockwise
gyres making up the principal circulation systems; one in the southern
basin, and a more elongated one in the northern part of the Lake. A
much smaller elongated clockwise gyral flow system was located along
the western shore near Milwaukee.
Townsend (78), in 1916, criticized the findings of Harrington,
and pointed out that since only the point of release and the point of
recovery of drift bottles are known, it is not possible to know the
path taken by the bottles. In 1932-36, Deason (25) studied Lake
Michigan currents using drift bottles, and his conclusions generally
followed Harrington's.
Church (l8, 19), in 19^2 and 19^5, made a comprehensive study of
the annual temperature cycle in a number of cross-sections of Lake
Michigan. His temperature data tended to support Harrington. In 1954-
55, the U. S. Bureau of Commercial Fisheries completed an intensive
study of surface currents using drift bottles and drift cards (Johnson,
Out of 6,000 releases, 3,000 were recovered. The results of the
study were inconclusive; in general, however, the drift was west
to east and north to south movements about equal in magnitude. A simi-
lar pattern was found in 1955, except that the drift in the eastern
areas was mainly from the south. Ayers et al., (2) 1958, published
the results of a series of synoptic surveys completed in 1955, in which
they used drift bottles and applied a modification of the dynamic-
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height* method to determine the circulation of Lake Michigan. The
result* of the drift bottle study shoved good agreement with
Harrington's study.
As pointed out by Ayers et al., the winds were westerly, which
he considers as being the aorsi for the summer months. Except for Church
(19) 19*»2, inferred from temperature, none of the above researchers
reported on wintertime lake circulation.
Geology
Various phases of the geology of Lake Michigan hare been report-
ed, but only the more recent will be mentioned here (see Figures 2-2,
2-3, and 2-fc).
In 1958, Hough (ko) showed that glacial till is a common bottom
material and that wave action in shallow water has winnowed out the
finer grains, leaving a concentration of gravel just offshore. Shepard
(71), pointed out that glacial erosion at the north end of the Lake is
indicated by fiord-like valleys, by rocky islands, and by complex bot-
tom topography. Thwaites (77) related the ridges around the lake
shore and on its floor to the presence of resistant dolomites, lime-
stones, and sandstones, and the deeper areas to less-resistant shales
and evaporites. The position and strike of the outcrop of these alter-
nating beds of hard and soft strata are controlled by the southeasterly
dip into the structural basin that underlies the State of Michigan.
Bsery (30) described the bathymetry and bottom deposits of Lake
Michigan.
Lake Michigan is located entirely within a region of Paleozoic
rocks (Fig. 2-2) that form part of a structural basin centered in the
State of Michigan. To the northwest are Pre-Cambrian rocks that com-
prise part of the Canadian Shield, onto which the Paleozoic rocks
onlap. Due to the structure of the area, the oldest rocks crop out in
the west; the rocks become progressively younger toward the structural
basin. The strike of these reeks generally follows the long axis of
the Lake.
In the north, the floor of the Lake is made up of evaporites,
limestones, and shales. The southern Lake basin is floored by shales.
Very few outcrops of these reeks exist, however, because they are
mantled by glacial debris deposited during the Pleistocene Epoch.
Although the Lake Michigan area has been an area of low topography with
numerous invasions of the sea, it was the glaciers that formed during
the Pleistocene Epoch which shaped the lake itself. These glaciers
developed to the north and migrated southward, gouging out the Lake
Michigan Basin. The topography of the region has been little modified
since.
-------
Uj
-J.
2 $
o o
S 3* 3
ssl
a
a.
O
>
K
^
s
5 « X
« si 3
S i. 1
O
o
K
O
s
U
o
E
HI
D
O
a
o , *
8
FIGURE 2-2
-------
NORTH
DIVIDE
SOUTH
LEGEND
CONTOUR IN METERS
270 •
240
210
180
I 50 «•"
120
90 •-
60
30
Area of Complex Bathymetry
Percent of Area
2O 40 60 80 100
: Sea Level
0 16 32 48
Km.
Scale
After Emery,1951
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
BATHYMETRIC CHART
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago Illinois
FIGURE 2-3
-------
BOTTOM SEDIMENTS
-43
'42
88'
87°
i
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SEDIMENTS OF LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN,
Great Lakes Region Chicago,Illinois
10
FIGURE 2- 4
-------
Physiography and Sediments
Lake Michigan can be divided into five area* having different
physiographic characteristics. However, for water quality purposes the
Divide Area is not classified separately. These areas are termed South
Basin, Divide, Borth Basin, Straits Area, and Green Bay (Fig. 2-3).
The South Basin extends fro* the southern tip of the Lake to a
line connecting Milwaukee and Grand Haven. This area has gentle topo-
graphy, suggesting excavation of a thick homogeneous formation, follow-
ed by silting caused by glacial outwash. The bottom materials consist
of sand along the shore and on the beaches, gravel largely at water
depths between 15 and 30 m, and mud in deeper water. Hough (^O) as-
cribes this distribution to the winnowing of glacial till by wave
action, whereby gravel is a lag deposit, sand is carried landward to
the shore, and mud remains in suspension until it reaches the quiet
water of the Lake bottom.
The next physiographic area is the Divide, which consists of two
separate ridges. According to Thwaltes (77), 19^7, the southern ridge
marks the position of the resistant Traverse limestone and the northern
one the resistant Dundee limestone. These ridges may also consist in
part of recessional moraines. Bottom notations on various charts show
the presence of boulders and clay near the west shore, probably indi-
cating glacial till. Sand forms a belt between water depths of about
1^ and 90 m on the west side and from shore to 38 m on the east side.
The few bottom notations in the middle of the section show mud almost
exclusively. Most likely, the tops of the ridges consist of coarser
material.
The third area, the North Basin, extends north from a line
between Manitowoc and Manistee to a line between Frankfort and Mani-
stique. It consists of one main basin which, unlike the South Basin,
is Irregular in shape. The topography is suggestive of excavation of a
thick nonhomogeneous rock with only slight mantling by later sediment.
The maximum lake depth is found in this basin. This section appears
most likely to have been excavated by glacial erosion. Along both
shores is a belt of rock that, on the west side, ranges in width up to
about 2k km. Gravel is probably common in the rock area. A belt of
sand of varying width borders the rock. In deep water, chart notations
show mud exclusively. In each of the three physiographic sections which
comprise the main area of the lake, coarser sediments are better repre-
sented on the east shore.
The fourth area, the Straits Area, is one of very irregular top-
ography, accounted for by the presence of alternating belts of hard and
soft rocks that were oriented perpendicular to the movement of the
11
-------
glacier*. The deep depreuiona and rocky ridge* are similar to the gla-
cial erosional topography found In the fiord coasts of Norway.
In the Straits Area is the outlet of Lake Michigan. Although the
narrowest point is in the Straits of Mackinac, the shallowest divide is
located 72 km westward, well within the wider part of the Lake. Between
these two points, and extending eastward into Lake Huron, is a narrow
canyon, approximately 8 km wide and 39 • deep. The complexity of the
bottosi contours is Batched by the variety of the bottom materials.
Figure 2-4 shows that rock occurs around the shores of all islands and
at the tops of submerged hills. Sand is abundant only in three large
areas near the extreme end of the lake. Mud occupies the depressions
and lower areas.
The Green Bay Area is fairly shallow, averaging about 2k m with
a maximum of 50 m near one of the entrances. The north end of the Green
Bay section is exposed to the waves of Lake Michigan and, as a result,
its floor consists principally of rock. Within the area of quiet water
at the south end of Green Bay, the sediments have a more normal distri-
bution, with rock along the shore, sand generally paralleling the rock,
and mud farthest offshore.
Hydrology
The water balance for Lake Michigan can most easily be determin-
ed by the water budget. Table 2-1 lists all the gaged tributary streams
into Lake Michigan. The total inflow as estimated by the USGS (79), av-
eraged from the total gaged and ungaged stream basins, is 1,102 m3 per
second (38,900 cfs). Table 2-2 lists the essential factors in the water
budget and shows that the computed outflow at the Straits of Mackinacia
about 1,134 m3 per second (40,000 cfs).
The extent of ground water exchange is not known, but is con-
sidered as minor in the computations.
The above figures could be checked by adding the Lake Huron
inputs plus the inflow at the St. Marys River and figuring the balance
at the Detroit River. The difference should approximate the Lake
Michigan contribution.
Using figures for precipitation and evaporation by Ovnbey and
Willeke (59) and inflow figures for the Michigan-Huron Basin, the dif-
ferences are considerable. Bergstrom and Hanson (8) report that the
combined tributary inflow for the two basins is 2,073 m^/see (73,200
cfs). Assuming the Lake Michigan inflow figures are valid (1,101
m3/sec), the Lake Huron tributary inflow can be estimated at 972 m3/sec
(34,300 cfs). Precipitation minus evaporation is estimated at 472
12
-------
TABLE 2-1
TRIBUTARY HFLOWB*
AVERAGE FLOW
RIVER
Michigan
Boardaan
Little Manistee
Manistee
Big Sable
Fere Marquette
White
Muskegon
Grand
Black
Kfl") MMHtQQ
Paw Pav
St. Joseph
Menoninee
Ford
Escanaba
Indian
Black
Wisconsin
Peshtigo
Oconto
Fox
Milvaukee
Cedar Creek
Indiana
Burns Ditch
CFS
186
162
1,933
137
608
36?
1,889
3,362
1*5-2
1,269
^ y^-*r^
373
3,025
3,098
324
895
369
25.1
832
569
4,11*0
381
62.3
127
M3/SBC
5-3
4.6
54.7
3.9
17.2
10.4
53-5
95.2
1.3
35.9
^s s
10.6
85.7
87.7
9-2
25.3
10.4
0.7
23.6
16.1
117.2
10.8
1.8
3.6
GAGED
SQ MI
223
200
1,780
12?
709
380
2,350
4,900
65.8
1,600
390
3,666
3,790
450
870
302
28
1,124
678
6,150
686
121
160
AREA
SQ KM
577.6
518.0
4,610.2
310.8
1,836.3
984.2
6,086.5
12,690.0
170.4
4,144.0
1,010.1
9,494.9
9,816.1
1,165.5
2,253-3
782.2
72.5
2,911.2
1,756.0
15,928.5
1,776.7
313.4
414.4
YEARS OF
RECORD
13
9
14
23
26
8
43
39
5
35
14
35
53
11
24
27
14
12
54
69
51
35
17
Totals
24,205.6 684.7
30,749.8
79,622.8
*USGS (79)
13
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TABLE 2-2
WATER BUDGET FOR LAKE MICHIGAN
Positive Contribution
AVERAGE FLOW AVERAGE FLOW
M3/SEC CFS M3/SEC CFS
Tributary Inflow^3' 1,104 39,000 1,101 38,900
Precipitation 1,374 48,500 1,466 51,750
Ground Water — — 11 400
2,478 87,500
Negative
Evaporation 1,286 45,400 994 35,100
Diversion (1940- 92 3,240 92 3,240
I960 avg)
1,378 48,640
Net Outflow 1,100 38,860 1,492 52,710
l) Precipitation and evaporation from Ownbey and Wllleke (59).
2) Precipitation, evaporation, and groundwater froa Bergstram and
Hanson (8), estimated at one-half the Michigan-Huron total.
(3) Includes ungaged tributary inflow.
14
-------
m3/sec and the St. Marys River inflow (66 year average, USLS) is 2,079
m3/sec (73,400 eta). The St. Glair Hirer outflow from Lake Huron (66
year average, USLS) is 4,993 »3/sec (176,300 efs). The resulting out-
flow for Lake Michigan is computed at 1,470 m3/sec (51,906 cfs). Obvi-
ously the precipitation-evaporation figures are the greatest sources of
error in the computations, and this problem is far from resolved today.
The conservative figures of Ownbey and Willeke (59) were used in most
of the Lake Michigan calculations for the remainder of the report.
Lake Levels
Lakes Michigan-Boron are considered hydraulically as one lake.
The reference datum for Lakes Michigan-Huron water surface, referred to
as "Low Water Datum," is 576.80 feet (175.81 m) above sea level on the
International Great Lakes Datum of 1955. The lowest monthly mean levels
during the past 105 years have occurred in the past few years, being
0.42 m below the datum in March 1964. The highest levels occurred in
June 1886 when the water was 1.56 m above the datum. The extreme range
is 1.98 m, or the greatest of all the Great Lakes ranges. While no
doubt the prevailing drought conditions contributed to the extreme
lowering of the Michigan-Huron Basin in 1964, during the same period
neither Lake Erie nor Lake Ontario experienced a similar drop in level,
even though the drought conditions were very similar in their drainage
basins. It is probable that changes made by man in the outlet channels
have contributed to the extreme range in the Michigan-Huron water lev-
els; the flow from Lake Superior is regulated by controlling locks on
the St. Marys River and is not subject to changes in the connecting
channels.
In addition to the long-term variations, which reflect changes
in storage volume, Lake Michigan has tides (lunar and solar), seiches,
and surges. These short period fluctuations do not result in a change
in volume, but a change in the water level shape. In general, tides are
minor, 7.2 mm lunar and 3.1 to 6.3 mm solar (Hutchinson, 44). The
seiches rarely exceed 0.3 m in height. The first five seiche periods,
of the longitudinal seiche, are shown in Table 2-3 (Rockwell, 67).
In a spectral study of surface level fluctuations, Mortimer (55)
interpreted dominant spectral peaks at approximately 9.0, 5.2, 3-7,
3.1, and 2.5 hours as corresponding to the first five longitudinal
modes and demonstrated a striking transverse first-mode seiche at 2.2
hours in the southern half of the Lake. In addition, he demonstrated
resonance in Green Bay between the free period of oscillation of the
Bay, at approximately 11 hours, with the lunar tide 12.4 hours and the
first Lake Michigan mode at 9.0 hours.
15
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TABLE 2-3
COMPUTED FBIIGB6 OT TEE FIRST FIVE MOOES
NODE HOURS
1
2
3
k
5
8.83
*.8?
3.5*
2.86
2.39
Vf.8 (Lakes Michigan-
Huron)
The interlake Mich*, V7.8 hour*, has been observed at 50 and 51
hours vith current Meters sad in a spectral analysis of the speed data.
The surge la Lake Michigan is unusual because of its suddeness
and its height. Wares of nearly 2 a have been observed and reported
since the surge of 195* which took the lives of seven people In
Chicago. Hughes (4l) reports on the operational basis for prediction
in Lake Michigan and an explanation of the wave. The wave is one which
was reflected back from the eastern side of the Lake and increases in
height due to the shallowing water. A pressure Jump and perhaps the
accompanying winds produce the original wave. The aitrlsnm transfer of
energy frosi wind to water appears to occur when the pressure Jvuap asso-
ciated with squall lines happens to be traveling at the speed of the
free wave in water, which is a function of the square root of the depth
(Donn and Ewing, 28).
16
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CHAPTER 3
IKTRODUCTIOH TO LAKE CUBREMT STUDIES
The study of currents In Lake Michigan reported herein Is part
of the overall program of investigations undertaken by the Great Lakes-
Illinois River Basins Project. The ultimate objectives of the studies
are: to assist in predicting the fate of pollutants introduced Into
the Lake; to assess the effects of waste Inputs on lake water quality--
effects both local and area-wide, both now and in the future; and to
aid in the making of wise decisions for protecting this valuable water
resource.
Waste-bearing waters are dispersed from a point of input to the
Lake by some combination of three processes: Molecular diffusion, tur-
bulent mixing, and mass transport. The relative importance of each
process depends on physical conditions in the Lake. For example, in
completely quiescent waters the predominant process would be molecular
diffusion. Turbulence (the existence of randomly-varied water veloci-
ties) in the vicinity of the point of input will greatly accelerate the
rate of dispersal over that effected by molecular activity alone. If,
superimposed on this random turbulence, there is a prevailing velocity,
then the water mass as a whole, and the accompanying waste waters, will
move in that direction. Knowledge of the existence (or absence) of
such movements is essential, both for predicting the fate of pollutants
and for planning strategic locations of waste input and water extrac-
tion points to minimize short-circuiting.
The objectives of the Lake Michigan current study are, then: to
determine the variations in physical characteristics, temperature and
density, of water within the Lake; to measure the water movement pat-
terns over a period of time; and to develop, from considerations of
cause and effect, a theoretical basis for generalizing the observed
conditions.
General Considerations
To comprehend the details of the data on currents it is logical
to review the theoretical concepts and the terminology of the study.
A pollutant which is a liquid or a suspension of small particles,
when introduced into a body of water, may be diffused (molecular scale),
mixed or diluted (larger scale), and advected or moved by currents
(still larger scale). All three scales of motion are present in Lake
Michigan. Each will be discussed in turn and its significance con-
sidered. It will be evident by the end of the discussion that there
are gaps in our knowledge of these various scales. Some of these gaps
IT
-------
have been filled by field investigations; the rest await advances In
theory and instrumentation.
Diffusion
Molecular diffusion is a complex randan notion directly associ-
ated with molecular notion and accelerated by the themal agitation of
individual molecules. It is perhaps the least important notion for
pollutants in Lake Michigan in comparison with the effects of larger-
scale movements. Other than acknowledging its existence, molecular
diffusion vill not be considered further.
Turbulent Mixing
Turbulent mixing is a complex random motion not directly associ-
ated vith the agitation of individual melecules. According to Corrsln
(2l) "...turbulence can be expected in a fluid whenever there is a
shearing flow and the inertia! effects are much larger than viscous
effects." These conditions are often satisfied in Lake Michigan. Tur-
bulence affects the dispersal rate of pollutants much more than does
molecular diffusion.
Generally speaking, ".. .much of the core of the turbulence prob-
lem has yet to yield to formal theoretical attack" (Corrsin, 21).
Mathematical difficulties in handling nonlinear expressions have
greatly hampered progress; the nonlinearity Implies that there are no
simple relationships readily susceptible to mathematical treatment.
Work relating to natural waters, both salt and fresh, has been publish-
ed by Richardson and Stommel (6*1), Stomnel (7*0, Joseph and Sendner
(46), Hoble (36), and others, in addition, there is significant unpub-
lished work by Schonfeld of the Motherlands, Okubo of the Johns Hopkins
University's Chesapeake Bay Institute, and others. Recent researches
into flow in stratified fluids are directly relevant to the Lake
Michigan problem, and these have been reviewed by Mortimer (5*0> A good
deal of research is now being carried out in this field, so long
neglected in comparison with turbulence in homogeneous fluids, and
theoretical and experimental progress is being made.
The wind, acting both directly and indirectly, appears to be the
chief force causing water motion in Lake Michigan, overcoming inertia
and stability and resulting in internal turbulence. Wind stress on the
water surface can cause waves, set-up, and currents, and if abruptly
terminated after a sufficiently long period, may result in a seiche.
If water temperatures are vertically isothermal, the wind can
stir the whole Lake. Wind results In waves and orbital particle motion
to depths of at least half a wave length if thermal stratification is
18
-------
not too strong. If the wind blows from the sane direction for a fev
hours, it will cause set-up; that is, wind stress vill drag surface
water to the leeward side of the Lake, causing a measurable piling up
of water against the shore. Mixing vill occur while water is moving
toward the shore and while part of the piled-up water is escaping by
moving parallel to the shore or by reverse flow as a subsurface
current. In addition, when the wind either stops bloving or shifts
direction, the piled-up water begins to move toward the opposite side
of the Lake. Often it surges back and forth across the Lake several
times with a period determined by basin geometry and fluid density;
this is called a surface seiche. The seiche results in further, though
less important, mixing. If there Is significant density stratification,
an internal seiche may also be started. The internal seiche, like the
surface seiche, is a wave form at a density interface, though in this
instance there is water above and below, while for the surface seiche
air is above and water below. Periods of internal seiches may be
longer and the amplitudes greater than surface seiches. Because of the
large amplitudes, internal seiches can accomplish more mixing at stable
thermocline depths - generally in excess of 22 m. Seiches may be uni-
or multinodal. The possibility of their presence makes a single
temperature observation suspect; observations should be repeated at
each location to ascertain conditions. Observations off Chicago by
Project personnel in October 196l, indicated 8-m vertical movement of
an isotherm within 3 1/2 hours. If such motion is typical, attempts to
estimate the volume of water available for mixing in the epllimnion (or
upper layer) without a set of simultaneous temperature-depth measure-
ments could be disastrously In error.
It is pertinent to insert a discussion of the Lake Michigan
temperature structure here, because temperature structure determines
density structure, which in turn determines stability. The most impor-
tant published works are by Van Oosten (8k), describing data from 136
stations occupied from mid-April to mid-November in the years 1930,
1931, and 1932; by Church (20), describing 2,000 bathythermograph
soundings made between November 19^1 and February 19kk; by Ayers et al.,
(2), describing four synoptic studies of 50 or more temperature sta-
tions occupied in June and August 1958; and by Mortimer (5*0 giving the
first detailed picture of temperature distribution in a cross section
(his figure 6), with a presentation of evidence of inshore upwelling
and wavelike changes in temperature provided by waterworks intake
records, and a prediction of the nature of the internal waves involved.
During early winter months the Lake surface cools and convective
mixing occurs as the denser colder water sinks. This mixing may not
affect the deeper areas of the Lake where water may already be at maxi-
mum density. At some time during this period the entire Lake will reach
a condition of maximum density, about U°C. At this time vertical con-
19
-------
vective mixing ceases. As the surface temperature continues to drop,
the less dense colder water remains at the surface except for such mix-
ing as may result from wind or wave action. Following the winter sea-
son, the temperature increases slowly until late spring, when the whole
Lake again reaches the temperature of maximum density. During this
latter period most of the Lake is again convectively mixed. Following
the spring period when the Lake is vertically isothermal at tempera-
tures somewhat higher than U°C, the surface temperatures will increase
rapidly until early August, by which time a very stable stratifica-
tion has developed, starting with the formation of a thermocline (a
layer of rapid temperature decrease 3 to 15 m thick). Thermocline
formation occurs first in the shallow inshore waters, and it is at this
time, when the central part of the Lake is isothermal at near k°C, that
the thermal bar described by Rodgers (68) may form. Ultimately,
however, the result of spring warming is to produce a homogeneous
surface layer over the whole of the Lake, with temperatures in the
region of 18° to 22°C separated by a thermocline (Church, 20 and Ayers,
2) from bottom water which maintains a temperature close to k°C. During
the time of intense stratification (greater temperature differential
within the thermocline), it is unlikely that even the strongest winds
could cause complete vertical mixing; only the water above the thermo-
cline (the epilimnion) is available for thorough mixing with pollutants.
Cooling of the epilimnion begins with September storms, and the thermo-
cline weakens as the surface homogeneous layers cool and increase in
depth until the whole Lake becomes isothermal at about k° to 5°C in
December.
According to Church (20), minimum surface temperatures (between
0.5 and U.O°C) are reached between the middle and end of March, at
which time the main body of the Lake is vertically isothermal. These
temperatures are lower than those producing maximum density; if such
low temperatures could be found in the deepest part of the Lake, then
their presence would conclusively demonstrate complete vertical mixing
of the entire Lake volume for the year (Birge, 9). (Church found them
in much shallower water on the rise between Milwaukee, Wisconsin and
Muskegon, Michigan.)
Dissolved oxygen (DO) enters the water mainly from the atmos-
phere. During periods of overturn the DO will tend to approach satura-
tion values, but during periods of stratification DO losses below the
thermocline will not be restored by vertical mixing. If pollutants
with sufficient Biochemical Oxygen Demand were introduced into or below
the thermocline, the DO concentration might drop rapidly to low levels.
Two points should be emphasized. First, the volume of water
available for mixing keeps changing throughout the year, and it is not
20
-------
known whether the entire Lake volume mixes completely. Thus, at certain
seasons of a year, only the uppermost water (15 m) may be available for
diluting pollutants, although events near shore, where the pollutants
enter, may often be complicated by the upvelling and downwelling phen-
omena described by Mortimer (51*). Second, there is a stable density
stratification for a significant portion of the year establishing three
zones, each having its own temperature and density characteristics.
Accordingly, the density of any pollutant introduced into the Lake
determines whether the pollutant would stay on the bottom, at inter-
mediate depths, or rise to the surface.
Advection
Mixing as accomplished by turbulent motion results from complex
random movements involving relatively little transport of a water par-
cel, but changes in its internal distribution. Advection is roughly the
opposite of turbulent mixing, and refers to linear movement or gross
motion of a water parcel with mixing along its boundaries. There are a
number of possible situations between the two extremes, random turbu-
lence and prevailing advection.
Advection theory, in part, is in a more advanced state than tur-
bulence theory; however, a situation often is so complex that it is
exceedingly difficult to obtain even semiquantitative predictions,
especially in the vicinity of shore lines (Hutchinson, kk).
In Lake Michigan the wind and pressure fields seem to be the
chief causes of advection (as well as internal turbulence, previously
discussed). Tides are negligible for most purposes, having a range of
some 1 cm (Judson, Vf). Seiches are important to advection only in
restricted areas, such as the Straits of Macklnac, and perhaps in the
entry channels to Green Bay. Precipitation minus evaporation, although
not known in definite detail, is small enough to be neglected in this
instance. Because of the large area of transverse cross section of the
Lake, net flowthrough produces negligible velocities of advection;
however, flow in the Straits of Mackinac is often reversed by seiches
and wind-tilt. Church (20) noted that during most of the year denser
water was in the center of Lake Michigan and less dense water at the
edges, implying a. slow counterclockwise density circulation superimpos-
ed on the net flowthrough. Project personnel found a similar distribu-
tion off Chicago in the fall of 1962. A careful review of the data
indicates the presence of more than one circulation pattern. This is
supported by differences in earlier studies by Harrington (36), Johnson
(45), and the four synoptic cruises by Ayers (2). According to Ayers,
major current changes caused by the wind are often superimposed on the
more stable, slower flow, and changing winds are responsible for the
varying currents observed.
21
-------
Balnea and Bryson (35) find that the speed of a surface current
is 1.3 percent of that of the wind producing it, provided the vind
speed is less than 5.9 a/sec (13 mph); above this critical speed, the
relationship is believed to be nonlinear. Shulman and Bryson (72) find
the direction of surface transport is about 20.6° to the right of the
wind direction and that the "depth of frictional influence" la between
1.8 and 3.3 m. These studies vere conducted on Lake Nendota at Madison,
Wisconsin and aay not be entirely applicable to Lake Michigan.
In the discussion of thermal structure it vas pointed out that
the thermocline separated the homogeneous leas-dense epilimnion from
the denser homogeneous bottom water. Bryson and Bunge (15) find that
when the wind suddenly drops or shifts direction after set-up is estab-
lished, a rapid increase in current velocity is observed Just above the
thermocline. They consider this current to be the first swing of an
Internal seiche. Accordingly, significant currents may exist both at
the top and bottom of the epilianion. Lathbury, et al., (49) found
significant currents below the thermocline also, which they consider
attributable not to seiches but to thexmally-and/or wind-induced pres-
sure gradients. Set-up causes a hydrodynamic pressure gradient, result-
ing in currents along or perpendicular to the shore. Shoreline and
bottom topography will also influence currents. Because of the multi-
ple forces to be considered, attempts to predict currents soon become
complicated.
Recent studies have shown that currents exist through the entire
vertical column of water. Current velocities over 50 cm/sec at a depth
of 30 m were measured by the Project.
On one occasion Project personnel found floating pollutants In
the vicinity of Chicago's beaches and water Intakes, for several con-
secutive days (USPHS, 82). Generally speaking, surface currents are
weak and southbound near Lake Michigan'a west shore, but narrower,
stronger, and northbound near its east shore. Sometimes there is
evidence of a counterclockwise eddy In the Lake's southern basin. Again,
it is emphasized that these conditions are variable.
Meteorology
The winds, precipitation, and evaporation over Lake Michigan
have rarely been measured. One study "Report on Wind Velocities at the
Lake Crib and at Chicago" by Hasten (37) (1883) was one of the few works
undertaken to determine the wind differential that exists between the
land and the lake. Major Ira Hunt (^3) U. S. Lake Survey, working on
Lake Erie, made some calculations on the wind differential that exists
over the Lake. Applying the results of this study to Lake Michigan it
would appear that winds over Lake Michigan can be 96 percent greater
than those over the City of Chicago at certain times of the year.
22
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Data on evaporation and precipitation over the Lake surface are
limited to estimates by the U.S. Lake Survey rather than precise obser-
vations. Radar studies of precipitation variations over the Great Lakes
are still in the experimental stage by both the United States and
Canadian Weather Bureaus. Verber (87) reports that convectional-type
rainfall over Lake Erie is less than at adjacent land stations. The
U.S. Lake Survey embarked on a similar study in northern Lake Michigan,
and the results were reported by Bloust (ll). Estimates on evaporation
have varied from 53 "to more than 76 cm per year. Estimates on precipi-
tation have also varied in the same range. The U. S. Lake Survey (8l)
states that the average annual precipitation over Lake Michigan (1900-
1960) is 77 cm.
Possible Fate of Pollutants
The following factors influence the fate of an effluent dis-
charged into Lake Michigan: (a) Existing current regime; (b) Winds;
(c) Bottom topography; (d) the Earth's rotation; and (e) Density dif-
ference between pollutant and Lake water.
If there is a current regime, it will transport any pollutants
introduced into it. As previously noted, there may be a counterclock-
wise gyre in the entire Lake or an eddy in the southern portion that
would be the prevailing circulation feature.
Wind-induced currents can move Lake pollutants. The wind cur-
rents may be superimposed on any previously existing currents and can
move in any direction.
Topography may determine whether a pollutant remains in an area
or not. If the pollutant is less dense than Lake water, then it may be
moved by wind currents until it is trapped against a shore. If the
pollutant is denser than Lake water, it may run along the bottom and
collect in depressions.
If an effluent is discharged into the southern basin of Lake
Michigan and there is a density difference between the effluent and the
Lake water the following situations are possible:
l) If the effluent is low density, it will rise to the surface
and under certain wind conditions may be carried along the southern and
western shores, possibly affecting adversely water supplies that serve
populations totaling several million people as well as heavily used
bathing beaches. Such conditions could last for many days.
2) If the effluent is soluble, it may be kept in the southern
end of the Lake by the eddy which is sometimes there. Under such condi-
-------
tions, concentrations of chemical constituents well In excess of those
nonftslly present may build up.
3) If the effluent is discharged at the bottom and has the
same density as the Lake water, there vill be little vertical movement.
Under certain wind conditions it may be carried by subsurface currents
to the Chicago vater intakes or bathing beaches with little opportunity
for dispersion or dilution, or brought to the surface by upwelllng.
Each of the three possible situations cited above will be con-
siderably more serious if it follows a period of low wind and water
currents during which effluent concentration may build up in the vicin-
ity of diffusers. Such conditions may occur even when no ice ie present
and, on the basis of existing wind records, may be expected most
frequently during summer months.
4) If the effluent is of high density, it will sink to the
bottom and may run down to and collect in the southern basin. Concen-
trations of various constituents may build up and seriously interfere
with existing aquatic life. The density of treated effluent is so
close to that of the Lake water, that, at different times of year,
temperature changes in the Lake may result in the occurrence of any of
the possibilities listed above.
Previous Studies
A detailed literature search disclosed three important studies
pertinent to the measurement of currents in Lake Michigan. In the
years from 1892 through 1894, Mark Harrington of the U. S. Weather
Bureau released over 1,500 drift bottles in the Lake, of which only
about 203 were recovered during the 3-year period (36). These returns
formed the basis of the first map of Lake Michigan surface currents.
In 195*1-55, James Johnson of the U. S. Bureau of Fisheries (45) com-
pleted an intensive study of surface currents using drift bottles and
drift envelopes. Out of 6,260 releases, some 2,870 were recovered dur-
ing this study. The study results indicated that during 1954 no stable
pattern of surface currents existed. In general, Johnson found the
drift was from west to east and the north-south movements were about
equal. A similar pattern existed in 1955 except that the drift in the
eastern areas was mainly to the north. In 1958, Ayers and others, (2)
published the results of a series of synoptic surveys, in which they
applied a modification of the dynamic height method and published the
first map of Lake Michigan showing subsurface water movement. The
method, however, is open to question because of the choice of boundary
conditions (Ayers, l).
Townsend (78), took sharp issue with Harrington on the method of
presentation of data. He stated that in such a confined area as Lake
-------
Michigan, Harrington could not assume curved line motion but should
ha** used straight line motion. Townsend's ideas were partially veri-
fied by studies on Lake Erie (Verber, 85).
It is difficult to translate drift card or bottle moveaente over
many days into those of actual currents. The only positive statement
that can be made about drift Methods is in reference to the points of
release and retrieval. Such movements at best can only demonstrate a
type of pattern between the times of release and recovery. The seem-
ingly random changes between Ayers' and Johnson's work graphically
illustrate this point. The more recent studies using bottles and cards
did not claim to show anything other than the conditions that existed
at that time and place. Harrington, however, tried to pin down speci-
fic current patterns from far less data over a much greater time span.
The meters which exist today were unknown ten years ago and earlier
scientists could only use the tools then available.
The dynamic height method of obtaining subsurface current data
has not been substantiated by means of current meters. Criticism of
the method is based on two assumptions. One, the method assumes a zero
velocity depth level which may or may not be correct. Two, the theory
assumes constancy in the isothermal lines over a short period of time,
whereas it is known that internal waves may produce very striking
thermal changes in lakes and also in the ocean (Verber, 86).
Since none of the past studies showed net circulation, maximum
current speeds, effects of storms, or detailed inshore circulation,
further work was necessary to give the answers needed today.
Procedures
Procedures for the study are a combination of old and new
techniques. These have been selected through consultation with
oceanographers of the Chesapeake Bay Institute, Harvard University, and
Mew York University.
The study period on the Lake involved approximately l£ years of
data collection. The review of past studies, experimental testing of
equipment, purchase of equipment, and the development of techniques
preceded the actual study and required nearly 18 months.
To provide quality control of the data, services were secured
from other agencies. The Project established cooperative arrangements
with the Rational Oceanographic Instrumentation Center for basic cali-
bration of the instrumentation. Aircraft and photographic techniques
used in the study of littoral currents were provided by personnel of
the U. S. laval Air Station at Qlenvlew, Illinois. The precision of
navigation was accomplished through utilization of vessels and person-
nel of the U. S. Corps of Bagineers and private facilities.
25
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Temperature Studies
Temperature studies on Lake Michigan were made from September
1961 to 196^. Approximately 20 cruises were made on the Lake during
this period, with more than 1,300 bathythermograph casts. Information
gained during these studies was used to establish the various config-
urations of the thermocline during spring, summer, fall, and winter.
Temperature information gained throughout the year was used to deter-
mine the depth of mixing and variations in density layers within the
Lake.
In addition to securing data from bathythermographs the Project
secured 200 temperature recorders, designed by Woods Hole Oceanographic
Institute, which were used in conjunction with the current meters to
determine the location of the thermocline and magnitude of internal
waves.
Tracer Methods
Drogues were used for inshore studies. The drogues consisted of
a cloth or metal vane suspended in the water at the desired depth by a
line attached to a small surface float. The cross section of the vane
is sufficiently large to make the movement of the assembly dependent on
forces acting directly upon the vane, with negligible effects from
forces acting on the line and surface float. The movement of the vane
below the water surface is followed by corresponding movement of the
surface float. Several drogue studies, using both a small boat and
aerial photography, were conducted in the Chicago area during the study
period. The first drogue studies made by the Project were used to
develop techniques and methods of study. Drogues were used to study
current patterns and mixing in shallow water.
Fixed-Position Current Metering
Of the available techniques for the investigation of currents,
the use of fixed stations with automatic recording meters was selected
as most applicable for studies of mass water movements in the Great
Lakes.
Three types of measuring systems were considered seriously by
the FWPCA: The Woods Hole Oceanographic Institution meter, developed
by Dr. William S. Richardson (65), a telemetry system devised in 1962
by the U. S. Corps of Engineers (80), for the Public Health Service;
and a modular system, Frantz (33), devised by Marine Advisers, Inc. The
first is completely self-contained and has an automatic mechanical
system for recording data on 16 mm photographic film. The other two are
dependent upon an external unit to supply power and record data elec-
tronically. All have many desirable features not found in other types
of current meters, such as:
26
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l) The ability to Measure low current speeds, down to about
1.0 cm (0.03 feet) per second by utilizing a Savonius rotor.
2) The ability to operate untended for up to four months while
recording observations hourly.
3) The ability to aeaaure direction ± 7°.
k) The ability to record observations at shorter intervals
than one hour.
Each meter has particular characteristics which make it desir-
able for use under certain conditions. After a careful review of the
three meter systems as they related to study requirements, the Woods
Hole meter was selected as the most suitable for anticipated field con-
ditions .
After the method of study was selected and testing of meters was
underway, plans were developed for selecting the number of stations to
be instrumented, their location, instrument servicing, and the process-
ing of data. The selection of stations and the number of meters per
station were subjects of a conference held In Chicago with scientists
from the Great Lakes States and Canada. It was decided that the stand-
ard procedure of equal area and depth coverage was the most logical
method. To study all of Lake Michigan it was agreed that between 30
and to stations should be set. The number of meters to be set posed a
problem because of the variability of the thermocline. It was readily
agreed that the meters should be set at fixed depths, and at closer
spacing in the upper layers. The depths selected were: 10, 15, 22,
30 m and each succeeding 30-m level. No meter was set less than 10 m
below the surface because of problems resulting from surface waves.
The preliminary recording of data was different for the various
types of meters. The telemetering station recordered hourly on its
internal recording system and transmitted the data every k hours by
radio to a receiving station. The telemetry system reported total
revolutions of the Savonius rotor in each ^-hour interval together with
one instantaneous direction reading made at the time of reporting. The
Woods Hole meter at different times was used on a continuous recording
mode and then on a mode recording 50 seconds continuously once every 20
minutes. The recording for the full-scale study was set at a continuous
50-second recording period once each 30 minutes for the winter months,
but intervals were reduced to 20 minutes for the rest of the year. The
longer period was adopted for winter operation to provide a margin of
safety against exhaustion of the power supply batteries inside each
unit. During severe winter weather it was impractical to visit the
stations for retrieving data, replacing batteries, and other servicing.
Approximately 200 Woods Hole current meters were used in the study.
27
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Equipment Testing
Many of the theoretical concepts of water movements in the
oceans and the Great Lakes hare defied testing because of the lack of
adequate instrumentation. With the advent of the Savonius rotor and
the development of the Woods Hole meter a valuable nev tool was made
available to the scientist. An equally important development and
essential to the mass use of the meter was the perfection of an auto-
matic readout system in July 1962. Reading speed and direction every
20 minutes, each of the 200 meters would record 52,560 observations a
year. The manual reading of this Information directly from film would
have been prohibitive in cost.
Description of Test Studies
The study of currents in Lake Michigan by using current meters
began October 21, 1961 with the setting of an experimental telemetry
station. The station was first set about UO km northeast of Chicago
(Figure 3-1), but was removed after three days because of a defect. It
was reset on Nay 15, 1962 about 2^ km northeast of Chicago. From Nay 15
through November 1, 1962, several different types of station were set
for the purpose of evaluating meter performance, mooring systems, and
other features of the instrumentation, preliminary to the full scale
study.
Results of Test Studies
This section will describe the results of the observations with
respect to the following factors:
l) The reliability and sensitivity of instruments under field
conditions.
2) Mooring characteristics.
3) The operating characteristics of different types of current
meter installations.
4) Flow characteristics.
5) The relationships between winds-on-shore and lake currents.
6) Correlation between meters at one station.
The results of the tests are shown on a series of graphs. These
graphs present results of statistical tests on the data obtained from
the current meters. Speed readings are given in centimeters per second.
28
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WISCONSIN
ILLWOtS '
Subsurface Current Station
October, 1961
Subsurface
Current Station
— May, 1962
O
o
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
CURRENT METER STATIONS
U.S.DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago,Illinois
FIGURE 3-1
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Direction readings are given In tena» of degrees clockwise frost mag-
netlc north. The readings for direction given in this section represent
the direction from which the current is coving.
Figures 3-2 and 3-6 vere examined for correlation and equality
in direction. If the absolute value of the Median difference of the
readings between two meters is significantly less than 90° a positive
correlation exists.
Reliability
The reliability and sensitivity of the meters were determined by
an examination of results, i.e., speed and direction data, rather than
by an analysis of the physical characteristics of the meters. A study
of the data alone will not disclose systematic errors in the measure-
ments; however, such errors are believed to be small, based on tank
tests in which the sensors were towed through still water.
The data used for reliability evaluation were from two separate
stations - the telemetry station with three meters, set at 18, 27, and
36 m, and a station with one meter of the Woods Bole type set at kO m.
The two stations were within 90 m of each other. The recording interval
for the telemetry station was once every four hours with some observa-
tions at 10-mlnute Intervals. The total time of recording was 63 days.
The Woods Hole meter recorded continuously and the data were printed
out at 1.25-minute intervals. The record length for this meter was
6 days, July 5 to 10, 1962.
Figure 3-lt shows a series of current meter readings taken during
a period of increasing flow. The data show two types of changes In the
speed, a long-period systematic rise and a short-term random fluctua-
tion. The long-period rise shows an Increasing current speed. The
short-term random fluctuation could be due to changes in the current
speed or to instrumental error. At this time It is not possible to
distinguish between the two changes and they are grouped together and
treated as physical measurement limitations. The amount of the randan
fluctuations is used to estimate the precision (repeatability or con-
sistency) of the data.
The problem of variation measurement is to measure the short-
term changes without including the long-term systematic variation. The
simplest solution to this problem is to assume that the long-term
systematic variation is approximately zero over a short period of time.
Thus, over a short period of time, the total variation can be used to
approximate the random fluctuation.
Under steady-state conditions, the larger the quantity of data
collected, the more accurately it will represent the data of which it
30
-------
is * sample. However, the larger the quantity of data used, the
greater the time span. Thus, the problem is to use a large quantity of
data without spanning a long period of tine. The solution is to have
as short a period of time between observations as possible.
The data in Figure 3-4 from the Woods Hole meter were plotted
from the readings made at 5-minute intervals. The figure is a plot of
magnitude (speed) against time. The plot represents a 12-hour portion
of a to-hour period and indicates that the meter is capable of detect-
ing long-term systematic changes in speed. However, initial tests
showed a large random variation in direction at higher speeds, due to
the type of mooring system used.
Mooring Characteristics
The original mooring system used by Dr. Richardson of Woods Hole
In the Atlantic Ocean was modified for use in Lake Michigan. The
Atlantic installation used a synthetic line anchored to the bottom and
held at the surface by a large float. Ice and severe winter conditions
prevented the use of a slack wire mooring system in Lake Michigan. The
Project used a taut wire system with a subsurface float which has a
positive buoyancy of 250 kilograms. A surface float, for use in ice-
free periods, was attached by a slack line to the subsurface float. An
examination of the original test data shoved unusual variations in the
direction vane. Observation disclosed that during windy periods the
large surface float was capable of Jerking the lower taut line in any
direction. To prevent this action and the consequent swinging of
direction vanes on the meters, the mooring system was changed to a two-
line system. This present system leaves the meter line almost com-
pletely free from external stress.
Operational Characteristics
The mooring system used at the telemetry station had a small
surface float relative to the subsurface float. Therefore, the pull of
the surface float did not affect the direction vane on the sensors.
Thus, the data from the telemetry station were used in the analysis of
direction reliability. The 10-minute time intervals were used for the
analysis. Figure 3-2 shows confidence limits using 10-minute intervals
(Dixon, 21, p. 29*0- The results in Figures 3-3 to 3-6 show acceptable
precision in both magnitude and direction at each of the depths (18,
27 and 36 a) •
The Savonlus rotor has been tested to determine its degree of
reliability, response in turbulent motion, and dependability over
periods of time. The rotor, as used, is sensitive to about 0.9 cm/sec
as shown by tow tank tests conducted by the Corps of Engineers. Test
by Gaul (3^) indicates that the rotor is very reliable between 0.8 and
212 cm/sec.
31
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35
FIGURE 3-5
-------
FIGURE 3-6
-------
The rotor is omnidirectional, which Beans that it will sense
action from any direction in a horizontal plane when set with its axis
of rotation vertical. The orbital motion of waves produces a surge
forward and then backward as it passes. This effect on a Saronius
rotor would show as an increased speed. Wave action, during severe
weather conditions, can be detected as deep as 15 m. For this reason,
the uppermost current meter is at the 10-m level and will only be
affected during the more adverse conditions. Figure 3-8 shows a typical
rating curve for the rotor made by the Corps of Engineers.
Flow Characteristics
A preliminary examination was made of the flow data. The follow-
ing were investigated: relationship between wind and water movement,
relationship between readings at different stations, relationship
between readings at different levels, range of speeds, and possible
predominant directions at different speeds.
Much of the report depends on statistical testing for relation-
ships or correlations between two variables. A positive result
(correlation) implies 95-percent confidence that a relationship or
correlation does exist. A negative result (no correlation) implies one
of the following two possibilities: either no relationship exists
between the variables in question or a relationship does exist but the
nature of the statistical test or the data was such that the relation-
ship could not be detected.
Two limitations on the applicability of the findings in this
report should be mentioned. The current meter data represent samples
from a changing physical system. Thus, physical relationships which may
occur for one period of time may not necessarily occur for any other
period of time. For example, it is possible that systematic seasonal
differences are not reflected in the tests reported herein. Also,
the relations which are here established represent average effects. The
only thing necessary to produce a nonrandom effect during the whole
period of time is a large enough nonrandom effect to balance out this
effect on the overall result. The conclusion that can be obtained from
a positive result is that one can expect (with 95 percent confidence)
that the result held more than 50 percent of the time, for the period
of study (Dixon, 27, p. 28o).
Winds and Currents
An attempt was made to correlate wind and current data. Wind
data were estimated (from shore based stations) for the 10-m level
(above the lake surface) and the current data were taken at 20 m below
the surface. Various relationships were tried, using a variety of ways
37
-------
of weighing past wind average* and correlating with present currents.
Mo positive correlation could be found. This does not necessarily mean
that wind does not affect water currents. There is every reason to
assume that such relationship exists, but detection is difficult at the
greater depths.
Correlation Between Meters at one Station
A test was made to correlate currents at different depths (l8,
27* and 36 m) at the same station. Both magnitude and direction showed
positive correlation at 95 percent confidence. Figure 3-3 shows the
magnitude (speed) relationship at 18 and 27 m. The positive correlation
can easily be seen. It can also be seen that the speeds at 18 m are
greater than speeds at 27 « on the average (a difference in medians at
95 percent confidence is shown). Speeds at the 36-m depth were gener-
ally lower than the minimum detectable speeds on the current meter.
Figures 3-5 and 3-6 compare directions at different depths. The mean
direction of current, for the whole period at 30 m, was to the right of
that at 20 m, whereas the mean at 40 m appeared slightly to the left of
that at 30 m, with 95 percent confidence. While the first result
might be considered as consistent with Ekman transport (75), the second
result is zero. As far as they go, these results confirm that,
because of shallow depth and seasonal stratification, fully developed
Ekman spiral flow will rarely be encountered in Lake Michigan.
Figure 3-7 is a histogram which is designed to show the range of
speeds at different depths. The abscissa is a group of speed ranges
and the ordinate is the percent of time that the readings fall into the
range specified in the abscissa. There are differences in speeds at
different depths, and the greater speeds are the bars which are farther
to the right.
Figures 3-9 and 3-10, show polar coordinate diagrams of speed
and direction at two of the depths observed. Table 3-1 shows the number
and percent of observations in each quadrant, the average angle and
speed for each quadrant, and the maximum number of times the current
was found in a specific quadrant. The number of times the readings
were in the northwest quadrant was unusually high, indicating a 95 per-
cent probability nonrsndom effect (Tate, 76, p. 35). One meter showed
northwest currents over four days in succession, Table 3-1.
The results of these preliminary tests in one area of the Lake
may be summarized as follows. The two current meters in the same area
shoved, on the average, correlation in direction and general correla-
tion in speed and direction at different depths. In general, speed
decreased with depth, and average shifts in direction at different
38
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«Mr*4 ot »
Itoy Z«, l»«2- J«rty 2«, IMS
X Average velocity for quadrant
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
POLAR DIAGRAM OF MAGNITUDE
AND DIRECTION AT 18 M.
U.S.DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN.
Great Lakes Region Chicago.llhnois
FIGURE 3-9
-------
MO*
900*
170
140*
I20»
210°
NOTE:
Mftgti »*«f f«wr hour*
tfinctiwi m«OMirW at «nd *f
••eh >«rlod.
PtrM: (toy Z«, 1*62-July 26, IMt.
The three points located outside the graph
limits are; 310°, 24Cms.288°, 23 Cms.
and 252°, 19 Cms.
X Average velocity for quadrant
WCF
150°
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
POLAR DIAGRAM OF MAGNITUDE AND
DIRECTION AT 27 M.
I'S.DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago,Illinois
- (0
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TABLE
Current Meter Reading* in Each Quadrant*
Meter 1 - 18 M Deep
Maximal
Consecutive Observation Average**
Reading* in Percent MagnitudeDirection
Quadrant Quadrant Bomber of Tine CM/SEC Degrees
0-90° k 62 24.3 5.6 42
90-180° 3 33 12.9 5.8 139
180-270° 3 58 22.8 6.6 228
270-360° 20 1O2 40.0 6.8 310
100.0
Meter 2 - 27 M Deep
0-90° k 77 25.6 5-3 43
90-180° 9 59 19-7 4.4 131
180-270° 5 60 20.0 5.6 228
270-360° 26 104 34.7 7.7 316
100.0
Meter 3 - 36 M Deep
0-90° 3 66 22.0 0.54 38
90-180° 6 63 21-0 0.012 138
180-270° 3 73 24.3 0.015 223
270-360° 13 98 32.7 0.33
100.0
"Readings ere approximately four hours apart.
**Aritbmetic average of magnitude and direction.
-------
depths vex* detected. For instance, the »ean current direction at
27 • l*y to the right of that at 18 m. The current* at 36 m appeared
to the left of those at 27 m. As Mentioned earlier, the current speeds
at kO m were frequently below the minimum threshold capability of the
rotor. It is probable that the vane response to movement was also close
to its minimum range of detection. The speed ranges are shown on the
histogram plotted. The polar coordinate diagrams and Table 3-1 indicate
a predominance of currents from the northwest during the period sampled.
Significance of Findings
The data show that an effluent discharged into the Lake, at any
depth, can have a prevailing direction of movement. Oaring the period
of Nay to July 1962, this movement at the test station would normally
have been from the northwest at the three levels observed. The maximum
consecutive readings from the northwest varied from three to more than
four days with an average drift of seven or more kilometers per day for
the 18- and 27-meter levels. The rate of flow is expected to be higher
in the upper layers.
Although mixing occurs during severe weather conditions the
exact rate or amount are unknown. Earlier studies when the Chicago
River was diverted into the Lake in September 1961, show that the dis-
charged waters maintained a detectable coliform count for 5 days, (82).
Therefore, it may be possible that even during periods of high veloci-
ties for 8 or more hours the effluent will not be mixed into the
surrounding water.
The worst condition appears to be when an effluent remains in
the general vicinity of its discharge point because of extremely low
velocities. After a period of building-up, the concentrated effluent
might then be moved, en masse, by the current. Relatively slow currents
could move the effluent for k or more days in one direction, as shown
in Table 3-1, or a fast moving current could produce the same result
within 5 to 8 hours.
This is the first occasion on which current meters have been
operated for continuous periods in Lake Michigan and, although they
demonstrate average trends, they also show a far greater variability of
flow than that indicated by previous studies.
Summary of Test Studies
The data and performance tests from the first meters set in Lake
Michigan were examined and evaluated. The tests were made to evaluate
the type of meters to be used and reliability of the instruments'
internal components. The test data were examined for persistency of
movement and the variations of speed with depth.
-------
The data tabulated for Nay to July 1962, show that under certain
conditions an effluent could move, at low speed with relatively little
mixing, for over k days. Movement during other periods of the year may
show that there are other quadrants in which the current will predom-
inate for longer periods of time.
The test data indicated that the reliability and sensitivity of
all meters for measuring both speed and direction were satisfactory for
study purposes. The data from the instruments using one type of mooring
system indicated that the large surface float had an effect on the vane
direction. An alternate mooring system was devised to eliminate this
possible source of error.
Three types of meter systems were evaluated and the Woods Hole
meter was selected because of the established performance record of its
internal components, type of data collected, and lover cost.
-------
CHAPTER 4
METHODS TOR MOCRHSS, DfSTRUMEHT CHECKS, FILM PROCESSING
AMD FUJI CQHVERSI01
Introductloo
To successfully complete the largest current study ever planned,
new methods and techniques had to be devised to Insure reliability,
efficiency, and standardization.
The instrumentation used was designed and tested at the Woods
Hole Oceanographic Institution. Since these Instruments were rela-
tively new, they have undergone some modification with time.
An instrument shop was established at each field station where
operations were being conducted. An instrument technician and assistant
were in charge of all repairs, loading and unloading film, and calibra-
tion systems.
Prior to each station installation, the instruments are given a
complete mechanical check. This checking includes the following Instru-
ments: current meters, temperature recorders, anemometers, lights, and
recovery buoys.
In setting a station, a form is filled out showing all Instru-
ment serial numbers, line lengths, etc. A sample diagram is shown in
Figure 4-1.
Mooring Systems
The meter mooring system used by the Federal Water Pollution
Control Administration in the Great Lakes has been basically standard-
ized with minor modifications as the program progressed.
The system used during the ice-free season is shown in Figure
4-2. The current meters, each paired with a water temperature
recorder, were suspended in a taut line between a subsurface buoy and
anchor. A slack line connected this anchor to another nearby anchor
which moored, on a slack line, a surface buoy. The surface buoy was
instrumented with a water temperature recorder, a wind recorder, and a
navigation light. Ordinarily, a small surface float was attached to the
subsurface buoy by a 0.6-cm (•£") slack manila line, and a staff marker
buoy was set separately but nearby. These markers were set to help
assure station recovery.
-------
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
STATION DIAGRAM
SUMMER
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lukes Region Chicago,Illinois
FIGURE 4-1
------- An error occurred while trying to OCR this image.
-------
Winter altering stations were similar except the instrumented
surface buoy was replaced by a subsurface recovery buoy set to surface
in the spring by use of a clock-controlled actuator (Figures It-3 &n&
4-4). A second recovery buoy was attached to the main subsurface buoy
to help assure recovery, Figure 4-5.
In detail, a metering station consisted of the following array
beginning with the subsurface support buoy (Figure 4-6). The top of
the subsurface buoy was approximately 7.2 a below the water surface.
A temperature recorder (Figure 4-7) was attached to the bottom of the
subsurface buoy with a 1.2-cot shackle. The temperature recorder was
attached to a current meter (Figure 4-8). At the bottom of the current
meter was shackled a 1.2-cm (£") by 12.5-cm (5") ring. The ring, in
turn, was shackled to a thimbled, 1.6-cat (5/8") braided polypropylene
line, 3.3 m long. At the bottom of the 1.9-cm (3/4") line another
temperature recorder was shackled and the sequence repeated. In this
manner, current meter-temperature recorder pairs were set at approxi-
mate depths of 10, 15, 22, and 30 m and every 30 m thereafter, depend-
ing upon total water depth.
The bottom of the instrument line was attached by a length of
1.0-cm (3/8") chain and shackles to a 362-kg railroad car wheel anchor
(Figure 4-9).
Another short length of chain was shackled to the instrument
anchor. Polypropylene 1.9-cm (3/4") rope was shackled to the chain and
leads across the bottom to a second wheel anchor at a distance equal to
or exceeding l£ times the water depth. The rope was again attached to
the second anchor by a short length of chain. At the Juncture of the
rope and chain was a 1.6-cm (5/8") by 12.6-cm (5") steel ring (Figure
4-10). To this ring the Instrumented surface buoy was moored by 1.9-cm
(3/4") polypropylene rope. This rope was slack and leads up to a 6-m
length of 1.0-cm (3/8") chain, which in turn waa shackled to the buoy
bridle. After some difficulty was experienced in pulling this anchor,
a weak link of 1.2-cm (•£") polypropylene rope was put into the system
between the anchor chain and ring.
A temperature recorder was installed in the bridle of the
surface buoy (Figure 4-11). A navigation light (Figure 4-12) was
mounted on the top platform of the buoy tower. A wind recorder (Figure
4-13) was mounted on the lower platform. Its velocity sensor was
mounted atop a pipe about 6l cm (2') above the top of the buoy tower,
3.6 m above the water surface (Figure 4-14). The surface and other
buoys are shown in Figures 4-15 and 4-16.
The entire station array is assembled on deck prior to launch-
ing. The subsurface buoy and attached instrument group are put in the
49
-------
RECOVERY
INSTRUMENT
LATCH PIN
RELEASE RING
1/2" SHACKLE
CHAIN
30" DIA.
ALUMINUM POLE
SCALE
4 IN.
10 CM.
FIBERGLASS FLOAT
(DAY-GLO FIRE ORANGE)
84
24"
12
LINE STORAGE CASE
HOSE CLAMP (5 REQ'D.)
24"
RUBBER DIAPHRAGM
WITH SLIT
7/16" BRAIDED
DACRON-NYLON LINE
THIMBLES
GALVANIZED STEEL
LIFTING EYE
FIBERGLASS
SUB SURFACE BUOY
(DAY-GLO FIRE ORANGE)
MATERIAL
STAINLESS STEEL OR ANODIZED.EPOXY-
PAINTED ALUMINUM.
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
RECOVERY BUOY SYSTEM
NOT TO SCALE
US OEPtfrTMCNT OF TMC MTCRlOft
FCOCHAi. WttCNPOtUITlON COWTHOL A0MN.
50
FK5URE 4 - 3
-------
LINK
MATERIAL
STAINLESS STEEL
TOP VIEW
MATERIAL
POLYVINYLCHLORIDE
FINISH
YELLOW EPOXY PAINT
THIS END TO RECOVERY
INSTRUMENT
SECTION A-A
THIS END TO LINK
7/16" BRAIDED
DACRON-NYLON LINE
LINE STORAGE CASE
NOT TO SCALE
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LINK 8 LINE STORAGE CASE
U.S Of P*MTI*€NT OF TM€ INTERIOR
FfCCRAL flUTE*POLLUTION CONTROL AOMIN
FIGURE 4-4
-------
—Recovery buoy
Sub-surface float
01
t»
a>
aJ
a.
UJ
o
10-
15-
22-
Recovery buoy
I)
(I
/• Temperature recorders-Woods Hole type
\
30-
Current meters-Woods Hol« type
.6 cm. braided poly line
pairs at each succeeding 30 meter level
1.9 cm. mono-polypropylene rope —
>0.95 cm. BBB chain \, concrete anchor
/ wheel anchor x^ 136 kg.
386 kg.
NOT TO SCALE
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
TYPICAL CURRENT STATION
WINTER
US DEPARTMENT OF TH€ INTERIOR
FEDERAL VWTER POLLUTION CONTROL AOMIN.
Ortot LuX«s Region Chlcogo.lllmott
flOUKE 4~5
-------
FIBERGLASS
WRAPPED
TOP VIEW
GALVANIZED STEEL
LIFTING EYE
MATERIAL
FIBERGLASS
FINISH
DAY-GLO FIRE ORANGE
30"-
SECTION A-A
6 LB. FOAM 24
2" O.D. X 1-3/4" I.D.
ALUMINUM TUBE
LENGTH - 25"
SCALE
5
IOIN.
i i i r
25CM.
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SUB SURFACE BUOY
U S OEPAWTMCNT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lukts Rtgton Chicago,Illinois
FIGURE 4-6
-------
MERCURY SWITCH
CAM ADJUSTMENT KNOB
(BACK SIDE)
TIMING CLOCK
TAKE UP ROLL
PEN PRESSURE ADJUSTMENT
TEMPERATURE SENSING
BULB
MATERIAL
ALUMINUM 8 STAINLESS STEEL
FINISH
OXIDE FINISH 8 YELLOW EPOXY PAINT
ON ALUMINUM PARTS
LIFTING PAD
(MAY BE USED ON BOTH ENDS)
PRESSURE CASE (ALUMINUM)
RECORDER SWITCH
CONTINUOUS OFF INTERVAL
SPINE
MOTOR CAM 8 SWITCH
RELEASE CATCH FOR SPOOL
SHAFTS
WAX-PLASTIC CHART PAPER
SUPPLY ROLL
TEMPERATURE ELEMENT
HIGH-LOW TEMPERATURE STOP
BASE CAP
SCALE
0 4IN.
Illl I I 1
IOCM.
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
TEMPERATURE RECORDER
US^DEPARTMENT OF THE INTERIOR
fEOCRAL WATER POLLUTION CONTROL ADMIN
Gr«ot Luk«sR«g,on Ch.coflO,Illinois
FIGURE 4-7
-------
MATERIAL
ALUMINUM a STAINLESS STEEL
FINISH
OXIDE FINISH 8 YELLOW EPOXY PAINT
ON ALUMINUM PARTS
LIFTING EYE
VANE
VANE FOLLOWER
CAMERA
PRESSURE CASE (ALUMINUM)
FIELD OF VIEW
TIMING CLOCK
COMPASS
BATTERY
TIE RODS (3)
ROTOR FOLLOWER
SAVONIUS ROTOR
SCALE
5 IOIN.
I I
1 I
25 CM.
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
CURRENT METER
WOODS HOLE TYPE
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POL LUTON CONTROL ADMIN.
Gr«dT Loktt Rtgion Chtco
-------
STEEL ROD EMBEDDED IN CONCRETE
25 GAL. DRUM
FILLED WITH
CONCRETE
(94.7 lifers)
STEEL ROD WELDED TO AXLE
AXLE
STEEL FREIGHT
CAR WHEEL
850 LB. WHEEL ANCHOR
(362 Kg.)
MATERIAL
AS SHOWN
225 LB. DRUM ANCHOR
(I 0 0 K g .)
GREAT LAKES 8 ILLINOIS
RIVER BASINS PROJECT
ANCHORS
NOT TO SCALE
U S DePAHTMENT OF THE INTERIOR
FCOCRAL WATER POLLUTION CONTROL AOMtN
Laktt lUgion
FIGURE 4 -9
-------
5/8" POLYPROPYLENE
LINE
THIMBLE
1/2" SHACKLE
1/2" X 4" RING
FRONT VIEW
MATERIAL
GALVANIZED STEEL
SIDE VIEW
SCALE
0 4IN.
I I I I I I I I
pi PHn i
o IOCM.
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
INSTRUMENT LINE COMPONENTS
NOT TO SCALE
US DEPARTMENT OF THE INTERIOR
FEOCRAL WATER POLLUTION CONTROL ADMIN
Great Latm Rtgion Chicago,Illinois
FK3URE 4-10
-------
GALVANIZED STEEL
EYE
5/8 X 4" GALVANIZED
STEEL RING
SCALE
inn i
4 IN.
GALVANIZED STEEL
JAW
IOCM
MATERIAL
STAINLESS STEEL
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
RIGID BRIDLE
NOT TO SCALE
U.S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lukts Region Chicago,Illinois
FtGURE 4-11
-------
22"
7/16 DIA. 6 HOLES
60° APART ON A
9-l/2"DIA. B.C.
MATERIAL
AS SHOWN
FINISH
AS SHOWN
SCALE
i_._ I
4 IN.
IOCM.
GLASS LENS
ALUMINUM WITH BAKED ENAMEL
FINISH
STAINLESS STEEL
POLYVINYLCHLORIDE
PLASTIC BATTERY CASE
YELLOW EPOXY PAINT
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
NAVIGATION LIGHT
NOT TO SCALE
U.S DEPAJRTWENT OF TM€ INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMHN
Grwt Luktl Region Chicago,
FIGURE 4-12
-------
TO ANEMOMETER
JO!
DIGITAL FILM RECORDER
MEASURING WIND SPEED
COMPASS BEARING
I"'T "
35
10*-
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
WIND RECORDER
U.S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN.
Great Lakes Region Chicago,Illinois
60
FIGURE 4-13
-------
13/32 DIA. 4 HOLES
>— 3
,32 3
yLJl
»1 ALUMINUM CUPS
OHO
DIA.
A-268 MAGNETIC SWITCH
ASSEMBLY
MATERIAL
ALUMINUM WITH STAINLESS STEEL FASTENERS
FINISH
BLACK ANODIZE FINISH ON ALUMINUM CUPS
61
SCALE
4IN.
IOCM.
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
HEAVY DUTY ANEMOMETER
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER PCL LUTION CONTROL AO*tN
Chlcogo.lllmcMi
rVGUPF 4 - 14
-------
ALUMINUM PIPE 1-1/4"
1.66 0.0. X .140 WALL.
LENGTH AS REQUIRED
GALVANIZED STEEL
LIFTING EYE
(DAY-GLO FIRE ORANGE)
U.S. GOVERNMENT PROPERTY
KEEP OFF
DEPT. INT. F.WPCA LA. 3-9SOO
EXT. 4103 CHICAGO, ILL.
ALUMINUM LEGS (3)
MARINE PLYWOOD PLATFORMS
(YELLOW)
FOAM
2 LB/FT3
MATERIAL
AS SHOWN
FINISH
AS SHOWN
NOTE
30" DIA.
SCALE
.0 4IN.
I I I I I I I
IOCM.
PAINT LEGS a BUOY DAY-GLO FIRE ORANGE
WITH CLEAR ANTI-FADE FINISH COAT.
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
INSTRUMENT BUOY
TOROIDAL SHAPE
NOT TO SCALE
U S DEPAWTMCNT OF THE INTERIOR
WATER POLLUTION CONTROL AOM»N
Gf*«t Lu»«»
FIGURE 4-15
-------
144
MATERIAL
AS SHOWN
FINISH
AS SHOWN
H
¥
o
CAST IRON
EYE
WATER
LINE -7
SPAR BUOY
CAN FLOAT 7
'
|
7/8" GALVANIZED
IRON PIPE
TOP VIEW
(BOTH ENDS)
35 GAL. DRUM (132.6 I.)
(DAY-GLO FIRE ORANGE)
l" STEEL BAND-BOLT,
NUT, a CHAIN.
COTTER
PIN
WASHER
1
2
8" -I
i
2<
'
»"
*"
2"
t 2
i r
i
i
i
• ; '"!'
!, 1'
V- 6" DIA.
x STYROFOAM
FRONT VIEW
CAN FLOAT
5 DIA.
LEAD WEIGHTS
SCALE
4IN.
0
SPAR BUOY
10 CM.
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
BUOY 8 FLOAT
NOT TO SCALE
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Grtor Loktt Rtgion Chicago,IllmoU
FIGURE 4-16
-------
water and the anchor is dropped. The surface buoy is then launched and
its anchor is dropped vhen the line between anchors becomes taut.
Retrieval of a station array is simple and consists of first
lifting the surface buoy followed by the remainder of the array in
order.
A winter array is launched and retrieved in a similar manner.
A lighter concrete anchor is used for the surface buoy part of the
system in winter, since it must moor only a small recovery buoy (Figure
Some difficulties were expected in the mooring system and
several have arisen. The main problems have been in the instrumented
surface buoy mooring. Apparently, the mooring line near the anchor
often was abraded by the anchor, setting the buoy adrift. Polypropy-
lene rope, used because of its strength, buoyancy, and resistance to
chemical and organic decay is, unfortunately, easily abraded.
Another problem with the surface buoy has been that it would
capsize during storms. The buoy is Just as stable inverted as right
side up. Chain in the mooring line lessened the frequency of this
occurrence but did not eliminate it. It became a major problem in Lake
Erie because of short steep waves in shallower water. It finally was
overcome by placing a 3-m length of railroad rail in the mooring line.
A weak link was put into the surface buoy mooring line to elimi-
nate the possibility of breaking the mooring line when pulling the
anchor. In Lake Michigan the weak link worked well, but in Lake Erie
it was unsuccessful apparently due to high frequency stresses of wave
action. Consideration had not been given to the results of weak link
breakage while the stations were unattended. When breakage occurred,
the surface buoy was then anchored to the meter by a very long line.
This line then wound around the instrument array, the line was abraded,
and the buoy was set adrift.
A major problem in the work on Lake Michigan was inadequate nav-
igation. Losses due to navigation have not occurred since the vessel,
Telson Queen, was contracted as the survey vessel. This vessel was
equipped with radar, gyro compass, and radio direction finder.
Some equipment and/or data have been lost because of vandalism,
passing ship damage, ice damage, corrosion, wave hammering, and array
assembly errors. All of these losses were relatively minor.
Except for the weak links, there have been no failures because
of exceeding the working strength of materials. Tables k-1 and k-2 list
the more important specifications of equipment which apply to mooring.
6k
-------
TABLE
SPKCIFICATIOaS OP HBTERHQ BftJIPMBIT
Item
Buoyancy Maximum
Operating
Lbs Depth (M) Construction
^L
Surface buoy 2,270 5,000
Recovery buoy 36 80
Subsurface buoy 227 500
Current meter -13.6 -30
Temperature -2.3 -5
recorder
Recovery last. -4.5 -10
Tension Strength
Kg Lbs
3,178 7,000
Fiberglass-
wrapped styrofoa*
18 Fiberglass-
wrapped styrofcam
18 Fiberglass-
wrapped styrofoam
2,700 Aluminum aad 2,270 5,000
stainless steel
1,350 Aluminum and
stainless steel
1,350 Aluminum and
stainless steel
6,810 15,000
3,600 8,000
1,816 4,000
TABLE 4-2
SPECIFICATIONS OF MOORING MATERIALS
Item
£" rope(1.2 cm)
3/4" rope(1.9 cm)
3/8" chain(9.6 cm)
7/16" shackled. 1 cm)
4" shackle (1.2 cm)
V shackle (1.9 cm)
" ringd.2 cm)
5/8" ring(l.6 cm)
5/8" braidd.6 cm)
7/16" braidd.l cm)
Working Strength
Construction
Polypropylene
Polypropylene
Galv. steel
Galv. steel
Galv. steel
Galv. steel
Galv. steel
Galv. steel
Polypropylene
Dacron and
nylon
Kg
1,362
2,724
1,362
1,135
1,816
4,086
2,724
3,178
2,724
2,724
Lbs
3,000
6,000
3,000
2,500
4,000
9,000
6,000
(yield)
7,000
(yield)
6,000
6,000
Use
Weak link.
Anchor line.
Anchor line.
Chain connection.
Line and instrume
connection.
Anchor connection
Current meter liz
connection.
Anchor line
surface buoy.
Instrument line.
Recovery buoy
line.
65
-------
When a station was recovered the station diagram was used to
recheck the various pieces of equipment used and all corrections noted
on the SOB* sheet. Savaged rotors, -vanes, or other items were listed.
The instruments were returned to the shop and a complete check Bade on
various components and entered against the instrument maintenance log.
When the current meter films were remored they were placed in a metal
container and the instrument serial number was taped to the container.
Later, a film log sheet (Table 4-3) was filled in, assigning permanent
film serial numbers to each record. The film series 200 000 has been
assigned to the Great Lakes. This has been further subdivided as
follows:
200 000 Lake Michigan
210 000 Lake Erie
220 000 Lake Ontario
230 000 Lake Huron
240 000 Lake Superior
The film log sheet was filled in and shipped with the film to a
film reading agency where the records are filed and the films are sent
for processing.
The Inspection Sheets, Tables 4-4, 4-5, and 4-6, were used both
before and after each use. A file was kept on each instrument with its
performance and maintenance background. Proper Inspection insures that
data are reliable.
Film Processing
Eastman Kodak, 16 am, double X, panchromatic, negative movie
film, DXM 449, on 30 m (lOO1) daylight loading reels was used in the
current meter camera (Figure 4-17)• The exposed film was delivered to
the processing contractor on 30 m reels in blacktape-sealed cans in the
original yellow boxes which have been marked in accordance with the
user's own identification and numbering information.
Upon receipt of the film the contractor perforated an identify-
ing number or code on the tail of each roll and on the flap of the
yellow box from which it was taken. The film was "tail out" on the
reel.
All films from a single order were then spliced together head to
tail for processing. This processing was described as "Extended
Processing."
A positive print was then made of the original film on fine
grain release film using emulsion-to-emulsion contact for maximum
66
-------
Date
film Serial Mo.,
Type of Inrt.
Date/Tlw Started,
Date/Tins Ended
Speed of Pila (Coat.),
Lat.:
Lake
Beginning Ft. Mark_
Batch Ho.
Processing Meg.
Edge Mo.'s Original^
Original Stored
1st Print Stored^
Film to be read
Continuous^
Recovery Buoy #
Copy
Geodyne
TABLE k-3
16 •• Film
fficATio
AID LOG
University of Wisconsin
_Permanent File
Other Files
Data
SHEET
Bsulsion Mo.,
Seri«d Mo.
Station Mo..
Depth
Tiae (Interval),
Long.:
Job:
Frames Skipped,
Positive^
Prints
Quantity
Interval
Teaiperatiire Recorder
Wad Recorder #
Sfc. Tentp. Recorder
67
-------
TABLE
INSPECTION SHEET-CURRKNT METERS TEAR-DOWN
STROBE
a.
8.
10.
11.
Seconds
Board and component*
Elect, connections
Cont. and strobe lights
Operational check
Secure
Elect, connections
Operational
fined
Cam
a. Secure
b. Elect, connections
c. Operational
d. Tined
e. Gear and shaft
t. KPM
MOTOR SWITCH
a. Secure
b. Elect, connections
c. Operational check
CLOCK SWITCH
a. Secure
b. Elect, connections
c. Arm adjustment
d. Operational check
JWITCH
Secure
Elect, connections
c. Functional check
POWEK SWITCH
a. Secure
b. Functional Check
c. Elect, connections
BATTERY
a. Secure - no leakage
b. Voltage
BATTERT CONNECTOR
a. Elect, connections
Clean
Resistance check
Secure
Lens tight
Lens' setting
Drive engaged
Pulley and rubber
Film record (L, S, N)
Clean
Magnets
Bearings
Adjustments
Free rotation
No visual damage
12. VANE FOLLOWER
13-
Ik.
15-
16.
17.
18.
19-
20.
21.
22.
23-
Secure
Leakage
Bubbles
No binding
Disc alignment
Lite
Lite pipes
Viscosity
Diaphram
Clean
Magnets
Bearings
Free rotation
No visual damage
Elect, connections
I-I lite
IO-I lite
e. Lite pipes
COMPASS
a. Secure
b. Leakage
c. Bubbles
d. No binding
e. Disc alignment
f. Lite
g. Lite pipes
h. Diaphram
READ PULSE
a. Secure
b. _ Elect, connections
c. Lite
d. _____ Lite pipe
FRAME~AND HARDWARE
a. Clean
b. Secure
"0""~K1UGS
a. Seats undamaged
b. No leakage
OPERKrTONAL CHECK
a. Advance of film
b. ^^.^ With film removed
POWEH SWITCH
a. Continuous
b. Off
c. Interval
CASH
a. No visual damage
EXTERIOR BOLTS
a. Tight
DATE
a. Open
68
-------
TABLE
IBSPECTIOB SfflEKT-CURHDrT MBHZIS BUILD-UP
1.
2.
7.
8.
10.
Seconds
Board and components
Hect. connections
Coot, and strobe lights
Operational cheek
Secure
Heet. connections
Rewind
12. TARE FOLLOWER
3. MOTCsT"
13-
Secure
b. Heet. connection*
c. —; Brushes cleaned
d. Timed
e. Gear and shaft
f. RPM
MOtCR SWITCH
a. Secure
b. meet, connection*
e. Operational cheek
CLOOTBtflTCH
a. Secure
b. Heet. connections
e. Arm adjustment
d. ""Operational check
MAC. SWITCH
a. Secure
b. """""" Elect, connections
e. Functional cheek
POtfJSf UWlTd
a. Secure
b. Hect. connect ions
c. """""' Functional cheek
BATfE?
15.
Secure
Voltage
CCMBBCTOK
Hect.
connections
Resistance check
Secure
deea
Lens* setting
EtriTe engaged
Pulley and rubber
Film loaded
11.
•6 visual damage
16.
17.
18.
19-
20.
21.
22.
23-
Secure
Leakage
Bubbles
Xo binding
Disc alignment
Lite
Lite pipes
Viscosity
Diaphram
di
Magnets
Bearings
Free rotation
Bo visual damage
Hect. connections
I-I lites
IO-I lites
Lite pipes
Secure
Leakage
Bubbles
Bo binding
Disc alignment
Lite
Lite pipes
_ Diaphram
R1A1THTL8E
a. _ Secure
b. """""" Blee. connections
e. - Lite
d. ""• Lite pipes
IBOflFICATIOB
a. _ Ser. no. on outside case
b. ' Type of cam (lobes)
"0"~MiJS
a. _ Seat clean
b. Properly seated
OFsfHIOBAL CfBCK
a. _ Without film
b. - With film
F0MEK BW1TCH F08HIOB
a. _ _ Continuous
b. _ Off
c. Jaterral
DBSSlCAVr
a. _ Installed
BcmrrcR BOLTS
a. _ Torqued
Open
dosed
a.
b.
69
-------
TABLE
INSPECTION SHEET - TEMPERATURE RECORDER TEAR-DOWN
1. GENERAL EXTERIOR
a. Exterior clean, no damage to case or end plates
b. Case properly seated
e. Tie rod nuts drawn up tight
d. Tie red nuts, where and end plates removed
e. No damage to case sealing surfaces
2. GENERAL INTERIOR
a. __._. Clock operating * note switch position
b» Battery voltage checked (record reading)
c. Graph tracking on spool (indicate end and date on graph)
d. Indicate length of graph as: long, short, none, normal
e. _ Operational check (indicate type of cam)
3. TEMPERATURE SENSOR
a* _ Sensor and components secure
b. Scribe tracking and secured to shaft
c. Sensor spiral free, no corrosion
d. Calibration check (record results)
e. Stops on slide bar properly positioned
f. Graph removed and identified as to serial number and date opened
k. SPOOLS
a. Spools and shafts free and clean, restraining clips secure
b. Check spring tension of shafts
e. Face plate smooth and clean
5. CLOCK MOUNT
a. Mount bracket secure
Electrically isolated from frame
Air gap between bracket and power switch
dock secure on bracket
Elect, connections.
Rewind (check and record timing)
dock micro switch secure and operational
MOTOR^SWITCH
Secured
Elect, connections
Functional check
8. MERC. SWITCH
Secure
Functional check
9. powEFswrrcH
a. Elect, connection
b. Functional check
10. MOTOR AND MOUNT
a. Elect, connections
b. Functional check
e. ""~" Timed
d. Gear and shaft secure
e. Ho binding of gear-train
f. Motor and mount secure
11. GENERAL
a. Removed battery
b. Battery leads checked
c. ^^ Starting at base all hardware secured
d. No evidence of corrosion
e. "0" ring grooved free of nicks, burrs, or dirt
f. Instrument clean and rotating parts lubricated
TO
-------
TABLE 4-5b
INSPECTION SHEET - TEMPERATURE RECORDER BUILD-UP
(WITH UTILITY BATTERY INSTALLED)
12. MOTOR
a. Brushes and armature cleaned and free
b. GOT. points cleaned and adjusted
c. ____ Leads properly soldered and routed with no strain
d. No visible damage to housing; shaft and gear secure
e. With motor disengaged, gear-train movement free
f. _____ Micro svitch secure and operational (leads properly routed)
g. Motor gear properly B*shed vlth gear-train
h. Motor and mount secured to instrument
1. _____ Operational and time check
13. CLOCir~
a. Installed, check arming mn^ timing
b. ^____ Leads secure vlth no damage or strain
c. Adequate clearance between elect, connector and motor
d. Mount bracket isolated from frame and power svitch
e. Cam installed (indicate number of lobes)
Ik. CLOaTRlCRO SWITCH
a. Svitch installed
b. Leads properly soldered and routed vith no strain
c. Verify routing of leads to other components
d. Actuator arm adjusted
e. _m_I functional check
15. TEMPERATURE SENSOR
a. Sensor and components secured
b. Sensor spiral free and no corrosion
c. No evidence of transfer fluid leakage
d. No damage or Improper routing of transfer tube
e. Scribe secured to shaft and indicating approx. temp.
f. Face plate smooth and clean
g. Spool shaft bushings clean and lubricated
h. Shaft locking clips secure vith free movement
16. SPOOLS
a. _____ Free and clean
b. __^ Shafts clean and proper spring tension
c. Test tape Installed, scribe adjusted
d. Operational test (2-3 veeks) completed
17. CALIBRATION
a. Install new tape, verify hole and sprocket alignment
b. Calibrate instrument (indicate range)
18. BATTERY
a. Voltage (note on tape ser. no., date, and starting point)
b. Operational check performed
19. "0" RINGS
a. Case clean, sealing surfaces free of damage or dirt
b. "0" rings installed in base and cover
20. POWER SWITCH
a. Continuous
b. Off
c. Interval
21. DESSlCANT
a. Installed
22. CASE
a. _____ Case and cover - tie rods installed and nuts torqued
b. Instrument identified vith ser. no. and type of cam
71
-------
TABLE k-6&
INSPECTION SHEET-WIND RECORDER TEAR-DOWN
1.
2.
k.
5.
6.
7.
8.
9.
10.
11.
STROBE
a. Seconds
b. Board and components
c. Elect, connections
d. Cont. and strobe lights
e. Operational check
CLOCK
a. Secure
b. Elect, connections
c. _____ Operational
d. Tined
e. Cam
MOTOR
a. Secure
b. Elect, connections
c. Operational check
d. Tijned
e. Gear and shaft
f. RPM
MOTOR SWITCH
a. Secure
b. Elect, connections
c. Operational check
CLOCK SWITCH
a. Secure
b. Elect, connections
c. Arm adjustment
d. Operational check
BATTERY CASE
a. Clean
b. Cover fasteners secure
c. No visible damage
POWER
a. Secure
b. Elect, connections
c. Operational check
BATTERY
a. Secure, no leakage
b. "' Voltage
BATTERY CONNECTOR
Elect, connections
Clean
Resistance check
Secure
Lens tight
Lens' setting
Drive engaged
Pulley and rubber
Film record (L,S,N)
Clean
Magnets
Bearings
Adjustments
Free rotation
No visible damage
12. VANE FOLLOWER
a. _ Secure
b. _ Leakage
c. _ Bubbles
d. _ No binding
e. _ Disc alignment
f . _ Lite
g. _ Lite pipes
h. _ Viscosity
i. _ Diaphram
ANEMOMETER
a. _ Frame secure
b. _ Pickup and leads checked
c. _ Bearings and free rotation
d. _ Cups and shaft secure
e. _ Operational check
BOARD AND LITES
a. _ Board and lites secure
b. _ Elect, connections
I-I lite
13.
17.
18.
19.
20.
21.
22.
23.
c.
d.
e.
^^^
15. COMEK53
a.
b.
c.
d.
e.
f .
g.
h.
IO-I lite
Lite pipes
Secure
Leakage
Bubbles
No binding
Disc alignment
Lite
Lite pipes
Diaphram
connections
_
16. READ PULSE
a. _ Secure
b. "' Elect,
c. - Lite
d. _ Lite pipe
FRAME AND HARDWARE
a. _ Clean
b. _ Secure
"0" RINGS
a. _ Seats undamaged
b. _ No leakage
OPERATIONAL CHECK
a. _ Film advance
b. With film removed
POVUSK SWITCH
a. _ Continuous
b. Off
c. Interval
_
CASE
a. _ No visible
EXTERIOR HARDWARE
a. _ Secure
DATE -
a. _ Open
damage
72
-------
TABLE k-6b
INSPECTION SHEET-WIND RECORDER BUILD-UP
n.
1. STROBE
a. Seconds
b. Board and components
c. Elect, connections
d. Cant, and strobe lights
e. Operational check
2. CLOCK
Secure
Elect. connections
Rewind
Timed
Cam
Secure
Elect, connections
Brushes cleaned
Timed
Gear and shaft
RPM
k. MOTOR SWITCH
Secure
Elect, connections
Operational check
5. CLOCK SWITCH
a. Secure
b. Elect, connections
c. Arm adjustment
d. Operational check
6. BATTERY CASE
a. No visible damage
b. Cover fasteners secure
c. Clean
7. POWER SWITCH
a. Secure
b. Elect, connections
c. Functional check
8. BATTERY
a. Secure
b. Voltage
9. BATTERY CONNECTOR
a. Elect, connections
b. Clean
c. Resistance check
10. CAKER7T
Secure
Clean
Lens' setting
Drive engaged
Pulley and rubber
Film loaded
Clean
Magnets
Bearings
Adjustment
Free rotation
No visible damage
Lite pipes
12. VANE FOLLOWER
a. Secure
b. Leakage
c. Bubbles
d. No binding
e. Disc alignment
f. Lite
g. Lite pipes
h. Viscosity
i. Diaphram
13. ANEHCHETER
a. Frame secure
b. Pickup and leads checked
c. Bearings and free rotation
d. Cups and shaft secure
e. Operational check
14. BOARD AND LITES
a. Board and lites secure
b. Elect, connections
c.
d. _____
e.
15. COMPASS
a. Secure
b. Leakage
c. Bubbles
d. No binding
e. Disc alignment
f. Lite
g. Lite pipes
h. Diaphram
16. READ PULSE
a. Secure
b. Elect, connections
c. Lite
d. Lite pipes
17. IDENTIFICATION
a. Ser. no. on outside
b. Type of cam (lobes)
18. "0" RINGS
a. Seat clean
b. Properly seated
19. OPERKTTOHAL CHECK
a. Without film
b. With film
20. POWER-SWITCH POSITION
a. Continuous
b. Off
c. Interval
21. DESSTCHNT
a. Installed
22. EXTMIOR BOLTS
a. Torqued
23. DATE
a. Closed
73
-------
SPROCKET
TAKE UP SPOOL
SUPPLY SPOOL
GUIDE ROLLERS
EMULSION SIDE
SCALE
I 2IN.
5CM.
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
CAMERA LOADING DIAGRAM
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POL LUTION CONTROL ADMIN
Great Lukes Region Chicago,Illinois
FIGURE 4-17
-------
clarity of reproduction. Due to this, the print and the original were
mirror images of each other as viewed from the sane, such as the emul-
sion, side. For reference it should be noted here that the original
film, when viewed from the emulsion side with the beginning (head) end
to the right, concluding (tail) end to the left, had the continuous
channel on top.
After developing the original and making the positive print,
both were edge-numbered serially using a common starting point for com-
plete coincidence. The numbering proceeded from the head of the first
30 m consecutively increasing throughout those spliced together to the
tail of the last. The four digit number (0000 to 9999) was preceded by
one of the following letters according to the user's choice: A, B, C,
D, £, F, G, H, J.
The original film was then broken down, rewound head out on the
original spools and returned to the original boxes.
The prints were broken down and rewound head out on individual
30 m reels and boxes. These boxes are marked according to the perfora-
tions made in the original film and the user's number as it appeared on
the original yellow box. The prints were then returned according to
Instructions.
Following the processing the exposed film was returned to the
reading agency and the length of record determined as well as other
information pertaining to the record.
The clear-edged prints were visually viewed for completeness.
The rotor pulses, timing marks, and direction channels were scanned for
normality (or what was interpreted as normal behavior). The processed
16-mm films were then ready for conversion to magnetic tape.
The film was converted on a Digital Film Recording instrument
onto a reel of standard magnetic tape. The tape was recorded at 200
characters per iach into aa IBM 7 channel binary format. Each 50-second
record was read by a flying spot scanner at less than 1-second inter-
vals. The format for reading on magnetic tape varied according to the
film reading agency used. One such format was as follows:
Format for Film Beading
a. 120-eharacter Hollerith identification Including lake name and
speed units.
75
-------
b. 120 characters of numeric information
1 15 Film number (5 digits, one zero omitted) 5
MX
2 13 Station Kumber 12
3X
3 13 Depth (meters) 18
3X
k 12 Time between observations 20 or 30 23
3X
5 Ik Starting foot mark 30
6 12 +9procket holes 33
2X
7 12 Month 01-12 37
8 12 Day 01 - 31 39
9 12 Year (last 2 digits) 41
10 12 Hours 43
11 12 Minutes 45
3X
12 14 Boding foot mark 52
IX
13 12 +Sprocket holes 55
2X
Ik 12 Month 59
15 12 Day 6l
16 12 Year (last 2 digits) 63
17 12 Hours 65
18 12 Minutes 67
IX
19 14 KuBber of read pulses 72
IX
Tape Data Format
11 type
13 conpass
12 such readings
13 vane
13 speed
Current meter speed was recorded In cm/sec. Current direction
was defined on strip charts and computed magnetic tapes as the direc-
tion toward which the current was flowing.
Wind speed was recorded in miles per hour. Wind direction was
defined on computed magnetic tapes as the direction toward which the
76
-------
wind was bloving. In processing data l80° was added to computed direc-
tion to present data in the standard manner, i.e., direction from which
the wind was coming.
A series of records, with Identifying headings, were then sent
for computer processing.
77
-------
CHAPTER 5
CURRENT METER FIIM PROCESSING
Specifications
The films for both the current and wind meters are read by a
film reading agency using a special film scanner in connection with a
computer. Both the compass and vane are read and reported in the orig-
inal Gray Binary Code. Readings of the vane and compass are taken, the
number of readings varying with the company.
Rotor speeds are read and interpreted by the computer. If a
reading is to be meaningful, at least tvo rotor pulses have to be
interpreted by the film reader. The instrument has tvo speed channels,
R-l for every rotor rotation and a R-10 for every 10 rotations. At
times the R-l rotor is Jammed because the signals are too rapid and
cannot be separated in the Interval. This is then interpreted by the
film reader as a single pulse since the light merely goes off-on-off.
The R-10 rotor is interpreted initially. If it is meaningful it
is reported on magnetic tape. If it is not, then the R-l rotor is
interpreted. If meaningful information is available from the R-l, it
is reported as a rotor speed; otherwise, it is reported as too slow or
too fast to be read. If the read pulse cannot be found at all, this is
reported, and in this case physical time is kept track of by using the
film sprocket holes as a guide.
The meter information is noted on magnetic tape in the following
specification format which has been adopted by the Project, the com-
puter processor, and the film reading agencies. One method is as
follows:
Each record consists of 1,080 characters.
The first record is the identification record. The first
60 characters are in IBM tape BCD code (20 = blank). These characters
are supplied by the reading company. They include the lake name, speed
unit, and date processed. The first character has a one as the first
bit. The next 60 characters are 20 18-bit binary integers. The first
19 are supplied by the computer processor. The 20th is supplied by the
reading company as the constant needed to change the speeds into proper
units (miles/hr for wind records, or cm/sec for current records).
Succeeding records are broken up into words of 36 bits.
Each word consists of:
78
-------
4-7-7-2-7-9 bits respectively:
k - diagnostic information
7 - vane 1
7 - compass
2 - type of data word
0: readable data word
1: no speed
2: nonreadable data
3: end of film
Note: If the word type is unity, the indicated speed will be given as
0 or 511 (the upper speed limit), depending on whether it cannot be
read because it is too low or too high, respectively.
Film is started and ended as specified in the identification
record. An end-of-file mark separates each film.
Each magnetic tape is checked by the computer. The printout
includes the identification record, the total number of read pulses,
and the first three and last three observations in each film.
Bit 1 (highest order) of the diagnostic word (first k bits) is
zero or one, depending upon whether the speed is computed from the R-l
or R-10 rotor, respectively. The R-10 rotor speed should be multiplied
by 2. This allows better resolutions for speeds.
The identification sequence as supplied by the computer service
consists of the following 19 numbers:
l) Film number (second digit denotes lake — 20 = Lake Michigan,
21 = Lake Erie, 22 = Lake Ontario, 23 = Lake Huron, 2k = Lake
Superior). All film codes are in the 200,000 series.
2) Station number — corresponds to physical location in lake.
3) Depth in meters. A zero depth is not a current meter record
but is a wind recorder.
79
-------
4) Time in minutes between observations — either 20 or 30
minutes.
5) Footmark of starting point. (Footmarks are marks on original
film at intervals of 1 foot.)
6) Film sprocket holes.
7) Month — an integer, 1-12.
8) Day — an integer, 1-31.
9) Year — last two digits of the year
10) Hours — based on S^tOO hours.
11) Minutes — an integer, 0-60.
12) Footmark of ending point.
13) Film sprocket holes.
Month.
Starting time for
>meaningful data.
15) Day.
16) Year. ^ Ending time for
meaningful data.
17) Hours.
18) Minutes.
19) Total number of read pulses (time slices).
Initial Processing
A copy of the field record sheet giving the salient film identi-
fications such as station number, starting time, ending time, depth,
time between observations, etc., is sent from the Project to computer
processor and to the film reading agency. After film processing, the
reading agency inspects the original film and determines the starting
and ending points of good data since there may be a lag of several
hours between the time the instrument is set in place and the time it
starts functioning properly. The starting time is reported as a combi-
nation of footmarks (which are numbered on the film at each foot) and
film sprocket holes.
80
-------
The 19 elements of the Identification vector are punched on
paper tape for input to the film scanner.
A simple consistency check is now performed on these identifica-
tions. The total number of recordings is:
a) given from inspection;
b) computable time from the given starting and ending date;
c) computable from the starting and ending footmark and film
sprocket holes.
Any discrepancy among these numbers is investigated and incon-
sistencies are reconciled. At this point the corrected paper tape is
sent on to film scanner.
The magnetic tape output is sent by the reading company to the
computer processor. It is then copied on a master tape by a special
control data 92k "MUPDATE" program.
The data input tape is composed of an arbitrary number of films
followed by a double end of file. Each file contains an arbitrary
number of records in low density. Each record contains 1,080 characters
of odd parity. The first 120 characters of the first record of each
file contain the file identification (i.e., IX, 9A6, A5, 20R3). The
first character is to be skipped. The second character to the 60th
inclusive is in binary coded decimal (still in odd parity). Each of
the next 20, three-character symbols, is to be interpreted as an 18-bit
binary integer.
The output tape is a master tape which contains an arbitrary
number of records of previous type (except that density is now high,
500 PSI) followed by a double end of file. Column one of the data card
is zero or one, depending on whether or not the master tape is blank.
The remaining columns are a job label.
Required processing: If the output tape is not blank, files are
skipped until a double end of file is reached. A count of the number
of files is found and noted. When new film is copied onto the master
tape the second end of file is eliminated by being written over.
As each file is copied, the ordinal number of the file is print-
ed followed by the first 120 characters of the first record in required
format, and the number of records in that file. A double end of file
is written at the end of processing. The copying program thus allows
the handling of a single master tape instead of its many component
81
-------
tapes. Furthermore, it allows a measure of insurance. In case of tape
failure, there remains the facility to write another master tape.
The computer is now ready for the processing of the master tape.
This data processing consists of three passes. Each pass (except the
first) has as its input the output tape of the preceding pass.
First Pass Program
The first pass program consists of the formation of a compact
binary input tape which the computer can read quickly and efficiently.
This makes it unnecessary to decode the special input formats more than
once.
This initial tape generation program is buffered, i.e., while
the computer is reading in one record, a previous one is being process-
ed into its individual components (compass, vanes, speed, etc.). Vane
readings are averaged into a single vane. By average, we do not mean
arithmetic average, since this mean at times yields poor results (i.e.,
the arithmetic average of 0° and 360° is 180°). A short algorithm
insures that vane readings are less than 180° apart, by Judiciously
adding 960° to the smaller where necessary. Only then are the angles
averaged and reduced by 360° where necessary.
Figure 5-1
82
-------
Both the compass and vane are given as a clockwise deflection
from the vertical (Figure 5-l), the convention used for the vertical y
axis as the major axis, and the horizontal x axis as the minor axis.
The angles, although clockwise, are still to be considered positive
angles, since they are formed from the major axis to the minor axis,
Figure 5-2. In fact, if the above diagram were rotated 90°> its mirror
image would take on the more familiar form. The basis direction is
defined to be compass + vane + 180° reduced by 360° (or 720°) if neces-
sary, so that the resulting angle is between zero and 360°. Thus, the
direction is given in its meteorological mode, i.e., the direction from
which the wind (or current) is coming. The speed is modified so that
it is in units of miles/hr for wind recorders and cm/sec for current
y = major
axis
Figure 5-2
meters. If the speed is below the instrument range of 0.8 cm/sec it is
recorded as zero. If above the instrument range, over 100 cm/sec, it is
recorded as -2. If the compass and vane cannot be read (because a read
pulse is missing), the speed cannot be read either. In this case both
speed and angle are recorded as -1.
The speed and angle for every time slice are preserved on binary
tape. In addition, the complete identification, the total number of
read pulses (time slices) and the maximum speed actually attained are
retained. This maximum speed is needed for future graphing routines so
that the scales can be immediately determined. The total number of read
pulses tells how to read the remainder of the data.
83
-------
The original magnetic tape should have on it the correct vector
identification arising from the paper tape prepared at New York Univer-
sity. However, under the exigencies of production processing, communi-
cations at tines break down. At tines the paper tapes are either
incomplete or totally missing. In view of the anomalous situation, the
first pass program has been modified to accept the identification
sequence from cards to override the false identification on tape. The
calculated risk in this procedure is readily acknowledged. A single
card out of order can spoil an entire tape and void all future process-
ing based on it. To insure against this eventuality, a special reading
program has been written to scan the binary tape and print out al.1
identifications.
Second Pass Programs
Second pass programs use the previously formed binary tape as
input. At present five such programs are being run.
l) Six-hour averages
2) Histograms
3) Envelopes
4) Spectral programs
5) Filters
Six-hour averages: Six-hour averages are computed at 0, 6, 12,
and 18 hours. These times were selected so that comparison could be
made with official weather maps. Pour parameters centered around the
midpoint of each 6-hour interval are computed. These are:
l) The number of meaningful data points in the 6-hour interval.
This may be zero.
2) Speed average.
3) Angle average. While speeds may be averaged, it is obviously
impossible to average angles. Therefore, both speeds and
angles are defined by means of horizontal and vertical com-
ponents and each set of components is averaged. The average
speed and angle are defined to be the vector resultant of
their respective average x and y components.
k) Standard deviation of speeds in order to show a measure of
dispersion.
-------
Two days of data including station depth and date are punched on
cards as a permanent record. Thus on one card we have data for eight
different time slices. Each slice contains four observations. Since a
card is limited to 80 columns, ve are limited to two columns per obser-
vation. Both the total number of observations and the speeds obey this
limitation. The angle is given to the nearest 10° so that the three-
digit number can be fitted in. Thus an angle of 2k signifies an angle
between 235° and
The standard deviation of speeds is more troublesome since it
cannot be reduced to two digits. However, it can be shown that in most
cases the standard deviation is less than the mean. Hence the standard
deviation is normalized by dividing it by the mean speed. This number,
which is unit less, is called the coefficient of variation. The printed
value is 100 multiplied by this coefficient of variation. The resulting
integer is not permitted to become greater than 99 to insure against
possible (though unlikely) overflow. In symbols, the number printed is
the nuliritipiiq of
00 100 x standard deviation of speed
' average speed
This unities s number describes the dispersion: the smaller the integer,
the smaller the dispersion. Standard deviations can be readily noted by
multiplying the given number by the average speed.
The resulting data are punched on cards and printed. Sample
output is shown in Table 5-1.
Histograms ; Two-dimensional distribution of speed versus angle
is given for each month of data. The distribution of all data of a
stated station at a stated depth for all months is also given. Each
such distribution is given by 36 angles (each of 10°) and of 18 speeds
(for current meters 3 cm/sec; for wind recorders 5 miles/hr) • Total
flow is given for each angle and also by total flow which is defined
as £31%, where Si is the speed in the i column (of a given row) and
Ni is the number of observations there.
The marginal distributions of both speeds and angles are com-
puted and printed. Each of these, of course, sums up the total number
of observations. Note that the number may be smaller than the total
number of time slices, as observations may be missing at some of these
times. A sample output is given in Table 5-2.
Envelopes : A visual display of the variations of both speeds
and angles in a 2-hour period was desired. A sample result is given in
85
-------
CABLE 5-1
FORMAT SEC-HOUR AVERAGES
SIX HOURLY AYERAQES-3TA. 13 . DEPTH 10 - TIME UCTERVAL 20 MIR.
DATE
4/11/64
V13/64
4/15/64
4/17/64
4/19/64
4/21/64
4/23/64
4/25/64
4/27/64
4/29/64
5/1/64
5/3/64
5/5/64
5/7/61*
5/9/64
5/llM
5/13/64
5/15/64
5/17/64
5/19M
5/21M
5/23/64
•
18
18
18
18
18
18
17
18
13
16
18
18
18
15
6
18
18
3
2
8
12
12
9
9
18
18
17
18
17
18
18
18
18
k
17
18
15
18
18
18
18
18
18
16
D
11
31
25
27
13
12
44
13
28
36
Ik
18
19
26
74
16
15
16
75
99
1*6
51
65
66
36
38
33
48
36
18
15
23
16
46
31
9
29
31
13
15
20
16
19
H6
AM
1
10
33
0
0
k
6
5
2
3*
35
6
10
9
k
36
36
6
5
29
27
7
2
36
29
33
33
3
1
k
3
6
7
32
29
36
9
k
13
0
0
k
2
32
0
SP
11
17
12
6
Ik
13
17
13
k
15
l*
7
10
6
5
9
6
2
9
6
5
3
if
5
5
6
7
14
k
5
4
15
11
5
6
5
3
5
12
5
5
5
6
k
M
18
18
18
18
17
18
16
18
17
17
16
18
18
15
12
18
15
5
5
8
8
8
17
6
17
5
8
18
18
17
18
18
18
9
17
10
k
18
18
k
18
15
18
16
D
18
48
24
23
25
11
41
15
28
18
26
25
19
80
59
35
28
99
74
53
95
26
27
46
21
52
71
17
20
14
8
21
23
97
21
20
42
32
13
34
7
72
27
31
AH
2
35
33
36
1
4
4
4
35
32
35
7
10
5
32
3
4
7
7
32
1
7
4
4
31
4
34
3
2
4
4
5
7
32
33
4
30
7
5
0
0
5
36
2
6
SP
10
17
16
8
11
13
15
11
3
13
10
6
8
4
6
6
5
5
8
3
5
2
3
8
12
8
6
14
5
4
4
16
7
4
5
3
11
3
11
3
5
5
9
4
•
18
18
18
18
18
18
18
18
13
18
18
17
18
12
10
15
16
6
10
5
5
9
11
7
18
13
18
18
18
18
18
18
18
5
11
5
5
18
18
13
18
18
18
4
D
25
31
31
13
18
8
25
23
41
12
18
31
14
42
28
24
33
27
44
67
73
57
63
21
18
54
36
38
25
20
20
15
56
26
30
50
94
63
25
29
17
25
22
41
AM
5
5
1
0
3
6
4
4
35
30
2
9
11
4
32
3
4
9
6
31
7
7
8
26
31
32
33
1
2
3
4
4
7
32
2
34
1
7
6
33
1
0
5
16
12
SP
9
18
10
8
6
13
17
7
5
12
6
7
9
4
3
3
3
2
3
8
8
4
4
4
13
6
14
11
4
5
3
14
5
2
4
3
5
11
8
4
6
7
8
8
M
18
17
18
18
18
18
17
18
15
18
18
16
18
16
15
14
16
5
11
7
11
2
1
18
18
18
17
18
18
18
18
17
7
17
10
15
8
18
17
18
18
17
9
17
D
24
10
13
15
10
26
14
31
47
16
15
25
18
99
41
27
22
97
86
64
26
21
0
32
25
21
33
23
11
22
49
12
84
28
57
17
83
24
22
14
20
23
95
38
AM
8
5
36
36
2
4
5
2
2
32
3
9
10
6
35
35
5
2
2
5
10
4
9
28
31
32
3
2
2
3
5
2
32
33
32
3
2
8
36
36
3
3
13
29
18
SP
15
13
7
13
12
18
14
4
6
12
6
9
8
6
5
4
3
5
4
5
3
2
3
7
9
11
18
5
5
5
9
14
8
4
5
3
6
15
5
5
4
7
8
4
86
-------
TABLE 5-2
SAMPLE FORMAT OF HISTOGRAM
TWO DIMENSIONAL SPEED-ANGLE DISTRIBUTION BY MONTH IN LAKE ERIE
STATION 5. DEPTH 10. TIME INTERVAL 20. AUG. 196k
SPEED ^ 123456789
1.5 ^.5 7.5 10.5 13-5 16.5 19-5 22.5 25-5 m/vnAT
ANGLE TOTAL FLOW
-515 142 10 000 00 17 139-5
52 15 837630000 27 181.5
15 3 25 3 22 10 13 3 0 0 0 2 53 406.5
25 4 35 4 17 4 6 8 i<- 0 0 0 43 3^9-5
35 5 ^5 7 21 6 18 2 0 0 0 0 54 366.0
45 6 55 9 26 43 37 12 0 0 0 0 127 1,003.
55 7 65 10 46 47 43 17 0 0 0 0 163 1,255-
65 8 75 12 36 62 50 13 1 0 0 0 174 1,362.
75 9 85 13 47 60 50 44 4 5 0 0 223 1,963-
85 10 95 25 52 50 22 22 4 0 0 0 175 1,240.
95 11 105 26 51 57 30 23 0 0 0 0 187 1,321-
105 12 115 24 42 46 28 1 3 3 2 0 149 1,030.
115 13 125 15 25 27 21 12 2 3 0 0 105 811.5
125 14 135 16 21 12 31 21 7 3 0 0 111 991.5
135 15 145 9 24 15 14 16 4 0 0 0 82 663.0
145 16 155 7 18 7 13 7 1 0 0 0 53 391-5
155 17 165 6 19 14 6 5 0 0 0 0 50 330.0
165 18 175 4 3 6 10 8 1 0 2 0 34 339.0
175 19 185 630300000 12 54.0
185 20 195 131200000 7 43.5
195 21 205 051500000 11 82.5
205 22 215 782230000 22 123.0
215 23 225 513820000 19 145.5
225 24 235 233300000 11 70.5
235 25 245 236521000 19 157.5
245 26 255 271300000 13 73-5
255 27 265 131100000 6 33.0
265 28 275 330220000 10 56.0
275 29 285 11 9 6 3 2 0 0 0 0 31 160.5
285 30 295 523210000 13 73.5
295 31 305 17 10 3 3 3 0 0 0 0 36 165.0
305 32 315 986700000 30 168.0
315 33 325 10 10 5 0 1 0 1 0 0 27 130.5
325 34 335 763230000 21 121.5
335 35 345 662300000 17 82.5
345 36 355 262510000 16 111.0
87
-------
Figure 5-3. Note that the number in the extreme left IB the ordinal
day of the year representing the data. The speed scale can be formed
immediately as the maximum speed is known. Instrument failure was
indicated by a random array of speeds.
Both the maxima and the minimum angle and speed in a 2-hour
interval were graphed side by side. If no real data points existed in
the 2-hour interval, no points were graphed.
At times a series of rotations showed up with an inertia! period
of about 17 hours, very close to the local inertial period vhich varies
with latitude and is 16.96 hours at ^5°N.
Spectral Analysis
Spectral analysis is a technique for investigating the variance
of a time series. It permits finding the individual components of the
variance. Any marked peak in the spectrum graph is Interpreted as a
vital frequency. The total area under the graph is exactly equal to the
variance. Thus, spectral analysis, unlike harmonic analysis, allows
one to determine the sizes of the important frequencies without pre-
knowledge of their locations.
The key number in spectral computations is an integer called the
lag. The greater the lag, the more resolution one gets in studying the
spectrum. The Hyquist Frequency is defined as 1/2/\ T where /^T is the
time between observations. The last element of the spectrum always
corresponds to this Nyquist Frequency. A lag of M will break up this
basic frequency into M parts.
Thus to determine long periods, i.e., small frequencies, we need
large lags. Often this is impractical because the shortness of the
series does not allow long lags to be used; and, as a rule of thumb,
there is nothing to be gained by using lags much longer than one-tenth
of the length of the series.
One way around this difficulty is to filter the series with a
low-pass filter (with consequent loss of high frequencies, although
this is usually not serious) and then to decrease the Nyquist Frequency
by taking, say, every fifth data point. A smaller lag, therefore, can
be used to give information on the required low frequencies, as illus-
trated by the following example.
The current meter and wind recorder record every 20 or 30 min-
utes. The Nyquist Frequencies for these two sampling intervals are
respectively, 1.5 and 1.0 cycles per hour (cph). If we apply a digital
filter to the data which does not pass frequencies above 0.25 cycle per
-------
- UJ
z
- oo
< 2
fe £
UJ I-
0 0
ON003S U3d 'HO-a33dS
S33«03a-NOI133aia
O c
cc « =
O _J o
^ o ?
X Z
*~ o
IJ- K-
tr -1
UJ •;
FIGURE 5-3
-------
hour, then 0.25 cph is an "effective" Nyquist Frequency. This means
that we can subsample the 30-minute records every kth data point (every
2hr) and subsample the 20-minute records every 6th data point (every
2hr). Subsampling every 2 hours yields a Nyquist Frequency of 0.25 cph«
Thus, the number of filtered data points which we must lag with each
other has been reduced four- or sixfold. Since the frequency resolu-
tion of a spectral analysis is given by fN/m (where m = number of lags),
it can be seen that, if a specific resolution is desired, the effect of
reducing fjj is to enable one to reduce m also. Thus, filtering and
subsampling the records, has enabled us to obtain good spectral resolu-
tion in the frequency range 0.0 - 0.25 cph using fewer lags and data
points than if we had not performed these operations.
Formulas
Suppose the series is x(t) for t = 1, K and M is the maximum lag.
The following sequence of operations computes the power spectrum S(i)
f or i = 1 to M.
a) The mean of the series is removed, i.e., x(t) is replaced by
1=1
b) The correlation function Q(i) is computed for i = 0 to M,
where
N-l
x(t) . x(t +i)/ (H - i)
t=l
Q(0) is the variance of the series.
c) Let F(i) be the Fourier cosine of Q(i) for i = 0 ... M, i.e.,
M
P=0
where Q(0) and Q(M) are replaced by half their values.
90
-------
d) The spectrum function is finally computed by smoothing the
above cosine transform by the 3-point Hamming formula:
S(i) = .25 F1+1 + .5 FI + .25 F±.!
vhere
P0 = F2 and FM + i w FM .. !
are defined to give meaning to S(0) and s(M+l).
e) The frequency in cycles per unit tine is computed in terms
of the lag number as follows:
FRE(i) =
2M . delt
for i = 0 to M where delt is the time between observations. If the time
is measured in hours, the frequency will be given in units of
cycles/hour, etc. The period is the reciprocal of frequency.
The power spectrum at a particular frequency is the amount of
power or variance in the frequency band centered around the frequency
in question. The width of this frequency is given by
2N delt
Cross Spectrum
A cross spectrum is a generalization of spectrum analysis as
applied to two series. It is actually made up of two numbers for every
frequency. One is called the co-spectrum while the other is the quad-
rature spectrum.
If the cross spectrum of a series with itself is taken, the co-
spectrum turns out to be the spectrum of the series while the
quadrature spectrum is identically zero.
91
-------
The formulas are quite analogous. Again we remove the average
from both sides. We then lag both series separately.
y(t + i)
H - i
Q(t) = £x(t + i) y(t)
» - i
We now define the correlation function to be half the sum and half the
difference of P and Q, i.e.,
Q2(i) -
We now find the Fourier cosine transform of Q^ and the Fourier sine
transform of Q2. (The formula for the latter is identical with that of
cosine transform of replacing cosine with sine.) After respective
three-point smoothings as before, the resulting functions are defined
as the co-spectrum (Co) and quadrature (quad).
Coherence, C(i), is the measure of the relation between both
series at a particular frequency.
C02(i) + quad2(i)
SPl(i)SP2(i)
where SPl(i) and SP2(i) are the respective spectra of the individual
series. It can be shown that coherence must be a number between zero
and one. A coherence close to zero shows very little correlation
between series. A coherence close to one means that series are highly
correlated at that frequency.
Graphing
Digital graphs are especially useful. For their description,see
Mehr
92
-------
An analog plotter was extensively used to replace the digital
envelope.
The resulting graph is both more accurate and esthetically sat-
isfying. However, its usefulness is marred by the long lag time between
the digital program and its resulting graph for long runs.
Third Pass Programs
Third pass programs employ 6-hour average cards as input.
Trajectory programs: The 6-hour speed and angle data were used
to plot the path of a mythical point being moved at these average
speeds. Two days of data were given a single diagram. Two diagrams
made up a page. The starting point was at the center of the diagram.
Succeeding points were designated by succeeding letters of the alpha-
bet. If a letter was missing, it had obviously been written over by a
succeeding letter. (See Figure 5-^.) Major trends over a period of
several days were thus readily observable.
Maps: To study the 6-hour data intelligently, it was necessary
to study data from all stations at a given depth at a given time. The
computer printed out a map of Lake Michigan for every 6-hour period for
every depth having data in a key 3-month period (October-December
1963). Each station was marked by an asterisk in its correct geograph-
ical position. Dots represented the boundary of the Lake. If data were
present at a particular station, the four parameters described above
(for 6-hour averages) were printed as four integers around the station.
10 15
*
These maps allowed us to assimilate many terms of data simulta-
neously, as illustrated by Figure 5-5«
Temperature Data
Hourly temperature data have been obtained from various stations
at several depths. Computations are used to determine the basic fre-
quencies by means of:
93
-------
« *
(T <
LJ
Ld —
tt tt
o
CC
O
L.
O
o:
Q.
cr
»~
^
to
ID
O)
CO
§
o.
LJ
Q
2
to
ID
cn
Q <
5-4
-------
TIME = 12
DATE =• 2/ 9/63
o
O G
O 18 12
O
19 10
16 12
00
• ° 29 23 O O
o o.
18 20 18 16
•O O 18 17 18 13
19 II 24 20 O O O ,
8 21 3 23
O .
DEPTH = 15
6 HOU R AVE.
No. of Data
Points
Angle
Average
18 12
o
29 29
Coefficient
of Variation
(Speed)
Speed
Average
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
FORMAT OF MAPPING
. PROGRAM
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes R«gion Chicugo,Illinois
95
FIGURE 5-5
-------
a) Spectral analysis.
b) Harmonic analysis.
It is known that any finite sequence can be written as a finite Fourier
Series. It is too costly to compute all frequencies. However, a band
of five harmonics was taken around every suspected major frequency.
Furthermore, the powers at these frequencies were computed so that the
percentage of the variance of the original series, that was accounted
for at each of these frequencies, could be found. Finally, the percent-
age of the variance that was unaccounted for by any of the frequencies
was noted.
c) Regression analysis.
A linear least squares model was computed based on particular sus-
pected frequencies. The standard error and the coefficient of correla-
tion were also computed. The former is the square root of the average
of the square of the deviations, while the latter is a measure of the
percentage of the variance that is accounted for by this particular
model.
Drogue Surveys
Drogue surveys of lake currents near Chicago were undertaken by
the GLIRB Project. The mechanical details are reported in Chapter 8.
The original data consisted of aerial photographs on color film. Every
drogue was identified by shape and color. Dr. Akira Okubo of Johns
Hopkins University proposed a series of computations on the data matrix
consisting of the x-y positions of each of the drogues at each of the
time slices. These computations consisted of the calculation of means
and standard deviations of x values and y values, in both time and
space. For each time slice, the center of gravity of the drogues was
found. The collection of distances between any two points was studied.
Histograms were formed, and moments computed. The results of these com-
putations and their interpretation have been reported by Dr. Okubo.
Most of the effort expended was comprised of obtaining the data
needed for the Okubo computations from the aerial photographs. Essenti-
ally the problem consisted of finding local coordinates for every time
slice, i.e., a common coordinate system had to be constructed for all
frames of a particular time slice. Global coordinates for every time
slice also had to be found, i.e., a common coordinate system had to be
constructed for all time slices.
It was assumed that the plane was flying level as the photographs
were taken. This implied that the equations of transformation from the
UV local plane to the xy global plane was:
96
-------
x = A(l)U + A(2)V -f A(3)
y = A(2)U -
vhere A(l) = f cos 0, (2) =/* sin 6 in terms of the magnification fac-
tor, p , the rotation angle 0, and the translation of the origin of UV
coordinate system to the point A(3), A(4) in the xy plane. Coordinates
of the two fixed points needed to be given in both coordinate systems
to determine the transformation constants, since this yielded four
equations in the four unknowns A(l), A(2), A(3), and
It is believed that more accurate results would have been
obtained without the assumption that the plane was level. However, we
could not proceed without it, since at times only two common points
were given. As a matter of fact, at times, even two fixed points could
not be found which were common to two successive frames. In these
cases, a slow moving drogue had to be considered as a temporary fixed
point. Since this assumption was not abused, it caused no difficulty,
i.e., it was used only between frames of the same time slice and not
between time slices. Furthermore, if the same drogue was used as a
fixed point at two separate times, it was given a different name to
avoid confusion.
At times as many as five fixed points could be found common to
the successive frames. In these cases the equations are over-
determined. It was decided to use least squares. The following quan-
tity was to be minimized:
A(2)V± + A(3) -
A(2)Ui -
Differentiating
following equations:
with respect to the unknowns A(i) yielded the
\
e 0 b c
0 e c -b
b c d e
c -b 0 d
A(2)
A(3)
\
g
\
97
-------
where :
wiVi
•y -
where v represents the weight of a particular observation. Thus a real
fixed point can be assigned a higher weighting factor than a temporary
fixed point. Varying weights are not used in the first run.
It can easily be verified that the required solution to the
matrix equation is
- (fd - bsx - csy)/Q
A(2) = (gd - csx + bsy)/Q
A(3) - (-fb - eg + esx)/Q
= (-fc + bg + esy)/Q
2 2
and where Q = ed - b c
The above relations are imbedded in subroutine TRANS (NAX, U, V, X, Y,
A) which determines A(i), i = l...k from MAX sets of xy and UV coordi-
nates .
The first program is called COFDC, the reduction of all fixed
points to a common coordinate system. At the start, we were given
global coordinates of only two points. To find the third point, we were
given local coordinates of the two fixed points and the third point.
We now computed the transformation and transformed the third point to
its global coordinates. These coordinates were punched out on cards for
future use and were added to the memory bank of fixed points.
98
-------
The computation of the fourth global coordinate depended on two
or three (in this case) fixed points. The sane subroutine was again
utilized. At each stage, the fixed points were recomputed. No dis-
crepancy could be found.
In general, the computation of the Nth fixed point depended on
N-l coanon fixed points to the global and the local coordinate system.
(In practice, no acre than six ccsmran points were found.) The output
of this program was the deck of fixed points in global coordinates.
The actual data were now ready to be processed and the global
coordinates of all data points in each time slice were computed as
required by the Okubo program.
The first card was a time slice identification card telling the
number of frames in the particular time slice and the corresponding
frame identifications. A frame identification card was processed for
each such frame. It consisted of:
(a) The number of drogues in the frame.
(b) The number of fixed points in the frame.
(c) Identification numbers for the fixed points of both x and y
local coordinates for each such fixed point in the frame.
Since the number in (b) was assumed no greater than five, it was
possible to get all the information in (a), (b), and (c) on one card in
addition to a job and time slice Identification in order to insure that
the cards were in proper order.
The global coordinates of these fixed points (which were read
into the computer memory) were now called on and the equation of trans-
formation from the frame to the global coordinates was found. The local
coordinates could now be read. The drogue data were read for the frame
which had drogue identification, and its corresponding x and y coordi-
nates. It was known from the frame identification how many drogues were
expected. Then each drogue was transformed to its global coordinate.
A check was made to find out if a global determination of this drogue
in this particular time slice had been made previously. If so, the two
determinations were averaged.
After completing the particular frame, another frame identifica-
tion card was read and continued as before. Since the expected number
of frames in a particular time slice was known, the end of a time slice
was known. The list of all drogues was saved for reference in that time
slice with their corresponding global coordinates.
99
-------
The computer distinguishes between real data and missing data by
denoting the latter by zero. In the printing program, missing data were
denoted by x = 0 and y = o. The only point at which a human might be
confused was the origin, which might conceivably be (0, 0) or, most
likely, missing. However, the computer cannot be confused since care
was taken to add some noise, about 10~25 at each meaningful point.
Therefore, the computer distinguished between a real zero and a ficti-
tious zero to denote a missing point. The fictitious zero was actually
zero while the real zero was simply very close to zero.
Each succeeding time slice was now processed in a similar manner
until all time slices were processed. The resulting tape was used as
input for further processing of the Okubo program.
100
-------
CHAPTER 6
CURRENT STUDIES
Introduction
Preceding sections of this report have described the methods,
techniques, testing, and other activities connected vith the study of
currents on Lake Michigan. This Chapter details the results of the
study.
Before the data from unattended current meters and anemometers
can be published or released for further usage, the first step must be
the assessment of reliability (timing, direction, and speed) of the
data. Assuring correct timing is one of the most difficult problems.
The clocks may run slow (or fast) by a fraction of a second in an hour
and thus be inaccurate for an hour or more at the end of a 6-month
record. Using techniques of 2-hour envelopes (showing the maximum and
minimum readings in a 2-hour period) and 6-hour averages does not elim-
inate the error but such errors are insignificant over such a short
period. In reporting monthly net flows and histograms, the probable
error is less than 0.5 percent.
It was noted early in dealing with the 6-hour averages that the
current speeds responded to a wind input. This response was found in
the currents from top to bottom regardless of current direction. All
speed records were analyzed to correct any obvious errors which may
have arisen from automatic scanning or instrument deficiencies.
By comparing, for each instrument, the length of the records
with the known times at which the instrument was set in and recovered
from the Lake, it is possible to arrange the records on a quality scale
as shown in Table 6-1. Over half of the records show differences
between recorded time and the known time of less than kO minutes, and
the maximum error for the remaining records, when corrected, was less
than 2^- hours.
TABLE 6-1
TIMING ACCURACY OF CLOCKS MAXIMUM HOURLY
QUALITY RANGE/MOKTH CORRECTED
A 0 to 1
B 1 to 2.5
C 2.5 to 5
D 5 to 10
E Over 10
101
-------
Ranges B, C, and D permit monthly evaluation but are not usable
for accurate 6-hour averages unless corrected. Range E, unless cor-
rected, is considered poor quality and normally discarded. On an
average, the maximum time error permitted is limited to 1 percent. The
quality of the time values is usually based on the percent error in the
total record.
Direction errors are not difficult to detect unless the meter is
off by an unknown number of degrees. The instruments are checked prior
to setting and after retrieval to reduce this error to zero. Under
certain circumstances the direction is meaningless, due to turbulence
or other factors; and a record of this type is discarded. A certain
objectivity enters into the search for errors in direction. Visual
scanning of millions of data points reveals certain constantly repeated
patterns. These patterns form the basis for ascertaining good versus
bad data. Water movements, especially direction patterns do not repeat
specific degrees over any long time period. Thus, a record which shows
repetition of the same degrees for more than k hours is immediately
suspect. Figure 6-1 shows a histogram of data which produced false
modes due to blurring of the light pipes. Blurring is due to the rapid
fluctuation of the vane and the light pipes appear (when scanning by
electronic methods) as permanently in the "on" position. This blurring
appears at certain stations and not others. All films were visually
inspected to remove films which had serious blurring problems. Quality
values based on the percent of blurring indicate the quality of the
direction data.
Speed values are scanned similar to directions. Values below 1
centimeter per second (cm/sec) are discarded. Long-term high or low
values are questioned and checked against similar stations nearby. On
many occasions high values occur and appear to be due to reading prob-
lems in the automatic scanning of the records. New reading techniques
have nearly eliminated these errors. Quality values, based on the per-
cent of spurious high values, indicate the reliability of the speed
data.
Data Compilation
After the data had been compiled into the several forms used for
review purposes by computer printouts, the master lists for identifica-
tion were prepared. Current data were identified in master lists by
film number (200 000 series, see Net Plows) and by station.
The original station number in Lake Michigan included 6l sta-
tions of which 38 were actually used in the study. One station was
added (number 62) near the tower erected for the U. S. Weather Bureau
at Muskegon, Michigan. The locations are shown on Figure 6-2 and are
Identified by longitude and latitude in Table 6-2.
102
-------
i
o
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o
o
s -
5 6
O r
< _
o 5
tr o
o
o
uJ o>
t- •>
< £t
< o
Ct -J
o
o
o
o
o
-S
UJ
LJ
ot
&
UJ
o
o
. o
05 in
10 £
VI t-
c o
.2 o
o S
o .5
~o a
o o
a
. O
O
in
o
o
o
o
o
o
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in
SNOIiVAd3S90 JO 'ON
103
FIGURE 6-1
-------
STA.I3
40 Kilometers
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CURRENT STATION LOCATIONS
U.S DEPARTMENT Of THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
flreot Loktc Region Chicago,Illinois
104
FIGURE 6-2
-------
TABLE 6-2
CURRENT METER RECORDS
H
w
o
W
02 8
O W
001 010 033 4l°48' 8T°20.5' 20.1 03/31/63 1020 07/26/63 1350 2812
003 010 004 42°02.5' 87°32'
015 005
004 010 000 42°01'
015 001
022 002
030 o44
022 203
010 34?
030 368
005 015 197 4l°59'
030 199
060 200
015 324
007 010 120 42°25'
015 121
010 185
010 321
008 060 049 42°23'
022 056
030 057
015 063
010 065
015 374
009 022 051 42°23'
120 052
030 053
090 054
060 058
015 062
*Estiaated
87°20'
87°00'
87C
87°25'
86°59'
19-5 12/17/62 1530 03/22/63 1300 2280
12/17/62 1530 03/22/63 1300 2280
2264
2264
2264
4827
3524
2077
2077
46.6 12/18/62 0815 03/22/63 1550
12/18/62 0815 03/22/63 1550
12/18/62 0815 03/22/63 1550
03/28/63 1125 10/15/63 1430
11/17/63 1300 04/12 /64 0916
04/12/64 0825 07/08/64 0705
04/12/64 0825 07/08/64 0705
62.5 11/25/63 0900 04/12/64 1455 3342
11/25/63 0900 04/12/64 1455 3342
11/25/63 0900 04/12 /64 1455 3342
05/12/64 1035 07/06/64 0855 1318
22.2 07/30/63 1500 11/09/63 1708 2450
07/30/63 1500 11/09/63 1708 2450
11/18/63 0800 04/02/64 0900 3265
04/10/64 1410 06/16/64 1300 1607
100.6 07/30/63 1730 10/16/63 1100 1866
07/30/63 1730 10/16/63 1100 1866
07/30/63 1730 10/16/63 lioo 1866
07/30/63 1730 10/16/63 1100 1866
07/30/63 1730 10/16/63 1100 1866
11/24/63 1000 04/10/63 1700* 3319
134.4 08/18/63 1330 10/17/63 1035 1435
08/18/63 1330 10/17/63 1035 1435
08/18/63 1330 10/17/63 1035 1^35
08/18/63 1330 10/17/63 1035 1435
08/18/63 1330 10/17/63 1035 1435
08/18/63 1330 10/17/63 1035 1435
105
-------
TABLE 6-2 (Continued)
CURRENT KETER RECORDS
SB O D
I—I »—•' O
&3 W W
{§ EH 0
010 015 050 42°23' 86°38' 66.1 08/16/63 1045 10/17/63 0805 1485
022 060 08/16/63 1045 10/17/63 0805 1485
030 061 08/16/63 1045 10/17/63 0805 1485
060 043 08/16/63 1045 10/17/63 0805 1485
015 230 11/25/63 1600 04/15/64 0900 3401
022 231 11/25/63 1600 04/15/64 0900 3401
030 232 11/25/63 1600 Ofc/15/64 0900 3401
060 233 11/25/63 1600 04/15/64 0900 3401
010 316 05/11/64 1535 07/05/64 1352 1318
015 317 05/11/64 1535 07/05/64 1352 1318
022 318 05/11/64 1535 07/05/64 1352 1318
Oil 015 123 42°21' 86°21' 20.1 08/06/63 0950 11/08/63 1220 2257
012 010 124 42°46' 87°42f 22.2 07/31/63 1020 11/10/63 0730 2445
013 010 236 42°45' 87°21.8' 117.0 11/19/63 1030 04/10/64 1002 3431
015 237 11/19/63 1030 04/10/64 1002 3431
022 238 11/19/63 1030 04/10/64 1002 3431
030 239 11/19/63 1030 04/10/64 1002 3431
090 241 11/19/63 1030 04/10/64 1002 3431
010 350 04/10/64 0915 07/08/64 1510 2142
015 351 04/10/64 0915 07/08/64 1510 2142
022 352 04/10/64 0915 07/08/64 1510 2142
030 353 04/10/64 0915 07/08/64 1510 2142
060 354 04/10/64 0915 07/08/64 1510 2142
090 355 04/10/64 0915 07/08/64 1510 2142
014 022 126* 42°4l' 86°55' 161.0 08/05/63 1530 11/07/63 1800 2018
030 127 08/05/63 1530 11/07/63 1800 2018
060 128 08/05/63 1530 11/07/63 1800 2018
120 130 08/05/63 1530 11/07/63 1800 2018
150 131 08/05/63 1530 11/07/63 1800 2018
015 022 183 42°44' 86°35' 87.8 08/05/63 1900 12/11/63 1030 3063
010 242 89.6 11/26/63 0830 04/15/64 1200 3388
022 244 11/26/63 0830 04/15/64 1200 3388
060 246 11/26/63 0830 04/15/64 1200 3388
*Previously labeled 200 174.
106
-------
TABLE 6-2 (Continued)
CURRENT METER RECORDS
OJ
CQ
fee O S o S
H ^-' O ~-^
EH H
016 010 133 42°44' 86°15' 20.1 08/04/63 1720 11/08/63 0900 2296
017 010 008 43°08' 87°51' 21.9 12/01/62 1035 Ok/19/63 1100 3096
015 180 07/16/63 looo 11/21/63 0830 3070
015 188 11/21/63 0900 04/02/64 1515 3196
010 356 04/02/64 1615 07/09/64 1225 2118
015 357 04/02/64 1615 07/09/64 1225 2118
018 010 009 43°09' 87°28' 79.8 11/29/62 1550 04/20/63 0900 3401
030 012 11/29/62 1550 Ok/20/63 0900 3401
060 191 43°08« 87°24.5' 11/21/63 1300 04/09/64 1236 3360
030 192 11/21/63 1300 04/09/64 1236 3360
020 015 015 43°08' 86°32' 104.2 11/28/63 1530 Ok/22/63 1345 3478
030 017 11/28/63 1530 Ok/22/63 1345 3478
090 019 11/28/63 1530 Ok/22/63 1345 3478
022 137 07/12/63 1115 11/07/63 1330 2834
060 139 07/12/63 1115 11/07/63 1330 2834
090 140 07/12/63 1115 11/07/63 1330 2834
010 247 12/07/63 0930 04/15/64 1830 3070
060 251 12/07/63 0930 04/15/64 1830 3070
010 306 05/10/64 1005 07/05/64 0745 1342
015 307 05/10/64 1005 07/05/64 0745 1342
022 308 05/10/64 1005 07/05/64 0745 1342
030 309 05/10/64 1005 07/05/64 0745 1342
090 311 05/10/64 1005 07/05/64 0745 1342
021 010 330 43°08' 86°19f 18.3 07/12/63 1230 06/02/64 1330 *
027 010 Il6**44°03' 87°33' 32.3 08/21/63 1000 10/28/63 1605 1638
022 118 08/21/63 1000 10/28/63 1605 1638
015 212 12/04/63 0845 04/23/64 1020 3385
010 358 04/23/64 1020 07/10/64 0600 1868
015 359 04/23/64 1020 07/10/64 0600 1868
022 360 04/23/64 1020 07/10/64 0600 1868
028 022 207 44°04.5' 87°l4.5' 137-2 12/04/63 1144 04/23/64 1430 3386
010 361 04/23/64 1400 07/10/64 0757 1866
015 362 04/23/64 1400 07/10/64 0757 1866
060 365 04/23/64 1400 07/10/64 0757 1866
120 367 04/23/64 1400 07/10/64 0757 1866
*Station originally lost, end computed.
**Previously labeled 200 Ol6.
107
-------
TABLE 6-2 (Continued)
CURRENT METER RECCRDS
co o B 5 03 SB o
029 010 10? 44°06.5' 87000' 157.3 08/20/63 1800 10/28/63 1220 1650
015 108 08/20/63 1800 10/28/63 1220 1650
022 109 08/20/63 1800 10/28/63 1220 1650
060 111 08/20/63 1800 10/28/63 1220 1650
030 015 254 44°04» 86°48f 152.4 12/05/63 0900 04/19M 0835 3263
030 256 12/05/63 0900 04/19/64 0835 3263
060 257 12/05/63 0900 04/19/64 0835 3263
090 258 12/05/63 0900 04/19/64 0835 3263
120 259 12/05/63 0900 04/19/64 0835 3263
150 260 12/05/63 0900 04/19/64 0835 3263
022 300 04/19/64 0705 07/04/64 0925 1826
030 301 04/19/64 0705 07/04/64 0925 1826
031 010 142 44°04' 86°33.3' 70.4 08/20/63 1015 11/06/63 1830 i860
015 143 08/20/63 1015 11/06/63 1830 i860
022 144 08/20/63 1015 11/06/63 1830 1880
030 145 08/20/63 1015 11/06/63 1830 i860
037 030 104 44°50' 87°09' 66.4 08/23/63 0930 10/29/63 1120 1610
010 261 12/02/63 0900 04/20/64 1717 3368
030 264 12/02/63 0900 04/20/64 1717 3368
022 295 04/20/64 1610 07/03/64 0740 1767.5
030 296 04/20/64 1610 07/03/64 0740 1767.5
060 297 04/2O/64 1610 07/03/64 0740 1767.5
°
038 010 215 4497.5' 86057.5* 162.8 12/02/63 1200 05/03/64 1615 3676
030 218 12/02/63 1200 05/03/64 1615 3676
120 221 12/02/63 1200 05/03/64 1615 3676
060 289 04/24/64 1210 07/03/64 1220 1680
039 090 027 44°42' 86°45' 246.9 12/02/62 1550 07/19/63 1000 5490
150 029 12/02/62 1550 07/19/63 1000 5490
210 031 12/02/62 1550 07/19/63 1000 5490
240 032 12/02/62 1550 07/19/63 1000 5490
022 150 44°45' 86°45f 08/22/63 1630 11/06/63 1045 1818
030 151 08/22/63 1630 11/06/63 1045 1818
120 154 08/22/63 1630 11/06/63 1045 1818
180 156 08/22/63 1630 11/06/63 1045 1818
150 155* ' 08/22/63 1630 11/06/63 1045 1818
*200 155 mislabeled 200 176.
108
-------
TABLE 6-2 (Continued)
CURRENT METER RECORDS
to
g o S o W0
040
041
046
047
048
054
06l
062
010
060
120
010
015
090
120
015
030
010
015
030
060
090
150
010
010
022
030
010
015
022
010
015
022
266
270
272
160
161
165
166
097
099
087
088
090
091
092
094
082
077
079
080
072
073
074
171
173
369
44°43'
44°39'
45°33'
45°22'
45°12'
45°48.5'
45°27'
Muskegon
86°3i- 195.7
86°20« 188.4
86°34' 43.3
86°14' 159-1
86°02' 45.4
84°44.5' 31.*
86°47' 48.8
Tower 15.0
12/03/63
12/03/63
12/03/63
08/22/63
08/22/63
08/22/63
08/22/63
10/06/63
10/06/63
10/04/63
10/04/63
10 /04/63
10/04/63
10/04/63
10/04/63
10/04/63
09/24/63
09/24/63
09/24/63
09/23/63
09/23/63
09/23/63
08/04/63*
08/04/63*
1130
1130
1130
1000
1000
1000
1000
1415
1415
1425
1425
1425
1425
1425
1425
1115
1505
1505
1505
1245
1245
1245
0930
0930
04/19/64
04/19/64
04/19/64
11/05/63
11/05/63
11/05/63
H/05/63
10/29/63
10/29/63
10/31/63
10/31/63
10/31/63
10/31/63
10/31/63
10/31/63
10/31/63
10/30/63
10/30/63
10/30/63
10/29/63
10/29/63
10/29/63
10/30/63
10/30/63
06/22/64** 0815 09/28/64
1627
1627
1627
1430
1430
1430
1430
1855
1855
1835
1835
1835
1835
1835
1835
2040
2115
2115
2115
1700
1700
1700
0800
0800
0800
3316
3316
3316
1804.
1804.
1804.
1804.
0557
0557
0653
0653
0653
0653
0653
0653
0658
0870
0870
0870
0868
0868
0868
2086.
2086.
2352
5
5
5
5
5
5
*Started on land 40.5 hrs earlier, time shown is in water only.
**Started on land 16 hrs earlier, time shown is in water only.
109
-------
The master list for data identification by film number is shown
in Table 6-3 and by station in Table 6-2. These two cross referenced
lists permit rapid identification of all data from the original com-
puter printouts. The data included in the master list have been cor-
rected for time by methods previously described, a check against master
listings, and individual film scanning.
In addition to the master listings and data printouts, a ques-
tionnaire was prepared for field use. This questionnaire is shown as
Table 6-4 and was used in conjunction with a map of the Lake. The
questionnaire was directed to local fishermen who had spent many years
fishing in local areas of the Lake. The purpose was to obtain detailed
information concerning local areas to compare with other data obtained
from the current study. Several of the questionnaires were sometimes
used in one interview and supplementary sheets were added as necessary
to record additional information. Unfortunately, the data secured were
widely scattered, especially as to time of occurrence. After a series
of interviews at three different cities, the information obtained was
reviewed and summarized. The data collected were inconclusive and much
too general in nature to be of any importance. Accordingly, the ques-
tionnaire method was dropped. A long-term, systematic approach might
produce tangible results from this type of investigation. Fishermen who
have sailed a specific area for many years are extremely helpful in
gathering general information about that area.
Table 6-5 includes a brief list of conversion factors for easy
reference where conversions are not shown.
Net Flows
A major objective of the current study was to determine the net
circulation of the Lake and relate this to wind movements for predic-
tion purposes. Perhaps if there were direct relationships they would
have been well understood many years ago.
Drogue studies in the upper 1.5 meters (5 feet) of water show
that the upper layers are directly wind-driven and respond to wind
shifts in about 1 hour. This would imply that the immediate surface
layers will respond to reversals in wind inputs in a matter of minutes.
The depth of direct wind-driven circulations will vary from place to
place, especially if a thermocline exists. The depth also depends on
the wind strength and duration. Direct wind control of currents under
moderate wind conditions (400 to 500 cm/sec), appears to extend to 3 to
5 meters in depth. Below this level a shear zone may exist, depending
on its location, movements in adjacent parts of the Lake, and the pres-
ence or absence of a thermocline.
110
-------
TABLE 6-3
CURRENT METER AND WIND RECORDER
RECORDS BY FILM NUMBER
FILM
HO.
200-
000
001
002
004
005
008
009
015
016*
019
027
029
031
032
033
037
038
043
044
049
050
051
052
053
054
056
057
058
060
061
062
063
065
066
067
STATION
004
004
004
003
003
017
018
020
027
020
039
039
039
039
001
005
001
010
004
008
010
009
009
009
009
008
008
009
010
010
009
008
008
008
009
DEPTH
(M)
010
015
022
010
015
010
010
015
010
090
090
150
210
240
010
000
000
060
030
060
015
022
120
030
090
022
030
060
022
030
015
015
010
000
000
FILM
NO.
200-
068
069
070
072
073
074
076
077
079
080
081
082
086
087
088
090
091
092
094
095
097
099
100
104
106
107
108
109
ill
115
116**
118
120
121
123
STATION
015
013
010
061
061
O6l
061
054
054
054
054
048
048
047
047
047
047
047
047
047
046
046
046
037
037
029
029
029
029
029
027
027
007
007
on
DEPTH
(M)
000
000
000
010
015
022
000
010
022
030
000
010
000
010
015
030
060
090
150
000
015
030
000
030
000
010
015
022
060
000
010
022
010
015
015
FILM
NO.
200-
124
126
127
128
130
131
133
137
139
140
141
142
143
144
145
150
151
154
155
156
160
161
165
166
169
170
171
173
180
183
185
188
191
192
197
STATION
012
014
014
014
014
014
016
020
020
020
020
031
031
031
031
039
039
039
039
039
O4l
041
041
041
O4l
018
062
062
017
015
007
017
018
018
005
DEPTH
(M)
010
022
030
060
120
150
010
022
060
090
000
010
015
022
030
022
030
120
150
180
010
015
090
120
000
000
010
015
015
022
010
015
060
030
015
*Number 200 116
**Mislabeled 200 016
111
-------
TABLE 6-3 (Continued)
CURRENT METER ADD WIND RECORDER
RECORDS BY FILM NUMBER
FILM
NO.
200-
199
200
203
207
212
215
218
221
223
224
230
231
232
233
236
237
238
239
241
242
244
246
247
251
254
256
257
258
259
260
261
264
266
270
272
STATION
005
005
004
028
027
038
038
038
017
007
010
010
010
010
013
013
013
013
013
015
015
015
020
020
030
030
030
030
030
030
037
037
040
040
040
DEPTH
(M)
030
060
022
022
015
010
030
120
000
000
015
022
030
060
010
015
022
030
090
010
022
060
010
060
015
030
060
090
120
150
010
030
010
060
120
FILM
NO.
200-
289
295
296
297
300
301
306
307
308
309
3H
316
317
318
321
324
330
334
337
338
339
340
341
342
345
346
347
350
351
352
353
354
355
356
357
STATION
038
037
037
037
030
030
020
020
020
020
020
010
010
010
007
005
021
005
004
015
017
027
028
030
040
007
004
013
013
013
013
013
013
017
017
DEPTH
(M)
060
022
030
060
022
030
010
015
022
030
090
010
015
022
010
015
010
000
000
000
000
000
000
000
000
000
010
010
015
022
030
060
090
010
015
FILM
B®.
200-
358
359
360
361
362
365
367
368
369
374
STATION
027
027
027
028
028
028
028
004
062
008
DEPTH
(M)
010
015
022
010
015
060
120
030
022
015
112
-------
TABLE 6-k
QUESTIONNAIRE
Name Age
Address Telephone
1. Type of boat used: 2. Years fished: __
3. Season or seasons you fish?
Spring Summer Fall Winter
k. Area normally fished: map 5. Miles off shore
6. Do you fish other areas: map 7. Miles off shore
8. Does the current in the area you normally fish, flow in one direction
during: Spring Summer Fall Winter
9- Can you say if a particular wind direction or directions usually occur
vith the currents:
Spring Summer Fall Winter
10. Have any of your nets broken loose? How many times?
Wind direction during storm: Where did nets go?
113
-------
TABLE 6-5
CONVERSION FACTORS
MULTIPLY
Centimeters
Centimeters/second
Centimeters/second
Cubic feet/sec
Cubic meters/sec
Fathoms
Feet
Feet/sec
Feet/sec
Knots
Knots
Kilometers
Kilometers/hour
Kilometers/hour
Kilometers/hour
Meters
Meters/second
Meters/second
Miles
Miles/hour
Miles/hour
Miles/hour
Miles/hour
Square feet
Square meters
0.3937
0.03281
0.02237
0.02832
35.31
6
30. 48
30.48
0.6818
1.15
1.85
0.6214
0.9H3
0.5396
0.6214
3.281
3.281
2.237
1.609
44.70
1.467
1.609
0.8684
0.0929
10.76
TO OBTAIN
Inches
Feet/sec
Miles/hour
Cubic meters/sec
Cubic feet/sec
Feet
Centimeters
Centimeters/se c
Miles/hour
Miles/hour
Kilometers/hour
Miles
Feet/sec
Knots
Miles/hour
Feet
Feet/sec
Miles/hour
Kilometers
Centimeters/sec
Feet/sec
Kilometers/hour
Knots
Square meters
Square feet
114
-------
The studies in the Chicago area were about 2 km (l.25 miles) from
shore in 8.2 meters of water. There is no doubt that the 6-meter
drogues are influenced less by winds than by bottom topography. They
are also affected by shifts in currents in the upper layers. Table 6-6
illustrates the variation of flow found in the 1.5-m and 6.1-m drogues.
Approximately 75 drogues were used for each run and they were allowed
to drift freely for 3.5 to 5.0 hours.
TABLE 6-6
DROGUE VARIATIONS
Date
6/25M
6/26/64
6/26/64
7/15/64
7/15/64
8/15/64
8/16/64
8/16/64
Drogue Depth
in Meters
6.1
1-5
6.1
1.5
6.1
6.1
1.5
6.1
Mean Wind
Direction
for Previous
10 Hours
59°
46°
46°
80°
80°
33°
15°
15°
that the
Mean Wind
Direction
During Study
47°
61°
61°
122°
122°
171°
94°
94°
Current
Direction
Over Study
Period
293°
84°
280°
147°
93°
102°
125°
215°
between the wind and
difference
the 1.5-meter depth was about 27° to the right of the pre-
It is very apparent
currents at
vailing mean wind. However, when considered against the mean winds of
the previous 10 hours, the angle is increased to 72°. The 6.1-m drogues
varied greatly, both right and left of the wind, ranging from 29 to
l4l° during the study and from 13° to 126° for the previous 10 hours.
A weak thermal discontinuity occurred between the two layers during
the period of study and a shear zone existed.
When the summer thermocline had become firmly established the
shear zone also existed at the interface between the epilimnion and the
hypolimnion. In general, there was found to be a reversal of current
direction at the thermocline such that the currents above and below
this layer were moving in approximately opposite directions, i.e.,
approximately 180° out of phase. Such a reversal is consistent with
the presence of internal waves of the first vertical mode, i.e., the
internal waves which would occur in a two-layered system and which
exhibit a current reversal across the boundary between the two layers.
But, in Lake Michigan, the velocity does not go to zero but appears to
115
-------
spiral to the right In very confined layers within the upper layers of
the themocline. A zero speed level at the thermocline-epilimnion
interface was not detected in any of the lakes. The so-called shear
zone appears rather as a very narrow level where the currents rotated
(clockwise) through 180° with increasing depth. This would account for
the wind-current relationships in the thermocline (Verber, 85). Figure
6-3 at station 8 illustrates this shift. Currents are l8o° out of
phase, and this is confirmed "by cross-spectra between velocity com-
ponents of current meter data above and below the thermocline. A high
coherence (0.9) was shown between the two meters at the local inertia!
frequency.
Internal waves of the first vertical mode, mentioned above, set
in motion in a lake with relatively homogeneous upper and lower layers
and a sharp thermocline, would be accompanied by .an upper layer current
similar in speed and direction at all depths down to just above the
thermocline, a lower layer current running in the opposite direction
and with little change in depth until just above the bottom. The rela-
tive speeds of the upper and lower layer currents will depend on the
relative depths of the two layers, to conform with the condition that
the local mass transport in each layer must be equal. This was observed
by Mortimer (private correspondence and paper read at the Tenth Con-
ference on Great Lakes Research, Toronto, April 1967, to be published)
at anchor stations in July and August 1963 in mid-lake east of
Milwaukee. Using current meters, with deck read-out, the vertical cur-
rent structure was measured at 2-meter depth intervals down to 20 meters
and at more widely spaced intervals thereafter for every 2 hours during
three periods covering seven days in all. The vertical distribution of
temperature was measured at the same time and a wave-like displacement
of the thermocline was noted which exhibited a main periodicity of
approximately 17 hours with a conspicuous component of about half that
period. This internal wave increases in amplitude after a wind dis-
turbance, and the currents, which were clearly coupled to the internal
wave, also increased in speed at that time. The current direction
rotated clockwise with a dominant period of 17 hours; the highest speeds
observed in the upper layer were close to kO cm/sec velocities and
directions were generally similar throughout the upper layer; a rever-
sal in direction occurred on passing through the thermocline; but the
speed of the current (also rotating) in the lower layer was very much
less, consistent with the greater depth of that layer.
These observations confirmed Mortimer's prediction (5*0 that the
dominant internal wave pattern in Lake Michigan, remote from the shores
and from the ends of the Lake, could be described in terms of Poincare'
waves with characteristic periods close to but always significantly
less than the local inertia! period (17.5 hours at the latitude of
Milwaukee) and with associated currents which exhibited clockwise
116
-------
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V
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117
FIGURE 6-3
-------
rotation having the same periodicity and following an elliptical track.
Mortimer shoved that, just as standing waves in a closed nonrotating
basin can be regarded as a combination of a progressive wave traveling
in one direction with an equivalent wave of the same amplitude travel-
ing in the opposite direction, so a pattern of standing Poincare waves
can be built up by the combinations of Sverdrup waves traveling in dif-
ferent directions, the Sverdrup wave being the type of long progressive
wave characteristic of rotating systems In regions remote from the
boundary. By contrast, near the shore where the rotating currents are
ruled out by the boundary, the occurrence of Kelvin waves was predicted.
In these waves, which are also a response to the Earth's rotation, the
wave crests run normal to the shore and decrease exponential1y in
amplitude away from it, and the associated currents, which decrease
in speed away from the shore, do not rotate but are constrained to run
parallel to the shore. In the internal wave mode, Kelvin waves are
expected to be of importance in Lake Michigan only in a near-shore
strip 10 or 15 km wide. If waves of this type do, in fact, occur, the
maximum currents associated with them will be close inshore and running
roughly parallel to the shore but reversing in direction from time to
time. Except for those waters close inshore, however, the theoretical
picture suggests that the influence of internal Poincare-type waves,
expressed by rotation of the currents at near inertial frequencies,
will be strongly felt elsewhere in the lake after wind disturbances.
With the destruction of a thermocline in the late fall, the internal
waves of both classes (Kelvin and Poincare), of course, disappear.
The above predictions appear to be directly relevant to the
Project's observations at mid-lake stations (6 km or more from the
shore). During stratified conditions the short-term analysis of data
does not indicate a wind-driven current system. The hour-to-hour cur-
rents are dominated by the internal wave regime which receives its
principal energy from the wind. The internal wave regime is also
affected by the Earth's rotation which tends to obscure the direct
relationship between winds as the driving force and currents produced
by internal waves. The internal wave rotation, with a period close to
the inertial frequency, is often altered by sudden wind inputs. This
regime lasts from late spring (April) into November or early December.
The rotating Influence is normal].y not found in the inshore waters.
By contrast, the winter circulation is less complex and almost
entirely wind-driven. The major exception appears when an ice cover
occurs or a reverse (winter type) thermocline develops in the central
basin.
A straight prediction model, based on wind, is not valid for
summer (stratified) conditions in mid-lake. Inshore current patterns in
the upper 5 m appear to have a wind-driven circulation throughout the
118
-------
year. The response to this system appears in about 1 hour under mod-
erate wind conditions.
The inshore zone varies in vidth and probably extends as much as
10 miles from the shore during the most favorable conditions and as
little as 2 miles during periods of upwelllng. Mid-lake circulation
patterns in winter are not under the influence of internal waves except
under very special conditions. Spectral analysis of current meter data,
for the winter period, gives no evidence of a dominant frequency which
could control current patterns. Winter patterns in mid-lake are, simi-
lar to the inshore areas during summer, wind-driven. The response time
of the mid-lake portion is probably the same as the inshore waters.
Although the winds are the primary driving force in winter,
other forces exist which complicate the pattern. When a wind reversal
occurs in one sector of the Lake, the remainder of the Lake is at or
attempting to maintain equilibrium under the prevailing wind regime.
No steady-state system can exist while external conditions are con-
stantly changing. For this reason, Lake Michigan probably never
achieves a steady-state or equilibrium condition everywhere at one time.
However, large sectors, such as the southern basin, do achieve a near-
equilibrium condition. Under these conditions, during the nonstratified
period, a prediction model is applicable.
Current data collected over Lake Michigan were programmed to
display monthly flow data in 10-degree Intervals in direction and 3-
cm/sec intervals in speed in a two-dimensional histogram. The total
flows were grouped into 30-degree increments, i.e., 0°, 30°, 60°, 90°,
etc., and the flows of the opposite angles subtracted. The result was
a net or residual flow. These flows were then translated into percent
so there would be continuity from one station to another.
Records of less than 1 month but more than 20 days were Included.
The use of the net flow value is purely relative and cannot be used to
determine average speed or varying local flow patterns. The data show
the long term flow in any single area and effectively mask out the
rotary summer flows. The histograms can be used to disclose the normal
flow at each station.
The net winds were computed for land stations at Green Bay,
Milwaukee, Chicago, and Grand Haven. These were used in addition to
the wind measurements made on the Lake, and are superimposed on the
monthly maps.
Flow lines have been used to connect one region with another.
Liberty was taken to smooth out minor differences between stations and
to use conforms! flow along the boundaries to the best conformance with
119
-------
the data. Data for the maps are normally from the current meters at
the 10- and 15-meter depths.
A hydrostatic head on the Lake is produced by an excess of in-
flowing water which makes the Lake surface higher than its outlet. This
head is present throughout the entire vertical column of water, but
only the volume above 35 meters (the depth of the sill of the outlet)
is affected by an outflow. The Michigan-Huron seiche, on a short-term
basis, will exceed the normal outflow by more than two orders of magni-
tude. Net circulation patterns in the vicinity of the Straits of
Mackinac are no doubt affected by the seiche. The permanent head,
however, is always present in the entire Lake. Although minor, the
head will exert a continual south to north influence.
General Circulation Patterns - Surface
Two basic patterns of water movement occur in the upper layers,
one in summer and one in winter. The effect of each current pattern on
nearshore currents can be modified by the prevailing or net winds. The
two winter patterns are shown in Figures 6-k and 6-5. Figure 6-U shows
the influence of the north-northwest winds. The currents along the
shore move southerly. This type of flow is usually found from November
through March, although not necessarily continuously. It can be
expected to occur about 25 to 30 percent of the year, and principally
in the winter months. The mid-lake pattern, shown in both figures, is
a large gyre that rotates around the basin. This rotation exists
because of the prevailing wind direction. The rotation is strengthened
by the southwest-northeast winds and slowed or reversed by the
northwest-southeast winds.
The flow shown in Figure 6-5 represents the south-southwest
winds which will occur normally from January to April, but on an inter-
mittent basis. The shore flow is reversed from that shown in Figure
6-k. The southwest wind predominates from January to March and north-
east wind occasionally occurs in April. This type of flow accounts for
20 to 25 percent of the movements during the year.
The reverse gyre does not occur with the same frequency, as the
prevailing winds normally occur from the south-southwest annually and
may directly influence the continuance of the rotation.
In summer, Figures 6-6 and 6-7, the shore currents again show
the influence of the prevailing winds. The mid-lake flow pattern breaks
down into several cells and shows more resemblance to the theoretical
models of standing Poincare waves presented by Mortimer (5^) and further
discussed by him in Chapter 10. The generalized gyre is shown, as the
cell may vary and becomes very complex. The entire circulation is dom-
120
-------
I 1 I
It, (
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
WINTER CIRCULATION
N-NW WINDS
U 3 DEPARTMENT OF THE INI £PlOR
FtDERAi. WATER POLLUTION CONTROL ADMIN
Great Lades Region r,hicugo.i..mois
121
GURE 6-4
-------
GREAT LAKES -* ILLINOIS
RIVER BASINS PROJECT
WINTER CIRCULATION
S-SW WINDS
U.S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago,Illinois
122
FIGURE 6-5
-------
111 i
GREAT LAKES ILLINOIS
RIVER BASINS PROJECT
SUMMER CIRCULATION
N NE WINDS
U S DEPARTMENT OF THE INTERIOR
rEDERAL WATER POLLUTION CONTROL AOMIN
Greot Lakes Region ' Chicago.liiino.s
123
FIGURE 6-6
-------
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
SUMMER CIRCULATION
S-SW WINDS
U.S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago,Illinois
124
FIGURE 6-7
-------
inated by the standing internal wave pattern during the stratified
period.
The break between the inshore and offshore circulation appears
to occur at or near where the thermocline intersects with the bottom of
the Lake. This means that the location will vary as the thermocline
gets deeper. In mid-summer the location will be in the vicinity of the
15- to 20-meter contour. The circulation inshore from this "fluid"
boundary is not dominated by the standing internal wave and is influ-
enced primarily by the prevailing winds and topography. The zone
between these regions is no doubt subject to unusual water movements.
For instance, during calm or near equilibrium conditions, flow may be
determined by proximity to a node or an antinode of an internal wave,
and during storm periods the thermocline may be depressed or tilted
upward and associated with the shear flows reminiscent of those found
in the Atlantic Gulf Stream.
The circulation of the central portion of the southern basin in
summer strongly suggests a cellular pattern, and clues to the possible
nature of this have been provided by Mortimer's 1963 (54) predictions
and by the observations he made to test these in Lake Michigan that year
(private correspondence and paper presented at the Tenth Conference on
Great Lakes Research, Toronto, April 1967, to be published in de-
tail) . These observations supported by the Office of Naval Research,
took the form of the current measurements at anchor station, already
described, in mid-lake off Milwaukee (from M. V. Cisco, of the U. S.
Bureau of Commercial Fisheries) and detailed bathythermograph studies
of the temperature distribution in the Milwaukee-Muskegon cross section.
With facilities made available by the Grand Trunk and Western Railroad,
bathythermograph casts were made routinely every 6 minutes (approxi-
mately every 2 km) from the company's car ferries on their regular
crossings. Over the interval July 14 through August 30, 80 cross sec-
tions of temperature distribution were plotted (not all complete because
of rough weather or instrument breakdown) down to a depth of 55 meters
which includes the upper part of the hypolimnion. The results of this
study, which are now being presented in a detailed report to the Office
of Naval Research, show large depth oscillations of the thermocline
often coupled with "upwelling" on one shore and "downwelling" on the
other. The gradient was relatively gentle when the observations began
in mid-July, but later became much sharper, particularly after strong
northerly winds on August 13 which set up a striking pattern of internal
standing waves across the basin, see Chapter 10, Figures 10-1 and 10-2.
Although these figures do not represent synoptic pictures
because the vessel's crossing takes approximately 6 hours, they do dis-
close the main features of the standing wave pattern, because the car
ferries pass the mid-lake position at roughly every 8 or 9 hours, or
125
-------
approximately every half-period of the predicted 17-hour internal wave.
A mid-lake node at 66 km from Milwaukee clearly persisted for 5 or more
days after the August 13 storm, and there is also evidence, less clear,
of a trinodal standing wave, probably combined with the uninodal oscil-
lation (Figure 10-2). Because the effect of a strong wind disturbance
is normally to produce upwelling of the tbermocline on one shore and
downwelling on the other, the number of transverse nodes for the
resultant internal wave must always be an odd number; and it is prob-
able that systems with 1, 3, and perhaps 5 nodes will be the ones most
frequently encountered, often with a mixture of all three in varying
proportions according to the initial conditions. This will, of course,
make the interpretation of any actual event complex; and it is only
during relatively simpler periods, like the one which occurred after
the August 13 storm, that the main factors controlling the flow pattern
can be described with reasonable certainty.
If the standing wave patterns (Figures 10-1 and 10-2) are inter-
preted, as Mortimer has done, in terms of standing Foincare waves, then
this implies that there must also be a nodal structure along the length
of the basin to satisfy the boundary conditions at the ends. It was not
possible, in 1963, to obtain much evidence on the characteristic dimen-
sions of the north-south internodal distances, but there were indica-
tions that these might be roughly twice as long as those observed on
the east-west cross section. If this is confirmed by research, then
the circulation cells associated with the internal waves will be elon-
gated in the north-south direction, but it should be emphasized that if
several longitudinal and transverse nodalities are present, the pattern
will be a complex one except during particularly simple episodes. No
doubt some nodalities will be commonly preferred, and patterns charac-
teristic for the Lake will recur from time to time.
It should also be emphasized that Mortimer's relatively simple
model of the super-position of Poincare (progressive and standing) and
Kelvin (progressive) wave solutions have been chosen to apply to the
central portion of the Lake, between kS° and kk north, which comes
close to a rectangular north and south channel. For conditions near the
ends of the basin, which the Project's studies also covered, the fol-
lowing mathematical models may prove to be more appropriate: the semi-
circular model (involving Bessel functions) closing the end of a long
channel, or a high-eccentricity elliptical model (involving Mathieu
functions).
The results from the current meters provide overwhelming con-
firmation that waves of near-lnertial frequency are the dominant
features of the circulation of the mid-lake area of Lake Michigan during
the period of stratification from early spring right through to
126
-------
November. In mid-winter, vhen a deep winter (reversed) thermocline is
present, the effects of internal waves on the currents can also be
identified. Two of the best documented examples of internal wave
effects are provided by stations 8 and 9 where the temperature and cur-
rent data were more complete during the summer of 1963 than at other
stations. These stations are approximately 35 km apart, and one series
of measurements between August 19 and August 24, 1963, showed that,
with the top of the thermocline at about 20 meters, the currents at 15
and 22 m were always in opposite phase to each other. Also, for short
intervals, the currents at any given depth at both stations were in
phase, suggesting that there was no node (or an even number of nodes)
between them.
General Circulation Patterns - Subsurface
Figures 6-8 to 6-Ik describe what appears to be the general cir-
culation found in the layers from 60 to 240 m. The general pattern
appears to be a counterclockwise rotation through all the layers and
very dominant near the bottom. Due to the smaller number of stations
in the subsurface layers, they were grouped together to form one map
for each level. Where net flows reversed at a station, the data are
included on the table with each figure. Although the counterclockwise
pattern prevails, it is by no means a permanent circulation. At least
to l80 m there are several instances at each depth level to show that
the pattern reverses. At the 210-m level and below, however, the net
flow pattern may be more stable. The day-to-day movements suggest that
there is as much variability at 2^0 meters as at the 10-meter level. In
summer and winter the rotary component of the horizontal flow patterns,
due to the internal wave on the thermocline, was found at the 2UO-meter
level, portraying movements very similar to surface movements in the
summer.
Figure 6-8, for 60 m depth, suggests that the subsurface flows
move across the bar region. Some of the stations indicate that the net
flows can be in the opposite direction and reverse patterns no doubt
can occur. Since the stations include data collected under all types
of external forces, it is understandable that reverse patterns can
exist.
On Figure 6-9, at the 90-meter level, the counterclockwise pat-
tern again is demonstrated. The ridge is clearly evident and two
pockets are defined. Several stations still indicate that reverse
patterns are present.
At 120 meters, Figure 6-10, the Lake is divided into two parts.
The south basin and the north basin apparently rotate in the same
direction although reversal is still evident from the data, especially
127
-------
Direction of Flow Average Speid
0
120
o o o
60-330-180
0- 150°
o
10
13
14
20
28
29
30
37
38
40
47
30
O
180
o
330
0 O O
330-60-150
300°
0 0
60-30
0 0
240-30
o o
210-0
o
210
0°
6.3
7.3
6.6
9.1
8.4
10.0
10.0
4.8
4.3
8.8
8.2
7.6
16.9
6.8
GREAT LAKES ~ ILLINOIS
RIVER BASINS PROJECT
SUBSURFACE NET FLOWS
U.S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOM(N.
Grtat Lad** Region Chicago,Illinois
128
FIGURE 6-8
-------
90 Meter Contour
Station
9
13
20
30
39
41
47
Direction of Flow
0°
180°
0°-I80°
30° 240°
o
180
0°
___
Average Speed
5.8
7.6
6.7
2,8
4.5
5.3,
3.7
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
SUBSURFACE NET FLOWS
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Great Lakes Region Chicago,Illinois
129
FIGURE 6-9
-------
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SUBSURFACE NET FLOWS
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Greot Lokes Region Chicugo,Illinois
FIGURE 6-10
-------
150 Meter Contour
Direction of Flow Average Speed
o
240
240°
2.0e
330
4.7
7.2
5.6
6.5
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SUBSURFACE NET FLOWS
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Gr«at Lake* Region Chicugo.Illinois
FIGURE 6-11
-------
ISO Meter Contour
Stotlon
Direction of Flow
Average Speed
39
210°
2.7 cms
132
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
SUBSURFACE NET FLOWS
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicugo,Illinois
FIGURE- 6- 12
-------
210 Meter Contour
Station
Direction of Flow
Average Speed
39
o
0
5.7cms.
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SUBSURFACE NET FLOWS
I) S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great LoKes Region Chiccgo.li;mois
133
FIGURES-13
-------
240 Meter Contour
Station
Direction of Flow
Average Speed
39
0°
9.3cms
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
SUBSURFACE NET FLOWS
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Laktt Rtgion Chicago.Illinois
13*
FIGURE 6-14
-------
in the north basin. There is a hint from station Ik that the south end
may have two gyrals occurring at the same time.
The 150-meter level, Figure 6-11, shows that reverse patterns
still exist from the data at station 30. The southern basin, although
now comparatively small, is still a complicated area of more than 100
square miles. It cannot be assumed that an area of such proportion
exhibits such a simple pattern, because the currents are still quite
complex. For the first time the pattern in the southern basin shows a
clockwise circulation. The net flow was 180° out of phase from the 120-
meter level.
Figures 6-12 to 6-Ik are based on data from the winter of 1962-
63. The data indicate a counterclockwise rotation at the three depths.
The data for station 39 shifts nearly l80° from the 180-meter level to
the 210-meter level. The area of the basin is reduced in size between
the 180-meter level and the 210-meter level. The change in shape main-
tains the same counterclockwise circulation pattern. Since stirring
occurs to the bottom of the Lake, the lower levels no doubt can reverse
direction.
The circulations just described under the heading "General
Circulation," which represent flow over long periods and which can be
either clockwise or counterclockwise, should not be confused with the
clockwise circulation coupled with internal waves which is sharply
tuned to the inertial frequency. Further examples of this, and of the
effect of wind on currents and on internal waves, are given in Chapter
10.
Spectral Analysis
While the near-inertia! frequency of current rotation associated
with internal waves in summer is very evident for shorter or longer
intervals and the records from many stations, our spectra of current
data are useful in detecting this and other frequencies and facilitated
the interpretation of a complex picture. The spectra presented here,
covering the period November 1962 to July 1964, are summarized in Table
6-7» and selected results are depicted graphically on Figures 6-15
through 6-^3. Station locations are shown on Figure 6-2.
Station 3 is located near the west shore at the southern end of
Lake Michigan. The data were gathered from January 17, 1963 to March
22, 1963, at 15 meters. There are no statistically significant peaks
in the speed, Vx and Vy spectra, the north-south and east-west compo-
nents of the current, although there was energy in the long period
disturbances.
135
-------
100
8.4
10'
o.
6
\
CJ
O
CO -
2
O
10
HOURS
L2 £5 20 16.7 14.3 I2.S Ml 10 9
(12/02/2-4/20/3)
STA. 20- 10m
(12/7/3-4/16/4)
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
100 50
33 25" 20 167
STATION - 18 20 38
DEGREES OF FREEDOM- 32 31 36
NO OF OBSERVATIONS -6482 6252 7316
WINTER CURRENT SPECTRA
LAKE MICHIGAN
U S.DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN.
GrMt Lakts Region
Chic ago,Illinois
130
FIGURE 6-15
-------
100 30 33 23
H 0 I/(R S
20 / 16.7
143
123
III
10
9.1 84
(8/16/3-10/17/3]
i
DEPTH 22m
Q.
6
X
CM
u
UJ
10'
SPEED-DEPTH
I Om
10
\
\
A
I \
I \
14.3
12.5
10
91
84
HOURS
100
5O
33
25
20
16.7
DEGREES OF FREEDOM- 20
NO OF OBSERVATIONS- 4455
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
STATION — 10
SUMMER CURRENT SPECTRA
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Greot Lodes Region Chicago,Illinois
•Of
FIGURE 6-16
-------
10'
10°
Q.
6
•^
fM
o
LU
CO
O _
10"
H 0 U \ R S
100 50 33 25
14.3 125 II.I 10 91 8.4
STATION 9 - 15m
Y AXIS 0° - 180°
jl l\ ,/lp / 9 I 8 4
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
DEGREES OF FREEDOM- 20
DATE - 8/18/3-10/17/3
NO. OF OBSERVATIONS- 4312
U 5 DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago,i:lino
-------
HOURS
I02
—
1
j. ~
O.
d ~
O
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DEGREES OF FREEDOM -20
DATE - 8/18/3 - 10/17/3
NO. OF OBSERVATIONS- 4304
—
—
—
—
4
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
t
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Rtqion Chiccgo. Illinois
139
FIGURE 6-18
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I 10 91 8.4
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100 50 33 25 20 16.7 14.3 125
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Y AXIS 0°- 180°
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
100 50 33
20 167
HOURS
DEGREES OF FREEDOM- 20
DATE - 8/18/3 - 10/17/3
NO. OF OBSERVATIONS - 4315
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THf INTERiOR
FEDERAL WATER POLLUTION CONTROL
Great LaKes Region ^tuci.g.. '
FIGURE 6-19
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14.3 12 5 II I 10 91
8.4
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25
20 167
HOURS
DEGREES OF FREEDOM -20
DATE - 5/11/4 - 7/5/4
NO OF OBSERVATIONS -3955
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lodes Region Chicago,Illinois
FIGURE 6-20
-------
HOURS
100 50 33 25 20 16.7 14.3 12.5 III '10 91 8.4
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100 50 33 25 20 167
HOURS
DEGREES OF FREEDOM-20
DATE - 5/11/4 -7/5/4
NO. OF OBSERVATIONS - 3057
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTFRIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Greol Lokes Region Chicago,iilirc s
FIGURE 6-81
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143 12 5 II I 10 91
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100 50 33 25 20 167
HOURS
DEGREES OF FREEDOM- 20
DATE - 4/10/4- 7/8/4
NO OF OBSERVATIONS - 6341
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT Of THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great LaK«i Region Chicago,Hlirois
FIGURE 6-22
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10'
10'
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100 50 33 25 20 16.7 143 12 S II.I IO
STATION 13 - 30m
Y AXIS 0°- 180°
143 12.5 III 10 91 84
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
100 50 33 25 20 167
HOURS
DEGREES OF FREEDOM- 21
DATE- 4/10/4 - 7/8/4
NO. OF OBSERVATIONS - 6417
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Greot Lakes Region Chicago,Mtinois
FIGURE 6-23
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167
U R S
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DATE - 4/10/4 - 7/8/4
NO
OF OBSERVATIONS - 6423
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GREAT LAKES — ILLWOIS
RIVER BASINS PROJECT
SPECTRA OF rOMPONFWT^
w i t w 1 i\ n \J i w W >n r w(V C. I" 1 O
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicugo, Illinois
FIGURE 6-24
-------
FIGURE 6-25
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10°
10*
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o
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100 50 33 25 20 'AI6.7 14.3 12.5 III 10 91 6.4
STATION 20 - 15m
Y A*IS 0° - 180°
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
167
HOURS
DEGREES OF FREEDOM- 20
DATE- 5/10/4- 7/5/4
NO. OF OBSERVATIONS -4029
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN.
Great Lakes Region Chicago,Illinois
FIGURE 6-26
-------
HOURS
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GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
20
HOURS
DEGREES OF FREEDOM- 20
DATE- 5/10/4-7/5/4
NO. OF OBSERVATIONS-4029
16.7
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lok«s R«gi«n Chicago,Illinois
FIGURE 6-27
-------
icr
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20 16/L 14,3
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143 12 5 III
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
100 50 33 25 20 167
DEGREES OF FREEDOM-20
DATE - 8/20/3-10/28/3
NO OF OBSERVATIONS - 4924
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
rEDERAL WATER POLLUTION CONTROL ADMIN
Greot Lak«» Region Chicago,Illinois
149
FIGURE e-28
-------
HOURS
100 90 33 25 20 16.7 14.3 12.5 III 10 91 84
STATION 29.-60m
Y AXIS 330° - 150°
100 50 33 25 20
HOURS
64
10
DEGREES OF FREEDOM- 20
DATE — B/20/3-10/28/3
NO OF OBSERVATIONS - 4950
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Great Lakes Region Chicugo.Illinois
FIGURE 6-29
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DATE - 6/20/3- 11/6/3
NO
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639
143 1C 5 11 1 10 9 8
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GREAT LAKES — ILLINOIS
Rr'ER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S OF^ARTMt NT OF T|-F INI ERiOP
FFDEPAL WATER POLLUTION CONTROL AuMIN
Great Lakes Jeg!on Ct>icugo,l.'ino s
FIGURE 6-30
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DEGREES OF FREEDOM -20
DATE - 8/20/3 -11/6/3
NO. OF OBSERVATIONS -5642
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Greot Lakes Region Chicugo. Illinois
FIGURE 6-31
-------
HOURS
100 5O 33 25 20 16.7
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100 50 33 25 20 167
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DEGREES OF FREEDOM- 20
DATE - 8/20/3- II /6/3
NO. OF OBSERVATIONS -5639
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4
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTFRIQR
FEDERAL WATER POLLUTION CONTROL ADMIN
Greot LaKes Region Oicago, i!liru,s
153
FIGURE 6-32
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DEGREES OF FREEDOM- 20
DATE -8/20/3 - 11/6/3
NO. OF OBSERVATIONS -5580
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14.3 12.5 III 10 91 84
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Gf«at Lakes Region Chicago, Illinois
15*
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DEGREES OF FREEDOM- 20
DATE- 8/22/63 - 11/5/63
NO. OF OBSERVATIONS- 5412
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago/Illinois
150
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DEGREES OF FREEDOM- 20
DATE- 9/24/3-10/30/3
NO. OF OBSERVATIONS -422 Sub-sample
143 12.5 II 10 91 8
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RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lake* Region Chicugo, Illinois
159
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DATE- 9/24/3— 10/30/3
NO. OF OBSERVATIONS -375 Sub-sample
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GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Grsot Lak«» Region Chicago, llnnois
loo
FIGURE 6-39
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Station k is located in the southern basin of Lake Michigan. It
is an offshore station and the data were collected between January k,
1963 and March 22, 1963. The recorders vere located at three depths;
10, 15, and 22 m. The principal peak located in the 10-m speed spectrum
was at 91 hours (hr) and in the 15- and 22-m speed spectra at 100 hr.
Another peak in the 15-m spectrum is at 8.9 hr. The 91- to 100-hr
period is probably due to long wave pressure systems, such as Rossby
waves. Apparently there is some forcing by meteorological disturbances
which tend to come at intervals, on the average, of about k or 5 days;
and this is confirmed in the spectra of wind data. The 8.9-hr period
is Lake Michigan's first mode. The Vx spectra were primarily noise and
no statistically reliable peaks were observed. The Vy spectra showed
important peaks at 91 hr in the 10-m record, 8.6 and 111 hr at 15 m,
and 100 hr at 22 m.
Station 5 is an offshore station in the southern basin of Lake
Michigan near the southeast shore. The data were gathered for two
depths, 15 and 22 m, during November 25, 1963 to April 13, 1961*. The
speed spectra contained no reliable peaks. The velocity components
showed tendencies of energy to peak around 10 and 20 hr.
Station 7 is an inshore station near the middle of the southern
basin. The data were gathered for two depths, 10 and 15 m> during
July 31> 1963 to November 10, 1963. The speed spectra have several
peaks which are reliable. At 10 m there is a peak at 45-5 hr while at
15 m there is a broad peak between 33 and 50 hr and also one at 16.7
hr. The energy was generally in the high frequency oscillations for
the speed spectra. In the Vx spectra at the 10-m depth, there are peaks
at 9.1, 18.2, and 50 hr, while at 15 m the peaks are at 18.2, 33, and a
broad peak between 8.8 to 9-5 hr. The Vy spectrum has a broad peak
between 50 and 100 hr and another peak at 18.2 hr in the 10-m record.
At 15 m there is a peak at 18.2 and 55 hr.
Station 8 is an offshore station in the southern basin and is
west of the center of the Lake. The date of these observations at
depths of 10, 15, 22, 30 and 60 m, was between July 20, 1963 and October
16, 1963. The speed spectra showed a gigantic inertia! frequency peak
at 17.2 hr in the 22-m record, 17.5 hr at 10, 15, and 60 m; and an
indication of peaking around 17 hr at 30 m. The Vx spectra have a
gigantic peak at 17.4 hr at 10, 15, and 22 m. The peaks in the Vy
spectra have identical period estimates as the Vx spectra but are
slightly smaller in energy magnitude at corresponding depths. The
inertia! period at this location is 17.8 hr.
Station 9 is located in the southern basin and approximately in
the center of the Lake, at this latitude. The data for the spectra were
collected between August 18, 1963 and October 17, 1963. Speed spectra
168
-------
for depths 15, 22, 30, 60, and 90 m were calculated from these data.
The velocity component spectra were computed for 15, 30, and 90 m. For
the speed spectrum, the principal peak is near the inertia! period with
each depth haying its peak at a different tine: 15 m (17-9 hr), 22 m
(19.6 hr), 30 m (l6.4 hr), 60 m (15-6 hr), 90 m (l4.9 nr). The 15-m
record also has a significant peak at 8.3 hr. The Vx spectrum gives
estimates with a 0.4-hr spread in the location of the inertia! period
from 17.5 hr for 30 m to 17.9 hr for 15 and 90 m. The 15-m spectrum has
another peak at 8.6 hr and the 30-m spectrum has a questionable peak at
8.9 hr. The Vy spectra show the same period estimates as do the Vx
spectra, Figures 6-17, 6-18, and 6-19.
Station 10 is an offshore station in the southern basin east of
the center of the Lake. The duration of the first data collection was
from August 16, 1963 to October 17, 1963. The data were collected at
depths of 15, 22, 30, and 60 m. At 15 m, two significant peaks are com-
puted in the speed spectra, one at 8.5 hr and the other at 17.4 hr. At
22 m a peak is found at 17.2 hr and an indication of a significant peak
at 8.8 hr. The 30-m spectrum is noise with more energy evident in the
low frequency. The 60-m spectrum has a peak at 17.2 hr. The Vx spectra
revealed a peak near the Inertial period of around 17. 4 hr at 15 m,
17.2 hr at 22, 30, and 60 m. Spectral peaks of the first mode of Lake
Michigan appeared at 8.8 hr in the 15- and 22-m records, 8.6 to 8.8 hr
at 60 m. For the Vy spectra two peaks are evident at the following
times and depths: 8.5 and 17.5 hr at 15 m, 8.8 and 17.2 hr at 22 m,
8.7 and 17.2 hr at 30 m, 8.6 and 17-1 hr at 60 m.
The second set of data was a winter record between November 25,
1963 and April 15, 1964 at 22 m. Only velocity components are avail-
able. The Vx spectra are mostly noise. The Vy spectra have two signi-
ficant peaks; one at 23.6 and the other at 18.2 hr.
The third set of data was recorded between May 11, 1964 and July
5, 1964 at 10, 15, and 22 m. The speed spectra show a peaking of energy
around 16 and 24 hr. The Vx spectrum has two peaks, one at 9-1 and
another at 17.2 hr, in the 10-m record; and one peak at 18.2 hr in the
15-m record. The Vy spectrum has the same features excepting the peak
at 9.1 hr is broadened into a square peak between 8.6 and 9 hr, Figures
6-20 and 6-21.
Station 13 is located in the southern basin of Lake Michigan,
west of the center of the Lake. Winter speed data for depths of 10, 15,
22, 30, and 90 m, during November 19, 1963 to April 11, 1964 show pri-
marily a random response due in part to a high number of zero speed
readings. The summer data were recorded between April 10, 1964 and
July 8, 1964 at 10, 30, 60, and 90 m. The speed spectra show a peaking
of energy around the inertial period but the Vx and Vy spectra show a
169
-------
very strong peaking at the inertia! oscillation at 17-4 hr for depths
of 10, 30, and 60 m. There is evidence of the first free oscillation
of Lake Michigan in the Vy spectra between 9 and 9-5 hr, Figure 6-22 to
6-24.
Station 17 is located in the northern part of Lake Michigan's
southern basin near the western shore. The data were collected during
the sunnier of 1964 from April 2 to July 9 at depths of 10 and 15 m.
The principal peak in the 10-m speed spectrum is that near the inertial
oscillation at 15.4 hr. There were no statistically significant peaks
in the speed spectrum at the 15-m depth. In the 10-m record the Vx and
Vy spectra show one significant peak around 16 hr, Figure 6-25.
Station 18 is an offshore station located near the northwestern
end of the southern basin. The data were collected between December 2,
1962 and April 20, 1963 at the 10-m depth. The speed spectrum has a
peak near the inertial period at 18.8 hr. The velocity component
spectra have the same peak at 18.2 hr; however, due to an abnormally
high number of zero speeds, the period estimates are not too reliable.
Station 20 is an offshore station located near the northeast end
of the southern basin. There are four sets of data starting November
1962 and ending July 1964. The first record is from November 30, 1962
to April 17, 1963. at 15 and 100 m. The 15-m depth shows an inertial
peak at 18.1 hr but also contained an unidentifiable peak at 33.3 hr
which might be due to spurious data. The 100-m speed spectrum has an
inertial peak at 18.5 hr and the Vx spectrum's inertial peak is at 17*8
hr. The Vy spectrum is mostly noise. The second record is from July
12, 1963 and November 1, 1963 at 22, 60, and 90 m. An inertial oscil-
lation shows a peak at 16.0 hr at 22 m, 17.4 hr at 60 and 90 m in the
speed spectra. The Vx spectra showed a broad inertial frequency peak
between 16.7 and 17-4 hr at both 22 and 90 m. The 90-m spectrum con-
tains a 100-hr peak. The Vy spectra show an inertial peak at 16.7 hr
at 22 m and one between 16.7 and 17.4 hr at 90 m. There is evidence of
Lake Michigan's first free oscillation at 22 m in both the Vx and Vy
spectra. The third record was obtained between December 7, 1963 and
April 16, 1964 at 10 and 60 m. These winter spectra show only noise.
The fourth record was gathered between May 10, 1964 and July 5> 1964,
at depths of 10, 15, 22, and 90 m for the speed spectra and at depths
of 15 and 90 m for the velocity component spectra. The principal peak
in the speed spectra is the one near the inertial period with values of
16.4 hr at 10, 15 and 90 m and 17-5 hr at 22 m. The Vx and Vy spectra
have a value of 17.5 hr at both depths for the inertial period oscilla-
tion. The spectral peak near Lake Michigan's first mode of free oscil-
lation showed a scatter of values at 8.3 hr (15 m) and 8.5 hr (90 m) in
the Vx spectrum, and 8.5 hr (15 m) and 8.9 hr (90 m) in the Vy spectrum,
Figures 6-26 and 6-27-
170
-------
Station 27 is located near Manitovoc on the western side of the
Lake. The spectra from this station resulted from data taken from April
23, 1964 to July 10, 1964 at 15 and 22 m. The 15-m record is not reli-
able due to numerous zero speed readings. The 22-m speed spectrum has a
I?.5-hr inertia! oscillation. The Vx and Vy spectra at 22 m show the
inertia! oscillation at 17•5 hr. The Vx spectrum has a smaller but
still significant peak at 8.6 hr which is near the first mode of Lake
Michigan.
1
Station 29 (inertial period of 17.25 hr) is an offshore station
located in the approximate center of the Lake. The data were gathered
between August 20, 1963 and October 28, 1963 at four depths, 10, 15, 22,
and 60 m. The speed data showed a period near the inertial frequency of
17.1 hr in the 10- and 6o-m records, 17.8 hr at 15 m, and 16.4 hr at
22 m. The Vx and Vy spectra have a very distinct period at the inertial
frequency of 17-25 hr at 15 and 60 m with the Vx inertial peak having
slightly more energy than the Vy inertial peak, Figures 6-28 and 6-29-
Station 30 is in the middle basin of Lake Michigan, located to
the east of the center of the Lake. The data were collected between
December 5, 1963 and April 20, 19614-. The speed spectrum for depths 15,
30, 60, 90, 120, and 150 m shows no statistically significant peaks;
however, there is a concentration of energy in the long period oscilla-
tions. Several smaller peaks are computed in the velocity component
spectra at depths of 30, 60, and 120 m. The questionable peaks in the
Vx spectra at 25 hr in the 30- and 60-m records and 17-5 hr for 120 m
and in the Vy spectra are around 20 hr in the 30- and 60-m records, and
at 18.1 in the 120-m record.
Station 31 is an inshore station near Ludington on the east side
of Lake Michigan. The data were collected between August 20, 1963 and
November 6, 1963- The speed spectra show periods ranging from 16.1 hr
at 30 m to 17-0 hr at 10 m, with values of 17-8 to 18.5 hr at 15 m, and
16.3 hr at 22 m. (See Figures 6-30, 6-31, 6-32, and 6-33.) The Vx
spectra show a similar scatter at all, depths instead of the usual
sharply defined inertial oscillation, with 15-3 hr at 10 m, 16.1 hr at
15 m, 16.0 to 16.7 hr at 22 m, and 16.0 hr at 30 m. The Vy period
estimate is also scattered, with 15-3 hr at 10 m, 17.0 hr at 15 m, 16.7
hr at 22 m, and 16.0 hr to 17.0 hr at 30 m. The problem of scattering
is due to the lack of resolving power in the spectral analysis proce-
dure; but by using harmonic analysis the scatter is resolvable.
Station 37 is a nearshore station near Sturgeon Bay on the
western side of the Lake. The first set of data was collected during
December 2, 1963 to April 21, 1964, for depths of 10 and 30 m. The
spectra were primarily noise with energy concentrations indicated in
the long period oscillations around 200 hrs. The second set of data was
171
-------
collected from April 20, 1964 to July 3, 1964 at 22, 30, and 60 m. The
speed spectra show a peaking of energy in the periods between 14 and 25
hr, with little elsewhere. The three most significant peaks in the
velocity spectra are the first free oscillation of Lake Michigan, the
near-inertia! period coupled with internal waves, and a long period
oscillation near 100 hr. The seiche period is near 8.7 hr at 60 m in
the Vx spectra and near 8.9 hr at 60 m in the Vy spectra. Those peaks
near the inertial oscillation had a period of 17.4 hr at 22 m and 16.7
hr at 60 m for both Vx and Vy spectra. A long period oscillation is
evident only in the Vy spectra and it is between 66 and 90 hr.
Station 38 is an offshore station in the northern basin of Lake
Michigan east of Sturgeon Bay and west of the Lake's center. The data
were gathered from December 2, 1963 to May 4, 1964 at 30 and 120 m. The
speed spectra showed a peak at the near-inertial frequency of 17.4 hr
at 120 m. The rest of the speed spectra have only noise, with energy
concentration in long period oscillations. Both of the velocity spectra
showed an oscillation at 16.7 hr very clearly at the 120-m depth. The
Vx spectrum had a significant peak at 66 hr.
Station 39 is in the middle of the Lake west of Frankfort,
Michigan. During December 4, 1962 to March 21, 1963, the speed spectrum
data were collected for 90, 150 and 210 m. Large peaks are seen at 15-3
hr at 150 m and 20 hr at 210 m; however, these estimates are just
indications of the periods due to the large number of zero speeds con-
tained in the data. The second set of data was collected between August
22, 1963 and November 6, 1963 at four depths of 22, 30, 120, and 180 m.
The speed spectra show broad peaks at 16.4 hr and 22 m, 15.6 hr and
30 m. The 15.3-hr peak at 120 m is very prominent and the 15.6-hr peak
at 180 m is also very sharp. The Vx and Vy spectra have near-inertial
periods at 16.4 hr at 22 m, 16.7 hr at 120 m with a broader peak in the
Vy spectrum. The energy in the Vx spectral peak is slightly greater
than in the corresponding peaks in the Vy spectra.
Station 40 is an offshore station in the northern basin west of
Frankfort and east of the Lake's center. The data were gathered from
January 22, 1964 to April 19, 1964 at 10, 60, and 120 m. The speed and
Vx spectra are mostly noise, but a period of 17.4 hr is clearly evident
in the Vy spectrum, Figure 6-34.
Station 41 is an onshore station near the east shore of the Lake
near Frankfort. The data were gathered between August 22, 1963 and
November 5, 1963, at four depths, 10, 15, 90, and 120 m. The speed
spectra show a period of 15.3 hr at 10, 90, and 120 m; and 18.7 hr at
15 m. A large amount of energy is indicated in periods between 30 and
50 hr. The Vx spectrum shows a broad peak at 10 m between 15-3 and 16.3
hr while the Vy spectrum at this depth shows a 16.1-hr period. The Vx
172
-------
and Vy spectra at 90 and 120 m show a 15.3-hr period. A reliable peak
of 12.5 hr appears at 90 m in the Vy data, Figures 6-35, 6-36 and 6-37.
Station 5k is located in the Straits of Mackinac between Lake
Michigan and Lake Huron. The data were recorded during the fall of 1963
from September 2k to November 30 at three depths; 10, 22, and 30 m. The
speed spectra have two principal peaks. The period near the inertial
oscillation is estimated to be 15.3 hr at 10 and 30 m and l6.k hr at
22 m. Peaks at 28 hours at 10 and 30 meters and 29.6 hr at 22 m are
interpreted as the half period of the oscillation of Lake Michigan and
Lake Huron, computed to be 56 hr. The spectra at the station are based
on current speed measured by the Savonius rotor. The rotor is omni-
directional and the spectra thus appear as the half-period. The Vx
spectrum has four principal peaks. The co-oscillation period of 56 hr
is recorded for all depths. The diurnal period is estimated to be 21 hr
for the 10- and 22-m records and 2k hr by the 30-m record. The semi-
diurnal period is estimated to be around 12 to 12.9 hr at all depths.
The first mode of Lake Michigan appeared at 8.8 hr in the 10-m record.
The Vy spectra are mostly noise and have no prominent peaks, Figures
6-38, 6-39, and 6-40.
Station 6l is located in the mouth of Green Bay. The data were
recorded during the fall of 1963 from September 23 to November 29 at
three depths; 10, 22, and 30 m. The chief peak at this location is
around 12 hr which represents a combination of energy from the first
mode of free oscillation of Green Bay and the semi-diurnal oscillation
(Mortimer, 5*0> a conclusion verified by harmonic analysis, Figures
6-in, 6-k2 and 6-k3.
Summary
The data can be conveniently divided into two groups, the winter
data and the summer data. The stratification of the Lake plays the
dominant role In the summer data, but also affects the winter data when
a deep reverse thermocllne is present.
The winter data can be divided into three groups. The first
group of data is that collected under an ice cover. The Lake, espe-
cially the area around stations 18 and 20 during the winter of 1962 to
1963> was under ice. Figure 6-15 ^a8 winter spectrum from station 18
during 1962-63 as an illustration of the first group and station 20,
illustrates the second group using 1963-614- winter data. The inertial
oscillation presumed due to the rotation of the earth is evident at
both stations. The second group is comprised of data of random oscill-
ations due to the turbulent nature of the Lake. There were no ice cover
or stratification evident at the time when noise spectra were collected.
173
-------
The third group of data results when there is a reverse themocline and
the internal vave oscillation causes a peak near the inertia! period.
Stations 33 and 39 show an inertia! peak at great depths near the
thermocline with winter spectra from station 38 in Figure 6-15 for the
third group.
The suomer data are dominated by the rotary currents largely
caused by the internal waves. The first free oscillation of Lake
Michigan is also readily evident along with some long period oscilla-
tions apparently due to long period meteorological disturbances. Figure
6-l6 shows a typical example of summer spectral data.
Monthly Histograms
The monthly histograms provided the data for the net flow analy-
sis. The data also provide the essential information on total flows,
mean direction, and speed variations at each station. Zero values were
not used in the tabulation and spurious high speed values not consistent
with the station were dropped from the data.
The prime value of the histograms is to visually disclose the
distribution of speed and direction over a period of time large enough
to mask the long period rotations. The 17-hour period accounts for only
2.5 percent of the total time during a month and the rotations are thus
effectively hidden.
Where the internal wave is most conspicuous the histograms show
little net movement in any direction, Table 6-8. In the winter most
stations show a to-and-fro movement if winds are variable, but are uni-
directional If winds are dominant from one quadrant. Along the shore,
during winter and summer, movements are usually blnodal. In general
currents parallel the axis of the Lake. The only major exception
appears in the ridge area between Milwaukee and Muskegon.
Speed profiles for currents are normally smooth, peaking in the
vicinity of the average speed of the station and decreasing out to a
maximum speed (Verber, 89). Ninety histograms were examined and summer
speeds were normally greater than winter speeds at depths from 10 to
60 m. Below this depth, the winter speeds were greater.
Station 6l, in the channel between Green Bay and Lake Michigan
had unusually low values for all three meters compared to other stations
in the Lake. If such speeds had occurred at one level the rotor values
would have been suspect, but the speeds were uniform within the column.
Station 51*-, in the Straits of Mackinac, had the highest individ-
ual speeds, over 60 cm/sec, in the Lake. The average speed, near 20
17k
-------
TABLE 6-8
HISTOGRAM
STATION 9, 15 METERS
OCTOBER 1-17, 1963
SPEED IN CM/SEC
ANGLE
0
30
60
90
120
150
180
210
240
270
300
330
TOTALS
4.5
11
9
15
11
11
7
k
3
8
11
10
15
114
13-5
27
30
35
35
29
39
3*
39
^3
46
28
26
411
22.5
25
25
25
33
35
51
56
46
40
24
16
28
404
31.5
13
24
21
16
12
25
25
17
19
11
23
14
220
40.5
4
5
2
2
4
3
1
2
3
1
5
4
36
49-5
1
0
0
1
0
0
0
0
0
0
0
1
3
NUMBER
81
93
98
98
91
125
119
107
113
93
82
68
1188
FLOW
1603.5
1984.5
1872.0
1922.0
1786.5
2554.5
2515-5
2110.5
2227-5
1573.5
1701.0
1707.0
175
-------
cm/sec, was not exceptionally greater than for stations 8 or 9 during
the stumer. In general, speeds on the eastern side of the Lake (near
the shore) averaged k to 5 cm/sec higher than the speeds on the western
side. Stations near shore did not show unusually higher speeds than
the offshore stations.
Six-Hour Averages
Some of the most useful data programmed for analysis work were
the 6-hour averages. Periodic functions in Lake Michigan are usually
18 hours or more and thus not completely obscured by the averages.
Similarly, long-term trends can be readily displayed without a mass of
detail. Daily averaging (2k hours) produces spurious results from the
summer data because of the averaging of the 18-hour inertial period.
The result is a fictitious 90-hour period.
Phenomena which occur over a 3-to-U-day period, such as current
speed responses to winds, are readily disclosed by plotting (Verber,
89). Table 6-9 illustrates 6-hour data from one station. The summer
data Include the average of 18 readings where all data were valid and
12 readings for the winter period. If speeds go to zero, the vane read-
ing is not included. A continuous plot of the 6-hour averages, speeds
and direction, was made for some analysis work. The effect of rotary
currents, produced by the internal wave is readily disclosed by the
plots.
Plotting of 6-hour average current speeds indicates that respon-
ses to wind energy can be traced from station to station and depth to
depth without difficulty. Current speeds at a station have been traced
from the shore and across the Lake and for more than 200 km in a north-
south direction. Although current speeds show a direct response to wind
stress (within 2 hours), the response to a change in direction is not
well established in mid-lake. The drogue study data included at least
three abrupt wind shifts, runs 3> 5> and 6. The 6.1-m drogues were not
affected by a wind shift on run 5> even after several hours. It is
believed that topography was the primary influence in maintaining the
direction. Wind shifts in run 3 indicated no shift in current direction
at 1.5 meters at the end of 1.25 hours. The study was terminated at
that point. On run 6, the current shifted with the wind within an hour
whereas the 6.1-meter currents did not show any abrupt shift.
Responses of current direction change to wind shifts are slow.
Within the Lake proper one must consider the previous wind regime, as
the force which must be changed, the newly applied force, and its areal
extent. The work by Ayers et al. (2), using a geometric series on the
winds is an attempt to uncover these relationships.
176
-------
TABLE 6-9
LAKE MICHIGAN SIX-HOUR AVERAGE WINDS
STATION 54
0
Month
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
Day
26
28
30
2
4
6
8
10
12
14
16
18
20
22
2k
26
28
Yr
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
An*
22
15
9
1
26
20
21
30
4
19
21
35
30
20
16
6
33
22
23
23
12
9
Ik
15
25
8
14
21
20
19
22
31
3^
0
Sp*»
12
7
13
12
16
11
20
17
7
5
12
7
12
7
3
8
10
7
18
5
6
k
3
5
7
16
15
9
8
14
8
12
8
9
6
An
24
22
11
36
33
21
23
3^
19
21
22
32
28
20
19
2
30
22
24
24
21
9
10
17
28
10
16
21
18
21
19
30
33
1
Sp
13
13
14
11
9
13
15
14
7
12
15
10
6
4
3
9
6
9
16
7
7
7
4
6
5
20
10
7
11
11
12
12
8
10
12
An
24
28
12
31
26
22
24
32
25
23
23
29
27
25
27
3
25
24
25
31
28
27
1
28
33
11
26
26
21
23
23
25
33
35
Sp
13
18
17
9
6
18
12
16
12
13
26
14
7
12
9
6
12
19
13
9
7
5
5
9
4
22
7
10
13
15
15
15
8
9
18
An
25
35
9
29
20
20
28
33
22
18
28
30
23
22
19
35
25
23
25
13
25
21
10
22
33
12
28
12
18
24
29
28
36
35
Sp
8
11
16
13
7
16
13
11
8
6
10
14
7
5
4
12
13
12
8
5
5
3
5
5
7
25
5
8
7
9
10
10
11
10
*Angle in tens of degrees.
**Speed in can/sec.
177
-------
Station 7 near the shore, and station 8, approximately 3*4- km
east of station 7> were compared for responses to wind shifts. Winds at
station 8 were used as being representative for the area.
Of the four vind shifts observed, vhich were due to frontal pas-
sages, station 7 responded in every instance as shown by the 6-hour
data. Station 8, dominated by rotary currents, continued to rotate,
with increased speeds, but the residual current did not change direc-
tion.
Station 7 reacted to the wind shifts in 18 to 30 hours depending
on the speeds of the wind. It is apparent from the 2-hour records that
the changes or response times occur much more quickly than the averages
indicate.
Two-Hour Envelopes
The 2-hour maximum and minimum values show the great stability
in water movements. No great changes occur within short (2-hour)
periods of time and complete shifts usually take more than 12 hours.
The rotary current, approximately 17 to 18 hours, usually represents
the greatest or most rapid reversal in direction for currents in mid-
lake. Complete reversals in the upper layers may occur in 1 or 2 hours
near the shore, as indicated by the drogues. It may take up to 18 hours
for the entire column of water to reverse direction.
The most significant use of the 2-hour envelopes is for visual
interpretation (see illustrations in Chapter 10). Problems of blurring,
extraneous high speeds, periodic changes, daily fluctuations, and other
features are seen instantly. Thirty centimeters (12 inches) of the com-
plete printout represents 5 days which include more than 300 data
points.
The summer current data in mid-lake (and some inshore stations)
are usually dominated by the internal wave and exhibit some rotary
motion. Stations 8 and 9> where the internal waves exert their purest
influence, have shown continuous rotary motion for more than kQ days'
duration. Both direction and speed illustrate the undulating or rotary
form. Verber (90) indicates the presence of five types of flow normally
found in the Lake. Straight line flow is most prevalent in winter and
at selected areas in summer, such as nearshore flows and channels. All
other types of flow in summer are some form dominated by the Internal
waves. Rotary motion in winter can be due to the deep internal wave on
the reverse therfflocline or to true inertial motion.
The visual display of the 2-hour envelopes makes them more valu-
able than the 6-hour envelopes.
178
-------
Flow at Straits of Mackinac
Station 5^ is located in the Straits of Mackinac, and current
meter records are available for approximately a 1-month period — from
the last week in September through the month of October 1963- The sta-
tion was first instrumented in December 1962, with intended recovery in
May 1963* but unfortunately those meters were lost. Summarized results
from the October 1963 record are given in Table 6-11 and on Figure 6-kk.
Current through the Straits reverses approximately every 26
hours, due to the Lake Michigan-Lake Huron 51-hour seiche. The nodal
point of the seiche is at the Straits and here the currents would be
strongest. Speeds in excess of 60 cm/sec are common in the record, and
speeds exceeding 30 cm/sec occurred 23 percent of the time. Table 6-11
shows the average speeds during the 1-month record, at each of the three
depths where meters were located and for both eastward and westward
flow.
For translating the velocity readings into volumetric rates of
flow, the cross sectional area of the Straits was divided into three
parts and apportioned among the three current meters at station Jk in
the percentages shown in Table 6-10. The resulting calculated flow
rates are shown on Figure 6-kk. The net outflow shown on the graph is
about 1,500 cubic meters per second for the period of record. As the
graph also shows, short-term flow rates approaching 20 times this
magnitude occur both into and out of Lake Michigan. Thus the periodic
seiches provide a mechanism for the exchange of large volumes of water
between Lakes Michigan and Huron.
Summary of Lake Currents
The data from Lake Michigan disclose that a simple pattern of
net circulation does not exist in summer, but that one can be identi-
fied in winter.
Movements close to the shore are fairly stable in both winter
and summer and respond to the winds prevailing over the Lake. In
general, the shore currents move northward on both sides of the Lake
except for periods during the late fall, winter, and early spring. Dur-
ing these periods more northerly winds prevail. The currents in the
western part of the Lake are noticeably slower than those in the eastern
part, except when northeasterly winds prevail. Average speeds on the
western side of the Lake range from 5 to 10 cm/sec while those on the
eastern side range from 12 to Ik cm/sec.
Inshore and offshore currents are quite separate from one
another. Offshore patterns are governed in the winter by long-term wind
179
-------
TABLE 6-10
CROSS SECTION OF THE STRAITS OF MACKINAC
SECTION
Top
Mid
Lower
DEPTH
IN METERS
15
12
37
AREA IN
SQUARE METERS
68,560
24,190
18,730
PERCENT
OF TOTAL
61.5
21.7
16.8
Total
111,480
100.
TABLE 6-11
AVERAGE SPEED AND DIRECTION IN THE STRAITS
EASTWARD
WESTWARD
SECTION
Top
Mid
Lower
ANGLE
276°
291°
271°
CM/SEC
20.05
20.80
ANGLE
120C
99
112"
CM/SEC
20.66
16.58
13-71
180
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FIGURE 6-44
-------
movements and pressure patterns. During the summer the internal wave
so overshadows all other features that the external effects are obscured
except in the current speeds. The internal waves produce a rotary
motion in the currents with a IT- to 18-hour period. In general,
epiliianion and hypoliamion flow are opposed in direction (l80° out of
phase). The opposing phase relationship applies only to the rotary
motion and not to the net flows. In a few instances certain layers
within the hypolimnlon will not be a perfect 180° opposite to the
epilimnion. These cases occur when external pressures produce an oscil-
latory current rather than a spiral flow. Although the currents are out
of phase during part of the cycle, the oscillatory current does not
complete a full. 360°. This shift of flow can occur in the epilimnion
as well as the hypolimnion. Net flows, over a month period, may be in
the same direction from the surface to great depths. In winter the
vertical profile indicates that extremely large masses of water will
react together and to 100 or more meters in depth.
In the summer the net circulation in the Lake breaks down into
cells which are largely controlled by standing internal waves. As it
takes time, after wind disturbance, to build up standing oscillations,
and as a mixture of waves of differing nodality may be present, each
decreasing in amplitude at a different rate, the boundaries of the cells
will not be rigidly fixed and the picture is likely to be complex. In
inshore waters, constraint and friction imposed by boundaries and shal-
low depth lead to a different current regime, with flow predominantly
parallel to the shore, and internal waves are not so evident in these
waters.
182
-------
CHAPTER 7
TEMPERATURE STUDIES
Introduction
Knowledge of temperatures within the waters of a lake, and of
variations in water temperature with respect to both time and place,
yields valuable insight into such phenomena as density stratification,
extent and effectiveness of mixing, and consequent variations in water
quality.
This section presents the results of temperature observations in
Lake Michigan, a review of and comparison with recorded previous studies
and the conclusions which may be drawn concerning temperature regimes
and their influence on water movement and mixing.
Field observations of temperature changes in Lake Michigan began
in September 1961, and continued on an intermittent basis until
September 1963. Temperature profiles were made throughout the Lake at
the water quality sampling station sites during cruises 1 to 8 and 10
through 18. Bathythermograph (BT) measurements were also made in the
deeper portions of the Lake during the fall and winter of 1961-62 dur-
ing cruises 50 through 52.
Definitions
Stratification occurs in a lake when its waters are divided into
layers having identifiable differences in temperature, density, or other
characteristics with rather sharply defined boundaries or zones of tran-
sition between layers. Thus, a lake in which the temperature was either
constant or varied uniformly from top to bottom would not be thermally
stratified. A deep lake in the temperate zone usually stratifies during
the summer and may stratify during the winter. Very shallow lakes rare-
ly stratify, due to constant mixing from top to bottom by wind action.
However, during prolonged calm periods in mid-summer, even shallow lakes
will stratify for short periods of time. A typically stratified lake
is divided into three thermal zones: the top zone, called the epilim-
nion; the bottom zone, called the hypolimnion, and a zone of rapid
temperature change called the thermocline. The thermocline is normally
defined as any abrupt change in temperature between two vertically
separated masses of water of different temperature. There may also be:
secondary thermoclines, where more than one exists; the winter thermo-
clines, where colder but less dense water lies over warmer but denser
water; and pseudo or false thermoclines, sometimes produced by unusual
local conditions.
183
-------
In Lake Michigan the epilimnion varies from a few meters thick-
ness in late spring or early stunner to over 6l meters in late fall. The
thermocline normally is about 6 meters thick but can be over 15 meters
in thickness or as little as 1 meter (during storm periods; see Figure
lO-l). The hypolimnion encompasses all the water below the thermocline.
An overturn is a descriptive term denoting vertical mixing or
circulation from top to bottom of the entire lake. If the lake is shal-
low a complete overturn may occur. Lakes which are extremely deep or
sheltered from the wind may only experience a partial or incomplete
overturn. An overturn occurs when the lake is isothermal and, therefore,
of the same density. According to Welch (92) the thermal resistance
under such conditions is at a minimum and relatively light winds could
cause complete circulation. Most lakes in the temperate zone have an
overturn in the spring and fall. In Lake Michigan a fall overturn
occurs in the southern basin when the Lake begins to cool, and is char-
acterized by the sinking and mixing of cold, dense water from the
surface, displacing the warmer and lighter water below. Cooling con-
tinues until the Lake reaches the temperature of maximum density and
the water mass offers little resistance to mixing from the wind energy
imparted by late fall storms. Figure 7-1 shows the temperature-density
curve for fresh water. In the deeper northern basin of Lake Michigan,
the bottom portion of the Lake remains permanently at the temperature
of mmriBmp density. The temperature of maximum density of water varies
with pressure and therefore with depth, being about k°C at the surface
and decreasing about 0.06°C per 31 meters of depth (see Eklund, 29).
This zone of constant temperature was found to extend from the 183-
meter level downward during the period of observations. The level
probably varies from year to year depending on the severity of the
winter. A spring overturn occurs in the southern basin of Lake Michigan
when the surface water temperature rises to k°C and the denser surface
water sinks through the less dense layers below. In the northern basin
there is also a partial overturn.
A thermal bar or barrier, as described by Rodgers (68), occurs
in both spring and fall. This bar appears to inhibit or restrict mixing
between the nearshore and offshore waters during the few weeks it is in
existence. A sharply defined thermal barrier was found during the 1961-
1962 bathythermograph studies in the Milwaukee region. Records indicate
that the bar or a condition similar to it may occur at any time of the
year.
Previous Studies
Five important studies on the temperatures of Lake Michigan have
been published. In addition, hundreds of observations are being taken
every day at water intakes by the plant operators. The bulk of these
-------
1.00000-
0.9 9 9 7 7 -
0.9 9 9 5 4 -
>- 0.9993 I-
I-
to
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I
0.99908-
0.99885-
0.99862-
0.99839-
0.998 I 6-
0.9979 3—'
NOTE
Welch, reference 10, page 350
TEM PERATURE
10
I
12 14
j . I
16
I
18 20 22
1 . I i I
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
DENSITY OF FRESH WATER
U S DEPARTMENT OF THF
FEDERAl WATER POLLUTION CONTROL ADMIN
Great Lakes Region >".hici.^c 'Ilir^ s
185
FIGURE 7 -1
-------
data normally is not published and thus not readily accessible for
general use. Several thousands of observations have been made over the
past 15 to 20 years by research groups or other interested agencies for
application to other problems, such as biological studies. The U. S.
Navy made observations during World War II in its submarine tests in
Lake Michigan (Hough, 40). The Great Lakes Research Institute of the
University of Michigan and the U. S. Bureau of Commercial Fisheries at
Ann Arbor, Michigan have collected and filed several thousands of tem-
perature soundings.
The five principal published studies on Lake Michigan are:
Van Oosten (84), Church (l8, 19), Millar (52) and Ayers et al. (2).
Van Oosten carried out most of his work in 1930-32 but the data were
not published until I960. The work by Church (l8, 19) in the 19^0's is
probably the most comprehensive published to date, covering all of the
seasons of the year. Millar's studies were for the surface waters of
the Lake and utilized the temperature recordings from ship's intakes.
The study does not include the mid-winter period. Ayers et al. pre-
sented detailed temperature profiles for various sections of the Lake
during four synoptic cruises in the summer of 1955* Van Oosten lists
several of the minor published studies on temperature in Lake Michigan.
Moffett (53) has detailed an instance of upwelling on the east shore of
Lake Michigan; and Mortimer (54) has assembled and interpreted summer
temperature records from 15 waterworks intakes.
Although many studies of temperature have been made in Lake
Michigan there has been a paucity of data for the winter period and
specifically from the deeper parts of the Lake.
Methods of Study
Instruments
The investigation by the Great Lakes-Illinois River Basins Pro-
ject utilized the instruments discussed below. The bathythermograph
(Figure 7-2) was invented and first described by Spilhaus (73). The
instrument was not generally available until the end of World War II,
and even then the cost was still prohibitive for its general usage. A
description of its operation and capabilities has been published by
Bralove (l4). The most accurate of all thermometers is the reversing
thermometer, often called a deep-sea thermometer. A detailed descrip-
tion and specifications have been reported by Welch (92). A hand ther-
mometer, of the armored type, is used for calibration of the BT. The
temperature recorder, Figure 7-3, developed at the Woods Hole Oceano-
graphic Institution, has been designed for long periods of recording,
unattended, and at great depths (Feyling, 32).
186
-------
CO
co
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a: tr
a.
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187
FIGURE 7-2
-------
CAM ADJUSTMENT KNOB
(BACK SIDE)
TIMING CLOCK
LIFTING PAD
(MAY BE USED ON BOTH ENDS)
END CAP
"0" RINGS
— PRESSURE CASE (ALUMINUM)
TAKE UP ROLL
PEN ARM
PEN PRESSURE ADJUSTMENT
PEN LIFTER
TEMPERATURE SENSING
BULB
RECORDER SWITCH
CONTINUOUS OFF INTERVAL
SPINE
MOTOR CAM 8 SWITCH
RELEASE CATCH FOR SPOOL
SHAFTS
— — WAX-PLASTIC CHART PAPER
SUPPLY ROLL
TEMPERATURE ELEMENT
HIGH-LOW TEMPERATURE STOP
- BASE CAP
SCALE
0 4IN
IOCM
MATERIAL
ALUMINUM 8 STAINLESS STEEL
FINISH
OXIDE FINISH a YELLOW EPOXY PAINT
ON ALUMINUM PARTS
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
TEMPERATURE RECORDER
188
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great LumjR.g.on Ch.cOflC.MImo.s
FIGURE 7- 3
-------
In general, the instruments have the following ranges of accu-
racy:
TABLE 7-1
DEGREE OF ACCURACY OF INSTRUMENTS
INSTRUMENT RANGE IN °C
Hand Thermometer i 1.0
Thermometer Recorder - 0.25
Bathythermograph - 0.1
Reversing Thermometer ±0.01
The BT is useful in obtaining a complete temperature profile,
taking a few minutes of time, in depths over 200 meters of water. The
reversing thermometer can get accurate temperatures at one depth (such
as a sampling depth) in a period of 3 to k minutes. A series of these
instruments is frequently used on a single line. The temperature
recorder can be placed at a specific depth and set to record the tem-
perature every 20 or 30 minutes on a strip-chart for periods as long as
6 months. Such recorders were used in conjunction with current meters
in the Great Lakes studies.
Bathythermograph Surveys
Beginning in September 1961, the Project began intermittent BT
soundings on all cruises in the Lake. The last continuous cruise to
collect BT data was number 18 which ended in September 1963. Approxi-
mately 1,300 BT records were taken and read. Figures 7-^ to 7-27 show
the map locations and Table 7-2 gives an example of the data.
Regular lakewide cruises were made by the Project from the
spring of 1962 through 1963. These were identified as cruises 1 to 18,
see Table 7-3- Since many temperature records were taken prior to the
regular scheduled cruises, they were identified as 50, 51, and 52.
Cruise 50 was principally in the south basin in 1961. Cruise 51 was all
in the deepest portions of the northern basin and cruise 52 was in the
southern basin early in 1962. Special attention was given to the winter
of 1961-62 to determine if winter stratification existed in the Lake and
if so, to what depth.
All data were read at 3-meter (10 feet) intervals for the first
31 meters and at 6-meter intervals (20 feet) to 6l meters. From 6l
189
-------
SCALE
0 5 10 ZO 30 MILES
I I I f I
O 1C 2O3O4O KILOMETERS
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. I
36 STATIONS SAMPLED
APRIL-MAY, 1962
US DEPARTMENT OF THE INTERIOR
w*ftTE* POLLUTION CONTROL ADMJN.
OfWt Lok«> »«4»on . CWcOflo,(IU«oit
FIGURE 7-4
-------
48°
44°
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
43"
SCALE
0 5 10 ZO 30 MILES
ill 1 I
O K> 2O3O4O KILOMETERS
LAKE MICHIGAN
CRUISE NO. 2
29 STATIONS SAMPLED
JUNE, 1962
US Df RAWTMCNT OF TM£ INTERIOR
FEOCRAL \dftTERPOLLUTiON CONTROL AD*HN
GrMt Lokt» Region Chtcogo.lllinon
191
FtGURE 7-5
-------
Kenosha
WIS. \ss
LIT)
Waukegar
SCALE
0 5 IO 2O MILES
1 I 1
0 5 10 IS SO 23 SO KILOMETERS
Benton Harbor 8fio
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 3
31 STATIONS SAMPLED
JULY, 1962
as DE«urr«*£NT OF TMC WTEWOK
FCOCftAL «*»TERPCLUITON CONTROL AOMtN
CWcoao,Hli*«»
FK3URE 7-6
-------
Momstee -s. g
Shcboygon
Btnton Horbor Bg0
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 4
69 STATIONS SAMPLED
AUG.-SEPT., 1962
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER P.-LLUTiCN CC.NTROL AOMIN
Gr«ot Lu«es Region Chicogo Illinois
CURE 7-7
-------
Shtboygan
143
MILWAUKEE
Kenosha
WIS. \so
0 5 tO 15 2O 25 SO KILOMETERS
SIBenlon Horbor 96o
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 5
63 STATIONS SAMPLED
OCT. 1962
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER PGLLUTK3N CONTROL ADMIN
Gr«at Luke* Region Chicago,Illinoi*
FIGURE 7-8
-------
I 2 3 4 S 6 7 8 9 IO II 12 KILOMETERS
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 6
32 STATIONS SAMPLED
OCT.-NOV., 1963
US DEPARTMENT OF TH£ INTERIOR
FEOCRAL WATER POLLUTION CONTROL AOMIN
GrMt Luk«» Region Chi«oao,IHin
-------
87°30
196
I
I "v-
1 KILOME'ERS
';J
GPL.'T I .'.-:3 - i . W
p iv "r- BASINS M-c,r ; "
L A ". f. */ 1 C H ' r- L
C ? '3E NO ".
-f -,-A-IONS SAM^LLD
jf T rev, ^-?
U 5 C£°«* "Mf- T 0" " H' , - f ;
FE.DCRAL WA'ER PC _^ iT-C/ ^To ;,(
tr"^1
f
IS! •
1
7 10
-------
KENOSHA
WISCONSIN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Grtot LoH«t Region
197
FIGURE 7-
-------
LWAUKEE
GREAT LAKES - iLuiNOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 6
86 STATIONS SAMPLED
OCT.-NOV, 1962
I—i
7 8 9 10 II IE KILOMETERS
U S DEPARTMENT Of THE INTERIOR
FEDCRAL WAT£«? POLLUTION CONTROL ADMIN
Grta' Lukes Region Chicago,Illinois
190
FIGURE 7-12
-------
Monistee v_ 86°
Kenosha
WIS. \50
ILL. )
Woukegan
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
IND.
MichiganCity
LAKE MICHIGAN
CRUISE NO. 7
26 STATIONS SAMPLED
OCT.-NOV., 1962
U.S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Gr«ot Lukes Region Chicago,Illinois
199
PK3URE 7- 13
-------
Monistee \ a
Sheboygon
43
MILWAUKEE
Kenosho
WIS. \30-_U-
0 5 10 I'S 2O 25 5O KILOMETERS
Benton Harbor 86o
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 8
22 STATIONS SAMPLED
NOV-DEC., 1962
S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lukis Region Chicogo,IUmoi$
7-14
-------
201
FIGURE 7-15
-------
85"
NORTH
NOTE
S isfor Special
All special stations on cruise
•#•11 were "Spoil Banks'.'
so' SI Grand Haven
S2 Ludmgton
S3 Manitowoc
34 Kewaunee
35 Frankfort
S6 Menommee
S7 Charlevoix
S8 Sturgeon Bay
S9 Manistique
45'
SCALE
0 S 10 20 30 MILES
III 1 l
0 O 30 30 4O KILOMETERS
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. II
49 STATIONS SAMPLED
MAY- JUNE, I963
U.S. DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN.
Great Lakes Region Chicago,Illinois
2O2
FIGURE 7- I 6
-------
Monistee \ §6°
Kenosha
WIS. \so
0 5 10 15 3D 25 5O KILOMETERS
Benton Harbor 86o
GRE.AT LAKES - ILuNOIS
RIVER BASINS PROJECT
Michigan City
LAKE MICHIGAN
CRUISE NO. 12
110 STATIONS SAMPLED
MAY-JUNE, 1963
U.S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Gr«at Lak«s Region Chicago,Illinois
203
fK~4jPF 7-17
-------
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 13
16 STATIONS SAMPLED
JUNE, 1963
US DEPAHTMCNT OF THE INTERIOR
FEDERAL *ATERPOLLUTION CONTROL ADMIN
3r'»ot Loli*} Region Chicago,Illinois
FK3URE 7-18
-------
-43°00-
NOTE:
Station No 14 not shown
Latitude_42° 55' 20"
Longitude_87° 50' 15"
87°54'
SCALE
1/2
I MILE
I KILOMETER
205
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 13
25 STATIONS SAMPLED
JUNE, 1963
U S DEPARTMENT OF THE INTERIOR
FEDERAL HATER POLLUTION CONTROL ADM»N
Great Lo»»» Region Chicoqo,lll.rttH»
FIGURE 7-19
-------
Mtnomin«t
s?
Manito
Manistee
LJuding-
heboygan
Fond DuLac
Port
Wash
-30' -O
Milwaukee
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
Racine
3O MIL ES
LAKE MICHIGAN
CRUISE NO. 14
103 STATIONS SAMPLED
JUNE, 1963
0 10 20 30 40 KILOMETERS
Kenosha
3o'-W!S.
ILL
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN.
Laktt W«9ion
PK3URE 7-20
-------
FlGURl- 7-21
------- An error occurred while trying to OCR this image.
-------
utkegon
Grand Hovtn
jgatuck
South
Hovtn
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
CRUISE NO. 17
114 STATIONS SAMPLED
AUG.-SEPT.-OCT., 1963
U.S.DEW*miENT OFTHC IHTEWOK
WETER POLLUTION CONTROL AOMIN.
Lake* Region CMcogo.lllinoic
FIGURE 7-23
-------
210
FIGURE 7-24
-------
Green Boy
Sheboygan
Milwaukee
CHICAGO
1961
LAKE MICHIGAN
BT Drop
I
2 to 5
6 to 9
10 to 16
17 to 30
31 to 34
35 to 39
40to 53
54 to 68
69to 75
76 to 82
SCALE
40 Kilometers
South Haven
3enton
Harbor
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
STATION LOCATIONS
CRUISE 50
U.S.DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN.
Great Lakes Region Chicago,Illinois
211
FIGURE 7-25
-------
FIGURE 7 -26
-------
Green Boy
Milwaukee
I - 25-62
2- 20-62
6-14 - 62
8-17 - 62
40 Kilometers
Benton
Harbor
CHICAGO
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
STATION LOCATIONS
CRUISE 52
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lake* Region Chicago,Illinois
213
FIGURE 7-27
-------
TABLE 7-2
TEMPERATURE DATA AND STATION LOCATION
CRUISE 001 TCEAR 1962
DEPTH STATION NUMBERS
FEET
000
010
020
030
o4o
050
060
070
080
090
100
120
140
160
180
200
300
1*00
500
600
700
800
MIXERS
000
003
006
009
012
015
018
021
021*-
028
031
037
0^3
049
055
O6l
092
122
153
183
214
244
002 003
(Temp., °C)
03.5 06.5
03-5 06.5
03-5 06.5
03.5 06.5
03.5 06.5
03.4 06.5
03-4 06-5
03.4 06-5
03-4
03.4
03-4
03-4
03-4
03-4
03.4
TIME 1347 0917
DATE 0424 0425
SURFACE TEMP. 03 06
TOTAL DEPTH 195 070
AVERAGE TEMP. 3.4 6.5
214
-------
TABLE 7-2 (Continued)
TEMPERATURE DATA AND STATION LOCATION
CRUISE
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
STATION
001
002
003
ook
005
006
007
008
009
010
Oil
012
013
014
015
016
017
018
019
020
021
022
023
02k
025
026
027
028
029
030
031
032
033
034
035
036
LATITUDE
424400
1*22300
420000
420100
414600
414600
420000
422300
422300
424400
424400
424400
430800
430800
433600
433600
440500
440500
440500
443200
442800
444500
444700
444300
444100
443900
442500
442300
443450
442100
440500
440500
433600
430800
430800
430300
LONGITUDE
861500
863500
863800
865920
870000
872000
871900
872500
870000
872300
870000
863500
870000
872500
874400
872200
873400
872000
870000
872700
870000
870000
871400
864400
863000
861700
864000
863200
861840
862000
863300
864400
863300
863500
861900
862410
215
-------
TABLE 7-3
SCHEDULE OF CRUISES
CRUISE
50
ti
n
it
it
it
STATIONS
SAMPLED
106
VESSEL
PHS-191
USCG-261
USCG-Woodbine
USCG-401
USCG-361
USCG-6V
DATES
9/27/61, 10/6/61
10/11/61
10/21/61
10/24/61, H/3/61,
11/8/61, 11/15/61,
11/21/61
11/29/61
12/21/61
OPERATING
AREA*
1
1
1
1
1
2
51
52
1
2
3
it.
5
6
7
8
9
10
11
12
13
14
15
16
17
18
17
18
36
29
31
69
63
215
26
22
70
40
109
41
105
123
22
114
51
R/V Kaho, USCG-Mesqu:
USCG-641
R/V Cisco
R/V Cisco
R/V Cisco
R/V Cisco
R/V Cisco
R/V Fitzgerald
R/V Kaho
R/V Kaho
THIS NUMBER NOT USED
T-509
R/V Cisco
T-509
T-509
T-509
T-509
T-509
T-509 Intermittent
T-509
3/1/62, 3/20-22/62 2
4/14/62, 4/26/62
1/25/62, 2/20/62, 1
8/17/62, 6/14/62
4/24-5/7/62 1, 3
6/5-18/62 2, 3
7/17-30/62 1, 3
8/29-9/9/62 1, 3
10/10-22/62 1
10/18-11/30/62 1, 3
10/28-11/7/62 1
11/28-12/6/62 1
5/8-23/63 3
5/23-6/3/63 2, 3
5/22-6/9/63 3
6/9-6/12/63 3
6/13-6/25/63 3
6/26-7/12/63 2
7/15-7/26/63 2
8/8/63-10/8/63 1, 3
8/20-9/19/63 3
*1 South Basin
2 North Basin
3 Shore or Harbor
216
-------
meters to the bottom the data were read at 30-meter intervals. The
date, time, surface temperature (using a hand thermometer), and total
depth were recorded. On many cruises two or more BT casts were made at
the station. In general, a cast was made prior to sampling the station
and after all sampling was completed.
Temperature Recorder Data
Temperature recorder data were collected at all current meter
stations in Lake Michigan, Figure 7-28. Approximately 2 million hours
of data have been collected. The purpose of the recorders was to
ascertain the relative position of the thermocline with respect to the
current meter.
Results - BT Surveys
Fall, 1961
Studies during the fall of 1961 were made only in the southern
basin. This period includes data from the latter part of September
through December. The inshore areas with depths to 20 meters were
nearly isothermal, with surface temperatures of 15.5°C and still 15.0°C
at 20 meters. The thermocline appeared sharply defined at depths up to
2k meters and less distinct at depths of 1*7 meters or more. With the
advance of colder weather, the thermocline receded to greater depths
and disappeared completely between November 16 and 20.
Winter, 1961
It is difficult to define the true winter period, as a thermo-
cline usually exists into late fall. The winter period, as classified
in this report, is the period from fall isothermal conditions to the
formation of a thermocline in early spring. Surface temperatures are
usually near 7.0°C or lower in the fall and 6.0° to 7.0°C in the spring.
The onset of true winter isothermal conditions is preceded by unusual
thermal characteristics.
Records taken in November 1961 (Cruise 50) illustrate these con-
ditions. Stations k&, 55, and 56 clearly indicate colder heavier water
overlying warmer lighter water. This may be accounted for by hystersis
in the instrument, but both the up and down traces were identical. It
is more probable that, as the water cools toward the temperature of
maximum density during calm periods, the mixing process is slowed
because the differences in density are very small. During storm peri-
ods, with a great amount of turbulence in the water, the mixing process
is accelerated.
217
-------
ES C A N * • A
G H I I
MAN
MlLWAUKEE
CH I C-AGO
SCALE
40 Kilometers
BthfTON HARBOR
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
TEMPERATURE R£CORDER LOCATIONS
U.S.DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL
Greot Lokes Region Chicogo.lllii.
-------
The mean temperature in the southern Basic decreased by a little
over 2°C between November 29 and December 21 and had fallen another
1.5°C by January 25-
By February 20 (Cruise 52) the low mid-winter temperatures had
been reached which, in the deeper parts of the southern Basin down to
150 meters, were characterized by uniformity, from 2.0° to 2.3°C, frosi
top to bottom indicating complete mixing. There is no doubt that mixing
from top to bottom occurs throughout the entire winter period during
every storm. The inshore area had an ice cover extending out in some
locations to nearly 1.6 km. Pack ice extended over 16 km (10 miles)
from shore.
A thermal bar or barrier was found on January 25 and February 20.
The inshore water, out to nearly 16 km (depth 42 meters) was at or
slightly less than 0.01°C. The adjacent water was nearly 2 degrees
warmer and under the cold upper layers. The barrier was very sharply
defined and from all appearances looked like a winter thermocline, but
was actually part of a thermal bar. The bar existed, in this case, when
all temperatures were several degrees less than the temperature of max-
imum density. A bar when temperatures are less than 4.0°C is typical
during the entire winter period.
The southern basin was nearly isothermal for the entire winter.
The northern basin had a true winter thermocline for the months of
March and April 1962. Cruise 51 shows the changes observed in the deep
hole of the Lake. Observations on March 22, 1962 between 1315 and 1920
hours indicate that a large internal wave may have occurred. Again on
April Ik and April 26 changes in the thermocline occurred. On April 14
there was an 18-meter change but on April 26 the change was kO meters.
The wave period of the winter thermocline was not precisely determined,
but it is probably close to those found in midsummer.
Although a thermocline is indicative of stratification, mixing
to the bottom in the deep hole probably occurred during the period
between the summer and winter thermocline. With a thermocline at the
180-meter depth and temperatures below TMMTImim density in the upper 180
meters, the evidence for mixing to this depth is evident. The data
indicate that the depth of mixing is a direct function of the density.
When isothermal temperatures (relatively speaking) occur between 3-5°
and 4.5°C, mixing might occur in Lake Michigan from top to bottom dur-
ing every storm. It is also possible, if a winter thermocline does not
exist, that the temperature range for mixing may be 1 or 2 degrees
greater.
219
-------
Spring, 1962
Cruise 1 covered two-thirds of Lake Michigan in late April and
early May 1962. Nearshore temperatures were as much as 7.0°C higher
than mid-lake. In general, the deep water stations of both basins were
nearly the same, ranging from 1.7° to about 3-50C. Some inshore regions
already had definite thermoclines established and surface temperatures
were up to 9-0°C. Cruise 2 in early June covered the eastern and far
northern third of the Lake and Green Bay. The practice of taking a tem-
perature reading before and after station sampling was begun on this
cruise. Normally, the two readings are about 1 hour apart. The ship
had some drift, but for all practical purposes it was in the same water
mass for both soundings. In most areas a thermocline existed except for
the deepest portions of the Lake. Surface temperatures ranged from 5.k°
to 10.6&C on June 3 and 6 and from 6.5° to l8.5°C on June 15 and 16.
The practice of taking two bathythermograph casts disclosed what
may be called short period internal waves. In a l^-hour period the
temperature changed 1.6°C at station 2, depth 6 meters. Less dramatic.
but similar changes occurred at other stations.
The thermocline begins its initial formation in the shallow water
and works its way outward toward the center of the Lake as warming
begins. During this process there is a "dome" of cold water in the
central portions of the Lake, and this has been cited as evidence for
clockwise circulation (l8). Actually, such a "dome" will occur every
spring regardless of the direction of flow. The so-called "dome" is
merely a result of the physical method by which a lake warms. Since
this process is reversed in fall, the Lake is in a steady transition
from the shallow to deep water throughout the year. Clearly, for con-
tinental lakes such as Michigan, gross thermal changes are poor
indicators of water movement except for the brief period during the
month of peak solar heating.
Summer and Fall, 1962
Cruises 2, k, 5, 6, 7> and 8 covered only the southern half of
the Lake. Cruise 3 reached a small part of the northern basin. Cruises
4 and 5 were limited to 20 miles from shore, but were very intensively
covered. The thermocline was well established in July. The mid-lake
temperatures in the southern basin were several degrees warmer than com-
parable temperatures in the northern basin. The top of the thermocline
varied considerably from one station to another. These variations prob-
ably resulted from BT casts during the progress of an internal wave.
The maximum temperatures were reached in mid-August and early September
after which the Lake began to cool slowly. A thermocline was still
found in mid-November, C6-138 and 157 at 55 meters and on December 2
and 3, C8-16, 18, and 19. No records were taken by the BT in the winter
of 1962-63. Data were collected by use of thermographs.
220
-------
Spring, 1963
Cruises 10, 11, and 12 were made in May and June. By this time
the thermocline was already established and surface temperatures were
around 12.QOC and, in the very shallow areas, up to 23-0°C. Temperatures
in the northern basin in May were nearly 20 degrees colder than some
areas in the south. The remnant of a winter thermocline was still evi-
dent, during Cruise 11 at the 214-meter depth. During a cool spring it
is very likely that a winter thermocline can remain until June. The
great diversity of temperatures occurring during this period illustrates
the slowness of mixing and movement that occurs in a large lake.
Summer, 1963
Cruises 13 to 18 cover the summer of 1963- Temperatures in the
northern basin were lower than those observed in the southern basin in
the previous year. Shore temperatures range up to 25.0°C (C15-123) and
as high as 21.6°C (C16-8) for the deeper waters. Maximum temperatures
again occurred in late August and early September. This type of heating
and then cooling appears to be the normal trend for the Lake.
Discussion
Bathythermograph records from 1961 through 1963 have revealed
several previously unknown features about the thermal distribution and
the mixing rates in Lake Michigan.
Normally, southern Lake Michigan has two well defined temperature
regimes: the period of summer stratification which begins in late May
and lasts through November and occasionally into December, and the
nearly isothermal period of constant mixing. The southern basin does
not stratify in winter. Temperatures as low as 2-3°C from top to bottom
indicate complete cooling and probably mixing throughout the winter-
spring period. Summer stratification begins at the edges of the Lake as
early as March and progresses outward and the basin becomes completely
stratified by late May.
The northern basin of the Lake undergoes three temperature
regimes. The summer regime does not become completely established until
late June and sometimes early July. Likewise, the thermocline can be
found as late as December. The winter isothermal (mixing) period is
very brief for the deeper parts of the basin, lasting only one or two
weeks in the early winter and again in late spring. The remainder of
the winter period, the basin has a winter-type or reverse thermocline.
This thermocline is deep, forming at the 120- to 180-meter depth.
Although mixing can occur from top to bottom for brief periods in late
winter and early fall the bottom part of the basin becomes sealed
221
-------
against active mixing for 11 months of the year. The total depth of the
Lake and the depth of the thennocline in succeeding years indicate that
a winter-type thermocline would normally occur every year.
The thermal barrier or bar appears to be a normal feature of the
Lake. Recent work by Rodgers (68) in Lake Huron disclosed the effec-
tiveness of this bar in preventing a free interchange between the shore
and offshore waters during the winter period. Observations indicated
that the bar forms when one zone is warmer than the temperature of max-
imum density and the other zone is colder. Records from Lake Michigan
revealed two water masses, lying side by side with nearly a 2°C temper-
ature difference and both below the temperature of maximum density.
Even in midsummer the shore waters maintain a higher temperature differ-
ential of 5°C or more than the offshore waters. The summer separation
of the two zones, in terms of distance, is not as marked as the winter
period. Chemical studies do indicate, however, that there is a differ-
ence between nearshore and offshore waters in the summer, similar to
those Rodgers found in Lake Huron.
The bars described by Rodgers (68) appear to be maintained by a
convergence mechanism operating at the Junction between the inshore
water mass, usually at temperatures above, and the offshore waters at
temperatures below, that of n»"H«nnn density. It is suggested, however,
that other factors — for instance, topography and the effective depth
of mixing — are principally responsible for maintaining a barrier to
offshore mixing.
By itself, topography exerts a powerful influence on the orien-
tation of water movements. Because water tends to follow the contours
of the Lake bottom, thus paralleling the shore, there is little inter-
change with the main body of the Lake, which can move in any direction.
A pollutant discharged near the shore thus tends to remain inshore by
the very nature of the bottom topography and shoreline orientation. For
similar reasons changes in temperature can result in a thermal bar and
tend to keep the two water masses separated. The shore zone due to its
shallowness and smaller volume, heats more rapidly in summer and cools
more quickly in winter. On this basis, a type of thermal bar appears
to exist most of the year. The relative resistance to mixing appears to
be related to the temperature differential and to the amount of turbu-
lence in the system. An onshore wind generating large waves may produce
mixing by forcing some of the shore water into the deeper layers of the
Lake along the bottom. An offshore wind produces the opposite effect,
tending to move the inshore surface waters out into the main body of
the Lake. The point at which the bottom topography does not exert a
controlling force on the water movement is not precisely defined. In
general, in summer it is between the 7- and 10-meter contour in Lake
Michigan, which corresponds to the zone where waves begin to "feel" the
bottom. The depth may be somewhat greater in winter when density
222
-------
differences between the upper and lower layers are at a minimum. Wind
mixing also is a major factor in the width of the zone. This is prob-
ably acre evident in early winter than in summer because of the lack of
resistance to mixing, and a well developed thermal bar may not be found.
Results - Temperature Recorder Data
Thermographs obtained in the winter of 1962 through the summer
of 1964 permit a much more complete interpretation of the thermal regime
than was previously possible. Figure 7-29 shows the analog record of
temperature at station k for the depths 10 and 15 meters. From March
31, 1963 until May 2k, 1963 the temperature spread between the two
levels was not discernible even though the column was gradually warming.
Both cooling and warming affected the two levels at the same time. To
distinguish between the two traces prior to the formation of the therm-
ocline, a constant of 0.2°C was added to the 10-meter trace until a
definite temperature separation was established. Station 1 at 10 meters
was added to show the period of the thermal bar between the two sta-
tions. From April 19 to May 14, or nearly one month, the two stations
were on opposite sides of the temperature of maximum density, although
this is probably not necessary to maintain the barrier.
The actual formation of the thermocline began on May 23 and 2k
when the mean daily temperature began to rise and the wind shifted to
the east and southeast. The thermocline appears to begin its formation
after the temperature of one layer is near 5-0°C, the temperature at
which the density begins to decrease rapidly with increasing tempera-
ture. Once two layers separate and the upper layer warms, thereby
increasing the density difference, the thermocline becomes firmly estab-
lished. The temperature spread increased between the two levels and
except for rare occurrences the temperatures remained apart until late
fall. Temperatures taken in deep water on the BT surveys compared
favorably with the thermograph for station k at the 15-meter depth. The
thermocline begins to decay in late September after the period of maxi-
mum heating. The decay is observed as a so-called deepening of the
thermocline. As the lake waters cool and the water temperatures in the
epilimnion approach those in the hypolimnion, a smaller amount of energy
is required to produce complete mixing between the layers.
Internal Waves
Since the summer of 1962, the Project has found internal waves
on the thermocline without exception, both summer and winter. The per-
sistence of the internal wave in the summer was not clearly identified
previously although its nature and importance were predicted (5^). Fig-
ure 7-30 shows the persistence of those waves.
Records appear to indicate that the internal waves, with a peri-
od near the inertial period, are standing waves. Precise timing of the
223
-------
22k
FIGURE 7-29
-------
— CD N If) TO —
CM — — — — —
(£
X
O
UJ
0)
UJ
l -J
l O
-------
records shews that the temperature oscillations at stations 8, 9, and 10
(mid-lake) usually vary at the same time rate but not necessarily in
phase (see Chapter 10). The temperatures at the edges of the Lake
reflect the severe changes, with temperature oscillations up to 12°C in
3 hours. These severe changes illustrate both the upvelling and down-
welling characteristics along the shore. Although large temperature
changes are associated with the mid-lake oscillations, they rarely
exceed 10°C in 16 hours.
Stations 12 and 11 on opposite sides of the Lake indicate that
the internal waves are occasionally also in phase.
A spectral analysis was run on seven sets of temperature data
for 1963; Figures 7-31, 7-32, and 7-33. These are on a common fre-
quency scale and are based on 750 to 2,600 hourly temperatures read to
the nearest 0.1°C during the months of July through October 1963. The
time span covered is as shown for each individual station. Station 11
had only 750 readings whereas the other stations had in excess of 1,600
readings.
To make the data compatible with recent spectra run on water
level data in Lake Michigan by Mortimer (55)> similar methods of analy-
sis were employed. The methods of Blackman and Tukey (10) were used.
A power spectrum was run on each set of data with 200 lags. The fre-
quency scale is linear, from 0 to 12 cycles per day. The abscissa
scale is amplitude squared per unit of frequency using an increment of
one scale for the base of another spectrum. The use of envelopes
permits an overlap of the data. Where the logarithmic scale becomes the
base of a. new spectrum, a double line is shown. The degrees of freedom
for each spectrum vary between l6 and 22 except for station 11 which
had the short record. The corresponding 95 percent confidence limits
are shown on the individual figures.
Figure 7-31 shows the spectra for stations 31 and kl on the
eastern side of the Lake. At first glance, there appears to be very
little similarity between the two spectra. Station 4l shows a pro-
nounced peak in the 16- to 18-hour range whereas station 31 does not
show such a sharp peak. The analog trace of the temperature record of
station 31 indicates that at the station depth shown the meter was in
the epiliranion for longer time periods than station ki. This may par-
tially account for the smaller peak at this period.
The spectrum for station 31 shows a distinct peak at the diurnal,
and a smaller one, of doubtful statistical significance, at the semi-
diurnal period. These peaks are not present in any of the other spectra
presented, and this indicates that internal tides are not generated or
at least are of minor importance. This is in contrast to the spectra of
226
-------
Scale
STA 41
10°
10"
I
6
4.9
3.4
10
27 2.4 22
12
LAKE MICHIGAN
LOCATION MAP
STATION 31, DEPTH 22m
AUG. - OCT.
STATION 41, DEPTH 22m
AUG - OCT
HOURS
49
4
Scale
STA. 31
I02
10'
10"
CYCLES / DAY
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF TEMPERATURE
RECORDS - 1963
U S DEPART we NT OF 'ME INT ERiOR
rFDERAi WATER POLLUTION CONTROL A.iMlN
G>»at I okes Region rmcug.i i • no s
.'.GuPE 7-31
-------
I I
24 22 2
Scale
STA.8
LAKE MICHIGAN
LOCATION MAP
STATION 8, DEPTH 30m
AUG.-SEPT. |Q
STATION 8, DEPTH 22m
AUG.-SEPT.
95%'
Confidence'
Limits
STATION II, DEPTH 15m
AUG -SEPT.
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF TEMPERATURE
RECORDS-1963
12315
CYCLE / DAY
b S Of (-ARTMFNT OF THF INI EPiOR
. WATER POLLUTION CONTDQL AUMIN
Great Lakes Region Chicogo l>. no s
228
GUPE 7-32
-------
Scale
STA.4
10'
10'
10'
,0 _
•o
a
O
o
10-' -
10-2 -
STATION 30, DEPTH 30m
JUL -OCT.
STATION 4, DEPTH 15m
MAR. - JUL
Scale
STA 20
- 10'
- 10'
_ IOU
10
12
CYCLE /DAY
229
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SPECTRA OF TEMPERATURE
RECORDS - 1963
U S DEPARTMENT OF THE iNTERu'
FEDERAL WATER POLLUTION CONTROL
Great LoKes Region ~t 1^1 ;
.'W'N
7-33
-------
surface water levels presented by Mortimer (55) in which tides, partic-
ularly the semidiurnal components, are conspicuous. A small peak at 105
hours also shows at station 11, Figure 7-32. Although the peak is small,
it may be quite significant as it also appears in the current spectra
and perhaps corresponds to the passage of high and low pressure systems
over the Lake.
Figure 7-33 shows the spectra for stations k and 20 which are
more mid-lake than stations 31 and kl. The 16- to 18-hour internal wave
overshadows by far all other peaks.
Figure 7-32, stations 8 and 11, also shows the long period Inter-
nal wave. The several peaks in the 13- to 18-hour range may be indica-
tors of the several types of wave phenomena found on the thermocline.
The six spectra presented here may also contain peaks corre-
sponding to the first five nodes of the longitudinal surface seiche but,
if so, these are buried below the noise level of the spectrum. The long
period internal wave system, near 16- to 18-hours, dominates most
records. Storm inputs excite this particular frequency and maintain the
internal wave. The dissipation of energy in the formation of internal
waves assists in maintaining the thermocline.
Analog Records
Figure 7-3^ shows the analog record at station 8 for 10, 15, 22,
and 30 meters. The records were exceptional in that they were within
0.2 percent difference in timing from one record to another for over
1,800 hours. The persistence of a regular temperature wave of close to
17 hours' period is evident and, where the phase relations can be reli-
ably determined, appears to be in phase at all, depths. As is pointed
out later in Chapter 10, this indicates an internal wave of the first
vertical node appropriate to a two-layered system. The interval occu-
pied by the first 15 waves in Figure 7-31*- indicates a mean period of
16.9 hours which corresponds to the highest peak in the Figure 7-32
spectrum. For the kind of period presented in Figure 7-3^ it may often
be more precise to determine the period visually than by spectral
analysis.
Summary
Temperature records taken during the winter of 1961 through the
summer of 196U indicate that the following conditions occur:
1. Temperature profiles from bathythermographs and temperature
recorders show that Lake Michigan overturns from top to bottom. The
southern basin, whose maximum depth is 172 meters (5»5 ft*)* overturns
230
-------
231
FIGURE 7-34
-------
every year. The northern "basin, whose maximum depth is 281 meters (923
feet) probably overturns every year. Overturning occurs only during
early winter and early spring periods, each about one month in length.
If no severe winds occur in either period, the northern basin may not
mix to the bottom.
2. A winter thermocline at a depth of about 183 m (600 feet)
occurs in the northern basin. Internal waves on the winter thermocline
suggest that amplitude may be as great as 60 meters from trough to
crest. Once the winter thermocline has been formed no mixing occurs
below this depth.
3. Inshore vertical cooling and mixing occur rapidly in mid-
winter with little or no horizontal exchange with the main body of the
Lake. This barrier is known as the thermal bar and inhibits mixing.
Even though the temperature of both areas (or zones) is less than k°C
as shown in the 1961-62 winter data, a barrier still occurs.
k. The northern basin usually lags 30 days or more behind the
southern basin during the late spring and early summer warming period.
5. The southern basin cools at a more rapid rate than the
northern basin.
6. Typical temperatures for Lake Michigan for a season or month
of the year are difficult to define. The temperature range during one
month varies considerably between the two basins at any one time. The
temperature range for any given month may be expected to vary widely
from year to year depending upon the severity of the weather.
7. Marked changes or configurations of the thermocline from one
end of the Lake to the other are characteristic of summer conditions in
the Lake.
8. Internal waves of a period near the inertial period, a little
less than 18 hours, occur constantly on the thermocline and are regen-
erated by every storm crossing the Lake. The waves appear to be stand-
ing waves (see Chapter 10). In summer vertical velocities of 0.2 cm/sec
were found by calculating the change of the isotherms from one level to
another. The formation of internal waves expends energy that would
normally produce mixing.
9. Alternating periods of warm surface water and cold deeper
water at a water intake may be due to internal waves or tilting of the
thermocline.
10. Under certain conditions, pollutants discharged into the
Lake could lie on the thermocline (because of similar densities) and be
232
-------
brought to the surface during the summer period, by tilting or oscilla-
tions of the thermocline.
11. The existence of thermoclines and thermal barriers during
extended periods of the year greatly reduces mixing of the shallower
shore waters and the waters of the hypolimnion with the main body of
the Lake. Such conditions promote a buildup of persistent pollutants
discharged into the isolated waters. Because of the prolonged periods
during which such conditions can continue, such buildups can impair the
uses of the waters adjacent to discharge points.
233
-------
CHAPTER 8
DROGUE STUDIES
*>y
Akira Okubo and James L. Verber
Introduction
Six drogue studies were made in Lakes Michigan and Erie and at
the mouth of the Detroit River. These studies were intended to obtain
information on the scales and intensity of horizontal dispersion in the
Great Lakes. The information, in turn, provides clues to the diffusion
of pollutants discharged continuously or intermittently from sewage
outfalls into the Lakes.
The basic report was prepared for the Project by Dr. Akira Okubo,
Chesapeake Bay Institute, Johns Hopkins University. Dr. Okubo assisted
staff members in outlining the study and contributed much toward the
technology used in the study. Drogue Runs 01 and 02 were made in Lake
Michigan and 03 to 06 in Lake Erie. Dr. Okubo submitted three reports,
one for each Run in Lake Michigan, and a final report including Runs in
Lake Erie. Also included are the field techniques used (J. S. Farlow,
31).
The approach used was to photograph from an airplane a group of
small floats attached to submerged drogues (current-following devices)
as they moved past an array of fixed reference markers. A series of
photographs was made from a height of about 2^0 meters above the water
surface once every 5 minutes for the first 2 hours and then once every
10 minutes for at least another hour. At this height the 22.9-cm square
photographs depicted an area 360 meters square. The photos were over-
lapped by 80 percent so that the small floats could be located despite
the large areas of glare on individual photographs. Sixteen fixed ref-
erence markers were anchored about 180 m apart in an approximately
rectangular grid. They were shape- and color-coded for positive identi-
fication. The drogues were launched about 18 m apart, also in a rec-
tangular grid pattern and were also color- and shape-coded. Between 50
and 90 drogues were used each day at each depth investigated, which
gave reasonable statistical stability.
Equipment
The drogues (Figure 8-1) were made from 1.2- x 2A-m rectangles
of 198-gram (7-ounce) nylon cloth, with the upper and lower edges
folded over and sewn to form tubes. Two such pieces were bent at right
angles at the middle and joined together at the angles by two vertical
-------
235
FIGURE e-i
-------
lines of stitching about 0.75 cm apart. Two 2.4-m lengths of 0.75-cm
diameter, zinc-coated, thin-walled electrical conduit were inserted in
the cloth tubes at the lover edge. Their ends were guyed by 0.19-cm di-
ameter nylon parachute cord so that the tvo pieces of conduit bisected
each other at right angles. The upper edges of the drogue were supported
by 17 aluminum fish-net floats, each approximately 7-5 cm long and 4 cm
in diameter. Slits in the upper edge of the cloth tubes containing the
fish-net floats allowed air to escape freely. The assembled drogue
weighed about 4-3 kg in air when dry and measured 1.2 m high by 2.4 m
across overall. When submerged in lake water, each drogue weighed less
than 0.22 kg (that is, one more fish-net float would make it buoyant).
A length of nylon parachute cord was tied around the two pieces of
electrical conduit and led up through the parallel rows of stitching
holding the two panels together to a small float at the Lake surface.
The weight of the submerged drogue was sufficient to keep this line as
nearly vertical as a diver can judge, and so its length determined the
drogue's depth. The equipment is relatively indestructible and requires
no maintenance.
The surface float (Figure 8-2) was a sandwich consisting of an
inch-thick piece of styrofoam held in place between two pieces of
quarter-inch plywood by an eyebolt, to which the cord supporting the
drogue was attached. The surface of the float had an area of 768 cm2
and its freeboard was about 0.63 cm. Assuming a wind speed of 13 knots
and a water speed of 44.7 cm/sec, the drag of the supporting elements
is only about 1 percent of that of the drogue itself. The size of the
drogue is such that it provides information on about 75 percent of the
horizontal turbulent energy that may be expected.
Surface floats were made in triangular, rectangular, and circular
shapes, and their upper surfaces were painted in one of five colors.
The red, green, orange, and yellow were of reflecting paint; the white
was traffic paint. As expected, the white floats were the hardest to
see, because they were easily confused with white caps and glitter
spots. Orange and red are the easiest colors to find from a boat or on
a photograph. Rectangles are the easiest shape to pick out on the
photos.
The floats were launched in order in groups of 15> each group
member having the same number. Each row contained only one shape, the
adjacent rows having different shapes. Each column contained only one
color, the adjacent ones having different colors. This ordered alter-
nation made it possible to keep track of the identities of 150 different
floats over the period of the study. However, because the drogues tend
to sink to their designed depth at different rates and because water
velocity tends to change with depth, it is essential to photograph the
drogues during the period of launching as well as after they are all
launched.
236
-------
<;\6"X9"Xl" ' t
^STYROFOAM
VON 1/4" PLY WOOD.
6"X9"xi" STYROFOAM
ON 1/4" PLY WOOD.
30
l3/2X4"Xl" STYROFOAM
ON 1/4" PLY WOOD.
1
4
1
12.3
B
SCALE
0
H
o
I FT.
I I
30 CM.
BOLT (A,B,aO
PLYWOOD TOP (A.B.aC)
7
STYROFOAM
PLYWOOD
LEFT END VIEW
A
SCALE
4IN.
IOCM.
MATERIAL
AS SHOWN
FINISH
REFLECTING PAINT
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
DROGUE SURFACE FLOATS
DROGUE STUDY
U S DEPARTMENT OF THE INTERIOR
FEOCRAL WATER POLLUTION CONTROL AOMIN
Ortot LaMs R«?ion Chlcogo.llfinon
237
FtGURE 8-2
-------
The reference markers (Figure 8-3) were each made of two sheets
of plywood and styrofoam which supported the ends of a 6.3-m length of
3.8-cm diameter, galvanized steel pipe. One float was a square 1.2 m
on a side, the other was a right triangle made by cutting one of the
squares in half along a diagonal. The floats, which were made of 1.9-cm
plywood with 25.4-cm styrofoam sheets nailed on the underside, were held
to the upper side of the pipe by pairs of u-bolts. The pipes were
capped to increase buoyancy. Eighteen-inch sections of old railroad
rails were used as anchors and fastened to each end of the marker by
0.63-cm manila line.
The photographer took vertical photos with a Zeiss RMK 15/23
camera with a 153 mm lens. The camera was loaded with five 22 m rolls
of Kodak aerial Ektachrome spliced end to end. This magazine was
replaced by another similar one about the time the photographic interval
was changed from 5 to 10 minutes, making a total of about 255 m of film
used on each day of field work. If camera tilt is less than 2 degrees,
the maximum distortion in the corner of the 22.9-cm square negative is,
at most, 10 microns.
Field Methods
On an average field day, a larger vessel (l4 m or more in length)
carrying the assembled drogues and reference markers and two smaller
vessels (about 6.0 m long) reached the study area about 0830. Test
drogues were set to the depths of interest, and watched for about 1/2
hour while the reference markers were readied for launching. When a
clear idea of the direction of drift was obtained, three parallel lines
of reference markers were launched about 180 m apart and parallel to
the direction of drift. The larger vessel cruised slowly tossing off
markers with one anchor attached, while the small boats followed behind
attaching the second anchors in a taut fashion so the markers would
neither translate nor rotate. Three lines of four reference markers
each took about 20 minutes to set. (There were four additional markers
remaining on board at the end of this first operation.) After these
first dozen markers had gone in, the test drogues were checked again to
see if any drastic changes in direction had occurred. By that time the
photo plane was making a high level run (about 1,800 m above the water)
to be able to get at least one frame showing all the reference markers.
While it was making this run, the larger vessel started setting the
deep drogues about 18 m apart, working upwind, laying successive cross-
wind lines. When the equipment was in good order, it took about 4 5
minutes to set some 75 drogues between two lines of reference markers.
The small boat followed the larger setting vessel, untangling any equip-
ment which became fouled during launching and righting capsized surface
floats. After the deep drogues were in, the shallow drogues were
238
-------
2I'0"
I2'0" -
40
\]/2 GALVANIZED STEEL PIPE
S 1^2 X l?8 O.D. END CAPS
•«— 3' 6"—
8/2 -
SCALE
0 4FT.
±1 , ,1 ,-L J
I20CM.
I 5 I
3/8 X 78 X /8 METAL STRAP
WITH U-BOLT.
END VIEW
PLYWOOD
STYROFOAM
MATERIAL
AS SHOWN
FINISH
REFLECTING PAINT
NOTE:
STYROFOAM NAILED TO PLYWOOD
SCALE
o
K
0
4 IN.
H
IOCM.
GREAT LAKES ~ ILLINOIS
RIVER BASINS PROJECT
REFERENCE MARKER
DROGUE STUDY
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POL LUTtON CONTROL ADMIN
LaM» Region Chicago, U
8-3
-------
launched in a parallel lane of reference markers. Drogues at different
depths hare been observed to move at right angles and also in directions
directly opposed to one another for some hours at a time. This was one
reason for putting out teat drogues. The outer boundaries of the groups
of drogues should be checked at least once every 3 A hour, so that addi-
tional reference markers can be put in or others shifted in such a way
as to keep the ground surrounded. General trends were noted and plans
were laid in advance to maintain a usable grid of markers among the
drifting drogues. The photo plane made additional high level runs as
necessary. It began making low level runs (about 2^0 m above the water)
as the first drogues were set. These runs were made every 5 minutes for
approximately 3 hours, after which the interval was increased to 10
minutes for the remaining 2 to 3 hours. At the end of about 6 hours,
the plane had used some 255 m of film and most of its fuel.
After the plane departed all boats started collecting drogues,
and also reference markers, if this was the last day of the study. At
least 3 hours were allowed, as finding the last half dozen usually took
considerable time. About 95 percent of the drogues were recovered.
Analysis Methods
The raw data from these studies were reduced to yield a time
series of the locations of a group of drogues at each depth. The posi-
tions of the drogues were transformed by a computer program into an
absolute coordinate system fixed to the Lake. New York University pro-
vided computer programs for the studies. The following calculations
were conducted by computer: the means, variances, and covariances of
each group of drogues at appointed times, the distance-neighbor separa-
tions (the pair-program), and the dispersion of drogues with respect to
their initial positions. A CalComp plotter was used in the program so
that graphs of a group of drogues could be prepared for each depth at
selected times. Lagrangian correlations of the drogue displacements
were also computed for two typical runs; however, the results are not
included in this report, since meaningful conclusions could not be
derived from them.
inscription of Experimental Results
On June 25 and 26, 196**-, two studies (Run 1 and Run 2) were made
In Lake Michigan about 2.U km WNVf of Indiana Harbor, Indiana, East
Breakwater Light, where the water depth is about 8.1 m (Figure 8-i). On
July 15 and 16, two studies (Run 3 and Run k) were conducted in Lake
Erie about 8 km WSW of Colchester, Ontario, where the depth of water is
approximately 7.5 m (Figure 8-5). Finally, on August 15 and 16, two
more studies (Run 5 and Run 6) were made in Lake Erie about 5.6 km west
of Cleveland, Ohio, West Pierhead Light, where the depth of water is
-------
87°40'
87°30'
4I°50'-
67°40
LEGEND
A = Water Intake
7.3= Meters
SCALE IN KILOMETERS
F•' r Vt N 1 . ! '"t- 'NT' •<• '"
FEDERAL WATER POLLUTION CONTROL ADMIN.
Great Lakes Region Chicago,lllinois
-4
-------
83°00'
42° 20'
- 42°00'
SCALE
I
32
Kilometers
GREAT LAKES - ILLINOIS
PIVER BASiNS PROJECT
STUDIED AREA
RUN 3 - RUN 4
US DEPARTMENT OF THE INTERIOR
FEDERAL WATE4 POL LUTIGTJ ^ONTROi. ADMIN
Great LaKes Region Chicago,Illinois
FIGURE 8-5
-------
about 12.6 m (Figure 8-6). All of the aerial films have been developed,
but computer runs have not been processed for Run k, so this report
will exclude analysis of Run 4.
On a typical experiment or run, a total of N-j_ drogues was
released at 6.1 m depth, each being launched about 18.0 m apart in a
rectangular grid pattern. In Runs 2, 3, and 6, after the 6.1-m drogues
were released, a total of tig drogues was also released at 1.5-m depth
in a similar manner.
A series of aerial photographs was taken from an altitude of
about 240 m once every 5 minutes or so for the first 3 hours and then
approximately every 10 minutes for the rest of the experimental period.
The probable error in locating drogues is estimated at 1 to 2 meters,
the higher figure to hold for later parts of the experimental period.
The early photos for Runs 2, 3* and 6 were not used in the computer
programs. Thus, for these runs, the analysis of diffusion covers the
period after both groups of drogues were set in the water. General
information on the runs is contained in Table 8-1.
Drogue positions at some typical times are shown in Figures 8-7
to 8-11, where the coordinate system is taken in such a way that the
X-axis points to the east and the Y-axis to the north. Some drogues
could not be located, chiefly because they were outside the field of
the aerial photographs. On a few occasions some drogues failed to be
detected even though they supposedly were in the field of the photos.
The approximate positions of those missing drogues, however, were
obtained by interpolating between the preceding and subsequent posi-
tions whenever possible.
Group size did not always tend to increase with time. Whereas
the 1.5-m drogues in Runs 2 and 6 and the 6.1-m drogues in Runs 1, 2,
and 3 exhibited the tendency of growth of group size with time, charac-
teristic of turbulent diffusion, the anticipated increase in group size
was not immediately recognizable for the 1.5-m drogues in Run 3 and the
6.1-m drogues in Runs 5 and 6.
Figures 8-12, 8-13, and 8-14 illustrate the time behavior of the
standard deviation for all the runs. There was, in fact, very little
dispersion of the drogues for Runs 3> 5> and 6 as was mentioned previ-
ously; the drogues were dispersed over approximately the same area at
the end of a few hours as at the beginning of the experiment, and at
times a certain number of drogues was noticeably reconcentrated in one
location or another (see Figure 8-10). It is evident that those drogues
encountered temporary convergences present at the depth of water where
the drogues were located.
-------
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FIGURE s- to
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RUN I - 20 fttt (6.1m)
500
cr
(m,}
200-
100-
e
©e ©
e 0e
0
O.I
0.2
0.5
I
t (hr)
RUN 2 - 0-20 feet (6.1m)
X-5 f««t (1.5m)
.000
500-
cr
(171)
100
XX
O.I
0.2
0.5
TIME VARIATION OF STANDARD
DEVIATION IN THE GROUPS OF
DROGUES
GREAT LAKES ^ ILLINOIS
RIVER BASINS PROJECT
TIME VARIATION
RUN I-RUN 2
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Grtot Lakes Region Chicago,Illinois
251
8-12
-------
TIME VARIATION OF STANDARD DEVIATION IN THE GROUPS OF
DROGUES
1,000"
500
200
100
50
< x x x x
0 000
*x* x
O.I
0 .2
0.5
( h r )
0 _ 20 f«»t (6.1m)
X - 5 f *«t (1.5m)
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
TIME VARIATION
RUN 3
U.S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Luk«s Region Chicago,Illinois
252
FIGURE 8-13
-------
200,
cr
100-
0
RUN 5
.1 0
•iD 0
0 00 OQ 0
2 0.5
D
t ( h r )
0 - 20feet (6.1 m)
R U N 6
500-
0"
(771 )
200-
100-
50-
0
0
X
0 e e
x
x
O
-------
The movement of the center of mass of the drogues and the wind
track on the day of experiment are shown in Figures 8-15 to 8-19. The
wind data are available from airports near the studied area, each loca-
tion being indicated on the field maps (Figures 8-4, 8-5, and 8-6). In
general, the movement of the 1.5-m drogues may be interpreted as a
result of the wind-driven current, the direction of which was somewhat
to the right of the down-wind direction. On a change of wind the direc-
tion of the flow at 1.5 m changes within an hour or so. On the other
hand, the movement of the 6.1-m drogues was generally against the local
winds. In other words, the drogues at 1.5 and 6.1 m moved in directions
opposed to one another. This implies that vertical shear in horizontal
velocity did exist in the experimental area. Typical velocities at 1.5
and 6.1 m are estimated to be k and 2 cm/sec, respectively.
During the summer, a sharp thermocline develops at 5.4 to 6.1 m
in the western part of Lake Erie. Thus the 6.1-m drogues were situated
in or a little below the thermocline. The summer thermocline is usually
not so conspicuous in southern Lake Michigan as in Lake Erie. The 6.1-m
drogues in Lake Michigan were located below mid-depth, where a rela-
tively weak stratification is present. The movement of the 1.5-m
drogues should represent the flow in the surface layer, above 3.0 to
4.5 m.
The wind factor, the ratio between the current speed and the
wind speed, is 0.008 at 1.5 m in Lake Michigan and in Lake Erie south-
east of the Detroit River, but the factor in Lake Erie off Cleveland is
about two times higher, i.e., 0.017- On the other hand, the wind factor
at 6.1 m ranges between 0.005 and 0.008, the only exception to these
values occurring in Lake Erie southeast of the Detroit River, where the
drogues were set close to the bottom. On days with moderately strong,
steady winds there should be a corresponding steady and uniform current
in the surface layer, the direction of which is nearly parallel to the
wind. The presence of boundaries should modify the current pattern;
thus, close to the shoreline the mean current is nearly parallel to the
shoreline even if the wind is offshore or onshore.
Characteristics of Diffusion
As previously mentioned, the standard deviations of the group of
drogues do not necessarily reveal a regular pattern of turbulent dis-
persion. In the case where suppression or reversal of diffusion
(apparently by convergence) is observed, no diffusion constants can be
derived from the variation of standard deviations with time. Instead,
the dispersion of drogues with respect to their initial position was
computed for each of the eight groups of drogues. By doing so, we can
regard the dispersion of drogues as if they were released consecutively
from the same point, provided that the turbulent field is homogeneous
254
-------
400
RUN I - 6.1 m
100 200
X (m)
400
600
800
200-
5 hr
CX
4hr 0,
3hr
Ihr
DROGUES
Ohr
1000
150
25 JU
i
Ohr «
NE 1964 .
1
1
5hr
4rO-
O
0
1
-------
DROGUES
200
Y
(m)
-200
-400
2.5 hr
1
J
I.Ohr
°0.5hr
6.1 m
1 l
_i L_
( /
/ 1
Ohr o- 0.5
*•«
1
hr
2.5
l.5hr o-**°
_^" I.Ohr
<
1.5 m
-600
-400
-200 200
X (m )
WIND
400
600
100
Km
26 JUNE 1964
1.5m DRO<
^^f
p-^~er 6 Im OR
/5.00
/
0
?0 00
END OF STUDY
^>^— -*
S 1500
5UESX°
10.00
DGUES IN
M
100
200
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
MOVEMENT OF DROGUES
8 WIND TRACK
RUN 2
US DEPARTMENT OF THE INTERIOR
FEDERAL \AATFP PQU-kJTION CONTROL ADMIN
Greot Lokes Region Chicago,Illinois
256
FKjURE 8-16
-------
o
-200-
Y
(m)
-400-
(
RUN 3
Ohr
\
\
c
(
1.5m
* )
DROGUE
I.Ohr
e 2. Ohr
S
1
c
i 200
f 1
; )
2.0h
0.8 hr
r
3Ohr
•*• — -*^
6.1m
400 600
X (m)
800
1000
WIND
100-
Km
50-
0-
15 JULY 1964
__^e-^*-
o.oo^^-* *~e
1
Km
5.
. —
OOirO
i-*-— ^
100
6.1m DROGUES 1
-.e-
0 \
20.0O 1
«-*-
j. 1.5m
lO.OO^-a. X
°v,
END OF STUt
M
DROGUES IN
— «>^
J 15.00 e
200
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
MOVEMENT OF DROGUES a
WIND TRACK - RUN 3
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AUMlN
Great Lakes Region
>.,hici:qo Kl'nc s
• GUHE 8-17
-------
200
Y
(m)
-200
-400
RUN 5
6.1 m
-600
P R 0 G U E S
0-Ohr
I.Ohr
-400 , -200
X(m)
3.0hr
S5.0hr
4.0hr
200
100
WIND
Km
f
J ^
?*0f
1
/
/
/
f O.OO
10.00
7T'
f
/
• 15.00
S\EMQ OF
^ 2O.OO
IN
IS AUG 1964
STUDY
Km
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
MOVEMENT OF DROGUES
a WIND TRACK - RUN 5
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Great Lakes Region Chicago lilino.i
8-18
-------
DROGUES
400
Y
(m)
200
o -A
-200
RUN 6
6.1m
. Ohr
I.Ohr
°20hr
0
0^3 Ohr
-200
l.Ohr
Ohr
1.5m
2 Ohr
C
3 Ohr
-r'g> i .no.s
GURc 8-19
-------
(Hinzc, 38). The adverse Influence of convergences on the dispersion
of the drogues may be partially eliminated in this manner. Figures 8-20
to 8-22 show the results.
When the scale of dispersion becomes large compared vith the
largest turbulent eddies present, its growth comes to resemble molecular
diffusion, i.e., the standard deviation increases vith the square root
of time and a constant diffusivity can be defined. It is, of course,
much larger than the molecular diffusivity. Thus, an effective diffu-
sivity, K«, may be computed from the formula
2
1 /dD s
where D? denotes the variance of drogues at a time t with respect to
their initial positions.
For the,1.5-m drogues in Run 6 and the 6.1-m drogues in Run 3,
however, the t* relationship was not observed during the period of
experiment (see Figures 8-21 and 8-22). Instead, a t3/2 relationship
characteristic of relative diffusion in homogeneous turbulence was
present In the D^-t diagrams. This behavior may suggest that the scale
of the large eddies responsible for the horizontal dispersion of the
drogues was not small in comparison with the group-size of drogues at
the end of the experiment.
The values of Ke computed from (l) are shown in Table 8-2. All
the values of the effective diffusivity lie in a relatively narrow range
from 2.9 X 1(A to 5.5 X 101* ca^/sec, though slightly higher values are
seen at 1.5 m.
The effective diffusivity may also be expressed as the product
of v', the intensity of turbulence and L, the integral scale of turbu-
lence (Hlnze, 38):
Kg = v'L . (2)
The scale L is a measure of the large-scale eddies and could be computed
from knowledge of the Lagrangian velocity correlation. Since the
Lagrangian correlations were unobtainable from the data, we must
260
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261
FIGURE 8-20
-------
RUN 3
x = 1.5 m « = 6.1m
D(m)
1000
500
200
100
20
10
O.I 0.2
0.5 I 2
5 10
STANDARD DEVIATION OF DROGUES WITH RESPECT
TO THEIR INITIAL POSITIONS VERSUS TIME
262
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
STANDARD DEVIATION
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AUMIN
Great Lakes Region Chicugo I iino s
• GURE 8-21
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FIGURE 8-22
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264
-------
estimate L by another method. As previously pointed out, D versus t
exhibits an asymptotic behavior when the scale of diffusion becomes
larger than L. Accordingly, the length-scale L nay be obtained approx-
imately from the D-t diagram as follows. Do, which is the lowest value
of D for which D is proportional to t2, is determined from the D versus
t figures. Provided the distribution of drogues is gaussian, a charac-
teristic length-scale of distribution may be given by 4 Do; that is,
approximately 95 percent of the drogues will be found within the dis-
tance i2 Do from the mean of the distribution. Hence, we take L = k Do.
Having obtained the values of K^ and L, we are now able to com-
pute v1 by (2). The results are summarized in Table 8-2. The intensity
of turbulence differs very little between Lake Michigan and Lake Erie
and also between the depths of 1.5 and 6.1 m. This is primarily due to
the fact that the mean velocity was nearly identical except at 1.5 m in
Run 6, for which no estimate of intensity of turbulence was given
because of the lack of an asymptotic relationship between D^ and t. The
relative intensity of turbulence, the ratio between the intensity of
turbulence and the mean velocity, is also computed (see Table 8-2). The
values range from 10 to 20 percent.
One way of treating relative diffusion is to observe the rate of
increase of mean separation of a pair of drogues with the same initial
separation,S&Q. Figures 8-23 to 8-26 show the root-mean-square separa-
tions versus time for various initial separations. For small initial
separations, the root-aean-square separations increase regularly with
time even in the case where the group of drogues encountered converges
so that suppression or reversal of dispersion occurred. Small-scale
turbulent motions allow a pair of drogues with small separations to
diffuse regularly, provided that the characteristic scale associated
with the convergences or divergences is large compared with the separa-
tion of the drogues. On the other hand, the effect of the convergences
on dispersion is marked for a pair of drogues having large initial sep-
arations. Apparently the large-scale convergences prohibit the drogues
from diffusing regularly. The results of the pair-program suggest that
the scale of the convergences was on the order of 100 meters.
A theoretical treatment of this relative diffusion, presumably
valid for the ideal case of homogeneous turbulence and uniform mean
flow has been developed by Batchelor (k). Dimensional arguments on the
basis of similarity theory of turbulence are applied to three regimes
of relative dispersion. These regimes are characterized by the follow-
ing behaviors with time of the mean square separations of a pair of
drogues which start with a same initial separation,
265
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ar2 =&Q2 H- Ci(Ejg t , t « ti ~ ^02 E-1 (initial)
(3)
2 3
crr = c2 E t _, t » t (intermediate)
, t -» oo (asymptotic)
(5) •
Here GI and C2 are constants of order unity, d ^ is the mean square sep-
aration of a pair of drogues, E is the rate of energy-dissipation per
unit mass through turbulence. For E the following relationship is also
noted (Batchelor, 5):
E = v'3/L*, (6)
with v1 the intensity of turbulence and L* the length scale of the
energy-containing eddies.
Figures 8-27 to 8-30 illustrate the time behaviors of the
increase of the mean square separations for some typical cases. The
Figures show that, in regular diffusion, the ^-relationship predicted
by the theory for the intermediate regime is easily recognizable, in
spite of the expected statistical scatter.
The rate of energy dissipation may be evaluated for the inter-
mediate phase by application of equation (4). Numerical values extracted
from the results are summarized in Table 8-2. At 1.5-m depth, the order
of magnitude of the energy dissipation is the same for the two Lakes,
typical values being 2 X 10"^ caf/aec3. On the other hand, at 6.1 m,
the rate of energy dissipation was higher by approximately an order of
magnitude in Lake Michigan, typical values being 2 X 10'^ cm2/sec3 for
Lake Michigan and 4 X 10~5 cn^/secS for Lake Erie.
The length scale of the energy-containing eddies can be computed
for the case where both values of E and v1 are available. Table 8-2
summarizes the results. A mean value of the scale of the energy-
containing eddies is several meters in both Lakes.
Theoretical treatments of the concentration distribution from an
instantaneous source in the sea have been developed (see papers reviewed
270
-------
271
FIGURE s-27
------- An error occurred while trying to OCR this image.
-------
FIGURE 8-29
------- An error occurred while trying to OCR this image.
-------
by Okubo (5) and Bowden (12). Horizontal dispersion of drogues in a
lake should also be described by those theories with minor modifica-
tions, among which either Joseph and Sendner's theory (46) or Okubo and
Pritchard's theory (58) is a satisfactory model for our purposes.
Both theories predict the temporal behavior of the standard
deviation of the distribution from a point-source as
cr = cut (?)
Pt (8)
wheretuand P represent a diffusion velocity in Joseph-Sendner's theory
and Okubo-Pritchard's theory, respectively. For dispersion of drogues
with a finite initial separation, however, equations (?) and (8) should
be modified as
ffr = u (t + tQ) (9)
p (t + t0) , (10)
where to is defined to be a fictitious time at which we regard the group
of drogues as concentrated at a point.
Figures 8-31 to 8-35 show the standard deviations versus time
for a pair of drogues starting with the same separations. In each Fig-
ure we also draw a theoretical line to fit the data points, so that the
values of w and P may be obtained. The results are shown in Table 8-2.
According to theory, the diffusion velocity is a measure of
intensity of turbulent diffusion. Thus the turbulent diffusion in the
surface layer, say at 1.5 », seems to be more intense in Lake Erie than
in Lake Michigan; but in the deeper layer, say at 6.1 m, the diffusion
velocity in Lake Michigan was higher than that of Lake Erie. In the
sea, for comparison, the diffusion velocity oj ranges from 0.7 to 2.5
cm/sec (58) while Pritchard and Carpenter (60) found w = 0.2 cm/sec in
Conowingo Reservoir.
275
-------
FIGURE a-31
-------
i nn
-------
200
100
(m)
200
100
(m)
STANDARD DEVIATION OF A PAIR OF
DROGUES VERSUS TIME
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
STANDARD DEVIATION
PAIR VERSUS TIME
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Great Lakes Region Chicago,Inino.s
278
FIGURE 8-33
-------
RUN 5 - 6.1m
200
(m)
100
0^°^
0 SJ^
o oooo3°2<
>0
£0 = 20m
>/°'
•
O
O
o ooo '
o'o
°o>^
-^^0°
>o-
2 3
t (hr )
STANDARD DEVIATION OF A PAIR OF
DROGUES VERSUS TIME
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
STANDARD DEVIATION
PAIR VERSUS TIME
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chiccgo,Illinois
279
FIGURE 8-34
-------
<*>
(m)
»
/
RUN 6- 1.5m
Ao = 20m
/
Q
«X~
o o
/
/ o
/ Q
o
/ °
o0o/°
O
3
RUN 6 - 6 Im
JL = 40m
o
012;
t (hr)
STANDARD DEVIATION OF A PAIR
0
G O
200
fr
(m)
1 00
n
4
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
OF
STANDARD DEVIATION
DROGUES VERSUS TIME PAIR VERSUS TIME
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago, Iliirvo s
280
8-35
-------
Noble (56) measured the rate of dilution of a dye patch in the
surface water of Little Traverse Bay of Lake Michigan. A Joseph-Sendner
diffusion velocity of 0.3 cm/sec was selected to obtain a good fit to
the experimental data. The value is in good agreement with the value
at 1.5 m obtained in the drogue study in Lake Michigan.
Csanady (22) studied the dispersion of small floating objects
and of fluorescent dye in Lake Huron at Douglas Point. The scale of
energy-containing eddies was consistently on the order of 10 meters,
ranging from 1* to 20 meters, which is slightly larger than that obtained
in the drogue studies, while an order of magnitude estimate for the
intensity of turbulence was 0.5 to 0.7 cm/sec in the surface layer,
which should be compared with the values O.k to 0.5 cm/sec obtained at
1.5 m in the drogue studies. By using Csanady's data, we can compute
the rate of energy-dissipation from equation (6). The result shows that,
in spite of a wide scatter of individual values ranging from 1 X 10~5
to 6 X 10~^ cn£/sec3, the average value of E takes 3.5 X 10~^ cm2/sec3,
which is quite consistent with the value of E at 1.5-m depth obtained
in the drogue studies.
Csanady (23) also studied diffusion of fluorescent dye from a
continuous source in the western basin of Lake Erie. Two measured dif-
fusivities were 2.6 X 103 and k.k X KP cm2/sec in August. These values
are very small compared with those obtained in the drogue studies. If
we accept a well-known law that the apparent diffusivity is proportional
to the 4/3 power of the scale (Richardson, 63) Csanady's values would
be close to the values of the drogue studies; thus Csanady's values
would correspond to 1.7 X 10^ and 2.8 X 10^ cn^/sec for a scale of 2^0
meters (Do estimated to be 60 meters), while the effective diffusivity
in Run 1 is 2.9 X 10^ cn^/sec for the same scale, and the agreement is
good.
It may, therefore, be concluded that the values of diffusion
characteristics estimated in the present study are consistent with
those obtained in other diffusion studies of the Great Lakes.
Theoretical Models of Pollutant Diffusion from Continuous Sources
The distribution of a pollutant from a continuous source may be
considered as the sum of the distribution of an infinite number of
infinitesimal instantaneous sources discharged in a rapid sequence of
time. Under this assumption, it is possible to superpose a solution for
an instantaneous source with respect to time to obtain the distribution
of concentration for the case of continuous discharge. Thus, in the
case where there is a variable flow, U(t), and where a pollutant is
discharged at a variable rate, Q(t), from a point source at (xOj yo)>
281
-------
the concentration, Sc(x,y,t), at (x,y) at t after initiation of dis-
charge is given by
S(x,y,t) =J S^Ll SlU-x0- J U(t")dt",y-y0,t') dt« , (ll)
c
o t-t
where Sj represents a concentration for instantaneous release from a
point source of unit intensity; D is the depth of water within which
the pollutant is assumed to be mixed uniformly. The depth, D, may be
taken as the mean depth in nonstratified water and as the depth of the
thermocline in stratified water.
Concentration from a finite-sized source can be obtained by
integrating (ll) with respect to xo and yo over the domain of source, A;
t t1
Sc(x,y,t) = J df JJ ax0dy0 £ SI(x-x0- J Udt",y-y0,t' ) ,(l2)
o A t-t1
where q(xo,y ,t') is the rate of discharge of pollutant per unit area
of the source.
The concentration distribution from a finite source becomes
identical with the concentration from a point at sufficient distance
from the source. If the distance is more than several times the size of
the source, the finite source can be regarded, to a good approximation,
as a point source with the same total rate of discharge.
We shall take Okubo and Pritchard's solution for Sj, since the
solution has a mathematical form which can easily be integrated with
respect to time; Joseph and Sendner's solution cannot be integrated
over time to yield an analytical expression. Okubo and Pritchard's
theory gives
c. n. \ c.
3t(J t CO
(13)
282
-------
Substitution of (13) into (ll) provides the concentration distribution
from a continuous point-source with a given release rate Q and field
velocity U. Consider the special case of uniform flow and constant
rate of discharge at xo = yo = 0. Equation (ll) can then be easily
integrated to give
*U) =
2
-a
where f\} - _ : is equivalent to the error function.
The concentration along the central axis of a pollutant plume
(y = 0) takes the following simple form:
Thus the concentration down the central line of plume varies inversely
with x for x "£ xji (l - 2.326 u) , where x^ = Ut and decreases rapidly
at large distances (x > x^ ). At the point x^ (the location of the
center of mass of the first patch released) the concentration is exactly
one-half of what it would be if it decreased everywhere inversely with
x. As time goes on, the inversely linear regime extends farther and
farther from the source. The upstream concentration reduces quite
rapidly with the distance from the source.
The situation where U is not constant, but a function of time, is
identical with the foregoing except that the releases are not uniformly
distributed along the center line of the plume, being more closely
spaced when released near slack water than when released under swift
current conditions. However, this more general case cannot be handled
except by computer. Carter (l?) used the Okubo and Pritchard solution
to compute an exclusion area around a sewage outfall in a tidal estuary.
He considered the constant current model to be adequate under conditions
of variable Q and U, if some care or adjustment was made for the ratio
u/U.
Equation (l4) may also be applied to a nonsteady case after a
change of current takes place in a completely opposite direction. There
we consider only a newly started plume. In fact, the old plume makes
283
-------
some contribution of contamination to the area of concern, but the
amount should be negligible compared with that due to the new plume.
Close to the shore area the effect of boundary must be taken into
consideration. Fortunately, the currents are predominantly longshore
in the regime, so that the method of images may be applied to handle
the proper boundary conditions (Carslaw and Jaeger, l6). Thus, where
there is a constant current parallel to a straight shoreline and a point
source is located at shore, the concentration distribution will be
simply twice that derived from equation (14).
Prediction of Pollution Distribution
The foregoing solutions for a continuous release with a given
rate of discharge contain only the physical parameters u», the diffusion
velocity, and U, the mean velocity. Since the drogue studies provided
information on probable values of these parameters, we may now predict
the concentration distribution of pollutant on the basis of the solu-
tions .
First of all we must clarify our pollution problem. In southern
Lake Michigan east of Chicago, the main sources of pollution are the
Calumet River system discharging into Calumet Harbor and Indiana Harbor.
The area of the drogue studies lay between these two sources. The
closest water intake is located 4.0 km SE of Calumet Harbor and about
6.4 km NW of Indiana Harbor. Other water intakes are situated about
6.4, 9.6, 20.8, and 27.2 km north of Calumet Harbor. The shoreline of
the area can be approximated by a straight boundary. The two sources
of pollution may be regarded as point sources placed at the boundaries
so far as the concentration distributions at these water intakes are
concerned. Distances of these water intakes from the shore are 1 to 4
miles. A depth of 8 m is considered to be the mean depth of the area
studied.
In western Lake Erie north of Cleveland, the main sources of
pollution are the Rocky River and the Cuyahoga River. In addition, a
300-m diffuser of sewage effluent is proposed for the eastern end of
Breakwater. Water intakes are located at about 4 miles NW of the mouth
of Cuyahoga River. Approximate distances from these intakes either to
the Rocky River or to the diffuser are 9-6 km. The shoreline of this
area can also be assumed to be a straight boundary. The size of the
pollutant sources, e.g., the width of the mouth of the Rocky River, may
also be assumed to be small with respect to the distances to the water
intakes. A depth of 12 meters is taken as the mean depth of the area.
In western Lake Erie south of the Detroit River, the main source
of pollution is the Detroit River, which discharges 5,150 m
284
-------
(175,000 cfs) of water under average conditions (Hunt, U2). We will
consider the distribution of pollutant in the shore regime of the State
of Michigan, extending from Pointe Mouillee to La Plaisance Bay; this
region may be assumed to be semi-bounded by a straight shoreline. A
depth of 5 meters is taken as the mean depth of the area. The width of
the lower Detroit River, being about 6.4 km, cannot be regarded as small
as far as the studied area is concerned.
I) Predictions for Lake Michigan (east of Chicago) and Lake Erie (north
of Cleveland).
We shall choose the solution (lit-), multiplying by 2 for the
reflective boundary condition at y = 0, for our predictions. Let us
transform the solution into a nondimensional form by taking b as a rep-
resentative length-scale and the mean velocity, U, as a representative
velocity. Designating u^ = ^/U, x^ = x/b, y1 = y/b, and tx = t/(b/U),
we express the solution as
C =
/_~7~~7 n o^fx^+v 2)A-"I w, v S x .,
i •'i
(16)
S
where C = = — (17)
Q SQ
with S ,,_^_ . (16)
The reference concentration, So, is what we would obtain if a
pollutant released during a time interval T were mixed uniformly
throughout a volume of water, y/jrbttJ/T. Thus, if a river discharges
a pollutant, Sj. being its concentration, at a speed of Ur at the mouth
of width br and depth DT, the reference concentration is given by
b D U
285
-------
A convenient unit of to is a mile for the two areas. Thus,
appropriate ranges of x± and y± for prediction of concentration of con-
taminant will be -5 § x g 20 and 0 § y ^ 10.Two values of ^ are
selected from Table 8-2:1 u^ • 0.2 and 0.4. These represent the two
extreme situations. Figures 8-36 and 8-3? show the steady-state
distributions of pollutant for the cases where ^i = 0.2 and 0.4,
respectively. Concentrations along the shore (yi » 0) and at y, » 2 and
y^ - 4 are shown in Figures 8-38 to 8-40 for the given values of ^i-
It may be noticed that, for the larger ^^, more contamination spreads
laterally, especially in the region of Rrnn.il values of x1? and some
contaminant is found in the upstream region.
For the nonsteady case we shall restrict the computation to the
central line, yj. « 0. Figures 8-4l and 8-42 show the distributions for
various times with u^ » 0.2 and 0.4, respectively, where the unit of
time t* corresponds to the time it takes a pollutant particle to travel
a distance xx » 20 with the speed Uj thus, at the end of t* - 1, the
center of mass of the first patch released has just arrived at x, « 20,
i.e., 20 miles from the source.
II) Predictions for Lake Erie (south of the Detroit River).
A steady-state case for a finite source in semifinite space has
to be treated by numerical computation. The following result is due to
H. H. Carter (unpublished notes).
Take a plane source of length b and depth D extending from the
shoreline perpendicularly into the Lake. A nondimensional form of the
solution is written as
o IP
=S~ = 2 J
2
-y U Xl +yt -yo
x
f Xl 11
! + *<—=— r—TT- Uy^ . (19)
I /„ 2,/. 2 „ 2\\l/2
O
The right-hand side of (19) is handled by machine computation. Thus the
relative concentration at a specific position depends only on the value
of the parameter ^.
Figure 8-43 shows the result of computation of the relative con-
centration for the case MI » 0.2. In the region where XT * 5, the
286
-------
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287
FIGURE e-36
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-------
CONCENTRATION ALONG THE SHORELINE
100
50
20
10
0.5
0.2
O.I
O.I
\
V
\
\
UJ,= 0.2
J,= 0.4
\
50 100
X,
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
RELATIVE CONCENTRATION
US DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago,Illinois
289
FIGURE 8-38
-------
0.5
0.2
O.I
0.01
0.001
0.000)
100
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
RELATIVE CONCENTRATION
AT = 2
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Gr«ot Lok«» Region Chicago,Illinois
290
FIGURE 8-39
-------
0.5
0.2
0 I
0.01
0.001
00001
10 20
X|
50 100
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
RELATIVE CONCENTRATION
AT = 4
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Great Lake* Region Chicuqo Illinois
291
FIGURE 8-40
-------
10
O.I
0.01
0.001
UU, = 0.2
100
20
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
NON-STEADY
AT
DISTRIBUTION
= 0(0.2)
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakit Region Chicago.Illinois
292
FIGURE 8-41
-------
UJ =0.4
0 01
0 001
100
GREAT LAKES - ILLINOIS
RIVER BASINS PROJECT
NON-STEADY DISTRIBUTION
AT y,= 0(0.4)
'U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago,Illinois
293
FIGURE 8-42
-------
to
_j o
-
h-
a
-------
relative concentration differs appreciably from that of a point-source
solution, as may be expected.
Discussion
The main purpose of the drogue studies in Lake Michigan and Lake
Erie was to provide basic information on the scale and intensity of
horizontal diffusion. The use of marked drogues for studying turbulent
diffusion, however, has limitations. One limitation is that the drogue
has a finite size so that small-scale turbulence will not be sensed by
the drogue. The drogue study will, however, obtain information on the
medium-scale and larger turbulence.
Another limitation is that the drogue provides no information on
the vertical component of turbulence. The effect of vertical diffusion,
in particular when combined with vertical shear in the mean flow, on
the mixing of a solute has recently received much attention by various
investigators (Bowden, 13, etc.).
Csanady (22) reported that longitudinal (i.e., along mean cur-
rent) diffusion of a dye patch in Lake Huron was considerably faster
than lateral diffusion and the difference was attributed to the shear
effect. In other words, horizontal diffusion is greatly accelerated,
compared with diffusion in uniform flow, in complex currents. Thus
effective longitudinal-diffusivities due to the shear effect may be
comparable with apparent diffusivities found by purely two-dimensional
experiments, e.g., drogue studies. This may suggest that our estimate
of the horizontal diffusion obtained from our drogue studies should be
regarded as a lower limit for mixing in a lake. In other words, the
drogue study provides upper limits of steady-state concentrations
resulting from the distribution of a pollutant.
Summary
The results of the drogue studies in Lake Michigan and Lake Erie
are summarized as follows:
1. More than half of the groups of drogues showed a regular
pattern of turbulent dispersion, whereas a few groups exhibited a sup-
pression or reversal of diffusion caused primarily by convergences.
2. The movement of the 1.5-m drogues was generally in the direc-
tion of local winds. On the other hand, the 6.1-m drogues moved against
the winds. The existence of vertical shear is obvious. Typical
velocities are k and 2 cm/sec at 1.5 and 6.1 m, respectively.
295
-------
k k
3. An effective diffusivity ranges frcan 2.9 X 10 to 5.5 X 10
cm^/sec.
k. The intensity of turbulence differs little between the two
Lakes. A typical value for the intensity of turbulence is 0.3 to 0.4
cm/sec.
5. In Lake Erie the rate of energy dissipation at 6.1 m is less
Toy an order of magnitude than that at 1.5 a. A similar order of magni-
tude exists between the two Lakes at 1.5-m depth, a typical value being
2 X 10-^ cm2/seC3.
6. The length-scale of the energy-containing eddies is estimated
to be several meters.
7. Diffusion velocities according to the theories of Joseph-
Sendner and Okubo-Pritchard are also computed. The result shows that
the turbulent diffusion in the surface layer seems to be more intense
in Lake Erie than in Lake Michigan.
8. Generally speaking, the values of diffusion characteristics
obtained in the drogue studies are consistent with those obtained by
other methods, e.g., dye studies.
9. Some predictions of concentration of a pollutant which is
discharged continuously are given on the basis of superposition of a
solution for an instantaneous point-source.
296
-------
CHAPTER 9
METEOROLOGICAL STUDIES
Introduction
Meteorological studies were conducted on Lake Michigan in con-
Junction with the work described in other parts of this report, for the
purpose of gaining knowledge about the relationship of lake currents
to weather. The conception, planning, and conduct of these studies were
achieved through a cooperative arrangement between GLIRB Project and
the U.S. Weather Bureau — now a part of Environmental Science Services
Administration (ESSA).
ESSA provided a resident meteorologist on full-time staff duty
with the Project. From the inception of the study through November,
196U, this position was filled by Mr. George Williams (now deceased);
his place was taken by Mr. J. B. Holleyman. Technical guidance on the
part of ESSA came from Dr. D. L. Harris.
The original intent of meteorological studies was to learn
enough about the relationship between winds over the Lake and winds
over adjacent land to be able to forecast lake winds from land observa-
tions, perhaps supplemented by data from ships. In addition, it was
hoped that sufficient knowledge about the response of lake currents to
wind regimes would be gained to permit translation of wind forecasts
into current forecasts. As will be seen, this far-reaching objective
has been only partially achieved to date.
The network installed in Lake Michigan late in 1962 consisted of
33 current meter stations with subsurface temperature recorders attach-
ed. Twenty-two of the stations also had instruments for recording wind
velocity. The network was in operation during 1963 and 1964.
During this time some of the instruments were damaged or
destroyed, thus reducing the size of the network. Figure 9-1 gives the
location of each of the network stations and the type of instrumenta-
tion in operation as well as the period of operation of each station.
Table 9-1 shows the wind data available from the network stations on
Lake Michigan.
Instrumentation and Collection of Data
The network stations in Lake Michigan were oriented in an east-
west line across the Lake and were spaced approximately 32 km apart,
see Figure 9-1.
297
-------
C E A E A
27 28 29 30 31
H
+ Current, Wind, Temperature
o Current, Wind
• Current, Temperature
1963
B 1964
c 1963, 1964
Current 8 Temperature
1963 8 1964, Wind 1963
_ Current 8 Temperature
1963 8 1964, Wind 1964
SCALE
0 25 MILES
40 KILOMETERS
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN
NETWORK STATIONS
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lakes Region Chicago,Illinois
298
FIGURE 9- I
-------
TABLE 9-1
LAKE MICHIGAN WIND DATA
STA-
TION
01
Ok
05
05
07
08
09
10
13
15
15
IT
18
20
20
27
28
30
37
4o
41
47
48
5^
61
62
DEPTH-
HEIGHT
METERS
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
003
LATITUDE
4l°48.0'
42°01.0'
4l°59.0'
4l°59.0'
42°45.of
42°23.0'
42023-0'
42023-0'
42°45.0'
42°44.0'
42°44.0'
43°o8.0'
43°o8.0'
43°o8.0'
43°08.0'
44°03.0'
44°o4.5'
44°04.0'
44°50.0'
1^043. o'
44°39. 0'
45°22.0'
45°12.0'
45°48.5'
45°47.0'
Muskegon
LONGITUDE
87°21.0'
87°20.0'
87°00.0'
87000.0'
87045. 0'
87°25. 0'
86°59.0'
86°38.0'
87°22.0'
86°35.0f
86°35.0'
87051.0!
87°24.5'
86°35.0'
86°35.0'
87°33.0'
87°l4.5'
86°48.0'
87°09.0'
86°31.0'
86°20.0'
8601U.O'
86°02.0'
8401^.5'
86°47.0'
Tower Buoy
FILM NO.
200-
038
334
037
333
346
066
067
070
069
068
337
338
170
141
339
340
341
342
106
345
169
095
086
081
076
371
DATE IN
07/24/63
06/22/64
08/08/63
05/12/64
04/10/64
07/30/63
08/18/63
08/16/63
07/31/63
08/05/63
05/11/64
04/09/64
07/16/63
08/04/63
05/10/64
04/23/64
04/23/64
04/19/64
10/06/63
04/19/64
08/22/63
10/04/63
10/04/63
09/24/63
09/23/63
07/22/64
TIME
CST
1350
1740
1145
1043
1410
1750
1330
1045
1330
1900
1005
0830
1500
1330
1025
1020
1400
0725
2035
1515
1000
1430
1120
1510
1310
1155
DATE OUT
09/04/63
07/06/64
08/26/63
07/06/64
06/16/64
10/16/63
10/17/63
10/17/63
10/18/63
10/17/63
07/05/64
07/09/64
11/10/63
11/07/63
07/05/64
07/10/64
07/10/64
07/04/64
10/29/63
07/03/64
H/05/63
10/31/63
10/25/63
10/30/63
10/29/63
09/24/64
TIME
CST
0900*
1640
1000*
0855
1300
1100
1035
0805
1900
1400
1105
1225
1115
1245
0745
0700
0757
0925
1005
1530
1325
1645
0305
1935
1625
1800
*Estimated
299
-------
TABLE 9-1 (Continued)
LAKE MICHIGAN WIND DATA
STA-
TION
01
04
05
05
07
08
09
10
13
15
15
17
18
20
20
27
28
30
37
40
41
47
48
5^
61
62
COMPUTED
TIME
INTERVAL
BETWEEN
RECORDS
20.02
19.90
20.00
19.16
20.01
20.01
20.02
19-99
19.98
20.00
20.02
20.02
20.00
20.03
20.03
20.00
20.01
20.00
20.01
20.02
20.79
20.00
20.00
20.00
SPEED
SCATTER
EST. OP 1%
07.0
00.0
03.0
05.0
50.0
00.0
04.0
03.0
05.0
00.0
07.0
00.0
00.0
02. 0
05.0
25.0
43.0
02.0
20.0
02. 0
04.0
01.0
04.0
10.0
....
io VANE
READINGS
DIFFER BY
30° 45°
....
00.4
....
02.9
....
03-5
02.9
01.9
02.6
02.5
01.3
00.1
06.0
00.3
01.6
01.7
02.3
03.7
02.6
02.6
01.4
01.5
O2. 4
02.1
01.9
«...
....
....
....
....
....
•»•»••••
*•«»•»•»
....
....
•••»•»•»
....
....
03.0
....
....
• ••*••
• *•••*»
....
....
•»•»•<•
__...
•§•••»«»
•••••M
**»«»*•
....
....
REMARKS
Statical broke loose, recovered
data.
Estimated time recovered.
Speeds too high, recomputed.
Record valid only to 6/16/64, 1300
Short record, light struck unknown
period.
Speeds too high.
Speeds too high.
Speeds too high.
Short record - recalculated.
Speeds high.
.... Unknown or not computed.
300
-------
The network station is a floating buoy which is moored and
untended. The vind instrument consists of a wind vane and three-cup
anemometer which are mounted approximately 3-0 m above the water sur-
face. Subsurface current instrumentation is described in other sections
of this report.
The three-cup anemometer which measures wind speed and the wind
vane which measures the wind direction were developed at Woods Hole
Oceanographic Institution.
Wind observations as well as current observations are recorded
digitally on 16 mm film in the form described by Webster (91). Each
recorded direction gives the orientation of a given Instrument to mag-
netic north and the wind direction relative to the instrument. Thus, it
is possible to determine the true wind direction in spite of the chang-
ing orientation of the buoy system. For the anemometer each revolution
and tenth revolution of the cups were recorded for a 6-second period in
each 20-minute interval.
The anemometer sensitivity varies with the direction of the wind
relative to the supporting framework. The direction calibration of two
of the anemometers used, as determined in the University of Michigan
Department of Meteorology and Oceanography wind tunnel, is shown in
Figure 9-2. The essential features of this calibration agree with that
determined at MET and supplied to GLIRB Project before the calibration
at the University of Michigan was completed. These instruments,however,
were more sensitive than the manufacturer's specifications stated. That
tested at MIT was less sensitive than the specifications.
A field comparison of all of the anemometers, carried out at
Cleveland during the winter of 1964-65, showed that the response of all
instruments after a year or two of field use agreed with that of the
instruments calibrated at the University of Michigan, within an error
of less than 5 percent, when the wind came from a direction nearly
opposite to the vertical support. This was true even of instruments in
which the cup shaft had been bent, presumably as the result of wave
damage.
Directional calibration is readily reproducible to within 5 per-
cent. Thus, corrections may be applied if the wind direction relative
to the buoy is known with sufficient accuracy.
The magnitude of the calibration problem was not fully recognized
until the summer of 1964 and the angle between anemometer and buoy
framework needed to correct the earlier data, was not recorded. In the
summer of 1964 a vane was added to the buoy stations, to keep the ane-
mometer oriented in a favorable direction most of the time (Figure 9-3).
301
-------
Tunnel Speed! 5 Meters per Second
270%°2IO—HI75 140 — 105—70 35
10°
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
CALIBRATIONOF GEODYNE ANEMOMETER
WITH RESPONSE AS A FUNCTION OF
DIRECTION OF SUPPORTING FRAMEWORK
U S DEPARTMENT OF THF INI £ R;.;f
FEDERAL WATER POLLUTION CONTOQl
Great LoKes Region >"''ic<,'i;<. 'Nino's
302
9-2
-------
ALUMINUM PIPE. 1-1/4"-
1.66 O.D. X .140 WALL
LENGTH AS REQUIRED
FIN
96"
12'0"
BATTERY CASE
U.S.GOVERNMENT PROPERTY
KEEP OFF
ANEMOMETER
2'6"
NAVIGATION LIGHT
WIND RECORDER
8'0" DIA.-
I INCH
2.54 CENTIMETERS
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
INSTRUMENT BUOY
TOROIDAL SHAPE
NOT TO SCALE
U S DEPARTMENT OF THE. INTERIOR
FEDERAL WATER PC L LUT ION CONTROL ADMIN
Great Lokti Region Chicago,lllinois
303
f.GURE 9-3
-------
The wind vane is more responsive than necessary for this type of
study. However, ouch of the overshooting of the vane proper is elimi-
nated by an oil-damped vane follower. The dynamic response of the full
wind vane system has not been investigated.
The wind speed is recorded on photographic film as a series of
light pulses spaced according to the speed of the anemometer. The wind
direction is recorded as vane and compass position in Gray Binary code
transmitted to the camera by fiber optic light pipes. The photographic
film was developed and transferred from the film to a low density IBM
compatible magnetic tape in binary format. The data from the magnetic
tape were programmed by computer in three forms: 6-hour averages of
wind directions and speeds, 2-hour envelopes, and histograms. The
averages for each 6 hours (0, 6, 12, and 18 hours) were tabulated to
include the number of observations, direction and speed, and the coef-
ficient of variation of speed, Figure 9-4.
Two directional readings were obtained for each observational
interval and the arithmetic mean of these two was accepted as the true
direction. This process was adopted to reduce the effect of vane over-
shoot. A detailed examination of data samples from several stations
indicated that the error due to overshoot was Insignificant about 90
percent of the time and that this simple correction was sufficient for
most overshoot errors.
Average winds were used rather than instantaneous winds because
it is believed that average winds are more representative of actual
conditions over a period of time. The average values considered were
for periods to conform to the synoptic interval on weather charts.
These values were obtained by converting velocity vectors into com-
ponents along the x and y axes, averaging each component separately,
and computing the vector resultant of these average components.
Two-hour envelopes as a rule smooth out enough of the small-scale
features to make the dominant features of the wind field discernible.
The 2-hour envelopes are obtained by plotting the maximum and minimum
values of wind speed and accompanying direction for each 2-hour period
being considered, Figure 9-5.
The histograms are two-dimensional distributions of wind speed
versus wind direction for the total number of observations for an entire
month, Table 9-4. From these values prevailing direction expressed In
terms of net flow can be calculated by taking the algebraic sum of the
products of wind speed and number of periods it occurs and that of a
wind blowing in the opposite direction.
304
-------
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FIGURE 9-s
-------
Climatology of Surface Pressures and Winds
The day-to-day winds, when combined into averages, give the cli-
matology of the wind field over Lake Michigan and the other Great Lakes.
The winds, Instantaneous and averages, respond to the overall pressure
field of the area. At this point it is veil to discuss the climatology
of the pressure and wind field in the Lake Michigan and Great Lakes area
before presenting the results of the wind study.
Lake Michigan and the Great Lakes in general lie in the path of
several of the major storm tracks that cross the United States. The low
pressure areas that follow these tracks are more frequent In the winter
than the summer, but traverse the Great Lakes area at all tines of the
year.
As a rule, low pressure areas that cross Lake Michigan follow
two main paths. Those that develop in Colorado and the northern Rocky
Mountains move northeastward or eastward across southern Lake Michigan.
They are the winter-time lows. Those that form in the Canadian province
of Alberta move southeastward across the northern United States and
recurve eastward in the Great Lakes area. Lows that follow this track
frequently cross Northern Lake Michigan and occur in the summer as well
as the winter.
The Great Lakes not only lie in the path of some of the major
storm tracks that cross the United States but also contribute to the
intensification of low pressure areas that cross the region. At times
lows intensify rapidly as they enter the western Great Lakes area of
Lake Superior and Lake Michigan. Intensification occurs during the fall
and winter when the water in the Great Lakes is warm in comparison with
the very cold arctic or polar air that may follow Immediately behind
the center of the low. The intensification of the low may be so great
that a major storm results.
Because of the great contrast In the fall and winter between the
warm water of the Great Lakes and the cold arctic or polar air that
crosses the bodies of warm water, low pressure areas may develop occa-
sionally in the Great Lakes area. The probability of actual development
is not great unless upper air conditions are right for the formation of
the surface low. At any rate most of the lows that cross the Great
Lakes develop farther to the west rather than over the Lakes them selves.
The prevailing winds over the Lake Michigan area reflect the
average pressure field. The storm tracks that cross the Lake influence
the average pressure field In such a way that the prevail ing winds are
from the southwest through west.
307
-------
Data Analysis and Discussion
In analyzing the Lake Michigan wind data, the following procedure
was followed:
1. Buoy winds were plotted on the printout charts of Lake
Michigan.
2. Ship observations including ship winds for the standard 6-
hourly synoptic times (OOC, 06C, 12C, and l8C) were plotted.
3. The observations for surrounding land stations for the
standard 6-hourly synoptic times were plotted on the same charts.
k. A pressure and frontal analysis was made on the chart so
that geostrophic winds could be calculated from the pressure gradient.
Strictly speaking, the gradient wind should be calculated, but for the
purpose of this study it was assumed that the gradient wind approximates
the geostrophic wind for the Lake Michigan area because spacing between
observation points is too great to make a detailed analysis of the wind
field to determine if there is a pronounced curvature In the stream-
lines.
The geostrophic wind is defined as a wind that exists in fric-
tionless straight flow when the pressure-gradient force balances the
Coriolis forcej in other words, a wind that flows parallel to straight
isobars.
The gradient wind is the counterpart of the geostrophic wind In
curved flow when the pressure-gradient force balances the Coriolis
force and centrifugal force; in other words, a wind that flows parallel
to curved isobars or streamlines.
The following discussion of results refers to the analysis of
data for the period which has been most thoroughly studied — September
1963.
The computer was used to prepare printout charts with the wind
data entered on them. A sample chart Including a few merchant ship
observations is shown in Figure 9-6. Agreement between the wind direc-
tions observed from the buoy stations and those obtained from nearby
vessels was excellent; differences in direction are usually in a range
of 10 to 20 degrees. The fact that the ship observations are taken at
a higher elevation than the buoy observations, and that the buoy winds
are 6-hour averages, explains the lower speed values of the buoy winds
as compared to ship winds.
308
-------
Printout chart with buoy winds, ship winds, and
observations at land stations for 06 C Septem-
ber 2, 1963.
62
LEGEND
NN DD
ddjvv
NN
DO
dd
w
TT PPP
wwo
ddjvv
TT PPP
wwo
SCALE
0 40 MILES
60 KILOMETERS
Buoy Station
Number of Observations
Coefficient of Variation of Speed
Wind Direction
Wind Speed
Ship Station
Land Station
64194
GREAT LAKES- ILLINOIS
RIVER BASINS PROJECT
LAKE MICHIGAN PRINTOUT
U.S. DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN.
Great Lakes Region Chicago , Illinois
309
FIGURE9-6
-------
In the investigation of the relationship of buoy and ship winds
to geostrophic winds, data were examined for station 18 in the southern
basin of Lake Michigan, and for station kl in the northern basin. Ship
observations were selected for points as close to these stations as
possible. For each of the two stations the data were divided into two
groups according to stability of the air mass. For this purpose, an air
mass with a lapse rate less than 6°C between water surface and the 850-
millibar (mb) was considered to be stable; and an air mass with a cor-
responding lapse rate of 6°C or more was classified as unstable. For
estimating the lapse rates, the surface temperature was assumed to be
approximated by surface water temperatures obtained from municipal water
intake records; temperature at the 850-mb level was interpolated from
meteorological records. The 850-mb level is approximately U,000 feet
above the Lake.
Table 9-2 shows the average ratios of buoy and ship wind speeds
to geostrophic winds over Lake Michigan for the month of September 1963.
In all cases shown, the ratios are less at station kl than at station
18, for reasons that have not been determined. The ratios are larger
for a steep lapse than for a small rate. This is to be expected, since
there is more mixing between the lower and middle layers of the atmos-
phere in unstable than in stable situations. The range of values shown
for steep lapse rates is 0.529 to 0.771, and for small lapse rates 0.481
to 0.585.
Table 9-3 shows the average clockwise deviation of buoy and ship
wind directions from geostrophic wind directions over Lake Michigan for
the same period. In all cases shown, the deviation at station kl is
consistently greater than at station 18. For steep lapse rates the
deviation of buoy and ship winds from geostrophic winds is less than
for small lapse rates. The range of values shown for steep rates Is
lk° to k2° and for small lapse rates 39° to 57°, respectively.
Statistical tests were made to determine whether the variations
in the relationship between observed and geostrophic winds for stations
18 and kl and for small and steep lapse rates were significant. The
tests were inconclusive for the difference between stations, but showed
that there is a significant difference in the wind relationship for
small and steep lapse rates.
Charts for the current records, constructed on the same basis
and for the same time periods as the wind charts, are not very enlight-
ening as to relationship of Lake currents to concomitant winds. The
rotary currents shown in Figure 9-7 (plotted from 6-hour means) fre-
quently dominate the record, but the phase of rotation may vary with
depth at one station and with horizontal distance at one depth. Numer-
ical filters have been used in an attempt to eliminate this inertial
310
-------
TABLE 9-2
RATIO GF BUOY AND SHIP WIND
SPEEDS TO GEOSTROPHIC WHO SPEEDS OVER
LAKE MICHIGAN FOR SEPT. 1963
STEEP LAPSE RATE
Buoy
#18 #41
0.629 0.529
Ship
SMALL LAPSE RATE
#18 #41
0.771 0.716
Buoy
#18 #41
0.481 0.385
Ship
#18 #41
0.589 0.523
TABLE 9-3
AVERAGE DEVIATION OF BUOY AND SHIP WIND
DIRECTIONS FROM GEOSTROPHIC WIND DIRECTIONS OVER
LAKE MICHIGAN FOR SEPT. 1963
STEEP LAPSE RATE
SMALL LAPSE RATE
Buoy
Ship
Buoy
Ship
#18
14°
#41
26°
#18
17°
#41
42°
#18
42°
57°
#18
39°
45
311
-------
TABLE 9-4
WINDS - STATION 5, AUGUST 1963
HISTOGRAM
DIRECTION
IN DEGREES
0
30
60
90
120
150
180
210
21*0
270
300
330
7
51
71
67
105
130
121
138
163
103
78
38
69
SPEED
19
81
91
to
32
15
21
44
51
32
14
10
18
AVERAGE IN KNOTS
32
30
15
0
5
1
0
7
5
1
1
5
14
45
6
0
1
1
0
0
1
1
0
0
4
4
58
0
0
0
1
1
1
0
2
0
0
0
0
NUMBER
168
177
108
144
147
143
190
222
136
93
57
105
TOTALS
1,134
449
84
18
1,690
312
-------
STATIONS DEPTH 10 METERS
AUG. 1-9,1963
320
280
240
LAKE MICHIGAN
SCALE
0 5 10 MILES
I I I I I I I I I I
I I I
0 5 10 15 KILOMETERS
120 160 200
40 80
cm/sec
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
CURRENT TRAJECTORIES
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Grtot Lok«t Rtgion Chicago,Illinois
313
FIGURE 9-7
-------
period from a few short samples of data, but further study is needed to
understand the significant features of the filtered data.
Lake Breeze Phenomenon
At times the lake breeze phenomenon is pronounced along the
shores of Lake Michigan. The wind data obtained from the buoys on Lake
Michigan help to clarify some details of the phenomenon. An example of
the lake breeze is given here for August 20 and 21, 1963- On those days
a large weak high was centered over the Ohio Valley with a weak pressure
gradient extending over the southern part of Lake Michigan, northern
Illinois, southern Wisconsin, and lower Michigan. Figures 9-8 and 9-9
show the weather charts for 12C (noon, Central Standard Time) August 20
and 21.
At 12C on both days, temperatures at the land stations near the
southern Lake Michigan shores ranged from around 72°F to 85°F. The Lake
temperature on August 20 was 63°F at Chicago and 50°F at Muskegon. On
August 21, Lake temperature was 56 °F at both Chicago and Muskegon. With
the Lake cooler than land the air in contact with the water would be
expected to be cooler than the air over land, thus making ideal condi-
tions for a lake breeze.
Two-hour envelopes of wind direction are presented in Figures
9-10 and 9-11 for stations 8 and 18 on August 20 and 21. At station 8
on the envelope for the first day, the wind is blowing from the south-
west through west until 10 o'clock. Then it shifts to southeast and
remains from that direction until 22C when it shifts to the southwest
and west for the rest of the night. The cycle is repeated on the second
day but the shift back to the southwest begins at about l8C rather than
22C. Station 18, Figure 9-11, shows the same type of cycle of wind
directions as station 8 for the two days.
The relationship between geostrophic and observed winds gives a
basis for a method of forecasting winds over the Great Lakes. Unfortu-
nately, the relationship between winds and lake currents is not as
straightforward.
A Comparison of Lake Wind to Land Wind
Wind data at Lake station 8 were compared to those from Midway
Airport, Chicago, Illinois for the month of September 1963- Six-hour
average winds for the two locations were compared over the 1-month
period.
Figure 9-12 shows the directional relationship between the sta-
tions. Disregarding occasional periods of calm, the absolute value
(without regard to whether clockwise or counterclockwise) of the
-------
140° I2O° IOO° 80
l-)|00«f **•
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SURFACE WEATHER MAP AT 1200 CST.
TAKEN FROM DAILY WEATHER MAP
U.S.WEATHER BUREAU AUGUST ao.1963
u s r>t PAKTMF N r of TMf ir.rf RIOR
R POL ^bT^ON CONTROL AOMIN
FIGURE 9-8
-------
140° 120° 100° 80
GREAT LAKES ILLINOIS
RIVER BASINS PROJECT
SURFACE WEATHER MAP AT 1200 C ST.
TAKEN FROM DAILY WEATHER MAP
U.S WEATHER BUREAU AUGUST 2 1,1963
U S DEPARTMENT OF THE INTERIOR
WATER POLLUTION CONTROL AOMIN
Great Lakes Region Chicago.Illinois
HGURE 9-9
-------
TWO HOUR SPEED-ANGLE ENVELOPE
AUGUST 20-21,1963
FILM- 20066 STA 8 DEPTH 0 TIME INTERVAL - 20
.0
72 0
ANGLE IN DEGREES
144.0
216.0
288.0
I
360.0
oo
02
04
06
08
10
12
14
P 16
in
o is
20
» 22
t- 00
02
04
06
08
10
12
14
16
18
20
22
AVERAGE CURVE
O V o
OX O
o s o
-'o
o
o\ o
O
o\ o
O \ O
0^
o ^
o \ o
o ) o
o
o^
o s'' o
317
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
TWO HOUR SPEED-ANGLE ENVELOPE
U S DEPARTMENT OF TMF iNTEKiOP
WATER POLLUTION CONTPOi A.iM'N
Greot LoNes Region Ci ICLT :. no -j
i- r,u^t 9-10
-------
TWO HOUR SPEED-ANGLE ENVELOPE
AUGUST 20-21,1963
oo
02
04
06
08
10
12
14
P 16
C/>
O 18
20
^ 22
p oo
02
04
06
08
10
12
14
16
18
20
22
FILM- 20170 STA. 18 DEPTH 0 TIME INTERVAL - 20
ANGLE IN DEGREES
0 72.0 144.0 216.0 288.0 360.0
Q x O
O X_ O
O ^ O
O _^> O
O/ O
0/0
O/O
O .^0
o \o
o ^
O \ O
0s*,. O
o /a
o I o
o I o
O \ O
AVERAGE CURVE
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
TWO HOUR SPEED-ANGLE ENVELOPE
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Great LoNes Region '"hiccgo l.i.no.s
318
FIGURE 9-M
------- An error occurred while trying to OCR this image.
-------
deviations averaged 32 degrees. The algebraic average deviation, con-
sidering a clockwise deviation of lake wind to land wind as positive,
was minus 17 degrees; that is, on the average the lake wind direction
was deflected counterclockwise from that over Midway Airport. As a
further indication of prevailing conditions during the month examined,
the deviation of lake wind to land wind was either zero or counter-
clockwise some 80 percent of the time.
Wind speeds during September were higher over the Lake than over
land, as expected for summer and fall. The reverse is probably true for
late winter and spring, but no Lake records are available. The average
wind speed at Midway was 16.0 km/hr (lO.O nrph) and at station 8 it was
19-6 km/hr (12.1 mph), or IT percent higher over the Lake. Figure 9-13
indicates close agreement in the lower speed to about 10 km/hr and the
difference widens until kO km/hr where there appears to be a break.
There are too few numbers beyond 40 km to estimate the trend.
Although winds do not alter current directions in mid-lake dur-
ing the summer period, there is a relationship between wind speed and
increased current speeds, even at great depths (Verber, 89).
Wind Spectra
This section covers the wind spectra computed from Lake Michigan
wind records collected during the summers of 1963 and 196k. Table 9-5
summarizes the wind spectra analyzed. In this table each station has
listed: the film number of the record, the length of each record, the
orientation of the axis for the velocity component computation, and
whether or not the station is near the shore. Speed spectra calcula-
lations were not made after test cases showed that estimates were unreli-
able.
The following stations from the summer of 1963 showed a diurnal
peak around 24 hr in one or both of the velocity components: Stations
1, 8, 10, 13, 15, 20, and kl. Stations 5 and 30 have no significant
peaks. Station kO (Summer 1964) has a diurnal peak.
The semidiurnal oscillation is evident in records from stations
8, 10, 13, 15, 20, 30, 40, and kl. Figure 9-14, station 13, illustrates
an example of wind spectra.
Long period oscillations around 115 hrs are evident and may rep-
resent some kind of average frequency of meteorological disturbances.
Whether they are physically present is still unknown, but they fit with
the energy peaks.
320
------- An error occurred while trying to OCR this image.
-------
TABLE 9-5
LAKE MICHIGAN WIND SPECTRA DATA
DATES OF
SPECTRAL RECORDS
VELOCITY
SPECTRA AXIS
STA-
TION
01
05
08
10
13
15
20
30
40
41
FILM NO.
200-
038
333
066
070
069
068
141
342
345
169
START
OT/24/63
05/12/64
07/30/63
08/16/63
07/31/63
08/05/63
08/04/63
04/19/64
04/19/64
08/22/63
ORIENTATION NEARSHORE
END (Y AXIS) STATION
09/04/63
07/06/64
10/16/63
10/17/63
10/18/63
10/17/63
11/07/63
07/04/64
07/03/64
11/05/63
0-180
30-210
30-210
170-350
160-340
0-180
0-180
0-180
30-210
0-180 X
OFFSHORE
STATION
X
X
X
X
X
X
X
X
X
322
-------
100
50
HOURS
20 16.7
I03
10'
a.
6
N^
f\J
o
UJ
tn
10
Y AXIS -160° - 340°
8 4
100 50 33 25 20
OF OBSERVATIONS- 5658
16.7
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
WIND
SPECTRA
- STA. 13
OF COMPONENTS
LAKE MICHIGAN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AuViN
Great Lakes Region Chiccgo ' ,IPO s
323
FIGURE 9-14
-------
Summary
The meteorological studies have revealed relationships between
geostrophic winds and observed winds over Lake Michigan; and between
winds over the Lake and winds at adjacent land stations. This provides
a basis for forecasting the speed and direction of wind at desired
specific locations over the Lake. Unfortunately this cannot, with pres-
ent knowledge, be translated into forecasts of water current velocity.
While there is no doubt that the wind is the primary force causing
motion of Lake Michigan water, the relationship is a complex one, the
water motion being modified by such factors as variations in atmospheric
pressure on the Lake surface and the earth's rotation. Once set in
motion by primary wind forces, the water velocity at a particular place
and time will be a function of antecedent conditions perhaps far removed
in time, and will exhibit internal wave patterns corresponding in peri-
odicity to seiches and the Lake's inertia! period. It is believed that
further study can yield a solution which will permit formulation of a
mathematical model Incorporating all of these factors, and make possi-
ble the forecasting of Lake currents.
324
-------
CHAPTER 10
CORRELATION OF WHO, CURRENT,
AMD TEMPERATURE IN SUMMER
by
Clifford H. Mortimer and James L. Verber
During the Project studies in the summer of 1963 the University
of Wisconsin was conducting specific internal wave studies in the region
between Milwaukee, Wisconsin and Muskegon, Michigan. These studies,
combined with Project studies, shed new light on the relationships among
wind, currents, and temperature.
At the University of Wisconsin, Dr. C. H. Mortimer was given a
"Visiting Professorship" for the opportunity to test hypotheses con-
cerning Internal waves and associated water movement in central Lake
Michigan. This work was supported by an Office of Naval Research con-
tract, Nonr-1202 (22), and some results of current measurements at mid-
lake anchor stations were outlined in Chapter 6. In addition, with
facilities provided by the Grand Trunk Western Railroad Company, tem-
perature distribution was measured from the Company's vessels on 80
crossings between July Ik and August 30, 1963. Apart from occasional
gaps due to change of vessel or instrument loss, the 127-km long section
was monitored on consecutive crossings with bathythermograph (BT) casts
every 2 km.
During the whole period the thermocline showed oscillations in
depth, often quite large, and often combined with or following strong
upwelling on one shore and downwelling on the other shore after wind
disturbances. For instance, two major storms, from the north on August
13 and 17 (see Figures 10-5 and 10-6), produced a strong downward tilt
of the thermocline on the western shore and upwelling on the eastern
shore which persisted for several days. The latter storm also generated
internal waves of large amplitude, illustrated by two consecutive tem-
perature sections in Figure 10-1. These pictures are not, of course,
synoptic, as the ferries take roughly six hours to cross the Lake; but
the standing nature of the internal waves is made evident in Figures
such as 10-1 by the fact that on consecutive runs the ferries normally
cross the midlake point at intervals of about 8 hours, i.e., approxi-
mately one-half of the local inertial period (17-55 hours). Internal
standing waves of near-inertial period should, therefore, show a change
in sign of wave slope near the midlake position and this was frequently
observed on successive crossings (Figure 10-1). The change in sign of
the thermocline slope at about 70 km from Milwaukee suggests that there
was a node in that region. This is confirmed and more strikingly
325
-------
(Mortimer, unpublished,April, 1967)
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
TEMPERATURE DISTRIBUTION
BETWEEN MILWAUKEE, WIS.
AND MUSKEGON.MICH.
USDEPARTMFNT Jf Tuf iNTfi ,»
WAUR POLLUTION CONTC'OL AuVIN
Grant LaHes Region ^'HCO^J I ''n '-
326
-------
demonstrated in Figure 10-2, in which the 10° isotherm (representing
approximately thermocline depth) is plotted for nine consecutive cross-
ings over the interval August 19-22. The Figure shows a definite and
persistent node in midlake at 66 km from Milwaukee, with less clear
indications of at least two other nodes. The most likely interpretation
of this Figure is in terms of a combination of transverse standing waves
of several nodalities, with first and third predominating and perhaps a
fifth also present. Odd nodalities must have been preferred, because
of the way in which the wind stress tilted the thermocline down on one
shore and up on the other; and the midlake nodes of each wave probably
coincided to give the clear picture at 66 km. Coincidence elsewhere
would not be expected.
Having demonstrated the generation of a large amplitude trans-
verse standing wave pattern, it will be helpful to recapitulate briefly
Mortimer's 1963 predictions (5*0 concerning the nature of internal waves
in central Lake Michigan, as illustrated in Figures 10-3 and 10-U, for
rectangular models of constant depth, rotating counterclockwise. The
wave surfaces shown in those Figures can be envisaged, either as a water
surface or as a thermocline interface between two homogeneous layers of
differing density, in which case the (highly) generalized currents,
associated with the waves, are shown for the lower layer (hypolimnion).
The corresponding currents in the upper layer will be exactly opposed
in direction; and the speed ratio will be the inverse of the depth ratio
of the two layers.
In a narrow channel (Figure 10-3, upper part) a Kelvin wave is
dominant, and this is also true near the shore in the other wide-channel
models. The currents are constrained to run parallel to the shore, and
the response to rotation takes the form of an exponential decrease in
wave amplitude and current speed along a line normal to the shore. For
the internal Kelvin wave case in Lake Michigan, this amplitude falls to
a negligible value 10 km or so away from the shore. Internal Kelvin
waves are, therefore, essentially shorebound. At greater distances
offshore, where the constraints of the boundaries can no longer be
"felt", the response to rotation, in a semi-infinite sea of constant
depth, Figure 10-3, lower part, is a Sverdrup wave, in which the wave
crests are horizontal but in which the currents rotate (clockwise in
the northern hemisphere).
Lake Michigan, however, is bounded; and just as in lakes small
enough for rotational effects to be neglected, seiches are set up by
wave reflection from opposing shores. In the special case, only possi-
ble in an infinitely long channel (Figure 10-U, upper part), two
equivalent Sverdrup waves, of equal amplitude, traveling in opposite
directions normal to the side of the channel, produce a standing wave
327
-------
kilometres from Milwaukee breakwater
80 80
100
120 127
LAKE MICHIGAN 1963- TEMPERATURE DISTRIBUTION, PC
IN THE MILWAUKEE-MUSKEOON SECTION
LEGEND
A-Sta. 17, II.5Km. North of Ferry
Track
B-MV'fcisco','l2Km.Northof Ferry
Track
C- Sta. 20,6 5Km.South of Ferry
Track
(Mortimer unpublished,April, 1967)
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
DISTRIBUTION of 10° ISOTHERM
MILWAUKEE to MUSKEGON
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Great Lak** Region Chicago.Illinois
-IGURE 10-2
-------
(A)
LEGEND
A - Qualitative Representation of A
Single Kelvin Wave
B - Qualitative Representation of Part
of A Semi- Infinite Rotating Sea with
A Kelvin Wave
After Mortimer, 1963(54)
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
QUALITATIVE REPRESENTATION of
KELVIN and SVERDRUP WAVES
U S DEPARTMENT OF THE INTERIOR
fEDERAt WATER POLLUTION CONTROL AOM'N
Great Loktt R«gion •"tucc.jo i, rn.- o
329
FIGURE 10-3
-------
WAVE
(B)
LEGEND
A.- Qualitative Representation of
Transverse Standing Waves
with Sverdrup and Kelvin Waves
B.- Qualitative Representation of
Standing Pomcare Waves
After Mortimer, 1963 (54)
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
TRANSVERSE STANDING.KELVIN,
SVERDRUP and POINCARE WAVES
Li S DEPARTMENT OF THf
FEDERAL WATER POLLUTION CONTROL AuWlN
Great Lakes Region Chicogo I mu s
330
"•.GURE 10-4
-------
WIND AT STATION 18 — LAKE MICHIGAN
30
SE
AUG.
5
10
12
14
15
IW
NW-SE
SE
SW
NW
SW»SE
W*N£
SE
NE
-SW
NE
N»-S
2O
20-
*
13
10
2CH
SE
-SW
WNW
MILWAUKEE
ssw
ssw-
sw
JL
IMNE
SSE-
ESE
NNE
SW
SSE -
SWi
NNW-
NNE
il III II
SE
NW-
WNW
S-
0-
GRAI^O RAPIDS
ssw-
NW
1J1
NW-
NNW
11
ssw-
wsw
wsw
NW
IllI
WNW
W
WSW-
WNW
SSE-
SSW
WSV
WNWf
NNW
W-
WSW
O-
5 •
SE-fSW
0-
W-NIW
CHICAGO -
SW
MIDWAY
SW NE-E
NE
NE
NNW-
E
SW
NW-
NNE
NNE
W-NW
CHICAGO -
r _
OH
NNE
SSE
WNW
i
O'HARE
ssw
NNE
NE
INNE
NNE
I
8
10 II
12
14 15
AUGU ST 1963
SPEED IN KNOTS
LAKE WIND - 2HOUR ENVELOPES
LAND WIND - HOURLY
ONLY SPEEDS OVER 9 KNOTS WERE
CONSIDERED AND PLOTTED ON A SQUARE - LAW
SCALE TO APPROXIMATE WIND STRESS
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
COMPARISON OF LAKE
.AND LAND WIND SPEEDS
U S DEPARTMENT OF THF INTERIOR
FEDERAL WATER POLLUTION CONTROL
Great Lakes Region Chici q••> l>
331
FIGURE 10-5
-------
WIND AT STATION 18 — LAKE MICHIGAN
S-SE
30
17
19
AUG
20
21
22
23
24
25
26
27
28
30
N-
NE
SW<
SE
20
S£
SE
SW
SW-SE
S-NE
NE
SE -- SW
NW»SW
W-»-NE
IS
10
0
J 11
II'II
20-
10-
20-
15-
10-
20-
15-
0-
5-
10-
ENE-
ESE
NE-E
AUKCI:
ESE-
SE
SW-
SSW
SW-
NNE
NE
ESE
SSE
-SE
WSW
SW-
S
GRAND RAPIDS
WSW
NW
WSW-
W
wsw-
w
JhUL
wsw-
WNW
wsw-
w
NE-E
ill!!!
ENE-
ESE
SSE-
WNW
W-
WSW
NW -
WNW
SW
CHICAGO -
NE
M10VU
W
SW
SW
NE
NE
H I
ssw
i.I
-SW
NW
NW
CHICAGO -
SSE NNE
OH ARE
NE-
ENE
WNW
NW .
mi
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
AUGU ST 1963
SPEED IN KNOTS
LAKE WIND-2HOUR ENVELOPES
LAND WIND- HOURLY
ONLY SPEEDS OVER 9 KNOTS WERE
CONSIDERED AND PLOTTED ON A SQUARE - LAW
SCALE TO APPROXIMATE WIND STRESS
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
COMPARISON OF LAKE
• AND LAND WIND SPEEDS
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AuViN
Great Lake* Region Chic< 30 i. nu s
332
FIGURE 10-6
-------
system with horizontal wave crests running along the length of the
channel. Because of the boundary condition, that the transverse com-
ponent of flow must always be zero at the shores, only a discrete num-
ber of waves can develop across the channel.
If the channel is not infinitely long but has ends, then Sverdrup
wave reflection will occur at these boundaries also; and a second dis-
crete set of standing waves will be set up, this time along the channel
and again meeting the boundary condition that there shall be no flow
normal to the ends. The combination of this longitudinal set with the
transverse set results in a cellular pattern of standing waves (Poincare
waves), and the dimensions of the cells are determined by the wave
lengths in the longitudinal and transverse directions. A portion of
such a system, representing the central part of Lake Michigan, is shown
in the lower part of Figure 10-k. This presents a model of thermocline
topography and also indicates part of a long shorebound Kelvin wave
close to each "shore". A and B represent water intakes, one of which
is above the "thermocline", i.e., in the warm upper layer while the one
on the opposite shore is in the lower cold layer—a common situation in
Lake Michigan.
Figure 10-4 depicts a system with a rather high number of nodes
across the channel, whereas Figure 10-2 suggested that the number
(normally an odd number) is small; 1, 3, or 5, perhaps in combination.
If, as seems likely, the rate of frictional damping increases with
nodality, the uniuodal pattern may be expected to persist longest after
a wind disturbance. This will be particularly true of the currents.
With decrease in nodality, more of the internal wave energy appears in
kinetic form (currents) and less as potential energy (thermocline dis-
placement) .
On the assumption that a combination of standing Poincare waves
and nearshore Kelvin waves is an acceptable model for central Lake
Michigan, the relationships between thermocline displacements, current
direction, and speed are sunniarized for the uninodal case in Figure
10-15. For the elucidation of these relationships we are indebted to
Dr. M. A. Johnson of the National Institute for Oceanography, Wormley,
Surrey, Qigland. For conditions near the ends of Lake Michigan, inter-
pretation in terms of models other than rectangular may provide abetter
fit with the observations; for instance, a semicircular portion
(involving Bessel functions) closing the end of a long channel, or an
elliptical basin of high eccentricity (involving Mathieu functions).
The observations on the Milwaukee-Muskegon section coincided in
time (summer 1963) with the maximum deployment of the Project's record-
ing instruments in the Lake. It is, therefore, worthwhile to see how
far each set of observations can aid in the interpretation of the other.
333
-------
The positions of the stations considered, for which both temperature
and current data were available and which were closest to the railroad
ferry track, are given in Table 10-1. The stations vere: 17, 1*2
(Mortimer's anchor station), and 20, near the ferry track, and station
15, ^9 km to the south of it.
Local wind observations were provided by station 18 (wind data
only) in the form of 2-hourly envelopes of maximum and minimum readings.
These are compared (Figures 10-5 and 10-6) with hourly Weather Bureau
readings of six land stations. In an attempt to represent the magnitude
and timing of the main wind stresses, wind speeds below 9 knots were
ignored and higher speeds were plotted on a square-law scale. The prin-
cipal wind directions are indicated on the Figures. These show good
agreement among the stations in the timing of the wind disturbances,
but speeds appear to be considerably higher at station 18 than at the
land stations. It should be pointed out, however, that the 2-hourly
envelopes at station 18 include, by definition, extreme values, whereas
hourly readings at the land stations will not normally include extreme
values. The square-law presentation considerably exaggerates this dif-
ference. Nevertheless, there seems little doubt that speeds were higher
over the water than over land.
Detailed comparison between wind at station 18 and current and
temperature fluctuations at stations 15, 17, and 20 were compiled (Fig-
ures 10-7 through 10-1^) for 15-day intervals within the period July 16
through August 30, 1963. The Figures display the following variables:
temperature at two depths for stations 15 and 17 and at four depths for
station 20; and, for all stations, 2-hour envelopes of current direc-
tion and speed at one depth. These take the form of vertical lines
Joining the extreme high and low values and covering the range of vari-
ation in current direction for each 2-hour period. Current directions
are those toward which the current is flowing (and this also applies to
Figure 10-15) and wind directions are those from which the wind is com-
ing. The Figures, which present a lot of information in compressed
form, show many significant correlations and points of interest, only a
few of which can be touched upon here.
Station positions are listed in Table 10-1. Of the Project's
two stations near the railroad ferry track, one, station 17, was close
inshore and the other, station 20, although not in mldlake, was more
representative of open lake conditions. The same can be said of station
15, some k-9 km south of the track.
As expected from its location k km from a N-S shore, station 17
frequently alternates between southerly and northerly currents, strongly
dependent on wind direction and showing a fairly rapid response to wind
changes, for instance August 22-26 (Figure 10-11). However, in spite of
shore proximity, there were quite long intervals of rotary currents
-------
TABLE 10-1
POSITIONS OF STATIONS
STATION
LATITUDE LONGITUDE
°N °W
DISTANCE (KM)
FROM W SHORE
DISTANCE (KM) FROM
MILWAUKEE-MJSKEGON
RAILROAD FERRY TRACK
17
18
(wind records
only)
(MV Cisco
anchor station)
20
15
87°51'
87°25I
87°08'
86°32'
86°36'
k
39
63
FROM E SHORE
18
31
12 N
12 $
6 Q
49 s
335
-------
SP
30
oc
20
to-
10°
5°
N^
EED IN KNOTS
AUG.
1
NW*SE
r_
1 hH
40
20
0
T
A
C
1
(|
SE
2
SE
.I
TEMPt
WIND AT STATION 18 - L A K
3
SW
111 III
4
NW
II 1
5
SW-SE
III 1
RATL>f
i
E —
15m -
30m-
DEOR
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CURRENT SPEED IN CENTIMETERS/SECOND
-
l
Jl
Mil
1
.1.1
1 ' 2 3 4 5.6 7
I>'I|.H,I i,
8
EMPERATURE AND CURRENT AUG.- 963
to
T STATION 15
T
URRENTS AT 22 m DEPTH
'WO HOUR ENVELOPES - WIND S CURRENT
F
G
1 *.
,,. I,,,,
• •1 '
f I-
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
IND AT STATION 18 COMPAREDTO
EMPERATURE a CURRENTS - STA. 15
U S DEPARTMENT OF THF INTERIOR
EDERAL WATER POLLUTION CONTROL AuNlN
reot Lakes Region i"hic(jgn ,IPC s
336
10-7
-------
SPEED IN KNOTS WIND AT
S»SE
SWi
SE
10- ',
IK! K/\
15 Jlf V
5°
Vv
N't (• • -
W '
17 18
N*NE SE
'l
1
19
SE -
ill
pfMPtJRATUfJE —
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AUG.
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l"
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U,
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STATION 18 - LAKE MICHIGAN
21
es
1
'/
C.
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ENT
22
SW»SE
23 2
S»NE •*
ME
1
, A
-
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"
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IENT
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SPEED
1 H
il
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i
16 ' 17 18 19 20 . 21 22
HOURLY
15m
\fA i
v r
MV\rv
ON — Dtp
nil
i .' ll ,
IN CEN
1 T
23
TEMPERATURE AND CURRENT AUG. - 963
• ui
AT STATION 15
CURRENTS AT 22 m DEPTH
TWO HOUR ENVELOPES - WIND 8 CURRENT
F
C
4 25
E NE
1
iia
26
E
I , 1
V V
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TIMETERS/SECONO
(
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l
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l
^
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
/IND AT STATION 18 COMPARED TO
TEMPERATURE S CURRENTS - STA. 15
U S DEPARTMENT OF THE iNlLRiOR
EDERAL WATER POLLUTION CONTPOl AOMIN
reot LoKes Region CMCI •}•' >n^ i
337
t 10-8
-------
SP
30
20-
15-
10-
15'
CO
N_
EEO IN KNOTS WIND AT
17
S
if
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STATION 18 - LAKE MICHIGAN
Jl
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23
E
DEGREES
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IN CENTIMETERS/SECOND
"'", ,
17 18 19 20 21 22 23 24
JULY — 1963
TEMPERATURE AND CURRENT
AT STATION 17
CURRENTS AT 15m DEPTH
TWO HOUR ' ENVELOPES — WIND & CURRENT
Hill.
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'I'll,,,,
r<.
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25 26 27 28 29 30 31
GREAT
RIVER
LAKES — ILLINOIS
BASINS PROJECT
WIND AT STATION 18 COMPARED TO
TEMPERATURE 8 CURRENTS — STA. 17
U S DFPARTMENT OF THF INTERIOR
FEDERAL WATER POLLUTION CONTROL AuWN
Great Lakes Region Ch,c<-g-. n« -,
338
10-9
-------
SP
30-
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10°
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TEMPERATURE AND CURRENT
AT STATION 17
CURRENTS AT 15 m DEPTH
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6
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
/IND AT STATION 18 COMPARED TO
"EMPERATURE 8 CURRENTS - STA 17
U.S. DEPARTMENT OFTHE INTERIOR
EDERAL WATER POLLUTION CONTROL AOMIN
r«ot Lake* Rtglon Chicago, Illinois
339
10-10
-------
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AUG. — 1963
EMPERATURE AND CURRENT
T STATION 17
lURRENTS AT 15 m DEPTH
WO HOUR ENVELOPES - WIND 8 CURRENT
i'l.l I''
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GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
WIND AT STATION 18 COMPARED TO
TEMPERATURE & CURRENTS - STA. 17
U S DEPARTMENT OF THF INTER'CR
FEDERAL WATER POLLUTION CONTROL AUMIN
Greot Lakes Region Chicago ' mo.s
t 10-11
-------
SP
30
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20
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17 18 19 20 21 22 23 24
JULY — 963
TEMPERATURE AND CURRENT
AT STATION 20
CURRENTS AT 60m DEPTH
TWO HOUR' ENVELOPES -WIND & CURRENT
25
0 C
-
E MICHIGAN
26
>
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27
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25 26 27 28 29 30 31
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
WIND AT STATION 18 COMPARED TO
TEMPERATURE & CURRENTS - STA.20
U.S. DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Grtot LakMRtglon Chlcago,lllinoit
FIGURE 10-12
-------
SPEED IN KNOTS
30
WIND AT STATION IB - LAKE MICHIGAN
IN CENTIMETERS/SECOND
TEMPERATURE AND CURRENT
AT STATION 20
CURRENTS AT 60 m DEPTH
TWO HOUR ENVELOPES - WIND 8 CURRENT
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
WIND AT STATION 18 COMPARED TO
TEMPERATURE 8 CURRENTS - STA. 20
us DEPARTMENT OF THF INTEPI ~f> '
FEDERAL WATER POLLUTION CONTROL AjMlN
Great Lak«s Region >",hicugi , .nc. •->
352
t 10- 13
-------
WIND AT STATION 18 - LAKE MICHIGAN
SPEED IN KNOTS
TCMP4RATU* E
DE3REES C
CURRENT SPEED IN CENTIMETERS/SECOND
24 25 26 27
28 29 30
16 17
18
19 20 21 22 23
AUG. — 1963
TEMPERATURE AND CURRENT
AT STATION 20
CURRENTS AT 6O m DEPTH
TWO HOUR ENVELOPES — WIND 8 CURRENT
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
WIND AT STATION |8 COMPARED TO
TEMPERATURE &• CURRENTS - STA.20
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL AOMIN
Greot LoK«« Region '".hici.^- I. no s
IO-I4
-------
j-17
17
• w
fit ' m
m n
w w W W w «
r «
» i
Mi
E E E E
E C •
1/2 CYCLE
2 CYCLE
SECTIONS, AT QUARTER CYCLE PHASE INTERVALS
ACROSS A UNINODAL AI\/D TRINODAL STAND-
ING POINCARE' WAVE IN A TWO-LAYERED
LAKE, ROTATING COUNTERCLOCKWISE,
REPRESENTING A SECTION ACROSS CENTRAL
LAKE MICHIGAN LOOKING NORTH.
(Mortimer,unpublished, April, 1967)
GREAT LAKES — ILLINOIS
RIVER BASINS PROJECT
SECTIONS ACROSS a UNINODAL
and a TRINODAL WAVE
U S DEPARTMENT OF THF INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMIN
Gr«at Lakes Region Chicoijo I MPC s
FIGURE 10-15
-------
associated with internal waves (August 4-9, Figure 10-10), or indica-
tions of rythmic fluctuation in direction, or the combination of a uni-
directional current with rotation (Figure 10-9, July 28-31 and Figure
10-10, August 4-9).
Compared with station 17, the open Lake stations (15 and 20)
were dominated by rotary currents for a much greater part of the time
and with a more circular current vector envelope (station 20 during
early August, Figure 10-13)', but there were also occasions, particularly
after strong winds, when more or less steady currents prevailed (station
15. Figure 10-7, August 14-15; and station 20, Figure 10-14, August 21-
2k). In general, the role of the wind in changing thermocline depth and
in setting currents and internal waves in motion is evident in the Fig-
ures; and these also give information on the relative timing of the
responses. It is also apparent that, particularly during intervals of
more or less steady flow, the current speeds and the range of speeds at
station 15 were much greater than at the other stations.
Another important result which the Figures demonstrate is that,
with rare exceptions (station 17, Figure 10-10, August 4-5) temperature
fluctuations at any one station, resulting from internal waves, were in
phase at all depths (station 15, Figure 10-8, August 18-22; and station
20, Figure 10-13, early August, but see earlier remarks concerning the
15-m trace). From in-phase behavior of this kind it can be inferred
that the internal waves are those of the first vertical mode, appropri-
ate to a two-layered system, in which the flow is in one direction in
the upper layer and in the opposite direction in the lower layer. This
was the current distribution found at the M. V. Cisco anchor station.
As mentioned in Chapter 6, there is evidence that the current reversal
across the thermocline is not characterized by a layer of zero flow,
but that there is a progressive rotation of the current vector, total-
ing l80°, on passing downward through the thermocline. A clear demon-
stration of this state of affairs is not provided by the Figures
presented here (although there were clear examples at other stations)
because, with the exception of station 17 on July 24, and during the
latter half of August, the current measuring depths were usually below
the thermocline. Perhaps the current behavior during the interval July
24-28 at station 17 when the thermocline moved upward through the cur-
rent measuring depth (15 m), might "be interpreted as a "change-over"
of this kind between a southerly current above and a northerly current
below the thermocline.
Of particular interest is the opportunity, provided by Figures
10-7 through 10-14, of testing conformity with theoretical predictions
derived from the standing Poincare wave model. A particular period, the
interval August 4-7 was selected when the records from stations 17, 20,
and 15 showed internal wave activity coupled with rotating currents,
and which included part of a M. W. Cisco anchor station series at M£
in midlake.
345
-------
To assist the Interpretation, Figure 10-15 presents, in simpli-
fied form, cross-sectional pictures of thermocline displacement from
the equilibrium level, and current distribution in the lower layer, for
a transverse uninodal and transverse trinodal internal standing Polncare
wave in a two-layered lake, rotating counterclockwise. It represents a
section across Lake Michigan looking north, but for simplicity, Internal
Kelvin waves or other mechanisms generating inshore currents parallel
to the shores have been omitted. The theoretical current distribution
in the upper layer will be everywhere l80° out of phase with that indi-
cated for the lower layer, and the current speeds in the two layers
will be Inversely proportional to the relative layer thicknesses. Only
internal waves of the first vertical mode, i.e., appropriate to a two-
layered system, are considered. The illustrations, for each nodality,
represent one complete cycle of the oscillation at quarter-cycle stages.
Letters display the direction toward which the current is flowing and
the size of the letter indicates current speed. Dots represent zero
current at the antinodes, on the assumption that the section bisects a
standing Poincare wave cell, i.e., passes through the points of maximum
elevation and depression of the thermocline. At other sections through
the cell the general current distribution is similar, but there are
small currents at the shores and at other antinodes, if other antinodes
are present (M. A. Johnson, personal communication). The nodes are at
the points marked X, and the relative positions of stations 17, Mg and
20 are indicated.
By inspection of the trinodal case, and dividing the section
into adjacent compartments bounded by each antinode and its nearest
node, a correlation table can be constructed (Table 10-2, with nodes at
X and antinodes at Y), and extended to derive the pattern for any
nodality, along the following lines: the uninodal pattern comprises
compartments 1 and 2; the blnodal pattern comprises compartments 1, 2,
3, and 4j the trinodal pattern is provided by the compartment series 1,
2, 3, k, 1, 2; the quadrinodal pattern by 1, 2, 3, k, 1, 2, 3, k} the
quintinodal by 1, 2, 3, b, 1, 2, 3> ^> 1> 2; and so on. In other words,
correlations between thermocline elevation and current directions
between a pair of stations can only Indicate which nodality is present
if the information is combined with knowledge of the geographical posi-
tions of the stations and of the observed or presumed position of the
nodes. It also appears likely that, at least as far as the currents
are concerned, the higher the nodality, the more quickly the wave will
die down, leaving the lower nodalities to dominate the scene. A further
guideline for Lake Michigan—in which the normal effect of a wind dis-
turbance is to force the thermocline to tilt downward on one shore and
upward on the other—is that odd-numbered transverse nodalities will be
the rule.
346
-------
Table 10-3 summarizes, for stations 17, Jfe» 20, and 15, during
the relatively simple episode, August *t-7, 1963, the temperature and
current information needed to make the comparison between theory and
erents in the Lake. The stations 17 and VQ form a pair in which the
thermocllne elevations and lover-layer currents were approximately in
phase; and the same is true of the station pair 20 and 15- The two
pairs, however, are approximately 180° (i.e., close to 8£ hours or one-
half period) out of phase with each other. This result, coupled with
the geographical location of these stations, is consistent with a
Poincare" wave of transverse nodality one (compare Figure 10-15 upper
part) on the assumption that the uninode lies to the east of MJ2 (and
that there is no longitudinal node between 20 and 15). The next para-
graph provides evidence of a uninode to the east of Hfcj. ^ *ne uni"
nodal picture is therefore accepted, the phase relationships between
thermocline elevation and current direction at all stations serve to
confirm the standing Poincare wave model, an important result. It will
also be noted that a fit with the trinodal case (Figure 10-15, lower
part) would be impossible. While—as pointed out in earlier discussion
concerning Table 10-2—a fit with some higher nodality than three is
conceivable in theory, this would be a most unlikely interpretation,
which in any case appears ruled out by consideration of wave period,
not discussed here.
During the interval August k-1, six temperature cross sections
were completed using railroad car ferries. When the 10°C isotherms,
which represent thermocline depth, are plotted on a common depth/time
scale, there is evidence of a node at J6 km from Milwaukee, at which
point the depth range of the thermocline did not exceed 2 m over the
whole interval. On this occasion, however, the presumed node was less
clearly defined than the 66-km node in Figure 10-2, perhaps because the
wave amplitudes were then larger, following the storm on August 16-17—
and it was also in a different position.
As mentioned earlier, Figure 10-2 for August 19-22 suggests a
combined response to a transverse uninodal and trinodal Poincare' wave
in which the midlake nodes of each system were coincident at approxi-
mately 66 km from Milwaukee. While the temperature records at stations
20 and 15 at that time showed clear indications of internal waves of
near-inertial period, set in motion by the storm on August 16-17, the
current pattern was too confused to attempt the correlations similar to
those carried out above for the August k-J episode. It appears that
strong unidirectional currents, set in motion by the storm, masked the
rotational components. All that can be said with certainty is that the
thermocline elevations at stations 20 and 15 were, on this occasion,
out of phase, suggesting that there may have been a longitudinal (or
transverse) Poincare node between them. The temperature recorders at
station 17 were in the upper layer and a long way from the thermocline;
3^7
-------
TABLE 10-2
CORRELATION TABLE FOR STANDING POINCARE WAVES OF VARIOUS TRANSVERSE
MODALITIES IS A RECTANGULAR TWO-LAYERED BA8IN ROTATING COUNTERCLOCKWISE
(COMPARE FIGURE 10-15, TRINODAL CASE)
nodes at:
Compartment No. *
Maximum "thermocline" elevation (+)
or depression (-)
Current direction in lower
layer, corresponding to the
above maximum elevations or
depressions .
Ief1
(v)
1
arvhlnnd*»H «.+.; v
trinodal case
-^
V binodal case /
Vuninodal case /
\ X ' X X
I I I
1 | 2 3 1 * 5 X 6
N N S S N N
t hand right hand
shore ^ ^ shore for 1
^ I I nodal case
f y v v
(E)
;ri-
*See text for definition.
348
-------
TABLE 10-3
CORRELATION BETWEEN TEMPERATURE 'WAVES' AND CURRENTS AT STATIONS
IT, M2 AND 20 ON OR NEAR THE MILWAUKEE-MUSKEGON SECTION (AND
AT STATION 15), AUGUST k-1, 1963. FOR STATION POSITIONS SEE
TABLE 10-1. DATA OBTAINED FROM MORTIMER'S UNPUBLISHED
OBSERVATIONS AT M~ AND ON RAILROAD FERRY SECTIONS, AND BY
INSPECTIONS OF FIGURES 10-10, 10-13, AND 10-7.
Station
Approximate mean thermocline depth
(inspection of ferry transects) — m
Depth of temperature record showing
greatest amplitude — m
Current measured at — m (all below
thermocline at this time)
Approximate hour (C.S.T.) of occurrence
of temperature "troughs," assumed
equivalent to internal wave "crests": I"
Irth <
\
Aug. 5th <
L
f
*observed "crests" at Mo 6th <
I
7th {
I
Approximate direction toward which
the current was traveling in the
lower layer at the above times.
Approximate mean current speed,
cm/sec.
17
10
10
15
7
2U
17
10
3
20
WE
5
Mj** 20
18 15-20
15
various 60
6*
15
23*
8
1
18
11
NNW SSE
10-15 10
15
17
15
22
23
16
9
SSE
15
**M.V. Cisco anchor station.
3^9
-------
Internal vave Indications are therefore unreliable, but such as they
are they suggest that station 17 May have been out of phase with sta-
tion 20. These indications are not conclusive but are not, as far they
go, inconsistent with the dominance of a transverse trinodal standing
vave pattern on that occasion.
350
-------
CHAPTER 11
RELATIONSHIP TO WATER USE AREAS
Introduction
Although not all of the Initial purposes of this study of water
movements in Lake Michigan vtre accomplished, the information gained
will contribute greatly to the development of more effective water pol-
lution control programs for the Great Lakes. For example, planners can
now determine the outer limits of diffusion rates in the Lake and the
net flow along the shore in the vicinity of an outfall, stream, or water
intake.
The wise utilization of the Lake, on a sound technical founda-
tion, has become a reality. The preservation of an acceptable water
quality for the future will depend on the course man takes in the dis-
posal of his wastes.
Physical factors affecting water use areas include a broad range
of forces which interact to produce a complicated relationship. Fortu-
nately one or two of the factors are usually most dominant and can des-
cribe the events which occur. Motions in the Lake can be characterized
as either horizontal or vertical. Vertical motions were inferred from
thermal gradients. Although vertical currents are very small, the max-
imum being in the range of 0.06 cm/sec, the distance scale in the
vertical is very small when compared to the horizontal scale. Vertical
currents may be an order of magnitude greater in the winter than in the
summer. Hutchinson (MO shows several instances of summer vertical
currents of an order of magnitude greater than those found in Lake
Michigan. The currents found in Lake Michigan are primarily a result of
displacement of the isotherms due to Internal wave motion and conse-
quently result In very little mixing. Horizontal and vertical motions
are produced by external, internal, and secondary forces. External
forces Include: wind, atmospheric pressure, and lunar or solar tide-
producing forces. Internal forces can properly be labeled density
gradients. These include changes in mass distribution in heat or in
dissolved solids. Secondary forces Include Coriolis force, friction,
turbulence, and centrifugal force. Secondary forces do not produce
currents but affect the currents that are produced by other means.
The above forces, whether producing massive turbulence, gentle
streamline flow, thermal bars, or thermoclines,influence water uses of
the Lake. They can rapidly disperse highly concentrated wastes of a
hazardous nature or they can transport them with little mixing to crit-
ical water use areas.
351
-------
The studies reported herein describe conditions under which pol-
lutants will "be moved from point to point and permit determination of
probable concentrations and effects on water use areas. From this know-
ledge appropriate pollution abatement measures can be devised to protect
and enhance the quality of the Lake waters for all legitimate uses.
Pollutants are discharged or put into Lake Michigan through many
sources such as: sewage outfalls, industrial waste discharges, vessel
discharges, dumping of dredged material, and storm overflow sewers. In
addition, storm-generated waves will resuspend detritus and other pol-
lutants and produce a recycling of these materials. These discharges
are the principal sources of waterborne wastes which will affect the
users of Lake Michigan water. Although some of the waste sources listed
may contribute minima.! amounts of pollution, the very long retention
period or flowthrough time requires a careful look at »n waste sources
and the development of a water pollution control program which places
appropriate emphasis on future conditions.
Water Use Areas Along Shore
Beach and water intakes along or near the shore will be affected
by nearby sources of pollution; proper location and design of waste
outlets can minimize such effects. Bottom materials are usually sand
in a beach area and normally swept free of settling debris that may be
recycled. Likewise, vessel discharges and the dumping of dredged
materials will normally occur 3 or more km from most beaches. Storm
overflow sewers, sewage outfalls, and industrial waste discharges pre-
sent the greatest hazards to public bathing.
The steady discharge of pollutants, as a sewage outfall or
industrial waste discharge, cannot be compared directly to the occa-
sional once a month, 4- or 5-b.our discharge of a storm sewer overflow
or the washing of oil tanks once a year. These can be called nonsteady-
state and represent pools of pollution. Such problems must receive
special consideration.
Based on studies of drogues, the maximum and minimum diffusion
factors were calculated for moderately calm conditions, and not criti-
cal or minimum diffusion rates. However, if a discharge were part of an
oil residue or other oil-based pollutant, little or no dispersion would
occur because of the lack of mixing. Therefore, all references to the
dispersion or mixing of discharges refer to wastes which are soluble
or mix readily with Lake water.
At 150 m (500 feet) from the source, under m-tni-nn"" mixing condi-
tions (calm periods), a pollutant will be at or near 100 percent of its
original concentration. At 750 m (2,500 feet) the pollutant will be 20
352
-------
percent of its original concentration, and at 1,500 m (5>000 feet) it
will be at 10 percent. Similar values are found for pools or "slugs"
of pollutants.
The greater the diffusivity, ^^ the more a pollutant moves out-
ward and upstream. It can be easily seen from the above percentages
why contaminants, such as taste- and odor-producing hydrocarbons, can
travel 15,000 m (50,000 feet) and still be 1 percent of their original
concentration, and thus cause problems.
Vessel discharges into restricted harbors, such as boat marinas,
constitute a potential hazard because of the number of vessels which
congregate in a small area. Since most harbors are restricted in area
and depth, and have a small entrance, physical factors do not play a
large role in dilution or dispersion. Currents or other water motions
are nearly nonexistent and stagnant water conditions may prevail. Unless
reasonable care is taken to limit the discharge of pollutants these
harbors can become severely degraded in a few years. Milwaukee Harbor
is an example of such conditions.
Thermal barrier conditions during the fall, winter, and spring
period limit the outward extent of the effective mixing volume. This
factor appears to be responsible for unusual solids build-up in the
nearshore waters during this period. The late spring storms and lake
overturn break up the zonation due to the thermal bar and create condi-
tions for effective mixing with the Lake proper. However, during the
summer when the thermal bar no longer exists, a similar build-up occurs.
Boundary effects, friction, and the southern gyre are probably respon-
sible for the lateral transfer of water along the shore. Upwelling and
downwelling in summer are positive signs that this restriction is much
weaker than during the winter period.
Water Use Areas in the Lake
Water supply intakes, fish and aquatic life, and recreational
boating are some of the more important uses of lake water away from the
shoreline. Outfalls or water intakes are fixed positions, rarely more
than 6.k km (k miles) from shore. The dumping of dredged materials is
normally confined to fixed geographical areas and is usually more than
1.6 km (l mile) from any water intakes. Vessel discharges in such areas
are restricted but much is still left to the discretion of the Captain
of the ship.
Normally wastes discharged into the Lake have more mixing than a
shore-discharged effluent. This arises from the fact that the pollutant
can rise through a column of lake water (if the pollutants are lighter)
and is continually mixed. If the currents are nearly stationary, then a
mass or pool of pollutants can build up and create a potential problem.
353
-------
Steady currents, of any magnitude, will assist in the dispersion
of pollutants discharged into the Lake. However, during summer periods,
the thermocline acts as a barrier against mixing, and all effluents
discharged above the thermocline will normally not be dispersed into
the lower levels unless density is an additional factor.
The sum total of the effects of physical factors indicates that
if the quality of lake waters is to be maintained for all legitimate
uses, indiscriminate discharges of wastes must be eliminated or placed
under strict control.
Significant Factors
There are several physical factors which contribute significantly
to the dispersion (or lack of dispersion) of pollutants. The processes
not previously identified In Lake Michigan and determined by Project
studies are:
1. Diffusion coefficients. The mftytmnm value found was wi = 0.4
and minimum ^^ = 0.2. In an area of convergence the minimum may be as
low as ^i = 0.08. These values represent the outer limits of diffusion.
2. Inshore zonation of suspended materials. Materials dis-
charged into the inshore zone, 0 to 6 km, will normally tend to remain
in the zone. During the late fall and early spring a thermal barrier
condition restricts the normal diffusion between inshore and offshore
waters. The thermal gradients are assisted by the fact that as one
approaches the shore the water movements tend to parallel the shore
rather than move in any direction under the wind influence. In summer
this conformality of flow, due to boundary conditions, is enhanced by
the tilting of the thermocline and the existence of the southern gyre
creating other artificial boundaries.
3. Lake Michigan has a winter thermocline at the 120- to l80-m
level which restricts turnover in the deep central basin. Although a
lake turnover does not appear to occur in this basin every year, it no
doubt occurs at least once every 10 years. The southern basin mixes
from top to bottom every year.
k. No permanent type of circulation pattern exists in the Lake,
but four general circulation patterns exist, depending on wind regimes.
Ice conditions on the Lake are sporadic and are rarely 100 percent
(perhaps once in 30 years). A complete ice cover preventing random wind
action permits the formation of true inertia currents which rotate with
a period of a half pendulum day. In the summer the internal wave, in
the main portion of the Lake, prevents the wind from directly affect-
ing the rotary circulation patterns. A small cellular structure occurs
354
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on the broad circulation patterns and produces a complex interaction
between wind and water movement.
5. The summer internal wave on the thermocline begins in late
spring and exists until early December. The direction of flow in the
epilimnion is generally 180° out of phase with the water in the thermo-
cline and below. The horizontal rotation of the water due to the inter-
nal wave exists from top to bottom in the Lake. The motion due to the
internal wave is independent of the net circulation pattern which may
exist.
6. Wind energy from storms is transmitted through the entire
column of water, both in summer and winter. No thermal barrier, such
as a thermocline, exists to inhibit energy transfer in the winter—
except for the reverse thermocline in the deep hole of the northern
basin. In the summer the direct input of energy from a storm excites
the internal wave pattern and produces extremely large waves (over 10
meters) and accomplishes some mixing at the thermocline interface. The
formation of the large waves in turn appears to transmit into the lowest
layers, increasing the speed within the rotating currents proportional
to the input. The decay of the energy input is related to friction.
355
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ACKNOWLEDGMENTS
To thank all the people who have contributed to this study would
virtually call for a whole new chapter. To those who have assisted
directly, the GLIRB Project staff will be always grateful. Noteworthy
among these are: Drs. C. H. Mortimer and A. M. Beeton, University of
Wisconsin-Milwaukee; Drs. V. E. Noble, J. C. Ayers, D. C. Chandler and
F. Bellaire, University of Michigan; Dr. E. Birchfield, Northwestern
University; Dr. G. Platzman, University of Chicago; Drs. B. Kinsman and
A. Okubo, Johns Hopkins University; Dr. K. Rodgers, University of
Toronto; Dr. R. A. Ragotzkie, University of Wisconsin; Dr. F. Webster,
Woods Hole Oceanographic Institution; Dr. H. Stommel, Massachusetts
Institute of Technology; Dr. W. J. Pierson, E. Mehr and F. Malone, New
York University; Dr. R. Gaul, Texas A & M; Dr. D. L. Harris, ESSA; and
Mr. T. L. Richards, Department of Meteorology, Canada.
356
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