CONSTRAINING MECHANISTIC MODELS OF INDICATOR BACTERIA AT
RECREATIONAL BEACHES IN LAKE MICHIGAN USING EASILY-MEASURABLE
ENVIRONMENTAL VARIABLES
By
Aaron Wendzel

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Environmental Engineering—Master of Science
2014

ABSTRACT
CONSTRAINING MECHANISTIC MODELS OF INDICATOR BACTERIA AT
RECREATIONAL BEACHES IN LAKE MICHIGAN USING EASILY-MEASURABLE
ENVIRONMENTAL VARIABLES
By
Aaron Wendzel
Beach closures have significant economic and human health implications. The ability to create
and use near-real time hydrodynamic and transport models that simulate fecal indicator bacteria
(FIB) levels at our nation’s recreational beaches is important to effectively managing coastal
resources.

Described herein is the development and application of an unsteady, three-

dimensional hydrodynamic fate and transport model constrained using easily measurable
environmental variables such as electrical conductivity (EC) and turbidity. The model was able
to simulate observed Escherichi coli (E. coli) concentrations at three beaches in close proximity
to the Burns Waterway along the Indiana Dunes National Lakeshore. This model utilized an
unstructured grid that has the ability to accurately represent local features in the area, including
the complex shoreline and breakwaters that influence hydrodynamics and mixing. This allows
for the better prediction of FIB at local beaches, reducing human health risks and decreasing the
number of unnecessary beach closures.

Copyright by
AARON WENDZEL
2013

To my family.

iv

ACKNOWLEDGEMENTS

I would like to thank my advisor Dr. Mantha S. Phanikumar for his guidance, knowledge, and
insight that helped me complete my thesis. I would like to thank my committee members, Dr.
Shu-Guang Li and Dr. Irene Xagoraraki, for their assistance and feedback.

I would like to thank Dr. Pramod Thupaki for his patience, support, and help with the FVCOM
program, providing knowledge in the areas I was lacking. Without him I would have been very
challenged to complete all of my research objectives. I would also like to thank my friend and
colleague, Tuan D. Nguyen, for the numerous discussions leading to the completion of my thesis.

Lastly, I would like to thank my family for the love and support they provided during this entire
process. My family is the reason why I have achieved all that I have and without them I
wouldn’t be the man I am today.

v

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................................... viii
LIST OF FIGURES ....................................................................................................................... ix
CHAPTER 1 ................................................................................................................................... 1
1.1 Introduction ........................................................................................................................... 1
1.2 Objective ............................................................................................................................... 3
1.3 Motivation ............................................................................................................................. 4
1.4 Literature Review.................................................................................................................. 5
CHAPTER 2 ................................................................................................................................. 11
2.1 Study Area .......................................................................................................................... 11
2.2 Current Data ........................................................................................................................ 13
2.3 E. Coli Data......................................................................................................................... 15
2.4 Electric Conductivity Data .................................................................................................. 16
2.5 Turbidity Data ..................................................................................................................... 16
2.6 Numerical Model ................................................................................................................ 16
2.6.1 Computational Grid ..................................................................................................... 17
2.6.2 Currents ........................................................................................................................ 20
2.6.3 Water Quality Model ................................................................................................... 23
2.7 Model Performance Metrics ............................................................................................... 24
2.7.1 Root Mean Square Error (RMSE)................................................................................ 25
2.7.2 Coefficient of Determination (R2) ................................................................................ 25
2.7.3 Percent Bias (PBIAS) ................................................................................................... 26
2.7.4 Fourier Norm (

) ....................................................................................................... 26

CHAPTER 3 ................................................................................................................................. 27
3.1 Lake Wide Model Verification: ADCP .............................................................................. 27
3.2 Near-Shore Model Verification: Electrical Conductivity ................................................... 29
3.3 E. coli Model....................................................................................................................... 34
3.4 Possible Sources of E. coli Concentrations in Burns Ditch ................................................ 39
3.5 Direct Comparison to a Past Ogden Beach Model ............................................................. 43
vi

CHAPTER 4 ................................................................................................................................. 48
4.1 Conclusions ......................................................................................................................... 48
4.1.1 Utilizing EC as a Tracer ............................................................................................... 48
4.1.2 Simulating E. coli Concentrations ............................................................................... 48
4.1.3 Identifying the Source E. coli in Burns Waterway ...................................................... 48
4.1.4 Importance of Unstructured Grids ............................................................................... 48
BIBLIOGRAPHY ......................................................................................................................... 50

vii

LIST OF TABLES

Table 1: Comparison of water flow velocities with previous investigators.................................. 29
Table 2: Mixing flow parameters .................................................................................................. 31
Table 3: Electrical conductivity comparison metrics.................................................................... 31
Table 4: Error norms for electrical conductivity models .............................................................. 32
Table 5: Parameters used for E. coli model .................................................................................. 34
Table 6: E. coli performance metrics ............................................................................................ 34
Table 7: E. coli comparison metrics between Thupaki et al.’s (2013b) models (with and without
sediment transport) and the present model ................................................................................... 46

viii

LIST OF FIGURES

Figure 1: Flow chart of the investigation ........................................................................................ 4
Figure 2: Lake Michigan and surrounding land masses ............................................................... 11
Figure 3: Near-shore region of interest ......................................................................................... 12
Figure 4: Example of ADCP experimental setup. ........................................................................ 14
Figure 5: ACDP deployment location in relation to the area of interest. ..................................... 15
Figure 6: Computational grid showing local features near Burns Waterway Outfall using a 40 m
grid resolution. .............................................................................................................................. 18
Figure 7: Grid resolution and bathymetry for the lake-wide and near-shore regions. .................. 18
Figure 8: A histogram of grid sizes used in the unstructured grid model ..................................... 19
Figure 9: Locations of weather stations utilized surrounding Lake Michigan ............................. 22
Figure 10: Along-shore and cross-shore, vertically integrated, velocity comparisons with the
Monitor ADCP .............................................................................................................................. 28
Figure 11: Electrical conductivity plots for observed values compared to the simulated values
with the grey-colored bands representing ± 0.5% uncertainty in the chemical measurements at (a)
OD1, (b) OD2, and (c) OD3. ........................................................................................................ 30
Figure 12: A histogram of the horizontal dispersion coefficient in the near-shore region ........... 33
Figure 13: E. coli comparison between observed and simulated values with the grey-colored
bands representing ± 50% uncertainty in the biological measuremnts at (a) OD1, (b) OD2, and
(c) OD3. Turbidity measurements are indicated by the color of each observation point. ............ 35
Figure 14: Example of E. coli plume in the area of interest ......................................................... 36
Figure 15: Probability plots for observed values of E. coli at OD1, OD2, and OD3 compared
with simulated results with the cyan-colored bands representing ± 50% uncertainty in the input
from Burns Waterway ................................................................................................................... 38
Figure 16: Comparison between Burns Waterway’s flow rate and E. coli measurements in Burns
Waterway ...................................................................................................................................... 40
Figure 17: Comparison between Burns Waterway’s flow rate and precipitation data measured at
NCDC Station #12899 .................................................................................................................. 41
ix

Figure 18: Comparison between turbidity and E. coli concentrations in the water column at all
three sample locations ................................................................................................................... 42
Figure 19: Comparison between an unstructured and structured grid in the area of interest ....... 44
Figure 20: E. coli comparison plots between Thupaki et al.’s (2013b) structured grid model and
the present unstructured grid model at (a) OD1, (b) OD2, and (c) OD3 ...................................... 45
Figure 21: E. coli probability plots comparison between Thupaki et al.’s (2013b) structured grid
models and the present unstructured grid model at (a) OD1, (b) OD2, and (c) OD3 ................... 47

x

CHAPTER 1
1.1 Introduction
One of the major indicators of decreased surface water quality is the increased presence of fecal
indicator bacteria (FIB), such as Escherichia coli (E. coli), within the water column. While most
E. coli are harmless, they are defined as FIB because they are an easily measured quantity and
can indicate the presence of health risks to humans. Since human interaction with surface water
most often occurs in the near-shore regions, FIB concentrations have become an essential
measurable quantity examined at many recreational beaches. For example, for water to meet
recreational standards in the State of Indiana, the E. coli concentration must be less than 235
colony-forming units (CFU) per 100 mL for any one sample with a geometric mean of less than
125 CFU/100 ml for an entire month (National Parks Service, 2014). However, measurement of
FIB concentrations contained in water samples requires approximately 18-24 hours to complete
the assays, making it difficult to identify when water quality advisories should be posted.
Currently, when a water sample is found to have a FIB concentration greater than 235 CFU/100
ml, the corresponding beach advisory is posted the following day and samples are continually
run each day until the beach FIB concentrations are below recreational standards (National Parks
Service, 2014).

The introduction of E. coli can come from many known sources, including storm and sanitary
sewers, natural rivers, surface runoff, animal and shorebird populations, and groundwater
discharge (McLellan, 2004). There are many variables that influence the fate and survival of E.
coli within a specific location, including the turbidity of the water, intensity of sunlight, and the
magnitude and direction of the water currents (Francy et al., 2013). As computational technology

1

has become more readily available, numerical models have been developed to simulate these
interactions to better predict E. coli concentrations and to address the management of coastal
regions.

Currently hydrodynamic model parameters are constrained by the model’s ability to simulate
observational current data. Observational current data can be obtained in many different ways,
but the most common method today is to utilize current measurements from an Acoustic Doppler
Current Profiler (ADCP) deployed at a specific location, measuring the current magnitudes and
directions at defined depth intervals throughout the water column. However, because of the cost
of ADCP units and the necessity for accurate data, they are most often deployed in regions where
human activities will not impact them, often resulting in deployments in deep water, far from the
near-shore region. While deep-water ADCP observational data is adequate to test the accuracy of
a model’s lake-wide hydrodynamics, they are deficient in the ability to verify near-shore
hydrodynamics and transport.

Tracer studies in the near-shore region can be used to reduce the uncertainty in mixing
parameters, which are needed to model solute transport accurately. However, tracer studies are
expensive and time consuming; therefore, the use of easily-measurable environmental
parameters may be more attractive to constrain transport model parameters. An analysis is to be
conducted that focuses on these near-shore hydrodynamic interactions, utilizing an unsteady,
unstructured, three-dimensional, hydrodynamic transport model. The analysis will focus on
further constraining the hydrodynamic and mixing parameters by using easily measurable near-

2

shore environmental variables, such as electrical conductivity (EC) and turbidity, and applying
those parameters to an E. coli transport model to obtain an accurate near-shore E. coli model.
1.2 Objective
The objective of this research is divided into three parts: (a) constraining hydrodynamic and
transport models using environmental variables, (b) using the constrained model to simulate E.
coli concentrations in the water column, and (c) comparing an unstructured grid model to a
structured gird model. The constraint placed on the hydrodynamic and transport model will be its
ability to simulate EC at the three sample sites in close proximity to a waterway’s outfall. This
analysis will utilize an unstructured grid to capture the near-shore hydrodynamic interactions in
an attempt to improve existing hydrodynamic and transport models. Model performance metrics
will be used to determine the quality of the hydrodynamic model produced.

From the

performance metrics, the goal is to provide insight into the use of EC as a parameter to constrain
hydrodynamic models. After the hydrodynamic/transport parameters are constrained, the model
will be coupled with an E. coli model to simulate E. coli concentrations in the near-shore region.
Model performance metrics will be computed to summarize the E. coli model’s ability to
simulate observed E. coli concentrations and then compared to previous models to determine its
accuracy. From this analysis, the goal is to provide insight into the use of an unstructured grid
and the use of the specified water quality parameters to estimate E. coli concentrations in the
near-shore region.

The coupled hydrodynamic and E. coli models will also be used to examine the relationship
between the measured turbidity in the near-shore region with the simulated E. coli
concentrations. After examining the relationship between these two parameters, it can be

3

determined if the use of a sediment-transport model is essential to the modeling of E. coli levels
that are above recreational standards or if a water quality model without sediment-transport is
sufficient in simulating E. coli concentrations. A graphical view of the process used to
investigate the objectives is shown in Figure 1.

Figure 1: Flow chart of the investigation

1.3 Motivation
The goal of this analysis is to better constrain hydrodynamic and transport models using easily
measureable environmental variables. One of the largest sources of uncertainty in near-shore
transport models is associated with mixing parameters and this uncertainty propagates into E.
coli fate and transport models as well. Every near-shore region is unique and has different
properties that impact the hydrodynamics differently. The main method used to accurately
quantify transport at this time is a dye tracer study. However, these studies are time consuming,
labor intensive, and in most cases only capture the transport characteristics for a short period of
time. Utilizing easily measurable environmental variables within the water column as a tracer
allows for hydrodynamic and transport data to be obtained inexpensively and for long periods of
time, in order to accurately constrain mechanistic models. These constraints can be easily applied
at any location as long as there are no unknown sources that contribute to the loss/gain of the EC
within the domain, allowing for more accurate transport models.

4

1.4 Literature Review
Hydrodynamic models have been employed to model a wide range of near-shore systems
throughout the world, ranging from those interacting with oceans to those interacting with inland
lakes. These models have utilized a variety of grids and numerical methods in an attempt to
accurately simulate the natural hydrodynamics. Coupling these hydrodynamic models with
transport models has allowed investigators to identify contaminant sources and predict future
contaminant concentrations in near-shore regions. As computational power has become more
accessible, an increased number of mechanistic models have been created to simulate
hydrodynamics in near-shore regions. Consequently, after these models were created they were
compared with observational data to ensure their accuracy.

In an attempt to validate a lake-wide transport model, an analysis employed EC as a conservative
tracer and recorded the measurements of EC at various locations throughout the body of water in
a four km long lake, with an average depth of 4 m in Berlin, Germany. This model utilized a
two-dimensional, finite-difference grid, with grid resolutions ranging from 10-150 m and
harnessed the increased EC introduced to the lake from two inflow rivers as boundary conditions
for the model (Schimmelpfennig et al., 2012). The model was able to successfully predict EC
throughout the lake (Schimmelpfennig et al., 2012). An important aspect of this study was the
application of EC as a conservative tracer, to test mechanistic lake-wide transport models. It was
also shown that EC performed better as a tracer than water temperature, another naturally
occurring measurable quantity within a water body (Schimmelpfennig et al., 2012).

5

Another model verification process was analyzed on a more comprehensive level to ensure
accurate hydrodynamic modeling. This analysis utilized a three-dimensional, structured, finitedifference, nested model to capture the large-scale lake-wide circulation, while also capturing the
small-scale near-shore circulation. Magnitudes and directions of water currents were measured
using bottom-mounted, upward-looking ADCP at five different locations in close proximity to
Burns Waterway for a period of 40 days (Thupaki et al., 2013a). A continuous-release dye study
was also conducted to observe the plume evolution and obtain breakthrough data at three local
beaches, while also measuring a mean horizontal dispersion coefficient to further constrain the
transport model (Thupaki et al., 2013a). Utilizing the five observational data points for water
velocity and the measured mean horizontal dispersion coefficient, the hydrodynamic and
transport models were constrained on a very comprehensive level. It was found that the model
was able to simulate the mean velocity field and energy contained in the larger scales of motion
(lake-wide), but the model significantly under-estimated the energy in the smaller scale, nearshore region. This showed that different methods should be utilized to validate near-shore
hydrodynamic models other than ADCP-data.

Attempts to verify hydrodynamic models on both large and small scales have led to the use of
these models, coupled with fate and transport models, to determine the sources of contamination
in the near-shore region. A study was conducted on the island of Oahu, in Hawaii, in order to
settle a dispute between the Sierra Club and Hawaii’s Thousand Friends against the city and
county of Honolulu (Connolly et al., 1999). The plaintiffs argued that the city and county were
violating the Clean Water Act (CWA) because of the discharge from the Sand Island Wastewater
Treatment Plant. A 3-D, time-dependent coastal ocean circulation model was applied to the

6

entire island of Oahu, utilizing grid cells ranging from 400 m to 4 km. The model utilized
observational E. coli, Enterococci, and C. Perfringens values at five recreational beaches on the
island. Prior to this study, there had not been a comprehensive coastal water quality assessment
of this size (Connolly et al., 1999). An important aspect of this study was its ability to show that
water quality parameters could be modeled successfully on a large scale. The study was also able
to identify multiple sources of E. coli and determine the contribution of each to the decreased
water quality values at the local recreational beaches. The results of the study indicated that a
large portion of the pathogenic organisms affecting the recreational beaches did come from the
wastewater treatment plant; however, another major source was identified, a local canal. The
study also reported an implied relationship between indicator organism counts at the eastern
beaches within the canal and rainfall in the region.

Studies were also conducted on the West Coast marine beaches (i.e., high salinity), in an attempt
to determine the sources of FIB in the water (Ho, 2011). Nine different ADCP deployments were
used for this study, obtaining long-term (~5 months) data at one position and short-term data (~3
days) at three other locations around Avalon Bay, California. An important observation of this
study was that anthropogenic activities within the Bay were shown to represent a significant
source to the variability in near-shore water quality (Ho, 2011). Utilizing still photos and ADCP
deployments, a relationship between boat activity and E. coli concentrations along the beach was
shown; however, the cause of the relationship was not proven (Ho, 2011). The study predicted
that the anthropogenic activities introduced increased shear stress to the sediment layer,
increasing the suspended sediments, re-suspending FIB within the water column.

7

Another West Coast study was performed at Newport Bay in California (Jeong et al., 2005). The
objective of their study was to identify the sources of FIB from various marinas near Newport
Bay. The study utilized thousands of water samples (n = 4132) in close proximity of two
marinas in Newport Bay. It was shown that both dry weather and wet weather runoff had a
significant impact on the FIB concentrations in the two marinas (Jeong et al., 2005). In fact, it
was found that the FIB concentrations at the two marina locations were fairly homogeneous,
indicating that a common source existed between the two marinas, large-scale runoff, from nonpoint sources (Jeong et al., 2005). The study determined that long-term strategies for treating
non-point sources would be more advantageous than targeting point sources because of the high
impact that the non-point sources had on the FIB concentrations near Newport Bay (Jeong et al.,
2005).

A number of other studies have been performed in the Great Lakes region in an attempt to
identify FIB sources. A tributary and a large ditch were analyzed in southern Lake Michigan to
identify the FIB variation at Mt. Baldy Beach for a period of one month (Liu et al., 2006). This
study utilized a two-dimensional, finite-element, structured grid model with resolutions
approximately 1-2 km for the whole lake and about 100 m near-shore. An overall first-order
inactivation coefficient of 0.5 – 2.0 per day was used, incorporating a time-dependent
inactivation rate by temperature, sedimentation, and observed solar insolation (Liu et al., 2006).
This study provided evidence that the tributary and ditch surrounding the beach were major
contributors to the E. coli contamination at the beach while also indicating that other sources of
E. coli may have existed in the area of interest.

8

Another analysis was performed along a 72 km shoreline of Lake Michigan, using two known
point sources (rivers) to perform a budget analysis of E. coli. This analysis utilized a threedimensional, finite-difference, nested model to capture the large-scale lake-wide circulation
while also capturing the small-scale near-shore circulation. An important aspect of this study was
that it showed that solar inactivation had a greater impact on the E. coli loss rates than the
settling of the particles, but that dilution due to advection and diffusion had the greatest effect on
the net loss of E. coli (Thupaki et al., 2010). While, this study did indicate a relationship between
bottom shear stresses and E. coli peaks, the relationship was not studied.

Thupaki et al., (2013b) incorporated a sediment-transport model into a three-dimensional, finitedifference, structured, nested model to analyze the significance of sediment-transport on E. coli
concentrations and to better predict E. coli concentrations. The analysis was performed on the
southern shoreline of Lake Michigan, near Burns Harbor, for a period of approximately 40 days.
The study was able to quantitatively determine the importance of sediment re-suspension on the
E. coli concentrations within the water column. It was observed that the addition of the sedimenttransport model to the hydrodynamic model provided significant improvement to the model’s
prediction of E. coli concentrations (Thupaki et al., 2013b). It was concluded that re-suspension
of E. coli from the bottom sediment was an important process in relation to near-shore water
quality (Thupaki et al., 2013b).

The present analysis being performed in the near-shore region, along the Indian Dunes
Lakeshore, is directly related to the previously mentioned studies; however, this analysis is
unique because it attempts to use EC values to constrain the transport parameters within the near-

9

shore region, and then applies the constrained transport characteristics to an E. coli model to
better predict the FIB concentrations at local recreational beaches. This analysis also utilizes an
unstructured grid, which has yet to be applied to Lake Michigan at the time of this study.

10

CHAPTER 2
2.1 Study Area
Lake Michigan is a unique body of water located within the continental United States. It is the
fifth largest freshwater lake by surface area in the world (58,000 km2) and the seventh largest by
volume, encompassing 4,920 km3. The lake is surrounded by four states: Michigan, Illinois,
Wisconsin, and Indiana, with its deepest point at about 300 m (Figure 2). The lake is utilized
commercially for drinking water, fishing, and as a mode of transport for goods, while also
providing numerous recreational beaches to local communities. Consequently, the wide variety
of demands on the lake and its economic impact to local communities has led to increased water
quality awareness.

Figure 2: Lake Michigan and surrounding land masses
11

The near-shore region investigated consisted of three recreational beaches: Ogden Dunes Beach
1 (OD1), Ogden Dunes Beach 2 (OD2), and Ogden Dunes Beach 3 (OD3), near Burns
Waterway, along the Indiana Dunes National Lakeshore (Figure 3). The land to the east of Burns
Waterway is used for commercial purposes and the land to the west of Burns Waterway is used
for recreational purposes. The recreational beaches’ water quality is of concern because of their
known increased FIB concentrations. For example, Indiana beaches along southern Lake
Michigan rank 24th (out of 30 states) for beach water quality (Beaches, 2014). It is thought that
the water quality at the three beach locations is significantly impacted by Burns Waterway
(Thupaki et al., 2013b).

Figure 3: Near-shore region of interest

12

2.2 Current Data
The method for measurement of water currents has come a long way since the beginning of
observational oceanography. Primitive measurement tools include bucket wheels that were used
to calculate the velocity of the water by the number of rotations for a defined period of time;
however, bucket wheels required a person to count every rotation, which is not feasible for long
periods of time. Primitive bucket wheels were eventually replaced by velocity meters that used a
propeller and the rotations were counted electronically; however, these meters needed constant
maintenance to ensure accurate measurements, making long-term deployments difficult.
Lagrangian drifters were developed to float on the surface of the water while collecting their
GPS locations to calculate the velocity between multiple locations; however, drifters were
limited to the top-most layer and unable to determine velocities throughout the water column.
ADCPs were developed allowing for the measurement of water velocities throughout the water
column at any given location. ADCPs transmit and receive sounds waves at a known frequency
from the water column, allowing them to calculate the fluid velocity (scalar) in the water column
based on the Doppler shift principle. Utilizing multiple transmitters allows the ADCPs to
calculate the fluid velocity in multiple directions (vector). Utilizing reliable and compact data
storage methods allows for ADCPs to be deployed for long periods, capturing the flow velocities
throughout the water column.

A single, upward-facing 600kHz RDI-Monitor ADCP (Figure 4) was deployed approximately 9
km from the study site (41.71059 N, 87.20996 W), at a depth of ~20 m, to collect observational
data for water velocities in the x, y, and z directions (Figure 5). The deployment lasted from May
to September 2008 to capture an extensive observational dataset. The ADCP was programmed to

13

utilize a ping rate of 0.1 Hz and the data was ensemble—averaged every five minutes. The
ADCP was programmed so the predicted standard deviation of the measurements was less than
0.1 cm sec-1 (Teledyne, 2006). The RDI Workho32rse Monitor ADCP was serviced on August 5,
2008, to replace the on-board battery.

Figure 4: Example of ADCP experimental setup.

14

Figure 5: ACDP deployment location in relation to the area of interest.

2.3 E. Coli Data
Water samples were taken at OD1, OD2, and OD3 beach locations and at the Burns Waterway
USGS Gauge (#04095090) location to evaluate the ability of the model to simulate the
observational E. coli concentrations at the Ogden Dunes beach locations. The water samples
were taken twice daily (morning and afternoon) from June 9–August 28 in 2008. The water
samples were collected from knee-deep water and analyzed for E. coli at the USGS Great Lakes
Science Center in Porter, Indiana, using membrane filtration methods according to section
9222G, APHA (1998). As described in Liu et al. (2006) the membrane filters were incubated on
mFC agar at 44.5 C° for 24 hours, transferred to EC-MUG agar (Difco, 222200), and incubated
for 24 hours at 44.5 C°. Individual colonies that produced florescence under a long wavelength
(366-nm) ultraviolet light were considered E. coli, reported in CFU/100 mL.

15

Both light-bag and dark-bag experiments were conducted during the sampling period when the
water samples were taken. The tests provided an estimate of the sunlight extinction coefficient
and light-based inactivation rate of the E. coli in the region. As described in Ge et al. (2012b) the
tests were constituted using 530 mL darkened and 200 mL transparent WhirlPak bags that
contained freshly collected water from Lake Michigan and were conducted on a typical sunny
day in June 2008. After the light-bag and dark-bag samples were created, all the samples were
placed in coolers on ice, held at 4 C°, and analyzed using the Colilert-18 method four hours after
collection. The base mortality coefficient,
inactivation rate,

, was calculated to be 0.55 d-1 and the solar

, was determined to be approximately 0.00301 m2 W-1 d-1.

2.4 Electric Conductivity Data
EC values were measured twice daily (morning and afternoon), using a standard YSI EC probe
(www.ysi.com), from June 9 – August 28 at the Ogden Dunes beach locations to validate the
simulated EC values obtained from the model. EC measurements were also taken with the same
frequency and duration at the Burns Waterway USGS Gauge (#04095090) to act as a boundary
condition for the model.
2.5 Turbidity Data
To compare the relationship between turbidity and E. coli, turbidity measurements were taken
twice daily (morning and afternoon) from June 9 – August 28 at the Ogden Dunes beach
locations. The turbidity was measured using a YSI sonde (model 6600).
2.6 Numerical Model
Various mechanistic models have been developed to simulate water circulation. Those models
either utilize the finite-difference method or the finite-element method. The finite-difference

16

method is the most basic and is advantageous because of simple coding and computational
efficiency. However, this method is unable to capture complex near-shore structures and other
features. The finite-element method is advantageous because of its ability to capture these nearshore structures, but is more difficult to code and may be less computationally efficient.

The model employed by this research was the Finite-Volume Community Ocean Model
(FVCOM) originally developed by Chen et al. (2003). FVCOM combines the advantages of both
the finite-different and the finite-element models, by discretizing the integral form of the
governing equations so that it is relatively easy to code and computationally efficient, while also
allowing the use of an unstructured grid.
2.6.1 Computational Grid
The graphical user interface (GUI), Surface-water Modeling System (SMS) by Aquaveo (2014),
was utilized to create an unstructured grid. The grid was able to capture the local features near
Burns Waterway’s outfall more accurately using a resolution of approximately 40 m (Figure 6),
while also utilizing grid resolutions of approximately 2-5 km for the rest of Lake Michigan
(Figure 7). To ensure accurate numerical calculations, a smooth transition from the increased
grid resolution to the decreased grid resolution must be achieved and is verified in Figure 8. The
grid was constrained to the south at 42.61 N Latitude, 46.13 N Latitude at the north, 84.76 W
Longitude in the west, and 88.04 W Longitude in the eastward direction. The computational grid
was made up of 12,684 nodes and 23,602 elements.

17

Figure 6: Computational grid showing local features near Burns Waterway outfall using a 40 m
grid resolution.

Figure 7: Grid resolution and bathymetry for the lake-wide and near-shore regions.

18

Figure 8: A histogram of grid sizes used in the unstructured grid model

To evaluate the hydrodynamics and mixing properties of the water column, bathymetry values
were interpolated to the grid nodes using Matlab R2012a (2012). Two data sets were combined
to obtain accurate data. The first data set was obtained from the National Oceanic and
Atmospheric Administration (NOAA) Lake Michigan 2008 LIDAR data set along the Indiana
coast, utilizing a horizontal resolution of approximately 2 m. This data set was utilized to ensure
accurate depth interpolations in the near-shore region where the hydrodynamics and mixing
properties are greatly influenced by the water depth. A second data set was obtained from NOAA
for the remaining area of Lake Michigan with a horizontal resolution of approximately 90 m.

19

2.6.2 Currents
Circulation throughout Lake Michigan can be modeled using basic hydrodynamic equations
derived from the Reynold’s averaged form of the Navier-Stokes equations for continuity
(Equation 1) and momentum (Equations 2 and 3) in the x-y directions. The momentum equation
in the z-direction can be simplified further to its hydrostatic form (Equation 4). The model
utilized 20 vertical (sigma) layers over the water column depth. Because of the Boussinesq
approximation, density is assumed constant except when multiplied by gravity.

(1)
(

)

[

(

)]

(

) (2)

(

)

[

(

)]

(

) (3)
(4)

The variables x, y, and z are the flow directions, u, v, and w are the mean flow velocities in their
respected direction,

and

are the local and reference density respectively and

and

are

the diffusivity terms in the horizontal and vertical directions for the momentum equations.
denotes the Coriolis paramter, introduced to account for the rotation of the earth, and

is the

gravitational acceleration.

Temperature transport is modeled using a scalar transport equation (Equation 5) where T is the
temperature of the water,

represents the sources and sinks for temperature, and

and

are the eddy diffusivity in the horizontal and vertical directions respectively for the transport
equation.

20

(

)

(

)

(

)

(5)

Boundary conditions affecting water currents and temperature were applied to the hydrodynamic
and transport equations utilizing observational metrological data. The meteorological
observations were obtained from both the National Climatic Data Center (NCDC) and the
National Data Buoy Center (NDBC) weather monitoring stations, at 44 locations surrounding
Lake Michigan (Figure 9). Direct meteorological observations that were utilized included wind
speed and direction, air temperature, and cloud cover. Long-wave solar radiation was calculated
using the model presented by Parkinson and Washington (1979) utilizing air temperature and
cloud cover. Short-wave solar radiation was calculated using the clear-sky value (Office, 1971)
and the measured cloud cover.

21

Figure 9: Locations of weather stations utilized surrounding Lake Michigan

To complete the hydrodynamic and transport equations (Equations 1-5),

and

must be

described. The horizontal eddy diffusivity term is calculated using the Smagorinsky eddy
viscosity model shown in Equation 6 (Smagorinksy, 1963).

| ⃗

( ⃗) |

22

(6)

The variable C is a non-dimensional constant parameter, and the grid sizes (

,

) are both

included in the calculation. Equation 6 assumes that the horizontal eddy diffusivity is isotropic
and equal in both x and y directions.

is related to

by Equation 7.

(7)

is the turbulent non-dimensional Prandtl number. FVCOM uses the Mellor-Yamada 2.5
turbulence closure model to describe vertical mixing,

and

(Mellor and Yamada, 1982).

2.6.3 Water Quality Model
A water quality model was coupled with the FVCOM transport model to simulate the EC and E.
coli concentrations within the water column. Our primary interest was to simulate the E. coli
concentrations within the water column; however, the EC concentrations were used to further
constrain the parameters used by the transport model to reduce uncertainty in the near-shore fate
and transport model.

The E. coli transport model solved a similar transport equation presented earlier for temperature
(Equation 5) and is shown in Equation 8. However, the E. coli transport equation utilizes a net
loss rate, k, due to inactivation and settling to describe the loss mechanisms (Equation 9).

(

)
( )

(

23

(

)
)

(

)

(8)
(9)

The variable
particles,

is the faction of E. coli attached to particles,
and

due to sunlight,
sunlight,

represent the thickness of each layer,

is the settling velocity of the
is the inactivation rate of E. coli

( ) denotes amount of short-wave radiation at the water surface due to

is the extinction coefficient,

is the base mortality rate, and

is the

dependence of the loss rate on temperature using the Beer-Lambert relation.

EC was modeled as a conservative tracer, utilizing the transport equation without the addition of
a source or sink term, with concentration depending only on the transport within the water
column (Equation 10). EC was considered to be conservative because the boundary condition for
EC, Burns Ditch outfall, was assumed to be much larger than all the other sources and sinks
affecting the Ogden Beach locations. In other words, the difference between the EC values at the
mouth of the river and the ambient lake values provides a clear range of EC values and a strong
signal that can be measured and modeled. This may not be the case at all sites.

(

)

(

)

(

)

(10)

2.7 Model Performance Metrics
To identify the ability of the model to accurately simulate various aspects of the observed data
(EC and E. coli), several metrics were employed. The metrics calculated at each observational
location were the root mean square error (RMSE), the coefficient of determination (R2), the
percent bias (PBIAS), and the Fourier norm ( ). The Matlab software (Matlab, 2012) was used

24

with predefined scripts to calculate each performance metric. All of the performance metrics
utilizing E. coli were calculated using

(

).

2.7.1 Root Mean Square Error (RMSE)
RMSE is a commonly used error index for model validation that is calculated by determining the
mean absolute error between the observed and simulated values (Equation 11). RMSE values
have been shown to be a good measure of hydraulic model efficiency because of the variability
of the values obtained from hydraulic systems (Legates and Mccabe, 1999). A RMSE value of 0
indicates a perfect fit between the observed and simulated values and values range from 0 to

√ ∑

(

)

.

(11)

2.7.2 Coefficient of Determination (R2)
The coefficient of determination describes the ability of the model to simulate the variance in the
measured data (Equation 12). R2 values range from 0 to 1, with 1 indicating the model does a
perfect job describing the model and 0 indicating the model was not able to describe any of the
variance in the observed data. Although R2 is a commonly used statistical term, it has been
shown to be over-sensitive to outliers in the data and insensitive to additive and proportional
difference between simulated and observed data (Legates and McCabe, 1999). However, R2 is
still calculated because of its wide range of use for model verification.

25

∑

(

)

∑

(

)

(12)

2.7.3 Percent Bias (PBIAS)
Percent Bias measures the average tendency of the model to over-estimate or under-estimate the
observed data and is shown in Equation 13 (Gupta et al., 1999). PBIAS values range from -∞ to
∞, with 0 being the optimal value. Under-estimation is represented by a negative value, while
over-estimation is represented by a positive value, indicating the bias in the model.

[

2.7.4 Fourier Norm (

∑

(

)(
∑

(

)

)

]

(13)

)

Fourier norm is the relative percentage of variance in the observed data that is not explained by
the simulated data as described by Beletsky and Schwab (2001) (Equations 14 and 15). A value
of 0 would indicate that the simulated results modeled the observed results with no errors and a
value of 1 would indicate that the model was not able to explain any of variances in the observed
data.

‖

‖

( ∑

|

| )

‖

‖
‖

26

‖

(14)
(15)

CHAPTER 3

3.1 Lake Wide Model Verification: ADCP
Simulated current values from the hydrodynamic model were compared to observational
measurements for the summer of 2008. In the near-shore region, along-shore (u’) and cross-shore
(v’) velocities are of more interest than north-south (v) and east-west (u) velocities, so the northsouth and east-west velocities were converted to along-shore, cross-shore velocities in relation to
the shoreline (Equations 16 and 17).
(

)

(

)

(16)

(

)

(

)

(17)

Comparisons were made between the observed and simulated (vertically integrated) along-shore
and cross-shore velocities and are shown in Figure 10. The RMSE value for the water current
comparison was 0.040 m s-1. This measurement was comparable to the work in previous studies,
comparing simulated water current velocities to observed ADCP measurements (Table 1). The
model demonstrated the ability to simulate lake-wide flow. However, the observed
measurements were taken at a location approximately 9 km away from the area of interest. Even
though the lake-wide hydrodynamics influence transport in the near-shore region, the transport
model still needs to be tested in the near-shore region to verify the transport parameters
influenced by the local features in the area of interest.

27

Figure 10: Along-shore and cross-shore, vertically integrated, velocity comparisons with the Monitor ADCP
28

Table 1: Comparison of water flow velocities with previous investigators
Location
Lake Michigan (M)
North Sea (Lower EMF)
North Sea (Upper EMF)
Lake Michigan (M)
Lake Michigan (S)
Lake Michigan (N1)
Lake Michigan (N2)
Lake Michigan (shallow ADCP)

Velocity RMSE (m/s)
AlongCrossTotal
Shore
Shore
0.048
0.031
0.040
0.060
0.083
-0.050
0.108
---0.031
--0.037
--0.048
--0.042
0.030
0.020
0.017

Source
Present Model
Grunnet et al., 2004
Grunnet et al., 2004
Thupaki et al, 2013a
Thupaki et al, 2013a
Thupaki et al, 2013a
Thupaki et al, 2013a
Ge et al., 2012

3.2 Near-Shore Model Verification: Electrical Conductivity
To further examine the transport parameters within the near-shore region, EC measurements
were utilized as a conservative tracer. The major ions that affect EC concentrations in lake water
include F, Cl, NO3, SO4, PO4, Na, Ca, Mg, and K, leading to many sources and sinks of EC in a
natural environment; however, it was assumed that because of the proximity of the three Ogden
Beach locations to Burns Waterway outfall (~1 km), no sources and sinks were considered
significant when compared to the Burns Waterway outfall boundary condition. EC measurements
have also been shown to be dependent on the temperature of the water (Hayashi, 2004);
however, the simulated temperature in the near-shore region was shown to be relatively constant
between the three sample locations, indicating that an EC-temperature relation was not needed.
Even with all of the uncertainty in the EC values in lake water, Schimmelpfenig et al. (2012)
concluded that EC could be a suitable tracer. Adjusting the mixing parameters (Table 2), the
physics of the model were altered to ensure accurate simulated transport by comparing the
simulated (vertically averaged) and observed EC measurements at the three observational
beaches (Figure 11) with a background concentration of 286 mhos/cm. These comparisons are
supported by the performance metrics presented in Table 3.

29

Figure 11: Electrical conductivity plots for observed values compared to the simulated values
with the grey-colored bands representing ± 0.5% uncertainty in the chemical measurements at (a)
OD1, (b) OD2, and (c) OD3.

30

Table 2: Mixing flow parameters
Parameter
Horizontal Mixing Coefficient
Vertical Mixing Coefficient
Horizontal Prandtl Number
Vertical Prandtl Number

Value
0.10 m s-1
m s-1
10
10

Table 3: Electrical conductivity comparison metrics
Location RMSE (µmhos cm-1)
PBIAS
0.696
0.489 -7.916 0.209
OD1
0.471
0.462 -2.581 0.136
OD2
0.622
0.454 -5.907 0.174
OD3

The PBIAS at all three Ogden Beach locations suggests that the model slightly underestimates
the EC of the water column (Table 3). However,

indicates that the model was able to explain

79.1%, 86.44%, and 82.65% of the variance in the observed values at OD1, OD2, and OD3,
respectively, indicating the model fit the observational measurements (Table 3). To further verify
the EC transport, the error norms (

and

) were calculated to perform a direct statistical

comparison to previous studies utilizing EC as a tracer (Equations 18 and 19).

∑

|

(

√∑

|

∑

|

|

(

√∑

)

)
(

(18)

(19)

)

is the mean absolute percent error (MA%E) proposed by Mayer and Butler (1993) and

is

the RMSE of the model divided by the root mean square of the observed data (RMSobs). The
error norms are comparable with the results of the study performed by Schimmelpfennig et al.
(2012) in Lake Tegel (Table 4); however, Schimmelpfennig et al. (2012) noted better agreement
31

between model and EC data. This is attributed to the fact that the Lake Tegel measurements were
taken outside of the near-shore region, where there is less uncertainty in the mixing of the water
column, while also utilizing a 2-D computational grid that does not account for the vertical
mixing of the water.
Table 4: Error norms for electrical conductivity models
Location
OD1
OD2
OD3
Lake Tegel

0.149
0.106
0.138
0.040

0.209
0.136
0.174
0.061

Source
Present Model
Present Model
Present Model
Schimmelpfennig et al., 2012

The performance metrics (Table 3, Table 4) show that the model was able to simulate the tracer
concentrations better at OD2 and OD3, the closest beach to Burns Waterway’s outfall (< 1 km).
As the distance increased from the outfall to the OD1 observational location (> 1 km), the model
was less accurate in its ability to simulate the observed data. It is speculated that the
Smagorinsky mixing parameterization used in the FVCOM caused excessive damping that
contributed to the degradation in model performance at larger distances although waves (ignored
in the modeling) and wave-current-interactions are also expected to play a role.

Based on the metrics presented in Table 3, the ability of the model to capture most of the peaks
and the low values in the data, the performance of the present near-shore transport model is
considered reasonable. The final mixing parameters (shown in Table 2) were then used in the E.
coli fate and transport model.

A specific near-shore parameter of interest is the horizontal dispersion coefficient (AH). AH is the
rate of mixing in the near-shore region and has a significant impact on the transport of materials

32

(Equation 5). The near-shore region was defined as the area from the shoreline to the 15 m
isobath (Nearshore, 2009). Using that criterion, the near-shore region for this investigation was
estimated to consist of the water approximately 4.5 km away from the area of interest, in all
directions. The estimated AH value in the near-shore region utilizing the “4/3 power law” and a
median length scale of 100 m is 0.05 m2 s-1. However, using the model, the median AH in the
near-shore region was calculated to be 1.96 m2 s-1 and a distribution of the values is shown in
Figure 12. The reason that the “4/3 power law” was shown to underestimate the near-shore
horizontal dispersion coefficient is thought to be due to its inability to account for wave
breaking, wave refraction, and the shear effect between the water currents and the bottom of the
lake introduced by the decreased bathymetry in the near-shore region. The calculated AH value is
within the range of measured total dispersion values in the near-shore region by Johnson (2004)
between 1.29 and 3.88 m2 s-1.

Figure 12: A histogram of the horizontal dispersion coefficient in the near-shore region

33

3.3 E. coli Model
The mixing parameters used to simulate the EC concentration (Table 2) were then used to
simulate the E. coli concentrations for the near-shore region. The parameters utilized by the E.
coli model to determine the E. coli net loss rate, k, are shown in the Table 5. All of the E. coli
net loss rate parameters were constrained by measured values and values that were shown to be
acceptable by previous investigators. The results of the E. coli model were compared to the
observed values at Ogden Dunes Beach locations (Figure 13). The comparison shows the results
of the simulation with a black line and ±50% uncertainty in the biological E. coli measurements
is shown using a grey band. Turbidity measurements are also displayed by the color of each data
point, corresponding to the color bar. An example of the plume evolution is shown in Figure 14
for Julian Day 219, 2008. The model performance metrics are presented in Table 6.
Table 5: Parameters used for E. coli model
Parameter

Value
1.07
1 m d-1
0.55 d-1
0.003 m2 W-1 d-1
0.05

Source
Epply, 1972
Based on the Estimates from Eadie, 1997
Ge et al., 2012b
Ge et al., 2012b
Estimate from Thupaki et al., 2013b

Table 6: E. coli performance metrics
Location RMSE (CFU/100 mL)
PBIAS
0.809
0.380 24.283 0.660
OD1
0.600
0.425 10.489 0.408
OD2
0.647
0.425
6.511 0.408
OD3

34

Figure 13: E. coli comparison between observed and simulated values with the grey-colored
bands representing ± 50% uncertainty in the biological measuremnts at (a) OD1, (b) OD2, and
(c) OD3. Turbidity measurements are indicated by the color of each observation point.

35

Figure 14: Example of E. coli plume in the area of interest
The

and the

values of the model (Table 6) for each individual beach indicate that the

model does a better job predicting the E. coli concentrations at OD2 and OD3 than OD1. The
increased distance from the waterway to OD1 (Figure 3) is assumed to be the reason that the
model was unable to capture the E. coli concentrations in the water. The decreased accuracy at
OD1 also aligns with the results of the EC tracer results (Table 3 and Table 4), suggesting that
the uncertainty is from the model’s ability to describe tracer transport at locations farther from
the outfall and not associated with biological processes. The RMSE values (Table 6) for the
present model have shown an improvement relative to previous studies reporting RMSE values
in the range of 5-10 CFU/100 ml (Connolly et al., 1999) and RMSE values in the range of 1.051.36 CFU/100 ml (Thupaki et al., 2013b) for models without sediment transport.

Probability plots of E. coli are shown in Figure 15. The comparisons provide further evidence
that the model was able to accurately describe the E. coli concentrations at the three beach

36

locations; however, the model was better able to describe the concentrations at OD2 and OD3
than OD1, aligning with previous observations.

37

Figure 15: Probability plots for observed values of E. coli at OD1, OD2, and OD3 compared
with simulated results with the cyan-colored bands representing ± 50% uncertainty in the input
from Burns Waterway

38

The PBIAS of the model indicates that the model had the tendency to over-estimate the E. coli
concentrations in the water column (Table 6); however, there were still some peaks the model
was unable to capture. The upper and lower 50% uncertainty bands for the E. coli plots (Figure
13) and the probability plots (Figure 15) shows that the model was unable to explain all of the
observational E. coli data. The model’s inability to describe all the peaks in the FIB data is
evidence that either other sources of FIB are present within the area of interest or that E. coli life
span was inaccurately represented. When E. coli is exposed to sunlight, particularly UV
bandwidths, it causes the DNA of the E. coli to become damaged, inactivating the E. coli
(Whitman et al., 2004; Sinton et al., 2002), although photo-oxidative effects have been shown to
be the main cause of inactivation in surface waters because of the high attenuation of short UV
wavelengths (Hipsey et al., 2008). However, the present model does not consider the attenuation
characteristics of the different wavelengths within the water column, resulting in an overestimate of E. coli inactivation. This provides one explanation for the model’s inability to capture
all the peaks. Another cause of decreased simulated E. coli concentrations could be due to other
E. coli sources not incorporated in the model. While it does appear that the major source, Burns
Waterway, was identified, other less significant sources of E. coli that could affect E. coli
concentrations in the water column include sediment re-suspension (Thupaki et al., 2013b),
anthropogenic activities (Ho et al., 2011), runoff (Jeong et al., 2005), and other point sources
(Liu et al., 2006).
3.4 Possible Sources of E. coli Concentrations in Burns Ditch
To investigate the other possible sources of FIB concentration near Burns Waterway, the
observed E. coli data were compared to the flow rate of the waterway recorded from its USGS
Gauge (#04095090) location (Figure 16). The comparison shows a correlation between the flow

39

rate of Burns Waterway and the measured E. coli values. An increased flow rate is shown
between Julian Day 215 and Julian Day 225, indicating that either a large storm event or an
increased point source flow rate may have occurred. However, an increased point source flow
rate that more than doubles the flow rate of Burns Waterway for a period of 10 days is unlikely;
thus it was assumed that the increased flow rate was due to a large precipitation event.

Figure 16: Comparison between Burns Waterway’s flow rate and E. coli measurements in Burns
Waterway
To further investigate the large storm event, observed precipitation data were analyzed from a
nearby (~14 km) NCDC Station (#128992) and compared to the E. coli measurements in Burns
Waterway (Figure 17). The comparison shows a clear relationship between the E. coli
measurements and the local precipitation. Figures 16 and 17 show that the increased flow rate
and the increased E. coli measurements are a cause of increased precipitation. While the cause of

40

the increased flow rate is fairly obvious, the relationship between precipitation and increased E.
coli measurements is not. It is speculated that the increased precipitation led to more run-off in
the area, carrying E. coli with it into the local waterways, indicating that precipitation data may
be a good indicator of E. coli concentrations in the water column. This aligns with the work of
Jeong et al. (2005), who stated that run-off has a significant impact on the E. coli concentrations
in the near-shore region.

Figure 17: Comparison between Burns Waterway’s flow rate and precipitation data measured at
NCDC Station #12899

41

Sediment re-suspension, indicated by turbidity in the water column, was also investigated as a
possible source for E. coli in the area of interest. Sediments in the near-shore region have been
shown to be a significant source of FIB in both marine (Phillips et al., 2011) and freshwater
environments (Whitman and Nevers, 2003; Ge et al., 2012a; Thupaki et al., 2013b). Figure 18
shows a comparison between the turbidity and E. coli observations at the three sample locations.
The comparison shows that the relationship between turbidity and E. coli is weak (R2=0.023),
indicating that while turbidity may slightly influence the E. coli concentrations in the Ogden
Beach region it is not a major source of E. coli. Francy and Darner (2002) found a similar
relationship between E. coli and turbidity with an R2=0.36. Figure 13 also shows that increased
E. coli measurements did not occur only when high turbidity was observed.

Figure 18: Comparison between turbidity and E. coli concentrations in the water column at all
three sample locations

42

3.5 Direct Comparison to a Past Ogden Beach Model
To further compare the present model with the known work of others, the timescale was
constrained to that used by Thupaki et al., (2013b), from Julian Day 163 to Julian Day 195 in
2008. Thupaki et al., (2013b) utilized the same observed data as in the present work for their
research; however, they applied a structured grid and utilized a sediment transport model to
better simulate the interactions between the E. coli and suspended sediment. A comparison of a
structured grid and unstructured grid model is shown in Figure 19. Since Thupaki et al., (2013b)
utilized a structured grid, making it more difficult to resolve the near-shore features, they were
unable to resolve all the local features at the Burns Waterway outfall that are important to the
transport of E. coli, while the present work was able to more accurately resolve the local features
using an unstructured grid. A direct comparison between the model grids utilized by Thupaki et
al. (2013b) and the present model is shown in Figure 20.

43

Figure 19: Comparison between an unstructured and structured grid in the area of interest

44

Figure 20: E. coli comparison plots between Thupaki et al.’s (2013b) structured grid model and
the present unstructured grid model at (a) OD1, (b) OD2, and (c) OD3

45

Figure 20 indicates that the present model was able to better describe the E. coli concentrations
at OD1, OD2, and OD3 beach locations than Thupaki et al.’s (2013b) model that did not utilize
sediment transport and was comparable to Thupaki et al.’s (2013b) model utilizing sediment
transport. Table 7 further verifies this observation from the given RMSE values. The reason for
the present model’s improvement is thought to be due to the use of an unstructured grid to better
represent the near-shore region, particularly the breakwaters influencing the outflow of Burns
Waterway, and the ability to constrain the transport model further using the EC concentrations at
the beaches.
Table 7: E. coli comparison metrics between Thupaki et al.’s (2013b) models (with and without
sediment transport) and the present model
Present Model
Thupaki et al. (2013b) Structured Grid Models
No Sediment
No Sediment
With Sediment (
Location RMSE (CFU/100 ml) RMSE (CFU/100 ml)
RMSE (CFU/100 ml)
0.75
1.36
0.52
OD1
0.51
1.36
0.53
OD2
0.62
1.05
0.56
OD3

)

Further analysis was performed on the model’s ability to predict the median E. coli
concentrations when compared to Thupaki et al.’s (2013b) models utilizing probability plots
(Figure 21). The comparisons further demonstrate the ability of the present model to produce
comparable results to Thupaki et al.’s (2013b) structured model utilizing sediment transport and
significantly out-perform the simulation not utilizing a sediment transport model, further
indicating that an unstructured grid is superior to a structured grid in the near-shore region.

46

Figure 21: E. coli probability plots comparison between Thupaki et al.’s (2013b) structured grid
models and the present unstructured grid model at (a) OD1, (b) OD2, and (c) OD3

47

CHAPTER 4
4.1 Conclusions
A mechanistic model was developed to simulate near-shore contaminant transport utilizing an
unstructured, three-dimensional grid. Easily measureable EC values were utilized as a
conservative tracer to further constrain the transport model and to verify the near-shore mixing
parameters. The transport model was used to predict E. coli concentrations at three recreational
beaches. After applying a time-varying boundary condition for measured flow and
concentrations at the mouth of the river (Burns Waterway’s outfall), the following results were
found.
4.1.1 Utilizing EC as a Tracer


Observed EC values were used to constrain the near-shore transport model.

4.1.2 Simulating E. coli Concentrations


The model was able to accurately simulate the E. coli concentrations at three beaches in
close proximity to Burns Waterway without utilizing a sediment transport model.

4.1.3 Identifying the Source E. coli in Burns Waterway


Utilizing observed E. coli concentrations, flow rate measurements, and local precipitation
data, run-off was shown to be the primary E. coli source within Burns Waterway.

4.1.4 Importance of Unstructured Grids


The ability to better capture the near-shore features significantly improves the model’s
ability to predict near-shore contaminants.

48

Utilizing these results in future models can lead to a more accurate representation of the nearshore water quality parameters, reducing human health risks at local recreational beaches.

49

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50

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