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EPA-905/9-79-004
January 1979
RED CLAY TURBIDITY AND ITS TRANSPORT
IN LAKE SUPERIOR
by
Michael Sydor
Richard T. Clapper
Gordon J. Oman
Kirby R. Stortz
Physics Department
University of Minnesota, Duluth
Duluth, Minnesota 55812
E.P.A. Grant No. R005175-01
Project Officer
Anthony G. Kizlauskas
U.S. Environmental Protection Agency
Region V
Great Lakes National Program Office
Chicago, Illinois 60605
GREAT LAKES NATIONAL PROGRAM OFFICE
U.S. ENVIRONMENTAL PROTECTION AGENCY
REGION V
CHICAGO, ILLINOIS 60605
-------
DISCLAIMER
off, rep°r5r has been "viewed by the Great Lakes National Program
Offxce Region V, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
reflect the V1ews and policies of the U.S. Environmental Protection Agency
nor does mention of trade names constitute endorsement or recommendation for
ii
-------
FOREWORD
The U.S. Environmental Protection Agency (EPA) was created because of
increasing public and governmental concern about the dangers of pollution to
the health and welfare of the American people. Noxious air, foul water, and
spoiled land are tragic testimony to the deterioration of our natural envi-
ronment .
The Great Lakes National Program Office (GLNPO) of the U.S. EPA was
established in Region V, Chicago, to provide a specific focus on the water
quality concerns of the Great Lakes. GLNPO provides funding and personnel
support to the International Joint Commission activities under the U.S.-
Canada Great Lakes Water Quality Agreement.
Several water quality studies have been funded to support the Upper
Lakes Reference Group (ULRG) under the Agreement to address specific objec-
tives related to pollution in the Upper Lakes (Lake Superior and Lake Huron).
This report describes some of the work supported by this Office to carry out
ULRG study objectives.
We hope that the information and data contained herein will help
planners and managers of pollution control agencies make better decisions
for carrying forward their pollution control responsibilities.
Dr. Edith J. Tebo
Director
Great Lakes National Program Office
iii
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ABSTRACT
Through the use of Landsat satellite imagery from 1972 - 1975 red clay
plumes in western Lake Superior are studied in order to determine the
relative magnitude of the three sources of the observed turbidity erosion
of the Wisconsin south shore red clay banks, resuspension of bottom sedi-
ments, and runoff from the many streams which flow through the red clay belt
and then into the lake. A comprehensive sampling program was conducted
during the spring of 1975 in order to determine the runoff contribution to
the total load observed in the lake. Analysis of Landsat transparency data
coupled with weather records enabled contributions from erosion and resuspen-
sion to be separated. It was found that approximately 75% of the observed
load in the lake during the ice free season, from May to November, is from
erosion, 20/, is from resuspension, and 5% is from runoff.
A numerical model for water transports in Lake Superior as a function
of winds is developed. This model is verified by comparison of observed and
predicted water levels at several locations around the lake, and by compari-
son of the predicted transport patterns to actual turbidity distributions
observed in Landsat imagery. Transport patterns are shown for western Lake
Superior and the entire lake for both an easterly and westerly wind. A model
of current profile with depth is also developed. The results of the trans-
port model are used to predict distributions of red clay from the south
shore and taconite tailings discharged into the lake at Silver Bay, Minnesota.
This report was submitted in fulfillment of Grant No. R005175-01 by the
Great Lakes National Program Office, Region V under the sponsorship of the
U.S. Environmental Protection Agency. This report covers a period from
October, 1974 to March, 1976 and work was completed as of January, 1979.
iv
-------
CONTENTS
Foreword
Abstract ................................ .jv
Figures .............................. '.'.'. v±
Tables ................................. ix
Acknowledgments
x
1. Introduction i
2. Conclusions 2
3. Recommendations 4
4. Runoff from Douglas County, Wisconsin 5
Rivers and streams analyzed 5
Method 7
Results 20
Rain Runoff 27
Conclusions 32
5. Sources and Transports of Turbidity in Western Lake Superior ... 34
Estimation of sediment resuspension and total loading .... 34
Turbidity transport and the distribution of turbidity sources 48
6. A Numerical Model of Transports in Lake Superior 56
Description of the model 55
Results of transport model 61
Current profile model 88
Turbidity transport model 95
References ^ 1Q4
Appendix
A. South Shore Data for the 1975 Runoff 105
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Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
FIGURES
General study area . .
Rivers and streams analyzed in Douglas County, Wisconsin .
Nemadji River basin . . .
Comparison of grabbed and integrated water samples . .
Cross sectional areas and discharge rates of analyzed streams
Discharge vs. stage for the analyzed streams
Soil map of northern Wisconsin
Daily snow and runoff data during snow-runoff period
Daily suspended load for analyzed streams during the entire
runoff period
Turbidity and suspended solids correlation
Total load vs. total discharge for the large streams
Daily rainfall and Nemadji River discharge and suspended
load data for a summer rain event
Turbidity calibration of Landsat images
Representative suspended solids distribution produced from
Landsat data
Lake grid spaces and regions used in Landsat image analysis
Spring ice shelf near Amnicon River
Average lake turbidity near Duluth
Average turbidity dissipation for easterly and westerly wind
storms
Actual turbidity dissipation for a large easterly storm . . .
Paep
o
6
8
9
10
11
14
19
21
22
26
28
32
35
36
37
41
42
45
45
vi
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Number Page
20 Average storm characteristics 46
21 Distribution of storm duration 46
22 Average turbidity distribution and transport for an easterly
storm 49
23 Average turbidity distribution and transport for a westerly
storm 50
24 Average turbidity distribution and transport by westerly
winds 51
25 Average turbidity distribution and transport for variable
winds 52
26 Average turbidity distribution for the ice-free season .... 53
27 Relative south shore erosion rate 54
28 Resuspension areas in Lake Superior 54
29 Duluth water levels for easterly wind 63
30 Actual Duluth water levels for westerly wind 63
31 Western Lake Superior transports for easterly storm 65
32 Landsat image for 11APR75 showing resuspension plume 68
33 Skylab image showing turbidity entrapment near Duluth .... 68
34 Landsat image for 23NOV73 showing taconite tailings plume
off Silver Bay 69
35 Western Lake Superior transports for westerly storm 70
36 Water level as a function of time at Duluth from the
transport model 72
37 Water levels for western Lake Superior for an easterly storm . 73
38 Water levels for western Lake Superior for westerly wind ... 73
39 Water levels for western Lake Superior from the Forristall
model 74
40 Entire Lake Superior transports from a 13 m/s NE wind .... 75
Vll
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Number „
Page
41 Entire Lake Superior transports from a 11 m/s westerly wind. . 80
42 Lake Superior water level station locations ......... 85
43 Modeled Lake Superior water levels from a northeast storm . . 86
44 Current vs. relative depth near surface ........... 91
45 Current meter station locations ............... 91
46 Current profiles for two values of v ............. 94
47 Peak measured surface currents vs. wind speed for several
northeast winds 0
48 Computer bottom currents near Duluth ............. 96
49 Lake sample settling in lab ................. 97
50 Modeled suspended solids distribution at several stages of
the storm .................... no
51 Landsat image for 03APR75 ..................
52 Modeled sediment accumulation at different stages of the
storm ................ -1Q2
vni
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TABLES
Number Page
1 Load Transported during April, 1975 25
2 Snow Runoff per Linear km of Stream Length and per Square km
of Basin Area for the Period April 10-27 29
3 Summer Rain Runoff for Nemadji River (1970 - 1974) 30
4 Yearly Input of Suspended Load 32
5 Percent Abundance of Particle Sizes by Number 33
6 Ratio of Average Turbidity to Surface Turbidity for Western
Lake Superior 38
7 Total Suspended Load in Western Lake Superior 39
8 Sources of Lake Turbidity 47
9 Comparison of Periods in Hours of Gravitational Modes in
Lake Superior 64
IX
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ACKNOWLEDGMENTS
We would especially like to thank Dr. Thomas F. Jordan, Physics Depart-
ment, University of Minnesota, Duluth, for his derivation of the current
profile model solution.
We are grateful to Mr. Steve Diehl, University of Minnesota, Duluth,
for his work on the transport model.
We are grateful for the assistance of the following individuals who
helped to collect and analyze material in this report: Dr. David G. Darby,
University of Minnesota, Duluth; Dr. Albert B. Dickas, University of
Wisconsin, Superior; Mr. David Smith, Mr. John Sorensen, Mr. Vasyl Shuter,
Mr. Gary Fandrei, and Mr. Wayne Maanum.
We are particularly grateful for the assistance of Mr. Steven Spray,
whose photographic and sampling efforts were most helpful during the diffi-
cult conditions of early spring.
We are grateful to Mr. Nelson A. Thomas, U.S. Environmental Protection
Agency, Large Lakes Research Station, Grosse lie, Michigan, for performing
the particle size analysis.
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1. INTRODUCTION
The transport of fine red clay particles from erosion of red clay banks
in Douglas County, Wisconsin, over large areas of the lake causes water
quality degradation and displeasing aesthetic appearance, which together are
often referred to as the Red Clay Problem. The turbidity within the lake
plumes results from three processes: lakeshore erosion, sediment resuspen-
sion, and stream runoff. The total turbidity within the entire plume can be
determined through remote sensing. The relative contribution of each source,
however, must be established from measurements of the individual sources.
The runoff can readily be evaluated with reasonable accuracy. The magnitude
of the other turbidity sources can be established by subtraction of the
contribution from runoff. The determination of the relative magnitude of all
three sources of red clay turbidity in the lake is essential in evaluation of
red clay-related problems, such as the deterioration of water quality and
property damage caused by severe erosion of the lakeshore. In the case of
water quality, it is particularly important to determine the magnitude of the
runoff, since the water quality problems resulting from shore erosion and
sediment resuspension may be quite distinct from those resulting from red
clay washed out by polluted rivers. For instance, the red clay particles
transported by the Nemadji River could adsorb and carry pollutants into the
lake. The contribution of runoff to lake turbidity is also useful for deter-
mining the effect of various erosion abatement programs currently in progress
in the red clay belt of Wisconsin and Minnesota.
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2. CONCLUSIONS
1) Turbidity measurements correlated with Landsat satellite data show that
lake turbidity originated from erosion of shore banks, resuspension of bottom
sediment, and river runoff. Using satellite data from August, 1972 to
August, 1975, the contribution of each source per open water season (May -
November) was estimated to be 4.0 x 106 metric tons from erosion, 1.0 x 106
metric tons from resuspension, and .32 x 106 metric tons from river runoff.
During the open water season, about 75% of the total sediment load is contri-
buted by erosion, 20% by resuspension, and 5% by river runoff.
2)^ The runoff mainly comes from the Nemadji River, which accounts for over
80% of the total sediment output from streams and rivers in Douglas County,
Wisconsin.
3) Winter storms which occur when the lake is ice-free but when the lake-
shore and the rivers are iced over, contribute roughly 2 x 106 metric tons
per season of additional suspended material in the lake. This largely comes
from sediment resuspension at the intermediate depths off Wisconsin and
Minnesota Points. Resuspension is greater during the winter months because
of the higher frequency of northeast winds and more nearly isothermal condi-
tion of the lake.
4) A numerical model for transports was devised for the lake. The model
was tested using water level data and by comparing the predicted transports
to the transport of turbid plumes observed by Landsat. The results of the
numerical model and the statistical analysis of Landsat data explain the
periodic contamination of the Duluth water intake by high concentrations of
red clay particles and asbestos particles.
5) The fine red clay material contaminates much of western Lake Superior
from Duluth to the Apostle Islands. The main transport of turbidity for
northeast winds occurs along the axis of the western arm of the lake from
Duluth towards the Apostle Islands. For west winds, the main transports
occur along the Wisconsin shore towards the Apostle Islands.
6) The distribution of lake levels as a function of winds is given for
Duluth and extreme western Lake Superior. The height of water level fluctua-
tion due to storm surges is on the order of 20 cm (8 inches), which is
comparable to the seasonal fluctuation in the water level. Changes in ero-
sion rates resulting from water level fluctuations could in principle be
obtained from Landsat data on the distribution of turbidity along the shore
after storm surges.
7) General circulations and transports for the entire lake are discussed.
The transport patterns for the two wind directions modeled here do not carry
-------
the fine red clay material directly across the international boundary. How-
ever, fine red clay particles are transported in the lake in detectable
concentrations (1 mg/£) for over 80 km.
8) The effective area of contamination for a storm surge and the long-range
transport of fine sediment was assessed by simulating a turbidity plume
generated by a steady two-day northeasterly wind storm with 13 m/sec (30
mph) winds followed by a westerly wind. The results show that an estimated
10" metric tons of material would be removed by erosion for such a storm
and dispersed in the area of the lake from Duluth to the Apostle Islands.
Although the computation simulated dispersion of clay for an equivalent of
only a 4-day period, in which time it showed that most of the suspended load
was deposited in western Lake Superior between Duluth and the Apostle Islands,
it is estimated that on the order of 3% of the material or ^ 105 metric tons
per year would disperse outside of this area. This result is also borne out
in the observation of extensive plumes through remote sensing which in some
instances shows the plumes extending well past the Apostle Islands.
9) Bottom currents near Duluth for westerly winds favor the presence of an
upwelling along the North Shore. The results of the calculation on bottom
currents for isothermal conditions indicate that resuspended material off
Minnesota Point would move out along an easterly direction for northeast
winds. Westerly winds would generally move the resuspended material towards
Duluth, with the exception of an area east and southeast of the Superior
entry, where the bottom currents point toward the Wisconsin shore.
-------
3. RECOMMENDATIONS
1) Correlation of Erosion and Lake Levels.
Examination of the results from the numerical model shows that the water
level along the red clay bank shore is a function of winds. The change in
water level produced by the wind appears to be accompanied by a change in the
relative turbidity along the shore as observed from the satellite.
Further work including the effects of wind, fetch, and turbidity distri-
bution along the shore in correlation with water level information obtained
from the numerical model should be made.
A series of manned overflights of the shore area for various wind condi-
tions using multispectral scanners would be fruitful in establishing the
dependence of the erosion rates on water levels. The overflights would also
help determine the boundary conditions necessary for modeling the shore
erosion as a turbidity source.
2) Water Quality.
The development of the numerical model for transports is a prerequisite
for water quality modeling. The next step should be concerned with water
quality modeling of the effects of harbor effluents from the St. Louis River.
The effluents tend to accumulate in extreme western Lake Superior for variable
wind conditions.
The overall quality of the water in the lake should also be considered.
The dispersion of very fine particulates and the dispersion of effluents from
various point sources should be studied through remote sensing coupled with
the modeling of long-range transport events.
Although it would be impractical to run a finer grid model for the
entire lake because of computer storage and time requirements, much higher
resolution could be obtained by submodeling on a finer grid scale at various
locations of interest around the lake. For example, future studies might
entail cutting the grid spacing by one half over the entire western arm of
Lake Superior, while leaving the remainder of the lake unaltered. This
would be especially beneficial for the comparison of modeled plumes to actual
satellite images which contain features comparable in size to the present
grid spacing.
-------
4. RUNOFF FROM DOUGLAS COUNTY, WISCONSIN
RIVERS AND STREAMS ANALYZED
Streams and rivers passing through Douglas County, Wisconsin were moni-
tored during the entire spring runoff in April, 1975. These streams run
through the major deposit of glacial-lacustrine red clay around Lake Superior.
The deposit averages 30 meters in depth and covers a 15-km-wide area along
nearly all of the Lake Superior shore in Douglas County, Wisconsin, and
beyond into Bayfield County, Wisconsin. The clay deposit shows critical
erosion along many areas of the lakeshore and along the river banks and
road cuts. A large fraction of the clay is made up of very fine particles
less than 6 y in size which are washed out into Lake Superior and are trans-
ported in the lake in high concentrations as far as 80 km. The transported
particles from the red plumes are frequently observed in western Lake
Superior and are a source of contamination of municipal water supplies.
The rivers and streams analyzed in this project include those flowing
into the lake between Dutchman Creek, which enters Lake Superior approximately
2.5 km east of the southeastern end of Allouez Bay, and Haukkala Creek,
Figure 1. This includes approximately 20 km of lake shoreline and twenty-one
rivers and streams. In addition, the Nemadji River was also observed.
Although the Nemadji River does not flow directly into Lake Superior but
rather into the Superior Harbor Basin of the Duluth-Superior Harbor, its
mouth is only 800 meters from the Superior entry to the harbor. Although the
percentage of the Nemadji River's suspended load which is deposited in the
lake has yet to be determined accurately, it is known that much of the fine
load does flow out to the lake. The volume of the Nemadji's load is so great
that if only 20% of it reached the lake, its contribution would still be
comparable with the combined output of all the other rivers and streams in
Douglas and Bayfield Counties.
From west to east, the rivers and streams analyzed and the monitoring
sites are as follows: Nemadji River at the bridge near the Nemadji Golf Club
in south Superior; Dutchman Creek at Hwy 13, 500 meters from the mouth;
Morrison Creek at Hwy 13, 150 meters from the mouth; Amnicon River at Hwy 13;
Ten Creek at Hwy 13, 600 meters upstream from the intersection with the
Amnicon River; Wagner Creek at Hwy 13, 600 meters upstream from the intersec-
tion with the Amnicon River; Hanson Creek at Hwy 13, 300 meters from the
mouth; Middle River at Hwy 13, 1 km from the mouth; Poplar River at Hwy 13,
800 meters from the mouth; Bardon River at Hwy 13, 800 meters from the
mouth; and Pearson Creek at Hwy 13, 2.5 km from the mouth.
Within the study area investigated by the University of Minnesota,
Duluth, there were fifteen unnamed intermittent streams. For purposes of this
study the unnamed streams were numbered consecutively from west to east,
-------
LAKE SUPERIOR
MINNESOTA POINT
SUPERIOR ENTRY
WISCONSIN POINT
Figure 1. General study area.
-------
#1 - #15. Figure 2 presents a map of all of the rivers and streams analyzed,
wnich incudes an outline of their drainage basins. Since the United States
Geological Survey has conducted considerable analysis of the Nemadji River
their figure for the total drainage area of this river was used. An outline
of the Nlmadji Basin which was taken from the report Red Clay Project appears
in Figure 3.
METHOD
Since it is the suspended material that adversely affects Lake Superior s
water quality, it was only the suspended load, or more specifically the wash-
load! of the^treams that was measured during this study. Particles included
in the bed-load and the saltation-load of the streams are too heavy to remain
suspended in the lake for any appreciable length of time.
A hand-held, rod-supported US DH-48 integrating sampler was used to
collect water samples, which were refrigerated and analyzed within 24 hours.
Parole size analyses were performed on Delected samples using a HIAC en *
Turbidity was measured with an AG1 Hach Meter, and suspended solids were de
termined by filtration through 0.45 y Millipore filters. On deep, swift
rivers such as the Nemadji it was impossible to stand in the river with the
US DH-48 sampler. Long extensions for the handle were const™c'e* *°*^°
allow sampling from bridges, culverts, and, at times, trees which had fallen
across the channels. To keep the sampler properly orientated in the swift
current i.e., the intake nozzle horizontal to the stream surface and di-
rected directly upstream, thin nylon lines were attached to the handle near
the sampler and tied-off upstream. Occasionally during the course of sam-
pling "dipped" or "grabbed" samples were also obtained for comparison with
?he Integrated samples. A comparison between integrated and dipped samples
appears in Figure 4.
Stream discharge rates were determined by measuring stream velocities (v)
with a Gurley Meter (622), Pygmy Gurley Meter (625), or both, depending upon
tne flow-rate and the accessibility. At the same time as the average velocity
was measured the depth profile was measured to determine the cross-sectional
«eal5 of the stream. Thus discharge (Q) was determined, where Q - Av. In
additil marked stakes were driven or marks placed upon permanent fixtures
such as culverts, bridge abutments, or trees at each sampling site, ^ng
these marks, the stages of the rivers and streams could f****^™*^^
determined when time or conditions prevented a current dept h prof Jle ^om
being taken. Provided that subsequent channel profiling indicated that the
contour of the channel had not changed, these stage indications were used to
interpolate discharge rates. At the sites where the staging ™**™*\™t
to determine the
nterpoae .
in contact with the stream surface, a hand level was used to determ
difference between the water surface and the staging mark. The cross
sectional areas for irregularly shaped stream contours were Determined by
reproducing scaled graphs of the profiles and tracing the outlines with a
ptanimeter Cross sections of the major rivers and streams analyzed appear
in Figure 5. Plots of discharge vs. stage are shown in Figure b.
- Article size analyses were performed by Nelson A. Thomas, U.S.
Environmental Protection Agency, Large Lakes Research Station, Grosse lie,
Michigan.
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LAKE SUPERIOR
oo
•STfiUWi
DRAINAGE SASNS _
SUB-BASINS
MONITOBNG SITES .
0 DUTCHMAN
A AMNCON
T TEN
W MftGNBt
H HAMSON
f K9KAI
ft MADON
Ai «ARSON
N
\
Figure 2. Rivers and streams analyzed in Douglas County, Wisconsin.
-------
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RELATIVE TURBIDITY
250
50 150 250
Grabbed Samples
Figure 4. Comparison of grabbed and integrated
water samples.
10
-------
6.0
UJ3.0
w 1.5
NEMADJI RIVER CROSS SECTION
Bridge near golf course
Stream Bottom
Siege
DISCHARGE RATE (m3/sec) 163
^135
35
~6~
12 15 18
WIDTH (m)
21
24
27
4.8
4.2
3.6
-. 3.0
6
LJ 2.4
CO
<
i.2
0.6
0
DUTCHMAN CREEK CROSS SECTION
HWYI3
Culvert Contour
Stage (entrance) ——
DISCHARGE RATE 3.9
0 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8
WIDTH (m)
AMNICON RIVER CROSS SECTION
HWY 13
Stream Bottom
Stage
-2.4
~ 1.8
£ 1-2
<0.6
r
-------
1.2
J0.9
UJ
<0.6
0.3
TEN CREEK CROSS SECTION
HWY 13
Stream Bottom
Stage
DISCHARGE _R ATE Jm3/sec)_ _ _2J5
_0,9_
0.2
1.5
3.0 4.5
WIDTH (m)
6.0
7.5
1L2
UJ
CO
MIDDLE RIVER CROSS SECTION
HWY 13
Strocm Bottom
Stags
DISCHARGE RATE (mVsec) 26
12
WIDTH (m)
15
POPLAR RIVER CROSS SECTION
MOUTH
Culvert Contour
WIDTH (m)
Figure 5. (continued)
12
-------
0.9
J.
oJ
.0.6
0.3
POPLAR RIVER CROSS SECTION
HWY 13
Stream Bottom
Stage
DISCHARGE RATE (mVsec) 5.2
1.5
3.0
4.5
WIDTH (m)
6.0
7.5
9.0
-?0.9
-^>
$0.6
£ n ^
0
BARDON CREEK CROSS SECTION
HWY 13
i\A
jDISCHARGE^RATEjir^/sec) V
.^center
Culvert Contour
Stage
__5.8
3.1
0.6
<07L
•
0 1.5 3.0 0 1.5 3.0
WIDTH (m)
DISCHARGE
RATE
(mVsec)
1.3
0.7
02-
O.I 2^=:
0.05
(
PEARSON CREEK CROSS SECTION
HWY 13
Culvert Contour
Stoge — —
III • 'I ^M^ W» — — — • — ^ *» ~
rj= ==__ — — — — — — -^
,1111 i 1
D 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2
WIDTH (m)
•
,4
1.2
CO
Figure 5. (continued)
13
-------
! DUTCHMAN CRFFK
»•-••*
o
o
y?
•v ! ^*O
fO * ' s-Vy
it
£T
G
.c:
NE^ADJi RiVER
-{bridge rear go!f /' -
course}'*?
/•'
/
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/
/
/
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V
i /
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w?
t-7
0 1.5
1
Hwy 15 X
/ "
' / '
/
/
/
/
/
-------
0.25 0.50 0.75
Siege (rn)
0 0.3 06 0.9 1.2
Stage(n)
Figure 6. (continued)
IS
POPLAR RIVER
(mouth)
o
o
•r
o
.c:
o
0
0
/ !
/ -i
0.6 1.2
Siage(m)
-------
POPLAR RIVER
Hwy.13
.oPS^TJ 41l[75SoH««Ern
"~ i VI
0.25 0.50
Stcge(rn)
c
0 0.3 0.6
Stage(m)
0.25 0.50 0.75
Stage (m)
Figure 6. (continued)
-------
Snow depth and the moisture content of the snow were measured by coring
the snow at various locations with a 4.45 cm (1.75 inch) diameter clear
plastic tube. The depth of the snow at the coring site was measured, and
the core was emptied from the plastic tube into a small plastic bag and
weighed to the nearest gram with a spring scale. Both the coring tube and
the weighing bags were transparent so that the snow could be examined to be
sure that debris such as grass, mud, sticks, and gravel were not present in
the sample. Accurate snow measurement depends upon the percent of land
covered by the snow as well as the depth. As the spring runoff progressed,
larger areas of open ground began to appear. Photographs were taken to assist
in determining the percent of land covered by the snow as well as the depth.
River and stream sampling for this project was conducted during the
period April 9 through May 23, 1975, with intensive sampling taking place
during the runoff period April 14 through May 7. During the period April 14
through May 7 stages were noted and water samples collected at all of the
major rivers and streams on all but six days, of which no more than two were
consecutive. This period was divided into a snow-runoff period, April 14 -
27, and a rain-runoff event, April 28 - May 7. Stream velocities were
measured on occasions when significant stage differences were noted. When-
ever possible, discharge rates were established and water samples were
collected for upstream and downstream sampling sites of the same river. This
was done in order to estimate the eroded load per km of stream length for a
particular stage. Unfortunately, manpower shortages prevented checking the
sampling sites of all the streams on any one day. During the first half of
the runoff period nearly all of the sampling sites were taken alternately in
order to reduce periods when data was not collected for the major streams
to not more than one or two days, although occasionally a three-day period
did elapse.
The difficulty in reaching good sampling locations caused certain sacri-
fices to be made. Ideally, sites should be on uniform, straight sections of
the streams. There should be no tributaries or ditches entering above the
location which are not well mixed with the main stream before reaching the
sampling site. In addition, the site should be on a "high" section of the
stream with no obstructions nearby downstream. This is necessary to permit
accurate interpolation of the discharge from stage readings. If damming or
restriction occurs, the backup destroys the relationship between stage and
discharge. One other factor enters into site selection when testing near
the lake. The sampling sites must be far enough upstream to prevent lake
level from altering water samples and current measurements. This was satis-
fied for times of high flow for all rivers. The summertime low-flow periods
on the Poplar River were subject to storage variation because of the gravel
bar buildup at the mouth of the river.
The slope of the stage vs. discharge curve is nearly linear except at
the peak flow or when a river rises above its normal banks and flows onto
the flood plain. If testing is made in well-confined areas with deep banks,
the change of slope due to flood plain overflow need not be determined.
17
-------
In one way or another nearly all of the sampling sites fell short of
the criteria just mentioned. However, the best locations which were reason-
ably convenient were selected, and appropriate data adjustments were made.
The sheer number of streams in this area prevented most of the intermit-
tent streams (#1 - #15) as well as Hanson Creek from being monitored except by
occasional visual inspection. The soil map of the entire test area, Figure
7, and topographical maps of the area, Figure 2, reveal that the soil and
topography of the test area are quite uniform. Therefore, estimates of eroded
load for the streams not monitored were determined by comparison of their
basin areas and stream lengths to those for which considerable data was
collected. All values determined strictly by estimate or interpolation
appear enclosed in parentheses in the data tables in Appendix A.
Many daily values of discharge and load for the major streams had to be
determined by interpolating from known values before and after the day. The
accuracy of interpolated values depends on the accuracy of the known points,
but it also depends upon assumptions made when interpolating. The following
assumptions were made:
1) The increase or decrease of discharge rate is linear between close,
consecutive measurements.
2) The increase or decrease of suspended load is linear between close,
consecutive measurements.
3) Streams of similar size and length contained within similar
geological and topographical boundaries will behave approximately
the same.
4) For any stream flowing through unchanging topography and soil
conditions the time average eroded load per unit length is
constant for short sections.
In estimating the total load carried during the spring runoff, there are
two sources of error for which no correction can be made at this time. The
first deals with the transport of winter fines at the onset of the runoff.
This error is limited primarily to the smaller, shallower streams and rivers
which freeze solidly or nearly solidly during the winter. As the streams
begin to thaw and flow begins over the frozen streams (often on the ice
surface or between the frozen top surface and the frozen bottom), many fine
particles are carried to points where ice restrictions cause the flow to
decrease to the point that suspended particles are deposited on the icy
bottom. After the runoff gains momentum,the bottom ice is freed and floated
to the surface. Ice chunks carrying sediment up to 5 cm thick are floated
downstream. Many of these chunks are broken up or overturned, thus depositing
the sediment into the stream, but many other chunks are carried into the
lake. No estimate of the extent of this contribution can be made at this
time. The second source of error deals with transport near the river mouths.
Wash-load transport is primarily a function of turbulence. As the streams
near the lake (most stream mouths are drowned), the channels widen and the
18
-------
i!Jij
I
Heavy
red clay
Scale hi.OOO 000
N
SUPERIOR
^'WV
Silt ioam with
well -drained
subsoil
Rocky
loamy acid
» - — x* ./• • fr**
BAYFIELD
COUNTY
DOUGLAS
COUNTY
ASHLAND
COUNTY
IRON
COUNTY
Figure 7. Soil map of northern Wisconsin.
-------
bottoms become smoother, both resulting in a decrease in turbulence and load
transport. Also on occasions high lake level and strong wave action cause
the flow to decrease tremendously, sometimes to the point that the flow runs
upstream for as much as 1 km. The result of this is heavy deposits of soft,
mucky fines above the stream mouths. Periodically high flow rates in the
spring or during severe rainfalls scour and cleanse these areas. However,
at peak runoff, the conditions are lessened by the high flow conditions.
No attempt to estimate the amount of this transient transport of material can
be made at this time. It is reasonable to assume that the sources of error
due to these factors are reasonably low, say 10%.
All the data collected during this study together with interpolated and
estimated values appear in Appendix A.
RESULTS
Snow measurements for the study correlate well with data obtained from
the National Weather Service Office, International Airport, Duluth, Minnesota.
Comparative plots of the snow remaining at Duluth Airport and the measured
rate of runoff vs. date for the period April 7 through April 25 are shown in
Figure 8. The data indicate approximately 25 cm more snow near Pearson
Creek than Weather Bureau measurements near Duluth. Past experience makes
this difference reasonable, although it should be noted that measurements
along the South Shore varied considerably, depending upon where the measure-
ments were taken. For instance, on April 14, snow measurements varied from
26 cm near Hwy 13, Dutchman Creek to 34 cm near the mouth of Pearson Creek.
Using the snow moisture content of the samples and basin sizes, the calcula-
tions of water content for the basins were compared with measured total
discharge values for both these river basins. During the period April 7
through April 26, the calculated discharge at Hwy 13, Dutchman Creek was 2.5
x 1C)6 m^. At Hwy 13, the calculated discharge for Pearson Creek during the
period April 14 through April 27, was 1.6 x 106 m3. The measured discharge
during this period totaled 1.5 x 10^ m^. These differences are small and
suggest that the snow measurements made at a few points were representative
of the entire basin areas. It should be pointed out, however, that snow
distribution is not uniform over large areas, and several widely spaced
stations must be monitored when determining the spring runoff. Thus, weather
data at the Duluth Airport is not sufficient for South Shore runoff studies.
Plots of total daily suspended load vs. date were constructed for all of
the major streams and are shown in Figure 9. It is interesting to note that
although the plots for all of the streams yield similar curves, a significant
difference exists between the large rivers (Nemadji and Amnicon) and all of
the smaller streams. In the smaller streams, the highest sediment load trans-
ported occurs at the onset of the runoff, although peak discharge does not
occur until later. For the large rivers peak daily load occurs during the
days of peak discharge. This difference can most likely be attributed to
the greater buildup of winter fines in the shallow streams where the flow
is reduced by ice obstruction. The large rivers are able to uniformly trans-
port the fines throughout the winter. The peaks of the suspended load curves
correlate well with the rate of runoff (Figure 8).
20
-------
o
c
M—
o
"c ^
JH • —
a _.
^> **^
"5 o
LU
M—
0) O
Icr
3.75
2.50
!.25
Figure 8. Daily snow and runoff data during snow-runoff period.
-------
15
ro
O
o
Q
10
c
o
o
"k_
1i>
SUSPENDED LOAD vs. TIME
i i
Nemadji River
f\
I
I
I
t
\
i i » i i »»» i i i » i i i i i i i i i i
15
Figure 9.
20 25 30 I 5
April May
Daily suspended load for analyzed streams during the
entire runoff period.
-------
SUSPENDED LOAD vs. TIME
DUTCHMAN CREEK
BARDON CREEK
IS 20 21 22 23 24 25 26 27 28 29 30
APRIL
234
MAY
80
70
60
£ 50
a
£40
o
o30
or.
£20
2
10
SUSPENED LOAD vs. TIME
TEN CREEK
PEARSON CREEK
20
APRIL
Figure 9. (continued)
30 I
MAY
23
-------
280
240
>-200
<
£160
K 120
o
E 80
40
SUSPENDED LOAD vs. TIME
Middle River
Amnicon River
15
20 25
APRIL
30
MAY
I
UJ
z
60
50
40
30
20
10
/\
\
\
/ \
1 \
1 \
• 1 \
1 \
1 \
1 \
1 \
1 \
1 \
. / V
1 >
' \+
1
t
1 1 1 1
SUSPENDED LOAD vs. TIME
.
POPLAR RIVER
.
X~x
/ ^N
/ ^X
/
\ '•>
\ / ^
\ / \
\_/ ^ / »
\ / "^^
\ / ^-^^
A / N
V_
""—-- — _ / ""———_
' i i i i i i i i r~~-f" i § i i t i r~—
15
20
25
30 I
APRIL
MAY
Figure 9. (continued)
24
-------
Because of the uniform nature of the clay deposits responsible for much
of the eroded load, it was hoped at the onset of this study that the suspended
solids and turbidity data could be correlated in order to obtain a reasonably
accurate estimate of suspended solids content of a sample by turbidity meas-
urements alone. At low concentrations this is quite feasible and has been
used extensively in lake turbidity analysis using remote sensing data, Figure
10. However, for high concentrations, the changes in suspended solids are
gross for small turbidity changes. This precludes linear interpolation
beyond turbidity levels higher than 100. This nonlinearity in turbidity
measured for high concentrations is due to turbidity generally being a meas-
urement of fines, rather than the large particles present in high concentra-
tion loads. An exponential curve for turbidity above 100 is also shown in
Figure 10.
The total suspended load transported for all rivers and the individual
stream loads for the runoff period appears in Table 1. A breakdown of the
TABLE 1
LOAD TRANSPORTED DURING APRIL 1975
River Load (metric tons)
Nemadji 106,892
Dutchman 453
Morrison 34^
Amnicon 3 ^57
Ten 431
Wagner 296
Hanson 14g
Middle 2,008
Poplar 1>637
Bardon 544
Pearson 842
Unnamed #1 - #15 553
Total 117,307
25
-------
CORRELATION of TJRBSD1TY and
ED SOLiDS
(0
-------
runoff load for each stream as a function of stream length and drainage area
is shown in Appendix A. It is interesting to note that the total load trans-
ported during the snow runoff and the April rain event by the Nemadji is
roughly ten times the load of all the other streams combined, yet the total
discharge of the Nemadji is less than twice the total discharge of the other
streams. This difference suggests that a nonlinear relationship exists be-
tween discharge and suspended load. Assuming an equivalence for the streams
because of similar geologic and geographic boundaries, the total discharge
vs. total load are shown in Figure 11. Although there are not enough large
streams in the study area for conclusive results, the logarithmic plot of
discharge vs. suspended load for the Nemadji, Amnicon, and Middle Rivers
appearing in Figure 11 suggests that an exponential behavior exists between
the load and the discharge.
Loads transported per km of stream length and per square km of basin
area are shown in Table 2. The uniformity of eroded load per km in Table 2
suggests correlation between the suspended load and stream length, rather
than the suspended load vs. basin area, particularly if the figure for the
stream length comprises the main stream plus a fixed percentage of the inter-
mittent stream tributaries. This suggests that the erosion is mainly due to
immediate bank erosion rather than to surface runoff area. This further
indicates that an excellent relationship between suspended load transported
and stream length could be obtained by uniformly mapping each stream into
main trunk, main branches, and tributary branches, and then deriving a total
stream length figure based upon the sum of the entire main trunk plus a fixed
percentage of the intermittent branches. The difficulty of this system lies
in the fact that USGS maps are not consistent enough for uniform detailed
mapping. The nature of each stream should be based on long-term observation.
Continual, detailed aerial photography would be sufficient for this purpose.
RAIN RUNOFF
To monitor the runoff during the summer, five stations including rain
gauges were set up: one on the Nemadji at the Golf Course Bridge, one each
at Hwy 2 and Hwy 13 on the Amnicon River, and one each on the Poplar River
at a county road 3 km south of Hwy 13 and a county road 4 km north of Hwy 13.
The necessity for measurement of rainfall rates and distribution becomes
evident from examination of the runoff data obtained at the rivers in compar-
ison to the rainfall recorded at Duluth during the same period. The Duluth
precipitation measurements are completely inadequate for this purpose,
although those are generally the only data readily available.
There are no significant rain runoff events from early July through
October 20, 1975; on two occasions 1.25 cm (0.5 inch) rainfall was recorded
at various stations, but the ground was so dry that the rainfall did not alter
the suspended load appreciably.
27
-------
o
'k_
-------
VO
TABLE 2
SNOW RUNOFF PER LINEAR KM OF STREAM LENGTH AND PER SQUARE KM
OF BASIN AREA FOR THE PERIOD APRIL 10-27
RIVER
DUTCHMAN
(south of Hwy 13)
TEN
(south of Hwy 13)
POPLAR
(south of Hwy 13)
+ POPLAR
(between stations)
* BARTON
(south of Hwy 13)
* PEARSON
(south of Hwy 13)
* PEARSON
(between stations)
% INTERMITTENT STREAMS
INCLUDED IN STREAM LENGTH
50%
50%
50%
100%
50%
50%
50%
TOTAL RUNOFF LOAD
PER LINEAR KM
METRIC TONS
9.1
10.1
8.0
17.4
7.0
12.7
13.9
TOTAL RUNOFF LOAD
PER SQUARE KM AREA
METRIC
16.3
19.3
15.2
29.6
9.4
18.8
26.8
TONS
+ 100% intermittents included because the stretch between the station does not include the
source area, which always includes a large number of intermittents.
* USGS map indicates entire stream to be intermittent, which is not correct in comparison with
similar streams.
-------
Thus the general monitoring of summer rain events was unsuccessful
However a rainfall event in the spring at the end of April was well estab-
lished for the entire area, as was a late June and early July rainfall event
for the Nemadji, Figure 12, which is the most important runoff source. The
ratio of suspended load in the Nemadji to the total load of the other Douglas
County streams observed during the snow runoff was preserved for the rain
runoff in the spring. This was largely because the soil conditions at that
time were the same as those during the spring runoff. The summer vegetation
may alter this ratio.
-i, «- u j rUn°ff characteristics of the Nemadji River, and assuming
that the load ratio for the Nemadji and the Douglas County streams was the
same as in the spring runoff, the output due to rain runoff for the past few
years is estimated in Table 3 and total yearly runoff due to all streams is
TABLE 3
SUMMER RAIN RUNOFF FOR NEMADJI RIVER (1970-1974)
(metric tons)
May
June
July
Aug.
Sept.
Oct.
Nov. 1-15
Total
1970
35,545
19,396
60,109
4,991
30,245
128,237
44,500
323,023
1971
58,959
34,305
75,765
71,991
51,618
87,173
23,182
402,993
1972
23,165
90,914
135,909
196,636
88,127
8,895
21,818
565,464
1973
89,455
37,182
25,682
147,664
93,464
74,223
809
468,479
1974
20,050
46,191
81,364
64,727
5,359
5,982
31,300
254,973
estimated in Table 4. Not included in the total in Table 4 is the contribu-
tion from Bluff and Bear Creeks, which flow into Allouez Bay, and contribu-
tions from streams such as the Pokegama River, which flows into the
St. Louis River.
An important question is how much of the Nemadji's load contributes to
Lake Superior turbidity. This is not known and has not been included in the
30
-------
tf> s
i— W-
o a)
•*= 9 3.75
^\ 1 "^L~
T_ VJ "^
\ ^
== 2 2-50
V— J5
cr
Discharge (m3/sec)
§ § 1
NEMADJ1 R\\
1
1
__jt_
t
/ER SUMMER RAIN EVENT
/• n<«:« _____
» ^
| ' Dischorgc -----
/T\ Load
; i \ :
/ \ \ :
_ ^H-r'^r^JlIl^^ '
23 25 27 29 i 357
JUNE JULY
o
•o
o
o
J
T3
O
5 5
c:
o
Q.
tn
Figure 12. Daily rainfall and Nemadji River discharge and suspended-load
data for a summer rain event.
-------
TABLE 4
YEARLY INPUT OF SUSPENDED LOAD
(metric tons)
Average
yearly rain
runoff
Spring
runoff
Total
Nemadj i
402,986
106,892
509,878
Doug. Co.
40,298
10,415
50,713
Bay. Co.
23,210*
6,000*
29,210
Total
466,494
123,307
589,801
* Based upon University of Wisconsin, Superior data for spring
runoff for Bayfield County Streams (EPA R-005169-01) .
measurements. Such measurements would have to account for the seiche actions
affecting the transports in Duluth-Superior Harbor and would require continu^
ous monitoring of the turbidity in the Nemadj i and along the Superior entry
A rough estimate can, however, be obtained from two approaches.
«h« Kt.uTT °f samPles from red clay banks off rivers and the lake-
shore by the University of Wisconsin, Superior (Bahnick et al., 1972) show
roughly that 30% of the material is less than 4 y in size. It is anticipated
that at least 25% of the Nemadji's load would wash out into the lake f^om-
?he Nemaali ? M s^H*" d±Stribution of the Particles in the lake and in
the Nemadj i Table 5, indicates that roughly 60% of the load finds its way
into the lake. This estimate of the fraction of load from the Nemadj i
entering the lake directly is in agreement with a rough order approximation
obtained from the satellite data for June 14, 1975, which show 14,000 tons
of material in the lake due to runoff while the output for that event in
the Nemadji totaled about 27,000 tons. Accounting for the output of the
Douglas County streams, this indicates roughly 50% output into the lake from
the Nemadji River. Based on the assumption that 90% of the particles 3 u
and less flow out into the lake, the estimate obtained from the particle-size
data indicates that nearly 40% of the coarser particles also flow out into
the lake.
CONCLUSIONS
The 1975 spring runoff for the rivers is estimated to be 117,000 metric
tons for Douglas County rivers and the Nemadji River, with the exclusion of
Bluff and Bear Creeks flowing into Allouez Bay. The Nemadji is responsible
32
-------
TABLE 5
PERCENT ABUNDANCE OF PARTICLE SIZES BY NUMBER
Particle Size
Netnad j i
Lake Near Shore
Lake Intermediate
Lake Deepwater
Dutchman Creek
0-2 y
2-3 y 3-4 y 4-6 y
6-20 y
12
21
30
30
19
10
15
17
16
13
24
24
23
23'
22
47
35
27
29
41
7
7
3
2
5
for 90% of the total runoff load in the spring. An estimated 75% of the
contribution to lake turbidity due to runoff comes from the Nemadji River
Basin. This contrasts with the total discharge of the Nemadji,which is ap-
proximately twice the runoff for the Douglas County streams. These numbers
may be accounted for by the fact that the erosion rate appears to increase
exponentially with the discharge irate.
The eroded load correlates better with river length as opposed to drain-
age area, indicating that immediate bank erosion is primarily responsible for
the load rather than the area of the drainage basin. The erosion per km of
stream length is roughly 10 tons for the spring runoff, and an estimated 0.7
tons/km per cm of precipitation runoff.
33
-------
5. SOURCES AND TRANSPORTS OF TURBIDITY IN WESTERN LAKE SUPERIOR
ESTIMATION OF SEDIMENT RESUSPENSION AND TOTAL LOADING
A measure of shore erosion and sediment resuspension can be obtained
from Landsat remote sensing and ground truth data. Reliable correlations
between satellite imagery data and measurements of turbidity and suspended
solids concentrations have made possible reasonable estimates of the total
suspended load in the lake and its distribution on satellite-overpass days.
This method of estimating lake loading has several advantages. Since only
a representative number of stations must be sampled on satellite-overpass
days, manpower and field-sampling requirements are limited. Furthermore,
this method measures primarily the fine particulates which remain in suspen-
sion for prolonged periods and hence pose an environmental problem. This
method also provides a better understanding of the transports of the loaded
material and subsequent resuspension processes as a function of meteorolog-
ical and lake conditions.
Analysis of Landsat Imagery
To be useful, remote sensing data must be correlated to ground truth
data. Numerous samples were taken on Landsat-overpass days. Satellite
imagery was analyzed in the vicinity of these sampling stations. A reliable
correlation was established between surface turbidity and relative Band 5
intensity, Figure 13. Relative-band intensity is defined as the difference
between the signal at a given site and the minimum signal observed in clean
sections of the lake, turbidity is in turn correlated with suspended-solids
concentrations, Figure 10. Since suspended red clay particulates from shore
erosion, sediment resuspension, and river runoff are fairly uniform and are
similar in nature, the correlations shown in Figure 10 and Figure 13 are
valid for the entire load of suspended red clay. These correlations make
possible the delineation of various levels of suspended-solids concentrations
directly from Landsat imagery, Figure 14.
In analysis of the Landsat data, 70 mm positive transparencies were
viewed on an optical density slicer. Band 5 intensities were determined by
comparison with the calibration step wedge provided on each transparency.
The study area of the lake bordered by Douglas County, Wisconsin, and St.
Louis, Minnesota, shores was subdivided into 77, three-kilometer-square grid
spaces, Figure 15. For each satellite image several readings were taken in
each grid square and averaged. The data was then processed on a computer.
The grid allowed for a comparison of the turbidities at various points to the
insitu measurements at those points. On a few days Landsat computer compat-
ible tapes were available. The Landsat tape data is more accurate and
allowed for a check of the optical data reduction methods. The tape data was
used in effluent tracing, to distinguish red clay from other particles in low
34
-------
ID
I-
JQ
y_
Z3
h-
M.S.S. BAND 5 TURBIDITY CALIBRATION
TB=2.0*(REL B5)-4.0
= 0.98
Relative Band 5 Intensity
Figure 13. Turbidity calibration of Landsat image.
-------
u>
(^
vMSfe
/
*/i
W&rS&ZW
WPcP,
> n o o
•&S~'°1
Pl o o'-r o o~'-
//',,"f,''-c—°-
V ''. ' -" ,'^^
'./•>K?>^K>
'oVoVo"o°^>
P^^v^,r
" " PrP-f «^0 O V0°0 ',
::;:i:i:;:;:|:;:;:;::::::::::::::i::::::X;:::v:jx;:;::::::::::
::^:-:::^:S::S:::::::::::::::::^^:^:^:S:::::::::
:::-x':x'::o:X:::::::Xx':x::::X^:x:x'£x'£x'^
•:^:^x^:::::::::::::::::X:X::-:^:::^x::::::::::::::
::::::S^:::::::::::::X:::::X::::;:^:^:^X::::-::X::
E SUPERIOR' 11111
•••.••'•'X-X'X'X-x x-X'Xvx-x-x-v'X-x-x
x:::x::::X:X:X:::::X::::::::::::::::::::::::::::::Xx:
:x
SU5
:£S:Wx:
COGCOOCK.
O O D O Q O O O
oc-oooooo
oooooooo
lOOCOOOOO
•.rxin^n^'^iO
3. SOLIDS mg/L(LAKE)
'"4 KSS 12-14
4-8 Vi*jS 14 +
8-12
^
^SUPERIOR
' o o oo co or o A o-o o r. o o
,0 O O •
.CO'O o o OJ
^W::"»°:
or. o no o
JMI
Uo^"o_o-o
^o.,o c.>>
•TOfifBiftefr
"•Wm&MoV
>
v> <•.• ,-.<:• o"o>
,te?M^^
V^0^°,",o"o°p2
•^r^-V^V^V^VV,:
;.,;--.,;',(-'^,%o0o.;,.,,.;.y,
^
1.5 3.0
km.
HARBOR a LAKE IMAGE DENSITY LEVEL Vs. LAKE TURBIDITY
ERTS E-1434-5 SEP 30 1973
Figure 14.
Representative suspended-solids distribution produced fro, Landsat data.
-------
Knife
SUPERIOR
Amnicon
Dutchmans) Creek
Figure 15. Lake grid spaces and regions used in Landsat-image analysis.
-------
descrlbed above> the distribution of surface
each image analyzed. To derive total suspended
11? T turbidit,ies' vertical P^files of suspended solids'concen-
est^ted. The study area was divided into seven regions
Fieurs M
!n?forn, ^ "T^"^ Bleated turbidity profiles in these regions were
uniform throughout each region and remained more or less constant throughout
sotidTi,; TT Kati°S °f SUrfaCe SUSPended solid« to average suspende
solzds in each of these regions are shown in Table 6. Using the values in
TABLE 6
RATIO OF AVERAGE TURBIDITY TO SURFACE TURBIDITY
FOR WESTERN LAKE SUPERIOR
Region
1
2
3
4
5
6
7
Ratio
1.0
1.1
1.2
1.1
1.5
1.2
1.2
this table, the surface turbidities derived from satellite data, and the
calibration between turbidity and suspended solids, the total suspended
loads shown in Table 7 and their distributions were derived.
Estimation of Sediment Resuspension
To determine the relative contribution to lake turbidity due to erosion
sediment resuspension, and runoff, the data was examined in light of weather '
records of winds and precipitation. The observed plumes were categorized to
distinguish between events which show predominant input from one source and
events displaying a mixture of contributions from various turbidity sources
For instance, spring events yield a measure of the magnitude of the sediment
38
-------
TABLE 7
TOTAL SUSPENDED LOAD IN WESTERN LAKE SUPERIOR
(metric tons)
12AUG72 88,000
060CT72 58,000
29NOV72 50,000
16DEC72 32,000
28MAY73 115,000
03JUL73 61,000
12SEP73 28,000
30SEP73 46,000
180CT73 32,000
190CT73 29,000
06NOV73 36,000
23NOV73 34,000
22MAY74 59,000
27JUN74 77,000
28JUN74 53,000
15JUL74 94,000
25SEP74 38,000
26SEP74 36,000
18NOV74 27,000
15MAR75 31,000
03APR75 198,000
11APR75 412,000
12APR75 338,000
09MAY75 94,000
18MAY75 58,000
27MAY75 58,000
14JUN75 61,000
23JUN75 64,000
19JUL75 38,000
06AUG75 51,000
02SEP75 51,000
11SEP75 39,000
080CT75 27,000
170CT75 54,000
180CT75 56,000
04NOV75 34,000
14NOV75 90,000
21FEB76 30,000
05APR76 78,000
06APR76 61,000
03MAY76 56,000
11MAY76 36,000
12MAY76 41,000
20MAY76 38,000
39
-------
resuspension term. The fact that the turbidity during spring events is
attributable to resuspension only is justified from the observation of the
lakeshores and the simultaneous monitoring of river runoff. For example,
examination of the photograph in Figure 16,which was taken on April 12, 1975,
shows that even in the absence of the lake ice cover, a substantial ice ledge
1-3 meters thick at the shore and 30 - 60 meters wide protected the south
shore from direct removal of the material from the clay bank. This ice shelf
left resuspension as the only major source of red clay turbidity until the
spring runoff began on April 13. Consecutive images on March 15 and 16, 1975,
showed an increase of about 2 x 103 tons of suspended load in resuspension
areas. Some of the turbidity in the March 16 image was attributable to
erosion of the North Shore, which had no protective ice shelf, but the
increase in the resuspension zones was probably caused by a 5 m/sec north-
easterly wind on March 16. Images from April 3 and April 11, 1975, yielded
observed suspended loads of 149 x 103 and 184 x 103 metric tons, respectively.
Weather records show strong northeasterly winds in excess of 5 m/sec prevailed
between these two satellite overpasses which resuspended on the order of 1.2
x 104 tons of material per storm-day. Such turbidity events occur on the
average two to three times for the ice-free conditions on the lake and gener-
ally leave the early spring and late fall average turbidity much higher than
the average turbidity during the months of June - November, Figure 17.
The total suspended load observed during the study period, including the
resuspension term in the months when the shores were ice-covered, was 9.18 x
105 metric tons as compared to the load of 6.1 x 10$ metric tons'for the May -
November season. Thus, at least 35% of the year-round lake turbidity was due
to the sediment resuspension. Since sediment resuspension is generated by
steady northeast winds in excess of 5 m/sec, it contributes up to 30%
of the total turbidity for severe storms in the summer months as well. Based
upon data from pure resuspension events, if winds in excess of 5 m/sec which
prevail over 24 hours resuspend about 10^ metric tons of fines per storm day,
then the total contribution due to sediment resuspension for the entire year
increases to about 45% of the total observed turbidity on the lake. Thus,
sediment resuspension should play an important part in the consideration of
the lake turbidity and its effects on the water quality and in considerations
of leachate from the red clay (Bahnick, 1972).
A better estimate of the fraction of the observed load attributable to
resuspension for the summer events was obtained by examination of the remote
sensing data in light of weather records. Only the images for the May -
November season on days when precipitation could be neglected were used.
Resuspension was considered significant only after easterly winds exceeding
5 m/sec and lasting approximately 2 or more days. These criteria were met
in about 35% of the events. Since the summer wind storms are usually mild
and short in duration, the resulting plumes usually are not transported far
from their sources. Thus, the suspended load in a series of source points
which extended from Amnicon River to Bardon Creek was considered a good
measure of erosion. These source points were in the middle of the south
shore erosion belt along a uniform red clay bank far away from known resus-
pension areas. Since the near-shore zone accumulates only a thin veneer of
red clay,which is quickly removed by succeeding storms, the turbidity in
40
-------
Figure 16. Spring ice shelf near Amnicon River
(1-3 meters thick).
41
-------
T 1 1 r
0
T r
-— 1973
4 year average
T r
T r
^X^-.JU^'
A -
1 - 1
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Figure 17. Average lake turbidity near Duluth.
-------
these source points was attributable almost entirely to erosion.
The fraction of the total turbidity due to resuspension was obtained by
comparing the total suspended load above background for resuspension and pure
erosion events. Assuming no other sources of turbidity were present, the
total load (T) was found by summing the contributions of erosion (E) and
resuspension (R). Letting the subscripts "r" and "e." denote resuspension and
pure erosionjevents the equations become:
T = E + R
r r r
T = E
e e
(1)
The contribution of erosion was assumed proportional to the suspended load (S)
in the erosion source points. Letting a denote the constant of proportion-
ality, equation (1) becomes:
T = aS + R
r r r
(2)
T = aS
e e
Summing overall observed events and eliminating a, the fraction (f) of
observed turbidity attributable to resuspension was found:
ER (ET - ET • SS )
r. = r r r ee rr
ET + ET ET + ET
rr re rr ee
Calculations using equation (3) indicated about 16% or about 10 tons of the
observed turbidity for the May - November seasons was due to resuspension.
This value is close to the one obtained from the resuspension rate per storm
day derived from observations of pure resuspension events.
Estimation of Shore Erosion
The actual eroded load throughout the year in its relation to the ob-
served suspended load depends on the total number of storms, the dispersion-
settling factor, and the cloudiness. These factors must be taken into con-
sideration in the determination of total shore erosion. The erosion process
takes place throughout the time when the shores are ice-free. Generally, as
will be pointed out in the numerical model, northeasterly winds raise the
lake level and produce waves which directly abrade the red clay bank toe.
Many times, large chunks of clay fall into the water, where they are rolled
around in the sand slurry and produce large round balls of red clay which
dissipate rapidly and give rise to high turbidity in the near -shore area.
Many areas of the beach have a veneer of sand covering the red clay which is
subject to erosion by the wave action. The erosion takes place in a season
roughly 210 days long.
-------
To determine the total eroded load from the data in Table 7, the
statistical nature of the problem was considered. If the events occurred
randomly, then the observed turbidity should be directly related to the total
turbidity input through the dispersion and settling rate and the probability
that an event was observed. This is true provided the overlap of the events
was reasonably small and the time for the decay of the event to the back-
ground turbidity values was short compared to the period between observations.
Both of these conditions are satisfied when images for successive days are
considered as a single observation. If "t" is the time after a storm, f(t)
the dissipation function, p(t) the probability density that a storm was
observed at time t given that the storm was observed, and So the total initial
suspended load, then the total observed load (T) is given by equation (4):
t
o
T = / f(t) • P(t) dt = S f(t) (4)
oo °
Using equation (4), the average suspended load of observed storms can be
calculated. Assuming all storms regardless of magnitude are equally likely
to be observed by satellite, the total load of all storms can then be
obtained by multiplying average load by the total number of storms.
Measurements of turbidity dissipation for easterly and westerly wind
storms, Figure 18, indicate that turbidity for a typical storm remains above
background for approximately 8 days. The turbidity dissipation for a large
storm in early November 1974 is shown in Figure 19. Assuming the dissipation
rates for other storms were similar, one obtains the typical dissipation
curve shown in Figure 20 using the relationship between turbidity and
suspended solids, Figure 10.
The two functions, f(t) and p(t), are not independent. The storm bvild-
up times for high easterly wind storms have a low probability of being
observed since they are almost always accompanied by cloudiness. This consid-
eration is important because the settling rate for the first day is very high.
Cloudiness is not the only obstacle in the successful observation of turbid-
ity. At the peak of the storm, concentrations of suspended solids often
exceeded 100 mg/£, the point at which the Landsat optical signal saturates.
Because of the nature of the sources and currents, very high concentrations
of suspended solids are often confined at the beginning of a storm to a
small area near shore which is susceptible to blockage by partial cloud
cover and the limits of spatial resolution of the satellite. Since the tail
of the storm is highly observable, the total observed load is a small fraction
of the initial or total load.
The function p(t) was approximated using weather records and the above
considerations, Figure 20. For most of the time during the storm decay,
p(t) assumed nearly a constant value. Numerical calculations give the
average observed storm intensity p(t) a value .11. Since most of the
turbidity observed was "fines," on the order of 11% of the total load was
44
-------
ADO — Easterly Storms
' -*- Westerly Storms
— —
i
1
I
- i A
\
x9
i
ft w
o A
^
^^ ^^^b^k^^k
^^^TsS^B^__^^
^^ ^^^^™^^P
1 1 1 1 1 1 1 1 1
"^nn
3 200
h-
^^
>*
"O
lo
w.
Z3
H 100
0
1 1 1 1 1 1 1 1
AMNICON POINT
1
\
-\
\
\
\
\
\
\
\
- \
\
X
X
1 1 t I 1 1 1 1
0 I 23456789 10
Days
Figure 18. Average turbidity dissipation for
easterly and westerly wind storms.
13579
November 1974
Figure 19. Actual turbidity dissipation
for a large easterly storm.
-------
T3
O
O
jQ
I 10
12345678
Storm Duration (days)
Figure 21. Distribution of storm duration.
-------
attributable to the fines. Particle-size data for lake samples and river
samples indicated that fines consist primarily of particles less than 4 u
(See Section 4.)
Wind data for western Lake Superior was analyzed for days showing steady
easterly and northeasterly winds in excess of 5 m/sec. Records of storms in
the past few years and insitu measurements have shown easterly wind storms
give rise to high turbidity in western Lake Superior. The distribution of
storms for the ice-free season from August 1972 - August 1975 is shown in
Figure 21. The category of storm depended on the duration and sequence of
wind; thus single-day events, double-day events, etc., were derived from
successive days of dominant high winds. The total number of events was 63.
Subtracting estimated contributions of resuspension and runoff, the total
observed load attributable to erosion is 4.37 x 105 metric tons. Since 20
images showed^turbidity above background, the average observed eroded load
was 2.19 x 10s metric tons. The total initial eroded load (S0) for an
average storm can be obtained by dividing by f(t). This gives S0 a value of
2.0 x 105. Assuming all storms were equally likely to be observed, the total
eroded load over the three-year year period, 1.26 x 107 metric tons, was found
by multiplying by the number of storms. Thus, about 4.0 x 106 metric tons of
eroded material is loaded into the lake per year.
Table 8 summarizes the estimated magnitudes of the various sources of red
TABLE 8
SOURCES OF LAKE TURBIDITY
Average Rate/Season % Contribution
(May - November) (Rounded off)
Metric Tons
Lakeshore erosion for Douglas
County, Wisconsin 4.0 x 10^ 75%
Sediment resuspension (May -
November) in extreme western
Lake Superior
River runoff contribution to
lake turbidity
Sediment resuspension
conditions (Dec., Jan
for winter
• , Apr.)
1.0
.32
2
x 106
x 106
x 106
20%
5%
47
-------
clay turbidity in western Lake Superior. As was established by insitu meas-
urements, the runoff comes principally from the Nemadji. Since runoff sources
were relatively small in magnitude and infrequent, insitu measurements
provided a good estimate of their magnitude. Shore erosion and resuspension
contribute much greater loads. In addition, their contribution is continual
and geographically more extensive. Landsat remote-sensing data were ideally
suited for estimating the contribution of these sources.
TURBIDITY TRANSPORT AND THE DISTRIBUTION OF TURBIDITY SOURCES
Statistical analysis of turbidity distributions for various wind condi-
tions yields information on turbidity transports and the nature of the
turbidity sources. Images were examined in light of weather records and
classified according to the kind of storm that gave rise to the observed
turbidity. The relative turbidity taken directly from the density slices
indicated that for an easterly wind storm, turbidity from red clay banks along
the Wisconsin shore is transported toward Wisconsin Point, where it is subse-
quently taken out in a return path along the axis of the lake, Figure 22.
This transport pattern was also established by a numerical model of currents
in Lake Superior. (See Section 6.) Similarly the transports for westerly
winds, derived from statistical analysis of the plume shapes, yields trans-
port paths shown in Figure 23 and 24. Variable winds tend to produce circu-
lation eddies, and periodically trap the degraded water from the St. Louis
River in the areas near Duluth, Figure 25. The range of transport of red
clay particles can be assessed from the analysis of the Landsat image for
April 11, 1975, where a resuspension plume traveled in high concentrations
for about 135 km between Grand Marais and the Apostle Islands, where it had
a concentration of 2 mg/Jl.
The distribution of turbidity sources can also be obtained from Landsat
data. The average turbidity for the ice-free season is shown in Figure 26.
Using this figure one obtains the map of relative erosion rate shown in Figure
27. Thus the 4.0 x 106 metric tons of material eroded along the lakeshore
is distributed fairly uniformly along the shoreline, with maximum rate just
west of the Amnicon River and near Middle River to roughly half the rate west
of the Brule River. For high northeasterly winds, sediment resuspension
takes place. Examination of the relative distribution of turbidity for such
storms, Figure 22, in comparison to turbidity distribution for other events,
Figures 23 - 26, indicates that the resuspension area exists north of Dutchman
Creek, which enters the lake at the southern most part of the lakeshore in
Douglas County, Figure 28. Intermediate depth areas along the Douglas County
shore are also subject to sediment resuspension after periodic accumulation
of material in those places during the quiescent times. The determination of
the resuspension areas are, however, quite difficult since for high northeast-
erly winds, considerable erosion takes place, the transports are rapid, and
the probability of observing a storm at the peak moment is low because of the
accompanying cloud cover. A good verification of the suspected resuspension
areas can be obtained from the early spring events which occur before runoff
and during the time when there is a protective ice shelf along the shore to
inhibit direct lakeshore erosion. These indicate that the south shore and
Dutchman Creek areas and the waters off Minnesota Point are the major resus-
pension areas, in agreement with Figure 28. The area off Minnesota Point
48
-------
* ->
""LAKE SUPERIOR
Jr
•W/S'AV *' *
***?***>'..&
Relative turbidity for Easterly storm
LAKE SUPERIOR
Km.
Turbidity transport for
North Easterly storm
Figure 22. Average turbidity distribution and transport for
an easterly storm.
49
-------
*LAKE SUPERIOR
* A
\ v v
Relative turbidity for N.W. S W. winds
LAKE SUPERIOR
km.
Turbidity transport for N.W. SW. winds
Figure 23. Average turbidity distribution and transport for a
westerly storm.
50
-------
N
"""LAKE SUPERIOR
km.
Relative turbidity for Easterly storm
followed by westerly dispersion
N
LAKE SUPERIOR
km.
Removal of easterly storm turbidity
by N.W.SW. winds
Figure 24. Average turbidity distribution and transport by
westerly winds.
51
-------
"""LAKE SUPERIOR
v
Relative turbidity for variable winds
LAKE SUPERIOR
Turbidity dispersion for variable winds
Figure 25. Average turbidity distribution and transport for
variable winds.
-------
Ui
OJ
N
^ <"
v " * * * *
\AKE SUPERIOR
\
km.
Average turbidity (NTU)
(ice free season)
Figure 26. Average turbidity distribution for the ice-free season.
-------
Relative erosion rate
for red clay bank
LAKE SUPERIOR
km.
Figure 27. Relative south shore erosion rate.
LAKE SUPERIOR
Likely resuspension areas
Active areas
km.
Figure 28. Resuspension areas in Lake Superior.
54
-------
should be particularly subject to periodic scouring since it lies between
two major river turbidity outputs, the St. Louis and the Nemadji rivers
At the same time the area midway off the Minnesota Point is the place where
major near-shore currents meet for the easterly storm conditions.
55
-------
6 . A NUMERICAL MODEL OF TRANSPORTS IN LAKE SUPERIOR
DESCRIPTION OF THE MODEL
Transport patterns of suspended material in Lake Superior have been
rather controversial. Drift-bottle studies (Ruschmeyer et al., 1961) in-
dicate an average overall counterclockwise summer circulation. Studies of
currents and turbidity transport through insitu measurements and remote
sensing studies in the extreme western arm of Lake Superior show that the
currents have complex patterns near Duluth (Sydor, 1973). These localized
currents give rise to an eddy circulation off Minnesota and Wisconsin
Points which transports red clay turbidity to the area of the Duluth water
intake and accounts for the general turbidity of the water near Duluth.
Numerical modeling provided a means of studying lake circulation. However,
to investigate transports in western Lake Superior— that is rnnohlv f*
nrp time-dependent mathematical model used for the
present study is based on a tidal simulation model developed by Leendertse
(1967) for the Rand Corporation. The model has several features which make
it an attractive choice for predicting water levels:
1) The nonlinear convective-inertia terms are retained in the equations of
motion resulting in higher accuracy in regions where the land-water
boundaries are complicated.
2) The space-staggered grid has the advantage that there are centrally
located spatial derivatives available for the linear terms of the partial
differential equations.
3) The multi-operational method used in the solution of the partial differ-
ential equations is accurate to 2nd order in time, yet requires only two
successive arrays to be stored for the water-level field and each of the
velocity fields. Furthermore, the method is unconditionally stable,
with no upper limit on the number of time steps. Numerical experiments
conducted by the Rand Corporation, as well as tests in this study,
showed that moderate variations in the time step size had a negligible
effect on the predicted water levels, which are needed later by the
current profile model. In order to model wind-induced water levels and
transports for Lake Superior, the effects of wind stress were incorpo-
rated into the tidal model.
56
-------
Mathematical Formulation
Consider a cartesian coordinate system in which z is increasing upward.
The equations of motion for a viscous fluid are given by
9u , 3u .
T— + ur— +
9t 3x
3u , 3u _ . 1 3p
fr h WT— - f V + T-*-
3y 3z p 3x
.
+ v
32u
(5)
3v
3v
3v
3v
,
+
32v,
32
(6)
3w . 3w , 3w , 3w ,. . 1 3p
— + u— + v— + w— + f v +
3t ^x ^y ^z e p 3z
r32w , 32w, , 32w , ,_.
VT + T~2"5 + v V~2" + 8 (7)
3x 3y vdz
where u, v and w are the x, y and z components of the water velocity, v and
vv are the horizontal and vertical eddy viscosity coefficients, p is the fluid
density and p is the pressure. The coriolis parameter f is equal to 2o) sin ,
where to is the angular velocity of the earth's rotation and $ is the lati-
tude. The eastward component of the water velocity is denoted by v
In studies of long-period water waves, the vertical accelerations and
velocities are generally assumed small enough ^o be ignored. The vertical
component of the coriolis acceleration is also quite small compared to g and
is dropped from eq. (7). The terms containing horizontal-eddy viscosity are
very small compared to the vertical-eddy viscosity term and are neglected in
this model. With these assumptions, the equations of motion become:
3t 3x
3y
_
p 3x
(8)
(9)
p 3z
= g
(10)
A uniform density is assumed so that pressure becomes a linear function of
depth. Consequently, the model is suitable for predicting flows only when
the water is well mixed. Since,in a typical year, stratification does not
develop until August and disappears by October, Lake Superior can be consid-
ered well mixed during the times of significant loading of red clay, i.e.,
the spring runoff and late fall storm surges. With the assumption of
57
-------
hydrostatic pressure, the horizontal derivatives of fluid pressure become
functions of the water slope:
p(z) = pg[h-z]
IlE =
p 3x
_3h
3x
=
p 3y 8 3y
where h is the displacement of the water surface from the undisturbed level.
Because they generate only weak currents, the atmospheric pressure gradients
have been ignored.
Vertically averaged velocities are introduced
U =
(H+h)
h
/ udz
-H
(H+h)
h
/ vdz
-H
where H is the depth of the undisturbed water. Vertically integrating the
simplified equations of motion from -H to h, and dividing through by H + h
gives :
(H+h) 3z
_
z=h (H+h) 3z
z= -H
+
3t
™
3y
U
3h
(H+h) 3z
z=h
(H+h)
_3V
3z
z= -H
The integrals of the non-linear terms are only approximate, but since these
are small, only slight inaccuracies result. The integration causes terms
containing the surface and bottom shear stress to appear on the right-hand
side, corresponding to the wind stress and bottom friction respectively.
The components of the bottom friction are taken proportional to the square
of the vertically averaged water velocity
3U
z= -H
= gc 2u(u2 +
3V
z= -H
-22 2 Is
gC V(U + V K
where C is the de Chezy coefficient. In general, the value of C depends upon
the roughness of the bottom, the bottom material,and the depth, and should be
determined by experiment. Tsai and Chang (1974) found that the water levels
predicted by the Rand model were relatively insensitive to the bottom frictior
used. Therefore, the values of C were calculated for Lake Superior according
58
-------
to the following formula which is based on table of de Chezy values versus
depth for lakes and rivers (Hutchinson, 1957);
. 0, . .168745
C = 25 x h
The Chezy coefficients obtained were somewhat lower but still comparable to
those found experimentally by Leendertse in modeling an estuary of the
Rhine River.
In its original form, the Rand model contained no wind-forcing function,
relying only upon water levels as a function of time along an open water
boundary as a driving force. In order to model wind-induced transports and
water levels in Lake Superior, the wind-forcing terms (Wilson, 1960)
v JHJ
(H+h) 9z
z=h
k „ ,„ 2^I7 2,h v 9V
- Wx(Wx +Wy )
were added to the vertically integrated equations of motion, where Wx and
Wy are the x and y components of the wind velocity and k is the wind-stress
coefficient. Following Tsai and Chang (1974), who did an extensive study of
wind-stress coefficients, k was taken as
k = 1.25 x 10~6 for W < W
W-W
k = 1.25 x 10~6+ 1.75 x 10"6sin (^— |- f) for V^ 1 W W2
k = 3.0 x 10~6 for W2 < W
where Wj_ = 5.1 m/sec, V^ = 15.4 m/sec and W is the wind speed. In their final
form, the vertically integrated equations for the horizontal motion are:
f
For an incompressible fluid, the continuity equation is written
— + J-Y. j. ^w
8x 9y 3z ~
59
-------
After vertically integrating, and applying the boundary conditions:
,, , dh dh . dh . dh , ..
w(h) = -r— = 1- u- 1- v— at the surface, and
dt dt dx y
dH dH
w(-H) = -UT v—- =0 at the bottom,
3x dy
the continuity equation becomes
|£ + |^ [U(H+h>] + |^ [V(H+h)] = 0 (13)
Numerical Procedure
The vertically integrated equations of motion and continuity must be
replaced by finite difference approximations which can be solved at points
on a spatial grid such that
U(jAx, kAy, nAt) = U(x,y,t) where Ax = Ay = As
j = 0, ± h, ± 1, ± 3/2, ...
k = 0, ± h, ± 1, ± 3/2, ...
n = 0, h, 1, 3/2, ...
A space-staggered grid is used in which the x and y components of velocity,
water levels, and depths are located at separate points.
k+l + - + -+ + water level (h)
k + % o | o | o Depth (H)
k + - + - + - x-comp. of velocity (U)
k - ^ | o j o | | y-comp. of velocity (V)
x
j-l j j+1
60
-------
The advantage of such a grid is that centrally located spatial derivatives
across only one grid space are available for the linear terms of the partial
differential equations. The land-water boundaries are fitted through the
depth locations, and the perpendicular component of velocity at the boundary
is fixed at zero.
In order to see how the numerical integration might be performed,
h(t + At) is expanded about h(t) in a Taylor's series:
h(t + 4t), h(t) + At
To first order in At, the new h is found in a single time step where
^(n+1) „ ^(n) + At _dh ig found by evaluating the continuity equation using
finite differences on the grid. This is the simplest scheme, however it has
the disadvantage that errors tend to build rapidly in time because of the
low order of accuracy.
In the Rand Model, a double time step operation is used to perform the
numerical integration. Each step has two time levels associated with it,
the first from time n to n + h, and the second from time n + h to n + 1. The
spatial derivative and coriolis force terms alternate between the old and new
time levels in each step such that over the two successive steps of the time
interval, these terms are either central or averaged in time. By using a
combination of central and time-averaged terms, the resulting integration is
accurate to second order in time while requiring only two successive fields
of information to be stored at any given time. During the first operation,
the fields of h(n4^), U(n+^) , and V(n-f^) are computed from the fields of
h(n), U(n), and V(n). Since the solution for h(n+3s) involves U(n+^) while
the solution of U(n+%) requires knowledge of h(n+%), the equations for an
entire row are written in matrix form and solved simultaneously to develop
recursion factors which enable the computation of h(n+33) and U(n4^) to be
carried out implicitly. Once these fields are known, V(n+^) can be solved
explicitly. Similarly, in the second operation, the fields of h(n+l),
U(n+l), and V(n+l) are computed from the fields of h(n+^), U(n+%), and
V(n+*5). In this case, h(n+l) and V(n+l) require each other for solution so
they are solved implicitly using a recursive scheme, and finally U(n+l) is
solved explicitly. Some of the nonlinear terms had to be approximated at a
lower time level in order to avoid an iterative procedure which would require
excessive computation time.
RESULTS OF TRANSPORT MODEL
Lake-Level Oscillations
Because of their observed importance in the transport of suspended
materials in western Lake Superior, two main types of wind stresses were
modeled, an easterly and a westerly. Both wind functions were constructed
from the composite of a large number of weather observations and thus
represent "typical" weather patterns. For example, the northeast wind becomes
61
-------
out of the southeast as one moves toward the east end of the lake, as though
a low-pressure area with its counterclockwise air circulation were PPnf*ro,1
south of the lake. Similarly, the westerly wind represents a low-pressure
center north of the lake.
The transport model was verified by comparing observed water levels for
easterly and westerly wind stresses with that obtained from the model.
Fourier analyses for both wind stresses are shown in Figures 29 and 30.
Notice that the 7.8-hour mode is dominant in both cases. A series of high-
frequency modes appear at the general frequencies reported by Rao and Schwab
(19/6) and found from experimental data by Mortimer and Fee (1976) Table 9
The model also appears to exhibit a 5.6-hour mode, which was also occasion-'
ally observed in the lake-oscillation data taken at Duluth. Similarly the
model exhibits a 2-hour mode which was observed in the lake data at Duluth.
This mode plays an important role in the mass transport in Duluth Harbor.
The transports from the model were also verified by comparing them to the
transports of turbidity obtained from statistical analysis of the Landsat
data (described in the section on Turbidity Transport), and the general
shape of the turbidity plumes observed in Landsat images.
Predicted Transports in Western Lake Superior
The results of transport calculations for northeasterly winds are given
in Figure 31. It is seen that for northeasterly winds which present a large
fetch at Duluth, there is a strong current along the North Shore from Silver
Bay to Duluth; Figures 31A - 31C. This generally accounts for the transport
of large concentrations of taconite fines to the Duluth intake area for high
easterly winds (Baumgartner, et al., 1973). For northeasterly winds, the
transport along the south shore is due west. This transport and the one
coming down the North Shore appear to turn and meet at Minnesota Point and
then return out in the middle of the lake along an axis running parallel to
the North Shore. This transport pattern is consistent with that obtained
from statistical analysis of Landsat images. Figure 32 shows a resuspension
plume after an extended northeasterly wind. Red clay from south shore
erosion and from sediment resuspension moved along the Wisconsin and Minnesota
Points, then abruptly turned out along the axis of the lake. The turbidity
on that date at Minnesota Point Airport was 50 mg/£ and dropped to 8 mg/i
1.5 km farther towards Duluth, where it generally reflects the near-shore
turbidities of the water coming in from the North Shore and from the St. Louis
River out of the Duluth entry.
As the northeast wind slackens, Figure 31E, the transports in extreme
western Lake Superior begin to subside and scramble. A large clockwise circu-
lation cell appears to form northwest off the Apostle Islands. The plume
moving out along the axis of the lake becomes unstable, and disperses. Thus,
for high-turbidity events, the Duluth intake becomes contaminated by red clay,
Figure 33. Figure 31F shows the transport pattern 14 hours after the north-
east wind was completely relaxed. A counterclockwise cell off Two Harbors
and a clockwise cell off Silver Bay have developed. The turbidity plume off
Silver Bay due to dumping of taconite tailings from iron ore processing is
shown in Figure 34. This image strongly suggests such a circulation pattern.
The currents near Duluth at the time of Figure 31E show the characteristic
62
-------
RELATIVE AMPLITUDE (Normalized) RELATIVE AMPLITUDE (Normalized)
OQ
U>
O
o
rt
C
*TJ
grn
£,*}
-o
so
5°
ro -^
w'c/)
i-h
O
CO
rt
ro
1-1
3
a.
p
ro
p
CD
O
bo
o
ro
oo
-------
TABLE 9
COMPARISON OF PERIODS IN HOURS OF GRAVITATIONAL MODES IN LAKE SUPERIOR
Mode
(As Identified
by Rao & Schwab)
1
2
3
4
5
Observed
(Mortimer & Fee)
7.89
4.84
3.80
3.37
3.02
Calculated
(Rao & Schwa
7.86
4.45
3.76
3.17
2.94
Observed at Duluth
(Sydor)
7.88
- -
4.88
3.96
3.58
2.93
1.98
Calculated Model
Values at Duluth
7.53
5.56
4.62
3.73
3.33
2.97
2.13
-------
TRANSPORTS
ONF ftRin QPAPC
CORRE
WIND - i;
RUN 5C
>NDS TO 2M/SEC
M/SEC NORTHEAST
TIME 6 OC
Silver
TRANSPORTS
ONE GRID SPACE
CORRESPONDS TO 4M/SEC ./" x
WIND - I3M/SEC NORTHEAST f' ' '
R'jN oC TIME 8 00 A
Silver
Two
HarborSjX,
Dulufh
<
Superior
r ~< .• \ • f i
Figure 31B.
Figure 31. Western Lake Superior transports for easterly storm.
65
-------
TRANSPORTS
ONE GRID SPACE
^NRgE-S^MN/DslcTN°0^ei? ^ / /
RUN 9C TIME 28 = 00
Silver
Ouiuth
Superii
TRANSPORTS
ONE GRID SPACE
CORRESPONDS TO 20M/SEC -,
WIND — I3M/SEC NORTHEAST ft
RUN 25 TIM£40^00 A
Silver
Two
Figure 31. (continued)
66
-------
TRANSPORTS
ONE GRID SPACE
CORRESPONDS TO 20M/SEC
WIND -I3M/SEC NORTHEAST
RUN 26
TIME 4600
Silver
/' / ' • y
f' //' '
/' ' > *,' ' -.:.
TRANSPORTS
ONE GRID SPACE
CORRESPONDS TO 20M/SEC ^ ,
WIND - I3M/SEC NORTHEAST f / '
RUN 28 TIME 6000 />^ _ * *
Silver
Figure 31. (continued)
67
-------
Figure 32. Landsat image for 11APR75 showing resuspension
plume caused by northeasterly winds.
Figure 33. Skylab image showing turbidity entrapment
near Duluth.
68
-------
Figure 34. Landsat image for 23NOV73 showing taconite
tailings plume off Silver Bay.
eddy circulation off Wisconsin Point where .large amounts of sediment settle
and can be subsequently resuspended.
The transports for westerly winds, Figure. 35, are quite different. The
Silver Bay area shows transports away from the shore, while the transport of
the red clay is confined to the south shore and is taken out along an easterly
direction past Bark Point, towards the Apostle Islands, where a large counter-
clockwise cell is established, Figure 35B. As seen in Figure 35A, the
transports along the North Shore bring in water from the center of the lake
towards Duluth, where the transports disperse, and show a return path up along
the North Shore. This generally accounts for the lack of red clay turbidity
at the Cloquet intake for such winds, the generally lower taconite tailing
concentration at the Duluth intake, and the flushing of the turbid water out
of the Duluth area. However, as pointed out earlier, variable winds often
tend to cause an entrapment of the turbid waters and harbor effluents in the
Duluth area. The summer transports near Duluth are somewhat complicated by
the presence of a warm-water cell near Duluth. This generally tends to shield
the Duluth intake in the summer from the influx of tailing fines even for
easterly winds. A fine-grid model for extreme western Lake Superior, together
with measurements of water levels necessary for the mathematical description
of an open boundary where the warm-water cell ends in the lake, together with
application of water quality models to the area will be the subject of subse-
quent investigation. '
69
-------
TRANSPORTS
ONE GRID SPACE
CORRESPONDS TO IOM/SEC
WIND - IIM/SEC WESTERLY
RUN 23 TIME 3000
Silver
Two
Harbors
' x..-
.-••N.
jr. /'•>'' •••*,*'•*-•••'n-
*v''. V ''&?&*$>
-'-'•- '- '^\tf&<
}^
>v
<#'''
Figure 35A.
TRANSPORTS
ONE GRID SPACE ,
CORRESPONDS TO IOM2/SEC
IND — IIM/SEC WESTERLY
' "' TIME 48 00
RUN 31
Silver
Ouluth
Superior
Figure 35. Western Lake Superior transports for westerly storm.
70
-------
Water Levels Due to Storm Surge
Water levels from the model for a northeasterly and westerly wind storm
are shown in Figures 36 - 38. High water levels are evident at the base of
Wisconsin Point and Minnesota Point. The water levels at the shore are
actually higher than those indicated in Figure 37 which reflects the water
height at points 3 km off shore. Thus the surge at Wisconsin Point and
Minnesota Point should be between 15 and 30 cm. A water-level distribution
for a model by Forristall (1970) is shown in Figure 39. It demonstrates
more vividly the near-shore water pileup, although this method of calcula-
tion was discarded because of other shortcomings. The Leendertse model
generally predicts a pileup of water in the corners of the grid which is
quite real and not a mathematical contrivance. Wisconsin Point was breached
on November 1, 1974, while the area at the base of Minnesota Point sustained
substantial property damage during the northeasterly storm of January, 1975.
It is difficult, however, to attribute the damage directly to the water
surge, without comparing it to the wave height for such storms. Significant
wave heights for a 13 m/sec (30 mph) northeasterly over the long fetch would
run 2-3 meters at Minnesota Point with about a 6-second period, and the
anticipated disturbance would reach a depth of 20 - 25 meters. It should
also be noted that the transport velocities due to storm surges are high;
thus,if one considers the dissipation of energy as proportional to the square
of the velocity, then significant damage can be assigned to the transport
velocities directly, say ^ 15 - 25% in comparison to the potential energy due
to wave height.
The importance of water level may also be assessed from the remote sens-
ing for Douglas County, which shows a greater erosion for mild northeasterlies
than severe westerly winds producing comparable wave action. The westerly
winds depress the water level along the Douglas County shore.
Transports for the Entire Lake
One of the concerns with regard to fine particles which remain in suspen-
sion for a period of months is the possibility of direct transport of these
particles in high concentrations across the international boundary. The
possibility of such an incident was reported in April, 1975, when asbestiform
fibers were observed in the water supply of Thunder Bay, Canada.
Predicted transports for the entire lake are shown in Figure 40 for
northeasterly and Figure 41 for westerly winds. Due to space limitations,
only the vectors for alternate grid points are shown, and therefore only the
gross features of the transport patterns are visible. At the height of the
northeasterly storm, Figure 40D, the transport streamlines are moving away
from the shore zone at Silver Bay to the Thunder Bay area. Later, the part-
icles dispersed to areas away from the shore zone would apparently be
rapidly transported to the Apostle Islands area. Streamlines peeling off
the main circulation pattern, however, might carry tailings into the complex
71
-------
ZL
Water Level (cm)
co" CD
c
1-1 .
CD
u>
ON
s: i>3
w
rt
(D
I—1
fD
I CD
ft)
en
H, ro
U fV
o_J
rt 1
§3
M,® OJ
**"•» CD
^ ^
s'~*
coy)
£•*— '
g CD
e
rt
34
hti »
11 _P^
O fv %
3 r\3
rt
3*
CD
rt
i-( ]\
a> •**
g co
T)
O
rt
a
O Cxi
CD -i^
*
CD
O
-------
T
13cm
JL
Figure 37. Water levels for western Lake Superior at one peak of the well-developed
seiche caused by a 13 m/s NE wind, 31:20 hours after start of wind (Rand
Corporation Model).
Figure 38. Water levels for western Lake Superior at lowest water level during modeled
storm. Wind is 11 m/s westerly. 30 hours after start of wind (Rand Corporation
Model).
-------
—J
.p-
15cm
MINN.
PT.
Figure 39.
DUTCHMAN
wise.
PT.
Water level for western Lake Superior after 15 hours of a 13 m/s NE wind. A simple
transport model by Forristall was used with a time step of 60 sec and a smoothing
coefficient of 0.95.
-------
Ni
Ouluth
Islands . . *^ -
LAKE SUPERIOR
I3M/SEC N.E.
TRANSPORTS FROM RUN 14
TIME - 6 6
AT= 180
SCALE 0.2 CM * .500M2/SEC
Figure 40. Entire Lake Superior transports from a 13 m/s NE wind.
-------
ON
LAKE SUPERIOR
I3m/sec N.E.
TRANSPORTS FROM RUN 15.
TIME = 12 12
AT= 180.
SCALE 0.2 CM = 2.000M2/SEC
Figure 40. (continued)
-------
/» *
^- *^ 4 ' V^» «• • • . • • \
s•-•• •:-:----:-:-^-:- /
^•^^^•m^4
•:/^;--.-;-:-v>x/•>•.•:•;.;.•:-:•;.•.•;•;.•.•,
v
X*.
X>
yx
Figure 40C.
LAKE SUPERIOR
13m/sec N.E.
TRANSPORTS FROM RUN 7.
TIME = 24 24
AT = 180.
SCALE 0.2 CM = 3.003M2/SEC
Figure 40. (continued)
-------
—I
oo
LAKE SUPERIOR
I3M/SEC N.E.
TRANSPORTS FROM RUN 24
TIME = 36 6
AT = 180
SCALE 0.2 CM = 3.003M2/SEC
Figure 40. (continued)
-------
/* v x>^ - I , • • . . * * •
s>? ' /Y '»».'.•••.•.•••
^*\%C^''.\4.fc • -"V • • .'.\
^^.V-','.-;^'1.•,%%•'.'.•,-.
K *^ » _ . ^* _» * • _
LAKE SUPERIOR
13 M/SEC N.E.
TRANSPORTS FROM RUN 28
TIME = 60 6
AT= 180
SCALE 0.2CM = 3.003M2/SEC
Figure 40. (continued)
-------
00
o
Figure 41.
LAKE SUPERIOR
II M/SEC W.
TRANSPORTS FROM RUN 21.
TIME = 18 18
AT = 180.
SCALE 0.2 CM = I.OOOM2/SEC
Entire Lake Superior transports from a 11 m/s westerly wind,
-------
00
LAKE SUPERIOR
11 m/sec W.
TRANSPORTS FROM RUN 23.
TIME = 30 30
AT= 180.
SCALE 0.2CM = 2.000M2/SEC
Figure 41. (continued)
-------
oo
N3
LAKE SUPERIOR
II M/SEC W.
TRANSPORTS FROM RUN 30
TIME = 42 6
AT* 180
SCALE 0.2 CM * L499M2/SEC
Figure 41. (continued)
-------
oo
u>
LAKE SUPERIOR
IIM/SEC W.
TRANSPORTS FROM RUN 31
TIME = 48 6
AT = 180
SCALE 0.2 CM = I.499M2/SEC
Figure 41. (continued)
-------
eddies seen southwest of Isle Royale, Figures 40D and 40E. Although it is
difficult to say, the tailings might then work their way toward the Thunder
Bay area, aided by the mixing processes and dispersion. Further studies
pertaining to the distribution of currents with depth and a long-duration
concentration model would shed more light on the problem.
According to the model, the rapid, well-confined transport of tailings
from Silver Bay is possible only to the Duluth area and the Apostle Islands,
for the wind stresses considered here. Similarly,the red clay particles
tend to be confined in high concentrations to far western Lake Superior or
are transported around the Apostle Islands. Thus,high concentrations of the
contaminants are generally confined to western Lake Superior. Another major
transport structure in the lake for the conditions modeled here is a circu-
lation cell off the Keweenaw Peninsula, where large transport values are
evident. This circulation cell for westerly winds is shown in Figure 41.
Figure 41C shows a counterclockwise loop, with extremely high transports
along the northern shore of the peninsula. Particles dispersing from Silver
Bay could be carried around the Apostle Islands to the Keweenaw circulation
cell. Comparison of currents at the south shore of the study area, where
currents on the order of 20 cm/sec were measured, indicates that the currents
along the Keweenaw would correspond to 40 - 60 cm/sec. Large transports are
also evident in Figure 41C in the strait between the North Shore and Isle
Royale but are of no direct interest here. The westerly winds in the near-
shore zone show transports directly away from the shore at Silver Bay.
Lake-level data from the model for the points shown in Figure 42 are
presented in Fourier Analysis form in Figures 29 and 43.
84
-------
BATTLE ISLAND
NO. 8
THUNDER BAY
NO. 7
GRAND MARAIS
NO. 3
MICHIPICOTEN
HARBOR
NO. 9
N0.4
ONTONAGON
NO. 5
MARQUETTE
TWO HARBORS
g NO. 2
DULUTH
NO. I
NO. 6
WHITEFISH
BAY
Figure 42. Lake Superior water-level station locations.
-------
98
RELATIVE AMPLITUDE (Normalized)
p
ro
p
at
p
00
RELATIVE AMPLITUDE (Normalized)
p
ro
ro
09
a 5
CO
X)
ro
i-i
H-
o
§
ro
ro
§
55
0)
oo
g
RELATIVE AMPLITUDE (Normalized)
p p p p —
ro * 09 b
RELATIVE AMPLITUDE (Normalized)
P
ro
P
o>
P
oo
o>
en
rt^
if*
o>
3T
3
; ro
-------
00
—I
1.0
0.8
0.4
UJ
<0.2
UJ
OC
FOURIER ANALYSIS - MODEL
Northeaster 8'00- 38:42
Four Full Cycles Pack To Peok
WHITEFISH BAY
Grid Location (2,73) No.6
8 10 12
PERIOD (hours)
14
16
18
1.0
==0.8
&
B
0.6
0.4
UJ
UJ
rr
FOURIER ANALYSIS-MODEL
Northeaster 8=00-38' 42
Four Full Cycles Peak To Peak
BATTLE ISLAND
Grid Location (48,69) No. 8
8 10 12 14
PERIOD (hours)
1.0
iO.8
UJ
0.6
ut
cr
1.0
'0.8
FOURIER ANALYSIS-MODEL
Northeaster 8«00- 38=42
Four Full Cycles Peak To Peak
THUNDER BAY
Orld Location (51,49) No. 7
8 10 12
PERIOD (hours)
14
16
18
FOURIER ANALYSIS-MODEL
Northeaster 8=00- 38=42
Four Full Cycles Peak 1b Peak
MICHIPICOTEN HARBOR
Grid Location (17,81) No. 9
16 18
Figure 43.
024
(continued)
8 10 12 14
PERIOD (hours)
16
18
-------
CURRENT PROFILE MODEL
or
valuable aid in predictine tt §enera f low Patterns and are a
little quantitativ" information aLTthe * ^T^ Sedim-t. Hoover,
surface and bottom currents can be nK/ maf ^udes and directions of
finite difference schemes utilizil threTd • "*, ^^^ Multi-level
these suffer from very large computer stor dimen*1Onal §rids «« possible, but
c lack
* **?*?*
the current profile at any point is evfluatfd H F°rrls1ta11 ^W> - which
the wind-stress and water-slope histories a ***CO™°1^™ integrals over
is obtained without the use of the contnn ll P°int< A Uni*ue solution
a large three-dimensional Jrid is disoen ^ty,e^Uation- Thus, the need for
evaluated only where desired dlsPensed with and the currents need be
Mathematical Formulation
undisturbed water level and I
cities and accelerations and
•otion, uhlch the current,
are the , and
« ,f SyStel° "Ith z ' ° «t the
-linear'""1 NeSlectl"S """ical velo
'1"
9w ^
,J - ifw - q + vJf
"here f Is the coriolis
parameter and v is the vertical eddy viscosity.
static pressure.
°f
88
-------
For the case of a pure drift current, we have
3w
2
.3 w
with the boundary conditions
w(z = -H) = 0
(z . o) - F(t)
0) - 0
where F(t) is the time-varying wind-forcing function. The solution used by
Forristall is
w(t,z) = Z n cos [n
H n— u
For a pure slope current
.- .
— = -ifw -q +
32w
with boundary conditions
w(z = -H) = 0
(z - 0) - 0
(t = 0) = 0
the solution is
W(t'z)
-2 B
H ^=
rt /t . -ifi -(n4J5)2ir2vT/H2
/oq(t-i)e e
The solution for the pure drift current was actually found to contain
three parts:
w(tfZ) = F(t)
(i)
- F(t) E= A cos [(tttJs)irz/H]
(ii)
22 2
2 » r/ ,i\ /TTT /-t^/ \ -ifT -(n-f^s) TT VT/H dx /...\
+ — Z cos [(n+*5)irz/H] / F(t-t)e e (iii)
H n=o o
89
-------
where A = 2- n
2 2
- Y
'n 4 + f2/v2
n
Y =
All three parts are needed to satisfy the differential equation, but parts
(i) and (ii) cancel each other in the sense that part (ii) is a Fourier series
for part (i) . All three parts satisfy the conditions that w(z = -H) = 0 and
w(t - 0) = 0. Part (i) satisfies the surface boundary condition
(z = 0) = F(t) with no contribution from parts (ii) and (iii). Part (ill)
has been used alone for a good numerical approximation to the solution even
though it does not match the surface boundary condition explicitly. However,
numerical calculations show that the slope -^- approaches the boundary value
1 oZ
v F(t) a small distance 6z away from z = 0. As seen in Figure 44, 6z
decreases but apparently never vanishes for increasingly large values of N,
the upper limit on the series.
Treatment of Time Integral
The time integrals appearing in the solutions are uneconomical in their
present form for numerical evaluation of the currents. For example, to
calculate the currents at two times T^ and T£, where T£ > T^, the effort done
in evaluating the integral from time 0 to T^ must be repeated to do the inte-
gral from 0 to T£. Therefore, a recursion formula was developed for the
computer program which allowed the integral to be evaluated at a series of
equally spaced times, without wasted computation. This was done by writing
the time integral from 0 to some time T^ = kAT as a sum of k integrals over
equally spaced intervals 0 to T-^, T^ to T£, etc. Making a change in the
integration variable, which allowed the values of the wind function and water
slopes to progress forward in time, yielded
Ck =
f'k F(t)e-9n(Tk - T)dt + e-VTC, .
\-l fc~1
90
-------
Component Of Current In Direction Of Wind (cm/sec)
-27 -26 -25 -24
N=200
N=IOO
NORTH SHORE
13 m/sec NE WIND
Model Time \2-00 Hours
t/=.OI5
Slope Needed To Meet.
Boundary Conditions
Nl
.01
o>
Q
o>
.021
0)
o:
.03
Figure 44. Current vs. relative depth near surface.
N
Superior Entry
km.
8 x 1974 Buoy Location
• Current Profile Grid Location
Figure 45. Current meter station locations.
91
-------
where C = 0
o
e = if + VB 2
n n
Assuming that F(t) changes slowly over the small interval from Ti
to Tk made it possible to further reduce the effort in obtaining the
integral by approximating it in closed form using the average value of Fft)
over that interval;
Tk-l
— 2
_ F r -3 VAt, 2 ?
4~~2—2 ^e n ("^ vcosfAT+fsinfAT) + 3 v]
3 v +f n n
n
— 2
iF r -g vAT, 2
T~^—9 [e n (-g vsinfAT-fcosfAT) + f]
3 v +f n
n
The time integral involving the water slopes is treated in the same manner.
Modeling Procedure
Six current-monitoring stations were set up in the western tip of Lake
Superior during the summer months of 1974, to provide data for the calibra-
tion of the model. Figure 45 shows the locations of the current-meter
stations superimposed on the grid used for the current profile model.
Surface currents were measured at a depth of approximately 2 meters and
bottom currents at a height of 1.8 meters above the lakebed. Stations 1, 2,
and 4 were monitored for both surface and bottom currents while only surface
currents were recorded at stations 3, 5, and 6.
The current profile model was implemented in the following manner:
1) First, the Rand Corporation model was applied to the entire Lake Superior
basin using a grid of 81 x 56 depth locations with a spacing of 6 km.
2) Time-dependent water levels and transports were computed for the north-
east and westerly winds, previously described in the section on trans-
ports, and stored every 12 minutes for the points located in the
western arm of the lake.
92
-------
3) The resulting water-level histories were spatially interpolated and
extrapolated to obtain the x and y components of the water slope at each
of the transport locations, and these values were stored for use by the
current model.
4) Finally, the current profile model was run,using the previously obtained
water slopes and the original wind-forcing functions to predict currents
in the western arm. Special attention was given to points at or near
locations where current meter data were available.
Before the model could be used, it was necessary to better understand
the effects of the vertical-eddy viscosity v. Figure 46 shows the computed
current profiles using two different values of v. The surface currents are
displaced to the right of the wind due to coriolis effects,and the subsurface
currents rotate clockwise with depth in a modified Ekman spiral, causing a
reversal of the currents near the bottom. Raising the viscosity has the
effect of decreasing the currents and somewhat altering the shape of the
profile. Lower viscosities decrease the momentum transfer between layers
of water, tending to uncouple the surface and bottom currents and also to
decrease the bottom drag. Thus, in the case of Figure 46, both the surface
current and bottom-return current increase while the transport changes only
slightly.
Because little is known about the actual value of the vertical-eddy
viscosity, the current model was "calibrated" by varying v and matching
predicted surface current speeds with measured values in the lake. A
comparison of peak surface currents versus corrresponding wind speeds is
shown in Figure 47. Stations 2 and 3 were selected because they are most
likely to be free from shore effects for northeast winds. Some of the
scatter in the points is probably caused by the fact that the wind measure-
ments, obtained from the Duluth Coast Guard, were generally taken only at
6-hour intervals,so little is known about their speeds and directions in the
interim period. Also the surface-current measurements, although averaged
hourly, are expected to be influenced by the violent wave turbulence caused
by higher winds. The relationship between the wind speeds and the surface-
current speeds is a complicated one which depends on the wind stress, wind
duration, total depth of the water, wave height, and vertical-eddy viscosity.
In reality, the value of the vertical-eddy viscosity must also vary as a
function of depth because of turbulence. When a wind stress appears over the
water, a turbulent surface layer associated with wave action is developed,
which implies a large surface-eddy viscosity. Deeper, the flow becomes more
laminar implying a lower eddy viscosity. At the bottom the eddy viscosity
may increase somewhat due to a thin layer of turbulence where the current
speeds suddenly approach zero. In the current profile model, the vertical-
eddy viscosity parameter had to be taken as a constant in order to find a
solution to the differential equation. To calibrate the model, a value of
.007 m /sec was used for v, which yielded peak currents at the depth of the
surface meters of about 36 cm/sec near stations 2 and 3 for the modeled
13 in/sec (30 tnph) northeast wind.
93
-------
40
••30
v = .01
Wind Direction
(13 m/sec)
v =.005
-40 -20
(cm/sec)
20
Figure 46. Current profiles for two values of v. Vectors
plotted every one-tenth of the relative depth.
£\J
15
1
I 10
•a
a
-------
Results
A detailed analysis of the model on currents is treated elsewhere
(Maanum, 1977). The primary need for modeling currents came from the
interest in movement of the sediment after its resuspension from major
sediment deposition areas in the vicinity of the harbor entries and from
dredging disposal areas. It is seen from Figure 48 that for the times of
high turbulence, the bottom currents for westerly winds would transport
the bottom layer of water towards the northeast shore, indicating an up-
swelling along that shore. For a small area east of the Superior entry,
however, the bottom currents point towards Dutchman Creek, making this
location a more suitable dredging disposal site from the standpoint of
currents.
For the northeasterly winds, the bottom layer of water generally moves
out in an easterly direction similar to the transport patterns near the
axis of the arm. The results for the wind directions modeled here gener-
ally confirm the measured current patterns. The bottom currents treated
here pertain to thermally unstratified conditions which are important in
questions of the occurrence of high turbidity and dredging disposal.
TURBIDITY TRANSPORT MODEL
A combination of 1) transports from the numerical model, 2) information
on the erosion along the south shore, and 3) turbidity settling measured in
the lab, Figure 49, produced the preliminary information needed for the
numerical modeling of turbidity transport and location of the settling areas
which become potential resuspension sources. A nearly maximum severity
condition was modeled. This entailed northeasterly winds at 13 m/sec (30 mph)
for 40 hours, followed by a lull in the wind and a subsequent westerly wind
patterned after actual weather observations. The boundary conditions for the
model were as follows: Erosion took place at a uniform rate throughout the
northeasterly wind, with the distribution along the south shore provided from
data on the relative shore erosion rates. Because of the high turbulence no
settling was allowed during the easterly, but at the end of the storm a
settling rate was applied everywhere except at the source locations. The
turbidity-source locations consisted of 1.5 x 3 kilometer blocks, i.e. half a
grid square, staggered adjacent to the south shore. (More experimental work
on the boundary conditions is essential for further detailed turbidity model-
ing.) In a sense, the horizontal eddy diffusivity process was automatically
taken into account by the unavoidable mixing after each time step of the
influx of higher turbidity from adjacent cells,with the suspended load already
present in a particular grid space. The flux of turbidity into each grid
space was determined by the transports and concentration in neighboring cells.
The results for the turbidity plumes are shown in Figure 50 at various stages
of the storm. The total suspended load for red clay is 1.3 x 10^ metric tons,
resulting from an input of 500 mg/£ constant suspended load at a source point
at Amnicon which is comparable to real values for such storms. This value of
total suspended load is roughly equal to ^ 25% of the yearly lakeshore
95
-------
Wind direction
at time of plot
/ / ,-•••••, ^
N. " •' : s^.'
km.
5 cm/sec
km.
5 cm/sec
Figure 48. Computed bottom currents near Duluth measured 1.8 m above the lake
after 24 hours of west wind and 30 hours of east wind.
bed
-------
PLUME MATERIAL REMOVAL
10 20
Days
Figure 49. Lake sample settling in lab.
30
97
-------
SUSPENDED SOLIDS (mg/l)
00
SUSPENDED LOAD CONCENTRATION
Duluth
Sup3ricr
MODEL TIME = 42 hours (2 hours into decay of 13 m/sec Northeasterly Wind)
Figure 50. Modeled suspended solids distribution at several stages of the storm.
-------
SUSPENDED SOLIDS (mg/l)
VO
10-20
20-50
SUSPENDED LOAD CONCENTRATION
Duluth
Superior
MODEL TIME = 60 hours (12 hours after end of I3m/sec Northeasterly Wind)
Figure 50. (continued)
-------
SUSPENDED SOLIDS (mg/l)
o
o
Duluth
Super!
a
HO
10-20
20-50
50+
SUSPENDED LOAD CONCENTRATION
MODEL TIME = 120 hours (18 hours after end of Mm/sec Westerly Wind)
Figure 50. (continued)
-------
erosion input from the entire red clay bank erosion in Douglas and Bayfield
Counties. Experimental data indicate that the major portion of the erosion
takes place during three t:o five severe northeasterly storms occurring per
season. It is interesting to compare the shape of calculated plumes to the
plume observed in the Landsat image for April 3, 1975, Figure 51. This
Figure 51. Landsat image for 03APR75.
plume was due largely to resuspension in the near-shore areas of Douglas and
Bayfield Counties and areas off Minnesota and Wisconsin Points. It looks
much like the model plume. The deposition areas produced in this model are
shown in Figure 52. Notice the high deposition rate east of the Superior
entry to the Duluth-Superior Harbor, Figure 52A. The Nemadji River output
is also near here ,though its load is normally transported in a southeasterly
direction. On navigation charts and USGS maps, this area is shown as actu-
ally about 4 meters shallower than the adjacent areas of the lake. This
roughly corresponds to about half of the amount of material which would be
deposited there at the rates shown in Figure 52B, taking the age of the lake
at 10,000 years. Of course, this is a rough result, probably fitting the.
data better than the roughness of the model deserves; yet it generally
reflects the actual conditions quite well. Some available data on cores and
sediment traps is yet to be analyzed and will possibly be done in the future.
There is a general need for measurements necessary to describe the boundary
conditious which would closely approximate the actual erosion source.
101
-------
Silver Boy
o
N>
Dufcth
Superior
ACCUMULATED SEDIMENT (g/cm*)
0.02-
0.02-0.06
Figure 52A.
SEDIMENT DEPOSITION
MODEL TIME = 60 hours (12 hours after end of 13 m/sec Northeasterly Wind)
Figure 52. Modeled sediment accumulation at different stages of the storm.
-------
ACCUMULATED SEDIMENT (g/cm2)
| | 0.02-
0.02-0.06
Sliver Boy
SEDIMENT DEPOSITION
Duluth
Superior
MODEL TIME * 120 hours (18 hours after end of II m/tec Westerly Wind)
Figure 52. (continued)
-------
REFERENCES
Bahnick, D. A., J. W. Horton, R. K. Roubal, and A. B. Dickas, 1972.
"Effects of South Shore Drainage Basin and Clay Erosion on the Physical
and Chemical Limnology of Western Lake Superior." Proc. 15th Conf.
Great Lakes Research, Int. Assoc. Great Lakes Res.
Baumgartner, D. J., W. F. Rittall, G. R. Dittsworth, and A. M. Teeter,
1973. "Investigation of Pollution in Western Lake Superior due to
Discharge of Mine Tailings, Data Report 1971." Studies Regarding the
Effect of the Reserve Mining Company Discharge in Lake Superior,
Pacific Northwest Environmental Research Laboratory Paper No. 10,
U.S. EPA, Washington, D.C., p. 423.
Forristall, G. Z., 1974. "Three-Dimensional Structure of Storm-Generated
Currents." J. Geophys. Res., 79(18), 2721-2729.
Hutchinson, G. E., 1957. A Treatise on Limnology. Wiley: New York,
Vol. 1, p. 263. ~~~
Leenderste, J. J., 1967. Aspects of a Computational Model for Long-
Period Water-Wave Propagation. RM5294-PR, The Rand Corporation.
Maanum, W. E., 1977. Numerical Prediction of Currents and Transports
in Western Lake Superior. M.S. Thesis, University of Minnesota, Duluth.
Mortimer, C. H. and E. J. Fee, 1976. "Free Surface Oscillations and
Tides of Lakes Michigan and Superior." Phil. Trans. Roy. Soc. London,
281, 1-61. ~
Rao, D. B. and D. J. Schwab, 1976. "Two-Dimensional Normal Modes in
Arbitrary Enclosed Basins on a Rotating Earth: Application to Lakes
Ontario and Superior." Phil. Trans. Roy. Soc. London, 281, 63-96.
Ruschmeyer, 0. R., T. A. Olson, and H. M. Bosch, 1961. Lake Superior
Studies 1956-61. Public School of Health, University of Minnesota,
Minneapolis.
Sydor, M. 1973. Current Patterns and Turbidity. U.S. Army Corps of
Engineers Report DACW-37-74-C-0014.
Tsai, Y. J. and Y. C. Chang, 1974. "Prediction and Verification of
Storm Surges in Lake Ontario and Lake Erie." Stone and Webster
Engineering Corporation, Boston, Mass. Paper presented at the 17th
Conf. on Great Lakes Research.
Wilson, B. W., 1960. "Note on Surface Wind Stress Over Water at High
and Low Wind Speeds." J. Geophys. Res., 65(10) 3377-3382.
104
-------
APPENDIX A
SOUTH SHORE DATA FOR THE 1975 RUNOFF
Note: Data enclosed in parenthesis ( )are
interpolated from measured data.
105
-------
TABLE A-l. SUSPENDED LOAD TRANSPORTED FOR SNOW RUNOFF
(APRIL 10 - 27, 1975) IN METRIC TONS
River
Nemad j i
Dutchman
Morrison
Amnicon
Ten
Wagner
Hanson
Middle
Poplar
Bardon
Pearson
Load South
of Hwy 13
224
149
2,093
260
134
47
1,583
351
225
220
Load Between
Hwy 13 and
Lower Station
88
146
350
102
124
81
138
920
192
446
Load From
Lower Station
to Lake
5
6
6
15
12
9
23
Total Load
Discharged
84,848
317
295
2,443
368
264
128
1,736
1,283
426
699
Unnamed
Stream #
1
2
3
4
5
Total Load
Discharged
6
66
39
20
12
Unnamed
Stream #
6
7
8
9
10
Total Load
Discharged
20
29
41
90
74
Unnamed
Stream #
11
12
13
14
15
Total Load
Discharged
24
17
14
54
13
Total load from all unnamed streams 519 metric tons.
106
-------
TABLE A-2. LOAD TRANSPORTED DURING RAIN EVENT
(APRIL 28 - MAY 5, 1975)
IN METRIC TONS
River
Nemad j i
Dutchman
Morrison
Amnicon
Ten
Wagner
Hanson
Middle
Poplar
Bardon
Pearson
Load South
of Hwy 13
108
17
616
26
11.4
4
218
71
48
29
Load Between
Hwy 13 and
Lower Station
30.8
29.2
98
35.7
18.6
16.2
48.3
278
67.2
103
Load From
Lower Station
to Lake
1.8
1.6
1.6
6
4.8
2.4
11
Total Load
Discharged
22,044
140.6
46.2
714
63.3
31.6
20.2
272.3
358.8
117.6
143
Unnamed
Stream ?/
1
2
3
4
5
Total Load
Discharged
0.4
4.4
2.6
1.3
0.8
Unnamed
Stream #
6
7
8
9
10
Total Load
Discharged
1.3
1.9
2.7
6.0
4.9
Unnamed
Stream #
11
12
13
14
15
Total Load
Discharged
1.6
1.1
0.9
3.6
0.9
Total from all unnamed streams 34.4 metric tons.
107
-------
TABLE A-3. SOUTH SHORE STREAM CHARACTERISTICS
River
Namad j ±
Dutchman
Morrison
Amnicon
Ten
Wagner
Hanson
Middle
Poplar
Bardon
Pearson
Total
Basin
Area
(km2)
1191
19
13
111 *
349 +
17
13
11
59 *
124 +
55 *
104 +
32
27
Total
Lengths
Main Streams
Intermittents
(km)
105
30.1
2.7
20.4
7.2
* 182 *
6.4 *
20.8
24.0
7.9
17.1
1.4
12.2
57.0 *
25.7 *
65.8 *
38.3 *
26.7
38.1
26.7
53.4
South of Hwy 13
• Basin Main Inter-
Area Streams mittents
(km2) (km) (km)
14 24.0 1.3
8 11.6 4.3
98 * VL60 * 5.0 *
13 15.3 20.6
7 2.7 11.6
4 1.4 3.5
52 * 48.8 * 20.8 *
23 * 38.9 + 11.1 *
24 16 32.3
13 16 6.8
Between Hwy 13
and Downstream Station
Basin Main Inter-
Area Streams mittents
(ko2) (km) (km)
5 5.6 1.4
5 8.8 2.9
13 21.1 1.4
4 4.8 3.4
.5 4.5 5.5
6 0 8.7
6 6.6 4.5
31 25.6 27.2
8 9.7 5.8
12 3.1 46.7
Between Downstream
Station and Mouth
Basin Main Inter-
Area Streams mittents
(Ion2) (km) (km)
0.5 0.5 0
00 0
00 0
0.3 0.6 0
0.3 0.6 0
00 0
0.8 1.6 0
1.0 1.3 0
0.8 1.0 0
2.6 3.5 0
o
00
+ University of Wisconsin measurement
* includes only portion within red clay belt
-------
TABLE A-4. SOUTH SHORE UNNAMED STREAM CHARACTERISTICS
Unnamed
Stream
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Total
Basin
Area
(km2)
0.5
3.6
2.3
1.6
0.8
1.0
1.3
2.1
3.9
4.1
1.0
1.0
0.8
3.1
0.8
Total Length
(km)
Main
Streams
0.5
6.6
3.7
1.8
1.3
1.4
0
0
0
0
0
0
0
0
0
Inter-
mittents
0.2
0.5
0.5
0.3
0
0.6
3.1
4.3
9.7
7.9
2.6
1.8
1.4
5.8
1.4
109
-------
TABLE A-5. SOUTH SHORE EROSION DATA (1975) FOR NEMADJI
GOLF COURSE AND HWY 53
Date
April 12
April 13
April 14
April 15
April 16
April 17
April 18
April 19
April 20
April 21
April 22
April 23
Water
Sample
Description
N-12-1
N-12-2
N-16-1
N-16-2
N-17-1
(D) Hwy 53
N-17-2
(I) Hwy 53
N-18-1
N-18-2
N-18-3
(D) Hwy 53
N-18-4
(I) Hwy 53
N-19-1
N-19-2
N-19-3
N-21-1
N-21-2
N-21-3
N-21-4
N-21-5
N-21-6
N-22-1
N-23-1
Hwy 53
N-23-2
Golf Course
N-23-3
N-23-4
N-23-5
Turbidity
(NTU)
50.0
143
220
215
148
143
152
158
162
162
148
152
205
242
260
258
Suspended
Solids
(mg/£)
61.7 (58.2)
54.7
(158)
(261)
(364)
472 (476)
(479)
580 (540)
417
(460)
523 (524)
530
521
(494)
465
463
439 (448)
432 (UWS)
457
416 (UWS)
852
1055
927 (1059)
1113
1065
1004
Stage Discharge
(cm) (m^/sec)
298 21.0
(348) (53.1)
(399) (85.2)
(450) (118)
497 150
504 152
542 163
509 154
(495) (148)
481 142
455 127
351
476 140
Total Load
(Metric Tons
Per Day)
105
725
1922
3692
6150
7080
6472
6975
6324
5508
9360
12801
(continued)
110
-------
TABLE A-5. (continued)
Date
April 24
April 25
April 26
April 27
April 28
April 29
April 30
May 1
May 2
May 3
May 4
May 5
lay 6
May 7
May 23
Water
Sample Turbidity
Description (NTU)
N-24-1
N-24-2
N-24-3
N-24-4
N-25-1
N-25-2
N-25-3
N-25-4
N-28-1
N-29-1
N-l-1
N-l-2
N-2-1
N-5-1
N-23-1
192
190
187
148
148
148
142
200
108
100
85
26.0
Suspended
Solids
(mg/Jl)
423
425
405
425
392
401
409
387
557
284
286
257
182
165
29.5
(424)
(397)
(347)
(307)
(290)
(420)
(285)
(232)
(207)
(173)
Stage
(cm)
512
489
(466)
(443)
420
456
(462)
469
390
(366)
(343)
319
(310)
(301)
Discharge
(m3/sec)
155
147
(132)
(116)
101
127
(131)
135
80.4
(65.3)
(50.2)
35.1
(29.2)
(23.2)
6.0
Total Load
(Metric Tons
Per Day)
5665
5031
3946
3090
2540
6120
4753
3319
1785
1310
898
552
436
331
15.2
111
-------
TABLE A-6. SOUTH SHORE EROSION DATA (1975) FOR DUTCHMAN, HWY 13
1
Water
| Date Sample
Description
April 7 D-7-1
D-7-2
April 8
April 9
April 10 D-10-1
D-10-2
April 11
April 12
Suspended Total Load
Turbidity Solids Stage Discharge (Metric Tons
(NTU) (mg/10 (cm) (m3/sec) Per Day)
65.5 (50)
65.0
(55)
(60)
66.0 71
61.5 (66)
(67)
(75)
0.11
0.14
0.17
0.23
0.37
0.54
0.49
0.67
0.88
1.29
2.13
3.49
April 11
i
April 12
i
I April 13
1
JApril 14
April 15
JApril 16
l
i
April 17
iApril 18
April 19
April 20
,
April 21
April 22
April 23
April 24
April 25
D-14-1
(I)
D-14-2
(D)
D-15-2
D-15-3
D-16-1
D-16-2
D-17-2
D-18-1
D-19-1
D-21-2
D-22-1
D-23-2
D-24-1
D-25-2
70.5
70.5
60.5
85.0
66.0
75.5
74.5
68.5
79.5
97.5
70.0
71.0
(67)
(75)
(84)
93.3 (92.6)
92.0
58.0 (66) 51
73.7
ICE JAM
119
53 ICE JAM
107 ICE JAM
83
(86)
86 51
(107) 53
128 51
49 43
48 38
0.54
0.71
0.85
2.17
3.86
3.48
3.09
2.72
2.36
2.08
2.36
2.08
1.20
0.69
3.49
5.14
6.80
12.4
39.7
16. 0
28.5
19.5
17.5
15.5
21.8
23.0
5.1
2.9
(continued)
112
-------
TABLE A-6. (continued)
Water
Date Sample
Description
April 26
April 27
April 28 D-28-1
April 29
April 30 D-30-1
May 1 D-l-1
(D)
May 2
May 3
May 4
May 5 D-5-1
(D)
May 6
May 7
Suspended
Turbidity Solids Stage Discharge
(NTU) (mg/£) (cm) (m3/sec)
(76)
(104)
113 132 52
(105)
80.0 78
70.0 (70.5) 41
(78) (34)
(86) (33)
(93) (30)
76.0 (100) 25
(80) (25)
(60) 24
1.19
1.70
2.21
4.11
1.47
0.57
0.45
0.38
0.28
0.14
0.14
0.11
Total Load
(Metric Tons
Per Day)
7.8
15.3
25.2
37.3
9.9
3.5
3.0
2.8
2.3
1.2
0.94
0.59
113
-------
TABLE A-7. SOUTH SHORE EROSION DATA (1975) FOR DUTCHMAN
MOUTH, MORRISON HWY 13, AND MORRISON MOUTH
April 9
April 15
April 16
April 17
April 18
April 21
April 23
April 25
April 30
Morrison,
April 16
April 25
April 28
April 30
May 5
Morrison,
April 16
April 25
D-9-1
D-15-1
D-16-1
D-16-2
D-17-1
D-18-1
D-18-2
(D)
D-18-3
(D
D-21-1
D-23-1
D-25-1
Hwv 13
Mo-16-1
Mo-25-1
Mo-28-1
Mo-30-1
(D)
Mo-5-1
Mouth
Mo-16-1
Mo-16-2
Mo-25-2
65.0
69.0
112
88.0
100
102
85.0
140
80.5
52.0
91.5
64.5
62.0
118
83.0
43.0
82.0 2.19
216
110
i
162
f
t
134
241
77 0.75
1.37
i
67
45 0.34
i
103
i
i
0.93
0.34
i
259
93
114
-------
TABLE A-8. SOUTH SHORE EROSION DATA (1975) FOR AMNICON, HWY 13
Date
April 10
April 11
April 12
April 13
April 14
April 15
April 16
i
April 17
April 18
April 19
April 20
April 21
April 22
April 23
April 24
April 25
April 26
Water
Sample
Description
A-10-1
A-10-2
A-14-1
A-14-2
A-16-1
A-16-2
(5 br
after
A-16-1)
A-17-1
(D)
A-17-2
(I)
A-18-1
(D)
A-19-1
A-21-1
A-23-1
Suspended
Turbidity Solids
(NTU) (mg/2.)
16.5 12.5
14.3 (13.4)
(40.3)
(68.2)
(96.0)
60.6 125 (122)
119
(100)
59.5 55 (81)
107
38.0 50
36.5
37.0 59
29.5 58
(45)
25.0 31
(51)
32.5 71
(66)
(62)
(58)
Total Load
Stage Discharge (Metric Tons
(cm) (m3/sec) Per Day)
61
(74)
(89)
(104)
(117)
(137)
157
178
178
169
(175)
183
(183)
193
183
(178)
(173)
0
0
(3.09)
(7.65)
(10.5)
(17.0)
24.8
32.1
32.1
28.3
(31.4)
34.7
34.7
39.1
34.7
(32.1)
(30.2)
0
0
18.2
63.4
110
147
173
138
164
142
122
93
153
240
198
172
152
(continued)
115
-------
TABLE A-8. (continued)
Water
Date Sample
Description
April 27
April 28 A-28-1
April 29 A-29-1
April 30 A-30-1
May 1 A-l-1
(D)
May 2
i
May 3
;May 4
iMay 5 A-5-1
(D)
May 6
May 7
May 23 A-23-1
Suspended
Turbidity Solids
(NTU) (mg/£)
— —
(54)
54.5 71
30.5 (50)
25.0 30
21.0 24
(22)
(19)
(17)
16.5 (14)
(11)
(8)
9.5 3.8 (7)
Stage
(cm)
(165)
170
183
183
165
155
(147)
(140)
132
(124)
117
Total Load
Discharge (Metric Tons
(m3/sec) Per Day)
(27.7)
29.0
34.7
34.7
27.7
23.2
(20.1)
(17.6)
15.9
(12.9)
9.63
129
178
150
90
57
44
33
26
19
12
7
116
-------
TABLE A-9. SOUTH SHORE EROSION DATA (1975) FOR TEN HWY 13,
WAGNER HWY 13, WAGNER MOUTH, AND HANSON MOUTH
Water Suspended
Date Sample Turbidity Solids
Description (NTU) (mg/£)
Ten,Hwy 13
April 10
April 14
April 15
April 16
April 17
April 18
April 19
April 20
April 21
April 22
April 23
April 24
April 25
April 26
April 27
April 28
April 29
April 30
T-10-1 75.0 63.3 (59)
T-10-2 56.0
(200)
T-15-1 113 235 (227)
T-15-2 219
T-16-1 103 160
(D)
T-16-2 102
(I)
T-17-1 70.5 69
T-18-1 91.0 123
T-19-1 73.0 104
(98)
(92)
T-22-2 69.0 86
T-23-1 69.5 41 (90)
(86)
(82)
(78)
(74)
T-28-1 102 71
T-29-1 85.5 120
T-30-1 76.0 64
* Ice Obstruction
Total Load
Stage Discharge (Metric Tons
(cm) (m3/sec) Per Day)
(112)*
46*
107*
58
53
39
(36)
(33)
29
32
(25)
(28)
(20)
(18)
23
37
36
(3.40)
3.96
2.69
2.53
2.17
1.13
(0.91)
(0.79)
0.66
0.75
(0.54)
(0.62)
(0.39)
(0.31)
0.46
0.97
0.91(1.04)
58.7
77.7
37.2
15.1
23.0
10.2
7.6
6.3
4.9
5.8
i
4.0
4.4
i
2.6
(
2.0
2.8 1
i
10.0
5.0
(continued)
117
-------
TABLE A-9. (continued)
Water
Date Sample
Description
May 1 T-l-1
(D)
May 2
[May 3
May 4
May 5 T-5-1
(D)
JMay 6
i
May 7
Wagner, Hwy 13
April 15 W-15-1
W-15-2
JApril 22 W-22-2
j April 28 W-28-1
I
JMay 1 W-l-1
i (D)
f
May 5 W-5-1
(D)
iWagner, Mouth
|
April 22 W-22-1
Hanson, Mouth
April 10 H-10-1
Suspended
Turbidity Solids
(NTU) (mg/A)
65.0 (55)
(50)
(45)
(40)
70.0 (90)
(60)
(55)
63.0 70.7
56.7
53.5
135 143
61.0
60.0
61.5 75
70.0 53.7
Total Load
Stage Discharge (Metric Tons
(cm) (m3/sec) Per Day)
17 0.28 1.3
(15) (0.25) 1.1
(15) (0.25) 0.97
(15) (0.25) 0.86
14 0.20 1.6
(14) (0.21) 1.1
(13) (0.18) 0.87
118
-------
TABLE A-10. SOUTH SHORE EROSION DATA (1975) FOR
MIDDLE HWY 13, AND MIDDLE MOUTH
Date
Water
Sample
Description
Suspended
Turbidity Solids
(NTU) (mg/£)
Stage
(cm)
Total Load
Discharge (Metric Tons
(m^/sec) Per Day)
Middle, Hwv 13
April 14
April 15
April 16
April 17
April 18
April 19
April 20
April 21
April 22
April 23
April 24
April 25
April 26
April 27
April 28
April 29
April 30
M-15-1
M-15-2
M-16-1
M-17-2
M-19-1
M-21-1
M-22-1
M-23-1
M-28-1
M-28-2
(ditch
near
river)
M-29-1
M-30-1
(80)
55.0 179 (178)
177
28.0 (80)
37.5 96
(90)
26.5 83
(65)
20.5 47
16.5 55
21.5 55
(44)
(34)
(26)
(16)
16.0 7 (16)
245 486
20.5 5 (65)
20.5 29
99
107
107
114
130
127
119
122
135
(127)
(122)
(112)
(107)
102
109
113
11.9
14.4
14.4
18.0
24.6
24.0
23.5
22.9
22.3
25.8
(24.0)
(22.3)
(16.7)
(14.4)
12.6
15.4
17.3
82.2
221
99.4
149
192
172
132
93.2
106
122
91.3
65.6
37.5
19.9
17.4
86.7
43.4
(continued)
119
-------
TABLE A-10. (continued)
Date
Water
Sample Turbidity
Description (NTU)
May 1
May 2 M-2-1 10.0
May 3
May 4
May 5 M-5-1 7.5
May 6
May 7
Middle, Mouth
Suspended
Solids Stage
(mg/£) (cm)
(22) 102
15 93
(13)
(11)
(9) 76
(9)
(9) 69
April 8 M-8-1 20.5 20.0 *
M-8-2 19.7
April 11 M-ll-1 40.5 *
April 16 M-16-10 40.0 *
April 18 M-18-1 85.0 279 *
(D)
M-18-2 89.5
(D
* Because of the depth and current at this station,
not be taken.
Total Load
Discharge (Metric Tons
(m3/sec) Per Day)
12.6 23.9
10.3 13.4
(9.74) 10.9
(8.01) 7.62
6.85 5.32
(6.17) 4.80
5.52 4.29
|
1
a bottom profile could
120
-------
TABLE A-ll. SOUTH SHORE EROSION DATA (1975)FOR
POPLAR HWY 13 AND POPLAR MOUTH
Water
Date Sample
Description
Poplar, Hwy
April 10
April 14
April 15
April 16
April 17
April 18
April 19
(April 20
JApril 21
April 22
April 23
April 24
April 25
April 26
April 27
April 28
April 29
April 30
May 1
13
P-10-1
P-10-2
P-14-2
P-14-3
P-14-4
P-15-1
P-15-2
P-17-2
P-19-1
P-21-1
P-22-2
P-23-2
P-24-2
P-28-1
P-29-1
Suspended
Turbidity Solids
(NTU) (mg/A)
12.0 6.9 (4.7)
2.5
40.0
71.3 (73)
76.0
76.5 159 (163)
167
(108)
30.5 52
(61)
20.5 70
(61)
16.0 51
13.5 34
15.0 34
9.4 12
(10)
(8)
(6)
16.0 3 (5)
16.0 10 (45)
(40)
(35)
Total Load
Stage Discharge (Metric Tons
(cm) (m3/sec) Per Day)
(25)
(51)
Ice
Blockage
(64)
69
71
75
80
83
75
77
64
70
(0.51)
(3.26)
(4.56)
5.17
5.47
5.86
6.40
6.54
6.68
5.86
(8.55)
6.12
(5.75)
(5.35)
(4.98)
4.62
5.30
(4.90)
(4.53)
0.21
20.5
64.2
48.2
24.6
30.9
38.7
34.4
29.4
17.2
25.1
6.34
4.97
3.69
2.58
1.99
20.6
16.9
13.7
(continued)
121
-------
TABLE A-ll. (continued)
-2-
Water
Date Sample Turbidity
Description (NTU)
May 2 P-2-1 8.9
May 3
May 4
i
May 5 P-5-1 7.0
May 6
i
May 7
Poplar, Mouth
Suspended
Solids Stage
(mg/£) (cm)
(15)
(13)
(ID
(9) 48
(9)
(9) 33
Discharge
(m-Vsec)
(4.13)
(3.74
(3.37)
2.97
(2.15
1.35
Total Load
(Metric Tons
Per Day
5.35
4.20
3.20
2.31
1.67
1.05
April 14 P-14-1
P-14-2
,April 15
i
April 16 P-16-1
April 17 P-17-1
April 18 P-18-1
i
April 19
April 20
April 21
April 22 P-22-1
April 23 P-23-1
April 24 P-24-1
April 25
April 26
April 27
60.0 92.7 (88)
83.7 ,
(119)
50.0 151
56.0 85 (158)
65.5 165
(184)
(160)
(134)
32.0 87 142
35.0 91 165
30.5 32 142
(26)
(21)
(16)
(5.49)
(7.73)
(8.75)
(9.26)
(9.94)
(10.8)
(11.1)
(11.3)
12.0
17.6
12.0
(9.74)
(9.06)
(8.44)
41.7
79.5
114
126
142
172
153
131
90.3
138
33.2
12.9
16.4
11.6
(continued)
122
-------
TABLE A-ll. (continued)
-3-
Water
Date Sample Turbidity
Description (NTU)
April 28
April 29
April 30
May 1 P-l-1 25.0
May 2
May 3
May 4
May 5 P-5-1 16.5
May 6
May 7
Suspended
Solids Stage
(mg/£) (cm)
(13)
(118)
(105)
(40) 122
(39)
(34)
(29)
(23) 116
(23)
(23)
Discharge
(nrVsec)
(7.82)
(8.95)
(8.30)
6.61
(7.05)
(6.31)
(5.72)
4.93
(3.65)
(2.29)
Total Load
(Metric Tons
Per Day)
8.78
91.2
75.3
24
23.8
18.6
14.3
9.79
7.26
4.56
123
-------
TABLE A-12. SOUTH SHORE EROSION DATA (1975) FOR
BARDON HWY 13 AND BARDON MOUTH
Water
Date Sample
Description
Bardon, Hwy
April 14
April 15
April 16
April 17
April 18
April 19
April 20
April 21
April 22
April 23
April 24
April 25
April 26
April 27
April 28
April 29
April 30
May 1
May 2
13
B-14-1
B-14-2
B-15-1
B-15-2
B-16-1
B-19-1
B-21-1
B-23-1
B-24-1
B-28-1
B-29-1
B-l-1
(D)
B-2-1
(D)
Suspended
Turbidity Solids Stage
(NTU) (mg/X,) (cm)
50.5 92.3 (92.6)
92.0
93.5 272 (275)
279
80.0 159
(131) 64
(103) 71
51.5 75 60
(55.5)
36.5 36 36
(38.5)
44.5 41 48
36.0 41 33
(40)
(40)
(40)
44.5 16 (60) 58
64.5 10 (100) 41
(80)
45.0 (60) 24
39.5 (54) 19
Total Load
Discharge (Metric Tons
(nrVsec) Per Day)
(0.71)
(1.50)
(2.29)
3.12
5.77
3.96
(2.52)
1.08
(1.64)
2.21
0.63 (0.96)
(0.85)
(0.74)
(0.62)
3.77
1.35
(0.99)
0.62
0.45
5.66
35.7
31.5
35.3
51.3
25.7
12.1
3.3
5.46
7.82
3.41
2.94
2.54
2.15
19.5
11.7
6.9
3.2
1.8
(continued)
124
-------
TABLE A-12. (continued)
Date
May 3
May 4
May 5
May 6
May 7
Water
Sample
Description
B-5-1
Suspended Total Load
Turbidity Solids Stage Discharge (Metric Tons
(NTU) (mg/£) (cm) (m3/sec) Per Day)
(48) (0.41) 1.5
(42) (0.37) 1.3
36.0 (36) 15 0.35 (0.33) 1.0
(30) (0.23) 0.68
(25) 9 0.14 0.3
Bardon, Mouth
April 9
April 14
April 16
April 17
April 18
April 21
April 23
April 24
May 1
B-9-1
(D)
B-9-2
(I)
B-14-3
B-14-4
B-16-2
B-17-1
(D)
B-17-2
(D
B-18-1
B-21-2
B-23-2
B-24-2
B-l-2
(D)
39.5 35.7 (31) Ice 0.21
Block-
36.0 27.0 age
102 186 (185)
105 184
108 327
115 201
105
130 311
60.0 73
70.0 91
51.0 35 36 1.20
60.5 29 0.74
125
-------
TABLE A-13. SOUTH SHORE EROSION DATA (1975) FOR
PEARSON HWY 13 AND PEARSON MOUTH
Water
Date Sample
Description
Suspended Total Load
Turbidity Solids Stage Discharge (Metric Tons
(NTU) (mg/Jl) (cm) (m3/sec) Per Day)
Pearson, Hwy 13
April 14
April 15
April 16
April 17
April 18
April 19
April 20
April 21
April 22
April 23
April 24
April 25
April 26
April 27
April 28
April 29
April 30
May 1
May 2
Pe-14-1
Pe-14-2
Pe-18-3
Pe-18-4
Pe-19-1
Pe-21-2
Pe-23-1
Pe-25-1
Pe-28-1
Pe-29-1
Pe-1-1
(D)
Pe-2-1
(D)
41.0 49.3 (51)
52.7
(105)
(158)
(210)
89.5 (200)
89.5
85.0 220
(140)
44.0 39 (50)
(50)
45.5 68
(65)
61
(58)
(54)
95.0 119
71.5 81
(75)
55.0 70
44.5 (64)
20
(30)
(41)
(53)
53
51
(42)
33
(28)
38
(36)
(33)
(28)
(23)
28
38
(30)
22
17
0.15
(0.40)
(0.76)
(1.33)
1.33
1.19
(0.82)
0.48
(0.33)
0.67
(0.58)
(0.48)
(0.33)
(0.19)
0.33
0.67
(0.40)
0.17
0.12
0.67
3.61
10.45
24.1
22.9
22.7
9.85
2.07
1.40
3.95
3.26
2.53
1.63
0.90
3.34
4.68
2.58
1.05
0.64
(continued)
126
-------
TABLE A-13. (continued)
-2-
Date
May 3
May 4
i
JMay 5
May 6
May 7
Pearson,
April 9
April 14
April 15
April 16
April 17
April 18
April 19
April 20
April 21
April 22
April 23
Water
Sample
Description
Pe-5-1
Mouth
Pe-9-1
(I)
Pe-14-2
(D)
Pe-14-3
(I)
Pe-14-4
Pe-16-1
(D)
Pe-16-2
Pe-18-1
Pe-18-2
Pe-18-3
Pe-21-1
Suspended
Turbidity Solids Stage
(NTU) (mg/£) (cm)
(60) (17)
(55) (16)
42.0 (50) 15
(50) (13)
(50) 10
39.5 37.3
74.0
74.0 126 (123)
120
(183)
96.5 238 (243)
249
(400) 86
115 397 85
115
152
(430)
(280)
74.5 81 48
(81)
(113)
Discharge
OrVsec)
(0.11)
(0.10)
0.094
0.072
0.054
0
(0.49)
(1.26)
(24.1)
4.19
4.19
(3.79)
(2.58)
1.53
(1.03)
(2.13)
Total Load
(Metric Tons
Per Day)
0.57
0.48
0.40
0.31
0.23
0
5.21
i
|
19.9
50.5
i
i
145
i
144
141
62
10.7
7.19
20.8
(continued)
127
-------
TABLE A-13. (continued)
-3-
Water
Date Sample
Description
April 24
April 25
;April 26
Upril 27
;April 28
April 29
April 30
May 1
SMay 2 Pe-2-2
t
May 3
1
May 4
;May 5
May 6
JMay 7
Suspended
Turbidity Solids Stage
(NTU) (mg/*.) (cm)
(147)
(138)
(131)
(122)
(270)
(184)
(170)
(159)
59.0 (145) 38
(136)
(125)
(114)
(114)
(114)
Total Load
Discharge (Metric Tons
(m3/sec) Per Day)
(1.84)
(1.52)
(1.03)
(0.61)
(1.03)
(2.12)
(1.26)
(0.55)
0.38
(0.35)
(0.32)
(0.30)
(0.23)
(0.17)
2.34
18.2
11.7
6.47
24.0
33.7
18.5
7.55
4.73
4.09
3.49
2.93
2.26
1.65
— — — —— — — — —
, U.S. GOVERNMENT PRINTING OFFICE: 1979-852-559/64
128
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing}
1. REPORT NO.
EPA-905/9-79-004
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Red Clay Turbidity and Its Transport
in Lake Superior
5. REPORT DATE
January 1979
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Michael Sydor, Richard T. Clapper, Gordon J. Oman,
and Kirby R. Stortz
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Physics Department
University of Minnesota, Duluth
Duluth, Minnesota 55812
10. PROGRAM ELEMENT NO.
2BA645
11. CONTRACT/GRANT NO.
R005175-01
12. SPONSORING AGENCY NAME AND ADDRESS
Great Lakes National Program Office
U.S. Environmental Protection Agency, Region V
536 South Clark Street
Chicago, Illinois 60605
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
Undertaken in support of the Upper Lakes Reference Group studies of pollution
in Lake Superior and Lake Huron.
6. ABSTRACT ' — —_^^______^___
Red clay plumes in western Lake Superior are studied using Landsat satellite
imagery to determine the relative magnitude of the three sources of the observed
turbidity: erosion of the Wisconsin south shore red clay banks, resuspension of
bottom sediments, and runoff from the many streams which flow through the red clay
belt and then into the lake. A comprehensive sampling program was conducted during
the spring of 1975 to determine the runoff contribution to the total load observed
in the lake. Analysis of Landsat transparency data coupled with weather records
enabled contributions from erosion and resuspension to be separated. It was found
that approximately 75% of the observed load in the lake during the ice-free season,
from May to November, is from erosion, 20% is from resuspension, and 5% is from runoff
A numerical model for water transports in Lake Superior as a function of winds
is developed. This model is verified by comparison of observed and predicted water
levels at several locations around the lake, and by comparison of the predicted
transport patterns to actual turbidity distributions observed in Landsat imagery.
Transport patterns are shown for western Lake Superior and the entire lake for both
an easterly and westerly wind. A model of current profile with depth is also devel-
oped. The results of the transport model are used to predict distributions of red
clay from the south shore and taconite tailings discharged into the lake at
Silver Bay, Minnesota.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Turbidity
Sediment transport
Erosion
Runoff
Water quality
Hydrodynamics
Remote sensing
Red clay, Landsat
Lake Superior, Numerical
transport models
Upper Lakes Reference
Group
International Joint
Commission
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