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IN

This is to certify that the
thesis entitled

HYDRODYNAMICS AND LONGITUDINAL DISPERSION
IN THE RED CEDAR RIVER

presented by

IRFAN ASLAM

has been accepted towards fulfillment
of the requirements for the

Master of degree in Environmental Engineering
Science

 

 

(iii/M, adage

Major Professors Signature

De <64» LW /3, 900.2

 

 

Date

MSU is an Affirmative Action/Equal Opportunity Institution

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LIBRARY
Michigan State
University

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

MAR 3 .0 2004'

 

 

 

 

FEB 2 8 2006

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HYDRODYNAMICS AND LONGITUDINAL DISPERSION IN THE RED CEDAR
RIVER

By

Irfan Aslam

A THESIS

Submitted to
Michigan State University
in partial fulfilment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Civil and Environmental Engineering

2002

ABSTRACT

HYDRODYNAMICS AND LONGITUDlNAL DISPERSION IN RED CEDAR RIVER
By

Irfan Aslam
A one-dimensional hydrodynamic model for the Red Cedar River based on the EPA
version of DYNHYDS is presented herein for simulating the unsteady flow conditions.
The model framework was built using bathymetric data from flood insurance studies.
Channel geometry of the model network was kept sufficiently simple so as to yield
characteristic results in a single spatial dimension. The objective was to accurately
predict the hydrodynamic parameters for use in simulating contaminant transport through
the river reach. A series of dye dispersion studies conducted for different flow conditions
offer a characterization of the river reach with regards to longitudinal dispersion, which is
an essential component in contaminant transport. The results of dye dispersion studies
confirm the variability of dispersion with space and time. The model itself and the
empirical equation developed for predicting the dispersion coefficient at any point within
the reach bounds can be used as a base for simulating contaminant transport by the water

quality model.

ACKNOWLEDGMENTS

I would like to express my special thanks to Dr. Thomas C. Voice for his advice and
guidance during this study. I also feel obliged to express my gratitude to Dr. M.S
Phanikumar and Dr. David T. Long who consistently guided me to achieve my objective
with valuable suggestions. I also acknowledge the cooperation by volunteer students who

worked in the field to collect data during the dye studies.

iii

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ACKNOWLEDGMENTS ............................................................................................... iii
1. INTRODUCTION ...................................................................................................... l
1.2 Scope Of Study - 4
2. DESCRIPTION OF THE STUDY AREA ................................................................. 5
2.1 Physical Settings
2.2 Flow Variations in Red Cedar
3. LITERATURE REVIEW ......................................................................................... 10
4. METHODOLOGY ........ 19
4.1 Selection of Model“ . 19
4.2 Fluorescein As A Water Tracer 20
4.3 Model Implementation 21
4.4 Model Segmentation ......... 22
4.5 Tracer Tests 23
4.6 Data Collection. 24
4.7 Manning’s Roughness Coefficient. 25
5. RESULTS AND DISCUSSION ............................................................................... 27
5.1 Model Calibration 27
5.2 Hydrodynamics 29
5.3 Effect of Grid On Model Performance 33
5.4 Effect of Time Step on Model Performance 38
5.5 Time of Travel 41
5.6 Dispersion by Moments Method 49
5.7 Dispersion By Mass Transport 52
6. CONCLUSIONS ....................................................................................................... 69

iv

7. APPENDICES .......................................................................................................... 71

 

 

 

 

 

 

 

 

Appendix A Junction and Channel Properties 71
Appendix B Input File 75
Appendix C Field Data 82
Appendix D Time-Concentration Data-Dye Release 1 84
Appendix E Time-Concentration Data-Dye Release 2 86
Appendix F Time-Concentration Data-Dye Release 3 88
Appendix G Time-Concentration Data-Dye Release 4 90
Appendix H Time-Concentration Data-Dye Release 5 92
8. BIBLIOGRAPHY ..................................................................................................... 94

TABLE Page

Table 5-1 Manning's Roughness Coefficients .............................................................. 28
Table 5-2. Regression statistics for hydrodynamic variables. ...................................... 33
Table 5—3. Time of travel data—dye release 1 (May 17, 2002). ..................................... 42
Table 5-4. Time of travel data-dye release 2 (May 31, 2002). .................................... 43
Table 5-5. Time of travel data-dye release 3 (Jun 6, 2002). ......................................... 44
Table 5-6. Time of travel data-dye release 4 (Jun 21, 2002). ....................................... 45
Table 5-7. Time of travel data-dye release 5 (Jun 25, 2002). ....................................... 46
Table 5-8 Dispersion Coefficients By Moments Method ............................................ 51
Table 5-9 Dispersion coefficients calculated using the mass transport equation. ........ 53

Table 5-10. Variation in concentration across a transect indicating the state of lateral

mixing. ......................................................................................................... 56
Table 5-1 1. Area under time-concentration curves for calculated concentration. .......... 58
Table 5-12. Area under time-concentration curves for observed concentrations ............ 59

Table 5-13. Comparison of areas under the time-concentration curve for predicted and
observed concentrations. .............................................................................. 59

Table 5-14. Comparison of calculated and predicted dispersion coefficients ................. 64

vi

FIGURE

Figure 2-1.

Figure 2-2
Figure 2-3.
Figure 2-4.
Figure 5-1.
Figure 5-2.
Figure 5-3.
Figure 5-4.
Figure 5-5.
Figure 5-6.
Figure 5-7.
Figure 5-8.
Figure 5-9.

Figure 5-10.
Figure 5-11.
Figure 5—12.
Figure 5-13.

Figure 5-14.
Figure 5-15.

Figure 5-16.
Figure 5-17.

Pa e
Map showing Red Cedar River Basin from Cedar Lake to the confluenceg
point of Grand River and Cedar River (Davood 1960) ............................. 6
River profile in the study reach ................................................................. 7
Mean annual stream flow in Red Cedar River from yr 1932-2000 .......... 8
Mean monthly stream flow in Red Cedar River for yr 2001 .................... 9

Predicted and measured velocity at Library Bridge (4-11 April, 02). 29
Predicted and measured head at Library Bridge (4-11 April, 02) ........... 30
Predicted and measured flow at Library Bridge (4-11 April, 02). .......... 30
Predicted and measured velocity at Kellogg Bridge (4-11 April, 02). 31
Predicted and measured head at Kellogg Bridge (4-11 April, 02) .......... 31
Predicted and measured flow at Kellogg Bridge (4-11 April, 02). ......... 32
Effect of different grids on predicted velocity at the Library Bridge. 35
Effect of different grids on predicted head at the Library Bridge ........... 35
Effect of grid on predicted flow at the Library Bridge. ................. '. ........ 36
Effect of different grids on predicted velocity at the Kellogg Bridge. 36
Effect of different grids on predicted head at the Kellogg Bridge. ........ 37
Effect of different grids on predicted flow at the Kellogg Bridge. ......... 37

Effect of different time step size on predicted velocity at Library

Effect of different time step size on predicted head at Library Bridge... 39
Effect of different time step size on predicted velocity at Kellogg

Bridge ..................................................................................................... 40
Effect of different time step size on predicted head at Kellogg Bridge. 40

Time-concentration curves-dye release 1 (May 17, 2002). .................... 42

vii

Figure 5-18.
Figure 5-19.
Figure 5-20.
Figure 5-21.
Figure 5-22.

Figure 5-23.

Figure 5-24.

Figure 5-25.

Figure 5-26.

Figure 5-27.

Figure 5-28.

Figure 5-29.

Figure 5-30.
Figure 5-31.

Figure 5-32

Figure 5-33.
Figure 5-34.
Figure 5-35.

Figure 5-36.

Time—concentration curves-dye release 2 (May 31, 2002). .................... 43

Time-concentration curves-dye release 3 (Jun 6, 2002). ........................ 44
Time-concentration curve-dye release 4 (Jun 21, 2002) ......................... 45
Time-concentration curves-dye release 5 (Jun 25, 2002). ...................... 46

Time of arrival of leading edge, peak and trailing edge of the dye cloud at
Farm Lane Bridge for different flow conditions. .................................... 48
Time of arrival of leading edge, peak and trailing edge of the dye cloud at
Kellogg Bridge for different flow conditions. ........................................ 48
Time of arrival of leading edge, peak and trailing edge of the dye cloud at
Kalamazoo Bridge for different flow conditions. ................................... 49
Dispersion coefficients calculated using moments method for medium

flow conditions ........................................................................................ 51

Dispersion coefficient calculated using mass transport equation under

different flow conditions. ........................................................................ 54
Dispersion coefficient at different downstream sampling locations. ...... 55
Predicted and observed concentration at 16.82 m3/sec flow ................... 61
Predicted and observed concentration at 14.41 m3/sec flow ................... 61
Predicted and observed concentration at 19.3 m3/sec flow ..................... 62
Predicted and observed concentration at 2.49 m3/sec flow ..................... 62
Predicted and observed concentration at 2.06 m3/sec flow ..................... 63
Relation between calculated and predicted dispersion coefficients ........ 64
Calculated and observed peak arrival time. ............................................ 65

Predicted and observed concentration using empirical relations at 16.82
m3/sec flow .............................................................................................. 67
Predicted and observed concentration using empirical relations at 14.41

m3/sec flow .............................................................................................. 67

viii

Figure 5-37 Predicted and observed concentration using empirical relations at 19.06

m3/sec flow .............................................................................................. 68

ix

1. INTRODUCTION

1.1 Overview

There are two basic reasons for representing natural water systems through
mathematical modelling. The first is to increase the level of understanding of the cause-
effect relationship operative in the evaluation of water quality. The second is to apply that
increased understanding to aid in decision-making processes (Thomann 1982). In surface
water quality modelling, characterizing the hydrodynamics correctly and quantifying
dispersion accurately is essential to develop numerical tools that are sufficiently robust in
their predictive capacity. Inclusion of longitudinal dispersion enhances realism and
accuracy in the assessment of transport in streams by accounting for contaminant mixing
and it is essential when longitudinal concentration gradients exist (Koussis and Mirasol

1998).

Hydrodynamic models are deterministic in nature but range considerably in
complexity and level of mathematical sophistication. A hydrodynamic model can be a
simple one-dimensional model with vertical and lateral averaging and on the other hand,
can also be a very complex three-dimensional model taking into account the lateral and
vertical stratification of the parameters. The majority of these models, whether one, two
or three-dimensional, rely on the numerical solution of the basic hydrodynamic equations
of flow, commonly known as St. Venent wave propagation equations (Ambrose 1993).
Research of flow simulation modelling in riverine systems began in 1950’s primarily by

scientists in the US Geological Survey (Schaffranek and Goldberg 1981). The objective

was to provide a strong physical basis for the development of methods which could
determine unsteady flows in channels affected by tides, flood waves or hydropower
regulation where flow inertial effects were appreciable. Various numerical methods for
treating the St. Venent wave-propagation equations were studied and various models
were constructed and reported in the literature. The earliest models were designed to treat
only a single reach since the numerical methods were primitive and computational
capabilities were limited (Schaffranek and Goldberg 1981). In the early 1970’s the use of
branch-channel network schemes started which gave rise to a new field for the
development of computationally efficient models. Important aspects of these models are
the channel properties, cross-sectional geometry, initial and boundary conditions and the
grid to adequately capture the desired hydrodynamic properties. Nevertheless, the
predictive ability of numerical and hydraulic models cannot be fully established and no
model can reproduce all that is related to external reality (Fischer 1981). One of the major
issues has been the accurate prediction of the longitudinal dispersion, which is considered

as one of the major process contributing towards concentration gradients.

Dispersion is the scattering of the particles in water that controls the concentration of
a constituent as it is transported downstream. This scattering takes place vertically,
transversely and longitudinally. Spreading in the direction of flow is primarily caused by
velocity profile in the cross-section and is referred to as “shear flow” (Fischer 1979).
Mixing in the vertical direction takes place first followed by mixing in transverse
direction. Once the cross-sectional mixing is complete, the process of longitudinal
dispersion is the most important mechanism, erasing all longitudinal concentration
gradients (Fischer et al. 1979). Therefore in order to apply any model for the prediction

2

of concentrations at a distance downstream from the point of discharge, selection of a
proper dispersion coefficient is most important and also the most difficult task (Seo and

Cheong 1998).

The Red Cedar River meanders through the campus of Michigan State University
over a stretch of approximately 5 km and is unique with regards to the layout as a number
of outfalls draining the campus area feed it with pollutants. The nature of the pollutants
varies depending on the sub-areas being drained by the outfalls. The resulting run-off
may be from parking lots, walkways, lawns or agricultural farms, which enter the stream
at different locations throughout. The reach also offers a unique study potential in terms
of a number of bridges over the river, which makes the sampling possible on these
locations at any point across the river width and offer an opportunity to study the

variations in the hydrodynamics and contaminant transport over short distances.

The use of fluorescent dyes and tracing techniques provide a means for measuring
the time of travel and dispersion characteristics of steady and gradually varied flow in
streams. Measurements of the dispersion and concentration of dyes give insight into the
behaviour of soluble contaminants that may be introduced into a stream. The
concentration of dye in the sample is directly proportional to its fluorescence. A plot of
concentration against time defines the passage of the dye cloud at each sampling site.
Time of travel is measured by observing the time required for movement of the dye cloud

between sampling sites.

1.2 Scope Of Study

Purpose of this study was to build a foundation for a one-dimensional water quality
model for the Red Cedar River, which has its base principally in correctly establishing
the hydrodynamics and dispersion. Keeping this specific purpose in mind, the study

objectives aimed at:

a. Developing a hydrodynamic model of Red Cedar River, which could predict

the hydrodynamics with a reasonable accuracy.

b. Quantifying the longitudinal dispersion under varying conditions of flow.

2. DESCRIPTION OF THE STUDY AREA

2.1 Physical Settings

The Red Cedar River is a warm water stream in south central Michigan. It originates
as an outflow from Cedar Lake, located in Marion Township, Livingston County,
Michigan. The stream flows past the communities of Fowlerville, Webberville,
Williamston and Okemos before entering the East Lansing and Michigan State University
area (Figure 2-1). Then it connects with the Grand River in Lansing (Ingharn County,
Michigan). Total stream length is 71.13 km. The river and its tributaries drain an area of
about 1230.25 kmz, one fourth of which is drained by Sycamore Creek. The river has an
average gradient of 0.475 m/km, with about one-half of the fall occurring within the
uppermost one-third of the river (Davood 1960). The bottom elevations were obtained
from flood insurance studies done for Cedar River by Snell Environmental Group
(Nalluswami 1978). The profile of the study section shows an average lepe of 0.413
meter per kilometre for the river reach through MSU campus (Figure 2-2). The elevation
of Cedar Lake is 284.68 m above sea level and the confluence of Cedar River with Grand
River is at an elevation of 249.02 m above sea level. A USGS gauging station is located
at the southwest abutment of the Farm Lane Bridge with the exact location being
42’43’40” latitude and 84’28’40” longitude. The gage datum is 251.27 meters above sea
level and it measures the runoff from about 919.45 (74.73 %) km2 of the basin. The mean

annual temperature for the area is 8.2 0C, with a winter mean of approximately —4.4 0C

Q‘
3’
~ .
o i
p
a
.
.
.
CI
'0“ Cc

"

Itlfl'

———*.

IILK’

Figure 2-1. Map showing Red Cedar River Basin from Cedar Lake to the

confluence point of Grand River and Red Cedar River (Davood

1960).

 

251,5 IIITT‘ITT—U'TIW—IIIIIUlIIrUIITIIrYIII

Pentium

1

  
  
   
    

 

 

 

: 1
A I-
3 E :
2 250.5 .:
v I- M“ q
r: : snug. 1
o 250 :' .:
7: t :
g L .
2 249.5 : :
I.l.l : 1
g 249 : :
3" 240 5 ’- 5
8 5 We. Kahuna» I
248 I- 1 n n a l n 1 1 1 l l 1 l l l 1 1 a n l n 1 Lamp. 1 1 a l n n 1 l j
o 1000 2000 3000 4000 5000 0000 1000

Distance From Hagadom Br (meters)

Figure 2-2 River profile in the study reach

The study section within the Michigan State University starts from Hagadom Road
Bridge at the upstream boundary and ends at Kalamazoo Street Bridge. The study section
is 5.079 km long and varies from approximately 16 meters to 40 meters in width with an
average width of 28 meters. Throughout the entire reach, 67 outfalls of varying sizes
drain into the river. Fifty-nine out of sixty seven outfalls exist on the university maps
prepared by the MSU Physical Plant. A weir is located opposite to the MSU main library.
The backwaters of this weir extend upstream a short distance and cause an impoundment
of water resulting in low velocity in the seetion. Downstream of the weir is a steep slope,
which causes the water to gain energy due to an increase in head. This also causes re-
aeration of water thereby improving the dissolved oxygen levels. Above the weir, the

bottom is principally muddy mixed with rock debris; however, the banks are extensively

vegetated at places. Below the weir the bottom is coarse gravel and sand covered by a
thin covering of silt and detritus. The banks are forested in some areas but much of the

river study section runs along parking lots and lawns of Michigan State University.

2.2 Flow Variations in Red Cedar

Statistical analysis of the annual stream flow (Figure 2-3) shows a variation in the flow in
various years with a mean of 214.6 ft3/sec and a standard deviation of 79.17 ft3/sec,
which is 36.9% of the mean annual stream flow. A plot of the mean monthly flows for
the year 2001 shows the seasonal variation in the stream flow (Figure 2-4). Diurnal
variations in the flow were also observed from time to time, which confirm the need for a

model that can handle transient flow.

 

I' III. IV

 

 

Flow (in...)
s

d
III

III

 

 

O
4 I

1m0194019501900 1970 1900 1990 2000
Year

Figure 2-3. Mean annual stream flow in Red Cedar River from yr 1932-2000.
(Source:http/lwaterdata.sugs. gov/mi/nwislannuall?site_no=041 125

00&agency_cd=USGS)

 

 

 

6W 1- I r I I I r I I I I I u

I 1

500 '- .--~ -‘

n .0 ~00 u:

A : .1 -.. 1'
I- .0 0 :1

§ 400 I i -:
e t r =
v 30° :- ,e" 1
3 I ' . :
.0. 200 :- "-b -‘
ll. I .. .1:
100 : "f3

7 ”m... “4,!” .

o " l l l L I l l l l l I

 

JanFebMarAprIlayJun Jul AugSepOctNovDoc
Months

Figure 24. Mean monthly stream flow in Red Cedar River for yr 2001.
(Source:http://waterdata.sugs.gov/mi/nwis/annuall7site_no=041 12

500&agency_cd=USGS)

3 . LITERATURE REVIEW

The contaminants or effluents, once discharged into rivers undergo various stages of
mixing as they are transported downstream. In broad terms these stages can be classified
into two types. In the first stage, commonly referred to as “initial period”, the mixing in
the vertical and transverse direction takes place due to turbulence and wall shear. During
this period an imbalance exists between advection and turbulent diffusion. The vertical
and transverse mixing is quantified by vertical and transverse mixing coefficients
respectively both expressed as a function of depth of flow and the bed shear velocity.
Fischer (1979) showed however, that the difference in the vertical and lateral dimensions
in natural channels makes the transverse mixing coefficient more than 90 times greater
than the vertical mixing coefficient, therefore, vertical mixing can safely be assumed to
occur instantaneously for a line injection. Nevertheless, determination of transverse
mixing coefficient is considered essential in determining the length of stream required for

the complete cross-sectional mixing.

The second stage after the cross-sectional mixing is complete is referred to as
“Fickian period”. During this stage a balance exists between advection and turbulent
diffusion. The most widely used equation to estimate the rates of longitudinal dispersion

is the l-D mass transport equation, more commonly known as l-D advection-dispersion

equation (ADE) i.e.

30 32C 80
—=D——— — 3-1
a: 'ax2 Uax ( )

10

The analytical solution of this equation for an instantaneous injection of a conservative

pollutant is given as:

C(x,t) = M]

M
——CX

(3-2)
where:

C = cross-sectionally and vertically averaged concentration
t = time

D; = longitudinal dispersion coefficient
x = distance in the direction of flow

U = mean longitudinal velocity

M = total mass of the contaminant

For the application of (3-1) the knowledge of an accurate value of dispersion
coefficient is necessary. The simplest way is to use a measured dispersion coefficient
(Seo and Cheong 1998). In the absence of a tracer test time-concentration data, prediction
of the longitudinal dispersion coefficient by other means can be resorted to. In the past

few years, the focus has been on the prediction of dispersion coefficients based on the

readily available bulk hydraulic parameters i.e., width to depth ratio [1;] and friction

 

term“)! ]. Seo and Cheong (1998) developed a new equation by using a combination of

11

dimensional analysis and regression methods using 59 data sets for 26 rivers in United

States to predict the longitudinal dispersion in natural streams. The equation is:

0.620 L428
hiding] [be]
' (3-3)

 

where:
K/hU* = dimensionless dispersion coefficient
W/h= width to depth ratio
U/U*= friction term defined by (ii/i)“2
f = Darcy- Weisbach’s friction factor

Seo and Cheong ( 1998) also proved that this equation allows for superior predictions
as compared to all other existing equations. Deng, et al (2001) proposed a new equation
incorporating the effect of transverse mixing and proved that the equation predicts closely
in 60.3% of the cases as opposed to 39.7% of the cases by the equation by Seo and

Cheong (1998). Their equation is:
K _ 0.15 [KFTET
hU * 88,0 h U, (34)

1.38
.,,=o.r.5+[_1_][.vz] [U]
3250 h U, ($5)

However the latest development in this area is the equation by Kashefipour and

 

 

where:

 

Falconer (2002) who postulated that longitudinal dispersion coefficient is a function of
velocity, width and depth of the channel, bed shear velocity, kinematic viscosity and

shape factor.

12

D,.=fiU, H, W, Ury 5,) (3-6)

where:‘

U: Cross sectional average velocity:
H = Depth of flow

W = Channel width

U.= Bed shear velocity

v = Kinematic viscosity

Sf: Shape factor

They argued that, since the flow in natural channels is generally fully turbulent and
rough with Reynold’s number effects generally being negligible, the kinematic viscosity
could be ignored. The approach followed by Kashefipour and Falconer (2002) is
essentially the same as that of Sec and Cheong (1998). The new equation proposed was
also developed using dimensional analysis and regression for 81 data sets measured in 30

rivers in the US, which is:

D, =10.612HU[U1:]

O

(3-7)

For 81 data sets, the results predicted by this equation have been reported to be better

than those predicted by equations by Seo and Cheong (1998).

13

Dispersion coefficients are used in the one-dimensional advection-dispersion
equation in order to predict concentrations at points downstream. This approach is limited
to locations far downstream from the source where the balance between advection and
diffusion is achieved (Taylor, 1954). During the “initial period”, advection and diffusion
are not balanced and the one-dimensional advection-dispersion equation cannot be
applied. Also, due to dominant effect of the velocity distribution during the initial period,
the longitudinal distribution of the cross-sectionally averaged concentration is highly
skewed, with a steep gradient in the downstream direction and a long tail in the upstream
direction. The variance of the longitudinal concentration distribution increases non-
linearly with time during the “initial period” and increases linearly with time during the
“Fickian period” for a steady uniform flow (Seo and Cheong 1998). For many rivers with
irregular boundaries, the process of dispersion is very complicated and many
investigators have questioned its characterization by a single coefficient (Seo and Cheong
2001). In the early stages of the transport process, the advective term in eq. (3-1), due to
turbulent velocity fluctuations, plays an important role in the diffusion process. As a
result, there is an imbalance between the two terms and consequently, the analysis of

Taylor (1954) cannot be applied in this section of flow (Kashefipour and Falconer 2002).

The limitation of the “Fickian” model is that it is not able to accurately represent
highly skewed concentration profiles often observed in natural streams (Swamee, Pathak
et al. 2000). Seo and Cheong (2001) also argue, that the skewness in the time-
concentration curves in natural channels is due to the storage zones that retain a portion
of solute mass as the main cloud passes by and then the solute is slowly released back

into the flow zone.

14

In cases where time-concentration data is available, an alternative to the one-dimensional
advection-dispersion equation has been provided by Swamee et al (2000), in which the
calculation of a number if dispersion parameters is suggested rather than relying on a

single value of dispersion coefficient. Their model is of the form:

 

m-l % -(n+1)
t-tx m+n n(m-l) t-tJr
c = c +
p m(n +1) m(n +1) t p - tx (3-8)

Here, m, n, tp, tx and Id are called dispersion parameters. The inception time t1, the
peak concentration Cp, and the time of peak concentration tp can be readily determined
from a time concentration curve. The parameters m and n can be determined by plotting
c/cp against (t-tx)/(tp-tx) on a double logarithmic plot where ml is the slope of the rising
limb and (m/n +1 ) is the slope of the recession limb. The optimised values of dispersion
parameters are obtained by minimizing the error between the observed concentration
profile and the concentration profile predicted by (3-8), which can finally be transformed
as the functions of the channel geometry and flow properties for a particular channel
geometry. These variables are finally reported in terms of distance from the injection
point, flow area, flow velocity and time and are independent of time-concentration data
for a subsequent use. Swamee et al (2000) proved that the results from this model are

superior when compared to a number of existing predictors.

Davis et al (2000) also presented a solute transport model incorporating the effects of
tracer storage in dead zones. They represent stream as consisting of the two parallel

regions; the bulk flow region and the dead zone. The bulk flow region occurs in the

15

central part where the longitudinal dispersive properties are described by one-
dimensional advection-dispersion equation, and the dead zone comprises the additional
cross-sectional area with slow moving water where tracer can be temporarily stored.
They represent exchange between the two regions using first order rate kinetics and the
combined shear flow dispersion-dead zone storage model (D-DZM). This provides a
much better and physically consistent description of the tracer clouds evolution compared
to the conventional one-dimensional advection-dispersion equation. The model is based
on the analytical solution of two different equations representing the bulk flow region and

the dead zones, which are:

2
ac Ua_c__Ka C:18C5

 

 

 

a: 8x 3x2 7 a: (39)
2
8C5 : Z—(C _ CS)
at r (3_10)

where:

x =(A/As)m is a relative measure of the effective area of the dead zone region

r = characteristic time scale for the exchange of tracer particles between the bulk

flow and the dead zones.

Davis et a1 (2000) obtained the solution of these two equations of the form:

C(x,t)- _ exp[—(4K ”ZU’) ——T—e"r] +61%
2A(72Kt)——}/2—e

. _ 2 . _, ii
I— exp':_(ifl_)_]ezz/rle A{_V-) [1[2_Zv%(t_v)yz]dv (3_11)
o 2A(,:v)ye 4Kv T t -v T

16

where v is a variable of integration and I, is a modified Bessel function of the first kind
and first order. This model by also involves obtaining the unknown parameters 7 , K and
zby comparing the observed values with those predicted by equation (3-11) and
minimizing the error using the least square estimator. They contend that this equation
models the decline of peak concentration, growth of variance and overall cloud shape
successfully while keeping the parameter values constant or narrow range, thus the dead

zone storage accounts for non-Fickian elements in the tracer cloud’s evolution.

Seo and Cheong (2001) also follow a similar approach and represent the differential

equations for the storage zone and flow zone, which are:

 

 

3C BC 2
—1-+U,——f—=kf:€+€T"(CS—Cf)

at dx x (3_12)
3C: =T"(C, —C.)

3’ (3-13)

where: C I = flow zone mean concentration
U f = flow zone mean velocity
K I = longitudinal dispersion coefficient in the flow zone

C5 = storage zone mean solute concentration

8 = ratio of storage zone area to flow zone area

T: residence time of the tracer in the storage zone = As/kP
As=cross-sectional area of the storage zone

P = wetted contact length between the flow zone and storage zone in the
transverse direction or vertical direction.

k = mass exchange coefficient.

17

The storage zone model by Seo and Cheong (2001) also is based on evaluating the
storage zone parameters by the temporal moments equations derived using moment
matching method and equating these to the observed temporal moments calculated from
the observed time concentration data. They made use of a robust constrained non-linear
equation solver to solve four non-linear equations to evaluate the storage zone
parameters. They applied the storage zone model to the measured time- concentration
data for the Missouri River and proved that the parameters of storage zone model
calculated by using the moment matching method could properly explain the natural

dispersion process in the actual streams.

l8

4. METHODOLOGY

4.1 Selection of Model

Several choices of models are available for use in river-quality planning studies.
Following definition of modelling objectives, a thorough review of existing data should
be performed. Some important factors which need to be considered in model selection
include (1) required accuracy; (2) study timeframe; (3) data availability, attainability and
adequacy; (4) availability of the computer program; (5) computational capability; (6)
model sophistication; and (7) the availability of source code (Jennings 1976). The
appropriate level of model complexity is best addressed by considering the (1) relative
costs and problems associated with the model; (2) data availability, and (3) scope of the
study being conducted. Since this study is being conducted within the overall framework
of Red Cedar River Watershed Project (MSU Water) which is directed at understanding
the influence of land use and other campus activities on the water quality of Red Cedar
River, it necessitates use of a comprehensive water quality model capable of simulating

both the conventional and toxic pollutants.

A number of models like RMA2 (Donnnell 1997), RMA4, HSPF, QUALZEU
(Brown and Barnwell Jr. 1987), CE-QUAL-RIVI and DYNHYD/W ASP (Ambrose 1993)
were considered. Of all the models considered, EPA’s hydrodynamic model DYNHYD

was selected for the following reasons.

a. DYNHYD is the driving hydrodynamic model for WASP (water quality analysis

simulation program) (Ambrose 1993), which is a generalized modeling

19

framework for contaminant fate and transport and can be applied in one, two or
three dimensions.

b. WASP is designed to permit easy substitution of user-written sub-routines into the
program structure.

0. WASP consists of two sub models i.e., EUTRO and TOXI, to simulate two major
classes of water quality problems.

4.2 Fluorescein As A Water Tracer

For the purpose of this study, the tracer used was fluorescein. Fluorescein is a green
dye with a generic name of Acid Yellow 73, which has a colour index of 45350.
Maximum excitation and emission for fluorescein occurs at 490 and 520 nm respectively.
Fluorescein has a sensitivity of 0.11 micrograms/litre per unit scale and a minimum
detectability of 0.29 microgram llitre (Smart and Laidlaw 1977). Its fluorescence is a
function of temperature and fluorescence intensity varies inversely with temperature.
(Kasnavia and Sabatini 1999). However, preparation of a calibration curve at selected
room temperature and analysing all the samples at a constant temperature can overcome
this limitation. Another major problem encountered in natural waters is of background
fluorescence, which can be due to natural dissolved material and suspended sediments.
The level of suspended sediments increases during the spring in Red Cedar with a high
discharge due to snow melt, which increases the background fluorescence and reduces
effective dye fluorescence due to light absorption and scattering by the suspended
particles. Background fluorescence in case of fluorescein is a bigger problem, as it is
many times stronger at the green wave band than at the orange. Fluorescence sorbs less as

compared to some other fluorescent dyes used in water tracing like rhodamine WT. Red

20

Cedar River offers a lot of sorption media in terms of weeds, tree branches and suspended

solids, hence the use of fluorescein was preferred for this study.

4.3 Model Implementation

The basis for DYNHYD are the equations of continuity and momentum, which are
solved for a channel-junction (link-node) computational network. Variable upstream

flows and downstream heads drive it. These equations are:

2
.82 -1122: -géfl+gL4/U2
at 3x 8x R 3 (44)
22:19
at 8x (4_2)

The first term in equation 4-1 is the local acceleration term and denotes rate of
change of velocity with time while the second term is the convective inertia term, which
represents the rate of momentum change by mass transfer. The first term on right hand
side denotes the effect of gravity on the water surface gradient and the last term describes
the effects of frictional resistance. The equation of motion (4-1), based on the
conservation of momentum predicts water velocities and flows. The equation of
continuity (4-2), based on conservation of volume predicts heads and volumes. This
approach assumes that the flow is predominantly one-dimensional and accelerations
normal to the direction of flow are negligible. Model assumptions include a constant top

width, a variable hydraulic depth, and moderate bottom slopes.

21

The "channel-junction" network solves the equations of motion and continuity at
alternating grid points. At each time step, the momentum equation is solved at the
channels to compute the velocities, while the heads are obtained by solving the equation
of continuity. The time step is selected based on the channel length such that the stability
restrictions are satisfied. Typical values of time step used in our computations varied
from one to five seconds. The resulting unsteady hydrodynamics are averaged over larger
time intervals and are stored for later use by the water quality program (Ambrose 1993).
The detailed schematisation of DYNHYD is covered in the user’s manual (Ambrose

1988).

4.4 Model Segmentation

Geometric and hydraulic factors as well as the computational considerations are the
base, upon which the subdivision of branches into segments is determined (Schaffranek
and Goldberg 1981). For the purpose of implementing the St. Venant equations, the entire
length of the river in the study section was divided into 103 junctions and 102 channels.
Each junction is a volumetric unit acting as receptacle for the water transported through
the connecting channels. Taken together all the junctions account for all the water in that
portion of the river and the channels account for all the water movement in the river. A
50 meters channel length for each channel was kept so as to conform to the
computational stability criteria commonly known as Courant’s condition (Ambrose
1993). Ideally the channel lengths should be such that the surface area of the junctions
remains close, if not equal, but this requirement was difficult to meet in our case as the
channel width varies across the entire reach of the river. Appendix A lists the geometric

properties of all the channel and junctions including width, junction surface areas and

22

direction. Based on these parameters the input file used to run the DYNHYDS for the

given period was prepared which is included in Appendix B.

4.5 Tracer Tests

Hagadom Road Bridge was selected as the injection site. The three sampling sites
selected were Farm Lane Bridge, Kellogg Foot Bridge and Kalamazoo Street Bridge
(Figure 2-2). Farm Lane Bridge was selected as a sampling site due to its accessibility
and the availability of USGS gage, which would serve as the index gage while
Kalamazoo Street Bridge was selected being at the boundary of the river reach under
study. The selection of Kellogg Bridge as one of the sampling points was arbitrary just to
have an intermediate sampling point at almost middle of the reach. Five tracer tests were
conducted for different flow conditions ranging from approximately 2 m3/sec to 19
m3/sec. Releasing the dye in the middle 75% of the channel width ensured to some extent
the conditions of instantaneous mixing. Extensive sampling was done at the three
sampling points at the rrriddle of the cross section for the first three dye releases, in which
the flow was 16.82 m3/sec, 14.41 m3/sec and 19.06 m3/sec respectively. During the fourth
dye release, in which the flow was 2.49 m3/sec, sampling could only be done at Bogue
Bridge located upstream of the first sampling point, due to extremely low velocity
(Figure 2-2), however, three different points across a transect could be sampled to
ascertain if complete transverse mixing has been reached. For the fifth dye release,
sampling was only done at Farm Lane Bridge and Kalamazoo Bridge only and sampling
at Kellogg Bridge had to be omitted due to long sampling interval at each sampling

station.

23

Fluorescein solution with a concentration of 179.06 grams per litre was used for all
the tracer tests in order to have a consistency. The volume of the dye used was based on a
desired peak concentration range of 10-20 micrograms/litre at the last sampling point

located at a distance of 5.079 kilometres from the release point.

4.6 Data Collection.

Collection and analysis of surface water data and information is a complex task. A
variety of instruments, measurement methods and analytical techniques are usually
required to produce a surface water record for a single site. Three comprehensive sets of
data are required to carry out flow simulations by mathematical models such as the
branch-network flow model. Initial condition data, channel geometry data and boundary-
value data constitute mandatory data requirements for flow computation by the branch

channel network flow model (Schaffranek and Goldberg 1981).

This study focused on recommended methods for data gathering and field
measurements in order to ensure data comparability with the data acquired by other
federal agencies like USGS. The Mid-section method as outlined in National Handbook
of recommended methods for Water Data Acquisition (1977) was used to calculate the
cross-sectional areas and discharges. Also a two-point method was employed to measure
the velocities at different cross sections. Field measurement at Library Bridge and
Kellogg Bridge was done for eight consecutive days from 04 April 2002 to 11 April

2002. The field data collected for the purpose of this study were:

a. Stage measurements at the downstream boundary (Kalamazoo street Bridge) to

generate head versus time as one boundary condition of the model.

24

b. Discharge measurements at Hagadom Bridge as one of the model inputs at the
first junction. Farm Lane gage is located 1400 meters downstream of the inlet
boundary at Hagadom Bridge, therefore the discharge measurements available
from USGS gage at the Farm Lane Bridge were extrapolated in terms of time to
yield the values for discharge at Hagadom Bridge.

c. Velocity and stage measurements at, Library Bridge and Kellogg Foot Bridge for
calibration of the model. These measurements were made using a Gurley
Precision price AA current meter and USGS bridge board set. The field data
collected is summarized in Appendix C.

4.7 Manning’s Roughness Coefficient.

Calculation of stream discharge and floodwater elevations requires the evaluation
of flow impeding characteristics of the stream channels and their banks. Manning’s
roughness coefficient is commonly used to assrgn a quantitative value to represent the
collective effect of these characteristics. In DYNHYDS, it acts as a tuning knob to
calibrate the model. Changing the value of “Manning’s n” in one channel affects the
upstream and downstream channels. Increasing the value of “Manning’s n” causes more
energy to be dissipated in that channel. As a result, the velocity head will decrease and
time of travel in that channel will increase. Lowering “Manning’s n” will decrease

resistance to flow, resulting in a higher velocity head and a shorter time of travel.

The user’s manual for DYNHYD gives a generalized value of “Manning’s n”
between 0.01-0.08. However Coon (1998) suggests a value of “Manning’s n” as 0.035-

0.100 for major streams with a top width greater than 100 ft at flood stage and with

25

irregular and rough section. Nevertheless it is mostly the velocities, which are more

sensitive to “Manning’s n “ values as compared to water surface elevations or discharges.

26

5. RESULTS AND DISCUSSION

5.1 Model Calibration

The head, velocity and discharge measured from 4 April 02 to 11 April 02 at the
Library and Kellogg bridges were used to calibrate the model. Calculation of stream
discharge and floodwater elevations requires the evaluation of flow impeding
characteristics of the stream channels and their banks. Manning’s roughness coefficient is
commonly used to assign a quantitative value to represent the collective effect of these
characteristics. In DYNHYDS, it acts as a tuning knob to calibrate the model. Changing
the value of “Manning’s n” in one channel affects the upstream and downstream
channels. Increasing the value of “Manning’s n” causes more energy to be dissipated in
that channel. As a result, the velocrty head will decrease and time of travel in that channel
will increase. Lowering “Manning’s n” will decrease resistance to flow, resulting in a

higher velocrty head and a shorter time of travel.

The major factors affecting the roughness coefficient are size, shape and distribution
of grain size material, channel surface irregularity, channel shape variation, obstructions,
type and density of vegetation and degree of meandering. Nevertheless it is mostly the

6‘

velocities, which are more sensitive to “Manning’s n values as compared to water
surface elevations or discharges. A range of 0.035 to 0.10 for major streams with a top
width at flood stage greater than 30 meters for an irregular and rough section has been
proposed by Chow (1959). For DYNHYD 5, a value of roughness coefficient for each
channel is required as a model input data. Most of the empirical equations used to

calculate “n” are based on the size of the bed material, for which no comprehensive data

existed for this reach. Therefore, Manning’s roughness coefficient values for each
27

channel were estimated basing on an empirical equation by V.B Sauer (Coon 1998). With
this equation, it is possible to calculate the roughness coefficient using the hydraulic

radius and the water surface elevations. The equation is:

n = 0.1 153'18R0'08
(5-1)

where:
SW = slope of water surface in meter/meter
R = hydraulic radius in meters

Basing upon this equation, following values were calculated for Manning’s

roughness coefficient.

Table 5-1 Manning's Roughness Coefficients

 

 

 

 

 

 

 

 

Channel Number Manning’s Roughness
Coefficrent

1-17 0.021

18-27 0.032

28-38 0.036

3945 0.022

46-62 0.03 1

63-68 0.036
69-102 0031

 

 

 

 

28

5.2 Hydrodynamics

The velocities, heads and flows predicted by the model at the library bridge were
generally consistent and in agreement with the observed values for all type of flow
conditions (Figure 5-1) to (Figure 5-3) although an under prediction of the velocities was
observed for flow lower than 14 m3/sec. At Kellogg Bridge the flows predicted by
DYNHYD are in general agreement with the measured flows, however the velocities
were higher than the measured velocities and the heads were less than the measured

values (Figure 5—4) to (Figure 5-6).

 

 

 

 

 

 

 

007 :IIII'UIIIIIIII'UT'Tl—UIIIIIUI'I'III'IIII:

I- in... II

0.6 3.: x =.

6 X x X a" :

0 | ‘ “mu-inns. . . -.

tn 0 5 "'-----:<-........~ -‘ 5

E 0.4 .:

V :

,3 0.3 -5

8 0 2 I ' E

3 . II Predicted Velocity

> 0.1 i X Measured Velocity

o I

0 1 2 3 4 5 6 7 8
Time (days)

Figure 5-1. Predicted and measured velocity at Library Bridge (4-11 April, 02).

29

 

 

 

 

 

    

3.5 :U'IIIUUUUIUIIIIIUri'IfiUITI'UIIU'I'II'T:

3 E- X Measured Head 2
70‘ E ——PredictedHead E
h 2.5 :- -:
2 : :
or 2 ':
E :
V 1.5 .:
g :
0r 1 1
I

0.5

 

 

0 1 2 3 4 5 6 7 8
Time (days)

Figure 5-2. Predicted and measured head at Library Bridge (4-11 April, 02).

 

 

 

 

35 . .*
30 ----- Predicted Flows 3
,A : ~ X Measured Flow .
o 25 : .
s e =
\ 2 -:
"E 0 1 ghee-I.
v 15 : .X -:
g : ,.’ g
10 i‘ ’7- .O' 1
E : k-.““.&-.-X-.-m.. :
5 . s:-

0 .5
o 1 2 3 4 5 e 7 8

Time (days)

Figure 5-3. Predicted and measured flow at Library Bridge (4-11 April, 02).

30

 

 

 

 

 

 

1.4 .1
12 X Measured Velocity f
6‘ Predicted Velocity :
a) 1 . 1
«n . .
E 0.8 l -;
g 0.6 : f x X:
0 1 X X X :
2 0.4 i X X 1
m i :
> 0.2 t .-
i :

0 I
0 1 2 3 4 5 6 7 8

Time (days)

Figure 5-4. Predicted and measured velocity at Kellogg Bridge (4-11 April, 02).

 

 

 

 

 

 

3 *.

2.5 .- Predicted Head
1;" 2 .. X Measured Head
5 .
.93
q; 1.5
E , 1
s i x
a, 0.5 X
= i 2......

0 fix X X X X-‘fl',

-0.5 '

0 1 2 3 4 5 6 7 8
Time (days)

Figure 5-5. Predicted and measured head at Kellogg Bridge (4-11 April, 02)

31

 

 

 

 

 

30 7 III'UIU[IIIIU'IUIU'UTIT'UIIIIIITIITITI:

25 Predicted Flow .1

A X Measured Flow X =
3 J
'0'“..- d

E “"‘a:
"’ .-' .'
E r' X :
g .. .--’ -3
E “'96-'36. 1

 

 

0 1 2 3 4 5 6 7 8
Time (days)

Figure 5-6. Predicted and measured flow at Kellogg Bridge (4-11 April, 02).

No specific guidance criteria for the error statistics for calibrating the hydrodynamic
model for a natural stream could be found in the literature, therefore the preliminary
guidance criteria by (Wu 1995) for estuarine water quality models was taken as a
guideline. According to these criteria, the correlation coefficient should be greater than
0.94 for hydrodynamic variables, 0.84 for transport of a conservative water quality
variable and 0.60 for water quality variables. Comparison of model predictions and
observed data was performed using linear regression techniques (Thoman 1982). Three
standard linear regression statistics were computed which are (1) square of the correlation
coefficient (2) slope of the regression line and (3) intercept of the regression line. The
slope of the regression line represents how well trends can be projected with the
calibrated model and the intercept indicates if any systematic error is present. The square
of correlation coefficient for all the hydrodynamic variables i.e., velocity, head and

discharge was calculated between 0.918 to 0.992 at the Library Bridge and 0.718 to 0.90
32

for the Kellogg Bridge respectively. Also, the root mean square error (RMSE), which is
the mean square of any residuals, is also a useable statistics to verify model forecasts, and
is applicable to a large number of analysis and forecast elements. The smaller the RMSE.

the better is the performance of the model. The regression analysis figures are tabulated

in (Table 5-2).

Table 5-2. Regression statistics for hydrodynamic variables.

 

 

 

 

Paramete Library Bridge Kellogg Bridge
r Velocity Head Flow Velocity Head Flow
R2 0.916 0.97 0.99 0.83 0.78 0.92
Slope 0.594 0.894 1.009 0.967 1.22 1.014

 

Intercept 0.237 0.106 -0. 151 -0.064 0.289 -0. 187
RMSE 0.0358 0.060 0.414 0.093 0.285 1.426

 

 

 

 

 

 

 

 

 

 

The velocity and head predicted by the model at the Kellogg Bridge were not as
close to the observed values as was the case for the Library Bridge. This could not be
improved by grid refinement. The sharp bend just before the Kellogg Bridge appears to

have an influence on the velocities, which could not be accurately captured by the model.

5.3 Effect of Grid On Model Performance

As described earlier, the entire reach needed to be divided into number of channels
(segments) for the implementation of computational scheme on a network. Different grids
were tried and implemented. Three different grids comprising 28 channels, 102 channels
and 153 channels were tested. For 28-channel grid, the mean length to width ratio was

7.5, with a maximum of 12.3 and minimum of 3.7. For the 102-channel grid, a constant

33

segment length of 50 meters was tested, for which the max, rrrin and mean length to width
ratios were 3.06, 1.24 and 1.85 respectively. For 153-channel-grid, a constant length to
width ratio of 1.2 was tried. Although the refinement of the model grid from 28 channels
to 102 channels refined the model output, further refinement of the grid to 153 channels
made the model predictions worse. This is likely related to a violation of the channel
length requirement in DYNHYD for some of the channels (Ambrose 1993), according to

which:

Ar, 2 (,ng, iU,)At
where:

Ax, = length of channel i, m

H,- = mean depth of channel 1', m
U; = velocity in channel i, m

At = computational time step

g = acceleration due to gravity

This also reduced the time step to almost 1 second thereby increasing the run time by
several orders. Also, the max river width is 40.2 meters, which entails that the
longitudinal dimension for a segment must be greater than this value in order to prevent

masking of the velocity profile in the longitudinal direction.

34

0.7 ‘

 

 

 

 

 

 

 

 

 

 

 

, .w’" "15?
0.6 _ ,2" X
x x X 3" “'-
§ 0'5 - N a" 1'.
E 0 4 ’ ~---—-——.._ "I
v . E “an“.f
.E' 0.3 I .3”,
o . ,.
o . - a:
- . -
g 0'2 t m‘ x Observed
: --o-- Predicted- 28 Channel grid
0.1 _ u-e— Predicted-102 Channel Grid
--o-- Predicted-153 Channel Grid
0 ‘ muff-mm
0 1 2 3 4 5 6 7 8
Time (days)
Figure 5-7. Effect of different grids on predicted velocity at the Library
Bridge.
35 ...... , ....... , ....... , ....... , ....... . ....... , ....... , .......
3 L X Observed
t —-e- Predicted-20 Chamei Grid
: -l- Predicted -102 Channel Grid
’0? 2.5 :- *Predicted-1530hanneicrld
h I
{-i 2
E
g 1.5
I 1
0.5
o l
0 1 2 3 4 5 6 7 8

Time (days)

Figure 5-8. Effect of different grids on predicted head at the Library Bridge.

35

     
 
 
 
 

 

m rvvvvw'vvvvvtv'vvvvvv—T"vvvvtv'vvvvvvv'vv—Vv—vvv

 

* .

. X Observed

. --e- Predicted-26 Channel Grid
-l- Predicted-102 Channel Grid
15 f --o— Predicted 453 Channel Grid

 

 

 

 

 

8
«0
a"
E 10

V
3
2
IL

5 I

- d

h d

o I ...... I ....... l ....... l ...... 1 ....... l ....... l ....... I ....... 1

0 1 2 3 4 5 6 7 6

Time (days)

Figure 5-9. Effect of grid on predicted flow at the Library Bridge.

 

 

 

0.9 ‘
x Observed
0 6 . --o—- Predicted-28 Channel Grid fl
' --I-- Predicted- 102 Channel Grid _ ”x
-0- Predicted -153 Channel Grid affix

 

Velocity (in/sec)

All.

 

 

 

 

0 1 2 3 4 5 s 7 s
Time (days)

Figure 5-10. Effect of different grids on predicted velocity at the Kellogg

Bridge.

36

 

1,5 b ..... , ....... , ....... , ....... , ....... , ....... , ....... , ......
. X Oburved

. --o- Predicted-28 Channel Grid

. —I- Predicted 402 Channel Grid
1 r -+-- Predicted -153 Channel Grid

 

 

 

 

 

 

Head (meters)

 

 

 

Time (days)

Figure 5-11. Effect of different grids on predicted head at the Kellogg Bridge.

 

 

     
   
 

 

    

 

 

 

 

20
u-o— Predicted-28 Channels
--I-- Predicted -102 Channel Grid ‘
15 --e-- Predicted -153 Channel Grid 1
’8‘ X l
i
”S i
E 10 '
v ‘
3 1
2 Ii
l i
5 .1
o 7 .l...4...l.......l.......1.2.2.2.lu-.u-ll.--...l....-..
0 1 2 3 4 5 6 7 8
Time (days)

Figure 5-12. Effect of different grids on predicted flow at the Kellogg Bridge.

37

5.4 Effect of Time Step on Model Performance

For a fixed length, as in this case, the Courant condition restricts the time increment

of the solutions accordingly, (Schaffranek and Goldberg 1981), i.e.

 

IU, i ng. I (5_2)

According to Schaffranek and Goldberg (1981), although the time step to
segment length ratio presented by Courant condition need not to be strictly upheld, the
conservative properties of the model, and hence the accuracy of the results, are the best
values close to the courant criterion. As per this condition, the value of the time step
calculated was close to 10 seconds using a constant segment length of 50 meters, the
maximum reach velocity of 0.7 m/sec, and maximum reach depth of 2 meters. However
the model became unstable for a time step of 7 seconds and above. Also the model runs
for different time steps within the stable range of 1, 2, 3, 4 and 5 seconds showed no
dispersion of the results as can be seen in (Figure 5-13) through (Figure 5-16), in which

the simulated parameter values for all the different time steps is exactly the same.

38

 

  

 

 

 

 

 

 

 

 

 

 

 

 

0.7 HUII'II'I'II'IIT'FrIHUII'I'rUITrTI[I'fi:
0.6 ':
T; 0.5 E 'i
0 5 ..
E 0.4 g 1
v 5 1
0.3 I "
g E mom Time Step = 1 second E
8 0.2 E merm- Time Step = 2 seconds E
'5 a «mom- Time Step = 3 seconds :
> 0-1 g ----X-- Time Step = 4 seconds
0 '_.‘. mem- Time Step = 5 Second I
I .
‘01 IIllllIlLllLllllllllllllllllIIILLLIIIll
0 1 2 3 4 5 6 7 8
Time (days)
Figure 5-13. Effect of different time step size on predicted velocity at Library
Bridge.
2.5 _
: «me-- Tirne Step = 1 second
2 E «m-«isi Time Step = 2 seconds
{a :2 ----e---- Time Step = 3 seconds
he . .
3 1.5 '1' ----X--- Time Step = 5 seconds
0 -: "HA" Time Step = 4 seconds
E 3
V r
g 1 3.
it ..-"“"'.""l-.
I j _I '
0.5 rt-.- . ,_____.
- ‘ ..~.‘~..~ ‘ _..e
t
o l
0 1 2 3 4 5 6 7 6

Figure 5-14.

Time (days)

Effect of different time step size on predicted head at Library

Bridge

39

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 II...Iiit—l—UIII...IIIUUVIF'I'IYUY‘r't‘r.
as i a
8 o 6 .- m
E : :
V 0.4 :' j
.‘E ' "'0"- Tlrne Step = 1 second ..
8 0.2 :1 met-- Time Step = 2 seconds J
T) : ........ Time Step = 3 seconds 2
> 0 L ---X-- Time Step = 4 seconds '3
- mew- Time Step = 5 seconds -
02 . ll.llulllJllllllllllIllLlllllLllllll
0 1 2 3 4 5 6 7 8
Time (days)
Figure 5-15. Effect of different time step size on predicted velocity at Kellogg
Bridge.
2.5 _
: ...0... Time Step = 5 seconds
2 :’ «nan-- Time Step = 4 seconds
A I -------0- Time Step = 3 seconds
3 15 :r .......x. Time Step = 2 seconds
.g j ----+-- Time Step = 1 second
h
E 1 :'
V I-
3 :
a 0.5 :‘r
I :
0 L _.r"‘""”""'"‘---. _
: mm..."...._,_,__.._m______.m..._"_,...
-0.5 ‘
0 1 2 3 4 5 6 7 8

Time (days)

Figure 5-16. Effect of different time step size on predicted head at Kellogg

Bridge.

40

5.5 Time of Travel

The sampling schedule for each dye study depended on the flow but the sampling
interval was between 1—4 minutes at all sampling points. The time-concentration data for
5 dye releases is presented in Appendix D through Appendix H and the time
concentration plots are presented in Figure 5-17 through Figure 5-21 for each dye release.
The time of arrival of the leading edge, peak, centroid and the trailing edge at each

sampling sites are presented in Table (5-3) through (Table 5-7).

41

Table 5-3. Time of travel data-dye release 1 (May 17, 2002).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time (minutes)

 

0:32!“ L333? Peak Centrold T332? Discharge P5“ Time of
sampling Injection at Index CWC- passage of
Location Point Travel Travel Travel Travel Gage C, dye cloud

Time Time Time Time 3
(Km) (mlns) (mlns) (mlns) (mlns) (m ,8“) (ugIL) (mlns)
Farm Lane
Bridge 1.4 46.15 59.15 63.57 86.17 16.82 41 40.02
Kellogg
Bridge 3.1 99 113.09 125.22 163 17.1 17.9 64
Kaf'amazm 5.079 146.88 175.72 181.76 274 17.1 15.4 127.12
Bridge
50 I I I I l U ' I I l I I I I I I I I I I I I I I I U i ' 'fi
5 Farm Lane Bridge 1
p u

3 4° r ':

3 I I

c 30 *- I .1.

2 : : Kellog Bridge .

e-n . .1

a . l .

1E 20 _' ‘i Kalamazoo Bridge 1

8 I *1 ix: ”8 1

c I ‘ I ‘4 .0. ‘0'. d

O 10 '- a l R .1. e -

O : \ g ". r' E5. 1

. i I s}; - 2
o I l l I- l l H Li L l L. ’.l I I I l l hi“ I I ‘
0 50 100 150 200 250 300

Figure 5-17. Time-concentration curves-dye release 1 (May 17, 2002).

42

 

Table 5-4. Time of travel data-dye release 2 (May 31, 2002).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Distance Leading Trailing Discharge
From Edge Peak Centroid Edge at Index 53:: 11"” 0'
Sampling Injection gage - passage of
Location Point Travel Travel Travel Travel c, dye cloud
Time Time Time Time (min s)
(Km) (mlns) (mlns) (mlns) (mlns) (ms/sec) ("9“)
Farm Lane
Bridge 1 .4 54 62 70 98 14.41 86.8 44
Kellogg
Bridge 3.1 109 125 135 174 14.16 36 65
Kalamazoo
Bridge 5.079 1 54 192 204 307 14.01 26.8 1 53
100 .llIlIrIltlllIl'llIl'IllllIlllllIll-
: Farm Lane Bridge :
d ' l' d
U) - \ a
3 " l "
1: 6° '.' i 1
3% : ‘_ Kellog Bridge :
— 3 _‘
*3 40 - 1‘ A‘ inlanazoo Bridge .
8 : 1 ’ \\ I". :
c _ l r‘ -.. _
8 2° - ‘1 f x i *4 .
: I ",3 . I»: I \“m 2
0 0 50 100 150 200 250 300 350
Time (Minutes)
Figure 5-18. Time-concentration curves-dye release 2 (May 31, 2002).

43

 

 

Table 5-5. Time of travel data-dye release 3 (Jun 6, 2002).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1:. di Trailin
Distance 98 ng 9 Peak
From Edge Peak Centroid Edge Dischsrge Conc. Time of
Sampling l tl 3‘ n 9" passage of
Location "ran?" 1;“8' Trrlavel Errvel Tlrlavel 989° C, dye cloud
ime me me me a (mine)
(Km) (mlns) (mlns) (mlns) (mlns) (m Isec) (“9“)
Farm Lane
Bridge 1.4 42 52 64.00 99 19.06 79.6 57
Kellogg
Bridge 3.1 91 106 118.00 175 18.77 36.8 84
Kalamazoo
Bridge 5.079 118 163 176.00 289 18.35 28.4 171
80 :
70 E- lFarm Lane Bridge
3 5° 5 h
3 :.
c 50 E g
.2 L | Kellog Bridge
IH 40 I;
g : 1 I“. kalamazoo Bridge
‘5 30 :' j I \ ,....
a, : ‘ t \x a"
g 20 :- ‘a l, ' I ‘-
o 5 t l \ 1.
0 1° F \ (I . ~'°-..
: .1 : -' . '°-~
0 ‘ .
0 50 100 150 200 250 300
Time (Minutes)
Figure 5-19. Time-concentration curves-dye release 3 (Jun 6, 2002).

 

Table 5-6. Time of travel data-dye release 4 (Jun 21, 2002).

 

Distance Leading Peak Trailing Discharge Peak Time at

 

From Edge 5599 at Index ”3””
iampllng Injection gage Conc. °t 0"
ocation Point Travel Travel Travel Ce Cloud

Time Time Time ’I (“9"-
(Km) (mlns) (mlns) (mlns) (m sec)) (mlns)

(Left) 0.865 129 1 56 287 2.492 52 1 58

 

 

(Centre) 0.865 129 1 53 209 2.492 71 .6 80

 

 

 

 

 

 

 

 

 

 

(Right) 0.865 1 33 1 55 241 2.492 65.1 108

 

Note: - The timings for the trailing edge are based upon extrapolated values up to 10% of the peak
concentrations observed. These samples were taken at Bogue Bridge located at 850 meters downstream of
injection point at Hagadom Bridge

 

 

 

 

 

so :' U I U l I U U U T' I U I' I i r T U l U U U I:
70 E. BogmBridge(Ce:_It.er) a
A : ! ‘ :
$60 :' : 4 3
3 ‘- I z .5
C 50 : \ :
g : .- :
‘6 4° =' "a 1
‘5 30 5- i E
a 5 ll “vi .=.
C 20 .'.' ‘ 1
O 1 1.1 E
0 1o :- l l“... '3
0 =....1....1..1.1..L.1...J
0 50 100 150 200 250
Time (Minutes)

Figure 5-20. Time-concentration curve-dye release 4 (Jun 21, 2002).

45

Table 5-7. Time of travel data-dye release 5 (Jun 25, 2002).

 

Distance Leading Peak Trailing Discharge Peak Time of

 

From Edge Edge at index passage
Sampling inlectlon gage Conc. °' d”
Location Point Travel Travel Travel C, cloud

(Km) Time Time Time (ma/sec) (“g/L) (mi...)

(mlns) (mlns) (mlns)

 

Farm Lane
Bridge 1.4 271 309 453 2.06 15.8 182

 

 

 

 

 

 

 

 

 

 

 

     

 

 

Kalamazoo
Bridge 5.079 588 768 NA 2.06 4.7 NA

16 ‘. .‘
14 7 1
s12 r . ':
a -. ‘ 4
: 1° : 45!} :
O L .1
z 8 D . I
E ' . :
'E 6 E f italamazoo Bridge 1
3 : l :
c 4 .‘ 1 W
8 : i 1
- -l
2 E A, :

0 .

 

0100200300400500600700800
Time (minutes)

Figure 5-21. Time-concentration curves-dye release 5 (Jun 25, 2002).

46

The time taken by the leading edge and the peak of the dye cloud showed a consistent
trend at 16.82m3/sec, 14.41 m3/sec and 19.06-m3/sec flows, however the trailing edge
deviated from the trend at Kellogg Bridge for a flow of 19.06 m3/sec (Figure 5-22) to
(Figure 5-24). At a flow of 2.49 m3/sec the leading edge reached the Farm Lane Bridge
271 minutes after the dye injection as compared to 54, 46 and 42 minutes for 14.41
m3/sec, 16.82m3/sec 19.06-m3/sec flows respectively. The extraordinarily long time
taken by the leading edge to reach Farm Lane at low flow conditions can be attributed to
the upward slope in the river reach between Farm Lane and Hagadom Bridge, which
retards the water movement in the absence of inertia due to low volume of flow. A
similar trend was observed for the peak of the dye cloud at low flow. The time to peak
concentration at Farm Lane was 309 minutes against 62,59 and 52 minutes at 14.41
m3/sec, 16.82m3/sec 19.06-m3/sec flows respectively. The steep slope of the lines from
2.06 m3/sec to 14.41 m3/sec is indicative of non-linearity in the trend for low flow
conditions. However for the medium flow range, the change in the arrival time for
leading edge, peak and the trailing edge in not considerable. The possible reasons for the
skewness in the trailing edge could be adsorption and desorption, transient storage or any

other process, which so far cannot be explained by the available data.

47

 

 

     
  

 

 

 
 

 

 

 

5m I I I I I I I l I I F I I I I I I I I .

: —-)(- Leading Edge :

4m - -I— Peak —

A ' -o— Trailing Edge '

3 I ’ 2
4.0

.2 3°° : 1

g h I

g 200 — -

c : :

1 m — —

t I

o - I I I I I I I I I I I I I I I I I I I d

0 4 8 12 1 6 20

Discharge (ma/sec)

Figure 5-22. Time of arrival of leading edge, peak and trailing edge of the dye cloud
at Farm Lane Bridge for different flow conditions.

 

 

 

 

 

 

160 — —l
A i- -)(—LeadingEdge -
.8 : —I—Peak :
g 140 — —o—Tiaiiing Edge 7 -
E " III
E 120 r- -‘
i: I 1

C

III

 

80 IIIIIIIIIIIIIIIIIIIIIIIIIIIII

14 15 16 17 18 19 20

 

Discharge (m°lsec)

Figure 5-23. Time of arrival of leading edge, peak and trailing edge of the dye cloud
at Kellogg Bridge for different flow conditions.

48

 

 

 

 

  
      

 

 

800 I I“‘I l I I I I I I I l I I I l I I Ii
700 '_'_ ‘5‘ -)(—Leading Edge _"

: I“ —l-Peak :

7; 600 l'_ \‘a. —o—Trailing Edge .1
0 : ’ :
E 500 E- -]
E b .
o 400 E- -:
.§ - .
i- T. -:
300 _ \.\ w -

:. \- .1

200 : N .
1m - I I I I I I I I I I I L I I I I I I -

 

N
O

4 8 12 16

O

Discharge (ma/sec)

Figure 5-24. Time of arrival of leading edge, peak and trailing edge of the dye

cloud at Kalamazoo Bridge for different flow conditions.

5.6 Dispersion by Moments Method

Two different methods were used to calculate the dispersion coefficients i.e. method
of moments given by Fischer (1968) by using the time concentration data at an upstream
and a down stream location and mass transport. The method of moments takes into
account the spread of the dye cloud about the centroid as it moves from one sampling
point to the second sampling point and hence entails a minimum of two data points to

calculate the dispersion in a given reach. By this method the dispersion coefficient is

given by:

49

2 2 2
= U aid _0m

DI
2 Id _tu (5-3)

 

where: -
D,‘ = dispersion Coefficient
U2 = reach average mean velocity

td, t“ = downstream and upstream mean time

0'2 = variance of the time concentration curve (extrapolated to 1% of the peak dye

concentration).

The mean time and the variance are calculated using the time—concentration data by

following integrals:

n-l

Z(Citi +ci+lti+ixti+i ”ti)

 

t = lion-’1
2(Ci + CH] Xtm -ti) (5'4)
i=0
n-l
[ci(ti' )2 +Ci+i(ti+i)21ti+i "’1')
0,2 : i=0 —t2

 

(Ci +cm Xtm ‘5) (5'5)

The time concentration data sets for the first and third sampling points were used to

calculate the reach averaged dispersion coefficients being better representative of the

entire reach for a flow of 14.41 m3/sec, 16.82 m3/sec and 19.06 m3/sec. The dispersion

coefficients for the low flow conditions couldn’t be calculated due to incomplete trailing

edge at Kalamazoo Bridge. The values of dispersion coefficients are presented in Table

5-8.
50

Table 5-8 Dispersion Coefficients By Moments Method

 

 

 

 

 

Flow Velocity Dispersion Coefficient
m3/sec m/sec mzlsec

14.41 0.459 33.3

16.82 0.52 25.24

19.06 0.545 41.4

 

 

 

 

 

However, the value of dispersion coefficient for a flow of 16.82 m3/sec was
recalculated as 37.49 mzlsec by interpolating the values for 14.41 m3/sec and 19.06

m3/sec because the trailing edge at Kalamazoo for a flow of 16.82 m3/sec was missed

during sampling.

 

 

 

 

 

 

 

m . I I I l I l I l I rfq
A 40 _ X _‘
8 ; O :
J4 : >< :
E so _. ..
V in Ii
c - x .
.2 I I
it“ '=
,2 I I
a 10 '- e Dispersion -interpoiated -
I X Dispersion-actual :
P d
o L l l I I I I I I I l l I L l I I J I I l I l l I l l l .
14 15 18 17 18 19 20
Flow (ma/sec)
Figure 5-25. Dispersion coefficients calculated using moments method for

medium flow conditions.

51

5.7 Dispersion By Mass Transport

The concentrations of a contaminant can also be determined by mass transport
equation (Thomann and Muller 1987) at a distance “x” downstream at any instant of

time. The equation is:

(5-6)

where:
C = average cross section concentration
x = distance from injection point to sampling point
t = elapsed time
D,r = longitudinal dispersion coefficient
A = average cross sectional area
M = total mass of the contaminant
U = average flow velocity
K = decay coefficient

A rearranged form of mass transport equation calculates the dispersion based upon

the peak concentration and the time of peak concentration at the sampling point.
52

D:

2
__M__

. 1 “915121 (5-7)
Therefore the dispersion can be calculated even by measuring the concentrations at

one location within the given reach. But the variability in the geometric configuration of

the channel necessitates sampling at greater number of points to yield better relationships

of dispersion with respect to distance on different flow conditions. The dispersion

coefficients at different flow conditions calculated using the above equation are listed in

Table (5-9).

Table 5-9 Dispersion coefficients calculated using the mass transport equation.

 

 

 

 

 

 

 

 

. Dispersion Coefficient at Various Flow
Distance From . . 2
Location Injection Point conditions (m /sec)
(km) 2.06 14.41 16.82 19.06
m3/sec m3/sec m3/sec m3/sec
PM? Lane 1.4 0.74 1.55 1.65 2.58
Bridge
Kellogg Not
Foot 3.2 . 5.96 6.27 7.66
. Available
Bridge
Kalainazo" 5.079 7.13 7.63 5.69 9.33
Bridge

 

 

 

 

 

Generally the dispersion coefficients calculated by mass transport equation showed
consistent trends. The dispersion increased with an increase in flow (Figure 5-26). The
dispersion value of 5.69 mzlsec at a flow of 16.82 m3/sec was not consistent with the
trends probably due to the missed trailing edge at Kalamazoo for which the
concentrations were extrapolated. Therefore, a dispersion value of 8.51 m2/sec was

calculated by interpolating the dispersion values at 14.41 m3/sec and 19.06 m3/sec. Also,

53

as the sampling for 2.06 m3/sec was only done at Farm Lane Br and Kalamazoo Bridge,
and the data real time concentration data were not available at Kellogg Bridge, a
dispersion coefficient value of 5.20 mzlsec was determined by interpolating the values for

Farm lane and Kalamazoo Bridge.

 

 

 

 

 

 

 

 

 

 

 

10 L I T ' fir l t I I I l I t 1 I I I If} ‘

a 8 r 4/

m . r— ,.- .

£ ' ‘0'. I

"a 6 :' 7"" '

v 6__ I
= I

.2 _ —---14oo Meters _‘

«n 4 _ .

g I * 3200 Meters I

m I .g‘ d

a. 2 - -I-- 5079 Meters - J1" -

+ if _ 5

o l l l j l l I I l l l I l l l l l l l
0 5 1O 15 20
Flow(malsec)
Figure 5-26. Dispersion coefficient calculated using mass transport equation

under different flow conditions.

The dispersion coefficient increased with distance also, as the water column moved
downstream, however the rate of increase in dispersion decreased as the dye cloud moved
further downstream The change in dispersion with distance at different flow conditions

can be observed in (Figure 5-27).

54

 

10 l l l I I I l I l l I l I I I I I I I l I I I I

 

 

 

 

 

 

 

’a 8 . .
3 t -
"\ 6 - _'
é . .
C ' ..
I2 I .- .. I
2 4 .- .". .:1:' .o" "-9-" 2.06 m3/sec "-'
a ' -o—- 14.41 m3/sec .
.2 2 .— . ,1“? I... —*— 16.82 m3/sec _"
D ' ‘I _."" —'*— 19.06 m3/sec .
E 0" :
o I I I I L I I I I l I l I I l I I I I l I I I I

 

1000 2000 3000 4000 5000 6000
Distance (meters)

Figure 5-27. Dispersion coefficient at different downstream sampling locations.

The application of one-dimensional advection-dispersion equation is limited to zones
of complete mixing as reported in the literature therefore it is essential that the zone of
complete mixing be determined in order to justify its application. The mixing length in
this case was determined to lie between 2,800 meters to 3,200 meters for a medium flow
range using the formula by Fischer (1979) for centerline injection. In real practice the
tracer was not dumped in the center but was poured instantaneously at the middle 75% of
the width so that a quasi-instantaneous mixing is achieved, therefore the mixing length is
not assumed to extend to calculated 2,800 meters length. Also, the sinuous nature of the
river meanders in the initial 1000 meters also enhances the process of mixing. But on the
other hand, the samples at different point at Bogue Street Bridge located at 850 meters

from the injection point indicate a variation of 27.37 % in peak concentrations and 12.7

55

% in areas under the curve (Table 5-10); which indicate a non-homogeneous domain.

Due to positive slope between Bogue Bridge and the Farm Lane Bridge, and the effect of

the damming action of the weir, the mixing length is assumed to extend beyond Farm

Lane Bridge up to the weir. Beyond weir, the channel could safely be assumed as

completely mixed. At low flow, the lack of turbulence increases the time for transverse

mixing. However, at medium flow and high flow, the turbulence and formation of whirl

pools and eddies can physically be observed, so transverse mixing time is reduced

 

 

 

 

considerably.
Table 5-10. Variation in concentration across a transect indicating the state of
lateral mixing.
Area Under ' Percent Percent
. Time- . . Peak . .
Location . Variation . Variation
Concentration. Concentration.
From Centre From Centre
Curve
Left 2284.3 -12.7 52 -27.37
Centre 2618.1 - 71.6 -
Right 2761.68 + 5.48 65 -9.2

 

 

 

 

 

 

 

Although settling, entrainment and transformation affect the peak concentrations

exponentially; the effect of the dye loss was not taken into account because the dye

recovery calculated could not be justified. In all the cases, the dye recovery was a little

more than the amount actually dumped. This was however attributed to the conditions of

incomplete mixing specially under the low flow conditions.

56

The classical application of the analytical solution of l-D advection dispersion
equation, when used with a constant value of dispersion coefficient, is based on the
assumption of a channel of uniform cross section for entire length in order to predict the
concentrations at a downstream location. If a constant value of dispersion coefficient is
used, there is a decrease in the peak concentrations and increase in the spread as a
contaminant travels downstream, but the area under the time-concentration curve remains
the same. In this case the width varies between 16 meters to 40 meters and so does the
cross sectional area, therefore the channel is characterized as non-uniform. The
dispersion coefficients were calculated for each sampling point basing on the observed
peak concentrations and the time for peak concentration. These values of dispersion
coefficients were used to predict the passage of the dye cloud through all the three
sampling points and respective areas under each time-concentration curve were
calculated. By use of different values, although the areas under each concentration curve
should remain the same, the overall shape of the time-concentration curve should
coincide with the observed time-concentration curve. The area under the time-
concentration curve for calculated concentrations (Table 5-11) shows a variation of 3.9
%, which is due to a variation in flow over the sampling period. However, the area under
the curve for observed concentration shows a variation of 14.8 %, 12.2 % and 16.07 %
for 14.41 m3/sec, 16.82 m3/sec and 16.82 m3/sec flow between the three sampling
locations (Table 5-12). These areas were found to be 17 % to 46 % more as compared to
those calculated by analytical solution for one dimensional advection-dispersion equation
(Table 5—13), which indicates that the equation does not take into account the effects of

storage zone presumed to be responsible for the prolonged evolution of the trailing edge

57

of the dye cloud. Nevertheless, this equation still can serve a good purpose in
quantification of longitudinal dispersion as the dispersion coefficients calculated by this

equation can make a good match of the rising limb and the peak concentrations.

Table 5-11. Area under time-concentration curves for calculated concentration.

 

 

 

 

 

 

 

 

 

 

 

 

Area Under Time Concentration Curves
Flow Farm Lane Kellogg Bridge Kalamazoo Bridge
Bridge
”-41 "“3““ 1035.50 1053.19 1065.00
16.82 m3/sec 470.17 462.45 472.53
19.06 m3/sec 935.00 951.00 97300
Note: The area under the time-concentration curves has been calculated by using the analytical

solution for one-dimensional advection-dispersion coefficient with different values of dispersion coefficient

58

 

Table 5-12. Area under time-concentration curves for observed concentrations.

 

 

 

 

 

 

 

 

 

 

Area Under Time Concentration Curves
FIOW Farm Lane Bridge Kellogg Bridge Kalamazoo
Bridge
3
3
3
19-06 m ’3“ 1195.00 1275.85 1423.95
Table 5-13. Comparison of areas under the time-concentration curve for

predicted and observed concentrations.

 

 

 

 

 

 

 

 

 

 

 

Net % Increase in Area Under Time Concentration
Flow Curve
Farm Lane Kellogg Bridge Kalamazoo
_ Bridge Bridge
14.41 jlsec 34.57 18.07 37.03
16.82 m3/sec 34.18 28.88 17.18
19.06 m3/sec 27.81 34.16 46.35
Note: The figures indicate percent increase in area under the time concentration curves for the

observed concentrations compared with the concentrations calculated using one-dimensional advection
dispersion equation.

As the one-dimensional advection-dispersion equation is limited to the zones of
complete mixing, the calculated dispersion coefficients increase sharply with distance
between first and the second sampling point. However, the increase in dispersion

becomes less in magnitude as the dye cloud moves further downstream. In a well-mixed

59

zone, the dye cloud evolution should approach a gaussian shape by use of a constant
value of dispersion coefficient. Although the dispersion coefficients calculated for the
second and third sampling point tend to increase with distance, the increase is much less
as compared to the increase between first and second sampling station, so the use of a
constant value of dispersion coefficient in the reach beyond the Farm Lane Bridge did not

alter much the time-concentration profiles.

In this case, the little increase in dispersion coefficient in the well-mixed zone can be
attributed to the change in width of the river across the river reach. The change in the
width along the reach effects the longitudinal dispersion due to sharpness or flatness of
the transverse velocity profile. These different values of dispersion coefficients calculated
for each sampling location were plugged in equation (5-6) to predict the concentrations at
the three sampling points for all five-dye releases. The relationships between observed
and predicted concentrations using equation (5-6) are presented in (Figure 5-28) through
(Figure 5-28). The predicted concentrations in these figures correspond to the analytical

solution for one-dimensional advection-dispersion equation.

60

0!
O

 

 

 

 

 

 

 

 

   

PI I I I l I I I I l I I I I l I I I I l I I I I l I I I I I r I I I q

C --------- Analytical solution I

3 40 '_ —o— Observed-Farm Lane .1
a : —*— Observed- Kellog Br 1
3 : —-0— Observed- Kalamazoo :

V 30 _. -
c " ‘

O I I

'5 - '
8 2° .- 1

OI! .. g ..
8 - i -

o 10 '- 1. _

c ; ': 2
o i- a '1
o 0 + a ~

0 50 100 1 50 200 250 300 350

Time (minutes)

Figure 5-28. Predicted and observed concentration at 16.82 m3/sec flow.

 

100 IIIIIIIIIj'IIII'IIII'IIII'IIIIITIII

 

--------- Analytical Solution
—0— Observed- Farm Lane
—-x— Observed - Kellog Br
—0— Observed- Kalamazoo

   
  

 

 

 

Concentration (ugIL)
...,...,...,...,...

lIllllllIlllllllllI

 

 

 

0 so 100150 200 250 300 350
Time (minutes)

Figure 5-29. Predicted and observed concentration at 14.41 m3/sec flow.

61

 

a“) ‘ I I III I I I I III I I I I I I I I l I I I I

 

 

 

 

 

 

 

 

70 E- --------- Analytical Solution
: E + Observed-Farm Lane
a, 60 .- —><—Observed-Kellog Br
3 E ' —°- Observed- Kalamazoo
v 50 r .

I: E : i
.9 4° .- a
E 30 Z- 5 a
E : i i
w 20 :—
g = E a .-'
8 10 E'- :5 3... :0.

0 ~‘ '

0 50 100 150 200 250 300

Time (minutes)

Figure 5-30. Predicted and observed concentration at 19.3 m3/sec flow.

 

I I I I I I I’l I I I l I I I l I I III I III I I I I I I I I

 

--------- Analytical Solution
—.._ Obsewe¢Bogue Bridge

   
   

 

 

IIIIIIIIIIIIIIIIIII'IIIIIIIIIIIIIIIIII
llllllllllllllllIllllllljll llllllll

l

 

 

 

Concentration (uglL)

...
lllllllllll“

100 120 140 160 180 200 220 240 260
Time (minutes)

Figure 5-31. Predicted and observed concentration at 2.49 m3/sec flow.

62

 

 

 

 

 

 

 

 

   

16 I I I I r: I l I I I l I I I I I I I I I I I l I I I .1

1 4 :- ,5 --------- Analytical Solution :

A .. i q
a 12 L —0—Observed- Farm Lane :
a 10 E —K—Observed- Kalamazoo E
C E .1
O 8 r '7.
'3 b II
E 6 L -:
E = 3
9 4 I- -I
g; : :
3 2 :- '2
o ‘I- .

0 200 400 600 800100012001400
Time (minutes)

Figure 5-32 Predicted and observed concentration at 2.06 m3/sec flow.

In order to plot a concentration profile at any point downstream the value of
dispersion coefficient must be known. The observed data yielded two different sets of
linear equations. The first set if equations comprises dispersion as a function of distance
from the injection point at a given flow condition. The second set of equations gave
dispersion as a function of flow at different points down stream. The statistical
combination of two different sets of equation yielded a single equation for dispersion
with two variables i.e. distance and flow.

DJr =O.104Q+0.001767x-1.713

(5-8)
Where:

Q = Flow (m3/sec)

x 2 Distance downstream from the injection point (m)

63

The values of dispersion coefficient were recalculated using equation (5-8) and are

presented in (Table 5-14).

 

 

 

 

 

 

 

 

Table 5-14. Comparison of calculated and predicted dispersion coefficients.
Dispersion Coefficient (mz/sec)
Distance from injection point (m)
1400 3200 5079
(1111731236 ) Calc I,” Prectl)1)cted Calc Py Pregyted C alc by Preacted
Analytical . . Analytical . . Analytrcal . .
Solution Empirical Solution Empirical Solution Empirical
Equation Equation Equation
2.06 0.74 0.97 5.2 4.25 7.13 7.47
14.41 1.55 2.25 5.96 5.44 7.63 8.76
16.82 1.65 2.51 6.27 5.69 8.51 9.01
19.06 2.58 2.74 7.66 5.92 9.33 9.24

 

 

 

 

 

 

 

 

 

An x-y plot of these two set of dispersion coefficients yields a linear relationship

with a correlation coefficient of 0.95985 (Figure 5-33)

 

   
 

 

 

 

10 b I I I I I I I l I I ' I’ ' Ifi‘
b d
h
A I b 1
. 1
N It
E. 6 : 1
K
a r-
1- 1
g ‘ D -
a 1
8 2 _ y.0.41001+0.92140x j
Hudson 1
o I I I I I l I A I I l I I A l I I AW
0 2 4 c a 10

Calculated D. (m’lsec)

Figure 5-33. Relation between calculated and predicted dispersion coefficients.

64

A relation for prediction of the peak concentration time at any point downstream

based on the dye study data could only be established for the medium flow condition. The

following correlation is:

Tp = 0.3826Q + 0.0338x

where:

(5-9)

Tp= time for peak concentration (minutes)

Q = discharge (m3/sec)

x = distance downstream from injection (meters)

The values of the peak arrival time recalculated using this equation exhibit good

correlation with the observed values, with an R2 value of 0.96 however, it does not hold

good for the low flow condition.

 

200 .

100-

Calculated Peak Tlme (mlns)

 

 

 

I 14 I I I I I I I I I I I

 

Figure 5-34.

50 100 150 200

Observed Peak Time (mlns)

Calculated and observed peak arrival time.

65

The equations for peak time (Tp) and dispersion coefficient (Dx) can be used in
predicting the downstream concentrations at any point while knowing only the discharge
which is available at the USGS Gage at half hour intervals. Of course, the validity of
these equations is, only for medium flow conditions. Another limitation is that these
values are to be used into the analytical solution for conventional l-D advection —
dispersion equation that is applicable only to the well-mixed conditions and it doesn’t
take into account the dead zones, more commonly described as “storage zones” in the
current literature therefore, the skewed nature of the time-concentration curve cannot be
predicted. The summary of the empirical equations to predict the concentration of a
conservative contaminant is as follows with known discharge in m3/sec and known mass

in grams.

Tp = 0.3826Q + 0.0338x

Dx= 0.104Q+0.00l767x-1.713
u: x/I'p

A=Q/u

_ M - (x - at)2
C (x,t) — [—224 F_th ]exp[—4Dxt ]

This procedure was applied to predict the time concentration curves for the tracer
tests. The predicted and observed concentrations are presented in the following figures.
However, a lag in time was observed for the Farm Lane Bridge, for which the actual
velocity is less than the predicted velocity due to an upward slope in the portion between

the Hagadom Bridge and the Farm Lane Bridge, therefore a factor of 1.1 was used to

66

predict the peak time (T p) with empirical equation. This factor was not used for a flow of

 

 

   

 

 

 

 

 

19.06 m3/sec.

m -I I I I I I I I I I I1 I I rT‘ I I I I I I l I I_I I I I I_—I 4
E ---- Predicted I
3 40 L —O— Observed-Farm Lane 2
a : —x—- Observed— Kellog Br :
:r t I

V 30 _
I: : I
.2 " d
H " Ii
2 2° .- -:
‘E i ‘
a t I
C . 1
O . .
O 0 ~ .

O

50 100 150 200 250 300 350
Time (minutes)

Figure 5-35. Predicted and observed concentration using empirical relations at
16.82 m3/sec flow.

 

100 IIII'IIIIIIIFFI'IIIIIIIIIIIIII'IrrI

I
I

 

----- Predicted

—0— Observed- Farm Lane
—>(— Observed - Kellog Br
—0— Observed- Kalamazoo

80

IIIIII

 

 

 

Concentration (uglL)

TII'IIjjIIIlIIIlII

   

IIIIIIIIIII

 

 

0 50 100 150 200 250 300 350
Time (minutes)

Figure 5-36. Predicted and observed concentration using empirical relations at
14.41 m3/sec flow.

67

80

 

 

 

 

 

 

: I I I I I I I I [j I I I l I I I I l I I I I I I I I I l I I I I :

70 E- ---- Predicted E

j E + Observed-Farm Lane E
B) 60 E- '—X— Observed-Kellog Br :
3 : —0—' Observed- Kalamazoo :
V 50 r in
c E E
O 40 -_- 1
3': : =
E 30 E- :
E = a
0 20 E- .:
‘c’ = a
0 " ,

 

 

   

0 50 100 150 200 250 300 350
Time (minutes)

Figure 5—37 Predicted and observed concentration using empirical relations at
19.06 m3/sec flow

68

6. CONCLUSIONS

The velocities and heads predicted by the one-dimensional model for Red Cedar
River based on DYNHYD are in reasonable agreement with the field measurements.
Further model refinement may be required to improve predictions at the Kellogg Bridge
where the model could not capture the variability in hydrodynamics due to sharp bends.
The model predicted results are more reliable for use in any contaminant transport model
over the reach average values. The river reach exhibited dispersion characteristics, which
varied with distance and the flow condition. The increase in the dispersion coefficient
with distance was found to be more pronounced in the initial reach extending a little
beyond the Farm Lane Bridge up to weir, which falls within the initial mixing length,
therefore the sub reach of the river bounded by Hagadom road and MSU library bridge
could not be characterized with a constant value of dispersion coefficient. However, the
rate of increase in dispersion coefficient beyond the initial reach sharply reduces tending
to reach a constant value. This less increase in the dispersion coefficient with distance as
compared with the initial sub reach is viewed to be a result of the variation in width of the
river, which narrows as it approaches the lower bounds, giving rise to a higher transverse
velocity profile, which increases dispersion longitudinally. The empirical equation
developed allow the calculation of dispersion coefficient at any point of the MSU river

reach for a particular flow condition by with a reasonable accuracy, but is site specific in

69

nature because as the basis of these equations are site specific tracer tests and hence

cannot be applied beyond the reach or to any other site.

70

7. APPENDICES

Appendix A Junction and Channel Properties

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Junction hannel Width Junction Bottom Angle
Number umber (m) Surface Elevation (Degrees)
Area (m2) (m)
1 699.5 0
2 1 28.0 1352.6 0.0000 70
3 2 26.1 1378.5 0.0036 70
4 3 29.0 1626.1 0.0072 74
5 4 36.0 1772.4 0.0108 68
6 5 34.9 1652.8 0.0143 63
7 6 31.2 1588.0 0.0179 68
8 7 32.3 1715.3 0.0215 71
9 8 36.3 1645.2 0.0251 90
10 9 29.5 1407.4 0.0287 105
11 10 26.8 1521.7 0.0323 120
12 11 34.0 1685.5 0.0359 134
13 12 33.4 1815.1 0.0394 131
14 13 39.2 1902.1 0.0430 119
15 14 36.9 1624.7 0.0466 106
16 15 28.1 1393.6 0.0502 92
17 16 27.6 1518.7 0.0538 87
l8 17 33.1 1690.1 0.0574 95
19 18 34.5 1758.7 0.0610 101
20 19 35.9 1765.6 0.0991 105
21 20 34.7 1820.4 0.1372 109
22 21 38.1 1830.3 0.1753 104
23 22 35.1 1739.6 0.2134 106
24 23 34.4 1671.8 0.2515 102
25 24 32.4 1584.2 0.2896 102
26 25 30.9 1495.0 0.3277 94
27 26 28.9 1540.8 0.3658 84
28 27 32.8 1601.7 0.4039 80
29 28 31.3 1536.2 0.4420 80

 

Junction and Channel Properties. . .continued

71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Junction hannel Width Junction Bottom Angle
Number umber (m) Surface Elevation (Degrees)
Area (m2) (m)

30 29 30.1 1401.7 0.3644 71

31 30 25.9 1341.5 0.2868 66
32 31 27.7 1488.9 0.2092 64
33 32 31.8 1514.6 0.1316 64
34 33 28.8 1385.8 0.0540 64
35 34 26.7 1387.8 -0.0236 51

36 35 28.8 1340.1 -0. 1011 56
37 36 24.8 1279.2 -0.1787 53
38 37 26.4 1373.4 -0.2563 59
39 38 28.5 1449.1 -0.3339 63

40 39 29.4 1427.1 -0.41 15 60
41 40 27.6 1385.3 -0.4158 60
42 41 27.8 1260.3 -0.4202 50
43 42 22.6 1152.9 -0.4245 48
44 43 23.5 1252.0 -0.4289 51

45 44 26.6 1339.1 -0.4333 50
46 45 27.0 1259.4 10.4376 46
47 46 23.4 1022.0 -0.4420 34
48 47 17.5 844.9 -0.4689 8

49 48 16.3 913.6 -0.4957 7

50 49 20.2 974.2 -0.5226 59
51 50 18.8 962.0 -0.5495 64
52 51 19.7 1045.5 -0.5764 74
53 52 22.1 1106.4 -0.6033 88

54 53 22.2 1342.6 -0.6302 95

55 54 31.5 1559.8 -0.6571 101
56 55 30.8 1539.2 -0.6840 90
57 56 30.7 1501.1 -0.7109 105
58 57 29.3 1449.3 0737 8 100
59 58 28.7 1259.1 -0.7647 147
60 59 21.7 1030.1 -0.7916 204
61 60 19.5 1039.1 -0.8185 216
62 61 22.1 1190.0 —0.8454 209
63 62 25.5 1298.8 .0.8723 203

 

 

 

 

 

 

Junction and Channel Properties. . .continued

72

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Junction hannel Width Junction Bottom Angle
Number umber (m) Surface Elevation (Degrees)
Area (m2) (111)

64 63 26.4 1417.3 -0.8992 197
65 64 30.3 1457.2 —0.9627 176
66 65 28.0 1307.0 -1.0262 151
67 66 24.3 1148.7 -1.0897 108
68 67 21.7 1107.1 -1.1532 96
69 68 22.6 1267.3 -1.2167 101
70 69 28.1 1293.6 -1.2802 101
71 70 23.7 1237.3 -1.3088 94
72 71 25.8 1371.3 -1.3375 87
73 72 29.0 1383.5 -l.3662 92
74 73 26.3 1294.3 -1.3949 95
75 74 25.4 1473.2 -1.4236 82
76 75 33.5 1516.8 -1.4523 65
77 76 27.2 1334.5 -1.4810 80
78 77 26.2 1367.6 -1.5097 106
79 78 28.5 1381.0 -1.5383 107
80 79 26.7 1274.7 -1.5670 130
81 80 24.3 1454.4 -1.5957 168
82 81 33.9 1527.3 -1.6244 120
83 82 27 .2 1290.7 .-1.6531 100
84 83 24.5 1238.7 -1.6818 74
85 84 25.1 1240.7 -1.7105 67
86 85 24.5 1391.2 -1.7392 22
87 86 31.1 1687.4 —1.7678 6
88 87 36.4 1452.9 -1.7965 86
89 88 21.7 1287.6 -1.8252 143
90 89 29.8 1754.2 -1.8539 127
91 90 40.4 2017.5 -1.8826 61
92 91 40.3 1927.3 -1.91 13 21
93 92 36.8 1640.8 -1.9400 102
94 93 28.8 1418.7 -1.9686 179
95 94 27.9 1304.5 -1.9973 165
96 95 24.3 1455.4 -2.0260 150
97 96 33.9 1316.1 -2.0547 136

 

 

 

 

 

 

Junction and Channel Properties. . .continued

73

 

 

 

 

 

 

 

 

 

Junction hannel Width Junction Bottom Angle
Number umber (m) Surface Elevation (Degrees)
Area (m2) (m)
98 97 18.7 954.1 -2.0834 134
99 98 19.5 965.0 -2.1121 122
100 99 19.1 990.5 -2. 1408 134
101 100 20.5 1091.2 -2.1695 134
102 101 23.2 1142.5 -2.1981 136
103 102 22.5 563.6 -2.2268 136

 

 

 

 

 

 

74

 

Appendix B Input File

MODELING OF RED CEDAR RIVER

MICH STATE UNIV, EAST LANSING.

iiiii PROGRAM CONTROL DATA *tittiittttiitiittfiititttitiiitiititiiiitit
103102 0 5 510300 82330

ititi OUTPUT CONTROL DATA *ititittttittttii'ktititiiiittttitittttititttt

0.0000E-01 0.500 103

12 3 4 5 6 7 8910111213141516
17181920212223242526272829303132
33343536373839404142434445464748

49505152535455565758596061626364
65666768697071727374757677787980
8182 83 84 85 86 87 88 89 90 9192 93 94 95 96
97 98 99100101102103
ititt HYDRAULIC SUMMARY CONTROL DATA itiiiiiiii*itiitiiiittitit
1 163012.50 1 1

****************J UNCT'ON DATAiiiiitititiiiit*iifi**t******t**titiiitiiiiiti

1 2.0 699.5 0.0 1 0 O O 0 0
2 2.0 1352.6 0.0 1 2 0 0 0 0
3 2.0 1378.5 .0036 2 3 0' O 0 0
4 2.0 1626.1 .0072 3 4 0 0 0 O
5 2.0 1772.4 .0108 4 5 0 0 0 0
6 2.0 1652.8 .0143 5 6 0 0 0 O
7 2.0 1588.0 .0179 6 7 O O 0 0
8 2.0 1715.3 .0215 7 8 0 O 0 O
9 2.0 1645.2 .0251 8 9 O 0 O 0
10 2.0 1407.4 .0287 9 10 0 O 0 0
11 2.0 1521.7 .0323 10 11 0 0 0 0
12 2.0 1685.5 .0359 11 12 0 0 0 O
13 2.0 1815.1 .0394 12 13 0 O 0 0
14 2.0 1902.1 .0430 13 14 0 O 0 O
15 2.0 1624.7 .0466 14 15 0 O 0 0
16 2.0 1393.6 .0502 15 16 0 0 O 0
17 2.0 1518.7 .0538 16 17 O 0 0 0
18 2.0 1690.1 .0574 17 18 O O 0 0
19 2.0 1758.7 .0610 18 19 0 0 0 0
20 2.0 1765.6 .0991 19 20 0 0 O 0
21 2.0 1820.4 .1372 20 21 O O 0 0
22 2.0 1830.3 .1753 21 22 0 0 O 0
23 2.0 1739.6 .2134 22 23 0 0 0 0

Input File. . .. Continued

75

24 2.0
25 2.0
26 2.0
27 2.0
28 2.0
29 2.0
30 2.0
31 2.0
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33 2.0
34 2.0
35 2.0
36 2.0
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38 2.0
39 2.0
40 2.0
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42 2.0
43 2.0
44 2.0
45 2.0
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47 2.0
48 2.0
49 2.0
50 2.0
51 2.0
52 2.0
53 2.0
54 2.0
55 2.0
56 2.0
57 2.0
58 2.0
59 2.0
60 2.0
61 2.0
62 2.0
Input File.

1671.8 .2515
1584.2 .2896
1495.0 .3277
1540.8 .3658
1601.7 .4039
1536.2 .4420
1401.7 .3644
1341.5 .2868
1488.9 .2092
1514.6 .1316
1385.8 .0540
1387.8 -.0236
1340.1 -.101 1
1259.1 -.1787
1080.3 -.2563
1449.1 -.3339
1427.1 -.41 15
1385.3 -.4158
1260.3 -.4202
1 152.9 -.4245
1252.0 -.4289
1339.1 -.4333
1259.4 -.4376
1022.0 -.4420
844.9 -.4689
913.6 -.4957
974.2 -.5226
962.0 -.5495
1045.5 -.5764
1 106.4 -.6033
1342.6 -.6302
1559.8 -.6571
1539.2 -.6840
1501.1 -.7109
1449.3 -.7378
1259.1 -.7647
1080.3 -.7916
1 140.0 -.8185
1265.0 -.8454
Continued

NNNNNN
QNGU‘IJBOD

$33$£6£3888388§88388

24
25
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29

31
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39
4O
41
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61
62

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOC

o0000000000OOOOOOOOOOOOOOOOOOOOOOOOOOOO

0000000000000OOOCOOOOOOCOOOOCOOOOOOOCOO

76

OOOOOOOOOOOOOOOOOOOOOCOOOOOOCOOOOOOOOOO

63
54
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1 01
102
103

****t CHANNEL DATA *iiiflii'kiiiitiiiiiiiititiit*“iititiiiiiiititttiiii

70 0.0210 0.00

1

2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0

1323.0
1417.3
1457.2
1307.0
1 148.7
1 107.1
1267.3
1293.6
1237.3
1371.3
1383.5
1294.3
1473.2
1516.8
1334.5
1367.6
1381.0
1274.7
1454.4
1527.3
1290.7
1238.7
1240.7
1391.2
1687.4
1452.9
1287.6
1754.2
2017.5
1927.3
1640.8
1418.7
1304.5
1455.4
1316.1

954.1

965.0

2.0 990.5
2.0 1091.2
2.0 1 142.5
2.0 563.6

50

28.0

-.8723

-.8992

-.9627
-1 .0262
-1 .0897
-1.1532
-1.2167
-1.2802
-1 .3088
-1 .3375
-1 .3662
-1 .3949
-1 .4236
-1 .4523
-1.4810
-1 .5097
-1 .5383
-1 .5670
-1 .5957
-1.6244
-1 .6531
-1 .6818
-1 .7105
-1 .7392
-1 .7678
-1 .7965
-1 .8252
-1 .8539
-1 .8826
-1.91 13
-1 .9400
-1 .9686
-1 .9973
-2.0260
-2.0547
-2.0834
-2.1121

85

87
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98

63
54
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82

83
34
85
86

87
88
89
9O
91
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95
96
97
98
99

-2.1408 99 100
-2.1695 100 101
-2.1981 101 102
22268 102 103

0.0

Input File. . .. Continued

OCOOOOOOCOOCOCOOOOOOOOOOOCCOCOOOCOOOOOOOO

OOOOOOOOOOOOOOOCOOOOOOOOOOOOOOCOOOOOOOOOO

OOOOOCOOOOO00000000009000COOOOCOOOOOOOOOO

77

OCOCOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOO

1

2

3388333338§380mflmmewm

23
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Input File. . ..

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50

26.1 0.0
29.0 0.0
36.0 0.0
34. 9 0.0
31.2 0.0
32.3 0.0
36.3 0.0
29.5 0.0
26.8 0.0
34.0 0.0
33. 4 0.0
39. 2 0.0
36. 9 0.0
28. 1 0.0
27.6 0.0
33.1 0.0
34.5 0.0
35.9 0.0
34.7 0.0
38. 1 0.0
35.1 0.0
34. 4 0.0
32. 4 0.0
30. 9 0.0
28. 9 0.0
32. 8 0.0
31.3 0.0
30.1 0.0
25. 9 0.0
27.7 0.0
31.8 0.0
28.8 0.0
26.7 0.0
28.8 0.0
24.8 0.0
26.4 0.0
26.5 0.0
29.4 0.0
27.6 0.0
27.8 0.0
22.6 0.0
23.5 0.0
26.6 0.0
Continued

74
74

63
71
105
120
134

131
119

101

83388888$82Efi28

0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0320
0.0320
0.0320
0.0320
0.0320
0. 0320
0. 0320
0. 0320
0.0320
0.0320
0.0360
0.0360
0.0360

0.0360

0. 0360
0.0360
0.0360
0.0360
0.0360
0.0360
0. 0360
0. 0220
0.0220
0. 0220
0. 0220
0. 0220
0.0220

0.00
0.00
0.00
0.00
0. 00
0. 00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0. 00
0. 00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
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0.00
0.00
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0.00
0.00
0.00

78

—L
ocooowmmhoom

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23
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25’

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—L
ocoooxtaam-c-eo

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Input Fi

8888888888838888888888888888888888888888888

H

27.0
23.4
17.5
16.3
20.2
18.8
19.7
22.1
22.2
31 .5
30.8
30.7
29.3
28.7
21 .7
21 .5
24.1
26.5
26.4
30.3
28.0
24.3
21.7
22.6
28.1
23.7
25.8
29.0
26.3
25.4
33.5
27.2
26.2
28.5
26.7
24.3
33.9
27.2
24.5
25.1
24.5
31.1
36.4

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
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0.0
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0.0
0.0
0.0
0.0
0.0
0.0

e. . .. Continued

fi$um§$

74

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74

67

0.0220
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0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0360
0.0360
0.0360
0.0360
0.0360
0.0360
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310
0.0310

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

79

45
47
49

51
52
53

55
57

59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76

78
79
80
81
82
83

85
86
87

$3882$

88 50 21.7 0.0 143 0.0310 0.00 88 89
89 50 29.8 0.0 127 0.0310 0.00 89 90
90 50 40.4 0.0 61 0.0310 0.00 90 91
91 50 40.3 0.0 21 0.0310 0.00 91 92
92 50 36.8 0.0 102 0.0310 0.00 92 93
93 50 28.8 0.0 179 0.0310 0.00 93 94
94 50 27.9 0.0 165 0.0310 0.00 94 95
95 50 24.3 0.0 150 0.0310 0.00 95 96
96 50 33.9 0.0 136 0.0310 0.00 96 97
97 50 18.7 0.0 134 0.0310 0.00 97 98
98 50 19.5 0.0 122 0.0310 0.00 98 99
99 50 19.1 0.0 134 0.0310 0.00 99 100
100 50 20.5 0.0 134 0.0310 0.00 100 101
101 50 23.2 0.0 136 0.0310 0.00 101 102
102 50 22.5 0.0 136 0.0310 0.00 102 103
if... CONSTANT lNFLOWS/OUTFLOWS *tiitittitittittittiititiiiiittfititt*tiitittt
0
i**** VARIABLE lNFLOWS/OUTFLOWS iiiti'ttttitiii'ttiti*‘kitittititii*ititttitittt
1
1 64
1 0300 -9.83 1 0600 -9.83 1 0900 -9.83 1 1200 -9.94
1 1500 -9.94 1 1800 -9.83 1 2100 -9.83 1 2399 -9.71
2 0300 -9.60 2 0600 -9.60 2 0900 ~9.49 2 1200 -9.37
2 1500 -9.26 2 1800 -9.15 2 2100 -9.03 2 2399 -9.03
3 0300 -8.92 3 0600 -8.81 3 0900 -8.69 3 1200 -8.58
3 1500 -8.47 3 1800 -8.35 3 2100 -8.24 3 2399 8.16
4 0300 -8.04 4 0600 -7.93 4 0900 -7.82 4 1200 -7.82
4 1500 -7.70 4 1800 -7.62 4 2100 -7.50 4 2399 -7.39
5 0300 -7.39 5 0600 -7.39 5 0900 -7.39 5 1200 -7.31
5 1500 -7.82 5 1800 -8.81 5 2100 -9.71 5 2399 -10.2
6 0300 -11.38 6 0600 -12.89 6 0900 -14.16 6 1200 -15.35
6 1500 -16.28 6 1800 -17.11 6 2100 -17.93 6 2399 -18.49
7 0300 -18.92 7 0600 -19.34 7 0900 -19.63 7 1200 -19.63
7 1500 -19.63 7 1800 -19.63 7 2100 -19.48 7 2399 -19.20
8 0300 -18.92 8 0600 -18.49 8 0900 -18.35 8 1200 -18.18
81500 -18.01 8 1800 -17.16 8 2100 -16.94 8 2399 -16.77

*i*** mWNSTREAM BOUNDARY DATA *ti‘iti‘kitttitkitititiitititttittitiiiiifkitil"!

1

310364000010

-1.48 1 1200
-1.48 1 2399
-1.51 2 1200
-1.52 2 2399

-1.48
-1.48
-1.51
-1.52

-1.48 1 0900
-1.48 1 2100
-1.51 2 0900
-1.52 2 2100

-1.48 1 0600
-1.48 1 1800
2 0300 -1.51 2 0600
21500 -1.52 21800
Input File. . .. Continued

10300
11500

80

30300
31500
40300
41500
50300
51500
60300
61500
70300
71500
80300
81500

0

0

0

*iiit CHANNEL GEOMEI'RY DATA tititittit*iiitititit*i’titt*titiitt‘kititifittii

0

0 0

-1.55
-1.58
-1.59
-1.59
-1.60
-1.48
-1.37
-1.26
-1.20
-1.19
-1.23
-1.26

30600
31800
40600
41800
50600
51800
60600
61800
70600
71800
80600
81800

-1.55
-1.58
-1.59
-1.59
-1.60
-1.48
-1.37
-1.26
-1.20
-1.19
-1.23
-1.26

30900
32100
40900
42100
50900
52100
60900
62100
70900
72100
80900
82100

-1.55
-1.58
-1.59
-1.59
-1.60
-1.48
-1.37
-1.26
-1.20
-1.19
-1.23
-1.26

81

3 1200
3 2399
4 1200
4 2399
5 1200
5 2399
6 1200
6 2399
7 1200
7 2399
8 1200
8 2399

-1.55
-1.58
-1.59
-1.59
-1.60
-1.48
-1.37
-1.26
-1.20
-1.19
-1.23
-1.26

ititi WIND DATA itittiiitititititiiitiiiiiittttfiitttitttittittii*ittitttttitiiititt

*tiit PRECIPITATION OR EVAPORATION DATA i'k'ktittt*tiititttttiiiittiitfk

*iii‘i JUNCTION GEOMETRY DATA tttiii*iittiiiititittitiitttiit*tttitittttttt

tiff! MAP To WASP4 *ittittttitititifltiiitttrkfiit‘k*tiitittiiit*‘tti‘kitfittitiiitii‘k

Appendix C Field Data

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Discharge Head at Library Bridge Kellogg Bridge
at Farm
Day Time Lane Kalamazoo
B' Bridge Head Vel Flow Head Vel Flow
ridge
1 3:00 9.83
6:00 9.83
9:00 9.83 -1.48
12:00 9.94 0 0.51 10.26
15:00 9.94
18:00 9.83 -l.48 0.48 0.53 9.12
21:00 9.83
0:00 9.71
2 3:00 9.60
6:00 9.60
9:00 9.49 -1.51
12:00 9.37 0.47 0.53 8.89
15:00 9.26
18:00 9.15 -l.52 003 0.49 9.65
21:00 9.03
0:00 9.03
3 3:00 8.92
6:00 8.81
9:00 8.69 -l.55
12:00 8.58 0.46 0.54 9.06
15:00 8.47
18:00 8.35 —l.58 -0.05 0.45 8.45
21:00 8.24
0:00 8.16
4 3:00 8.04
6:00 7.93
9:00 7.82 -l.59
12:00 7.82 0.44 0.5 8.1
15:00 7.70
18:00 7.62 -l.59 -0.07 0.41 7.55
21:00 7.50
0:00 7.39
5 3:00 7.39
6:00 7.39
9:00 7.39 —l.6
12:00 7.31 -0.09 0.4 7.09
15:00 7.82

 

Field Data ...continued

82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Discharge Head at Library Bridge KelloggBridge
at Farm
Day Time Lane K211393200
B . Bridge Head Vel Flow Head Vel Flow
ridge
18:00 8.81 -1.48
21:00 9.71
0:00 10.20
6 3:00 11.38
6:00 12.89
9:00 14.16 -1.37
12:00 15.35 0.65 0.61 15.4
15:00 16.28
18:00 17.11 -l.26 0.05 0.69 13.69
21:00 17.93
0:00 18.49
7 3:00 18.92
6:00 19.34
9:00 19.48 -l.2 0.89 0.61 19.8
12:00 19.63 0.56 0.62 21.96
15:00 19.63
18:00 19.63 -1.19
21:00 19.48
0:00 19.20
8 3:00 18 92
6:00 18.49 __-__
9:00 18.07 -1 23 0.82 0.62 18.17
12:00 17.64 0.51 0.57 18.47
15:00 17 25
18:00 16.82 -1.26
21:00 16.43
0:00 16.00
Note: Filed data collected was from 04 April 2002 to 11 April, 2002.

83

 

Appendix D Time-Concentration Data-Dye Release 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Farm Lane Bridge Kellogg Foot BM Kalamazoo Bridge
Time since Time since Time since
injection Dye Conc. injection Dye Cone. injection Dye Conc.
(mlns) my.) (mlns) (uglL) (mlns) (ug/L)
45.13 0.04 97.03 0.00 146.88 0.03
46.15 0.50 99.00 1 .39 148.92 0.96
47.15 0.74 101.00 4.65 150.95 2.82
48.15 0.97 103.00 6.51 153.00 4.68
49.15 0.97 105.02 9.77 155.03 5.61
50.13 2.83 107.08 12.56 157.12 7.47
51.15 7.94 109.00 13.95 159.15 8.40
52.15 15.15 111.03 16.28 161.15 10.26
53.15 25.15 113.07 17.90 163.18 10.73
54.13 18.64 115.02 17.67 165.25 12.12
55.17 35.38 117.00 16.74 167.28 12.82
56.15 34.45 119.00 16.74 169.33 13.05
57.13 36.31 121.00 16.74 171.73 13.52
58.15 37.24 123.00 14.88 173.78 13.05
59.15 40.96 125.02 20.46 175.72 15.38
60.15 27.48 127.03 13.49 177.77 12.35
61.13 34.45 129.02 12.09 180.02 11.19
62.15 32.83 131.02 11.16 182.08 10.73
63.15 28.87 133.00 14.88 184.05 10.73
64.13 25.15 135.02 9.30 186.07 8.40
65.15 23.29 137.00 8.37 188.33 8.17
66.17 20.50 139.00 7.44 190.40 7.00
67.15 20.73 141.00 6.51 194.00 6.02
68.15 17.71 143.02 5.58 198.00 4.97
69.13 15.85 145.00 4.65 202.00 4.10
70.15 14.46 147.00 4.18 206.00 3.38
71.15 14.46 149.00 3.72 210.00 2.79
72.15 11.90 151.02 2.79 214.00 2.30
73.15 11.20 153.03 1.86 218.00 1.90
74.15 12.13 155.00 1.86 222.00 1.57
75.15 9.34 157.00 1.39 226.00 1.30
76.13 9.34 159.00 0.93 230.00 1.07
77.15 7.71 161.00 0.93 234.00 0.88
78.15 6.55 163.00 0.93 238.00 0.73
79.15 6.08 165.00 0.00 242.00 0.60

 

84

Time-Concentration Data - Dye Release 1.... Continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Farm Lane Bridge Kellogg Foot Bridge Kalamazoo Bridge
Time since Time since Time since Time since
injection Dye Conc. injection injection Dye Cone. injection
(mlns) (ufl) (mlns) (mlns) (lg/L) (mlns)
80.17 4.69 246.00 0.50
81.15 3.76 250.00 0.41
82.15 3.76 254.00 0.34
83.15 2.83 258.00 0.28
84.15 5.62 262.00 0.23
85.15 1.90 266.00 0.19
86.17 1.90 270.00 0.16

274.00 0.13
Note: - 2.65 Litres of Fluorescein Dye Released at 10:00 am on May 17, 2002.

85

 

Appendix E Time-Concentration Data-Dye Release 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Farm Lane Bridge Keli Foot Brigg Kalamazoo Brldge
Time since Dye Cone. Time since Dye Cone. Time since Dye Cone.
injection (uglL) injection (ufl) Injection (uglL)
(mlns) (uglL) (mlns) (ugly (mlns) (ug/l.)
53.92 1.11 109.28 2.98 154.00 0.49
54.92 1.34 111.33 15.22 157.00 1.42
55.90 4.57 1 12.37 9.67 160.00 3.26
56.90 12.42 113.40 13.37 163.00 5.57
57.92 19.35 114.43 17.52 166.00 8.34
58.95 38.97 115.45 19.60 169.00 12.04
59.92 60.90 116.45 27.22 172.00 16.19
60.92 71.98 117.47 26.76 174.00 19.42
61 .92 86.76 1 18.55 29.07 176.00 20.81
62.92 85.37 1 19.58 32.76 178.00 22.66
63.92 83.99 120.60 33.22 180.00 24.04
64.92 82.60 121.60 33.68 182.00 24.96
65.92 71.52 122.60 34.61 184.00 25.43
66.92 70.14 123.62 35.07 186.00 24.96
67.92 64.60 124.67 35.99 188.00 25.89
68.92 59.06 125.68 34.15 190.00 26.35
69.92 50.28 126.70 34.15 192.00 26.81
70.92 44.28 127.72 33.68 194.00 25.43
71.92 38.74 128.78 33.22 196.00 24.04
72.92 36.89 129.80 33.22 198.00 22.42
73.92 32.97 130.80 32.99 200.00 21 .27
74.92 30.89 131.88 31.84 202.00 21.27
75.92 28.58 132.95 30.45 204.00 20.35
76.92 29.97 133.97 29.53 206.08 18.50
77.92 29.04 134.98 29.07 208.00 16.65
78.95 20.27 136.12 26.99 210.00 15.73
79.93 21.66 137.13 26.30 212.00 15.73
80.93 20.27 138.13 23.99 214.00 14.81
81 .92 18.42 139.15 24.45 216.00 16.65
82.92 19.35 140.17 23.53 218.00 13.19
83.92 20.27 141.20 22.37 220.00 12.04
84.92 19.35 142.27 22.60 222.00 10.65

 

Time-Concentration Data - Dye Release 2. . .continued

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

87

 

 

Farm Lane Brldge Kell Foot Briggs Kalamazoo Bridge
Time since Dye Cone. Time since Time since Dye Cone. Time since
injection W) injection injection (uglL) injection
(mlns) (uglL) (mlns) (mlns) QM) (mlns)
85.92 12.88 143.30 21.22 224.00 10.19
86.92 1 1 .50 144.32 20.29 226.00 9.27
88.25 9.65 145.33 19.37 228.00 8.57
89.25 9.19 146.37 19.14 230.00 7.88
90.25 9.19 147.40 17.52 232.00 7.88
91.25 8.27 148.47 17.06 234.00 7.88
93.25 12.42 149.55 16.14 236.00 6.96
95.25 1 1 .50 150.57 15.22 238.00 6.03
96.27 5.96 151 .60 14.75 240.00 6.03
97.28 3.65 153.70 13.37 242.17 8.34
155.70 11.98 244.00 5.57
158.02 10.60 246.00 6.50
160.03 9.21 248.00 4.65
162.03 8.06 251.00 3.73
164.10 7.37 254.00 4.65
166.10 6.90 257.00 4.19
168.12 6.90 260.00 2.80
170.10 5.06 263.00 2.34
172.13 3.90 266.00 2.34
174.15 3.67 269.00 2.34
272.00 1.88
275.00 1.42
278.00 0.95
281.00 1.88
284.00 0.95
287.00 0.95
290.00 0.95
293.00 1.42
296.00 0.95
298.00 1.42
301.10 0.95
304.28 0.95
307.00 1.42
Note: - 5.0 Litres of Fluorescein Dye Released at 10:00 am on May 31, 2002.

 

Appendix F Time-Concentration Data-Dye Release 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Farm Lane Bridge KellogglFoot Bridge Kalamazoo Bridge
Time since Time since Time since
lruection Dye Cone. injection Dye Cone. injection Dye Cone.
(mlns) (uglL) (mlns) (uglL) (mlns) (ugé)
41.37 0.00 91.02 1.35 118.00 0.00
42.37 0.44 92.02 3.54 1 18.00 0.84
43.37 0.00 93.02 4.41 122.00 0.84
45.33 2.62 94.02 7.48 125.00 0.40
47.33 4.37 95.02 10.54 128.00 0.40
48.33 19.25 96.03 14.48 132.00 0.84
49.33 47.69 97.05 17.98 135.00 1 .27
50.33 54.69 98.02 20.60 138.00 3.46
51.33 67.82 99.03 25.85 141.00 6.53
52.33 79.63 100.12 27.60 144.00 10.90
53.33 74.38 101.03 29.57 147.00 15.71
54.33 78.32 102.17 31 .98 149.00 17.90
55.35 73.07 103.03 32.85 151.00 21.40
56.33 59.94 104.03 33.29 153.00 23.59
57.33 49.44 105.00 35.48 155.00 24.90
58.33 56.88 106.07 36.79 157.00 27.31
59.33 55.56 107.00 36.79 159.00 27.53
60.33 30.20 108.02 36.79 161 .00 27.53
61 .33 35.88 109.03 36.79 163.00 28.40
62.33 37.19 1 10.02 36.35 165.00 27.96
63.33 37.19 1 1 1.10 36.79 167.00 28.40
64.33 30.63 1 12.02 35.91 169.00 27.53
65.35 32.70 1 13.00 34.16 171.00 26.21
66.33 22.75 114.03 34.16 173.00 25.78
67.33 19.69 1 15.00 31.98 175.00 24.03
68.33 20.56 116.20 31.54 177.00 23.15
69.33 20.13 117.00 30.23 179.00 21.40
70.33 35.20 1 18.00 30.66 181.00 19.65
71.33 18.81 119.00 29.35 183.00 19.21
72.33 14.00 120.50 27.60 185.00 17.46
73.33 1 1.38 121.25 27.82 187.00 15.49
74.33 12.69 122.00 25.85 189.00 13.09
75.33 37.70 123.00 24.98 191 .00 13.53
76.33 9.63 124.00 23.66 193.00 12.65
77.35 9.19 125.00 22.79 195.00 10.90
78.33 7.44 126.00 21.91 197.00 11.12

 

Time - Concentration Data - Dye Release 3. . .continued

88

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

89

Farm Lane Brfle KelloglFoot Bridge Kalamazoo Bridge
Time since Time since Time since Time since
injection Dye Conc. injection Injection Dye Cone. injection
(mlns) (ufl (mlns) Lmins) (Lg/L) (mlns)
79.33 6.56 127.00 21.04 199.00 9.59
80.33 40.20 129.33 17.98 201 .00 8.28
81.37 7.00 130.00 17.10 203.00 7.84
82.35 7.00 131.00 17.10 205.00 7.40
83.33 5.25 132.00 14.48 207.00 6.96
85.33 42.70 133.00 15.35 209.00 5.65
86.33 2.62 135.35 13.60 211.00 6.09
87.35 2.62 137.33 12.29 213.00 5.21
88.33 2.19 139.00 10.10 215.00 4.77
89.33 2.19 141.00 9.66 217.00 4.34
90.35 45.20 143.00 7.48 219.00 3.90
91.35 1.75 145.00 6.60 221.00 3.90
92.33 1 .75 147.00 5.73 223.00 3.02
94.33 0.87 149.00 5.73 225.00 3.02
95.35 47.70 151 .00 4.85 227.00 3.02
96.33 1.31 153.00 3.54 229.00 2.59
97.33 0.87 155.00 3.10 232.00 2.59
98.33 0.44 157.00 2.66 235.00 0.84
99.33 0.00 159.00 2.22 238.00 1.71

161.00 2.22 241.00 2.37
163.00 1.79 244.00 1.27
165.00 1.35 247.00 1.27
167.00 0.91 250.00 1.27
169.00 0.91 253.00 0.84
171.00 0.91 256.00 1.06
173.00 0.47 259.00 0.84
175.00 1.13 262.00 0.84
177.00 0.04 265.00 0.40
179.00 0.04 268.00 0.40
181.00 0.04 271.00 0.40

274.00 1.27

277.00 1.27

280.00 1.27

283.00 0.84

286.00 0.84

Note: - 6.0 Litres of Fluorescein Dye Released at 10:00 am on June 06, 2002

 

Appendix G Time-Concentration Data-Dye Release 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BOfle Bridge (Left) Bogue Bridge (Centre) Bogue Bridge fightj
Time since Time since Time since
injection Dye Conc injection Dye Cone Injection Dye Cone

(mlns) (ug/L) ImIns) (ug/L) (mlns) (uglL)
61.00 0.00 127.13 0.00 101.88 0.00
66.00 0.03 129.13 0.87 133.50 3.07
72.00 0.03 131.22 11.78 135.40 1.32
129.00 3.09 133.13 24.44 137.40 8.31
132.00 0.90 135.12 21.82 139.30 23.59
134.00 5.71 136.88 42.78 141.27 41.27
136.00 7.89 138.90 53.69 143.30 23.59
138.00 7.45 140.83 62.43 145.30 28.39
140.00 15.75 142.88 65.48 147.27 38.87
142.00 55.04 144.95 66.35 149.17 51.97
144.00 25.79 146.95 68.10 151.27 59.39
146.00 29.28 148.93 68.97 153.27 47.60
148.00 27.97 150.97 71 .59 155.28 65.06
150.00 22.73 152.97 71.59 157.27 52.84
152.00 40.63 154.95 48.02 159.28 63.32
154.00 41.07 156.93 63.74 161.33 55.68
156.00 51 .98 158.93 47.15 163.27 57.20
158.00 38.89 160.92 43.87 165.20 55.46
160.00 34.52 162.97 42.34 167.22 49.35
162.00 34.96 164.93 42.78 169.23 47.60
164.00 35.83 167.10 38.41 171.33 43.67
166.00 39.32 169.05 30.56 173.00 42.36
168.00 34.08 171.05 27.06 175.00 37.99
170.00 34.08 173.07 27.94 177.00 38.43
172.00 35.83 175.07 23.57 179.00 41.05
174.00 34.08 177.07 29.68 181.00 40.18
176.00 31 .46 179.07 22.26 183.00 31.88
178.00 28.41 181.05 18.11 185.00 36.69
180.00 29.28 183.12 12.66 187.00 25.77
182.00 27.97 185.12 13.97 189.00 26.21
184.00 28.41 187.12 13.53 191.00 23.59
186.00 25.79 189.08 16.59 193.00 24.90
188.00 26.44 191.10 16.80 195.00 27.08
191.00 20.55 193.08 13.97 197.00 18.79
193.00 23.61 195.07 9.60 199.00 19.66
195.00 18.37 197.05 10.47 201.00 26.64

 

Concentration Data - Dye Release 4.. .continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

91

Bogue Bridge (Left) Bogue Bridge (Centre) Bogue Bridge (RiLht)
Time since Time since Time since Time since
Injection Dye Conc injection Injection Dye Cone injection
(mins) (uglL) (mins) (mins) (uglL) (mlns)
197.00 21 .42 199.08 9.60 203.00 17.04
199.00 20.11 201.10 8.73 206.00 16.17
201.00 22.30 203.08 11.35 208.00 17.04
203.00 21.86 205.07 9.60 211.00 13.98
205.00 20.1 1 207.03 8.73 213.00 11.80

207.00 18.37 209.05 7.42

209.00 18.58 211.10 8.29

211.00 18.37 213.05 4.36

213.00 16.18

Note: - 2.0 Litres of Fluorescein Dye Released at 10:00 am on June 21, 2002

 

Appendix H Time-Concentration Data-Dye Release 5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Farm Lane Bridge Kalamazoo Bridge
Time since Time since
injection Dye Cone. injection Dye Cone.

(mins) (uglL) (mins) (uglL)
271.00 0.00 585.00 0.00
273.00 0.24 588.00 1.15
275.00 1.23 591.00 1.54
277.00 0.44 594.00 0.00
279.00 1.23 597.00 0.16
281.00 3.99 600.00 0.36
283.00 1 .43 603.00 0.36
285.00 2.02 606.00 0.00
287.00 3.20 609.00 0.36
289.00 2.81 612.00 0.16
291.00 2.02 615.00 0.36
293.00 3.01 618.00 0.36
295.00 3.60 621.00 0.00
297.00 4.78 624.00 0.00
299.00 4.78 627.00 0.95
301.00 7.15 630.00 1.15 __
303.00 6.76 633.00 1.15
305.00 8.34 636.00 1.54
307.00 7.94 639.00 1.15
309.00 15.84 642.00 0.95
312.00 11.10 645.00 1.15
315.00 7.55 648.00 1.15
321.00 11.89 651.00 1.54
324.00 13.47 654.00 1.54
327.00 15.05 657.00 1.54
330.00 8.73 660.00 3.12
333.00 8.93 663.00 1.94
336.00 10.31 666.00 2.33
339.00 11.50 669.00 2.73
342.00 7.94 672.00 2.33
345.00 8.34 675.00 2.73
350.00 7.15 678.00 2.73
353.00 8.73 681.00 3.12
356.00 9.52 684.00 3.52
359.00 7.15 687.00 3.12
362.00 7.94 690.00 3.52
365.00 8.53 693.00 3.12
368.00 7.55 696.00 3.12
371.00 4.78 699.00 3.91
374.00 6.36 702.00 3.12
377.00 5.57 705.00 3.91

 

 

Concentration Data - Dye Release 5. . .continued

92

 

Farm Lane Bridge

Kalamazoo Bridge

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time since Time since
injection Dye Cone. injection Dye Cone.
(mlns) fig/L) (mlns) (uglL)
380.00 4.59 708.00 3.91
383.00 5.18 711.00 3.91
386.00 3.99 714.00 3.91
389.00 5.57 717.00 3.32
392.00 2.41 720.00 3.91
395.00 2.81 723.00 3.91
726.00 3.91
729.00 4.31
732.00 3.72
735.00 3.91
738.00 3.91
741.00 3.91
744.00 3.91
747.00 3.91
750.00 3.91
753.00 4.31
756.00 4.31
759.00 3.91
762.00 3.91
765.00 3.91
768.00 4.70
771.00 4.31
774.00 4.31
777.00 3.91
780.00 4.31

 

 

 

Note: -

1.0 Litres of Fluorescein Dye Released at 10:00 am on June 25. 2002

93

 

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