NEARSHORE HYDRODYNAMICS AND THE FATE AND TRANSPORT OF
INDICATOR BACTERIA IN LAKE MICHIGAN: FIELD EXPERIMENTS AND
NUMERICAL MODELING
By
Pramod Thupaki

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Civil and Environmental Engineering
2012

ABSTRACT
NEARSHORE HYDRODYNAMICS AND THE FATE AND TRANSPORT
OF INDICATOR BACTERIA IN LAKE MICHIGAN: FIELD
EXPERIMENTS AND NUMERICAL MODELING
By
Pramod Thupaki

Human interactions with the oceans and large inland lakes occur primarily in the nearshore
regions, therefore coastal water quality is important from a human health point of view.
A number of studies have demonstrated that a causal relationship exists between illnesses
and recreational water quality as measured by indicator bacteria such as E. coli (EC) and
enterococci. The traditional approach to beach management is slow and requires 24 hrs to
run the assays. The focus of this study is the predictive modeling of indicator bacteria which
represents an attractive alternative to the traditional laboratory based approach.
Bacteria entering the nearshore environment are transported and diluted due to the
action of currents and waves. Environmental factors such as sunlight, temperature, pH and
turbidity affect the rate of bacterial inactivation in the water column. Bacteria also attach
to suspended sediment particles, undergo settling, and resuspension. In this study, we use
field experiments and numerical models to systematically examine the different processes
that affect the fate and transport of bacteria in Lake Michigan to improve the accuracy of
predictive recreational water quality models.
The coastal boundary layer (CBL) acts as the interface between the lake-wide flows and
the small-scale, friction-dominated flow closer to the shore. We examine the important
features describing circulation and transport in the CBL using a three-dimensional hydrodynamic model as well as extensive hydrodynamic measurements made at different distances

from the shoreline. Tracer studies are used to assess the ability of the Smagorinsky turbulence scheme to describe mixing in the horizontal directions.
The relative importance of various physical and biological processes that influence the fate
and transport of EC were examined via budget analysis and a first-order sensitivity analysis
of model parameters. The along-shore advective flux of EC was found to be higher compared
to its cross-shore counterpart; however, the sum of diffusive and advective components was of
a comparable magnitude in both directions showing the importance of cross-shore exchange
in EC dilution. Although the vertical fluxes were small compared to the horizontal fluxes,
examination of the individual terms in the EC mass balance equation showed that the
vertical dimension plays a key role in the overall EC transport. Dilution due to advection
and diffusion accounted for a large portion of the total EC budget in the nearshore. The rate
of net EC loss within the water column was an order of magnitude smaller compared to the
horizontal and vertical transport rates; however, this assessment is potentially complicated
due to the strong coupling between the vertical exchange and the depth-dependent EC loss
processes such sunlight inactivation and settling. Sensitivity analysis indicated that solar
inactivation has the greatest impact on EC loss rates.
Sediment is a potential source of bacteria in the nearshore region. Settling and resuspension rates determine the fate of indicator bacteria in the sediment and the water column.
In order to assess the role of sediment on recreational water quality, sediment-water interactions were modeled using a three-dimensional transport model coupled to the hydrodynamic
model. A semi-empirical wave model was used to simulate the wave climate and bottomshear stresses due to wind-wave action. Results show that sediment-bacteria interactions can
explain background concentrations. Resuspension may be an important secondary source of
EC contamination, depending on the bacterial survival and re-growth rates in the sediment.

To my parents

iv

ACKNOWLEDGMENTS

I would like to thank my advisor Dr. Mantha S. Phanikumar for his support and guidance
throughout this dissertation and for his patient encouragement to solve the problems encountered. Through his dedication to research and quest for perfection, he has taught me to
be a better researcher. I would like to thank Dr. Roger Wallace, who taught me how to be
a better teacher, and my committee members Dr. Shu-Guang Li and Dr. Farhad Jaberi for
their assistance and feedback.
The field studies would not have been possible without the generous help from Drs.
Richard Whitman, Richard Zepp, Meredith Nevers, Muralidhara Byappanahalli and Marc
Blouin of the United States Geological Survey. Discussions with them were helpful in planning the deployments and understanding of the processes important at the site. I would
like to thank Dr. David J. Schwab and Dr. Dmitry Beletsky of the National Ocean and
Atmospheric Administration for their assistance and guidance in modeling hydrodynamics
in Lake Michigan. I would also like to thank my friends and colleagues Dr. Chaopeng Shen,
Kashi Telsang and Jie Niu for their help in conducting the field studies.
Finally, I would like to thank my family for their love and affection and all my friends
for their support throughout my doctoral study.
This study was funded by the NOAA Center of Excellence for Great Lakes and Human
Health and an EPA summer fellowship during the year 2009. I also wish to acknowledge
the support of the Michigan State University High Performance Computing Center and the
Institute for Cyber Enabled Research.

v

TABLE OF CONTENTS

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of Figures

viii

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Introduction
1.1 Problem Description . . . . .
1.2 Transport Processes . . . . . .
1.3 Biological Processes . . . . . .
1.4 Sediment-bacteria Interactions
1.5 Structure of the Thesis . . . .

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

2 Experimental Methods and Numerical Modeling
2.1 Experimental Methods . . . . . . . . . . . . . . .
2.1.1 Currents . . . . . . . . . . . . . . . . . . .
2.1.2 Waves . . . . . . . . . . . . . . . . . . . .
2.1.3 Temperature and Turbidity . . . . . . . .
2.1.4 Escherichia coli enumeration . . . . . . .
2.1.5 Eddy-diffusivity and Mixing . . . . . . . .
2.2 Numerical Models . . . . . . . . . . . . . . . . . .
2.2.1 Currents . . . . . . . . . . . . . . . . . . .
2.2.2 Waves . . . . . . . . . . . . . . . . . . . .
3 Identifying the Dominant Energy-Carrying
the Nearshore Region of Lake Michigan
3.1 Summary . . . . . . . . . . . . . . . . . . .
3.2 Introduction . . . . . . . . . . . . . . . . . .
3.3 Methods . . . . . . . . . . . . . . . . . . . .
3.3.1 Study Site . . . . . . . . . . . . . . .
3.3.2 Numerical Model . . . . . . . . . . .
3.3.3 Wavelet Decomposition . . . . . . . .
3.4 Results . . . . . . . . . . . . . . . . . . . . .
3.5 Discussion . . . . . . . . . . . . . . . . . . .
3.6 Conclusion . . . . . . . . . . . . . . . . . . .

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

Techniques
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .

.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.
.
.

ix

.
.
.
.
.

1
1
5
8
9
11

.
.
.
.
.
.
.
.
.

13
13
14
16
20
22
23
24
24
29

Scales Driving Circulation in
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

35
35
36
39
39
40
41
42
57
59

4 Mixing and Transport in the Coastal Boundary Layer of Southern Lake
Michigan
61
4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
vi

4.2
4.3

4.4

4.5

Introduction . . . . . . . . . . . . . . . . . .
Methods and Materials . . . . . . . . . . . .
4.3.1 Study Site . . . . . . . . . . . . . . .
4.3.2 Numerical Modeling . . . . . . . . .
4.3.3 Shear-augmented dispersion . . . . .
Results and Discussion . . . . . . . . . . . .
4.4.1 Hydrodynamic Model . . . . . . . . .
4.4.2 Turbulence in the nearshore . . . . .
4.4.3 Vorticity Dynamics in the Nearshore
Conclusion . . . . . . . . . . . . . . . . . . .

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

. 62
. 66
. 66
. 67
. 68
. 70
. 70
. 78
. 80
. 100

5 Budget Analysis of Escherichia coli at a Beach in Southern Lake Michigan102
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.6 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6 Sediment-bacteria Interactions at Beaches
6.1 Summary . . . . . . . . . . . . . . . . . .
6.2 Introduction . . . . . . . . . . . . . . . . .
6.3 Methods and Material . . . . . . . . . . .
6.3.1 Study Site . . . . . . . . . . . . . .
6.3.2 Hydrodynamic and Wave Models .
6.3.3 Sediment-bacteria Model . . . . . .
6.4 Results . . . . . . . . . . . . . . . . . . . .
6.4.1 Hydrodynamic Model . . . . . . . .
6.4.2 Wave Model . . . . . . . . . . . . .
6.4.3 Sediment-bacteria Model . . . . . .
6.5 Discussion . . . . . . . . . . . . . . . . . .
6.6 Conclusion . . . . . . . . . . . . . . . . . .
7 Conclusions and Recommendations

in Southern
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .

Lake Michigan
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .

.
.
.
.
.
.
.
.
.
.
.
.

134
134
135
138
138
139
139
146
146
146
150
160
166
168

A Deployment Plans
173
A.1 Teledyne RD Instruments, Workhorse Monitor . . . . . . . . . . . . . . . . . 173
A.2 Teledyne RD Instruments, Workhorse Sentinel . . . . . . . . . . . . . . . . . 174
A.3 Teledyne RD Instruments, BBACDP . . . . . . . . . . . . . . . . . . . . . . 175

vii

LIST OF TABLES

Table 2.1 Important locations for the field study conducted in Summer 2008 . . .

19

Table 2.2 Beam-specific scaling factors for RDI-Sentinel and RDI-Monitor . . . . .

22

Table 6.1 RMSE values between observed and modeled EC values at the Ogden
Dunes Beaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

viii

LIST OF FIGURES

Figure 1.1 Aerial photograph of the sediment plume from the Burns Ditch outfall
located in southern Lake Michigan. For interpretation of the references to
color in this and all other figures, the reader is referred to the electronic
version of this dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

Figure 1.2 Sources of bacterial contamination at Michigan beaches . . . . . . . . .

6

Figure 1.3 The front between lake and contaminated waters from an outfall . . . .

8

Figure 1.4 Biological processes affecting concentration of indicator bacteria in the
water column. I(x, y, z, t), S(x, y, z, t), T (x, y, z, t) are the sunlight intensity,
suspended sediment concentration and temperature as they vary in the water
column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

Figure 2.1 Map of Southern Lake Michigan showing the important locations for
the field study conducted in summer of 2008. M and B mark the location
where the Monitor and BBADCP were deployed. S, N1, and N2 mark the
locations where the Sentinel and two Nortek ADCPs were deployed. Water
samples were collected at beaches in Ogden Dunes and have been marked by
OD1, OD2, OD3. The vertical temperature profile was measured close to the
sentinel deployment (S). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

Figure 2.2 RDI-Monitor being readied for deployment . . . . . . . . . . . . . . . .

18

Figure 2.3 ADCP being deployed in Lake Michigan on May 29th 2008 . . . . . . .

18

Figure 2.4 The RDI-Sentinel being readied for deployment on May 29th 2008 . . .

19

Figure 2.5 Coastline of Lake Michigan showing locations of NDBC meteorological
observation stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

Figure 2.6 (a) Finite-difference mesh of Lake Michigan used to compute the lakewide circulation, (b)Part of the mesh used to compute nearshore circulation
and transport showing the bathymetry . . . . . . . . . . . . . . . . . . . . .

31

ix

Figure 3.1 Energy spectrum at offshore location B . . . . . . . . . . . . . . . . . .

44

Figure 3.2 Energy spectrum at offshore location M . . . . . . . . . . . . . . . . .

45

Figure 3.3 Energy spectrum at nearshore location S . . . . . . . . . . . . . . . . .

46

Figure 3.4 Energy spectrum at nearshore location N1 . . . . . . . . . . . . . . . .

47

Figure 3.5 Energy spectrum at nearshore location N2 . . . . . . . . . . . . . . . .

48

Figure 3.6 Energy contained in different scales of motion in the along-shore direction
as we approach the shore . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

Figure 3.7 Power spectrum of the along-shore velocity at location M . . . . . . . .

53

Figure 3.8 Power spectrum of the cross-shore velocity at location M . . . . . . . .

54

Figure 3.9 Power spectrum of the along-shore velocity at location S . . . . . . . .

55

Figure 3.10 Power spectrum of the cross-shore velocity at location S . . . . . . . .

56

Figure 4.1 The mechanism of shear-augmented dispersion (Ojo et al., 2006a). (a)
Initial distribution of a tracer in a shearing flow; (b) Tracer dispersal due to
diffusion increases the effective rate of mixing; (c) Final state of tracer due to
shear-augmented dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

Figure 4.2 Velocity comparison at location M with lake-wide hydrodynamic model

71

Figure 4.3 Velocity comparison at location B with the nearshore nested grid model

72

Figure 4.4 Velocity comparison at location M with the nearshore nested grid model 73
Figure 4.5 Velocity comparison at location S with the nearshore nested grid model

74

Figure 4.6 Observed versus simulated velocity comparison at locations (a) N1 and
(b) N2 with the nearshore nested grid model . . . . . . . . . . . . . . . . . .

75

Figure 4.7 Comparison of vertical velocity profiles with measurements at the offshore location M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

x

Figure 4.8 Comparison of the vertical velocity profiles with measurements at the
nearshore location N2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

Figure 4.9 Comparison of observed and simulated flow reversal times in the alongshore direction near Ogden Dunes . . . . . . . . . . . . . . . . . . . . . . . .

79

Figure 4.10 Comparison between observed and simulated temperature in the nearshore
region at location S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Figure 4.11 Vorticity and current fields near the Burns Ditch outfall in the nearshore
region of southern Lake Michigan on Julian Day (JD) 158 . . . . . . . . . .

82

Figure 4.12 Vorticity and current fields near the Burns Ditch outfall in the nearshore
region of southern Lake Michigan on Julian Day (JD) 159 . . . . . . . . . .

83

Figure 4.13 Vorticity and current fields near the Burns Ditch outfall in the nearshore
region of southern Lake Michigan on Julian Day (JD) 165 . . . . . . . . . .

84

Figure 4.14 Vorticity and current fields near the Burns Ditch outfall in the nearshore
region of southern Lake Michigan on Julian Day (JD) 168 . . . . . . . . . .

85

Figure 4.15 Comparison of wind and current vectors at a location 300 m from the
shoreline (location S) showing the weak correlation between instantaneous
wind and current directions . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

Figure 4.16 Shear-augmented diffusion rate in the nearshore at location S based on
ADCP observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

Figure 4.17 Shear-augmented diffusion at nearshore location S based on the 3D
hydrodynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

Figure 4.18 Deviatoric strain components observed and calculated from the nearshore
model for location M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

Figure 4.19 Deviatoric strain components observed and calculated from the nearshore
model for location N2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

Figure 4.20 Model comparison with observations of Rhodamine concentrations at
Ogden Dunes beaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

xi

Figure 4.21 Comparison of observed and simulated Rhodamine WT plumes in the
nearshore region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

Figure 5.1 Map of Southern Lake Michigan and the Indiana Shoreline . . . . . . . 107
Figure 5.2 (a) Finite-difference mesh of Lake Michigan used to compute the lakewide circulation (b)Part of the mesh used to compute nearshore circulation
and E. coli transport showing the bathymetry . . . . . . . . . . . . . . . . . 110
Figure 5.3 Comparison between observed and simulated velocity time-series at the
Burns Ditch location in the along-shore and cross-shore directions . . . . . . 113
Figure 5.4 Comparison of observed and simulated vertical velocity profiles for alongshore (u) and cross-shore (v) velocities on different days during summer 2006 114
Figure 5.5 Comparison of observed and simulated short-wave radiation at Trail Creek115
Figure 5.6 Observed and simulated temperature in the nearshore . . . . . . . . . . 115
Figure 5.7 Loading from Trail Creek and Kintzele Ditch during summer 2004 used
as model inputs for the simulation period . . . . . . . . . . . . . . . . . . . . 118
Figure 5.8 Observed and simulated E. coli concentrations at (a)Central Avenue
Beach and (b)Mt. Baldy Beach . . . . . . . . . . . . . . . . . . . . . . . . . 119
Figure 5.9 Spatial extent of EC plumes at two different instants of time on Julian
Day 217. The plumes are shown traveling in opposite directions . . . . . . . 120
Figure 5.10 Probability plots of EC (observed versus simulated) for the Central
Avenue and Mt. Baldy beaches . . . . . . . . . . . . . . . . . . . . . . . . . 122
Figure 5.11 Normalized shear stress and EC for summer 2004 . . . . . . . . . . . 124
Figure 5.12 Grid points in the nearshore used for the budget analysis . . . . . . . 126
Figure 5.13 Results of budget analysis for EC showing the relative contributions of
different processes within the water column . . . . . . . . . . . . . . . . . . . 128
Figure 5.14 Variation of the magnitudes of vertical advection and diffusion within
the water column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
xii

Figure 6.1 Significant wave height compared at location M . . . . . . . . . . . . . 148
Figure 6.2 Significant wave height compared at location S . . . . . . . . . . . . . . 148
Figure 6.3 Wave height compared at nearshore location N1 . . . . . . . . . . . . . 149
Figure 6.4 Wave height compared at nearshore N2 . . . . . . . . . . . . . . . . . . 149
Figure 6.5 Directional power spectrum at location S during the resuspension event
on Julian Day 182 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Figure 6.6 Directional power spectrum at location S during the resuspension event
on Julian Day 186 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Figure 6.7 (a) Suspended sediment concentration (SSC) compared with observation
at location S; (b)-(d)Suspended sediment concentration at the Ogden Dunes
Beaches (OD1 – OD3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Figure 6.8 EC concentration at (a) Burns Ditch (the source) and at the beach
sites (b) OD1, (c) OD2, and (d) OD3. Results are from model simulating the
transport and inactivation without sediment-bacteria interactions. . . . . . . 155
Figure 6.9 EC concentration at (a) Burns Ditch (the source) and the beach sites
(b) OD1, (c) OD2, and (d) OD3. Results are from model simulating the
transport, inactivation and sediment-bacteria interactions. . . . . . . . . . . 156
Figure 6.10 Attached fraction (fp ) for EC in the top and bottom layers of the water
column at (a) offshore (S) and (b) nearshore (OD1) locations . . . . . . . . . 158
Figure 6.11 Comparison between the two models (with and without sediment processes) at the beach sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

xiii

Chapter 1
Introduction

1.1

Problem Description

Large centers of population around the world are found on or close to shorelines. Nearly 53%
of the total population in the United States live in coastal counties (Crossett et al., 2004).
Of this, nearly 18% are found in the Great Lakes region alone (Crossett et al., 2004). Surface
run-off from urban and agricultural sources, effluent outfalls, ground water discharge, and
water from the ballast tanks of ships introduce toxic chemicals, biological contaminants, and
invasive species into these coastal environments (Dor et al., 2003; Boehm, 2003; Boehm et al.,
2004a; Grant et al., 2005, 2001; Strayer, 2010). Popular recreational areas and city water
intakes also lie on or close to shorelines. The Great Lakes of North America have a large
number of cities and beaches that are popular for recreational use during the summer months.
Water quality at recreational beaches is monitored and beaches are closed to the public or
advisories posted when water samples fail to meet standards (Dorfman and Rosselot, 2008,
2010). For example, the Michigan guidelines require that any beach with E. coli levels
1

greater than 300 CFU/100mL be closed for recreational purposes. This number for Indiana
is 235 CFU/100mL. Recently there has been an increase in the number of beach closures in
the Great Lakes region due to a number of reasons (Dorfman and Rosselot, 2008, 2010). The
year 2009 saw the sixth highest levels of beach closings and advisories in 20 years. Incidence
of infections as a results of recreational water use has also increased over the past decades
in spite of efforts at reducing this problem (Yoder, 2008). It has been estimated that the
typical closure of a beach can cause a net economic loss of as much as $37,030/day to local
communities (Rabinovici et al., 2004). As such, water quality at beaches and in the coastal
and nearshore region of seas and large lakes is of interest from the human health point of
view.

Surface runoff is the main source of contamination that results in beach closures across
the country (Dorfman and Rosselot, 2010). Runoff starting as rain and snowmelt washes
off pollutants which eventually end up in coastal environments or inland lakes. In addition
to chemical pollutants, fecal matter is also washed away by the runoff. Untreated sewage
discharge from combined sewer overflows (CSOs), illicit dumping of waste, and accidental discharges due to aging or faulty sewer lines can also enter surface water systems and
contaminate beach water (Dorfman and Rosselot, 2010). Site-specific contribution by bird
droppings and wave action on foreshore sand have also received attention (Boehm et al.,
2004b; Byappanahalli et al., 2003; Grant et al., 2001; Whitman et al., 2003; Whitman and
Nevers, 2003). At Michigan beaches, about 17% of the contamination is attributed to wildlife
(Dorfman and Rosselot, 2010). In the Great Lakes region, CSOs have been identified as the
major source of beachwater contamination near urban areas, with as many as 43,000 overflow
events occurring every year (Dorfman and Rosselot, 2010). Dry-weather runoff due to agri2

cultural irrigation and commercial activity can also be a significant source of contamination,
especially for beaches along the California coast (Grant et al., 2005; Grant and Sanders,
2010). While the urban runoff and CSO events are major problems near large urban centers,
runoff from agricultural areas is responsible for nearly 40% of all water contamination in
rivers and streams (EPA, 2009).
High levels of bacterial contamination in recreational and drinking waters correlate to
gastrointestinal (GI) outbreaks (Griffin et al., 2003; Pruss, 1998; Yoder, 2008). Studies have
shown the linkage between GI and elevated levels of indicator organisms such as E. coli
and enterococci (Pruss, 1998). Water quality monitoring involves testing for these indicator
organisms which, while themselves usually harmless, have a strong correlation with pathogens
that can cause GI and other infections (Pruss, 1998; Wade et al., 2003; Wong et al., 2009).
However, natural sources of these indicator bacteria also exist (Sanders et al., 2005) that
are not associated with fecal contamination sources which increase the importance of source
tracking using DNA-based methods. As much as 75% of the contamination at Michigan
beaches is due to unknown sources as shown in Figure 1.2
Traditional laboratory-based methods of issuing advisories consist of collecting water
samples and testing them in the lab for fecal indicator bacteria (FIB). A period of 18–24 hrs
is required for incubating the samples. Advisories based on laboratory testing are therefore
based on water samples collected as much as 24 hrs in the past. However, studies have
shown that the water quality at beaches is highly variable and can change completely in a
few hours (Boehm, 2007; Boehm et al., 2009; Nevers and Whitman, 2005; Liu et al., 2006).
While efforts to reduce the incubation time for water samples by developing rapid-testing
methods is an active area of research and receiving considerable attention (Scott et al., 2005),
3

predictive modeling of beach water quality is an attractive alternative.
Statistical models are able to predict concentrations of indicator bacteria based on observations of wind speed, wind direction, temperature, and other explanatory variables (Nevers
and Whitman, 2005; Nevers et al., 2007). A statistical relation is established between explanatory variables and the predicted variables using a regression analysis. These statistical
models are easy to use and can be implemented quickly. However, they are site-dependent
and need a vast observational data bank to be able to create and validate a statistical model.
With the most accurate statistical models being able to account for only 71% of natural variability in E. Coli concentrations (Nevers and Whitman, 2008; Olyphant and Whitman, 2004),
these models may not be accurate enough when it comes to making predictions regarding
human health issues. However, they may be better than using previous day’s estimates of
bacterial concentration for determining beach safety.
Analytical models (Boehm et al., 2005; Kim et al., 2004) have been used to identify
sources of pollution. However, they are able to model only simple systems. The fate and
transport of indicator bacteria in marine and inland lake environments is determined by a
number of physical and biological processes which cannot be simplified to a degree where
analytical solutions would be possible. In a recent paper (Grant and Sanders, 2010), a new
conceptual model framework based on the beach boundary layer has been presented for
examining the relative importance of different possible sources of contamination.
Process-based numerical models solve equations that simulate transport in the water
column and the biological processes that affect the growth and inactivation (loss of bacteria per unit time) of indicator bacteria using the conservation principles of mass, energy
and momentum. These processes include both biotic and abiotic stresses and depend on
4

environmental variables such as temperature, pH, salinity, dissolved oxygen, and nutrient
concentrations (Sinton et al., 1994, 1999, 2002). The mathematical representations of these
processes are arrived at using controlled experiments in the lab. Several of these factors are
inter-dependent and interactions in the field are an area of study. Solving the equations for
conditions present in the field involves discretizing the domain to represent the important
spatial scales of the process being simulated. Considering the large range of scales that need
to be resolved, process-based predictive models require small grid sizes and fast computers. With declining computational costs, the use of mechanistic or process-based numerical
models for predicting bacterial concentration in recreational waters is becoming more practical. These models are also helpful in gaining a detailed process-level understanding of the
complex interdependencies between environmental variables, hydrodynamics and bacterial
concentrations. These models are being developed and used to arrive at a better understanding of the underlying processes affecting bacterial concentrations. The eventual objective of
such models is to help develop reliable, robust and accurate water quality forecasting tools.

1.2

Transport Processes

Nearshore hydrodynamics is driven by wind, tides and density gradients. In Lake Michigan,
the currents are wind-driven and tidal forces are minimal (Beletsky et al., 1999). The absence
of sustained wind speeds in any particular direction results in low average current velocities
compared to the typical marine environment. Lake-wide circulation is also a significant
source of energy that drives nearshore hydrodynamics (Rao and Schwab, 2007). Frequent
changes in direction of the alongshore current are observed close to the shore in Southern
5

Figure 1.1: Aerial photograph of the sediment plume from the Burns Ditch outfall located
in southern Lake Michigan. For interpretation of the references to color in this and all other
figures, the reader is referred to the electronic version of this dissertation

a

b

c

d

a - Stormwater runoff (6%)
b - Sewage (2%)
c - Wildlife (17%)
d - Unknown (75%)
Figure 1.2: Sources of bacterial contamination at Michigan beaches

6

Lake Michigan and this is one of the important characteristics of circulation in this region
(Liu et al., 2006; Nekouee, 2010). Currents transport contaminants from sources to nearby
beaches and directly affect water quality. Sources such as outfalls and rivers can also display
significant near-field buoyancy and momentum-driven flow (Nekouee, 2010) as compared to
sources distributed over a large area. The location of contamination sources and circulation
patterns are significant factors affecting contamination levels at nearby beaches and other
recreational and economically important areas (Grant et al., 2005; Connolloy et al., 1999;
Liu et al., 2006; Boehm et al., 2002). Resolving circulation in the nearshore region using an
accurate hydrodynamic model is therefore essential in order to predict contaminant levels.

The interaction between nearshore and offshore circulation is dynamic and cannot be
represented using simple analytical expressions. The natural variability in wind conditions
and effects of large-scale circulation, result in a highly turbulent flow regime in southern Lake
Michigan. Turbulent eddies and offshore exchange result in mixing with ambient lake waters
which generally have a lower contaminant concentration, as shown in Figure 1.3. The process
of mixing due to dispersion and turbulent eddy diffusion is one of the most important factors
affecting contaminant levels. The mixing process is resolved in numerical models by having
an adequately small grid size. The mean-flow resolving Reynolds averaged Navier-Stokes
(RANS) equations are popular for application to the coastal areas and oceans. Small-scale
mixing processes in these models are described by using a turbulence closure model. There
are several turbulence closure models that are used to describe nearshore hydrodynamics.
These closure models vary in complexity and their accuracy. Scaling laws that relate eddy
diffusion rates to the length-scales are a popular method for parameterizing mixing in ocean
and lake models (Okubo, 1971; Lawrence et al., 1995; de Brauwere et al., 2011). However,
7

Figure 1.3: The front between lake and contaminated waters from an outfall
scaling laws for estimating eddy diffusion rates for the smaller scales (10 m – 100 m) have
not received sufficient attention.

1.3

Biological Processes

Enteric bacteria are the most widely used indicator organisms for monitoring microbial contamination in recreational and drinking waters (Scott et al., 2005). The indicator bacteria
are seldom harmful themselves, however, high concentrations of indicator bacteria are indicative of the presence of fecal contamination and pathogenic organisms such as viruses.
They are also easier to test for than pathogens and water samples can be analyzed in 18–24
hrs. Beach monitoring programs across the country test water samples, collected at recreational beaches, for indicator bacteria such as E. coli or enterococci. Beaches are closed or
8

advisories are posted if concentration of indicator bacteria is higher than the standards set
by the EPA.
Indicator bacteria face a number of biotic and abiotic stresses when they leave the host
and enter the aquatic environment. The biotic stresses include various biota that compete for resources or predate on the bacteria and abiotic stresses include temperature, pH,
salinity, and sunlight (Sinton et al., 1994, 1999, 2002). Some of the important biological
processes taking place in the water column are shown in Figure 1.4. Biological process-rates
are sensitive to temperature. The growth, die-off and predation rates display a non-linear
dependence on temperature, and this is usually modeled using the Arhenius relation (Liu
et al., 2006; Hipsey et al., 2008; Thupaki et al., 2010). Direct sunlight causes photo-oxidation
and damages the DNA of bacterial cells. This can lead to temporary inactivation or permanent die-off depending on the dose. The solar intensity, wavelength of sunlight as well as
the bacterial species can all influence the rate of inactivation due to sunlight. In the aquatic
environment, intensity of sunlight changes with time of day and year as well as water quality
(turbidity). Dissolved organic matter content in the water is also known to be a significant
factor affecting solar-extinction rate in the water column (Hipsey et al., 2008). As shown in
Figure 1.4, the environmental variables affecting biological process-rates vary dynamically
in the water column, and are coupled to the hydrodynamic and transport processes.

1.4

Sediment-bacteria Interactions

Suspended particles in the water column settle into the bed sediment layer under favorable
hydrodynamic conditions (Douillet et al., 2001; Eadie, 1997). Bacteria are known to attach
themselves preferentially to sediment particles of a certain size class (16 µm – 30 µm) (Hipsey
9

Sunlight

T(x,y,z,t)

Predation
Dark death

I(x,y,z,t)

Inactivation due to sunlight

Water
Column

S(x,y,z,t)

Resuspension
Growth

Settling
Dark death

Sediment

Figure 1.4: Biological processes affecting concentration of indicator bacteria in the water
column. I(x, y, z, t), S(x, y, z, t), T (x, y, z, t) are the sunlight intensity, suspended sediment
concentration and temperature as they vary in the water column

et al., 2006; Oliver et al., 2007) and settle into the bottom sediment layer. The higher nutrient
concentration and favorable environmental conditions in the sediment can lead to a higher
microbial concentration in the sediment than in the water column (Whitman and Nevers,
2003). Bacteria also exist in free-swimming state in the water column, in the pore-spaces
of the sediment or form bio-films that improve bacterial survival in the sediment (Sanders
et al., 2005; Decho, 2000). However, settling leads to a temporary removal of bacteria from
the water column and a reduction in concentration of bacteria in the water column. In
the nearshore region, the combined action of waves and currents can cause the loosening of
sediment particles and result in their resuspension into the water column. Bacteria attached
to the sediment particles get resuspended back into the water column (Bai and Lung, 2006)
and sediment resuspension is known to be a source of bacterial contamination in marine
10

waters (Sanders et al., 2005; Gao et al., 2011). Attachment and detachment of bacteria to
the sediment particle also occur, changing the fraction of net bacteria attached to sediment
particles. The existence of bio-films can also significantly affect resuspension characteristics
(Sanders et al., 2005) as well as bacterial survival and regrowth (Decho, 2000). Resuspended
sediment also affects sunlight penetration into the water column (Chapra, 1997). Inactivation
due to sunlight is the most important component of the overall bacterial inactivation rate
in the water column (Thupaki et al., 2010). Therefore, suspended sediment concentration
can also have a significant indirect effect on bacterial inactivation rates. (Sanders et al.,
2005) and (Gao et al., 2011) have examined the role of sediment as a source of bacterial
contamination, however, the coupled nature of the sediment’s role as a transient source of
bacteria and its effect on biological inactivation processes in the water column has not been
examined in the literature.

1.5

Structure of the Thesis

Reducing bacterial contamination in recreational water, making timely predictions, and improving beach safety requires a better understanding of the processes affecting fate and
transport of fecal indicator bacteria (FIB) in the nearshore region. This study aims to investigate coupled hydrodynamic and biological processes affecting concentration of indicator
bacteria at beaches along southern Lake Michigan. Observational methods such as Acoustic
Doppler Current Profilers (ADCPs), temperature micro-loggers, underwater fluorometers,
and tracer/dye studies have been used to collect extensive field data in order to describe
the hydrodynamics, temperature profiles, eddy-diffusion, and wave climate in addition to E.
coli data in southern Lake Michigan during summer months. Three-dimensional numerical
11

models to describe the hydrodynamics, transport and sediment-bacterial interactions in the
nearshore region have been developed and used to draw conclusions about the relative importance of fate and transport processes affecting indicator bacteria in southern Lake Michigan.
All numerical models and field data collections methods have been described in Chapter
2. Given the scope of the topic, the main body of this thesis is divided into four principal
chapters (Chapters 3 – 6), each focusing on a different aspect of the problem.
• Identifying the Dominant Energy-carrying Scales Driving Circulation in the Nearshore
Region of Lake Michigan
• Mixing and Transport in the Coastal Boundary Layer of Southern Lake Michigan
• Budget Analysis of Escherichia coli at a Southern Lake Michigan Beach
• Sediment-bacteria Interactions at Beaches in Southern Lake Michigan

12

Chapter 2
Experimental Methods and Numerical
Modeling Techniques

2.1

Experimental Methods

Our understanding of many natural processes depends on the type and amount of observational data that can be collected. Due to the length-scales and time-scales involved, observing
processes taking place in the oceans and coastal areas can be a daunting task. In the past,
observations the marine environment were labor intensive, expensive, and limited to the
upper-most part of the water column, which was easily accessible. Technology now enables
scientists and engineers to make measurements with relative ease and much greater accuracy.
These datasets are used for improving our understanding of the processes taking place and
developing more accurate numerical models.
The site of interest for this study is the nearshore region of southern Lake Michigan.
Circulation in this region is of the scale of tens of km to sub-meter scale turbulent mixing.
13

Tidal forcing is negligible and circulation is primarily wind driven (Beletsky et al., 1999).
Flow-reversals in the alongshore direction are a characteristic feature of circulation in the
nearshore region. Low wind speeds and a limited fetch results in a mild wave climate with
average wave height of less than 0.5m. This section will describe the methods used in this
study to observe the hydrodynamic parameters, eddy-diffusion rates and suspended sediment
concentrations in southern Lake Michigan.
Current velocity and wave climate describe the hydrodynamics in coastal flows. The
Earth’s rotation, wind shear, and temperature and salinity gradients drive the large-scale
circulation in the coastal oceans. The seasonal heating and cooling of the water column
coupled with the stochastic nature of wind blowing on the surface results in a highly dynamic
and turbulent flow-field. Analytical models of simplified representations have been used to
describe circulation in the global scale since Sverdrup and Munk (Mortimer, 2004). Faster
computers have now enabled numerical models to begin to describe the complexity in the
world oceans using global ocean models such as MITgcm (Adcroft et al., 2008). On the
other hand, numerical models of coastal circulation focus on a small part of the coastline.
However, the processes of interest are smaller in scale, keeping the computational cost of
modeling about the same.

2.1.1

Currents

Current meters have been used since the beginning of observational oceanography for measuring Eulerian velocity time-series. They started with small mechanical devices that measured speed by counting rotations of a bucket wheel. Impeller and electro-mechanical type
current-meters were more autonomous and enabled faster measurements. However, these
14

are susceptible to bio-fouling, difficult to set up and unreliable. Instruments would need to
be cleaned at regular intervals, making long term deployments expensive and difficult. Data
from offshore locations in deep-water were therefore difficult to collect. Lagrangian drifters
are a more robust method of collecting hydrodynamic data. However, drifter measurements
are limited to the topmost layers. With the development of Acoustic Doppler Current Profiler(ADCP) technology, it has become possible to measure current velocities in-situ. At
their simplest description, ADCPs are an acoustic transceiver and can transmit and receive
sound waves of a particular frequency range. The sound waves propagating through the water column reflect off surfaces, including sediment particles suspended in the water column.
Doppler shift in reflected sound waves can be used to calculate fluid velocity in the water
column. Analysis of multiple, angled, acoustic beams and analysis can resolve fluid velocity
in all three directions. Acoustic Doppler Velocitimeters(ADVs) are able to measure velocity
of a volume ∼1 cc in size, however, ADCPs measure velocity over the entire water column
and use spatial averaging to improve accuracy. For the purpose of observing currents over
the entire water column, ADCPs are therefore more useful than point velocity measurements
made using ADVs. Phase coherent technology used in some ADCPs, makes use of the phase
difference to estimate the Doppler-shift and distance to echo source. The phase-coherent
mode of operation for ADCPs has enabled greater accuracy and reduced bin-size in current
profile measurements. Reliable and compact data storage methods also mean that long-term
observations can be stored on-board. Line-of-sight radio links and satellite connections of
course, also enable long-term deployments at remote locations and real-time data reporting.

Field studies were conducted between May and September of 2008 to collect an extensive
observational dataset describing hydrodynamic parameters, temperature distribution in the
15

vertical, and eddy-diffusion in the nearshore region of southern Lake Michigan. A total of
five ADCPs were deployed in southern Lake Michigan, at locations shown in Figure 2.1 and
Table 2.1. These locations were chosen based on prior numerical studies to ensure that
the observational dataset would include information about the offshore as well as nearshore
environment. Bottom-mounted, up-looking ADCPs made by Teledyne-RDI R instruments
make use of broadband technology and offer reliable long-term deployments using highcapacity on-board batteries. Three such instruments were deployed on May 29th (Figure 2.4
– Figure 2.2). They were the 600 kHz BBADCP (location B, depth of ∼24.0 m), 1200 kHz
Sentinel (location S, depth of ∼11.5 m), and 600 kHz Monitor (location M, depth of ∼20.2
m). Intensive data sampling was conducted in the nearshore environment for a period of
one week starting June 19th , using two Nortek Aquadopp R 2 MHz profilers deployed closer
to the shoreline (depth of 4.5 m and 7 m) at locations N1, N2 shown in Figure 2.1. The
ADCPs were installed at the location by USGS divers from a boat using a hoist as shown
in Figure 2.3. Accurate locations for each of the ADCPs were recorded using a marine GPS
with sub-meter resolution. The Sentinel and Monitor were serviced on August 5th and the
on-board batteries were replaced and the instruments were redeployed to collect an extended
dataset for the nearshore and offshore locations. The deployment plans used to program the
ADCPs are included in the Appendix.

2.1.2

Waves

Observations of wave height by visual techniques have been used since early mariners ventured out to sea and used to assess wave height based on sea-conditions and wind-speeds.
Modern visual observation techniques based on stereoscopic images taken by elevated cam16

0

Lake Michigan

2

4

km

ADCP
Beaches
Streams

B

M

S
OD1

Burns
Harbor

N2

N1

OD2OD3

Burns
Ditch

87o10’0’’W

87o0’0’’W

Figure 2.1: Map of Southern Lake Michigan showing the important locations for the field
study conducted in summer of 2008. M and B mark the location where the Monitor and
BBADCP were deployed. S, N1, and N2 mark the locations where the Sentinel and two
Nortek ADCPs were deployed. Water samples were collected at beaches in Ogden Dunes
and have been marked by OD1, OD2, OD3. The vertical temperature profile was measured
close to the sentinel deployment (S).

17

Figure 2.2: RDI-Monitor being readied for deployment

Figure 2.3: ADCP being deployed in Lake Michigan on May 29th 2008
18

Figure 2.4: The RDI-Sentinel being readied for deployment on May 29th 2008

ID
M
B
S
N1
N2
OD1
OD2
OD3

Latitude
41.71059
41.69717
41.63813
41.66677
41.63315
41.62790
41.62990
41.62980

Longitude
-87.20996
-87.10078
-87.18539
-87.06297
-87.18839
-87.19660
-87.18750
-87.18310

Description
RDI-Monitor (offshore)
RDI-BBADCP (offshore)
RDI-Sentinel (nearshore)
Nortek (nearshore)
Nortek (nearshore)
Beaches at Ogden Dunes

Table 2.1: Important locations for the field study conducted in Summer 2008

19

eras can assess the sea-surface elevation over a large area. Using satellite images it is now
possible to determine the wave climate on a global scale. Instrument-based measurement
techniques such as buoys or pressure transducers can give more accurate measurements of
the wave-climate, however, they are sensitive to corrosion, bio-fouling and the harsh marine
environment. ADCPs are also popular in-situ methods to measure the wave climate. They
make use of on-board pressure transducers to determine the instantaneous height of the water column. Fourier analysis of the height of the water column can be used to calculate the
significant wave height (HS ) and the wave spectrum. Using the linear wave theory (Witham,
1999), the associated wave energy spectrum is calculated, which is used to estimate the wave
height, time period and direction spectra. It should be noted that measurements are indirect
estimates and may have an uncertainty of as much as 10% associated with them. Since the
pressure and orbital velocity signals due to a passing surface wave attenuate exponentially in
the water column, measurements of wave parameters made at greater depths have a larger
uncertainty associated with them. Wave parameters were measured in the offshore by the
Monitor and in the nearshore using the Sentinel and Nortek profilers that were deployed
about 350 m from the shoreline.

2.1.3

Temperature and Turbidity

Temperature and salinity gradients can be important drivers of circulation. This is particularly important in marine waters where salinity and temperature both vary considerably
over the depth. Seasonal variation in surface heat flux results in stratification and overturning in all large water bodies that experience seasonal variations in temperature. The
Great Lakes are fresh water lakes and have low salinity (<2 ppt) content. Variations in
20

heat flux over the year, however, result in stratification during summer and winter months
and a spring overturning. The effect on thermal inversions on nearshore circulation and the
resulting baroclinic flow is not as important as wind-driven barotropic flow (Csanady, 1973).
However, temperature inversion and the movement of colder, nutrient-rich waters to the
surface, ensures that the hypolimnion is nutrient rich for fishes and other marine organisms,
including bacteria.
Temperature measurements over the entire water column were made near the Sentinel
(location S in Figure 2.1) using a thermistor chain made up of ten Nexsens R temperature
sensors with a sensitivity of +/-1 o C and a range of -10 o C to 35 o C. The sensors were
placed inside individual waterproof housing and attached to a cable with uniform separation
of about 1 m. The cable was anchored at one end and attached to an inflatable buoy
at the other to ensure that it remained vertical. The sensors were programmed to record
temperature measurements once every hour, for a total deployment duration of 85 days.
ADCPs measure the vertical velocity-profile based on the Doppler shift in the reflected
echo. In addition to the velocity, the echo intensity is also recorded by the ADCPs. This
echo (backscatter) intensity can be used to calculate the suspended sediment concentration.
However since ADCPs operate on a single frequency, change in backscatter intensity could be
due to change in particle size distribution or a change in the concentration of suspended sediments. The recorded backscatter intensity from instrument specific values can be converted
to decibels (dB) using Equation 2.1, where Sv is the backscattering strength in dB, LDBM
is the 10 log10 (transmit pulse length(m)), PDBW is the 10 log10 (transmit power (Watts)), Tx
temperature in o C, R is the slant distance to the scatterers, α is the absorption coefficient
of water (dB/m), and θ is the beam angle to the vertical (Deines, 1999; Wall et al., 2006).
21

Instrument
RDI-Sentinel

RDI-Monitor

Beam
1
2
3
4
1
2
3
4

RSSI Slope (dB/Count)
0.3914
0.3960
0.3877
0.3849
0.3848
0.3785
0.3847
0.3736

Table 2.2: Beam-specific scaling factors for RDI-Sentinel and RDI-Monitor
The RDI-Sentinel measured backscatter intensity in counts (Teledyne, 2006) which was
converted to decibels using the beam-specific scale factors (Table 2.2) supplied by TeledyneRD Instruments R . Suspended sediment concentration is a function of backscatter intensity
in decibels (Equation 2.2), however, the site specific calibration constants (a1 , b1 , c1 ) have to
be calculated using independent sediment concentration measurements. For southern Lake
Michigan and using a 1200 kHz ADCP, Lee (Lee et al., 2005a) calculated the calibration
constants to be (a1 = 0.0196, b1 = 3.5275, c1 = 160.25)

Sv = C + 10log10 (Tx + 273.16) R2
−LDBM − PDBW + 2αR + KC E − ER

C = a1 (Sv − S0 )2 + b1 (Sv − S0 ) + c1

2.1.4

(2.1)

(2.2)

Escherichia coli enumeration

Water samples were collected from knee-deep water and analyzed for E. coli levels at the
USGS Great Lakes Science Center in Porter, Indiana. E. Coli concentrations were evaluated
using membrane filtration methods according to section 9222G, APHA APHA (1998). As
22

described in (Liu et al., 2006), membrane filters were incubated on mFC agar at 44.5 o C
for 24 hours, transferred to EC-MUG agar (Difco, 222200), and incubated for 24 hours at
44.5 o C. Individual colonies that produced fluorescence under a long-wavelength (366-nm)
ultraviolet light were considered E. coli. Colony-forming units (CFU) per 100 mL were
recorded.

2.1.5

Eddy-diffusivity and Mixing

Hydrodynamics in the nearshore region is highly turbulent. The transport of contaminants
in such an environment is controlled by mixing due to dispersion of material. Estimates of
the mixing rates can be obtained using Lagrangian drifters, tracer studies and from current
measurements. Lagrangian drifters have the advantage of being reusable and large lengthscales can be easily covered by experiments. However, instrument bulk and inertia can be
a factor affecting the accuracy of the data obtained. Dye (tracer) release studies are better
for estimating mixing characteristics, close to a boundary or where other obstructions can
be a factor. Shear-augmented dispersion can significantly increase mixing rates in vertically
sheared flows (Fischer, 1978; Taylor, 1954).
A dye study was conducted on June 19th using Rhodamine WT as tracer. The dye was
released into the Burns Ditch outfall at a constant rate. The target concentration at the
mouth of the outfall was 20 ppb due to the presence of water intakes nearby. Concentration of
the dye entering the lake was measured using a Turner Designs R Self Contained Underwater
Fluorescence Apparatus (SCUFA R ) unit moored at the mouth of the outfall and the data
was later used to provide a boundary condition for the tracer transport model. Temporal
evolution of the plume was tracked by taking multiple transects of the plume using a towed
23

SCUFA unit and a Magellan Mobile Mapper-CX GPS unit with sub-meter accuracy on a
small motor boat. The procedure was repeated to obtain snapshots of the dye plume at two
different instants of time. Tracer breakthrough data at the beaches were obtained by taking
water samples in knee deep water, every hour, close to the outfall.

2.2

Numerical Models

Numerical models are increasingly being used to get a better understanding of nearshore
processes. These are usually process-based models that solve fundamental equations that
describe the various processes of interest. In the past, problems in resolving the different
scales of these processes resulted in less accurate results. The lowered cost of computing
power today, means that processes can be resolved at scales that would have been too
computationally expensive in the past. Creating a numerical model also requires a large
amount of data. This is used to provide boundary conditions as well as test the model
output. Modeling a system as complex as hydrodynamics coupled with waves, sediment
and indicator bacteria, using a process-based approach requires accurate description of the
meteorological conditions, bathymetry, and boundary conditions. The numerical methods
used to model processes in the nearshore will be outlined in this section.

2.2.1

Currents

Wind driven circulation can be modeled using the hydrodynamic primitive equations (Equation 2.3, Equation 2.4 and Equation 2.5). They are derived from the Reynolds averaged form
of the Navier-Stokes equations for momentum and scalar transport. In its hydrostatic form
presented here, the momentum equation in the z-direction can be written as Equation 2.5.
24

Making the Boussinesq approximation, density is assumed constant except when multiplied
by the acceleration due to gravity in the buoyancy term.

∂u
∂u
∂u
∂u
1 ∂P
∂
∂u
+u
+v
+w
− fv = −
+
2AM
∂t
∂x
∂y
∂z
ρo ∂x
∂x
∂x
∂u ∂v
∂
∂
AM
+
+
+
∂y
∂y ∂x
∂z

KV M

∂u
∂z

(2.3)

∂v
∂v
∂v
∂v
1 ∂P
∂
∂v
+u
+v
+w
+ fu = −
+
2AM
∂t
∂x
∂y
∂z
ρo ∂y
∂y
∂y
∂
∂u ∂v
∂
+
+
AM
+
∂x
∂y ∂x
∂z

KV M

∂v
∂z

(2.4)

∂P
= −ρg
∂z

(2.5)

Where, (u, v, w) are the mean flow velocities in (x, y, z) directions, AM , KV M

are the

eddy viscosity in the horizontal (x, y) and vertical (z) directions. ρ0 and ρ are the reference
density and local density respectively, P and g are the pressure and gravitational acceleration
respectively. f is the Coriolis term (f = 2ω sin φ) and depends on the latitude of a place φ
and the angular velocity of Earth’s rotation ω (Mellor, 1998; Vallis, 2006).

∂ψ
∂ψ
∂ψ
∂
∂ψ
+u
+v
+w
=
∂t
∂x
∂y
∂z ∂x
+

AH
∂
∂z

∂ψ
∂x

KV

+

∂ψ
∂z

∂
∂y

∂ψ
AH
∂y

+ Sψ

(2.6)

Temperature and salinity transport are modeled using the scalar transport equation Equation 2.6, where ψ is the scalar variable being conserved and Sψ are the sources and sinks.
AH , KV

are the eddy diffusivity in the horizontal and vertical directions and related to

25

the turbulent viscosity AM , KV M based on the turbulent Prandtl number (P r). Seasonal
and diurnal changes in temperature of the water column depends on heat flux due to solar
insolation and ambient air temperature. These fluxes are calculated based on meteorological
observations recorded at NDBC and NCDC weather monitoring stations. The sedimentwater column interface is modeled as an adiabatic boundary in the temperature transport
equation. E. coli and suspended sediment concentrations are also solved using the same
scalar transport equation with appropriate source and sink terms as explained further in
subsection 6.3.3 on page 139.
Horizontal eddy diffusion in the momentum transport equations (Equation 2.3 and Equation 2.4) was modeled using the Smagorinsky eddy viscosity model shown in Equation 2.7.
The Smagorinsky model is a simple mixing-length turbulence closure scheme and is popular
in ocean models.
AM = C∆x∆y

1
2

→
−
V +

→ T
−
V

(2.7)

Here, AM is the turbulent eddy viscosity in the horizontal directions. Isotropic conditions
are assumed and eddy viscosity in x and y directions are equal. Grid size (∆x, ∆y) is
automatically included in the formulation, so that eddy viscosity is dependent on the scale
of the unresolved processes. (C) is a non-dimensional parameter which is around 0.1. The
Princeton Ocean Model makes use of the Mellor-Yamada 2.5 level closure model to describe
mixing in the vertical (Mellor and Yamada, 1982). The Mellor-Yamada turbulence closure
model was developed in order to improve prediction of thermal stratification and inversion.
Solving these equations, for any reasonable length of time, on a large domain using a
fine grid-size, can become computationally expensive. This is because of the existence of
the fast barotropic mode, driven by pressure differences; and the slow, baroclinic mode
26

that is driven by temperature, salinity or density differences. Exploiting this feature, it is
possible to split the equations into the vertically-integrated barotropic mode that solves for
the elevation and vertically-integrated velocities, and the baroclinic mode that solves the full
three-dimensional form of the equations using a longer time-step than the barotropic mode
(Simons, 1974; Madala and Piacsek, 1977; Blumberg and Mellor, 1987).
The Princeton Ocean Model (Mellor, 1998), which was modified by the National Oceanic
and Atmospheric Administrations’s Great Lakes Environmental Research Laboratory (NOAAGLERL) in Ann Arbor for the Great Lakes, uses a finite difference approach to solve the
equations. The horizontal directions are discretized by an Arakawa-C grid and the vertical
is discretized using σ−levels that follow the contours of the bathymetry. The momentum
equations are solved using a leap-frog method for the internal mode and the second-order
accurate Smolarkiewicz scheme is used to solve for advection. The tracer transport equation
is also solved in the internal mode, since this is a ’slow’ process. Divergence due to the
leap-frog method is rectified using a smoothing function at each internal time-step. Each
time-step for the internal mode is divided into multiple iterations over which the external
mode calculations are performed. The internal and external time-steps are synchronized
every internal step.
Lateral boundary conditions are implemented automatically using land masks to determine water and land cells. A no-flow boundary condition at the land-water interface is used
for the whole lake model. The Mackinaw Strait contributes mass and momentum to Lake
Michigan resulting in a residence time of about 100 years for Lake Michigan. Since the
Mackinaw St. does not significantly affect lake-wide hydrodynamics (Beletsky et al., 1999)
and the study site is located in southern Lake Michigan, mass and momentum flux at the
27

Mackinaw Strait have been neglected. The 1-way interaction between the large-scale and
nearshore models is implemented using open boundaries in the nested grid model. Details
of the finite different approximations used at the boundary have been presented in (Mellor,
1998).
Nearshore hydrodynamics is affected by large-scale circulation. The features of interest in
the nearshore are, however, small-scale and resolving these features requires a small grid-size.
Therefore, a nested-grid approach is used in order to reduce the model computation time to
reasonable levels. Results from the coarse-grid model covering the whole of Lake Michigan
are used to generate the boundary conditions for the nearshore model. Interaction between
the lake-wide and nearshore models are at the boundary and interpolated from the coarse
grid using a bi-linear interpolation method. A Dirichlet boundary condition is used for water
surface elevation and for velocity in the horizontal directions. The Sommerfield radiation
boundary condition (Mellor, 1998) is used to ensure outflow condition at the boundary is
implemented accurately.
Wind shear at the water surface is the prime driver of circulation in Lake Michigan. This
value is calculated based on wind speed and direction recorded at meteorological stations
located around Lake Michigan. Quality controlled wind measurements are made available by
the National Climatic Data Center (NCDC) and National Data Buoy Center(NDBC) on their
websites. Wind speeds are recorded at different intervals which varies from a few minutes up
to an hour. Interpolated wind fields are provided to the hydrodynamic model using spatial
and temporal averaging. Wind speeds are averaged using 2 hour moving time window by
including the time difference into the nearest distance calculations by using a scaling speed.
A scaling speed of 10 km/hr was found to give good results (Schwab and Beletsky, 2000).
28

Spatial averaging is implemented using a nearest neighbor interpolation method with a 30
km smoothing radius (Schwab and Beletsky, 2000). Since wind measurements at the coast
under-estimate over water wind speeds, an empirical correction was used to convert from
overland measurements to over-water values (Schwab and Morton, 1984).

2.2.2

Waves

Third-generation numerical wave models calculate the wind-driven wave climate by solving
the wave action-balance equation (Equation 2.8).

∂
∂
∂
∂
S
∂N
+
(cx N ) +
cy N +
(cσ N ) +
cθ N =
∂t
∂x
∂y
∂σ
∂θ
σ

(2.8)

Here, N (σ, θ) is the action density spectrum and is defined as the energy density spectrum
E (σ, θ) /σ, where σ is the relative frequency (wave frequency in constant current) and θ is the
propagation direction in radians. cx , cy are the group velocities for the wave spectrum and
accounts for shoaling, cθ account for depth and current induced diffraction, and cσ accounts
for effect of ambient currents on the wave frequency. S includes the energy source terms
due to wind, dissipation terms due to wave breaking and bottom friction, and non-linear
wave-wave interactions.
The energy contained in wind-generated waves is determined by the wind speeds and
fetch or the distance over which the wind acts on the water surface. Since wave climate in
Lake Michigan is fetch-limited and wind speed are also lower, a simplified wave model can
be developed (Donelan, 1977; Schwab et al., 1984) based on a semi-empirical wave model.
In this simplified wave model, non-linear wave interactions are neglected in favor of a model
that is easy to solve and can be integrated with a 3D hydrodynamic model to include wave29

46.5
46

45.5

45

44.5

Latitude

44
NDBC Observation
Station

43.5

43

42.5

42

41.5
−89

−88

−87

−86

−85

−84

Longitude
Figure 2.5: Coastline of Lake Michigan showing locations of NDBC meteorological observation stations

30

(a)

(b)
Depth
2m
6m
10m
14m
16m
18m
20m
24m
28m

Figure 2.6: (a) Finite-difference mesh of Lake Michigan used to compute the lake-wide
circulation, (b)Part of the mesh used to compute nearshore circulation and transport showing
the bathymetry

31

current interactions (Mellor, 2003; Mellor et al., 2010). (Liu et al., 2002) compared four
different wave-prediction models and concluded that they all did equally well in predicting
the wave environment in Lake Michigan. Being simpler to implement and integrate into a
3D hydrodynamic model, the GLERL/Donelan wave model (Schwab et al., 1984; Liu et al.,
2002) has specific advantages to other third-generation wave models solving the spectral
action-balance equation and has therefore been used in this study.
The numerical model originally proposed by Donelan (Donelan, 1977) and later used
for predicting waves in the Great Lakes (Schwab et al., 1984, 1986), solves Equation 2.9
describing change in wave momentum under the action of wind stress.

∂Mx
∂Mx
τx
∂Mx
+ cx
+ cy
=
∂t
∂x
∂y
ρw
∂My
∂My
∂My
τy
+ cx
+ cy
=
∂t
∂x
∂y
ρw

(2.9)

The x and y components of wave momentum Mx , My can be written as 2.10, where
ρw is the water density, cx , cy are the group velocities and E(f, θ) is the two-dimensional
spectrum of wave energy, as a function of angular frequency θ and frequency f . τx , τy are
the shear stress due to wind, c(f ) is the phase velocity for a given wave frequency based on
the dispersion relation.
∞ 2π
Mx = g
0 0
∞ 2π
My = g

E (f, θ)
cos θdθdf
c (f )
E (f, θ)
sin θdθdf
c (f )

(2.10)

0 0
Using the deep water linear wave theory and assuming that the wave energy is related to
32

mean wave direction as the cosine squared (Schwab et al., 1984) has shown that the wave
momentum flux can be calculated using Equation 2.11. Here, Cp is the phase velocity of the
peak frequency.

|M | Cp 2
1
cos θ0 +
4
2
|M | Cp
cx My = cy Mx =
cos θ0 sin θ0
4
|M | Cp 2
1
cy My =
sin θ0 +
4
2
cx Mx =

(2.11)

Momentum input by the wind into the wave field consists of two orthogonal parts, the part
parallel to the wind vector (τu ) and the part parallel to the wave momentum vector (τm ) so
that τx = τu + τw . Scalar values of the two components can be written as Equation 2.12 as
suggested by (Donelan, 1977). Here, θ0 is the angle between the wind vector and the wave
direction, λ is the fraction of wind stress transferred to the waves as a result of wave drag
(Equation 2.13).

λ
ρa Du U − 0.83cp cos θ0 U − 0.83cp cos θ0
2
λ
τm = ρa Dm U cos θ0 − 0.83cp U cos θ0 − 0.83cp
2
τu =

Du =
Dm =

2
κ
ln(10/zo cos θo )
2
κ
ln(10/zo )

(2.12)

(2.13)

Here, (κ = 0.4) is the Von Karman’s constant and zo is the roughness length. These
equations result in a wave model that is robust and easy to solve numerically, (Schwab
33

et al., 1984) has presented a detailed discussion on numerical techniques used to solve the
equations. The wave momentum transport equations are discretized using a combination
of upwind and centered-difference schemes on the same computational grid as used by the
hydrodynamic model. The variables are computed at the center of each grid cell and the
model provides the significant wave height, wave period and wave direction as output. The
wave model has been used by (Schwab et al., 1984), (Liu et al., 1984) and (Lou et al., 2000)
and shown to be able to accurately predict the wave height and direction for fetch limited
conditions. However, energy dissipation processes such as bottom friction and wave breaking
are not included and shallow water wave transformation processes and non-linear wave-wave
interactions are also not included in the formulation compromising resulting in errors in the
predicted wave period.

34

Chapter 3
Identifying the Dominant
Energy-Carrying Scales Driving
Circulation in the Nearshore Region
of Lake Michigan

3.1

Summary

Lake-wide circulation is tightly coupled with nearshore hydrodynamics. The role of lakewide circulation as a source of energy is explored in this chapter. The principal goal is to
identify the dominant energy-carrying scales of motion in the nearshore region. Using extensive velocity-profile data measured at different distances from the shore, the transition of
energy from the offshore to the nearshore is examined to identify the location and extent of
the inertia-dominated and friction-dominated boundary layers. The ability of the Reynolds
35

averaged Navier-Stokes (RANS) equation to describe the energy cascade in the nearshore
region is assessed. It was found that the hydrodynamic model is able to describe the energy cascade in the inertial boundary layer adequately; however, the accuracy reduces in
the friction dominated boundary layer closer to the shoreline. The higher frequencies are
consistently under-predicted as a result of using a 100 m grid with a Smagorinsky based
eddy-viscosity model. Using wavelet analysis it was also possible to identify that most of
the energy in the nearshore is transported in the inertial scales of motion.

3.2

Introduction

Hydrodynamics in the nearshore region of Lake Michigan is highly turbulent and a result
of interaction between the coastal boundary and lake-wide circulation. Assuming a characteristic length of 100 m and velocity of 0.1 m/s the typical Reynolds number for nearshore
circulation is O 107 . The circulation is driven by energy transferred from the large-scale
lake-wide circulation as well as local wind shear at the water surface. The large and smallscales are tightly coupled by the turbulent energy cascade and non-linear interactions at
different scales. The larger scales invariably contain much of the energy and affect hydrodynamics the most. In the oceans, kinetic energy is dominated by the geostrophic eddy
field and is driven by Earth’s rotation (Ferrari and Wunsch, 2009). In a flow where the
vertical velocities have not been suppressed by stratification, a direct turbulent energy cascade results in energy being transferred from larger to smaller scale (Kolmogrov, 1941).
Inverse energy cascades, responsible for the transfer of energy from small-scale eddies to the
large-scale eddies, have also been observed in large-scale circulation using satellite altimetry (Scott and Wang, 2005). The pathways toward dissipation of the dominant geostrophic
36

eddy kinetic energy depends on the directions of energy cascade but are difficult to quantify because of serious observational difficulties for wavelengths shorter than approximately
100-200 km (Ferrari and Wunsch, 2009). Quasi-2D flow regimes and inverse-energy cascades
have also been observed in depth-constrained environments in shallow waters (Ghidaoui and
Kolyshkin, 1999).
In Lake Michigan, the circulation is wind-driven and geostrophic flow is not as important
(Beletsky et al., 1999; Csanady, 1983; Schwab and Beletsky, 2000). However, the large-scale
circulation is an important source of energy into the nearshore environment. Wind forcing
generates barotropic flows in large lakes (Csanady, 1973) and several researchers (Murthy
and Rao, 2003; Rao and Schwab, 2007) have shown the significance of large-scale circulation
as a source of mass and energy, on nearshore hydrodynamics in the Great Lakes. Murthy and
Dunbar (1981) have described the structure of flow within the Coastal Boundary Layer (CBL)
based on the dominant processes. The CBL can be divided into the Frictional Boundary
Layer (FBL) and the Inertial Boundary Layer (IBL), based on the relative importance of
inertial and frictional forces respectively. In their study Murthy and Dunbar (1981) identified
IBL and FBL for Lake Huron to extend ∼10 km and ∼2 km from the shoreline respectively.
Close to the shore, within the FBL, velocity gradients are steeper and viscous dissipation
becomes the dominant factor describing the hydrodynamics. The FBL is also important
from a transport modeling point of view, since this is where contaminants from outfalls get
transported and diluted.
Contaminants introduced by outfalls located at or near the shoreline get advected and
dispersed close to the coast, within the coastal boundary layer, depending upon the hydrodynamics. Turbulent mixing processes are responsible for the transport of energy as well
37

as contaminants. For the predictive modeling of hydrodynamics and transport the typical
scales of motion from a practical view point range from the lake-wide gyres down to a few
meters. The ability to accurately account for this variability is essential for any numerical
model. Numerical models for describing the hydrodynamics and transport of contaminants
close to the shoreline have to use local grid refinement using either unstructured grids (Liu
et al., 2006) or nested-grid techniques Thupaki et al. (2010). The hydrodynamics are typically modeled using the RANS equations to describe the mean flow and horizontal viscous
dissipation in these models is modeled using constant eddy-viscosity or simple length-scale
models based on the Smagorinsky model. Recent work in open channel flows have focused on
accurately describing the horizontal quasi-2D turbulence regime in bottom-confined shallow
water flows (Uittenbogaard and van Vossen B., 2004; Awad et al., 2009) and these can be
extended to lake-wide circulation.

In this study we examine the energy driving the circulation in nearshore region of southern Lake Michigan. The importance of lake-wide hydrodynamics as a source of mass and
energy for nearshore circulation of a large enclosed lake such as Lake Michigan is recognized.
Information about the modes of energy transfer from the offshore to the nearshore region
and the important energy scales for modeling hydrodynamics in the nearshore are not available in the literature. Model assessment using the current velocities conveys only part of
the picture. Identifying the important scales of energy and the transition that occurs as we
move closer to the shore is required in order to make substantial improvements to the ability
to model circulation in the nearshore region. This has thus far not been explored in the
literature to the best of our knowledge. The focus of this study is, therefore, to use current
measurements using acoustic Doppler current profilers (ADCPs) deployed at different loca38

tions in the nearshore region of southern Lake Michigan to determine the important energy
carrying scales and their transformation as we approach the shoreline. Detailed comparisons
between observations and model results are included in Chapter 4. The energy cascade and
the pathways taken for this transfer of energy will be examined and the important energy
carrying scales identified using wavelet analysis. A fully three-dimensional numerical model
based on the Princeton Ocean Model (POM) will be used to assess performance of the RANS
equations in predicting the different energy-carrying scales, their transition, and the turbulent energy cascade in the nearshore region. Improvements in future numerical models will
be suggested. While these results are for a specific period of the year, conclusions should be
valid in general for any depth-constrained, low wave-energy environment.

3.3
3.3.1

Methods
Study Site

The focus of this study is the Ogden Dunes beaches in Indiana during the summer months
(June – August), when the number of visitors to beaches is highest. The beaches are located
in southern Lake Michigan near Portage, Indiana, Figure 2.1. Vertical profiles of the hydrodynamic variables were measured using acoustic Doppler current profilers (ADCPs). In all
a 600 kHz RDI Monitor R , a 1200 kHz RDI Sentinel R , a 600 kHz RDI Broadband ADCP
(BBADCP) and two 2.0 MHz Nortek R Aquadopp current profilers were deployed near the
study site to collect current data. All the instruments except the BBADCP are capable of
concurrently recording wave and current information. Current data were collected in the
offshore region using the BBADCP and the Monitor ADCP deployed in a bottom-resting,
39

up-looking configuration. Data were collected at the rate of 0.1 Hz and 1.0 Hz and ensemble averaged every 15 min and 5 min respectively. The Sentinel was deployed closer to the
shoreline to record observations in the nearshore region. Data was collected at the rate of
1 Hz and ensemble averaged every 5 min. In order to get a better picture of the nearshore
circulation and to help validate the numerical model close to the shore two Nortek Aquadopp
ADCPs were deployed for a week long intensive sampling period between JD 172–JD 179.

3.3.2

Numerical Model

The Princeton Ocean Model (POM) (Blumberg and Mellor, 1987) is a three-dimensional hydrodynamic model that solves the hydrodynamic primitive equations (Equation 2.3–Equation 2.5).
These equations resolve the mean (Reynolds averaged) flow field and parameterize the eddy
diffusion using the Smagorinsky eddy-viscosity model (Smagorinsky, 1963) in the horizontal
directions. Eddy viscosity is assumed to be isotropic in the horizontal directions as shown
in Equation 2.3 and Equation 2.4. The eddy viscosity in the vertical direction is calculated
using the Mellor-Yamada 2.5 level turbulence closure model (Mellor and Yamada, 1982). A
finite-difference orthogonal grid with a 2 km resolution was used to resolve large-scale lakewide circulation. Small-scale features close to the shoreline were resolved using a nested-grid
model with a 100 m grid resolution. Nesting was one-way and information from the large
scale lake-wide model was interpolated to provide boundary conditions for the nearshore
model. The computational domain for the lake-wide and nearshore models are shown in
Figure 2.6. Details of the hydrodynamic model including the numerical methods and equations solved are described in Section 2.2.
40

3.3.3

Wavelet Decomposition

Analysis of the observed time-series can yield important information about the underlying
processes. The Fourier transform and wavelet analysis are two methods popularly used
to analyze a discretely sampled signal that has power at several frequencies. The Fourier
transform of any signal results in the decomposition of the time-series into its constituent
sinusoidal signals. One of the drawbacks of this method is that the analysis not localized in
time. A Fourier transformed signal provides information of the component frequencies and
respective powers, however, information about the temporal location is not available. On the
other hand, the wavelet method uses a basis function for decomposing the time-series. These
basis functions are transformed in phase, scale and location to recreate the original signal in
a process called convolution. While the Fourier transform of a time-series loses information
of the temporal variation of the constituent sinusoidal signals, wavelet analysis uses basis
functions localized in space and time to retain important information regarding the temporal
location of the signal. Wavelet analysis can therefore be used to locate singularities, de-noise
time-series, analyze images and compress and study signal evolution over time. In this study
the wavelet analysis method is used for its ability to isolate particular scales of motion in
the time-series from the ADCP measurements.
There are several basis functions that can be used in wavelet analysis. They are broadly
classified into orthogonal and non-orthogonal basis functions. The Morlet wavelet, shown
in Equation 3.1, is a non-orthogonal wavelet function that can be used for either discrete
(DWT) or continuous (CWT) wavelet transform (Torrence and Compo, 1998), and is used
here.
2
ψo (η) = π −1/4 eiωo η e−η /2
41

(3.1)

N −1
Wn (s) =


x ψ∗ 
n

n =0

n − n δt



s



(3.2)

Here, ωo is the non-dimensional frequency and η is the non-dimensional time variable. Using
convolution (a “shift, multiply and sum” operation) discrete time-series can be created from
a basis function. Using the convolution theorem the wavelet transform for any discretelysampled time-series is given by Equation 3.2. Here, ψ ∗ is the complex conjugate, s is the scale
and t is the translation of the function in Equation 3.1 along the localized time axis. Using
a discrete Fourier transform (DFT) can speed up the convolution of a discretely sampled
time-series (Torrence and Compo, 1998). In this study, wavelet analysis was used on the
velocity time-series collected by the ADCPs deployed at various distances from the shore, as
well as results from a 3D hydrodynamic model, to separate the individual time-scales.

3.4

Results

A hydrodynamic model was set up to describe circulation in the nearshore region of southern
Lake Michigan. Lake-wide circulation was resolved using a regular orthogonal grid with 2
km resolution covering the entire Lake Michigan and Green Bay. Nearshore circulation is
affected by the boundary conditions, river plumes and bottom topography. These smallscale features were resolved using a 100 m grid resolution in the nearshore model. Detailed
comparison of model results with observed hydrodynamic variables at different distances
from the shoreline are presented in Chapter-4.
Circulation in Lake Michigan is driven primarily by wind-shear and the Coriolis force due
to Earth’s rotation. Energy is supplied at time-scales typical of the processes involved and
transported to different scales due to the turbulent energy cascade (Kantha and Clayson,
42

2000; Kolmogrov, 1941; Vallis, 2006). This system of non-linear interactions that transfer
energy to larger and smaller scales has been observed in the world’s oceans (Scott and
Wang, 2005; Ferrari and Wunsch, 2009). The importance of the Coriolis effect in large-scale
circulation in Lake Huron has been identified by studying the kinetic energy spectrum at
different distances from the shoreline (Murthy and Dunbar, 1981). The inertial frequency f
(f = 2ω sin φ, where ω is the angular speed of rotation and φ is the reference latitude) for
Lake Michigan is ∼12 hours and the energy supplied to the circulation at this frequency can
be observed in Figure 3.1 and Figure 3.2 that compare the observed and modeled kinetic
energy spectrum for the surface layer at offshore locations B and M respectively. It is clear
from these comparisons that the model is able to describe the inertial effects, characterized
by the peak at the inertial frequency, observed in the offshore locations. The energy cascade
in the inertial scale is also well described, despite using a RANS model to describe the mean
flow. The dissipation scale is averaged out in a RANS formulation and this affects the higher
frequencies. This is also missing from the observed energy spectrum, since observations were
ensemble averaged to improve instrument accuracy. Details of the deployment plans used
have been included in the Appendix.
The total kinetic energy in the larger scales for the along-shore direction, is higher than
the peak at the inertial frequency, this can be due to an inverse energy cascade which has
been observed in the open oceans using satellite altimetry by Scott and Wang (2005) and in
shallow depth-confined flows (Awad et al., 2009). Lateral boundary conditions and smaller
maximum eddy-size in the cross-shore direction might also be the cause of the lower energy
in the cross-shore direction as compared to the along-shore direction.
Closer to the shoreline, at location S, the transition of the flow from inertia-dominated
43

Along-shore

0

10

10

Observed
Model

−1

Observed
Model

−1

10

10

−2

−2

10
Energy

10
Energy

Cross-shore

0

−3

10

−3

10

−4

−4

10

10

−4

10

−2

10
Cycles per hour

0

10

−4

10

Figure 3.1: Energy spectrum at offshore location B

44

−2

10
Cycles per hour

0

10

0

10

Along-shore
Observed
Model

−1

10

−2

−2

10
Energy

Energy

10

−3

10

−3

10

−4

−4

10

−5

Observed
Model

−1

10

10 −4
10

Cross-shore

0

10

10

−2

10
Cycles per hour

0

10

−4

10

Figure 3.2: Energy spectrum at offshore location M

45

−2

10
Cycles per hour

0

10

Along-shore

0

10

10

Observed
Model

−1

Observed
Model

−1

10

10

−2

−2

10
Energy

10
Energy

Cross-shore

0

−3

10

−3

10

−4

−4

10

10

−4

10

−2

10
Cycles per hour

0

10

−4

10

−2

10
Cycles per hour

Figure 3.3: Energy spectrum at nearshore location S

46

0

10

10

Along-shore

0

10

Observed
Model

−1

Observed
Model

−1

10

10

−2

−2

10

10

Energy

Energy

Cross-shore

0

−3

−3

10

10

−4

−4

10

10

−5

10

−4

10

−2

10
Cycles per hour

0

10

−4

10

−2

10
Cycles per hour

Figure 3.4: Energy spectrum at nearshore location N1

47

0

10

10

Along-shore

0

0

10

Observed
Model

−1

Observed
Model

−1

10

10

−2

−2

10

10
Energy

Energy

Cross-shore

−3

10

−3

10

−4

−4

10

10

−4

10

−2

10
Cycles per hour

0

10

−5

10 −4
10

−2

10
Cycles per hour

Figure 3.5: Energy spectrum at nearshore location N2

48

0

10

to friction-dominated regime is reflected in the decay of the peak at the inertial frequency,
as shown in figure 3.3. Location S is at a distance of ∼1 km from the shoreline and this
is consistent with earlier studies (Murthy and Dunbar, 1981) that identified the FBL to
be about 2 km wide for Lake Huron. At locations N1 and N2 where the depth is about
5 m and 7 m respectively (Figure 2.1), the hydrodynamics are dominated by small-scale
processes and sharp velocity gradients due to boundary conditions. This results in greater
viscous losses. The energy dissipation processes are over-predicted by the Smagorinsky eddyviscosity model as shown by the comparison with observations in figures 3.4, 3.5. Model
accuracy in resolving the energy spectrum deteriorates at locations closer to the shore. With
a grid size of 100 m and the Smagorinsky turbulence closure model, the numerical model
is unable to predict energy-dissipative processes in the FBL accurately. Processes in the
larger time scale (associated with larger eddies) are modeled better, as is the along-shore
component compared to the cross shore current component. The difference in the along
and cross shore directions and the relative accuracy of the model also raises questions about
the need to include anisotropy in subgrid scale dissipation schemes to better describe field
observations.

As circulation in Lake Michigan is driven by wind and energy dissipation is mostly at the
boundaries, the energy contained in the nearshore is expected to be less than the offshore
region. However, comparisons between energy spectra from ADCP observations in the offshore (Figure 3.1 &Figure 3.2) and nearshore (Figure 3.4 & Figure 3.5) show that circulation
in the nearshore has as much or more energy than in the corresponding scales in the offshore
region. This might be an artifact of the sampling size which was only 7 days long for the
N1, N2 locations in the nearshore, but more than 2 months for the offshore locations.
49

The importance of large-scale circulation on nearshore hydrodynamics and the role of
cross-shelf exchange on mass and contaminant exchange are well known. (Murthy and Dunbar, 1981) make use of current measurements at different distances from the shore to identify
the transition of flow from an inertial dominated flow regime to a more friction dominated
one. While the measurements were made on Lake Huron, similar features are expected in
Lake Michigan. The importance of different scales of motion and their transformation as
we move closer to the shoreline has been examined using wavelet analysis to decompose the
observed velocity time-series based on the time scales. Figure 3.6 shows results from the
wavelet analysis used to calculate the percent of the net energy contained in the different
scales.

ADCP data from locations M, S, and N2 (9.18 km, 0.88 km and 0.35 km from the shoreline
respectively) have been shown in Figure 3.6. The comparisons show that the percent of
total energy in the larger time-scales (and therefore the larger eddies) increases as we move
closer to the shore. This observation is consistent with a quasi-2D flow regime observed in
shallow, depth-constrained flows (Uittenbogaard and van Vossen B., 2004). According to the
Kolmogrov hypothesis of energy transfer between the different scales, energy from the larger
scales is transferred to the smaller scales at a rate that is described by the inertial range
scaling law (Pope, 2000). The energy is eventually dissipated due to viscosity at the molecular
scale. This is the typical or ‘direct’ energy-cascade. Comparisons of the observations (dashed
lines) with numerical model (solid lines) shown in Figure 3.6, shows the accuracy of the model
in predicting the energy content in the different scales. The dominant energy carrying scales
at different distances from the shore are clearly around the inertial frequency of 12 hours,
however, the dominance of larger scales increases as we approach the shoreline.
50

While the peak energy-carrying scale is correctly identified in the offshore region, there
is a divergence between modeled and observed energy carrying scales as we move closer to
the shoreline. The model consistently over-predicts energy at the large-scales while underpredicting the energy carried in the smaller scales (associated with higher frequencies). These
smaller scales do not carry much energy and can be considered negligible for modeling
hydrodynamics. However, small scale fluctuations in the flow field control the mixing rates
due to dispersion and can be important for modeling contaminant transport.
If we examine the energy-cascade in the spectral domain (as shown in Figures 3.1, 3.2,
3.3, 3.4, and 3.5), for energy balance at a particular frequency the rate of turbulent kinetic
energy production and transfer through the scales should be equal to the rate of dissipation.
The difference between the observed and modeled energy content in the smaller scales suggests that the Smagorinsky eddy viscosity model is highly damping and over-predicts energy
dissipation.

51

30

% Energy

25

0.88 km from shoreline
0.35 km from shoreline

9.18 km from shoreline
RDI−Monitor
Simulation
RDI−Sentinel
Simulation
Nortek (N2)
Model

20
15
10
5
0 −3
10

−2

10

−1

10
Frequency (1/hr)

0

10

1

10

Figure 3.6: Energy contained in different scales of motion in the along-shore direction as we
approach the shore

52

Velocity (m/sec)

a) Along-shore velocity

4
2
0

−2
−4
−6

185

190

200

205

b) Wavelet power spectrum

2
Period (hrs)

195
JD of 2008

4
8
16
32
64

128
185

190

195
JD of 2008

200

Figure 3.7: Power spectrum of the along-shore velocity at location M
53

205

Velocity (m/sec)

a) Cross-shore velocity

5

0

−5

185

190

185

190

Period (hrs)

2

195
200
JD of 2008
b) Wavelet power spectrum

205

4
8
16
32
64

128
195
JD of 2008

200

Figure 3.8: Power spectrum of the cross-shore velocity at location M
54

205

Velocity (m/sec)

a) Along-shore velocity

4
2
0
−2
−4

185

190

195
JD of 2008
b) Wavelet power spectrum

200

205

185

190

195
JD of 2008

200

205

Period (hrs)

2
4
8
16
32
64

128

Figure 3.9: Power spectrum of the along-shore velocity at location S
55

Velocity (m/sec)

a) Cross-shore velocity

4
2
0

−2
−4

185

190

200

205

200

205

b) Wavelet power spectrum

2
Period (hrs)

195
JD of 2008

4
8
16
32
64

128
185

190

195
JD of 2008

Figure 3.10: Power spectrum of the cross-shore velocity at location S
56

Wavelet analyses of the ADCP measurements in the along-shore and cross-shore directions have also been presented in Figure 3.7 – Figure 3.10 to show the observed and simulated surface velocities in the offshore (3.7 and 3.8) and nearshore (3.9 and 3.10) regions.
The advantage of wavelet analysis is that it preserves the temporal evolution and reveals the
structure of the energy cascade. The energy spectra have been normalized to simplify comparisons between nearshore and offshore locations and contours show the features containing
5% of the total energy.

3.5

Discussion

Circulation and transport in the nearshore region is a result of the interaction between the
lake-wide circulation and local boundary conditions. Studies have shown that large-scale
circulation in Lake Michigan is wind-driven and tidal and geostrophic forcing is limited due
to the size of the basin. Outfalls from large rivers only affect the hydrodynamics close to
the shore, particularly in the near-field where momentum of the outfall dominates over lake
circulation (Nekouee, 2010). Results and analysis of the numerical hydrodynamic model
(presented in Chapter 4) show that large-scale circulation in Lake Michigan can be resolved
using a 2 km lake-wide grid. Small-scale features dominate transport in the nearshore and
these were resolved using a nested-grid model with a 100 m grid resolution. The focus of
this chapter was on analyzing the dominant energy scales in the nearshore and the numerical
models’ ability to resolve energy dissipation and transport.
Since circulation in Lake Michigan is wind-driven, energy is transferred from wind to the
upper layers of the water column and subsequently to different length scales as a result of
direct and inverse energy-cascades. ADCP observations at a distance of ∼9 km from the
57

shoreline show the presence of strong large-scale influence, in the form of a peak at the inertial
frequency (Figure 3.2 and Figure 3.1). The comparisons with the model, also included in
the figures, indicate that the interaction between the large-scale, lake-wide circulation and
nearshore circulation is well described using a boundary forcing at the nested-grid interface.
The energy spectrum at the nearshore locations shown in Figure 3.3 – Figure 3.5 are
consistent with a friction dominated boundary layer(FBL) of about 2 km in width similar
to calculations made for Lake Huron (Murthy and Dunbar, 1981). Comparisons with the
results from the numerical model show that the model is able to predict the inertial peak
as well as the energy cascade in both the offshore and nearshore regions. However, as we
move closer to the shore, the slope of the observed energy spectrum is smaller, indicating
that lateral boundary effects are not adequately accounted for in the model.
The energy contained in the different scales shows a clear transition from the smallscale to the large-scale as shown in Figure 3.6. This is indicative of the presence of an
inverse energy-cascade due to the depth-constrained nature of flow in the nearshore region
of southern Lake Michigan where variations in bathymetry are low and the average bottom
slope is 3 in 1200. At equilibrium, the kinetic energy generated by surface stresses and
forces is balanced by viscous dissipation and energy transfer between scales. As large-scale
turbulent flows approach the shore, the energy in the larger scales gets dissipated to the
smaller scales.
Comparisons with model results show that the peak energy carrying scales are correctly
identified in the off-shore but not the nearshore region. The magnitude of energy is overpredicted in the larger scales and under-predicted for the smaller scales. Wavelet analysis of
current measurements in the offshore and nearshore, shown in Figure 3.7-Figure 3.10 indicate
58

that while the small-scale processes contain less than 5% of the total energy, they dominate
mixing and transport observed in the nearshore.
This underestimation of the energy in the small-scale could be due to excess viscous
dissipation (modeled using the Smagorinsky closure model) or an inaccurate bottom friction
boundary condition. Recognizing the fact that higher viscosity preferentially affects the
smaller scales of motion, it can be inferred that the Smagorinsky closure model for the
nearshore is unable to accurately predict the subgrid dissipation and mixing processes. A
hydrodynamic model with a more comprehensive subgrid scale parameterization that solves
for the transport of kinetic energy in the horizontal directions is needed to improve the
quality of model prediction closer to the shore.

3.6

Conclusion

Nearshore hydrodynamics is controlled by energy and mass transfer from the large-scale
circulation. Different scales interact and energy is transferred along a cascade that results in
its eventual dissipation in small-scale processes. The energy cascade in the offshore shows the
prominence of large-scale circulation and its importance as a source of energy. The relative
importance of the inertial frequency closer to the shoreline indicates the presence of a friction
dominated boundary layer at least 1 km wide. This is consistent with other studies in the
Great Lakes region. Comparisons with the model results are promising, with the energy
cascade being reproduced accurately in the offshore and nearshore regions. Errors appear to
increase as we move close to the shoreline due to increased importance of boundary effects
and energy losses due to small-scale processes.
Wavelet analysis is a useful tool for analyzing the individual components in the velocity
59

time-series. Comparisons between model and observations show that the dominant energy
carrying scales in the offshore are around the inertial frequency and about 0.1 hr-1 . This
reduces as we move closer to the shoreline and is about 0.01 hr-1 at a distance of about 0.35
km from the shoreline. The model is able to predict the frequency of the energy peak in the
offshore accurately, but not in the nearshore. The magnitude of energy carried in the peak
frequency is also over-predicted consistently in the offshore and nearshore region. Small-scale
velocity fluctuations represent less than 5% of the total energy. These are under-predicted
by the model and as a result can have significant impact on modeling dispersion and mixing.
It should also be noted that most of the features associated with the nearshore circulation
and which are important from the stand-point of contaminant transport have the time scale
of less than 10 hr and would therefore fall into the low energy or less than 5% of the total
energy.
With a 100 m grid resolution, processes in the 1 hr timescale should be adequately
resolved by the nearshore model. However, model under-performance closer to the shore
is probably due to drawbacks in the turbulence closure model used to describe the energy
dissipation due to turbulent viscosity in the nearshore. A more advanced turbulence closure
model with explicit energy transport equation or a large-eddy simulating model would be
able to better represent the energy cascade as well as the small-scale dissipation processes,
essential to model transport processes accurately in the nearshore region.

60

Chapter 4
Mixing and Transport in the Coastal
Boundary Layer of Southern Lake
Michigan

4.1

Summary

Mixing in the nearshore region controls the transport and fate of chemical contaminants as
well as bacteria. In this study we focus on the coastal boundary layer (CBL). This region of
the coastal ocean acts as an interface between the inertial-scale flow in the offshore region
and the small-scale, friction dominated flow regime close to the shore. We examine the important features describing circulation and transport in the CBL using a three-dimensional
hydrodynamic model. Model results are compared to ADCP measurements made within
the CBL at different distances from the shore. A dye release study was also performed to
assess the accuracy of the Smagorinsky eddy viscosity model used to describe horizontal
61

mixing in the numerical model. We found that while mean circulation fields are resolved
accurately, vertical variations of velocity and the shear structure are not. The Smagorinsky turbulence closure model did not describe the deviatoric strain component accurately.
Model comparisons with data from a dye tracer study conducted at the Burns Ditch outfall
in southern Lake Michigan confirm that mixing rates could be described by using a mean effective shear-augmented diffusion coefficient of 5.3 m2 /sec. The mixing due to eddy diffusion
and shear-augmented diffusion were found to be highly anisotropic and time dependent.

4.2

Introduction

Nearshore hydrodynamics is highly turbulent and mixing is the result of small-scale features,
which result from the turbulent cascade of energy from larger to smaller scales (Kolmogrov,
1941). The large-scale turbulent eddies also interact with the smaller scales and are oriented
and elongated by the mean strain rate so as to align with the mean flow direction (Kantha
and Clayson, 2000). However, much of the large body of literature in the field of turbulence
deals with homogeneous, isotropic conditions and is less informative of turbulent eddies of
O (100) m, anisotropy, and coherent flow-structures that dominate nearshore hydrodynamics.
The larger scales also, invariably, carry much of the energy and affect transport the most.
The fluid mechanics of river plumes discharging into the ocean or lake environments
formed the basis of several earlier studies (Jones et al., 2007). Based on the relative importance of processes involved, these analyses often separate the spatial domain into: (a)
near-field where mixing is dominated by buoyancy and momentum of the plume and (b) the
far-field where plume dynamics is controlled by turbulent diffusion. At the Lake Michigan
beach sites in the present study, a transport model should have the ability to describe two
62

key aspects of the river plumes (both related to hydrodynamics) accurately: (a) advective
transport including flow reversals and the frequency of flow reversals and (b) the nature and
strength of mixing near the shoreline (which controls the size and shape of the river plume).
Advective transport in the nearshore region of Lake Michigan is dominated by winddriven circulation. Lake-wide circulation features ranging from the inter-annual and climatological time scales (Beletsky et al., 1999; Beletsky and Schwab, 2001, 2008) to the inertial
time-scale have been successfully described in the past by eddy-resolving hydrodynamic
models with 2 km grid resolution (Beletsky et al., 2006).
The Coastal Boundary Layer (CBL) (Murthy and Dunbar, 1981), where much of the
anthropogenic effects are experienced, is composed of the Inertial Boundary Layer (IBL),
where the inertial forces dominate, and Friction Boundary Layer (FBL), where the lateral and
bottom friction forces are dominant. The smaller time-scales and larger velocity gradients
in the FBL result in larger energy losses due to dissipation and this region could also be
called the viscous boundary layer. Field observations have shown that the CBL for Lake
Huron extends 10 km offshore, of which the FBL is about 2 km wide. The length-scale of
the largest eddies in the FBL is of the order of 1 km and numerical models have revealed
that contaminant transport within the FBL is dominated by the presence of flow reversals
(Liu et al., 2006; Thupaki et al., 2010; Nekouee, 2010). It is known that these flow-reversals
are due to the interaction of the mean flow with lateral and bottom boundary conditions in
the nearshore region. However, the nature of these flow-reversals, mechanisms driving them,
and the hydrodynamic models’ ability to resolve them has not been explored in detail.
The horizontal turbulent diffusion coefficient (K) for oceanic conditions is often described
using a power-law relation (Equation 4.1) based on the work of Okubo (Okubo, 1971) and
63

Murthy (Murthy, 1976). Oceanographic data from Okubo’s work and data for Lake Ontario
based on Murthy’s work plot as a straight line on a log-log graph following Equation 4.1.

K = a∆b

(4.1)

Here the coefficients a and b include the effects of several factors such as wind speed, direction
and fetch, surface heat fluxes, vertical stratification, current and wave fields etc. ∆ is a
typical length-scale. The assumption of homogeneous, isotropic turbulence leads to the
exponent b = 4/3 in Equation 4.1. The ‘4/3 power-law’ has a theoretical basis following the
Kolmogorov hypothesis and the work of Batchelor (Batchelor, 1950). However, homogeneous,
isotropic turbulence is an idealization rarely found in nature and data reported from field
studies produced values of b < 4/3 (∼ 1.333). For example, Borthwick (Borthwick, 1980)
obtained b = 1.12 in the surface layer of the Swansea Bay. The Equation 4.1 was found to
describe diffusion (away from any shoreline) in small lakes as well for length scales ranging
from 10 m to > 100 m. For example, Lawrence et al. (Lawrence et al., 1995) were able to
fit their tracer data for a small lake in Vancouver, British Columbia using the coefficients
a = 3.2 × 10−4 and b = 1.1.
Okubo’s study (Okubo, 1971) involved dye patches that were not constrained by any
shoreline. However, the transport of tracers and bacteria in the nearshore region is constrained by the shoreline. Correctly describing the mixing of tracers close to the lateral
boundary is important for accurately modeling transport. This is particularly true in the
case of bacterial transport since an uncertainty in the mixing coefficients can introduce
errors into the description of biological processes. For example, dispersion and bacterial dieoff rate coefficients are competing parameters as both parameters can influence the peaks
64

of breakthrough curves. Ojo et al. (2006a) have shown that the interplay between vertical
turbulent diffusion and shear currents becomes important as one approaches the shoreline.
The presence of shear structure was shown to be responsible for significantly enhancing the
spreading of material in the nearshore regions. Therefore shear-augmented diffusion can
result in an effective diffusivity that is 10 to 20 times higher compared to estimates based
on turbulent diffusion alone (Ojo et al., 2006a). When diffusion is controlled by shear, the
exponent b in equation 4.1 is known to approach the limiting value of 1.0 while the other
limit of b = 4/3 represents diffusion in the inertial subrange (Murthy, 1976). Although significant progress was made in the application of models such as the Princeton Ocean Model
(POM) to describe lake-wide circulation and transport in the Great Lakes including Lake
Michigan (Beletsky and Schwab, 2001; Beletsky et al., 2006), efforts aimed at understanding
and quantifying nearshore processes are relatively limited. The Smagorinsky model used to
describe horizontal mixing in the POM is an eddy viscosity model (details can be found in
(Pope, 2000)). The major advantage of the Smagorinsky formulation lies in its simplicity and
its computational stability. However, it is well-known that the model introduces significant
damping due to excess eddy viscosity. Improvements to the standard Smagorinsky model
have been proposed including a dynamic Smagorinsky model (in which the proportionality
constant C in Equation 2.7 is evaluated every time-step) or the shear-improved Smagorinsky
model, (L´vˆque et al., 2007). In this chapter we use current data obtained from several
e e
ADCPs as well as tracer concentrations from a dye release study to evaluate the ability of
the standard Smagorinsky model to describe tracer plumes near the shoreline. Data from
the field experiments and estimates of shear-augmented diffusion coefficients are expected to
be useful in identifying suitable models for describing nearshore transport.

65

4.3

4.3.1

Methods and Materials

Study Site

The Ogden Dunes beaches are located near Portage, Indiana, along the Southern Lake Michigan coastline. These beaches face water quality concerns, mainly due to contamination from
the nearby outfall of Burn Ditch (USGS Gauge#04095090). Numerous field experiments
were conducted at this location between June, 2008 and August, 2008, in collaboration with
the USGS Great Lakes Environmental Center (Indiana) and EPA. The data from these field
experiments form the basis for evaluating the numerical models presented in this chapter.
Five bottom-mounted Acoustic Doppler Current Profilers (ADCPs) were deployed in
an upward looking configuration. Figure 2.1 shows the location of the ADCPs and other
important features near the site. The ADCPs were programmed to measure vertical velocity
profiles with a ping rate of 1 Hz for the 600 kHz RDI-Monitor and 1200 kHz RDI-Sentinel
while a ping rate of 0.1 Hz was used for the 600 kHz RDI-BBADCP. The data were ensemble
averaged every 5, 10 and 15 min respectively. Deployment locations were chosen based on
earlier numerical studies (Liu et al., 2006; Thupaki et al., 2010) to give velocity measurements
in different flow regimes of the CBL (Murthy and Dunbar, 1981). The 600 kHz RDI-Monitor
and RDI-BBADCP were deployed at a depth of ∼20 m (locations M and B respectively) and
the higher frequency 1200 kHz Sentinel was deployed in shallow waters, at a depth of ∼10 m
(location S). Intensive velocity sampling was conducted using two Nortek Aquadopp current
profilers operating at 2 MHz frequency during a one week period (JD 172-JD 179) close to
the shore (locations N1 and N2) at depths of ∼5 m and ∼7 m respectively. Instruments
were programmed so that hydrodynamic measurements had a predicted standard deviation
66

less that 0.1 cm/sec (Teledyne, 2006).
A dye study was conducted using a tracer (Rhodamine WT), which was released into
Burns Ditch outfall (shown in Figure 2.1) at a constant rate. Concentration of the dye entering the lake was measured using a Turner Designs R Self-contained Underwater Fluorescence
Apparatus (SCUFA R ) unit moored at the mouth of the outfall. The data were later used to
provide a boundary condition for the tracer transport model. Plume-evolution was tracked
by taking multiple transects of the plume using a towed SCUFA unit and GPS with submeter accuracy on a small motor boat. The procedure was repeated to obtain snapshots of
the dye plume at two different instants of time. Tracer breakthrough data at the beaches
were obtained by taking water samples in knee deep water, every hour, close to the outfall.

4.3.2

Numerical Modeling

The Princeton Ocean Model (POM) (Blumberg and Mellor, 1987) is a three-dimensional hydrodynamic model that solves the hydrodynamic primitive equations (Equation 2.3–Equation 2.5).
These equations resolve the mean (Reynolds averaged) flow field and parameterize the eddy
diffusion using the Smagorinsky eddy-viscosity model (Smagorinsky, 1963) in the horizontal
directions. Eddy viscosity is assumed to be isotropic in the horizontal directions as shown
in Equation 2.3 and Equation 2.4. The eddy viscosity in the vertical direction is calculated
using the Mellor-Yamada 2.5 level turbulence closure model (Mellor and Yamada, 1982). A
finite-difference orthogonal grid with a 2 km resolution was used to resolve large-scale lakewide circulation. Small-scale features close to the shoreline were resolved using a nested-grid
model with a 100 m grid resolution. Nesting was one-way and information from the large
scale lake-wide model was interpolated to provide boundary conditions for the nearshore
67

Line source

Stretching/
sheared advection

z

(a)

diffusion

(b)

kz

Apparent
diffusion

(c)

x
Figure 4.1: The mechanism of shear-augmented dispersion (Ojo et al., 2006a). (a) Initial
distribution of a tracer in a shearing flow; (b) Tracer dispersal due to diffusion increases the
effective rate of mixing; (c) Final state of tracer due to shear-augmented dispersion

model. The computational domain for the lake-wide and nearshore models are shown in
Figure 2.6. Details of the hydrodynamic model including the numerical methods and equations solved are described in Section 2.2.

4.3.3

Shear-augmented dispersion

The theory of shear-flow dispersion is well known in the environmental fluid mechanics
literature (Taylor, 1954; Csanady, 1966; Fischer et al., 1979). Taylor (Taylor, 1954) proposed
that flow variability in the vertical increases mixing in the flow direction. This process has
been graphically shown in Figure 4.1 for a one-dimensional flow. This process is called shearaugmented dispersion and it can dominate the turbulent diffusion rates in shallow waters
of lakes and estuaries (Ojo et al., 2006a). By splitting the longitudinal velocity profile
h
¯
(u = u (z, t)) into a mean u = 1 udz and the deviations from the mean u = u − u ,
¯
h
0
effective diffusivity (Kx ) can be written as Equation 4.2. Here, (Kz ) is the vertical eddy
diffusion coefficient and (u) is the longitudinal velocity.
68

Kx = −

1
h



h

z


u 
0

0


1 

Kz

z





 
u dz  dz  dz

(4.2)

0

Defining non-dimensional variables and re-arranging the terms, we can re-write Equation 4.2,
as Equation 4.3. Similarly, assuming that shear in xz and yz planes are not coupled, a similar
set of equations can be written for Ky .

Kx = Ix h2 u 2 /Kz
 


z
1
z
 

1 
 u dz  dz  dz
Ix = − u 
 
 Kz
0
0
0

(4.3)

u = u / u 2 ; K z = Kz /Kz ; z = z/h

The non-dimensional integral (Ix ) is defined as the shear coefficient and describes the shear
structure (Fischer et al., 1979). Values of the shear coefficient for rivers and estuaries usually
lie between 0.06 – 0.15 m2 /sec (Fischer, 1973). More details, including assumptions and
limitations of the analysis can be found in Ojo et al. (2006b). Since high-resolution velocity
data can be obtained using ADCPs deployed in the nearshore region, we can use Equation 4.3
to calculate the shear-augmented dispersion coefficient and compare the estimates with 3D
model-derived values. These results will be reported later.

69

4.4
4.4.1

Results and Discussion
Hydrodynamic Model

Results from the hydrodynamic model of the nearshore region of southern Lake Michigan
show that a regular orthogonal grid with 2 km resolution is able to resolve circulation at
the lake scale. The model was able to resolve large-scale processes reasonably well as shown
by Figure 4.2. However, small-scale features close to the shore and high frequency fluctuations in the velocity could not be adequately resolved. Results from the lake-wide circulation
model were therefore used to drive a nearshore nested grid model with 100 m grid resolution.
Results from the nearshore model have been compared with observations made at locations
B (Figure 4.3), M (Figure 4.4) and S (Figure 4.5). The nested grid model reproduced hydrodynamics close (∼300m) to the shore (where bottom and lateral friction effects dominate
inertial scale oscillations) better than the results from the large-scale model (Figure 4.2 versus Figure 4.4). Vertical profiles of the velocity in the nearshore and offshore regions are
shown in Figure 4.7 and Figure 4.8. It is clear that using 20 σ-layers, the numerical model
is able to reproduce the general features of velocity structure in the vertical. As expected, a
top and bottom boundary layer in the water column develops due to the wind-driven nature
of lake-wide circulation. Flow reversals indicated by zero-crossings are reliably predicted by
the numerical model as well, as shown in Figure 4.9. However, small-scale features in the
water column and velocity magnitudes in the top boundary layer are not accurately reproduced. This is similar to the experience of others who have used the Princeton Ocean Model
for simulating nearshore hydrodynamics (Nekouee, 2010).

70

(a) Along shore velocity

Observed
Model

m/sec

0.4
0.2
0

-0.2
-0.4
160

170

180
JD of 2008

190

200

180
J D of 2008

190

200

(b) Cross shore velocity

m/sec

0.4
0.2
0

-0.2
-0.4
160

170

Figure 4.2: Velocity comparison at location M with lake-wide hydrodynamic model

71

(a) Along shore velocity

Observed
Model

m/sec

0.4
0.2
0

-0.2
-0.4
160

170

180
JD of 2008

190

200

180
JD of 2008

190

200

(b) Cross shore velocity

m/sec

0.4
0.2
0

-0.2
-0.4
160

170

Figure 4.3: Velocity comparison at location B with the nearshore nested grid model

72

(a) Along shore velocity

Observed
Model

m/sec

0.4
0.2
0

-0.2
-0.4
160

170

180
JD of 2008

190

200

180
JD of 2008

190

200

(b) Cross shore velocity

m/sec

0.4
0.2
0

-0.2
-0.4
160

170

Figure 4.4: Velocity comparison at location M with the nearshore nested grid model

73

(a) Along shore velocity

Observed
Model

m/sec

0.4
0.2
0

-0.2
-0.4
160

170

180
JD of 2008

190

200

180
JD of 2008

190

200

(b) Cross shore velocity

m/sec

0.4
0.2
0

-0.2
-0.4
160

170

Figure 4.5: Velocity comparison at location S with the nearshore nested grid model

74

Along shore velocity

Observed
Model

m/sec

0.4
0.2
0
-0.2
-0.4

174

178

176
JD of 2008

178

m/sec

Cross shore velocity
0.4
0.2
0
-0.2
174
-0.4

176
JD of 2008

(a) N1

m/sec

Along shore velocity
0.4
0.2
0
-0.2
-0.4

Observed
Model

174

176
JDof 2008

178

174

176
JDof 2008

178

Cross shore velocity

m/sec

0.4
0.2
0
-0.2
-0.4

(b) N2
Figure 4.6: Observed versus simulated velocity comparison at locations (a) N1 and (b) N2
with the nearshore nested grid model
75

0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1

D epth (m)

-5

-10

-15
172

0

174

J D of 2008

176

O b s e rv ed (c ro s s s h or e)

D epth (m)

-10

-15
174

J D of 2008

176

Mo de l ( alon g s ho re )

0

-10

-15
172

m/s ec

178

0

m/s ec
0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1

-5

178

0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1

-5

172

m/s ec

D epth (m)

O b s e rv ed (a lo ng s h or e)

174

J D of 2008

176

178

m/s ec

Mo de l ( cros s s ho re )

0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1

-5
D epth (m)

0

-10

-15
172

174

J D of 2008

176

178

Figure 4.7: Comparison of vertical velocity profiles with measurements at the offshore location M
76

O b s e rv ed (a lo ng s h or e)

-4

D epth (m)

0

174

J D of 2008

176

O b s e rv ed (c ro s s s h or e)

-4
174

J D of 2008

176

D epth (m)

Mo de l ( alon g s ho re )

178

-2

172

m/s ec
0

174

J D of 2008

176

Mo de l ( cros s s ho re )

-2
-3
-4
-5
172

178

m/s ec
0.05
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05

-1

178

m/s ec
0.05
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05

-4

0.05
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05

-2

172

0

0.05
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05

-2

172

m/s ec

D epth (m)

D epth (m)

0

174

J D of 2008

176

178

Figure 4.8: Comparison of the vertical velocity profiles with measurements at the nearshore location N2
77

Lake Michigan experiences thermal inversions twice annually, in the beginning of summer,
when water temperature starts rising (faster in the shallow waters close to the shore) and
again in the beginning of winter (when water temperature falls, again faster in the shallow
waters) and there is a brief period of unstable stratification. In the summer months, which
were the focus of this study, differential warming and resultant buoyancy driven circulation
was implemented using the Boussinesq approximation. Model results have been compared
with the temperature measured in the nearshore region in Figure 4.10. It is clear that the
thermal inversion process is completed by JD190 in the nearshore and vertical temperature
profile is almost uniform.

4.4.2

Turbulence in the nearshore

Turbulence closure in the vertical direction is implemented using the two-equation MellorYamada closure model (Mellor and Yamada, 1982). Comparison of the temperature profile
shows that vertical mixing is well-resolved. Model-generated values of vertical eddy diffusion
KM are comparable to values reported in the literature for nearshore regions (Oakey and
Greenan, 2004). Detailed comparison of the performance of various schemes for modeling
eddy diffusion in the vertical have been presented in (Burchard and Bolding, 2001). The
focus in this section is on describing horizontal eddy diffusion rates in the nearshore region.
Subgrid scale turbulence in the horizontal directions was modeled using the Smagorinsky
relation (Equation 2.7) (Smagorinsky, 1963). Figure 4.19 and Figure 4.18 show the deviatoric
strain values in the along-shore and cross-shore directions in the nearshore (location N2)
and offshore (location M) respectively. The eddy diffusion field is clearly anisotropic but the
net deviatoric strain component is comparable in the along-shore (x) and cross shore (y)
78

200

Time of flow reversal as predicted by model (JD)

195

B
M
N1
N2
S

190
185
180
175
170
165
160
155
155

160

165

170 175 180 185 190 195
Time of observed flow reversal (JD)

200

Figure 4.9: Comparison of observed and simulated flow reversal times in the along-shore
direction near Ogden Dunes

79

Temperature (oC)

30
28
26
24
22
20
18
16
14
12
10

172

174

176

178

180

182

184 186 188 190
Julian Day of 2008

192

194

196

198

200

Figure 4.10: Comparison between observed and simulated temperature in the nearshore
region at location S
directions.

4.4.3

Vorticity Dynamics in the Nearshore

Vortices are generated at a no-slip boundary condition and transported by the mean flow.
The hydrodynamic model used a no-slip lateral boundary condition and a quadratic bottom
boundary layer. The strongest vortices observed were, therefore, generated at the shoreline
and advected by the mean flow. Figure 4.11 - Figure 4.14 show the evolution and transport
of vortices in southern Lake Michigan. Contours show regions of high and low vorticity
and velocity vectors have been included to show the relation between currents and vorticity
magnitude. Vorticity is a measure of the rate of rotation of a fluid parcel. Regions of high
vorticity therefore have higher circulation rate. Figure 4.13 and Figure 4.14 show typical
circulation patterns around vortices. Figure 4.13 in particular, showcases the role that
80

advected vortices can have on circulation in the nearshore region. Figure 4.12 - Figure 4.14
show how vorticity generated at a different location can be transported with the mean flow.
This transport of vorticity means that direction of rotation of a fluid parcel (or eddies) can
vary quickly from one direction to another. As shown in Figure 4.11 and Figure 4.12, this
change can happen in as little as a few hours, despite no significant change in the wind
direction (see Figure 4.15). In the field this is experienced as rapid flow reversals without
the associated change in wind direction or lag time associated with change in direction of
wind-driven currents. There also appears to be a lateral boundary layer extending to about
300 m from the shore, within which the vortices dissipate rapidly, possibly due to the frictiondominated energy dissipative flow-regime in this region (this has been discussed in greater
detail in Chapter 3). Based on the results of the numerical model for summer conditions
observed in the simulation period chosen, this thickness appears to vary between 300 m to
1000 m. This region within the CBL is of vital interest for any transport model attempting
to model contaminant transport since it can cause entrainment of contaminant plumes and
significantly reduce cross-shore transport.

81

J D 158.12
50

s e c -1
5.0E -04
3.3E -04
1.7E -04
0.0E +00
-1.7E -04
-3.3E -04
-5.0E -04
-6.7E -04
-8.3E -04
-1.0E -03

45

40

35

30
0.5 m/sec

25
80

100

120

Figure 4.11: Vorticity and current fields near the Burns Ditch outfall in the nearshore region of southern Lake Michigan on
Julian Day (JD) 158

82

J D 159.25
50

s e c -1
5.0E -04
3.3E -04
1.7E -04
0.0E +00
-1.7E -04
-3.3E -04
-5.0E -04
-6.7E -04
-8.3E -04
-1.0E -03

45

40

35

30
0.5 m/sec

25
80

100

120

Figure 4.12: Vorticity and current fields near the Burns Ditch outfall in the nearshore region of southern Lake Michigan on
Julian Day (JD) 159

83

J D 165.83
50

s e c -1
5.0E -04
3.3E -04
1.7E -04
0.0E +00
-1.7E -04
-3.3E -04
-5.0E -04
-6.7E -04
-8.3E -04
-1.0E -03

45

40

35

30
0.5 m/sec

25
80

100

120

Figure 4.13: Vorticity and current fields near the Burns Ditch outfall in the nearshore region of southern Lake Michigan on
Julian Day (JD) 165

84

J D 168
50

s e c -1
5.0E -04
3.3E -04
1.7E -04
0.0E +00
-1.7E -04
-3.3E -04
-5.0E -04
-6.7E -04
-8.3E -04
-1.0E -03

45

40

35

30
0.5 m/sec

25
80

100

120

Figure 4.14: Vorticity and current fields near the Burns Ditch outfall in the nearshore region of southern Lake Michigan on
Julian Day (JD) 168

85

Comparisons between observed and simulated velocity time-series in southern Lake Michigan verify the accuracy of the numerical model. While the coarse 2 km grid was able to
model large-scale circulation [Figure 4.2], a finer grid with 100 m resolution is required to
resolve the small-scale features in bathymetry and shoreline. As expected the nested grid
configuration was able to improve the accuracy of the numerical model [Figure 4.3 - Figure 4.6]. Observations and model results show a similar vertical structure in the nearshore
[Figure 4.8] as well as the offshore region [Figure 4.7]. Velocity variation and flow-reversals
shown by the alternating red and blue areas are considerably stronger in the top layers, due
to the top and bottom boundary layers, as expected. Direct comparisons with observations
in the top boundary layer are not available due to insufficient resolution (ADCP bin-size).
However, general comments can be made based on the trends observed. Flow variations in
the top boundary layer are considerably over-predicted, the size of the top boundary layer
extends up to 7 m from the surface and the currents in the water column below this are not
correlated with the top layers. In the cross shore direction, fluctuation in velocity magnitude
is over-predicted while the direction is accurately modeled. These observations are consistent
with other studies performed using the POM (Nekouee, 2010). Similar results are obtained
when we move closer to the shore, with the notable exception being the limited vertical variability due to the top boundary layer extending to the lake bed. This is consistent with the
presence of a well developed Inertial Boundary Layer (IBL) and Friction Boundary Layer
(FBL) in the Great Lakes (Murthy and Dunbar, 1981). However, it is clear that despite
using 20 σ-layers in the vertical, description of the velocity profile in the water column is
not satisfactory (Figure 4.8).
Inadequate representation of velocity variability in the vertical has a significant impact on
transport. The mixing process, in the presence of a shear structure, is increased by dispersion
86

Wind vector

157

157.5

158

158.5
159
Julian Day of 2008
Current vector

157

157.5

158

158.5
159
Julian Day of 2008

10 m/sec

159.5

160

0. m/sec
1

159.5

160

Figure 4.15: Comparison of wind and current vectors at a location 300 m from the shoreline
(location S) showing the weak correlation between instantaneous wind and current directions

87

processes (Taylor, 1954). In an estuarine environment, the magnitude of shear-augmented
mixing rates can be 10-20 times greater than turbulent diffusion (Ojo et al., 2006a). Observed
and modeled vertical shear structure can be compared using the non-dimensional vertical
shear coefficient Ix , Iy calculated using Equation 4.3. In the offshore (location M) the
mean value (Ix =0.4062, Iy =0.4272) is consistent with observations made for riverine and
estuarine environments (Fischer, 1973), however large variance and periodicity in variations
is an important feature of shear structure at this location. The time scale of these variations
is consistent with the inertial scale and indicates the importance of large-scale circulation
on the shear structure in the nearshore. These results can also be observed in the nearshore
location where the mean (Ix =0.2934, Iy =0.3572) change to reflect the relative importance
of the inertial and friction forces as we move from the inertial boundary layer (IBL) to the
friction boundary layer (FBL). Comparing these observations with the modeled values of
shear coefficient in Figure 4.16 and Figure 4.17, reveals that the model is unable to adequately
resolve the shear structure in the CBL and consequently, shear-augmented diffusion is under
estimated. Also of note is the complementary nature of the shear coefficients in the alongshore and cross-shore directions, which results in a highly anisotropic mixing regime. Due
to the underestimated shear-augmented mixing rates and inadequate representation of the
shear structure, the model requires a higher diffusion coefficient to predict scalar transport
accurately. The mean observed shear-augmented diffusion rate is 2.5 m2 /sec in the nearshore,
assuming a mean vertical mixing rate of 10-3 m2 /sec, which is close to the value of 3 m2 /sec
used in the transport model to describe observed tracer concentrations as described later.

88

4

2

K x (m /sec)

6

2
0
172

173

174

175

176

177

178

173

174

175
JD of 2008

176

177

178

4

y

2

K (m /sec)

6

2
0
172

Figure 4.16: Shear-augmented diffusion rate in the nearshore at location S based on ADCP
observations

89

2

K x (m /sec)

0.4
0.2
0
172

173

174

175

176

177

178

173

174

175
JD of 2008

176

177

178

y

K (m 2/sec)

0.6
0.4
0.2
0
172

Figure 4.17: Shear-augmented diffusion at nearshore location S based on the 3D hydrodynamic model

90

In order to improve the velocity prediction and better resolve the shear structure in
the water column, it is necessary to examine the turbulence formulation in the numerical
model. Comparing the shear structure from the results of the coarse grid and fine grid
model, it was determined that increasing the horizontal grid resolution twenty fold did not
yield significantly improved accuracy of the shear structure. Vertical resolution of 20 layers
(layer thickness ∼0.5 m in the nearshore) can also be expected to reproduce the ADCP
observations with a 1 m bin size, reasonably well. Therefore, insufficient grid resolution is
not seen as a reason for the lack of vertical variability in the model.
The stress tensor acting on a parcel of fluid is modeled in Equation 2.3 using Equation 4.4
by assuming that subgrid scale turbulent mixing is analogous to molecular processes (Blumberg and Mellor, 1987), after neglecting the Reynolds Stress terms that exist in the Reynolds
averaged (RANS) form of the momentum transport equations.

Fx =

∂
∂x

∂u
2AM
∂x

+

∂
∂y

AM

∂u ∂v
+
∂y ∂x

+

∂
∂z

KM

∂u
∂z

(4.4)

Reynolds stresses are apparent stresses due to fluctuations in the unfiltered velocity
field. The main aim of the various turbulence closure models is to find a suitable approximation of this term, thereby closing the governing equations. The Smagorinsky closure
scheme Equation 2.7, parameterizes the subgrid scale turbulent mixing processes based on
the gradient/rate-of-strain hypothesis. However, the Reynolds stress term is not resolved
explicitly in Equation 2.3 and Equation 2.4.
In order to evaluate the effect of this simplification, we can examine the stress tensor
acting on a fluid particle (Equation 4.5). The terms in the square brackets can be considered
91

to be the deviatoric/rotational and the isotropic/irrotational components of the stress tensor.

τij = µef f
¯

∂ uj
¯
∂ ui
¯
+
∂xj
∂xi

¯
2 ∂u
− δij k
3 ∂xk

(4.5)

Here τij is the stress-tensor, µef f is the effective fluid viscosity, u’s denote the velocity
¯
components and δij is the Kroeneker delta function. Comparing the corresponding terms
in Equation 4.5 with terms in Equation 4.4 and neglecting the vertical velocity gradient in
the horizontal directions, we see that τxz = KM ∂u . Similarly from Equation 2.4, we have
∂z
τyz = KM ∂v . τxy and τyz are the deviatoric stress components and are a measure of
∂z
the rate of strain in the xz and yz planes respectively. The xz and yz planes can also be
considered to be components in the along-shore and cross shore directions. The accuracy
of the deviatoric stress term depends on the turbulence model used to calculate turbulent
mixing coefficient KM for tracer transport in the vertical direction, i.e. the Mellor-Yamada
formulation. This has been discussed in great detail in a number of studies (Feddersen, 2006)
and hence, we will focus on the deviatoric strain component and the horizontal turbulence
model. The deviatoric strain can also be seen as an indicator of the shear instability in the
water column.
Deviatoric strain component at an offshore location (M) is shown in Figure 4.18. It
is clear that while the strain rates are comparable, the model over-predicts values in the
top boundary layer. The circulation model is based on the observation that shear stress
due to wind is the prime motive force for circulation in the nearshore. This is reflected
in the high strain rates, in both the along-shore and cross shore directions, displayed in
the model. Observations on the other hand would suggest that the interface between the
upper boundary layer and the deeper waters is where most of the shear instability is present
92

in the water column. It is also clear that the observed deviatoric strain is dominated by
rapid fluctuations in magnitude and direction. This is largely absent in the model. This
observation is consistent with earlier results presented in Figure 4.3–Figure 4.6 that indicate
that observed time-series include a significant amount of high frequency fluctuation, absent in
the numerical model. It is expected that any improvements in modeling the high-frequency
velocity fluctuation will also improve the representation of the shear structure and hence
transport. As we move closer to the shore, differences between the observed and modeled
deviatoric strain values increase, as shown in Figure 4.19, and the shear structure breaks
down. In the nearshore region, the flow field appears to have developed into an isotropic,
fully turbulent flow field. With length scale smaller than the grid size, numerical models with
grid size of O(10) m (or smaller) might be required to reproduce the variability seen close to
the shore. Direct comparisons of the grid size with resolved frequency is however, simplistic
and can be misleading, this is shown by the fact that while the large-scale model has a
grid size 20 times that of the nearshore model, velocity comparisons at the offshore location
are comparable for the hydrodynamic models with coarse (Figure 4.2) and fine grid (Figure
4.4) at the same location. Improving the representation of the deviatoric component of the
turbulence model and using a more advanced turbulence closure scheme for the horizontal
direction, may be the best way to improve results.

93

Depth( m)

-5

-10

-15
172
0

173

174

175
176
JD of 2008

177

178

Deviatoric Strain (cross shore)

Depth( m)

-5

-10

-15
172

173

174

175
176
JD of 2008

177

178

Model

0

-10

-15
172

179

1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03
0.0E+00
-2.0E-03
-4.0E-03
-6.0E-03
-8.0E-03
-1.0E-02

-5

179

1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03
0.0E+00
-2.0E-03
-4.0E-03
-6.0E-03
-8.0E-03
-1.0E-02

Deviatoric Strain (along shore)

Depth( m)

0

1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03
0.0E+00
-2.0E-03
-4.0E-03
-6.0E-03
-8.0E-03
-1.0E-02

0

173

174

175
176
JD of 2008

177

178

Deviatoric Strain (cross shore)

-5
Depth( m)

Observed

Deviatoric Strain (along shore)

-10

-15
172

173

174

175
176
JD of 2008

177

179

1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03
0.0E+00
-2.0E-03
-4.0E-03
-6.0E-03
-8.0E-03
-1.0E-02

178

Figure 4.18: Deviatoric strain components observed and calculated from the nearshore model for location M
94

179

Observed

Model

Depth( m)

-1
-2
-3
-4
-5
172

173

174

175
176
JD of 2008

177

178

Deviatoric Strain (cross shore)

0

Depth( m)

-1
-2
-3
-4
-5
172

173

174

175
176
JD of 2008

177

178

0

-2
-3
-4
-5
172

179

1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03
0.0E+00
-2.0E- 03
-4.0E- 03
-6.0E- 03
-8.0E- 03
-1.0E- 02

0

173

174

175
176
JD of 2008

177

178

Deviatoric Strain (cross shore)

-1
-2
-3
-4
-5
172

179

1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03
0.0E+00
-2.0E- 03
-4.0E- 03
-6.0E- 03
-8.0E- 03
-1.0E- 02

Deviatoric Strain(along shore)

-1

Depth( m)

Deviatoric Strain (along shore)

0

Depth( m)

1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03
0.0E+00
-2.0E- 03
-4.0E- 03
-6.0E- 03
-8.0E- 03
-1.0E- 02

173

174

175
176
JD of 2008

177

179

1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03
0.0E+00
-2.0E- 03
-4.0E- 03
-6.0E- 03
-8.0E- 03
-1.0E- 02

178

Figure 4.19: Deviatoric strain components observed and calculated from the nearshore model for location N2
95

179

Flow reversals are the dominant feature affecting advective transport in the CBL. These
features are believed to be caused by changes in wind direction. Using a non-parametric
Spearman correlation, the correlation between wind and current direction for the entire simulation period was found to be weak (Spearman ρ=0.11). For the simulation period of 10
days (JD155-JD165), characterized by quick changes in flow direction, the correlation was
(Spearman ρ=-0.02), with a p-value of 0.72, showing that current direction and flow reversals are not correlated to wind-direction. It was noticed that the mean flow interacts with
the shoreline to give rise to coherent structures that are advected a considerable distance
before dissipating. Coherent structures or vortices are generated at fluid interfaces with
large velocity gradients, as in the case of Kelvin-Helmholtz (KH) instability, or at no-slip
boundaries. They are subsequently advected and dissipated as a tracer (Vallis, 2006). The
emergence of these coherent structures can be used to obtain information about the nature
of the flow structure, and the length scales important for predicting mixing rates. (Sadourny
and Maynard, 1997) and (Sundermeyer et al., 2005) have found that vortical mode stirring
can be an important process affecting mixing in the coastal ocean. Analysis of the vorticity has also been used to separate flow into hyperbolic regions (dominated by strain) and
elliptic regions, where vorticity dominates (Doglioli et al., 2007; Weiss, 1991). The method
however, only works for the core of the vortices with the strongest vorticity (Basdevant and
Philipovitch, 1994).

96

RhWT Concentration (PPB) − OD3
5

0
176.5

177

177.5

178

178.5

RhWT Concentration (PPB) − OD2
5

0
176.5

177

177.5

178

178.5

RhWT Concentration (PPB) − OD1
5

0
176.5

177

177.5

178

178.5

Figure 4.20: Model comparison with observations of Rhodamine concentrations at Ogden
Dunes beaches

97

N 41.64

Latitude

(a )

1:00p m- 2:00p m

Model

RhWT(PPM)
12. ppm
5
10. ppm
0
7.5 ppm
5.0 ppm
2.5 ppm

SCUFA observations

N 41.63

Ogden Dunes
W87.20

W87.19

W87.18

W87.17

W87.16

Longitude
N 41.64

Latitude

(b )

Model

4:30p m- 6:00p m

RhWT(PPM)
12. ppm
5
10. ppm
0
7.5 ppm
5.0 ppm
2.5 ppm

SCUFA observations

N 41.63

Ogden Dunes
W87.20

W87.19

W87.18

Longitude

W87.17

W87.16

Figure 4.21: Comparison of observed and simulated Rhodamine WT plumes in the nearshore region
98

Analysis of the vorticity from the model results show that circulation in the nearshore is
characterized by emergence of occasional flow structures which result from the interaction of
the large-scale mean-flow with the coastal boundary. These are advected along the boundary.
Interactions of these structures with flow close to the boundary results in regions of high
vorticity gradient. Advection of these structures by the mean flow can also explain the weak
correlation between wind and velocity vectors. Regions with high vorticity are also expected
to result in large mixing rates (Batchelor, 1967), a prediction consistent with observations
and field studies. Since, many of the high vorticity regions are also near built-up areas and
of interest from a contamination transport point-of-view, higher grid resolution and better
modeling of subgrid scale processes are required. Interfaces with high velocity gradients,
within the lake, were not observed and conditions that might lead to KH instability were
detected only very close to the shore, as shown in Figure 4.14. While model results did not
show any structures that could be attributed to the KH instability, it is expected that higher
grid resolution, coupled with improved closure schemes, will be able to resolve small-scale
features close to the shore.

The principal focus of this study was on the ability of the numerical model to predict
scalar transport in the nearshore. Observed data based on water samples collected along the
shore-based sampling points, during the dye plume study, have been compared to results from
the numerical model in Figure 4.20. It is clear that a dispersion coefficient of around 3 m2 /s
is required to be able to predict the breakthrough curves observed. The sampling station
OD3, being closest to the outfall, was most accurately predicted by the model. Moving
further from the outfall also reduces the accuracy of the numerical model. Model results are
characterized by an excessive damping of the peak (due to the Smagorinsky formulation)
99

while the peak decays much more slowly in the observed data. Spatial extent of the observed
Rhodamine plume has been compared with results from the nearshore model in Figure 4.21.
Lack of sufficient sampling points prevents a more quantitative comparison, however, the
anisotropic nature of the observed plume and importance of modeling dispersion accurately
is clear. Improving the accuracy of the model would require a larger dispersion rate. This is
consistent with recent work (de Brauwere et al., 2011; Stacey, 2003) where scale dependent
dispersion coefficient of D = 0.03∆1.15 has been used. Here, D is the dispersion coefficient
in m2 /s and ∆ is the length-scale. Including a description of the anisotropic field in the
CBL can also be expected to significantly improve quality of predictions.

4.5

Conclusion

The structure of the velocity profile shows a great deal of variation in the vertical direction.
Temperature profile measurements in the nearshore, point toward a well-mixed system. However, the hydrodynamics reveal the existence of a clear top and bottom boundary layer of
nearly constant size. The size and strength of these boundary layers vary within the CBL
and is strongly correlated with the relative importance of friction and inertial forces, as we
move closer to the shore. The quadratic bottom boundary layer description used in the
numerical model, in conjunction with the wind-driven forcing, is able to describe the general flow structure qualitatively. Layer specific comparisons of the modeled and observed
velocities, however, are not satisfactory within the top boundary layer. The other principal
feature of the hydrodynamic field in the CBL, flow reversals, is accurately described by the
model.
Turbulent eddy-diffusion calculated using the Smagorinsky method, shows that mixing
100

rates are highest at the top with a secondary maximum at the bottom. In addition to turbulent diffusion, shear-augmented dispersion is significant in nearshore environments. Smallscale, high frequency fluctuations, typical of the highly turbulent nature of the flow field,
were observed in the measured velocity time-series. Comparison with the three-dimensional
velocity field reveals the models’ inability to describe the vertical shear structure adequately.
Eddy-viscosity based turbulent scheme and the grid-size are two of the principal reasons for
the models’ inability to describe the high-frequency fluctuations in velocity. Comparisons
with the hydrodynamic results from the 2 km grid model indicate that further improvements
in the hydrodynamic description will need re-assessment of the horizontal turbulence closure
scheme as well as the top and bottom boundary layer description.
Circulation within the CBL is a result of the interaction between the large-scale circulation, lateral and bottom boundary conditions closer to the shore. Large-scale circulation
drives the nearshore hydrodynamics, with the energy sinks located at the boundaries. Flow
reversals, an important feature of hydrodynamics in the nearshore, are generally thought
to be a result of changes in wind direction. However, this is inconsistent with the weak
correlation between the wind and current vector fields. Our analysis of the vorticity field
in the CBL, however, indicates that the quick, short timescale, changes in direction of the
flow field, could be due to the vortices generated at the boundary and transported by the
mean flow field. The predominantly two-dimensional nature of circulation in the CBL also
reduces dissipation of these vortices. Further analysis of the role of these coherent structures
on mixing and transport of contaminants, within the CBL, is necessary.

101

Chapter 5
Budget Analysis of Escherichia coli
at a Beach in Southern Lake Michigan

5.1

Summary

Escherichia coli (EC) concentrations at two beaches impacted by river plume dynamics in
southern Lake Michigan were modeled using three-dimensional hydrodynamic and transport
models. The relative importance of various physical and biological processes that influence
the fate and transport of EC were examined via budget analysis and a first-order sensitivity
analysis of model parameters. The along-shore advective flux of EC (CFU/m2 s) was found to
be higher compared to its cross-shore counterpart; however, the sum of diffusive and advective components was of a comparable magnitude in both directions showing the importance
of cross-shore exchange in EC dilution. Although the vertical fluxes were small compared to
the horizontal fluxes, examination of the individual terms in the EC mass balance equation
showed that the vertical dimension plays a key role in the overall EC transport. Dilution
102

due to advection and diffusion accounted for a large portion of the total EC budget in the
nearshore. The rate of net EC loss within the water column (CFU/m3 s) was an order of
magnitude smaller compared to the horizontal and vertical transport rates; however, this assessment is potentially complicated due to the strong coupling between the vertical exchange
and the depth-dependent EC loss processes such sunlight inactivation and settling. Sensitivity analysis indicated that solar inactivation has the greatest impact on EC loss rates. Our
results support the choice of the wind vector as an important predictor in statistical models
of beach closures. Processes influencing the transport and in-activation in the nearshore are
complex 3D processes with significant variation in the vertical. Although the results are
site-specific, they clearly bring out the relative importance of various processes involved.

5.2

Introduction

Increased beach closures due to impaired water quality have been a cause for concern in
recent years. Numerous studies have shown a causal relationship between illnesses such
as gastrointestinal disease and recreational-water quality as measured by indicator bacteria
such as Escherichia coli (EC) and enterococci (Pruss, 1998). Coastal water quality has a
significant impact not only on human health but also on local economies (Rabinovici et al.,
2004). One study estimated economic losses as a result of closing a Lake Michigan beach
due to pollution as ranging between $7,935 and $37,030 per day (Rabinovici et al., 2004).
The presence of fecal indicator bacteria (FIB) in nearshore waters is used to determine beach
closures. Predictive modeling of FIB represents an attractive alternative to the traditional
approach based on observation; how-ever, to further refine mechanistic and statistical models, an assessment of the relative importance of different processes influencing FIB levels is
103

needed.

Significant progress has already been made in describing the concentration of indicator
bacteria at marine and freshwater beaches using mathematical models (Boehm and Weisberg, 2005; Grant et al., 2005; Kim et al., 2004; Liu et al., 2006; McCorquodale et al., 2004;
Sanders et al., 2005). In addition, there is a large body of literature (mainly based on field
and laboratory studies) on the importance of various mechanisms influencing FIB levels in
coastal waters; however, the in-formation is often qualitative in nature. To the best of our
knowledge, a systematic budget analysis of FIB examining fluxes and the relative importance of various processes using field observations and detailed mechanistic modeling is not
available in the literature. A notable exception is the work of Kim et al. (Kim et al., 2004)
who applied a macroscopic mass budget analysis based on the Reynolds Transport theorem
to determine the sources of pollution for a marine beach in California. Budget analysis is
important for identifying the key components of a predictive model and is a nontrivial task
for a number of reasons. First, a majority of the beach sites in many states are impacted by
unknown sources of contamination. An uncertainty in the nature, strength, and location of
sources introduces significant uncertainty into the modeling making it difficult or impossible
to infer processes. Second, a number of complex and often interrelated processes control
the levels of FIB in nearshore waters including turbulent diffusion and dispersion, alongshore transport, growth, natural mortality, sunlight-dependent inactivation, sedimentation,
and resuspension. Hipsey et al. (Hipsey et al., 2008) recently described these processes in
detail with-in the context of process-based modeling. FIB levels in the water column are
influenced by processes that are time-dependent and three-dimensional in nature placing significant demands on data and computational resources for 3D modeling (e.g., high-resolution
104

bathymetry, time-series of hydrodynamic and FIB data, etc.). Liu et al. (Liu et al., 2006)
used two-dimensional, vertically integrated flow and transport models to describe the fate
and transport of EC and enterococci at two beaches (Mt. Baldy and Central Avenue) along
the Indiana shoreline in Southern Lake Michigan. Their modeling indicated that two nearby
creeks draining into Lake Michigan are the primary sources of contamination impacting the
beaches. Nevers and Whitman (Nevers and Whitman, 2008) recently examined EC data
from 12 beaches along a 35-km length of the Indiana shoreline and proposed improved statistical models with only two variables: the wave height and an interaction term containing
wind direction and creek turbidity. An assessment of the relative importance of different
processes in the nearshore is needed for identifying the essential components of a predictive
(either statistical or mechanistic) model. The aim of this paper is therefore to (a) combine
fully three dimensional hydrodynamic and transport modeling with ob-served concentrations
of EC at the beach sites described in Liu et al. (Liu et al., 2006) to quantify various fluxes of
EC (due to advection, diffusion, inactivation) as a function of time; (b) report the results of
a sensitivity analysis of different parameters influencing EC levels and rank them in order of
importance; and (c) examine processes within the water column including vertical velocity
profiles and loss of EC within the water column to understand the importance of the vertical
dimension.

5.3

Methods

The primary area of interest includes approximately 72 km of Lake Michigan shoreline within
the state of Indiana. Since summer is the primary swimming season and the lake freezes over
in winter, hydrodynamic and water quality data were collected during the summer months
105

at two beach sites (Mt. Baldy and Central Avenue, shown in Figure.5.1). Also shown in
the figure are the three main tributaries. Tributaries contributing flow to Lake Michigan
within the study region are Burns Ditch (USGS 04095090) near Burns Harbor, Trail Creek
at Michigan City Har-bor (USGS04095380), and Kintzele Ditch. Based on historical water
quality monitoring data and the modeling study reported in Liu et al. (Liu et al., 2006),
Kintzele Ditch and Trail Creek are considered to be the main sources of EC impacting the
two beaches for the period of simulation (July-August 2004). Water samples were collected
in knee deep water at the two beaches during the summer months (July-August, 2004) when
beach attendance is highest. Daily samples were also collected at nearby outfalls, Trail Creek
and Kintzele Ditch, which represent sources of bacterial contamination for the beaches. A
stage-discharge relation was established for the Kintzele Ditch site. Loading and discharge
volume for the two tributaries, Kintzele Ditch and Trail Creek, have been presented in
Figure 5.7. Samples were collected and analyzed for EC using membrane filtration technique
as described in (Liu et al., 2006). Further details of these analyses as well as model inputs
for the two tributaries (flow, temperature and EC time-series) are available in (Liu et al.,
2006). Hydrodynamic data were collected during the summers of 2004 and 2006 near Burns
Ditch using a 600 kHz Teledyne RD Instruments Acoustic Doppler Current Profiler (ADCP)
deployed in an up-ward looking configuration. For the 2006 deployment data reported in
this paper, the ADCP was located at a depth of 10.6m at coordinates N41o 38.120, W87o
12.179. Examination of the 2004 ADCP data indicated potential issues with an internal
compass; therefore the 2006 data were used to validate the hydrodynamic model used in
the study. Solar radiation was measured at Trail Creek using a Campbell Scientific total
radiation pyranometer. Locations of both instruments are shown in Figure 5.1.

106

Figure 5.1: Map of Southern Lake Michigan and the Indiana Shoreline

107

5.4

Modeling

Our primary interest was in examining EC fluxes in different coordinate directions. Thus,
we used fully three-dimensional hydrodynamic and transport models to describe flow, temperature, and EC concentration fields as a function of space (x, y, z) and time (t). The
Princeton Ocean Model (POM), which uses a mode-splitting strategy to increase accuracy
and reduce computation time, was used in the present study. POM solves the hydrodynamic
primitive equations Equation 2.3, Equation 2.4, Equation 2.5 and makes the Boussinesq
assumption to model density variation and hydrostatic assumption in the vertical. The horizontal plane was discretized using an Arakawa-C grid, and explicit time-stepping using the
leapfrog method was used. Details of the POM model are available in (Mellor, 1998). The
EC transport model solves the transport equation (Equation 5.1), where k is the net loss
rate due to inactivation and settling and is calculated using Equation 5.2.

∂c
∂c
∂c
∂
∂c
+u
+v
+w
=
∂t
∂x
∂y
∂z ∂x
+

k = −(

AH
∂
∂z

∂c
∂x

KV

+
∂c
∂z

∂
∂y

∂c
AH
∂y

− kc

fp υS
fp υS
−
+ kI I0 (t)e−ke z + kd )θT −20
∆zi
∆zi−1

(5.1)

(5.2)

In Equation 5.2 the first two terms in the parentheses denote loss of EC due to settling
to the layer below and gain from the layer above, and ∆zi denotes the thickness of layer
i. T denotes the temperature, fP denotes the fraction of EC attached to particles, υS is
the settling velocity, kI is the sunlight-dependent inactivation rate, I0 (t) is the sunlight at
the surface, ke denotes the extinction coefficient, and kd is the base mortality rate (also
called the dark death rate). The attenuation of sunlight within the water column was
108

modeled using the Beer-Lambert relation. Dependence of the loss rate k on temperature was
modeled using the Arrhenius relation as shown in Equation 5.2. In addition to solving the
equations of momentum, temperature, and EC concentration, the model uses the MellorYamada 2.5 level turbulence parameterization and solves equations for turbulent kinetic
energy and turbulence length scale. Nearshore circulation is influenced by the large-scale
lake-wide circulation patterns. This effect was modeled by running the hydrodynamic model
in a nested grid configuration. The whole-lake coarse grid model used a 2 km uniform grid
spacing and 20 σ-layers in the vertical. The results were then used to drive the nearshore
fine grid model, which used a 100 m uniform grid and the same number of vertical levels as
the coarse grid. Information transfer between the two models was one way, with results of
the coarse grid model interpolated to the boundary of the fine grid. This method allowed
us to simulate nearshore hydrodynamics accurately while avoiding the problem of specifying
arbitrary open boundary conditions for the fine-scale model. The two computational domains
as described by the coarse and fine grids are shown in Figure 5.2. The POM version used
in the present study was adapted to the Great Lakes and was tested extensively in the past
(Beletsky and Schwab, 2001).

Heat and momentum inputs to the surface of the lake were used as model forcing functions during simulation. Hourly meteorological data including cloud cover, air and dew
point temperature, wind speed and direction were obtained for several stations from the
NOAA National Climatic Data Center and NOAA National Data Buoy Center and interpolated to the model grid. Water level data were obtained from the Center for Operational
Oceanographic Products and Services (CO-OPS), NOAA, and the National Data Buoy Center. Surface heat flux was calculated in the model to simulate temperature and the thermal
109

Figure 5.2: (a) Finite-difference mesh of Lake Michigan used to compute the lake-wide
circulation (b)Part of the mesh used to compute nearshore circulation and E. coli transport
showing the bathymetry

110

structure in the lake using heat flux methods described in (McCormick and Meadows, 1988).
Briefly, the surface heat flux was calculated as the sum of short-wave radiation from the
sun, sensible and latent heat transfer, and the long-wave back radiation to space. Due to the
dependence of EC inactivation on the short-wave radiation, this component was of particular
interest in this work. The short-wave radiation I(t) was calculated based on its clear-sky
value (calculated using the EPA method, (Office, 1971)) and as a function of cloud cover.
The finite-difference numerical model was solved on a cluster computer at Michigan State
University and was compiled and optimized for the parallel environment.

5.5

Results

The hydrodynamic model was tested by comparing simulations with current measurements
made during the summer of 2006. Comparisons of the observed and simulated (vertically
integrated) velocities (Figure 5.3 show that currents in the nearshore are characterized by
a strong alongshore (u) component and a relatively weak cross-shore (v) component. The
dominant along-shore velocity component means that contaminant plumes tend to follow
isobaths and nearshore-offshore advective exchange is limited by the small cross-shore current component. Frequent flow reversals observed during field studies (Nevers and Whitman,
2008) and reproduced in our simulations also increase dilution of contaminant plumes in the
nearshore regions. Vertical velocities are relatively small and comparable in magnitude to
the settling velocities used (5–10 m/day) in earlier studies (McCorquodale et al., 2004; Liu
et al., 2006). Turbulent fluctuations in the vertical velocity could significantly increase the
residence time of particles in the water column. Model comparisons with observed velocity profiles are shown in Figure 5.4 to demonstrate the models ability to reproduce vertical
111

variations in velocity. Turbulent mixing and shear in the vertical produced well-mixed conditions; however, it is possible for vertical variations to be much more significant in the
presence of stratification. Exposure to sunlight, in particular the UV bandwidths, causes
inactivation of bacteria due to direct DNA damage (Whitman et al., 2004; Sinton et al.,
2002) although photo-oxidative effects are the primary inactivation mechanism in surface
waters due to the high attenuation of short UV wavelengths (Hipsey et al., 2008). Due to
lack of detailed information on the attenuation characteristics of different wavelengths in the
water column relative to the action spectrum of EC, short-wave radiation I0 (t) considered in
our modeling included all wavelengths between 150 and 3000 nm with a single attenuation
coefficient ke . Although the inactivation effect weakens at higher wavelengths, the justification for this choice is based on the fact that the higher wavelength energies excite sensitizer
compounds that eventually oxidize organic molecules (Hipsey et al., 2008). Calculated shortwave radiation based on the geographic location, time of the year, time of the day, and the
reported cloud cover is shown in Figure 5.5. Effect of cloud cover on ambient sunlight was
included in the model by interpolating observed values recorded at meteorological stations
along Lake Michigan shoreline. Reasonable agreement was obtained between the observed
and calculated solar radiation indicating that the radiation algorithm is suitable for making
EC predictions except on days with significant cloud cover. Spatial and temporal variability
of cloud cover and errors in interpolating this over large areas could be the reason for the
models inability to predict ambient sunlight on days with significant cloud cover. Water
temperature has been observed to influence rate of inactivation and loss processes of bacteria in the water column; the accuracy of the numerical model in predicting diurnal and
seasonal variation in temperature has been shown in Figure 5.6 by comparing with observed

112

Figure 5.3: Comparison between observed and simulated velocity time-series at the Burns
Ditch location in the along-shore and cross-shore directions

temperature measurements made in the nearshore.
Comparisons between observed and simulated EC for one set of parameters is shown in
Figure 5.8. Reasonable agreement was obtained for the following set of parameters: a light
dependent inactivation rate kI of 0.0026 W-1 m2 d-1 (3x10-8 W-1 m2 s-1 ), a base mortality
rate kd of 8.6x10-5 d-1 (1x10-9 s-1 ), a settling velocity νS of 1 m/d (based on the estimates
in (Eadie, 1997)) with an attached EC fraction fp ) 0.1 (McCorquodale et al., 2004) and a
light extinction coefficient of 0.55 m-1 . It is important to note that the formulation used in
Equation 5.2 to describe EC losses does not allow us to uniquely estimate model parameters,
since any combination of para-meters that produces the same net loss of EC (relative to a
113

Figure 5.4: Comparison of observed and simulated vertical velocity profiles for along-shore
(u) and cross-shore (v) velocities on different days during summer 2006

114

1200

S imulation
O bs ervation

S olar R adiation (W /m^2)

1000
800
600
400
200
0

190

200

210

220

J ulian D ay 2004
Figure 5.5: Comparison of observed and simulated short-wave radiation at Trail Creek

Figure 5.6: Observed and simulated temperature in the nearshore
115

conservative tracer) will still result in a good agreement with data. Although our model
describes the attenuation of incident sunlight (and hence inactivation) with depth, kI itself
is the result of more complex processes (Hipsey et al., 2008). To estimate kI uniquely, fundamental processes such as dynamic attachment to particles, suspended sediment transport
including settling and resuspension, attenuation of different bandwidths of incident radiation
within the water column as a function of suspended material, dissolved oxygen, etc. need to
be simulated; however, this will further complicate the modeling in addition to introducing
several new model parameters. As noted earlier, the net loss of EC relative to the hydrodynamic processes of advection and diffusion can be quantified uniquely using our modeling.
Observed and simulated concentrations presented as probability plots in the Supporting Information indicate that the high as well as low levels of EC can be described using the
current model. Modeling results (and rates) presented here are similar to those shown in Liu
et al. (2006) although the present model described the data better. For example, the RMSE
value based on log-transformed EC concentrations for the Mt. Baldy beach is 0.41 for the
present 3D model compared to a value of 0.808 reported in Liu et al. (2006) for a vertically
integrated model. The improvement in RMSE is partly due to the use of 3D models and
partly due to refinements in inputs (3 arc-second bathymetry blended with high-resolution
LIDAR data was used in our nearshore modeling). The inactivation formulation (5.5) used
in this paper includes a base mortality rate which was absent in Liu et al. (2006). To quantify
the relative importance of various processes contributing to the loss of EC, we conducted
a first-order sensitivity analysis and computed condition numbers for each parameter. The
condition number for a parameter k (defined as Ck = (k/c)(∂c/∂k) where c denotes EC
concentration) is higher for parameters that produce large variations in model predictions.

116

Computed condition numbers for parameters kI , fP , υS , kd , ke are 83, 58, 99, 63, and 102,
respectively, indicating that the extinction coefficient for sunlight in the water column is the
most important parameter in Equation 5.2. Examination of the relative contributions of
various EC loss mechanisms indicated that for the parameters used in Figure 5.8, sunlight
inactivation accounted for 96% of the total losses in the water column, while base mortality
and settling accounted for the remaining 4% of the losses.
While the time-series and RMSE values of comparisons between observed and simulated
values of EC is essential to assess model performance, it is often useful to examine the
comparison as probability plots. Figure 5.10 shows that the model was able to describe both
the lower and higher limits of EC concentrations. Changes in wind-direction and influence
of large-scale circulation on the nearshore region results in a highly variable hydrodynamic
field. Flow reversals are common and are characteristic of contaminant plumes entering the
nearshore region. Figure 5.9 shows the spatial extant of the EC plume in the nearshore
region, before and after a flow reversal event on JD 217 of 2004.

117

Temperature ( o C)

(a)

25
20

0
2
(b)
1.5
1
0.5
0
190

15

E. coli

4

4

E. coli (CFU/100 mL) x 10

195

200

205

210

215

220

225

Trail Creek

230
Temperature (oC)

Discharge (m3/s)

Kintzele Ditch
Discharge
Temperature

0.5

Discharge (m 3 /s)

E. coli

1

25

(c)

2

20

0
2

15
1

(d)

1
0
190

0.5
195

200

205
210
215
Julian Day, 2004

220

225

0
230

Figure 5.7: Loading from Trail Creek and Kintzele Ditch during summer 2004 used as model
inputs for the simulation period

118

Figure 5.8: Observed and simulated E. coli concentrations at (a)Central Avenue Beach and
(b)Mt. Baldy Beach

119

Figure 5.9: Spatial extent of EC plumes at two different instants of time on Julian Day 217. The plumes are shown traveling
in opposite directions

120

Periods of high bottom-shear stress, caused by currents or wind-generated waves, can
cause bacteria in the sediment to be resuspended into the water column along with sediment.
Although a comprehensive assessment of the role of sediment in contributing EC to the water
column has been dealt with in greater detail in Chapter 6, here we have computed the bottom
shear stress to understand the relation between high shear-stress events and EC peaks. In
the nearshore region, the shear stress exerted by currents is generally small compared to the
contribution from waves and the total shear stress can be approximated as the sum of current
and wave shear stresses (Chao, 2008). Bottom shear stress due to currents was calculated
using Equation 5.3 neglecting wave-current interactions (Jewell et al., 1993).

(5.3)

τC = CD ρVB VB

Where τC is the bottom shear stress due to currents, VB is the velocity at the bottom
layer, ρ is the density of water and CD is the drag coefficient calculated using the log law.
In shallow waters near beaches bottom shear stress due to wind generated waves can be
significant (Chao, 2008). This was calculated using Equation 5.4:



τ W = H ρ



3 0.5
ν 2π

T


2 sinh 2πd 
L



gd
gH
= 0.283 tanh 0.53
2
UW
UW 2

3/4

(5.4)

1/2



 0.00565 gF



UW 2


 × tanh 



3/8 


gd
 tanh 0.53

UW 2


121

(5.5)

Figure 5.10: Probability plots of EC (observed versus simulated) for the Central Avenue and
Mt. Baldy beaches

122


3/8


gT
gd
= 7.54 tanh 0.833
UW
UW 2

L=

1/2



gF


0.0379


2
UW


 × tanh 



3/8 


gd
 tanh 0.833

UW 2


gT 2
tanh
2π

2πd
L

(5.6)

(5.7)

Here, τW is the bottom shear stress due to waves and F is the fetch. A bottom roughness
height z0 of 1 cm has been used (Weatherly and Martin, 1978). UW is the wind speed at
10 m height and d is the water depth at the location. The net bottom shear stress can be
expressed as:
τnet = τC + τW
To facilitate comparison between EC peaks and the bottom shear stress, the net bottom
shear stress was normalized using the relation:

τ =

τnet − τnet,min
τnet,max − τnet,min

(5.8)

Here, τnet,max and τnet,min are the maximum and minimum values of the bottom shear
stress. The normalized shear stress and EC are shown in Figure 5.11. The comparison shows
that a majority of the peaks in EC are associated with high shear stress events. It is interesting to note that immediately after the high shear stress event around Julian day (JD) 218,
no EC peaks were observed although there were multiple high shear stress events. The result
points to the finite nature of the sediment as a source of EC. Comparisons between normalized values of the total bottom shear stress and observed EC ((p − pmin )/(pmax − pmin ),
where p denotes EC concentration or the shear stress) show that while sediment resuspen123

Normalized shear stress or E. coli

1
0.9

Shear stress
E. coli

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
170

180

190

200
210
Julian Day (2004)

220

230

Figure 5.11: Normalized shear stress and EC for summer 2004

sion is a complex nonlinear process with significant spatial variability, some of the peaks in
EC could be due to sediment resuspension. Perhaps more important is the observation that
at the study site the sediment appears to represent a time-dependent source of finite size
so that a single high shear stress event has the potential to resuspend virtually all the EC
on the sediment bed leaving subsequent shear events with no more EC to resuspend until
further deposition takes place. This behavior, which can be seen around Julian days (JD)
220 and 225, has important implications for modeling EC deposition and resuspension.
Contaminant transport in southern Lake Michigan is characterized by the presence of
a dominant along-shore velocity component and a relatively weak cross-shore component.
Frequent reversals in direction of the alongshore velocity are also observed (Nevers et al.,
2007). Sharp fronts are sometimes observed increasing the importance of nearshore-offshore
exchange due to large cross-isobath gradients (Rao and Schwab, 2007). To better understand
124

the relative importance of these processes and to quantify EC fluxes in the nearshore, we
conducted a budget analysis by examining the fluxes entering and leaving a control volume
(100 m long in the along-shore direction, 100 m wide in the cross-shore direction, and 4.5
m deep at the center) at the Central Avenue beach. POM uses a staggered grid in the
horizontal (referred to as the Arakawa-C grid, Figure 5.12) in which variables such as EC
concentration and temperature are defined at the cell centers and velocities are defined at
cell faces (Figure 5.12). To calculate the fluxes at the cell faces, concentrations at the cell
faces are needed. These were calculated as the arithmetic averages of the concentrations at
the neighboring cell centers since uniform grid spacing was used in our computations. The
fluxes (units: M L−2 T −1 ) are defined and computed as shown below. EC fluxes due to
advection and turbulent diffusion, as well as the net flux as defined below were calculated in
different directions.
Jadv,x = uc, Jadv,y = vc, Jadv,z = wc,

(5.9)

∂c
∂c
∂c
Jdif f,x = −AH , Jdif f,y = −AH , Jdif f,z = −KV
∂x
∂y
∂z

(5.10)

Here, (u, v, w) denote the velocity components in the alongshore (x), cross-shore (y), and
vertical (z) directions, and AH , KV

denote the eddy diffusivity for EC in the horizontal

and vertical directions, respectively. Using the staggered grid shown in Figure 5.12, these
fluxes are approximated as shown below. Net advective flux in the x-and y-directions:

Jnet,adv,x = ui,j

Jnet,adv,y = vi,j

ci−1,j + ci,j
2
ci,j−1 + ci,j
2

125

− ui−1,j

ci,j + ci+1,j
2

(5.11)

− ui,j+1

ci,j + ci,j+1
2

(5.12)

(i,j+1)

(i-1,j)

(i,j)

(i+1,j)

(i,j-1)
Beach
along-shore velocity (u)
cross-shore velocity (v)
E. coli concentration (c)

Figure 5.12: Grid points in the nearshore used for the budget analysis

126



 

AHi,j ci,j − AHi−1,j ci−1,j
AHi+1,j ci+1,j − AHi,j ci,j
−−

Jnet,dif f,x = −
∆x
∆x
(5.13)

AHi,j+1 ci,j+1 − AHi,j ci,j
AHi,j ci,j − AHi,j−1 ci,j−1
−−

Jnet,dif f,y = −
∆y
∆y
 



(5.14)
Similar expressions were used to compute the vertical fluxes in the z-direction. For the
budget analysis, the 3D transport equation is used to understand the relative importance of
different processes. The transport equation for EC (Equation 5.1) can be written in terms
of the above fluxes as shown below:
∂ Jadv,y
∂ Jadv,z
∂ Jdif f,x
∂ Jdif f,y
∂ Jdif f,z
∂c ∂ Jadv,x
+
+
+
+
+
+
∂t
∂x
∂y
∂z
∂x
∂y
∂z

= −kc
(5.15)

Once the fluxes in equations Equation 2.3, Equation 2.4, Equation 2.5 were computed,
they could be used to evaluate the different terms in equation Equation 5.15 by evaluating
each term as the difference between the fluxes entering and leaving a control volume divided
by the step size in the appropriate direction. For example, the advective flux in the alongshore direction can be approximated as:
∂ Jadv,x
∂x

=

Jadv,x,in − Jadv,x,out
∆x

(5.16)

Each term in the transport equation Equation 5.15 represents a mass flow rate for EC
with units M L−3 T −1 . Mass flow rate results are presented in Figures Figure 5.13 and
Figure 5.14.
Examination of the fluxes in Equation 5.9 indicated that advective transport in the
127

Figure 5.13: Results of budget analysis for EC showing the relative contributions of different
processes within the water column

128

Figure 5.14: Variation of the magnitudes of vertical advection and diffusion within the water
column
129

along-shore direction dominated over its cross-shore counterpart; however, the sum of advective and diffusive fluxes was comparable in the two directions. Smaller cross-shore velocity component resulted in greater concentration gradients in the offshore direction so that
nearshore-offshore exchange was dominated by diffusion processes. Dilution due to advection
and diffusion accounted for a significantly large portion of the total EC flux in the nearshore.
While information about the fluxes is useful, it does not provide information about the relative importance of different processes. To understand this, the individual terms representing
advection, diffusion, and loss processes in the EC transport equation (with units CFU/m-3 )
were computed and are plotted in Figure 5.13 and Figure 5.14. It is clear that net mass
flow rate in the along-shore direction was comparable to that in the cross-shore direction.
However, while the advective along-shore component of the mass flow rate was almost always
positive (inflow into the control volume is positive, Figure 5.13), the advective component
in the cross-shore direction was usually negative and caused removal of contamination from
the cell. Net mass flow rate, however, was almost always positive in both along-shore and
cross-shore directions indicating that contaminant plume behavior is complex in the presence of frequent flow reversals (Nevers et al., 2007) and constantly varying concentration
gradients. Figure 5.14 reveals that vertical transport in the water column was dominated
by turbulent mixing, and transport rates in the upper layers were significantly greater than
those in the lower layers (Figure 5.13 and Figure 5.14) resulting in a complicated 3D plume
front, which cannot be adequately described using vertically integrated models. The high
vertical diffusion (Figure 5.14b) indicates well-mixed conditions due to turbulence in the
water column. We also notice that the total loss term (due to settling, light, and base mortality) was an order of magnitude smaller compared to the horizontal advection terms. This

130

result has two important implications. First, for well-mixed summer conditions similar to
those simulated here, EC plume shapes can be predicted well using models similar to the
present one if sources and loading are known. Second, for highly stratified flows depth dependent EC loss mechanisms (such as sunlight-dependent inactivation) could assume much
greater importance in describing EC concentrations in the vertical compared to the conditions simulated here. The tight coupling between vertical transport and inactivation leads
us to conclude that simulation of more fundamental processes (e.g., suspended sediment
transport, attenuation of different light energies within the water column, etc.) is required
to quantify the loss of EC in the water column for well-mixed and stratified cases alike since
conditions in the water column are dynamic. Although these results are site-specific and
cannot be generalized to all beaches, they have important implications for modeling beaches
impacted by river plume dynamics in the Great Lakes region.

5.6

Discussion and Conclusion

In this paper we examined the relative importance of processes influencing the fate and
transport of FIB in the nearshore region of Lake Michigan and demonstrated the complex
nature of the processes involved. ADCP measurements of currents were used to validate the
hydrodynamic model. EC observations at sources and nearby beaches have been used to
show that biological processes can be modeled accurately for summer conditions using the
present model. For the conditions simulated here, dilution due to advection and diffusion was
an order of magnitude higher compared to the net loss processes within the water column.
Budget analysis considering individual terms in the EC mass balance equation indicated that
turbulent mixing within the water column dominated the overall EC transport consistent
131

with our observations of well-mixed conditions at the site (e.g., uniform vertical profiles of
velocity and temperature). The amount of vertical mixing in the water column is controlled
by the degree of density stratification in the nearshore, therefore simulation results depend,
among other factors, on inflows (volume of water entering the lake per unit time) as well
as source conditions including water temperature and the vertical distribution of materials
at the source. Thermal buoyancy contribution of inflowing water as well as conditions at
the source (well-mixed based on our observations) were taken into account in our modeling.
Strong vertical stratification can prevent vertical mixing changing the importance of processes in the water column. The importance of vertical mixing is site-specific (and changes
with time at a given site), but useful insights can be obtained by comparing EC plume
dynamics at different sites based on dimensionless numbers such as the gradient Richardson
number (which represents the opposing contributions of buoyancy and shear). A more accurate estimation of the importance of various EC loss processes will require refinements to the
inactivation formulation used in this work. For example the effect of water clarity (CDOM
and SSC) on inactivation rates can be quantified by coupling EC and sediment transport
models to better understand the linkages between environmental variables and EC levels.
High frequency biological observations are also needed to accurately assess the importance
of biological processes associated with different time scales. Analysis of the bottom shear
stresses due to current and waves in the nearshore reveals a connection between observed EC
peaks and high shear stress events. Linkages between these processes can be studied by coupling sediment transport descriptions with a wind-driven current and wave model. Results of
sensitivity analysis clearly demonstrate the importance of sunlight inactivation and the role
played by the extinction coefficient associated with different wavelength bands. Quantitative

132

information on the attenuation of different energy bands within the water column and their
role in EC inactivation is needed to further refine EC fate and transport models.

133

Chapter 6
Sediment-bacteria Interactions at
Beaches in Southern Lake Michigan

6.1

Summary

Bed sediment represents a potential source of indicator bacteria in the nearshore region.
Settling and resuspension rates determine the levels of indicator bacteria in the sediment
and the water column. In this study, we model Escherichia coli (EC) concentrations, taking
sediment-bacteria interactions into account in a three-dimensional hydrodynamic and transport model. The hydrodynamics are simulated using the Princeton Ocean Model executed in
a nested grid configuration. A semi-empirical parametric model is used to simulate the wave
climate and to calculate bottom shear due to wind generated waves. The hydrodynamic and
wave models were compared with ADCP measurements made in the nearshore and offshore
regions. The hydrodynamic model was found to describe currents accurately. Wave height
and period were accurately represented by the wave model. EC measurements from wa134

ter samples collected daily in knee-deep waters of beaches in southern Lake Michigan were
simulated using an EC fate and transport model that was coupled with the hydrodynamic
model. The total sampling duration was over 85 days during the summer (July – Aug 2008)
months. The simulations have focused on a 40 day period when conditions were favorable
for resuspension events close to the sampling locations.
Results show that resuspension can explain background concentrations better than just
the outfall dynamics. Resuspension might be an important secondary source of EC contamination, depending on the bacterial survival and re-growth rate in the sediment. Using the
linear isotherm model to calculate the attached fraction, the fraction of bacteria attached to
sediment in the water column was found to be highly variable with an average of 0.19 in the
offshore and 0.37 in the nearshore for an attachment coefficient KD = 1.

6.2

Introduction

Contaminant levels exceeding acceptable levels result in beach closures due to human health
considerations (Pruss, 1998; Rabinovici et al., 2004). Water samples take approximately 24
hrs to process and can be ineffective in predicting water quality. It is therefore necessary to
improve our ability to predict beach contamination levels using numerical models. Surfacerunoff and discharge from CSO outfalls are the main sources of contamination at beaches on
Lake Michigan (Dorfman and Rosselot, 2010). Transport of contaminants in the nearshore is
determined by nearshore hydrodynamics. Various biotic and abiotic variables also result in
die-off/inactivation of indicator bacteria as they are transported through the water column.
Furthermore, the sources are often unknown (Boehm et al., 2004b, 2003) and mechanisms
such as sediment resuspension also contribute to elevated levels of indicator bacteria at
135

beaches (Whitman et al., 2003). Bacteria attach themselves to sediment particles and settle
into the sediment layer. The attachment and detachment processes are controlled by the
nature of the bacterium, which can be gram-negative or gram-positive, as well as pH, ionic
strength, salinity and sediment characteristics. Effects of these variables on the attachment
of gram-negative bacteria such as Escherichia coli (EC) are well-documented in the literature
(Ginn et al., 2002; Guber et al., 2005; Li and McLandsborough, 1999; Lytle et al., 1999). With
a high nutrient concentration, lack of predators and little sunlight, the sediment provides a
relatively hospitable environment for survival and/or growth to occur. Resuspension events
result in the bacteria being re-introduced into the water column.

Settling is a major contributor to the removal of indicator bacteria from the water column
(Thupaki et al., 2010). In quiescent water, settling rates depend on the Stokes velocity which
is a function of particle size. Settling associated with indicator bacteria in the free-swimming
or planktonic state is negligible due to their small size (1 µm–2.5 µm)(Bergey and Breed,
1994). Motility in chemotactic bacteria can be considered a net effective diffusive flux. However, this is negligible when compared to turbulent diffusion in environmental flows. Settling
therefore, affects only the sediment and bacteria in the attached phase and studies (Soupir
et al., 2008; Characklis et al., 2005) have shown that EC display preferential attachment to
sediment particles between 3 µm and 63 µm. The ratio of attached to unattached bacteria in
the water column under freshwater conditions is a linear function of the suspended sediment
concentration (Guber et al., 2005). The value of the slope is denoted by the attachment
coefficient (KD ). However, the relative concentrations of bacteria and suspended sediment
strongly affect the attached fraction (Lindqvist and Enfield, 1992). Non-linearity has also
been observed in the presence of organic material such as manure (Guber et al., 2005). For
136

the same concentration of bacteria in the water-column, as the suspended sediment concentration reduces, availability of attachment-sites becomes the determining factor and the
concentration of attached bacteria plateaus (Chapra, 1997). The value of the attached fraction, therefore, is variable and not a constant as is usually assumed (Chapra, 1997; Guber
et al., 2005). The value is also highly transient and the time-scale for this process to reach
equilibrium are on the order of hours to days (Chapra, 1997). This is comparable to the
time-scale of important processes in nearshore hydrodynamics , where flow reversals can
completely change the direction of flow in a matter of a few hours.

Settling leads to the temporary removal of bacteria from the water column resulting
in only an apparent reduction in the concentration of bacteria. Nutrient-rich sediments
also provide a safe growth environment (Savage, 1905; Roper and Marshall, 1979; LaBelle
et al., 1980; Davies et al., 1995; Desmarais et al., 2002) and can act as sources during
resuspension events. Survival and re-growth of bacteria have in fact been recognized as
important processes in the sediment in tropical watersheds (Hardina and Fujioka, 1991;
Fujioka et al., 1998), foreshore sand in surf zones (Whitman and Nevers, 2003), and marine
wetlands (Sanders et al., 2005). In the nearshore region, the combined action of waves and
currents can cause the loosening of sediment particles resulting in their transport within
the water column (Gao et al., 2011). The settling velocity of flocculated cohesive-sediment
can be expressed as ws = adm b (Burban et al., 1990). Here, a = 9.6 × 10−4 (SG)−0.85 ,
b = − 0.8 + 0.5 log SG − 7.5 × 10−6

. The median floc-diameter (in cm) is given by

dm = (α0 /SG)0.5 , where S is the sediment concentration in gm/cm3 and G is the fluid
shear stress in dyne/cm3 . The floc-size for suspended sediment was not calculated, however,
these relations were used to arrive at approximate values for estimating the final parameters
137

used in the numerical model. Bacteria attached to sediment particles are resuspended into the
water column and transported by the currents. Southern Lake Michigan is a low wave-energy
environment with a mean wave height of about 0.2 m during the summer months. Most of
the large sediment-resuspension events are due to storms in winter and spring months (Eadie,
1996). Resuspension events close to the shoreline are more common due to the shallow waters
and wave action in the surf zone. Inactivation due to solar insolation is the major contributor
to net inactivation of EC in the water column (Thupaki et al., 2010). Resuspended sediment
in the water column also affects water quality and sunlight penetration into the water column
thereby increasing the survivability of EC in the water column. The interaction between
sediment concentration and EC concentrations is complex and highly variable.
The objectives of this chapter are to develop and test a coupled sediment resuspension
and transport model that simulates the interactions between EC and sediment. Variability
of the attached fraction will be assessed and observations of EC and hydrodynamics will
be used to compare with results from a numerical model to determine the importance of
sediment-resuspension on bacterial fate. The contribution of resuspended bacteria to the
overall levels in the water column will be quantified and the role of sediment as a source of
EC will be assessed.

6.3
6.3.1

Methods and Material
Study Site

Detailed descriptions of the site and observation methods collected have been included in
Chapter 3 (Page 39). In all, four acoustic Doppler current profilers (ADCPs) were used
138

to measure hydrodynamic variables. Wave height, period and direction were measured at
offshore and nearshore locations as well. Suspended sediment concentration in the water
column was calculated from echo intensity recorded by the 1200 kHz RDI-Sentinel ADCP
located at S (Figure 2.1).

6.3.2

Hydrodynamic and Wave Models

Lake hydrodynamics was simulated using the Princeton Ocean Model (POM) as described
earlier in Chapter 3. Wave climate is mild in Lake Michigan with mean wave height of
about 0.2 m in southern Lake Michigan during the summer months. However, sediment
resuspension rates are significantly affected by wave-induced bottom shear stress. Wave
conditions were simulated using a parametric wave model that has been described along
with the hydrodynamic model in Chapter 2 (Page 24 – Page 34).

6.3.3

Sediment-bacteria Model

Indicator bacteria, such as EC, in the water column are transported by the currents and
undergo biological processes that result in the inactivation and/or die-off. These processes
have been included in Equation 6.1, which can be used to model the various processes
that impact the concentration of indicator bacteria in the water column. Here, CT is the
net EC concentration in CFU/m3 (net concentration of bacteria (CT ) = concentration of
free-swimming bacteria (CD ) + concentration of attached bacteria (CP )). The horizontal
turbulent mixing value KH has been calculated using the Smagorinsky closure model as
139

described in Chapter 2.

∂C
∂C
∂C
∂CT
∂
+u T +v T +w T =
∂t
∂x
∂y
∂z
∂x
+

∂CT
∂C
∂
+
KH T
∂x
∂y
∂y
∂FSC
∂CT
KV
− knet CT −
∂z
∂z

KH
∂
∂z

(6.1)

knet = kI I0 (t)e−ke z + kd θT −20

(6.2)

FSC = ws CP

(6.3)

Here knet is the net inactivation rate for bacteria in the water column, kI is the EC inactivation rate due to DNA damage caused by sunlight, I0 is the intensity of sunlight, ke is the
extinction coefficient for sunlight in the water column, kd is the dark death rate for EC, and
θ is the temperature dependence for EC inactivation rate. The solar extinction coefficient
ke is calculated using the suspended sediment concentration and the relation presented by
Chapra (1997). FSC is denotes the settling flux. Resuspension and settling fluxes at the
interface between sediment layer and water column are calculated to determine the bottom
boundary condition shown in Equation 6.4. Diffusion across the sediment-water interface is
assumed to be zero and concentration of bacteria attached to suspended sediment (CP ) is
calculated at each time-step using Equation 6.7. A zero flux boundary condition is applied
at the top surface of the water column. The bottom boundary condition appears as shown

140

below.

∂CT
= FSC − FRC
∂z
τ
FSC = max 0, ws CP 1 − bot
τcr,d

(6.4)

w s CP + K V

(6.5)

FRC = FRS CSed

(6.6)

The settling flux of EC in the water column (FSC ) can be calculated using Equation 6.3
where, ws is the settling velocity, h is the depth and CP is the concentration of EC in
attached phase. Resuspension of bacteria in the sediment layer is represented as a source
term (FRC ) and calculated at the sediment layer-water column interface using Equation 6.4
where (FRS ) is the resuspension flux for suspended sediment from the bottom sediment
layer and CSed is the mass-specific concentration of EC in the bed-sediment. The net
inactivation rate knet is defined as shown in Equation 6.2. It is modeled on Equation 5.2 but
couples the sunlight extinction rate to the computed, spatially variable, suspended sediment
concentration (S). Following Chapra (Chapra, 1997) and assuming that bacteria attach to
sediment particles indicated by the partition coefficient KD , we can calculate the attached
and free-swimming fractions of the bacteria using:

fP =

KD S
;
1 + KD S

CP = fP CT

fD =

1
;
1 + KD S

CD = fD CT

fP + fD = 1;

KD = ζ/CD

CT = CD + CP = CD + SKD CD
141

CP = Sζ

(6.7)

Here, fP and fD are the fraction of EC in particulate (attached) and planktonic (freeswimming) states. The value of the partition coefficient (KD ) has been determined by
experiments to be around 10-4 - 10-6 L/mg for saturated groundwater flow (Gantzer et al.,
2001; Lindqvist and Enfield, 1992; Reddy and Ford, 1996). But, values of 0.01 L/g to 10
L/g have been used by models to describe the attached fraction in fresh water systems (Bai
and Lung, 2005; Gao et al., 2011). ζ is the mass-specific concentration of EC attached to
suspended sediment in the water-column, with units of CFU/kg (Chapra, 1997), while CP is
the volume-specific concentration of EC attached to suspended sediment in the water column
and has units of CFU/m3 .

∂S
∂S
∂S
∂
∂S
+u
+v
+w
=
∂t
∂x
∂y
∂z
∂x
+

∂
∂z

KH
KV

FSS = ws S

∂S
∂x

∂S
∂z

∂
∂S
KH
∂y
∂y
∂FSS
−
∂z
+

(6.8)

(6.9)

Considering the turbulent nature of flow in the nearshore and the low Stokes velocity for a
particle the size of a bacterium, settling losses for unattached bacteria have been neglected.
Fine grained sediment is subject to flocculation and greater settling velocity. The attached
fraction of the total bacteria is also expected to settle at the rate determined by sediment
floc-size. Suspended sediment concentration in the water-column was modeled using Equation 6.8. Outflow from rivers and streams can be a significant source of suspended sediment
in nearshore waters. Wave action at the swash zone can also result in a distributed loading
along the shoreline of southern Lake Michigan (Lee et al., 2007). Since the aim of this study
is to examine the role of sediment on bacteria, resuspension is treated as the only source of

142

sediment concentration in the water column. Rate of settling FSS is defined in Equation 6.9
where, S is the suspended sediment concentration (SSC) in kg/m3 , and ws is the settling
velocity of suspended sediment particles. Settling velocity is the same as described before.
At the bottom boundary, settling and resuspension fluxes are implemented by applying
the boundary condition shown in Equation 6.10. Diffusion KV across the water-sediment
interface is assumed to be zero. A zero-flux boundary condition is used at the water surface.

∂S
= FSS − FRS
∂z
τ
FSS = max 0, ws S 1 − bot
τcr,d
w s S + KV

FRS = max 0, M

τbot
τcr,ero

−1

(6.10)
(6.11)
(6.12)

Here, τbot is the net bottom shear stress, τcr,ero is the critical shear stress for erosion,
τcr,d is the critical shear stress for deposition and M is the erodibility coefficient in kg/m2 .s
(Rijn, 1989). Based on the description in (Krone, 1962) and (Mehta and Partheniades, 1975)
deposition and erosion rates of cohesive sediments can be described using Equation 6.10 at
the boundary.
The amount of sediment available for resuspension on the lake bottom depends on settling and erosion fluxes. The mass of sediment in the sediment layer is calculated using
Equation 6.13. Here, msed is the mass of bed sediment per unit area in kg/m2 , FSS is the
depositional flux, and FRS is the sediment flux due to resuspension. Mass is conserved since
erosion and settling fluxes are used to define the boundary condition for the water column in
Equation 6.10. As additional sediment layers are deposited on the lake bottom, weight of the
sediment and the water column above, can result in sediment compaction. The nearshore
143

region in southern Lake Michigan is, however, a low depositional environment (Lee et al.,
2007) and sediment compaction and burial dynamics have not been considered in view of
the short time-scales of interest in our modeling.

∂msed
= FSS − FRS
∂t
τbot = τc 2 + τw 2

1/2

(6.13)

(6.14)

The net bottom shear stress is due to the combined action of currents and waves. This is
calculated from the results of the wave and hydrodynamic model using Equation 6.14. Nonlinear interactions between current and waves have not be included, since the shear stress
due to currents was found to be less than 5% of the total bottom shear stress in southern
Lake Michigan (Chapter 5). Shear stress due to current (τc ) has been calculated using the
empirical formula, Equation 6.15. The bottom shear coefficient Cb was calculated using
Equation 6.16, assuming a logarithmic bottom boundary layer.

1
τc = ρCb u2 + v 2
2

Cb =

2
κ
ln (∆z/2z0 )

(6.15)

(6.16)

Here, κ is the von Karman constant and the roughness height, zo was set to 0.8 mm or
approximately four times the mean size of sand particles (Lee et al., 2007). Wave action is
considerably more important than effect of currents when calculating the net bottom shear
stress. In southern Lake Michigan, bottom shear due to wave action accounts for more than
90% of the total shear stress. Using the linear wave theory, the bottom shear stress in shallow

144

lakes due to waves (τw ) can be calculated using Equation 6.17 (Luettich et al., 1990).
1
τw = ρfw Ub 2
2

(6.17)

The wave friction factor fw has been calculated using Equation 6.18 and the maximum
orbital velocity Ub and the maximum orbital amplitude Ab , are given by Equation 6.19.

fw = 2

Ub Ab −0.5
ν

1
πH
; Ab =
Ub =
T sinh (2πd/L)
2 sinh (2πd/L)

(6.18)

(6.19)

Here, d is the water depth and L is the wavelength. Indicator bacteria in the attached state
(CP ) undergo settling and can survive/grow in the sediment layer. The concentration of
bacteria in the bed sediment (CSed ) was modeled using Equation 6.20.
∂CSed
F
= SS (ζ − Csed ) − knet CSed
∂t
msed

(6.20)

Here, Csed is the concentration of bacteria in the sediment in CFU/kg and ζ has units of
CFU/kg and is defined as the mass-specific concentration of indicator bacteria attached to
sediment suspended in the water column. Following the description of (Sanders et al., 2005)
and (Gao et al., 2011), FIB resuspension at the bottom boundary is implemented using
Equation 6.4.

145

6.4
6.4.1

Results
Hydrodynamic Model

The Princeton Ocean Model (POM) (Blumberg and Mellor, 1987) is a three-dimensional hydrodynamic model that solves the hydrodynamic primitive equations (Equation 2.3–Equation 2.5).
These equations resolve the mean (Reynolds averaged) flow field and parameterize the eddy
diffusion using the Smagorinsky eddy-viscosity model (Smagorinsky, 1963) in the horizontal
directions. Eddy viscosity is assumed to be isotropic in the horizontal directions as shown
in Equation 2.3 and Equation 2.4. The eddy viscosity in the vertical direction is calculated
using the Mellor-Yamada 2.5 level turbulence closure model (Mellor and Yamada, 1982). A
finite-difference orthogonal grid with a 2 km resolution was used to resolve large-scale lakewide circulation. Small-scale features close to the shoreline were resolved using a nested-grid
model with a 100 m grid resolution. Nesting was one-way and information from the large
scale lake-wide model was interpolated to provide boundary conditions for the nearshore
model. The computational domain for the lake-wide and nearshore models are shown in
Figure 2.6. Details of the hydrodynamic model including the numerical methods and equations solved are described in Section 2.2.

6.4.2

Wave Model

Results from the wave model were compared with the significant wave height observed at
locations M (offshore) and S (nearshore) (Figure 2.1). As shown in Figures 6.1 and 6.2, the
significant wave height HS is under-predicted by the model. The error increases as we move
closer to the shoreline as shown by the comparison at location S, which is in the nearshore.
146

However, large resuspension events such as the ones on JD 158, JD 182 and JD 185 are
described by the wave model. A modeling exercise testing different wave models (Liu et al.,
2002) has shown that the GLERL wave model is able to predict wave climate accurately in
nearshore regions. The quality of results from a wave model is extremely sensitive to the wind
conditions. A 10% error in wind velocity could result in as much as 20% error in predicted
wave height and up to 50% error in predicted wave energy (Komen et al., 1994). Considering
that the wave model performs better in the offshore, errors in wind speeds are less likely to
be the cause of model error. However, improvements in interpolated wind-stresses used by
the wave model, might be able to reduce error in predicted wave heights.
Observations made at a distance of 0.35 km from the shoreline, at locations N1 and N2
were used to assess the model performance very close to the shore at depths of approximately
5 m. Figure 6.3 and Figure 6.4 further confirm that model performance deteriorates as we
approach the shoreline. This could be due to the fact that nearshore and shallow water
effects, such as refraction and diffraction, on wave propagation are not explicitly described
by the wave model.
Considering that the primary objective of this study is to examine the importance of
sediment-bacteria interactions and not wave-current interactions, results from the wave
model have been used to predict sediment resuspension events. A 15 day period (JD 180 –
JD 195) was chosen for detailed study because of two major resuspension events that were
observed on JD 182 and JD 185. The role of sediment on bacterial contamination at beaches
is examined during this period. The observed wave direction and power-spectrum shown in
Figure 6.5 and Figure 6.6 show that the waves during the resuspension events were from a
NNW to NNE direction. This is as expected given the orientation of the shoreline, since
147

Wave Height
2
Observed
Model

HS (m)

1.5

1

0.5

0
150

160

170

180

190

200

Figure 6.1: Significant wave height compared at location M

Wave Height
2
Observed
Model

HS (m)

1.5

1

0.5

0
150

160

170

180

190

Figure 6.2: Significant wave height compared at location S

148

200

Wave Height
2
Observed
Model

HS (m)

1.5

1

0.5

0
172

173

174

175

176

177

178

179

Figure 6.3: Wave height compared at nearshore location N1

Wave Height
2
Observed
Model

HS (m)

1.5

1

0.5

0
172

173

174

175

176

177

178

Figure 6.4: Wave height compared at nearshore N2

149

179

m2/√Hz.deg
9

0

0.5 Hz

330

0.4 Hz

30

0.3 Hz

300

6
60

3
1

270

90

120

240

210

150
180

Figure 6.5: Directional power spectrum at location S during the resuspension event on Julian
Day 182
the fetch available in these directions is the greatest and results in the largest waves. Low
frequency swells also develop due to non-linear interactions between the wave components
and are the result of waves generated a long distance away.

6.4.3

Sediment-bacteria Model

The suspended sediment concentration (SSC) in the water column was calculated using
backscatter values measured by the ADCP at location S. The minimum SSC is about 2
mg/L and the maximum is less than 10 mg/L over the entire period of observation. This
150

330

m2/√Hz.deg
9

0

0.5 Hz
0.4 Hz

30

0.3 Hz

300

6
3

60

1

90

270

120

240

210

150
180

Figure 6.6: Directional power spectrum at location S during the resuspension event on Julian
Day 186

151

is consistent with the past observations that indicate large resuspension plumes in Lake
Michigan are associated with storms generally during Winter and Spring. The observed
time-series has been compared with SSC results from the model in Figure 6.7. The SSC
transport and resuspension model is accurate only in the simulation period JD 180 – JD
195. The model was initialized to a constant sediment mass and the model was allowed to
spin-up to give better comparisons. This process takes a long time for a sediment model
since the time-scale for changes in bottom sediment mass is much larger than that observed
in nearshore hydrodynamics. A thin layer of sediment is consistent with other models (Lee
et al., 2005a) and observations in the field that have shown that in Lake Michigan, at depths
of less than 30 m, sediment deposition rate is low with a fine-grained sediment concentration
of less than 10% in the bottom sediment. The maximum depth in the domain is 35 m and
can be described in entirety as a low-depositional environment.

A parameter estimation exercise was conducted to find out the values that provided
the optimal results. The code was optimized for the High-performance Computing Center
(HPCC) at Michigan State University. However, the entire variable space could not be
explored due to the computational time required for such a task. The initial sediment mass
of 20 gm/m2 was used with a sediment settling velocity of 5 m/day. SSC concentration
is particularly sensitive to the critical shear stresses for erosion and deposition. Lee et al.
(2005b) calculated the critical shear stress for erosion and deposition in deeper waters to
be 0.05 N/m2 and 2.0 N/m2 respectively. Results presented in Figure 6.7 used values of
0.1 N/m2 and 2.0 N/m2 for critical erosion and deposition stress. The difference can be
attributed to the fact that the model has been optimized using observations at a depth of
10 m which experiences higher mean bottom shear stress. Sediment erodability rate (M ) is
152

10
0

SSC(mg/L)

30

`spin-up’
time

Observed
Model
comparison

(c)

Model

10

Model

10

30

170
180
190
Julian Days 2008
(d)

Model

20
10
0

170
180
190
Julian Days 2008

(b)

20

0

170
180
190
Julian Days 2008

20

0

SSC(mg/L)

20

(a)

30

SSC(mg/L)

SSC(mg/L)

30

170
180
190
Julian Days 2008

Figure 6.7: (a) Suspended sediment concentration (SSC) compared with observation at
location S; (b)-(d)Suspended sediment concentration at the Ogden Dunes Beaches (OD1 –
OD3)

153

typically between 5x10-4 and 1x10-5 kg/m2 .s (Chao, 2008) and a value of 5x10-5 kg/m2 .s
was required to obtain results presented in Figure 6.7.
Deposition and resuspension rates are higher close the coast where the current and wave
conditions would be most significant. It is however clear that conditions represented in the
10 day long simulation are representative of summer months and a long-term simulation
would be required to calculate morphological trends in the bathymetry in southern Lake
Michigan.
The comparison between observed and simulated EC values for the period JD 180 – JD
195 is shown in Figure 6.8. In this observation record, conditions warranting beach closure
(350 CFU/100mL) were observed on only one occasion. The peak EC values have been
accurately predicted by the model. Comparing concentrations at source (Burns Ditch) and
beaches (OD1–OD3), it is clear that outfall dynamics of the Burns Ditch plume dominates
the observed concentration at the Ogden Dunes beaches. However, several observations were
not adequately described by considering only the Burns Ditch outfall.
Comparisons with observations during the JD 180 - JD 190 period shown in Figure 6.8
indicates that while the most of the peak EC values are reliably predicted by the model,
model comparisons at OD1 (farther from the outfall) deteriorates. The vertical variability in
concentration of EC is also shown in the figure to be highly spatially variable. Contaminant
in the nearshore is well-mixed vertically, while there is a considerable difference in the surface
and bottom layer concentrations as we move offshore.
In order to assess the impact of sediment-bacteria interactions on observed EC values,
Figure 6.9 compares observed concentrations of indicator bacteria (EC) with results from
a model that included sediment-bacteria interactions. All parameters used to define die154

5000

500
E. Coli (CFU/100mL)

E. Coli (CFU/100mL)

4000
3000
2000
1000
0
165

170

175

180

185

190

400
300
200
100
0
165

195

170

Julian Days 2008

180

185

190

195

500
Observed
Model

400
300
200
100

170

175

180

185

190

Observed
Model

(d)
E. Coli (CFU/100mL)

(c)
E. Coli (CFU/100mL)

175

Julian Days 2008

500

0
165

Observed
Model

(b)

(a)

195

Julian Days 2008

400
300
200
100
0
165

170

175

180

185

190

195

Julian Days 2008

Figure 6.8: EC concentration at (a) Burns Ditch (the source) and at the beach sites (b) OD1,
(c) OD2, and (d) OD3. Results are from model simulating the transport and inactivation
without sediment-bacteria interactions.

155

6000

500
(b)
E. Coli (CFU/100mL)

E. Coli (CFU/100mL)

(a)
5000
4000
3000
2000
1000
0

Model
Observed

100

170
180
190
Julian Days 2008

(d)
E. Coli (CFU/100mL)

E. Coli (CFU/100mL)

200

500
(c)

300
200
100
0

300

0

170
180
190
Julian Days 2008

500
400

400

Model
Observed

400
300
200
100
0

170
180
190
Julian Days 2008

Model
Observed

170
180
190
Julian Days 2008

Figure 6.9: EC concentration at (a) Burns Ditch (the source) and the beach sites (b) OD1,
(c) OD2, and (d) OD3. Results are from model simulating the transport, inactivation and
sediment-bacteria interactions.

156

Location
OD1
OD2
OD3

RMSE
(without EC resuspension)
1.7033
1.5700
1.0155

RMSE
(with EC resuspension)
0.9538
1.2103
1.0106

Table 6.1: RMSE values between observed and modeled EC values at the Ogden Dunes
Beaches

off/inactivation of bacteria in the water column were kept unchanged. Parameters used
to describe inactivation and loss processes of EC in the water column were obtained from
the earlier sensitivity and budget analysis presented in Chapter 5 and in Thupaki et al.
(2010). Solar inactivation rate (kI ) of 1x10-8 /sec, dark death rate or base mortality (kD )
of 1x10-9 /sec, sediment-attachment coefficient (KD ) of 1.0 L/gm were used in the results
presented in Figure 6.9. Extinction of sunlight in the water-column was calculated using
the suspended sediment concentrations computed by the model using the relation (ke =
0.55m) given by Di Toro et al. (1981), where m is the suspended sediment concentration
in mg/L. Clearly, model performance improves after including the effect of sediment on EC
concentrations in the water column.
Model accuracy can be determined by calculating the RMSE (Equation 6.21) values
between EC values observed and predicted by the model at the Ogden Dunes beaches.
RMSE values for the numerical model with and without sediment-bacteria interaction are
given in Table 6.1.

RM SE =

1
N

N

log10 Csim − log10 Cobs 2

(6.21)

i=1

where, Csim , Cobs are the simulated and observed EC concentrations
Concentration of EC in the attached phase at a nearshore location and an offshore location
157

1

fp = CP/CT

(a)

Top
Bottom

0.8
0.6
0.4
0.2
0
165

170

175

180
Julian Days 2008

185

1

fp = CP /CT

(b)

190

Top
Bottom

0.8
0.6
0.4
0.2
0
165

170

175

180
Julian Days 2008

185

190

Figure 6.10: Attached fraction (fp ) for EC in the top and bottom layers of the water column
at (a) offshore (S) and (b) nearshore (OD1) locations

158

is shown in Figure 6.10. Results presented in the figure are calculated using an attachment
coefficient (KD ) of 1.0 L/g and the linear isotherm. As shown in Equation 6.7, the attached
fraction (fp ) is a function of the concentration of suspended sediment (S). As expected, the
SSC concentration is more variable in the deeper waters (offshore). In shallower waters, the
water column is well-mixed with littler variation in the vertical. The top layers with lower
SSC concentration presented fewer attachment sites for the bacteria and therefore have lower
fraction of EC in the attached state. A higher concentration of SSC in the water column
results in a greater fraction of EC in the attached state. This also increases the rate of
removal of EC from the water column due to settling. The mean value of fp in the offshore
was 0.19 in the top layer and 0.31 in the bottom layer for the simulation period shown in
Figure 6.10. In the nearshore, the value of fp in the water column showed little variation and
was 0.37 in the top layer and 0.39 in the bottom layer. This is consistent with the low SSC
values in the offshore waters, which result in a smaller attached fraction. Since unattached
bacteria settle at a negligible rate, the low attached fraction in offshore waters results in a
lower settling rate in the low turbidity environment found in offshore waters. Settling rate of
EC in the free-swimming state is negligible. Only the EC in attached phase settles from the
water column at any significant rate. Therefore, accurate modeling of the attached-fraction
is necessary to correctly calculate EC loss due to settling.

Under favorable conditions, EC settling out of the water column can survive and continue
to grow in the sediment. The EC population in the sediment layer can then act as secondary
source of contamination. In the results presented here, growth rate in the sediment and
the initial concentration of EC in the sediment were set to zero. It is clear that despite
a zero growth rate, sediment concentration of EC rises rapidly due to settling of EC in
159

the attached state. High nutrient concentration and beneficial conditions could result in regrowth of bacteria in the sediment, thereby increasing the importance of sediment as a source
of EC in the nearshore. A direct comparison between the two models (with and without
sediment-bacteria interactions) is shown using probability plots in Figure 6.11. At all three
beach sites, the model with the sediment processes describes the observed data better.

6.5

Discussion

The fate of contaminants and sediment in the nearshore is determined by hydrodynamics
close to the shore. Results from the three-dimensional circulation model used in this study
show that small-scale features in nearshore hydrodynamics can be accurately modeled using
a nested grid numerical model. While the coarse grid model is unable to describe small-scale
features close to the shore, the 100 m fine-grid model is able to resolve details by making
use of the results from the coarse grid model as boundary conditions at the interface.
The semi-empirical parametric wave model used in this study was developed by (Donelan,
1977) and modified by (Schwab et al., 1984) to create the GLERL wave model. This model
was successfully used to predict wave characteristics in the Great Lakes (Schwab et al., 1984),
(Schwab et al., 1986) and (Liu et al., 2002). Comparisons with well known third generation
wave models presented in (Liu et al., 2002) show that the GLERL wave model is an accurate
and reliable wave model. Wave climate in the offshore and nearshore was observed using
ADCP deployments. Comparisons with results from the numerical wave model show that
performance of the model was acceptable in deeper waters (Figure 6.1). However, errors
increase as we get close to the shoreline, as shown in Figures 6.2, 6.3, and 6.4. This could
be due to the lack of explicit implementation of refraction and diffraction processes in the
160

E. coli Concentration (CFU/100 mL)

250
200
150

(a) OD1

100
50
0
.1

E. coli Concentration (CFU/100 mL)

Observed
No Sediment Model
With Sediment Model

1

1200

5 10 2030 50 7080 90 95 99 99.999.99
(b) OD2

1000
800
600
400
200
0
.1

1

5 10 20 30 50 70 80 9095 99 99.999.99

E. Coli Concentration (CFU/100 mL)

1200
(c) OD3

1000
800
600
400
200
0

.1

1

5 10 2030 50 7080 9095 99 99.999.99
Probability (%)

Figure 6.11: Comparison between the two models (with and without sediment processes) at
the beach sites
161

governing equations solved by the model. Errors in interpolated wind fields can also result
in large inaccuracies in results from wave models (Komen et al., 1994). However, model
predictions deteriorate as we move to shallow waters confirming that the use of deep water wave approximation of the dispersion theory might be the main source of error. The
use of ADCPs for calculating wave parameters can also introduce significant uncertainties.
ADCPs make use of the pressure (P) and velocity (U, V) measurements to calculate the
surface elevation and significant wave height. Time period is inferred indirectly from the
calculated power spectrum. Measurements of wave direction can therefore include significant measurement uncertainties. Studies that focus on accurate modeling of wave-current
interactions and nearshore processes would have to opt for a more detailed wave model.
Improvements in the nearshore bathymetry might also be required to take full advantage of
a more detailed wave model. In order to assess the importance of sediment on observed EC
concentration at beaches, SSC was compared between model and observations at location S.
Figure 6.7 shows that the model performs well between JD 180 and JD 195 after the initial
“spin-up” time. However, during the initial periods of the simulation the model is unable
to predict SSC resuspension accurately. This could be due to the limited performance of
the wave model as shown by comparisons between observed and simulated wave heights in
Figure 6.3 and Figure 6.4. Since, the net bottom shear stress is is dominated by the bottom
shear stress due to wave action, improvements in the numerical wave model are expected to
significantly increase accuracy of the SSC transport and resuspension model as well. The
period between JD 180–JD 195 is characterized by two resuspension events, on JD 182 and
JD 185. Observations during this period show that both these resuspension events are due
to waves coming in from a northerly direction as shown by the direction power spectrum

162

shown in Figure 6.5 and Figure 6.6.
The locations close to the shore reveal a more dynamic environment with large sediment
fluxes. This is consistent with the fact that bottom shear stresses are larger in shallow waters.
Sediment scouring due to limited sediment source as well as the large resuspension flux is
also observed at all three nearshore locations but only once at location S. On average, the
nearshore location could be classified as a low-depositional environment, while the deeper
waters experienced more sediment deposition.
The spatial variability in sediment-flux shows that the deeper regions are morphologically
stable and this is shown by the final sediment mass being about the same as the initial
sediment mass. Much of the region close to the shoreline is a high depositional region.
The presence of a shallow sandbar a few hundred meters off the coast can also be observed
and is consistent with bathymetry measurements using LIDAR and SONAR. Long term
simulations will, however, need to be run before any general assessment of the general trends
in bathymetry can be made. These observations are only for typical summer conditions and
depositional rates over other times of the year might be different. Lake Michigan experiences
annual storms in the winter and spring seasons (Eadie, 1996).
Results from the EC inactivation and transport model were compared with EC observations at the Ogden Dunes beaches in Figures 6.8 and 6.9. RMSE values are given in Table 6.1
and show that accuracy of the numerical model declines as we move farther from the outfall
(Burns Ditch). It clear that the major source of EC contamination in the nearshore is the
Burns Ditch outfall. However, some of the observations are not adequately described by the
model. A simple transport and first-order inactivation model (without sediment-bacteria
interactions) is able to predict observed EC reasonably well close to the outfall (OD3), but
163

as we move further away from the mouth of the outfall (OD2 and OD1), the model accuracy
sharply declines. Sites closer to the outfall are dominated by the outfall dynamics, but sites
farther from the outfall are dominated by the sediment processes. EC in the attached state,
settle into the sediment layer along with sediment particles. The sediment layer is usually
nutrient-rich and provides a more hospitable environment than the water column. Bio-films
formed by bacteria in the sediment are also associated with higher bacterial growth rates.
Sediment can therefore act as a secondary source of bacteria observed at beaches (Sanders
et al., 2005). High bottom shear stress events can result in resuspension of bacteria from the
sediment layer, back into the water column.

Comparisons between the observed EC concentrations and results from the numerical
model that included sediment-bacteria interactions, indicate that the model is able to predict most of the observed EC peaks. RMSE values for the model predictions, with and
without including sediment-bacteria interactions are given in Table 6.1. Clearly, the model
performance improves when we include sediment-bacteria interactions. Sediment resuspension events result in introduction of EC into the water column, where it is transported by
the currents. Model improvements in Figures 6.9 and 6.11 show the importance of sediment
as a source of EC into the water column especially away from the outfall. EC resuspended
from the sediment could be a significant factor contributing to higher EC concentrations at
beaches. Bacteria survival and growth rate in the sediment is a subject of active research.
Bacteria in the sediment can be attached to vegetation or sediment and can also secrete extracellular polymers to increase survival rates (Decho, 2000). It should be pointed out that
the results shown here assume that there is no net growth rate for the EC in the bottom
sediment layer and that the rate of inactivation is the same in water and the sediment. At
164

the Ogden Dunes beaches the major contamination events are determined by the outfall
dynamics. However, resuspended EC does contribute to overall concentrations of EC in the
water column. This effect becomes particularly noticeable away from the outfall at shown in
Figure 6.11. Under conditions that favor resuspension due to wave and current action resuspended EC can significantly impact water quality. Results of RMSE presented in Table 6.1
show that the model performance without sediment deteriorates as we move further from
the outfall (Burns Ditch). Location OD3 is closest to the outfall and OD1 is furthest from
the outfall. The importance of sediment-bacteria interactions also increases in importance
as we move away from the outfall. Closer to the outfall, the contaminant plume dynamics
dominates all other secondary sources of contamination. This is as expected. It was also
observed that the importance of sediment as a source of EC is sensitive to the resuspension
rate as well as the EC concentration in the sediment. For the purposes of this study, it was
assumed that the initial EC concentration in the sediment was zero and settling from the
water column was the only source of EC for the bottom sediment. However, sediment in the
surf zone is known to be a major source of EC (Whitman and Nevers, 2003; Whitman et al.,
2003). Parameter estimation by varying initial concentration of EC in the sediment would
improve RMSE values presented in Table 6.1, but this is not attempted here.

Removal of EC from the water column due to settling is a major part of the net inactivation rate of EC in the water column (Thupaki et al., 2010). Given the size of an EC cell
(∼2 µm) and the highly turbulent nature of flow in the nearshore, settling rates of bacteria
in the free-swimming state is negligible. Accurate modeling of the attached and unattached
fractions of bacteria in the water column is therefore extremely important for assessing the
overall inactivation rate of EC. Figure 6.10 shows the highly variable nature of the concen165

tration of bacteria attached to sediment particles. Assuming the linear isotherm and using
a KD value of 1.0 L/g the mean value of attached fraction in nearshore waters was found
to be 0.37 over the simulation period. Value in the offshore was lower and showed a much
higher variability in the vertical with a mean values of 0.19 in the top layer and 0.31 in the
bottom layer. This implies that EC losses due to settling are lower in the clearer offshore
waters than in the nearshore region.

6.6

Conclusion

A nested-grid hydrodynamic model was coupled with a semi-parametric wave model to simulate hydrodynamics, sediment transport and sediment-bacteria interactions in the nearshore
region of southern Lake Michigan. EC observations at three beaches and measurements of
suspended sediment concentration at a nearshore location were used to verify the numerical
models. Wave and current measurements at ADCPs deployed at offshore and nearshore
locations were also compared with the hydrodynamic and wave models. The mean wave
height in Lake Michigan was found to be ∼0.21 m in the nearshore region of southern Lake
Michigan, with occasional episodic events with significant wave height (HS ) greater than
1 m. The semi-empirical wave model used in the study was able to describe wave climate
at locations upto 1 km (depth of approximately 10 m) from the shore. However, model
performance deteriorated closer to shore, due to the lack of shallow water processes in the
model description.
The plume dynamics of the Burns Ditch outfall simulated using the bacteria transport
and inactivation model for EC was able to predict some of the observed contamination events
at nearby beaches.
166

The accuracy of the model improved after including sediment-bacteria interactions into
the numerical model. Results show that resuspension can explain observed EC concentrations
better than just the outfall dynamics especially at sites far from the outfall. Resuspension
might be an important secondary source of EC contamination, depending on the bacterial
survival and re-growth rates in the sediment. Using the linear isotherm to calculate the
attached fraction (fp ), the fraction of bacteria attached to sediment in the water column
was found to be highly variable in the deeper offshore waters. Closer to the shore, fp was
almost constant over the water column.

167

Chapter 7
Conclusions and Recommendations
The aim of this study was to examine the factors affecting recreational water quality at
beaches in southern Lake Michigan. This was achieved using a combination of observational
techniques, model development and analysis of the observations and model results.
Nearshore hydrodynamics is controlled by energy and mass transfer from the large-scale
circulation. Different scales interact and energy is transferred along a cascade that results
in its eventual dissipation in small-scale processes. The energy cascade in the offshore shows
the importance of large-scale circulation and its role as a source of energy. The relative
importance of the inertial frequency closer to the shoreline indicates the presence of a friction
dominated boundary layer at least 1 km wide. This is consistent with other studies in the
Great Lakes region. Comparisons with model results are promising, with the energy cascade
being reproduced accurately in the offshore and nearshore regions. Errors appear to increase
as we move close to the shoreline due to increased importance of boundary effects and energy
losses due to small-scale processes.
Using wavelet decomposition it was shown that the dominant energy carrying scales in
168

the offshore are around the inertial frequency and about 0.1 hr-1 . This reduces as we move
closer to the shoreline and is about 0.01 hr-1 at a distance of about 0.35 km from the
shoreline. The model was able to predict the frequency of the energy peak in the offshore
accurately, but not in the nearshore. The magnitude of energy carried in the peak frequency
is also over-predicted consistently in the offshore and nearshore regions. Small-scale velocity
fluctuations represent less than 5% of the total energy. These are under-predicted by the
model and as a result can have significant impact on modeling dispersion and mixing.
With a 100 m grid resolution, processes in the 1 hr timescale should be adequately resolved by the nearshore model. However, model under-performance while describing tracer
transport is probably due to the inability to accurately represent the dissipation processes
in the nearshore. A more advanced turbulence closure model with explicit energy transport
equation or large-eddy simulating model would be able to better represent the energy cascade as well as the small-scale dissipation processes, which are essential to model transport
processes accurately in the nearshore region.
Observations of the hydrodynamic variables in the nearshore region show a great deal
of variation in the vertical direction. While the model is able to predict the mean flow
direction and magnitude accurately, layer-specific comparisons of the modeled and observed
velocities are not satisfactory within the top boundary layer. The other principal feature of
the hydrodynamic field in the coastal boundary layer, flow reversals, is accurately described
by the model.
Turbulent eddy-diffusion calculated using the Smagorinsky method was found to cause
excessive damping by averaging the small-scale fluctuations in velocity field. Eddy-viscosity
based turbulent scheme and the grid-size are two of the principal reasons for the model’s
169

inability to describe the high-frequency fluctuations in velocity. Comparisons with the hydrodynamic results from the 2 km grid model indicate that further improvements in the hydrodynamic description will need re-assessment of the horizontal turbulence closure scheme
as well as the top and bottom boundary layer descriptions.
A budget analysis of the different processes was conducted to determine the relative
importance of different processes. It was found that for a site affected by plume dynamics
from an outfall, dilution due to advection and diffusion was an order of magnitude higher
compared to the net loss processes due to biological processes and settling losses within the
water column. The magnitude of vertical mixing in the water column is controlled by the
degree of density stratification in the nearshore and is therefore dependent on site as well
as time of the year. Inactivation of bacteria due to solar insolation was the most important
loss process, however it was found that settling processes and sediment-bacterial interactions
have to be included to provide an accurate estimate of the importance of various EC loss
processes.
Finally, after including sediment-bacteria interactions in the biological model, it was determined that in the nearshore, sediment can act as a significant source of EC. The suspended
sediment concentration is highly variable and affects the sunlight penetration as well as loss
due to settling of the bacteria in attached phase. The importance of sediment-bacteria interaction is definitely site-dependent and requires detailed observation datasets at times when
wave and current conditions are favorable for resuspension events. The model with sedimentbacteria interactions was found to describe the EC concentrations better, especially at sites
farther away from the outfall.
This study has shown clearly that given the meteorological forcing and concentrations at
170

sources, it is possible to predict the concentration of indicator bacteria at different locations
in the nearshore region. The ultimate aim of such an exercise is to develop a tool that can be
used by beach managers to determine risks to beach-users. Several statistical methods are
being developed, however, process-based models have the potential to provide more accurate
predictions while describing contamination levels at beaches in addition to offering useful
insights into the key processes. Coupling a watershed model that makes use of precipitation
and land-use data to predict contaminant levels at the outfall can be undertaken to arrive at
a predictive model. Mixing in the nearshore due to shear-augmented diffusion and turbulent
dispersion is an order of magnitude higher than inactivation rates due to biological processes.
The Mellor-Yamada and Smagorinsky turbulence closure schemes are able to qualitatively
describe mixing rates, however, more advanced closure schemes should be tested to improve
model accuracy and to describe observed features (Figure 1.1) of outfall plume dynamics
including sharp interfaces.

171

APPENDICES

172

Appendix A
Deployment Plans
A.1

Teledyne RD Instruments, Workhorse Monitor

CR1
CF11101
EA0
EB0
ED190
ES2
EX11111
EZ1111111
WA255
WB0
WD111100000
WF88
WN22
WP300
WS100
WV175
HD111000000
HB5
HP2400
HR01:00:00.00
HT00:00:00.50
TE00:05:00.00
TP00:01.00
CK
CS

173

A.2

Teledyne RD Instruments, Workhorse Sentinel

CR1
CF11101
EA0
EB0
ED100
ES2
EX11111
EZ1111111
WA255
WB0
WD111100000
WF44
WN13
WP300
WS100
WV175
HD111000000
HB5
HP2400
HR01:00:00.00
HT00:00:00.50
TE00:10:00.00
TP00:02.00
CK
CS

174

A.3

Teledyne RD Instruments, BBACDP

WP00440
WD111110000
WN012
WS0200
WF0200
WM4
TP00:02.00
WV175
BP000
TE00:15:00.00
ET1500
ES02
ED0200
EZ1111111
EX11111
CF11101

175

BIBLIOGRAPHY

176

Bibliography
A. Adcroft, JM Campin, S. Dutkiewicz, C. Evangelinos, D. Ferreira, G. Forget, B. FoxKemper, P. Heimbach, C. Hill, E. Hill, et al. The mitgcm user manual, 2008.
American Public Health Association APHA. Standard Methods for the Examination of Water
and Wastewater. 1998.
E. Awad, E. Toorman, and C. Lacor. Large eddy simulations for quasi-2d turbulence in
shallow flows: A comparison between different subgrid scale models. Journal of Marine
Systems, 77(4):511 – 528, 2009. ISSN 0924-7963.
S. Bai and W. S. Lung. Three-dimensional modeling of fecal coliform in the tidal basin and
washington channel, washington, dc. Journal of Environmental Science and Health Part
a-Toxic/Hazardous Substances & Environmental Engineering, 41(7):1327–1346, 2006. Bai,
Sen Lung, Wu-Seng.
S. Bai and W.S. Lung. Modeling sediment impact on the transport of fecal bacteria. Water
Research, 39(20):5232–5240, 2005.
C. Basdevant and T. Philipovitch. On the validity of the ”weiss criterion” in two-dimensional
turbulence. Physica D: Nonlinear Phenomena, 73(1-2):17–30, 1994.
G. K. Batchelor. The application of the similarity theory of turbulence to atmospheric
diffusion. Quarterly Journal of the Royal Meteorological Society, 76(328):133–146, 1950.
ISSN 1477-870X.
G. K. Batchelor. An Introduction to Fluid Dynamics. Cambridge Mathematical Library.
Cambridge University Press, 1967.
D. Beletsky and D. J. Schwab. Modeling circulation and thermal structure in lake michigan:
Annual cycle and interannual variability. Journal of Geophysical Research Oceans, 106:
19,745–19,771, 2001.
177

D. Beletsky and D. J. Schwab. Climatological circulation in lake michigan. Geophysical
Research Letters, 2008, 2008.
D. Beletsky, J. H. Saylor, and D. J. Schwab. Mean circulation in the great lakes. Journal of
Great Lakes Research, 25(1):78–93, 1999.
D. Beletsky, D. Schwab, and M. McCormick. Modeling the 1998-2003 summer circulation
and thermal structure in lake michigan. Journal of Geophysical Research Oceans, 111,
2006.
D. H. Bergey and R. S. Breed. Bergey’s manual of determinative bacteriology. Williams &
Wilkins Co., 9 edition, 1994.
A. F. Blumberg and G. L. Mellor. A description of a three dimensional coastal ocean
circulation model. Journal of Geophysical Research Oceans, 1987.
A. B. Boehm. Model of microbial transport and inactivation in the surf zone and application
to field measurements of total coliform in northern orange county, california. Environmental Science & Technology, 37(24):5511–5517, 2003.
A. B. Boehm. Enterococci concentrations in diverse coastal environments exhibit extreme
variability. Environmental Science & Technology, 41(24):8227–8232, 2007.
A. B. Boehm and S. B. Weisberg. Tidal forcing of enterococci at marine recreational beaches
at fortnightly and semidiurnal frequencies. Environmental Science & Technology, 39(15):
5575–5583, 2005.
A. B. Boehm, B. F. Sanders, and C. D. Winant. Cross-shelf transport at huntington beach.
implications for the fate of sewage discharged through an offshore ocean outfall. Environmental Science & Technology, 36(9):1899–1906, 2002.
A. B. Boehm, J. A. Fuhrman, R. D. Mrse, and S. B. Grant. Tiered approach for identification
of a human fecal pollution source at a recreational beach: Case study at avalon cay, catalina
island, california. Environmental Science & Technology, 37(4):673–680, 2003.
A. B. Boehm, D. B. Lluch-Cota, K. A. Davis, C. D. Winant, and S. G. Monismith. Covariation of coastal water temperature and microbial pollution at interannual to tidal periods.
Geophysical Research Letters, 31(6), 2004a.
A. B. Boehm, G. G. Shellenbarger, and A. Paytan. Groundwater discharge: Potential association with fecal indicator bacteria in the surf zone. Environmental Science & Technology,
38(13):3558–3566, 2004b.
178

A. B. Boehm, D. P. Keymer, and G. G. Shellenbarger. An analytical model of enterococci
inactivation, grazing, and transport in the surf zone of a marine beach. Water Research,
39(15):3565–3578, 2005.
A. B. Boehm, N. J. Ashbolt, J. M. Colford, L. E. Dunbar, L. E. Fleming, M. A. Gold, J. A.
Hansel, P. R. Hunter, A. M. Ichida, C. D. McGee, J. A. Soller, and S. B. Weisberg. A sea
change ahead for recreational water quality criteria. Journal of Water and Health, 7(1):
9–20, 2009.
I. Borthwick. Diffusion and dispesion characteristics in Swansea Bay: Some preliminary
results. Industrialised embayments and their environmental problems: A case study of
Swansea Bay. Pergamon, pages 367–382, 1980.
P.Y. Burban, Y.J. Xu, J. Mcneil, and W. Lick. Settling speeds of flocs in fresh water and
seawater. Journal of Geophysical Research, 95(c10):18213–18220, 1990.
H. Burchard and K. Bolding. Comparative analysis of four second-moment turbulence closure
models for the oceanic mixed layer. Journal of Physical Oceanography, 31(8):1943–1968,
2001.
M. N. Byappanahalli, D. A. Shively, M. B. Nevers, M. J. Sadowsky, and R. L. Whitman.
Growth and survival of escherichia coli and enterococci populations in the macro-alga
cladophora (chlorophyta). Fems Microbiology Ecology, 46(2):203–211, 2003.
X. Chao. Three-dimensional numerical modeling of cohesive sediment transport and wind
wave impact in a shallow oxbow lake. Adv. Water Res., 2008.
S. C. Chapra. Surface Water-Quality Modeling. McGraw-Hill, 1997.
G. W. Characklis, M. J. Dilts, O. D. Simmons, C. A. Likirdopulos, L. A. H. Krometis,
and M. D. Sobsey. Microbial partitioning to settleable particles in stormwater. Water
Research, 39(9):1773–1782, 2005.
J. P. Connolloy, A. F. Blumberg, and J. D. Quadrini. Modeling fate of pathogenic organisms
in coastal waters of oahu, hawaii. J. Environ. Engg., 125(5):398–406., 1999.
K. M. Crossett, T. J. Culliton, P. C. Wiley, and T. R. Goodspeed. Population trends along
the coastal united states: 1980-2008. Technical report, National Oceanic and Atmospheric
Administration, 2004.
G. T. Csanady. Accelerated diffusion in the skewed shear flow of lake currents. Journal of
Geophysical Research, 71(2):411–420, 1966.
179

G. T. Csanady. Wind-induced barotropic motions in long lakes. Journal of Physical Oceanography, 3(4):429–438, 1973.
G. T. Csanady. Coastal Dynamics: Circulation in the Coastal Ocean. D. Reidel Publishing
Co., Boston, 1983.
C. M. Davies, J. A. H. Long, M. Donald, and N. J. Ashbolt. Survival of fecal microorganisms
in marine and fresh-water sediments. Applied and Environmental Microbiology, 61(5):
1888–1896, 1995.
A. de Brauwere, B. de Brye, P. Servais, J. Passerat, and E. Deleersnijder. Modelling escherichia coli concentrations in the tidal scheldt river and estuary. Water Research, 45:
2724 – 2738, 2011. ISSN 0043-1354.
A. W. Decho. Microbial biofilms in intertidal systems: an overview. Continental Shelf
Research, 20:1257–1273, 2000.
K. L. Deines. Backscatter estimation using broadband acoustic doppler current profilers.
In Current Measurement, 1999. Proceedings of the IEEE Sixth Working Conference on,
pages 249–253. IEEE, 1999. ISBN 0780355059.
T. R. Desmarais, H. M. Solo-Gabriele, and C. J. Palmer. Influence of soil on fecal indicator
organisms in a tidally influenced subtropical environment. Applied and Environmental
Microbiology, 68(3):1165, 2002. ISSN 0099-2240.
D. M. Di Toro, J. D. Mahony, D. J. Hansen, K. J. Scott, and J. P. St. John. Analysis of fate
of chemicals in receiving waters. Chemical Manufacturers Association, 1981.
A. M. Doglioli, B. Blanke, S. Speich, and G. Lapeyre. Tracking coherent structures in a
regional ocean model with wavelet analysis: Application to cape basin eddies. Journal of
Geophysical Research-Oceans, 112(C5):–, 2007.
M. A. Donelan. A simple numerical model for wave and wind stress prediction., 1977.
F. Dor, R. Bonnard, C. Gourier-Frery, A. Cicolella, R. Dujardin, and D. Zmirou. Health
risk assessment after decontamination of the beaches polluted by the wrecked erika tanker.
Risk Analysis, 23(6):1199–1208, 2003.
M. Dorfman and K. S. Rosselot. Testing the waters 2008: Aguide to water quality at vacation
beaches. Technical report, Natural Resources Defence Council, 2008.
M. Dorfman and K. S. Rosselot. Testing the waters 2010: A guide to water quality at
vacation beaches. Technical report, Natural Resources Defence Council, July, 2010 2010.
180

P. Douillet, S. Ouillon, and E. Cordier. A numerical model for fine suspended sediment
transport in the southwest lagoon of new caledonia. Coral Reefs, 20(4):361–372, 2001.
B. J. Eadie. Recurrent coastal plume in southern lake michigan. Eos Trans. AGU, 77:337 –
338, 1996.
B. J. Eadie. In probing particle processes in lake michigan using sediment traps. Water,
Air, & Soil Pollution, 99:133 – 139, 1997.
EPA. National water quality inventory: Report to congress, 2004 reporting cycle. Technical
report, EPA 841-R-08-001, 2009.
F. Feddersen. Vertical structure of dissipation in the nearshore. Journal of Physical Oceanography, 37:1764–1777, 2006.
R. Ferrari and C. Wunsch. Ocean circulation kinetic energy: reservoirs, sources, and sinks.
Annual Review of Fluid Mechanics, 41:253–282, 2009.
H. B. Fischer. Longitudinal dispersion and turbulent mixing in open-channel flow. Annual
Reviews., 1973.
H. B. Fischer, E. J. List, R. C. Y Koh, J. Imberger, and N. H Brookes. Mixing in Inland
and Coastal Waters. Academic Press, San Diego, 1979.
H.B. Fischer. On the tensor form of the bulk dispersion coefficient in a bounded skewed
shear flow. Journal of Geophysical Research, 83(C5):2373–2375, 1978.
R. Fujioka, C. Sian-Denton, M. Borja, J. Castro, and K. Morphew. Soil: the environmental
source of escherichia coli and enterococci in guam’s streams. Journal of applied microbiology, 85(S1):83S–89S, 1998. ISSN 1365-2672.
C. Gantzer, L. Gillerman, M. Kuznetsov, and G. Oron. Adsorption and survival of faecal
coliforms, somatic coliphages and f-specific rna phages in soil irrigated with wastewater.
Water science and technology: a journal of the International Association on Water Pollution Research, 43(12):117, 2001.
G. Gao, R. A. Falconer, and B. Lin. Numerical modelling of sediment-bacteria interaction
processes in surface waters. Water Research, 2011.
M. S. Ghidaoui and A. A. Kolyshkin. Linear stability analysis of lateral motions in compound
open channels. Journal of Hydraulic Engineering, 125:871, 1999.
T. R. Ginn, B. D. Wood, K. E. Nelson, T. D. Scheibe, E. M. Murphy, and T. P. Clement.
Processes in microbial transport in the natural subsurface. Advances in Water Resources,
25(8-12):1017–1042, 2002.
181

S. B. Grant and B. F. Sanders. Beach boundary layer: A framework for addressing recreational water quality impairment at enclosed beaches. Environmental Science & Technology, pages 4818–4824, 2010.
S. B. Grant, B. F. Sanders, A. B. Boehm, J. A. Redman, J. H. Kim, R. D. Mrse, A. K.
Chu, M. Gouldin, C. D. McGee, N. A. Gardiner, B. H. Jones, J. Svejkovsky, and G. V.
Leipzig. Generation of enterococci bacteria in a coastal saltwater marsh and its impact on
surf zone water quality. Environmental Science & Technology, 35(12):2407–2416, 2001.
S. B. Grant, J. H. Kim, B. H. Jones, S. A. Jenkins, J. Wasyl, and C. Cudaback. Surf zone
entrainment, along-shore transport, and human health implications of pollution from tidal
outlets. Journal of Geophysical Research Oceans, 2005, 2005.
D. W. Griffin, K. A. Donaldson, J. H. Paul, and J. B. Rose. Pathogenic human viruses in
coastal waters. Clinical Microbiology Reviews, 16(1):129–+, 2003.
A. K. Guber, D. R. Shelton, and Y. A. Pachepsky. Effect of manure on escherichia coli
attachment to soil. J. Environ. Qual., pages 2086–2090, 2005.
C. M. Hardina and R. S. Fujioka. Soil: The environmental source of escherichia coli and
enterococci in hawaii’s streams. Environmental toxicology and water quality, 6(2):185–195,
1991. ISSN 1098-2256.
M. R. Hipsey, J. D. Brookes, R. H. Regel, J. P. Antenucci, and M. D. Burch. In situ evidence
for the association of total coliforms and escherichia coli with suspended inorganic particles
in an australian reservoir. Water Air and Soil Pollution, 170(1-4):191–209, 2006.
M. R. Hipsey, J. P. Antenucci, and J. D. Brookes. A generic, process-based model of microbial
pollution in aquatic systems. Water Resources Research, 44(7), 2008.
P. W. Jewell, R. F. Stallard, and G. L. Mellor. Numerical studies of bottom shear stress and
sediment distribution on the amazon continental shelf. Journal of Sedimentary Petrology,
63(5):1015–1015., 1993.
G. R. Jones, J. D. Nash, R. L. Doneker, and G. H. Jirka. Buoyant surface discharges into
water bodies. i: Flow classification and prediction methodology. Journal of Hydraulic
Engineering, 133:1010, 2007.
L. H. Kantha and C. A. Clayson. Small Scale Processes in Geophysical Fluid Flows. Academic
Press, 2000.
J. H. Kim, S. B. Grant, C. D. McGee, B. F. Sanders, and J. L. Largier. Locating sources
of surf zone pollution: A mass budget analysis of fecal indicator bacteria at huntington
beach, california. Environ. Sci. Technol., 38(9):2626 – 2636, 2004.
182

N. A. Kolmogrov. Dissipation of energy under locally isotropic turbulence. Dolk. Akad. Nauk
SSSR, 30:16–18, 1941.
G. J. Komen, L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, and P. Janssen.
Dynamics and Modelling of Ocean Waves. Cambridge, 1994.
R. B. Krone. Flume studies of the transport of sediment in estuarial shoaling processes.
Technical report, Hydraulic Engineering Laboratory, University of California, Berkeley
California., 1962.
R. L. LaBelle, C. P. Gerba, S. M. Goyal, J. L. Melnick, I. Cech, and G. F. Bogdan. Relationships between environmental factors, bacterial indicators, and the occurrence of enteric
viruses in estuarine sediments. Applied and environmental microbiology, 39(3):588, 1980.
ISSN 0099-2240.
G. A. Lawrence, K. I. Ashley, N. Yonemitsu, and J. R. Ellis. Natural dispersion in a small
lake. Limnology and Oceanography, 40(8):1519–1526, 1995.
C. Lee, D.J. Schwab, and N. Hawley. Sensitivity analysis of sediment resuspension parameters
in coastal area of southern lake michigan. Journal of Geophysical Research, 110(C3):
C03004, 2005a.
C. Lee, D. J. Schwab, D. Beletsky, J. Stroud, and B. Lesht. Numerical modeling of mixed
sediment resuspension, transport, and deposition during the march 1998 episodic events
in southern lake michigan. Journal of Geophysical Research Oceans, 112, 2007.
J. L. Lee, M. H. Teng, and I. N. Kang. Modeling of sediment transport in a coral reef
environment. Journal of Coastal Research, pages 303–308, 2005b.
E. L´vˆque, F. Toschi, L. Shao, and J.P. Bertoglio. Shear-improved Smagorinsky model for
e e
large-eddy simulation of wall-bounded turbulent flows. Journal of Fluid Mechanics, 570
(-1):491–502, 2007. ISSN 1469-7645.
J. Li and LA McLandsborough. The effects of the surface charge and hydrophobicity of
escherichia coli on its adhesion to beef muscle. International Journal of Food Microbiology,
53(2-3):185–193, 1999.
R. Lindqvist and C. G. Enfield. Cell-density and nonequilibrium sorption effects on bacterial
dispersal in groundwater microcosms. Microbial Ecology, 24(1):25–41, 1992.
L. Liu, M. S. Phanikumar, S. L. Molloy, R. L. Whitman, D. A. Shively, M. B. Nevers, D. J.
Schwab, and J. B. Rose. Modeling the transport and inactivation of e-coli and enterococci
in the near-shore region of lake michigan. Environmental Science & Technology, 40(16):
5022–5028, 2006.
183

P. C. Liu, D. J. Schwab, and J. R. Bennett. Comparison of a two-dimensional wave prediction
model with synoptic measurements in lake michigan. Journal of Physical Oceanography,
14:1514–1518, 1984.
P. C. Liu, D. J. Schwab, and R. E. Jensen. Has wind-wave modeling reached its limit? Ocean
Engineering, 29(1):81–98, 2002.
J. Lou, D. J. Schwab, D. Beletsky, and N. Hawley. A model of sediment resuspension and
transport dynamics in southern lake michigan. Journal of Geophysical Research, 105:
6591–6610, 2000.
R. A. Luettich, D. R. F. Harleman, and L. Somlyody. Dynamic behavior of suspended
sediment concentrations in a shallow lake perturbed by episodic wind events. Limnology
and Oceanography, 35(5):1050–1067, 1990.
D. A. Lytle, E. W. Rice, C. H. Johnson, and K. R. Fox. Electrophoretic mobilities of
escherichia coli o157: H7 and wild-type escherichia coli strains. Applied and Environmental
Microbiology, 65(7):3222, 1999.
R. V. Madala and S. A. Piacsek. A semi-implicit numerical model for baroclinic oceans. J.
of Comp. Phys., 23(2):167 – 178, 1977.
M. J. McCormick and G. A. Meadows. An intercomparison of four mixed layer models in a
shallow inland sea. Journal of Geophysical Research Oceans, 1988:6774 – 6788, 1988.
J. A. McCorquodale, I. Georgiou, S. Carnelos, and A. J. Englande. Modeling coliforms in
storm water plumes. Journal of Environmental Engineering and Science, 3(5):419–431,
2004.
A. J. Mehta and E. Partheniades. An investigation of the depositional properties of flocculated fine sediment. Journal of Hydraul Research, 13(4):361–381, 1975.
G. L. Mellor. Users guide for a three-dimensional, primitive equation, numerical ocean model,
1998.
G. L. Mellor. The three-dimensional current and surface wave equations. Journal of physical
oceanography, 33(9):1978–1989, 2003. ISSN 1520-0485.
G. L. Mellor and T. Yamada. Development of a turbulence closure model for geophysical
fluid problems. Rev. Geophys. Space Phys., 20:851–875, 1982.
G. L. Mellor, M. A. Donelan, and L. Y. Oey. A surface wave model for coupling with
numerical ocean circulation models. J. Atmos. Oceanic Technol., 25:1785–1807, 2010.
184

C. H. Mortimer.
029917834X.

Lake Michigan in motion.

Univ. of Wisconsin Press, 2004.

ISBN

C. R. Murthy. Horizontal diffusion characteristics in lake ontario. Journal of Physical
Oceanography, 6(1):76–84, 1976.
C. R. Murthy and D. S. Dunbar. Structure of the flow within the coastal boundary layer of
the great lakes. Journal of Physical Oceanography, 11:1567–1577, 1981.
C. R. Murthy and Y. R. Rao. Circulation and turbulent diffusion processes in the great
lakes. Proc. Indian Natn. Sci. Acad., 5:633–644, 2003.
N. Nekouee. Noaa technical memorandum glerl-151: Dynamics and numerical modeling of
river plumes in lakes, 2010.
M. B. Nevers and R. L. Whitman. Coastal strategies to predict escherichia coli concentrations
for beaches along a 35 km stretch of southern lake michigan. Environmental Science &
Technology, 42(12):4454–4460, 2008.
M. B. Nevers and R.L. Whitman. Nowcast modeling of escherichia coli concentrations at
multiple urban beaches of southern lake michigan. Water Resour. Res., 20:5250–5260,
2005.
M. B. Nevers, R. L. Whitman, W. E. Frick, and Z. F. Ge. Interaction and influence of two
creeks on escherichia coli concentrations of nearby beaches: Exploration of predictability
and mechanisms. Journal of Environmental Quality, 36(5):1338–1345, 2007.
N. S. Oakey and B. J. W. Greenan. Mixing in a coastal environment: 2. a view from
microstructure measurements. Journal of Geophysical Research, 109(C10014), 2004.
Environmental Protection Agency Water Quality Office. Effect of geographical location on
cooling pond requirement and performance. Technical report, Environmental Protection
Agency, March 1971.
T. O. Ojo, J. S. Bonner, and C. Page. Observations of shear-augmented diffusion processes
and evaluation of effective diffusivity from current measurements in corpus christi bay.
Continental Shelf Research, 26:788–803, 2006a.
T.O. Ojo, J.S. Bonner, and C. Page. Studies on turbulent diffusion processes and evaluation
of diffusivity values from hydrodynamic observations in corpus christi bay. Continental
Shelf Research, 26(20):2629–2644, 2006b.
A. Okubo. Oceanic diffusion diagram. Deep Sea Res., 18:789–902, 1971.
185

D. M. Oliver, C. D. Clegg, A. L. Heathwaite, and P. M. Haygarth. Preferential attachment of
escherichia coli to different particle size fractions of an agricultural grassland soil. Water,
Air, & Soil Pollution, 185(1):369–375, 2007.
G. A. Olyphant and R. L. Whitman. Elements of a predictive model for determining beach
closures on a real time basis: The case of 63rd street beach chicago. Environmental
Monitoring and Assessment, 98(1-3):175–190, 2004.
S. B. Pope. Turbulent Flows. Cambridge University Press, 2000.
A. Pruss. A review of epidemiological studies from exposure to recreational water. Int. J.
Epidemiol., 27:1–9, 1998.
S. J. M. Rabinovici, R. L. Bernknopf, A. M. Wein, D. L. Coursey, and R. L. Whitman. Economic and health risk trade-offs of swim closures at a lake michigan beach. Environmental
Science & Technology, 38(10):2737–2745, 2004.
Y. R. Rao and D. J. Schwab. Transport and mixing between the coastal and offshore waters
in the great lakes: a review. J. Great Lakes Res., 33:202–218, 2007.
H. L. Reddy and R. M. Ford. Analysis of biodegradation and bacterial transport: Comparison
of models with kinetic and equilibrium bacterial adsorption. Journal of Contaminant
Hydrology, 22(3-4):271–287, 1996.
V. Rijn. Handbook sediment transport by currents and waves. Technical report, Delft
Hydraulics, 1989.
M.M. Roper and KC Marshall. Effects of salinity on sedimentation and of participates on
survival of bacteria in estuarine habitats. Geomicrobiology Journal, 1(2):103–116, 1979.
ISSN 0149-0451.
R. Sadourny and K. Maynard. Formulations of lateral diffusion in geophysical fluid dynamics
models. In Numerical Methods of Atmospheric and Oceanic Modelling, pages 547–556,
1997.
B. F. Sanders, F. Arega, and M. Sutula. Modeling the dry-weather tidal cycling of fecal
indicator bacteria in surface waters of an intertidal wetland. Water Research, 39(14):
3394–3408, 2005.
W. G. Savage. Bacteriological examination of tidal mud as an index of pollution of the river.
Journal of Hygiene, 5(02):146–174, 1905. ISSN 1469-4409.
D. J. Schwab and D. Beletsky. The 1998 coastal turbidity plume in lake michigan. Estuarine
Coastal Shelf Sci., 50:49–58, 2000.
186

D. J. Schwab and J. A. Morton. Estimation of overlake wind speed from overland wind
speed: A comparison of three methods. Journal of Great Lakes Research, 10(1):68–72,
1984. ISSN 0380-1330.
D. J. Schwab, J. R. Bennett, P. C. Liu, and M. A. Donelan. Application of a simple numerical
wave prediction model to lake erie. Journal of Geophysical Research, 89(C3):3586–3592,
1984.
D. J. Schwab, J. R. Bennett, and E. W. Lynn. A two-dimensional lake wave prediction
system. Environmental Software, 1(1):4–9, 1986.
R. B. Scott and F. Wang. Direct evidence of an oceanic inverse kinetic energy cascade from
satellite altimetry. Journal of Physical Oceanography, 35(sept):1650–1666, 2005.
T. M. Scott, T. M. Jenkins, J. Lukasik, and J. B. Rose. Potential use of a host associated
molecular marker in enterococcus faecium as an index of human fecal pollution. Environmental Science & Technology, 39(1):283–287, 2005.
T. J. Simons. Verification of numerical models of lake ontario: Part i. circulation in spring
and early summer. Journal of Physical Oceanography, 4:507–523, 1974. ISSN 0022-3670.
L. W. Sinton, R. J. Daviescolley, and R. G. Bell. Inactivation of enterococci and fecalcoliforms from sewage and meatworks effluents in seawater chambers. Applied and Environmental Microbiology, 60(6):2040–2048, 1994.
L. W. Sinton, R. K. Finlay, and P. A. Lynch. Sunlight inactivation of fecal bacteriophages
and bacteria in sewage-polluted seawater. Applied and Environmental Microbiology, 65
(8):3605–3613, 1999.
L. W. Sinton, C. H. Hall, P. A. Lynch, and R. J. Davies-Colley. Sunlight inactivation of fecal
indicator bacteria and bacteriophages from waste stabilization pond effluent in fresh and
saline waters. Appl. Environ. Microbiol., 68(3):1122 – 1131, 2002.
J. Smagorinsky. General circulation experiments with the primitive equations. Monthly
weather review, 91(3):99–164, 1963.
M. L. Soupir, S. Mostaghimi, and N. G. Love. Method to partition between attached and
unattached e. coli in runoff from agricultural lands. JAWRA Journal of the American
Water Resources Association, 44(6):1591–1599, 2008. ISSN 1752-1688.
M. T. Stacey. Estimation of diffusive transport of turbulent kinetic energy from acoustic
doppler current profiler data. J. Atmos. Oceanic Technol., pages 927–935, 2003.
187

D. L. Strayer. Alien species in fresh waters: ecological effects, interactions with other stressors, and prospects for the future. Freshwater Biology, 55:152–174, 2010.
M. A. Sundermeyer, James R. Ledwell, Neil S. Oakey, and Blair J. W. Greenan. Stirring
by small-scale vortices caused by patchy mixing. Journal of Physical Oceanography, 35:
1245–1262, 2005.
G. Taylor. The dispersion of matter in turbulent flow through a pipe. Proceedings of the
Royal Society of London Series a-Mathematical and Physical Sciences, 223(1155):446–468,
1954.
R. D. I. Teledyne. Self-Contained ADCP Applications: WinSC and PlanADCP User’s Guide.
Teledyne, R. D. I., 2006.
P. Thupaki, M.S. Phanikumar, D. Beletsky, D.J. Schwab, M.B. Nevers, and R.L. Whitman.
Budget analysis of escherichia coli at a southern lake michigan beach. Environmental
Science & Technology, 44(3), 2010.
C. Torrence and G. P. Compo. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society, 79(1):61–78, 1998. Yu676 Times Cited:2145 Cited References
Count:31.
R. Uittenbogaard and van Vossen B. Subgrid-scale model for quasi-2d turbulence in shallow
water. In Shallow Flows, pages 575–582–. Taylor & Francis, September 2004.
G. K. Vallis. Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, Cambridge, U.K., 2006.
T. J. Wade, N. Pai, J. N. S. Eisenberg, and J. M. Colford. Do us environmental protection
agency water quality guidelines for recreational waters prevent gastrointestinal illness? a
systematic review and meta-analysis. Environmental Health Perspectives, 111(8):1102–
1109, 2003.
G.R. Wall, E.A. Nystrom, S. Litten, New York (State). Dept. of Environmental Conservation,
and Geological Survey (US). Use of an ADCP to Compute Suspended–sediment Discharge
in the Tidal Hudson River, New York. US Dept. of the Interior, US Geological Survey,
2006.
G. L. Weatherly and P. L. Martin. On the dynamics and structure of the oceanic bottom
boundary layer. Journal of Physical Oceanography, 8(4):557–570, 1978.
J. Weiss. The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica
D: Nonlinear Phenomena, 48(2-3):273–294, 1991.
188

R. L. Whitman and M. B. Nevers. Foreshore sand as a source of escherichia coli in nearshore
water of a lake michigan beach. Applied and Environmental Microbiology, 69(9):5555–5562,
2003.
R. L. Whitman, D. A. Shively, H. Pawlik, M. B. Nevers, and M. N. Byappanahalli. Occurrence of escherichia coli and enterococci in cladophora (chlorophyta) in nearshore water
and beach sand of lake michigan. Applied and Environmental Microbiology, 69(8):4714–
4719, 2003.
R. L. Whitman, M. B. Nevers, G. C. Korinek, and M. N. Byappanahalli. Solar and temporal
effects on escherichia coli concentration at a lake michigan swimming beach. Applied and
Environmental Microbiology, 70(7):4276–4285, 2004.
G. B. Witham. Linear and nonlinear waves, 1999.
M. Wong, L. Kumar, T. M. Jenkins, I. Xagoraraki, M. S. Phanikumar, and J. B. Rose.
Evaluation of public health risks at recreational beaches in lake michigan via detection
of enteric viruses and a human-specific bacteriological marker. Water Research, 43(4):
1137–1149, 2009.
J. S. Yoder. Surveillance for waterborne disease and outbreaks associated with recreational
water use and other aquatic facility associated health events-united states, 2005-2006.
Technical Report 57, Centers for Disease Control and Prevention, September 2008.

189