• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 List of Tables
 List of symbols
 Abstract
 1. Introduction
 2. Principles and instrumentat...
 3. Calibration of three-frequency...
 4. Duck94 nearshore field...
 5. Determination of the suspended...
 6. Conclusions
 Reference
 Biographical sketch






Group Title: UFLCOEL-95018
Title: Determination of concentration and size of suspended sediments in the coastal zone using acoustic backscatter measurements
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00085024/00001
 Material Information
Title: Determination of concentration and size of suspended sediments in the coastal zone using acoustic backscatter measurements
Series Title: UFLCOEL-95018
Physical Description: xiii, 83 leaves : ill. ; 28 cm.
Language: English
Creator: Marusin, Konstantin V., 1963-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1995
 Subjects
Subject: Suspended sediments -- Acoustic properties -- Atlantic Coast (U.S.)   ( lcsh )
Marine sediments -- Acoustic properties -- Atlantic Coast (U.S.)   ( lcsh )
Suspended sediments -- Measurement -- Atlantic Coast (U.S.)   ( lcsh )
Marine sediments -- Measurement -- Atlantic Coast (U.S.)   ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Konstantin V. Marusin.
Thesis: Thesis (M.S.)--University of Florida, 1995.
Bibliography: Includes bibliographical references (leaves 81-82).
 Record Information
Bibliographic ID: UF00085024
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 34549612

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Acknowledgement
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Figures
        Page vi
        Page vii
        Page viii
    List of Tables
        Page ix
    List of symbols
        Page x
        Page xi
    Abstract
        Page xii
        Page xiii
    1. Introduction
        Page 1
        Page 2
        Page 3
    2. Principles and instrumentation
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
    3. Calibration of three-frequency acoustic concentration profiler
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
    4. Duck94 nearshore field experiment
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
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        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
    5. Determination of the suspended sediment concentration and size using three-frequency acoustic concentration profiler
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
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        Page 71
        Page 72
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        Page 75
        Page 76
        Page 77
    6. Conclusions
        Page 78
        Page 79
        Page 80
    Reference
        Page 81
        Page 82
    Biographical sketch
        Page 83
Full Text



UFL/COEL-95/018


DETERMINATION OF CONCENTRATION AND SIZE OF
SUSPENDED SEDIMENTS IN THE COASTAL ZONE
USING ACOUSTIC BACKSCATTER MEASUREMENTS




by



Konstantin V. Marusin






Thesis


1995













DETERMINATION OF CONCENTRATION AND SIZE OF SUSPENDED
SEDIMENTS IN THE COASTAL ZONE USING ACOUSTIC BACKSCATTER
MEASUREMENTS.














By

KONSTANTIN V. MARUSIN


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


1995














ACKNOWLEDGMENTS


I wish to express sincere appreciation to my academic advisor and chairman of the
advisory committee, Dr. Daniel M. Hanes, for his support and encouragement not only
during the work on this thesis but also during my whole sojourn in the United States.
I also would like to thank Dr. Robert G. Dean, the Chairman of Coastal and
Oceanographic Engineering Department, for giving me the opportunity to study at this
department and for participating in my advisory committee. I am grateful to Dr. Robert G.
Thieke for teaching an excellent fluid mechanics course and for serving as a member of
my advisory committee.
I would like to express my special appreciation to Dr. Christopher E. Vincent (the
University of East Angela, Great Britain) for permission to use his instrument and for
helpful discussion of the results obtained. I also wish to thank Dr. Tae Hwan Lee
(Daewoo Corporation, Korea). His dissertation served me as a guide in the field of
acoustic measurements and as an example of excellent writing.
I am grateful to the Coastal Engineering Department faculty, especially to Dr. Li-
Hwa Lin, Dr. Ashish J. Mehta, Dr. Hsiang Wang, for sharing their knowledge with me. I
will never forget the brilliant course in sediment transport taught by Dr. Bent A.
Christensen (Civil Engineering Department). His course not only provided me strong
background but also helped to select the area of interest for any future scientific career.
Great thanks go to all staff members of the Coastal Engineering Laboratory.
Without their participation this work would never been finished successfully. I am
specifically grateful to Mr. Charles S. Broward II and Mr. John P. McCardle, electrical
engineers. Under their guidance, my basic knowledge and technical skills in electronics
have been tremendously improved.
I also wish to thank the clerical and secretarial staff of the Coastal Engineering
Department, dear Mrs. Sandra J. Bivins, Mrs. Rebecca H. Hadson, Mrs. Lucy E. Hamm,








Mrs. Helen T. Twedell, Mrs. Cynthia J. Vey, and Mr. John M. Davis, whose hospitality
and professional assistance are sincerely appreciated.
I am grateful to all former and present coastal engineering graduate students, whom
I have met here, for being together.
My final thanks go to Florida for providing an extensive survival training in a
different climatic zone.















TABLE OF CONTENTS

page

ACKNOWLEDGMENTS..................................................................................... ii

LIST O F FIG U RES................................................................................................. vi

LIST O F TA B LES.................................................................................................. ix

LIST O F SY M B OLS.............................................................................................. x

ABSTRACT..................................................................................................................... xii

CHAPTERS

1. INTRODUCTION............................... ................. ................................... 1

2. PRINCIPLES AND INSTRUMENTATION.................................................. 4

2.1. Basic Principles of the Acoustic Measurements of
Sedim ent Suspension................................................ ..................... 4
2.2. Governing Acoustic Backscattering Equation........................... ...... 6
2.3. The Signal Inversion Procedure..................................................... 13
2.4. Three-Frequency Acoustic Concentration Profiler (TFACP).............. 15

3. CALIBRATION OF THREE-FREQUENCY ACOUSTIC
CONCENTRATION PROFILER.......................................................... 18

4. DUCK94 NEARSHORE FIELD EXPERIMENT........................................ 32

5. DETERMINATION OF THE SUSPENDED SEDIMENT
CONCENTRATION AND SIZE USING THREE-FREQUENCY
ACOUSTIC CONCENTRATION PROFILER............................................. 49

5.1. Theoretical Development.............................................................. 49
5.2. Field Results.................................. ................ ................................. 54
5.3. D iscussion........................................................................................ 57








6. CONCLUSIONS...................................................................................... 78

REFERENCES...................................................................................................... 80

BIOGRAPHICAL SKETCH...................................................... ........................ 82














LIST OF FIGURES

Figure page

2.1 The water attenuation coefficient (aw) as a function of
water temperature for the operational frequency values
used in this study...................................................... ........................ 9

2.2 The sediment scattering function X(ka)..................................................... 9

2.3 The sediment form function /(ka)............................................................ 10

2.4 Three-Frequency Acoustic Concentration Profiler (TFACP)......................... 16

3.1 Cumulative size distribution of the sand sampled at the site
of TFACP location during field experiment 'DUCK94' and
used for the calibration.............................................. ......................... 20

3.2 The burst rms. signal profiles of 5.65MHz transducer....................................... 25

3.3 5.65MHz transducer calibration data versus equation (3.1)............................ 26

3.4 5.65MHz-transducer system constant calculated for different
concentration levels.............................. .............. ...... ................ 27

3.5 The file rms profiles of 0.97MHz transducer............................................... 28

3.6 The interaction of 0.97MHz transducer sound beam with the
returning flow jet in the calibration tank................................ ........ 29

3.7 0.97MHz transducer calibration data versus equation (3.1)........................... 30

3.8 0.97MHz transducer system constant calculated for different
concentration levels.................................................. ....................... 31

4.1 Location of the Field Research Facility [Birkemeir et al, 1985].................... 32


4.2 The system deploym ent................................................................................. 34








4.3 Water depth variations measured for three time periods.............................. 37


4.4 Waves and current measured during DUCK94 field experiment
August 20th August 28th........................................... .................. 38

4.5 Waves and current measured during DUCK94 field experiment.
September 1st September 9th...................................................... 39

4.6 Waves and current measured during DUCK94 field experiment.
October 9th October 15th........................................... ................. 40

4.7 The burst averaged distance from TFACP down to the sea bed
measured for three time periods..................................................... 41

4.8 The burst averaged suspended sediment concentration profiles
measured by TFACP transducers. Burst 'ds05041' at
Septem ber 3rd, 03:00................................................. ..................... 43

4.9 The burst averaged suspended sediment concentration profiles
measured by 0.97MHz and 2.35MHz transducers............................ 44

4.10 The burst averaged suspended sediment concentration profiles
measured by 2.35MHz and 0.97MHz transducers............................ 45

4.11 Suspended sediment concentration values observed in the period
August 20th- August 28th. (2.35MHz transducer data).................... 46

4.12 Suspended sediment concentration values observed in the period
September 1st September 9th. (2.35MHz transducer data)............... 47

4.13 Suspended sediment concentration values observed in the period
October 9th October 15th. (2.35MHz transducer data)................... 48

5.1 The quantity 'ln(Fm2/Fml)' involved in equation (5.4) versus the
mean of the size distribution (p,)........................................................ 53

5.2 The quantity 'as2/Fml' involved in equation (5.4) versus the mean
of the size distribution (p,)................................................................... 53

5.3 Linear approximation of the quantity 'ln(Fm2/Fml)' involved in
equation (5.4)...................................................... ......................... 55

5.4 Linear approximation of the quantity 'as2/Fml' involved in
equation (5.4)...................................................... ......................... 56









5.5 Sediment concentration and mean size. Burst ds05010.............................. 58

5.6 Sediment concentration and mean size. Burst ds05017.......................... 59

5.7 Sediment concentration and mean size. Burst ds05047.......................... 60

5.8 Sediment concentration and mean size. Burst ds05050.......................... 61

5.9 Sediment concentration and mean size. Burst da24118............................. 63

5.10 Sediment concentration and mean size. Burst da25126............................. 64

5.11 Sediment concentration and mean size. Burst da24117............................ 65

5.12 Sediment concentration and mean size. Burst da25128............................. 66

5.13 Sediment concentration and mean size. Burst da25134............................. 67

5.14 Sediment concentration and mean size. Burst ds05042............................ 68

5.15 Sediment concentration and mean size. Burst da25132............................. 69

5.16 Sediment concentration and mean size. Burst ds06083............................. 70

5.17 Sediment concentration and mean size. Burst ds05044.............................. 71

5.18 Sediment concentration and mean size. Burst ds05043............................ 72

5.19 Sediment concentration and mean size. Burst ds05037........................... 73

5.20 Sediment concentration and mean size. Burst ds05030............................ 74

5.21 Vertical profiles of the mean size of the suspended sediment................... 75

5.22 Vertical profiles of the suspended sediment concentration........................ 76

5.23 Vertical profiles of the sediment concentration.................................... 77














LIST OF TABLES

Table page

2.1 The basic characteristics of Three-Frequency Acoustic
Concentration Profiler............................................... ....................... 17

2.2 The parameters of Three-Frequency Acoustic Concentration
Profiler which are important for the data inversion............................ 17

3.1 The water attenuation coefficients (aw), the sediment
attenuation coefficients (as), and the sediment
backscattering factor (Fm) of TFACP transducers............................ 20

3.2 The data files acquired during TFACP calibration ................................... 21

3.3 The system constant values of each TFACP transducer
determined during the calibration.................................................... 24

4.1 Typical values of the system burst parameters.......................... ........ 33

5.1 The linear approximation parameters of the functions of
equation (5.4)................................... ............... ................................. 54

5.2 The bursts, which give the reasonable results for
concentration and mean size.......................................... ................ 62














LIST OF SYMBOLS


Latin

a suspended particle radius, m;
B strength of the source, N m / m2;
B2 (p c)-1 the source power, N m / (m2 s);
C sediment concentration, kg/m3;
c sound speed in the water, 1482m/s;
C(i), C(i-1) sediment concentration at the locations corresponding to bins # i and
#(i-1), kg/m3 ( or g/l);
C(r) suspended sediment concentration in the scattering volume, kg/m3;
d sediment size, assumed to be equal to the mean size at the bed, d = 0.1476 mm;
f the operational frequency, MHz;
F(r) sediment backscattering term, which characterizes the backscattering ability of the
particles in the scattering volume, m2/kg;
Fm sediment backscattering factor, m2/kg;
Fm(i) sediment backscattering factor value at bin #i, m2/kg;
Fmj(i) sediment backscattering factor value ofj-th transducer at bin #i, m2/kg;
g gravitational acceleration, 9.81 m/s2;
i bin number in successive order;
I(i-l) sediment attenuation integral value ( I as(r) C(r) dr ) at the distance corresponding
to bin #(i-l);
I(1) = I as C(r) dr sediment attenuation integral for the starting point.
Ib(t) energy intensity of backscattered acoustic wave at the transducer surface at the
moment of measurement, N m / (m2 s);
Ij(i-1) the approximation of sediment attenuation integral value of the j-th transducer
( I asj(r) C(r) dr ) at the distance corresponding to bin #(i-l);
Lo(r) energy intensity of the outgoing pulse at distance r from the source, N m / (m2s);
j =1..480 the number of profiles collected in the burst;
k = 2 Tr f / c acoustic wave number, 1/m;
Ls(r) reduction of energy intensity due to sediment scattering along the sound path;
Lw(r) reduction of energy intensity due to sound attenuation by the water along the
sound path;
M the mobility number;
p(a) particle size probability density function, 1/m;
P(t) acoustic pressure acting on the transducer surface, N / m2
R radius of the transducer surface, m;
r corresponding distance along the sound path, m;








r-2 energy intensity loss due to the spherical spreading of the backscattered acoustic
wave in the far field, m-2
r(i) distance from transducer corresponding to bin #i, m;
ro near field limit distance, m;
ri- distance from the transducer corresponding to bin #i, m;
s sediment specific gravity, s = 2.65;
Sys = (37t / 32) (B2 T 02 c / p2) the system constant, volt m2;
Sysj the system constant of the j-th transducer, volt m2;
T water temperature, C;
t time delay between the moment of firing the outgoing acoustic pulse and the moment
of measurements, s;
to the time delay (to) between the moment of firing the outgoing pulse and the moment at
which ACP starts to sample the analog output signal, s;
Ub maximum near bed horizontal wave velocity, calculated by linear wave theory from
the wave data measured (Hmo, Tp), m/s;
V(i) the signal value at bin # i, volt;
V(t) output signal of the transducer, volt;
Vj(i) the signal value of the j-th transducer at bin # i, volt;
vj (i) signal value at bin # i of the j-th profile in the burst, volt;
W(r) the pulse scattering volume at distance r from the source, m3.

Greek

as sediment attenuation coefficient, m2/kg;
as(i), as(i-1) the sediment attenuation coefficient value at the locations corresponding to
bins # i and #(i-l), m2/kg;
aw water attenuation coefficient, 1/m;
p pressure to voltage conversion factor, N / (m2 volt);
Ar distance offset, m;
8r distance increment corresponding to the unit increment of bin number, m / bin;
p water density, kg/m3;
ps sediment density, kg/m3;
N(ka) the form function, which is a nondimensional function of the particle radius (a)
normalized by the acoustic wave number k;
X(ka) the scattering function, which is a nondimensional function of the particle radius
(a) normalized by the acoustic wave number k;
0 angular width of beam of the acoustic pulse;
z the outgoing acoustic pulse duration, s.














Abstract of Thesis Presented to the Graduate School of the
University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science.


DETERMINATION OF CONCENTRATION AND SIZE OF SUSPENDED
SEDIMENTS IN THE COASTAL ZONE USING ACOUSTIC BACKSCATTER
MEASUREMENTS.

By

Konstantin V. Marusin

August, 1995

Chairman: Daniel M. Hanes
Major Department: Coastal and Oceanographic Engineering

An objective of the study is to obtain information about concentration and size of

suspended sediment in the coastal zone from the acoustic backscatter sensor data

collected during DUCK94 Nearshore Field Experiment conducted on the East Coast of

the United States (DUCK, NC) in August October 1994. A method, which allows the

extraction of information about suspended sediment concentration and mean size from

the original backscattered signals of two acoustic transducers operating at different

frequencies, is developed and applied to the acoustic data. The time-averaged vertical

profiles of suspended sediment concentration and mean size obtained by this method are

reported.

The inversion for suspended particle size was successful for approximately 10% of

the measurement period. The reasons for failure during the rest of the time is not currently








understood. For mobility numbers between 4000 and 800 the successful inversions

indicate 10% to 20% decreases in mean suspended sediment diameter within 4 cm of the

seabed, and nearly uniform suspended sediment diameter above 4 cm. For conditions

with mobility numbers between 200 and 400, the mean suspended sediment diameter was

uniform, but approximately 30% smaller than the mean sediment diameter found on the

seabed.














CHAPTER 1

INTRODUCTION


An objective of the study presented here is to obtain information about
concentration and size of suspended sediment in the coastal zone from the acoustic
backscatter sensor data collected during DUCK94 Nearshore Field Experiment conducted
on the East Coast of the United States (DUCK, NC) in August October 1994. A method
which allows the extraction of information about suspended sediment concentration and
mean size from the original backscattered signals of two acoustic transducers operating at
different frequencies is presented. The time-averaged vertical profiles of concentration
and mean size obtained by this method are reported.
Simultaneous measurement of concentration and size of the particles in suspension
is very important for understanding sediment transport phenomena and for developing the
appropriate mathematical models. It is well-known that the time-averaged concentration
of suspended material at any given height from the bed is determined largely by the
vertical turbulent flux and settling under gravity. The sediment settling velocity is
controlled primary by particle size. The measurements of both size and concentration
profiles would in principle permit direct estimates of the vertical mass flux due to
settling, which would then provide an indirect measure of the time-averaged vertical
turbulent flux of suspended sediment. The latter quantity is a critical element in the
sediment transport problem but is not itself easy to measure directly.
There have been very few simultaneous measurements of sediment concentration
and size, which have been made by using suction samplers and bottle samplers [Nielsen
et al, 1982; Kennedy et al, 1981]. However, those devices do not provide good spatial and
temporal resolution of measurements and also they disturb the natural flow conditions.
The acoustic backscatter sensor represent one of the more promising alternatives in this
measurement problem.






2
The acoustic backscatter sensor (ABS) also called 'Acoustic Concentration Profiler'
(ACP) was introduced into practice of sediment suspension measurements in the marine
environment 15 years ago [Huff and Fisk, 1980]. The device operates by ensonifing the
suspension by a short high-frequency sound pulse and then 'listening' for the
backscattered echo. Strength of the echo detected at given time gives indications of
suspended sediment concentration and size at certain location along the sound path. This
instrument has a number of advantages over the others, in particular, it does not disturb
the natural flow conditions in the area of interest, it can operate with spatial resolution
less than a centimeter and it provides almost instantaneous monitoring of the sediment
suspension. It can also identify the location of the sea bed.
However, the information of both concentration and size of the suspended sediment
cannot be obtained from the backscattered signal of the single-frequency acoustic
transducer. Therefore, in order to determine the concentration, one has to assume that the
sediment size distribution in suspension at all heights and at all times known and
invariant. This single-frequency approach has been widely used for making the acoustic
measurements of suspended sediment concentration in different environments ranging
from the coastal zone to the continental shelf [Hay, 1983; Hess and Bedford, 1985;
Vincent and Green, 1990; Thorne et al. 1991; Vincent et al., 1991].
Recently Hay and Sheng[1992] have demonstrated that it is possible to measure
suspended sediment concentration and size by using a set of the acoustic backscatter
sensors operating synchronically at different frequencies. The study presented here deals
with application of this idea to the acoustic backscatter data collected by three acoustic
transducers having different frequencies during DUCK94 Nearshore Field Experiment.
Chapter 2 provides a brief review of the physical and technical principles of the
acoustic measurements. The governing Acoustic Backscattering Equation, which
describes a relationship between the backscattered acoustic signal and the properties of
sediment suspension (particle concentration and size), is presented and discussed. It is
shown that there is a theoretical possibility of determining concentration and size
distribution parameters of the suspended sediment from the acoustic backscattered signals







3
at three different frequencies, assuming that the size distribution is log-normal. This

chapter also gives a description of the acoustic instrument utilized in this study.
Chapter 3 describes the acoustic instrument calibration. This procedure has to be
conducted to determine a value of so called 'system constant' involved in the governing
Acoustic Backscattering Equation. This parameter depends on the instrument
characteristics only. The calibration also allows observation and evaluation of the
instrument performance in general.

Chapter 4 gives a summary of the whole data set collected during DUCK94
Nearshore Field Experiment. A special emphasis is on quality of the acoustic data. It is
shown that one of the acoustic transducers was not operating properly. Consequently, the
study has to be restricted to determine suspended sediment concentration and mean size

only.
In Chapter 5, a method, which has been developed to extract the information of
suspended sediment concentration and mean size from the original backscattered signals
of two acoustic transducers operating at different frequencies, is presented. The time-
averaged vertical profiles of concentration and mean size of the suspended sediment
obtained by this method are reported and discussed.














CHAPTER 2

PRINCIPLES AND INSTRUMENTATION


This chapter provides a brief overview of physical and technical principles of
acoustic measurements of sediment suspension in the marine environment and describes
the instrument used in this study. A complete discussion can be found in the literature
(see for example, [Hay, 1983; Thorne et al, 1991; Vincent et al., 1991]). Two sources of
information [Lee, 1994] and [Thorne, 1993] have been utilized primarily in this chapter.


2.1. Basic Principles of Acoustic Measurements of Sediment Suspension


Acoustic measurements of sediment suspension are based on the fact that some part
of energy of an acoustic pulse, which propagates through the water containing suspended
sediment particles, is continuously scattered by those particles back to the source of the
pulse. The amount of energy scattered back depends on many factors but mainly on
concentration and size of the scatterers. This process results in the acoustic wave going
back to the source and containing information of sediment suspension properties. If the
source of the pulse operates not only as a transmitter but also as a transducer, the energy
intensity (i.e. energy flux) of this wave can be determined by measuring the pressure
variations on its surface, because the energy intensity of an acoustic wave is proportional
to the pressure value squared. The pressure is converted into voltage, and then that
continuous analog signal is sampled and digitized with a certain frequency.
Since the sound speed is constant and known, the time delay between the moment
of firing the outgoing pulse and the moment of measurement of incoming backscattered
wave is related to the distance from the source. Therefore, a particular point in space,
with which the signal measured at given time is associated, can be identified. However,
because the sound pulse has finite length and beam width, the signal detected by the








transducer at a certain time represents the suspension not at a single point in space but in
a finite volume around that point, which is called 'the scattering volume'. Because the
concentration of sediment at the sea bed is much greater than in the suspension, the
acoustic wave reflected from the bottom produces the strongest maximum of the signal so
that the sea bed position can be detected as well.
An instrument implementing the ideas discussed above operates by ensonifing the
suspension by a short sound pulse and then 'listening' for the return echo. The strength of
the echo detected at certain time is an indication of suspended sediment concentration and
size at certain location. Such an instrument is usually called 'Acoustic Concentration
Profiler (ACP)' or 'Acoustic Backscatter Sensor (ABS)'. Here and further the first term
will be used.
The main element of ACP is a small round crystal which produces the sound pulse
(sound wave train) by oscillating with high frequency (usually 1MHz or more). It also
serves as a transducer for the incoming backscattered wave. The frequency of the crystal
oscillation, which can be also called as 'the operational frequency', is a key parameter of
this kind of measurements. Special electronic devices included into ACP control the
crystal performance and provide the data acquisition. They generate the crystal
oscillations, convert the pressure acting on the crystal surface into an electrical signal
sample, and digitize that signal and so on.
As one can see from the previous discussion, the acoustic measurements are of
indirect type. Hence, the ACP output signal has to be inverted into the parameters of
interest (sediment concentration and size of suspended particles). It is not an easy task,
because there are many other factors besides backscattering, which affect energy intensity
of a sound wave while it propagates through the water with sediment particles in
suspension. The sound absorption by the water and scattering by the particles are the most
significant ones. Furthermore, in the case of ACP, the sound is not confined by any means
along its path, so that there is additional energy loss due to spherical spreading of the
acoustic wave. Also, it should be mentioned that, the relationship between the amount of
acoustic energy scattered back by sediment suspension in the scattering volume around
the certain point in space and the characteristics of that suspension (sediment








concentration and size of suspended particles) is nonlinear and very complex. However, it
is possible, of course, under some approximations, to describe all those processes
mathematically and to obtain the basic equation, which relates ACP signal detected at
certain moment to the suspension characteristics at a certain distance from the transducer.
This equation and the algorithm usually applied to invert ACP signal into suspended
sediment concentration are outlined in the next section.


2.2. Governing Acoustic Backscattering Equation


The relationship between the output ACP signal detected at a certain time t after
firing the acoustic pulse and the sediment suspension parameters at corresponding
distance r far from the transducer is obtained by considering the changes of energy
intensity which occur while the acoustic wave propagates forward to the point at distance
r and then back to the source:


Ib(t) = { o(r) F(r) C(r) W(r) } Lw(r) Ls(r) r-2 (2.1)
* Ib(t) energy intensity of backscattered acoustic wave at the transducer surface at the
moment of measurement, N m / (m2 s);

* Io(r) energy intensity of the outgoing pulse at distance r from the source,
Nm/(m2s);
* F(r) sediment backscattering term, which characterizes the backscattering ability of
the particles in the scattering volume. Consequently, the term underlined in the right
hand side of the equation (2.1) represents the amount of energy scattered back to the
source, m2/kg;
* C(r) suspended sediment concentration in the scattering volume, kg/m3;

* Lw(r) reduction of energy intensity due to sound attenuation by the water along the

sound path;
* Ls(r) reduction of energy intensity due to sediment scattering along the sound path;
* r-2 energy intensity loss due to the spherical spreading of the backscattered acoustic

wave in the far field, m-2;








* r corresponding distance along the sound path, m. This distance is related to the time
t by the straightforward formula:
r = ct / 2 (2.2)
* c sound speed in the water, 1482m/s;
* t time delay between the moment of firing the outgoing acoustic pulse and the

moment of measurements, s;
* W(r) the pulse scattering volume at distance r from the source, m3. This scattering
volume is determined as follows:
W(r) = c 7rc (r 0)2/ 8 (2.3)
* T the outgoing acoustic pulse duration, s;

* 0 angular width of beam of the acoustic pulse.


The energy intensity of the outgoing acoustic pulse at distance r from the source
(Io(r)) can be expressed as:
Io(r) = B2 (p c)-1 Lw(r) Ls(r) r-2 (2.4)
* p water density, kg/m3;

* B strength of the source, N m / m2;
* B2 (p c)1 the source power, N m / (m2 s).

Inserting equations (2.3) and (2.4) into equation (2.1) leads to the following expression:


Ib(t) = (7t / 8) (B2 2 0 / p) [Lw(r)]2 [Ls(r)]2 r-2 F(r) C(r) (2.5)


It has been mentioned previously that the energy intensity is proportional to the
acoustic pressure squared, and the pressure acting on the transducer surface is converted
linearly to the electrical signal (voltage), so that the energy intensity of backscattered
acoustic wave at the transducer surface can be expressed as:

Ib(t) = (P(t))2 (p c)-1 = (p V(t))2 (p c)-1 (2.6)

* P(t) acoustic pressure acting on the transducer surface, N / m2;
* p pressure to voltage conversion factor, N / (m2 volt);








* V(t) output signal of the transducer, volt.
Consequently, equation (2.5) takes the following form:


V(t)2 = (T / 8) (B2 T 02 c / p2) [Lw(r)]2 [Ls(r)]2 r-2 F(r) C(r) (2.7)


It has been found (Thorne, 93) that the energy losses due to water attenuation and
sediment scattering along the sound path can be described by exponential functions as
follows:
r-
Lw(r) = exp(-2 aw r); Ls(r) = exp(-2 j cXs(r) C(r) dr) (2.8)
0
* aw water attenuation coefficient, 1/m. This coefficient is a function of the

operational frequency (f) and water temperature (T) which is described by the
expression:
Cw = (55.9 2.37 T + 0.0477 T2 0.000384 T3) 10-3 f2 (2.9)

* T water temperature, C;

* f the operational frequency, MHz.

Figure (2.1) shows the water attenuation coefficient (aw) as a function of the water

temperature for the operational frequency values used in this study.

* as sediment attenuation coefficient, m2/kg. This parameter characterizes the

scattering properties of the particles in suspension at particular location and depends
on the operational frequency and the size distribution of suspended particles:

as = (3 / (4 ps)) ( a2 X(ka) p(a) da) / ( a3 p(a) da) (2.10)
0 o
* a suspended particle radius, m;

* p(a) particle size probability density function, 1/m;

* ps sediment density, kg/m3;

* k = 2 7 f/ c acoustic wave number, 1/m;

* X(ka) the scattering function, which is a nondimensional function of the particle
radius (a) normalized by the acoustic wave number k. For the quartz sand, this
function is described (Thorne, 93) by the following empirical expression:

X(ka) = 0.24 (ka)4 / (1 + (ka)2 + 0.24 (ka)4) (2.11)











Equation (2.11) is illustrated by figure 2.2.


0.2F


15 16 17 18


19 20 21 22
Temperature, C


23 24 25


Figure 2.1. The water attenuation coefficient (cw) as a function of the water temperature
for the operational frequency values used in this study. The solid line -
0.97MHz; the dashed line 2.35MHz; the dotted line 5.65MHz.







100 -----








03
a
CO


Figure 2.2. The sediment scattering function X(ka).


I









The term F(r) involved in equations (2.1, 2.5, 2.7) characterizes the backscattering

ability of the particles in the scattering volume at a particular location and depends on the

operational frequency and the size distribution of the suspended particles:
00 O
F = (3 / (4 ic)) ( a2 [J(ka)]2 p(a) da) / (p a3 p(a) da) = (3 / (4 7t)) Fm (2.12)
00 U (0 0
* Fm = ( a2 [W(ka)]2 p(a) da) / (ps f a3 p(a) da) sediment backscattering factor.
o 0
* y(ka) the form function, which is a nondimensional function of the particle radius

(a) normalized by the acoustic wave number k. For non-cohesive sedimentary

material, this function can be described (Thore, 93) by the following empirical

expression:

W(ka) = Vo 1.14 (ka)2 / (1 + 1.14 (ka)2) (2.13)

0o = (1 0.37 exp(-{ [ka 1.4] / 0.5}2) (1 + 0.28 exp(-{[ka 2.8] 2.2}2)

The form function (W(ka)) is plotted in figure 2.3.








100




0
5

0



10 1


Figure 2.3. The sediment form function y(ka).








It is clear that the parameters B, ', 0, 3 depend only on the characteristics of a

particular ACP and do not depend on properties of suspension, also, the speed of sound in

water is about a constant. Consequently, all those values can be incorporated into one
parameter which is called 'the system constant'. The value of the system constant for a
particular ACP must be determined during its calibration.
Finally, taking into account equations (2.2, 2.8, 2.12), equation (2.7) can be written
in the following form:

V(r)2 = Sys r-2 Fm(r) C(r) exp(-4 aw r) exp(-4 J as(r) C(r) dr) (2.14)
0
* Sys = (3t / 32) (B2 T 02 c / 32) the system constant, volt m2;

* r=ct/2,s.
Equation (2.14) is called as the 'Acoustic Backscattering Equation'. It relates the ACP

signal measured at a certain time (t) to the sediment suspension properties at a certain
distance (r) away from the transducer.
Two basic assumptions have been involved in the development of this equation.
First, the transducer has been considered as a point source so that the equation is not valid
very close to the transducer surface in the area which is called the 'near field'.
Theoretically, the distance from the transducer corresponding to the near field limit (ro)
can be estimated by the expression:
ro = k R2 /2 (2.15)

* ro near field limit distance, m;
* R radius of the transducer surface, m.

On the other hand, in the region very close to the sea bed the signal is contaminated by
the strong bed reflection, therefore, there is also the near bed limit of measurements (rb)
i.e. the distance from the bed below which the signal can not be taken into consideration.
This distance is determined by the formula:
rb = c T/ 4 (2.16)

Second, it has been assumed that the acoustic wave backscattered from each particle in
the scattered volume travels directly back to the transducer i.e. there is no multiple
scattering between particles. However, when there are too many particles in suspension
i.e. the suspended sediment concentration is high, the chance of occurrence of this effect








is significant. Third, transducer assumed linear dependence of V from P. Unfortunately,
there is no satisfactory theoretical work describing the correction that need to be applied
to account for multiple scattering.
It has been mentioned in the first section that the continuous analog output of ACP
is sampled and digitized with a certain frequency (fs). Hence, one deals with discrete data
points (bins) rather than with continuous variables. The set of bins collected by firing a
single pulse is called the 'elementary signal profile'. Each bin corresponds to certain
distance from the transducer through 'bin versus distance' relationship:

ri = i 6r + Ar (2.17)

* ri- distance from the transducer corresponding to bin #i, m;

* i bin number in successive order;

* 8r distance increment corresponding to the unit increment of bin number, m / bin.:

8r = c / (2 fs) (2.18)

* Ar distance offset, m. This offset is caused by the time delay (to) between the

moment of firing the outgoing pulse and the moment at which ACP starts to sample

the analog output signal. Its value is determined by equation (2.2);

Ar = to c / 2 (2.19)

* to the time delay (to) between the moment of firing the outgoing pulse and the
moment at which the ACP starts to sample the analog output signal, s.
As one can see from equations (2.6, 2.7), the frequency with which the analog output
signal is sampled influences the spatial resolution of the measurements.
The set of bins collected by firing the single pulse is called the 'elementary signal
profile'. However, this profile has no significant information because the scattering is a
random process. Instead, the ensemble rms. signal profile calculated over a certain
number of the elementary profiles must be considered in the analysis
Since the actual data collected is discrete, the Acoustic Backscattering Equation has
to be used in the discrete form i.e. in terms of bins so that the integral in the right hand
side has to be changed for summation by using, for example, the Trapezoidal Rule:








K(i) = Fm(i) exp(-2 8r a,(i) C(i)) C(i);

K(i) = ( V(i)2 r(i)2 / Sys) exp(4 (aw r(i) + I(i-1)) + 2 6r as(i-l) C(i-1)); (2.20)
* i the number of particular bin;

* Fm(i) sediment backscattering factor value at bin #i, m2/kg;

* C(i), C(i-1) sediment concentration at the locations corresponding to bins # i
and #(i-l), kg/m3 ( or g/l);
* V(i) the signal value at bin # i, volt;

* r(i) distance from transducer corresponding to bin #i, m;

* Xs(i), oCs(i-l) the sediment attenuation coefficient value at the locations

corresponding to bins # i and #(i-l), m2/kg;
* I(i-l) sediment attenuation integral value ( J as(r) C(r) dr ) at the distance
0
corresponding to bin #(i-1).
Equation (2.20) is called the 'Acoustic Backscattering Equation in discrete form'. This
equation together with 'bin vs. distance relationship' is a basis of inversion of the values
measured (volts) into the real parameters of the suspension (concentration and size). This
operation is outlined in the next section.


2.3. The Signal Inversion Procedure


The goal of the inversion procedure is to obtain the characteristics of the suspension
(sediment concentration and size distribution of suspended particles) from ACP signal
(voltage) detected. However, the character of this kind of measurements and the present
state of art are such that it cannot be reached without making additional assumptions of
the suspension nature.
First, there are too many unknown parameters to be found from the single Acoustic
Backscattering Equation (2.20). For each particular location, one has to determine
sediment concentration, the backscattering factor (Fm) and sediment attenuation

coefficient (cs). The last two are very complicated functions of the type and parameters of

sediment size distribution (see equations 2.10 2.13). One of the possible solutions of
this problem is to assume the sediment size distribution in water column to be constant.








For example, the size might be chosen the same as one on the sea bed at the site of ACP
location, which is usually very close to the log-normal type (normal in phi-units) and its
parameters can be determined by sieving analysis. So only the sediment concentration
values remain to be determined. Such an assumption is called 'constant size assumption'
and it is commonly utilized in practice of the measurements (see for example, Lee[1994]).
This is a crucial assumption. Common sense and the data available dictate that the size of
suspended sediment does vary with distance from the bed, although, sometimes such
variation can be insignificant.
Second, according to equation (2.20), the inversion procedure implies the
successive (bin by bin) order of calculations, therefore, the concentration at the previous
point has to be known to calculate its value at the next one. The first point of calculation
(the starting point) must be placed at some distance from the transducer, namely, behind
the near field limit. Equation (2.20) in this case has the following form:

V(1)2 r(l)2 / Sys = Fm C(1) exp(-4 (aw r(l) + I(1)) (2.21)

* I(1) = J as C(r) dr sediment attenuation integral for the starting point.
This integral cannot be calculated, because Acoustic Backscattering Equation is not valid
in the near field i.e. very close to the transducer. There are two ways to overcome this
problem. One can assume that the concentration is a constant in the region between the
transducer surface and the starting point, this is the so-called 'uniform suspension'
assumption. Consequently, the equation for the first point is changed as follows:
V(1)2 r(1)2 / Sys = Fm C(1) exp(-4 (Xw r(l) + as C(1) r(l)) (2.22)
On the other hand, the sediment attenuation in that region can be assumed negligible ('no
attenuation' assumption), so that the sediment attenuation integral (I) in equation (2.21) is
considered to be zero. This assumption is probably more correct than the previous one,
because ACP transducer is usually located quite far away from the bed (about Im) where
the concentration and size of suspended sediment are very small, and also, because it does
not involve any hypotheses about concentration profile which is itself the object of study.
The previous discussion shows that it is impossible to determine the concentration
and size distribution of suspended particles using a single ACP. However, Hay and Sheng
[1992] have demonstrated that this can be done by operating three transducers with








different operational frequencies simultaneously and by assuming the size distribution to
be a log-normal type. Hence, three independent equations for three unknown variables
(concentration, the mean, and the standard deviation) can be obtained and solved. The
instrument utilized for that purpose in this study is described in the next section.


2.4. Three-Frequency Acoustic Concentration Profiler (TFACP)


The Three-Frequency Acoustic Concentration Profiler (TFACP) which we have
used was designed and built by A.J.Downing and C.E.Vincent at University of East
Anglia (Great Britain). It has been used previously several times for studying suspended
sediment concentration and the bed forms. The instrument consists of three transducers
with operational frequencies 0.97MHz, 2.35MHz, 5.65MHz and the electronic unit,
which controls the transducers and provides communication with a data logger (Figure
2.4). Each transducer is connected to the unit by the cable so that the instrument is
flexible. The transducers can be separated in space or mounted together as shown in
Figure 2.4.
Typical TFACP operation can be briefly described as follows. The external

command, coming from the data logger to the electronic unit, initiates the instrument
'burst' i.e. the period of continuous data collection. All TFACP transducers fire the pulses
synchronically with the same repetition rate. The special board samples analog signals of
the transducers, stories the elementary signal profiles, and calculates the ensemble rms.
profiles. These ensemble rms. profiles of each transducer are final output of the
instrument during its burst. They usually are stored in the data logger as a data file. The
data logger also controls the main parameters of the instrument burst: the number of bins
in the elementary signal profile, the number of elementary signal profiles in ensemble
rms. profile calculation, the number of ensemble rms. profiles to collect for each
transducer during the burst.
The basic TFACP characteristics depended on the hardware are reported in table
2.1. The parameters, which are important for the data inversion process are shown in table








The basic TFACP characteristics depended on the hardware are reported in table
2.1. The parameters, which arc important for the data inversion process are shown in table
2.2. They have been calculated from the basic characteristics according to the theoretical
expressions discussed above.


Figure 2.4. Three-Frequency Acoustic Concentration Profiler (TFACP). Three
transducers mounted together and the electronic unit are shown.








Table 2.1. The basic characteristics of Three-Frequency Acoustic Concentration Profiler.

Transducer radius (R), mm 5

Acoustic pulse duration (t), ts 13

Data sampling frequency (fs), KHz 200

Time delay before sampling the data (to), Rs 30


Table 2.2. The parameters of Three-Frequency Acoustic Concentration Profiler which are
important for the data inversion.
0.97MHz transducer 2.35MHz transducer 5.65MHz transducer

Bin vs. distance 7.41 7.41 7.41
gain, mm

Bin vs. distance 9.99 9.99 9.99
offset, mm

Near field limit, mm 51 (Bin #6) 124 (Bin #16) 300 (Bin #40)

Near bed limit, mm 6 6 6














CHAPTER 3

CALIBRATION OF THREE-FREQUENCY ACOUSTIC
CONCENTRATION PROFILER


As mentioned in the previous chapter, it is impossible to invert the data originally
collected by ACP into the real parameters of sediment suspension (concentration and size
distribution) unless the system constant (Sys) involved in the governing Acoustic
Backscattering Equation (2.14) is known. This parameter is unique for each particular
ACP and it depends on the instrument characteristics only. A special procedure conducted
to determine this constant is called 'the instrument calibration'.
From the theoretical point of view, determination of the system constant is possible
if the concentration is uniform and the sediment size distribution is the same at any point
along the sound path so that Acoustic Backscattering Equation (2.14) takes a simple
form:
ln(V(r) r) + 2 aw r = 0.5 ln(Sys Fm C) 2 r as C (3.1)

* V(r) output signal detected at distance r from the transducer, volt;
* r distance from the transducer along the sound path, m;
* aw water attenuation coefficient, 1/m;

* Sys system constant, volt m2;
* Fm sediment backscattering factor, m2/kg ;
* C sediment concentration, kg/m3;

* as sediment attenuation coefficient, m2/kg.
Equation (3.1) allows direct calculation of the system constant (Sys) if the other
quantities involved in it are known:
Sys = (V(r)2 r2 / (Fm C)) exp(4 r (cw + as C)) (3.2)








Theoretically, the value calculated from equation (2.2) must be a constant regardless of
any variations of the parameters.
Conditions, which are approximately close to ones required for the system constant
determination are created in a laboratory by using a special device called 'the calibration
tank' [Lee, 1994]. This is basically a vertical cylinder filled with water and equipped with
the circulation system which continuously moves the water from the bottom of the
cylinder to the top. Because the water volume in the tank is fixed and known, a certain
concentration level can be achieved by simply putting a corresponding volume of sand in
the tank. Uniform conditions are provided by intensive mixing through the water column.
The water attenuation coefficient is determined by equation (2.9) from the water
temperature measurements. The sediment attenuation coefficient and the backscattering
factor can be estimated by their theoretical expressions (2.10, 2.12 ) from the data of
sieving analysis of the sand utilized in the calibration process.
Each transducer of Three-Frequency Acoustic Concentration Profiler (TFACP) has
been calibrated in the calibration tank using the sand sampled at the site of the instrument
location during field experiment 'DUCK94'. The value of uniform concentration has
been varied from 0.02g/l up to 30.0 g/l The sand grain size distribution can be well-
described by a log-normal (normal in phi-units) one (see Figure 3.1) with the following

parameters: the mean g,= 2.76phi ( 0.1476mm);
the standard deviation c, = 0.34phi.

The water temperature in the tank was 20C. The sediment attenuation coefficient, the
water attenuation coefficient, and the sediment backscattering factor calculated for these
conditions are shown in Table 3.1.
The data acquired during the calibration has been stored in the files listed in Table
3.2. Each file corresponds to the particular burst of the instrument. All those files have
been collected under the same burst parameters:
* The number of the ensemble rms. signal profiles collected in the burst 480;
* The number of bins per the profile collected 120;
* The number of the elementary profiles in the ensemble average 24;
* The burst duration 2 min.










100

90

80

70

60

50

40

30

20

10

0 l o


1 1.5 2 2.5
Size, phi-units


Figure 3.1.


Cumulative size distribution of the sand sampled at the site of TFACP
location during field experiment 'DUCK94' and used for the calibration.
'o' sieving analysis data. The line represents the log-normal size
distribution with g,= 2.76phi and o, = 0.34phi.


Table 3.1. The water attenuation coefficients (aw), the sediment attenuation coefficients
(as), and the sediment backscattering factor (Fm) of TFACP transducers.
5.65MHz transducer 2.35MHz transducer 0.97MHz transducer

aw, 1/m 0.7824 0.1353 0.0231

as, 1/m 1.4395 0.2517 0.0173

Fm, m2/kg 3.6192 0.8224 0.0935


3 3.5









Table. 3.2. The data files acquired during TFACP calibration .

Uniform 5.65 MHz 2.35MHz 0.97MHz

Concentration, g/l. transducer transducer transducer


0 da09001.mat da09003.mat da09002.mat
0.02 da09004.mat da09006.mat da09005.mat
0.06 da09007.mat da09009.mat da09008.mat
0.14 da09010.mat da09012.mat da09011.mat
0.23 da09013.mat da09015.mat da09014.mat
0.48 da09016.mat da09018.mat da09017.mat
0.50 da09019.mat da09021.mat da09020.mat
1.0 da09022.mat da09024.mat da09023.mat
1.5 da09025.mat da09027.mat da09026.mat
2.0 da09028.mat da09030.mat da09029.mat
2.5 da09031.mat da09033.mat da09032.mat
3.0 da09034.mat da09036.mat da09035.mat
3.5 da09037.mat da09039.mat da09038.mat
4.0 da09040.mat da09042.mat da09041.mat
5.0 da09043.mat da09045.mat da09044.mat
7.0 da09046.mat da09048.mat da09047.mat
9.0 da09049.mat da09051.mat da09050.mat
11 da09052mat da09054.mat da09053.mat
15 da09055.mat da09057.mat da09056.mat
25 da09058.mat da09060.mat da09059.mat
30 da09061.mat da09063.mat da09062.mat


To eliminate the influence of possible spatial and temporal variations of

concentration and sediment size, which could occur in the tank, the burst rms. signal

profiles have been utilized in the further analysis. Such a profile has been calculated for

each file collected according to the following formula:

V(i)=J( 1/ 480 ) X vj (i) 2 (3.3)

* V(i) signal value at bin # i in the burst rms. profile, volt;

* vj (i) signal value at bin # i of the j-th profile in the burst, volt;








* j =1..480 the number of profiles collected in the burst;
* i=1-120 the number of bins per profile collected.
This operation also allows a reduction of the amount of data to be analyzed and the
compression of the original 63 data files into three files named 'cdrev1.mat', 'cdrev2.mat'
and 'cdrev5.mat', which contain the burst rms. signal profiles for 0.97MHz, 2.35MHz,
and 5.65MHz transducers respectively.
In practice, the instrument response may diverge, sometimes significantly, from the
theoretical behavior described by equation (3.1). One of the possible reasons for that is
nonuniformity of the calibration conditions, which could not be totally eliminated by the
burst rms. profile calculation. Another reason is related to the fact that at a certain
concentration level, the basic assumptions of the governing Acoustic Backscattering
Equation can be violated. In particular, for high concentrations, the multiple scattering
effect may become significant. Also, there can be some nonlinearity in the electronic
components of the instrument, which can affect the results. In general, this nonlinearity
must be quantified and than removed from the original data collected [Lee, 1994]. That
has not been done in this study. However, as previous experience shows [Vincent,
personal communication], the instrument nonlinearity seems to be quite weak and appears
only at low concentration levels.
Therefore, to establish the system constant value for each transducer of TFACP, one
has to select appropriate distance range and concentration levels over which it should be
calculated. They must satisfy the following requirements:
* The distance range selected must be in the far field of the transducer.

* The value of the signal must be above the noise level ( 0.0013volt ).
* The signal profiles must be free of spikes and any other significant disturbances.
* The signal profiles must demonstrate theoretical behavior described by equation (3.1)

This implies that, first, quantity 'ln(V(r) r) + 2 (ow r' plotted versus distance 'r' ( or the

bin number) must represent a straight line with negative or zero slope and, second, the
value of the system constant calculated by equation (3.2) must be approximately the
same over the distance range and concentration levels selected.








Values of the system constant calculated according to equation (3.2) over distance range
and concentration levels selected should be averaged to obtain the final result. Further
discussion will be concentrated primarily on the selection of concentration levels but
similar reasoning can be applied to find the appropriate distance ranges.
Figure 3.2 shows the burst rms. signal profiles of 5.65MHz transducer. As one can
see, for the concentration values exceeding 2.0g/l the signal drops down to the noise level
very rapidly due to the large sediment attenuation coefficient so that the region, in which
the governing equation is valid, remains totally uncovered. At the same time, the profiles
obtained under concentrations 1.0g/l, 1.5g/l, and 2.0g/l clearly diverge from the behavior
described by equation (3.1) (see Figure 3.3). Also, the system constant calculated for the
lowest concentration 0.02g/l is considerable smaller than the others (see Figure 3.4).
Hence, only the profiles corresponding to concentration levels 0.06 0.5g/l should be
accepted for the calculation of 5.65MHz transducer system constant.
Figure 3.5 shows the burst rms. signal profiles of 0.97MHz transducer. All of them
have large spikes located at the same place (34 42cm. away from the transducer). That
indicates the constant presence of a large scatterer. The water-sediment jet caused by the
mixture coming back to the tank from the circulation system could be such a scatterer .
The transducer sound beam, which is the widest one, could interact partially with this
strongly disturbed area. Moreover, it should be mentioned that the profiles of 2.35MHz
transducer, which has more narrow beam, have spikes at that location too, but they are
much smaller. The profiles of 5.65MHz transducer (its beam is the most narrow) do not
have them in that region at all. Figure 3.6 illustrates the situation. Despite those spikes,
the signal basically stays above the noise level. However, the profiles obtained under the
concentrations higher than 0.23g/l should be discarded due to their nontheoretical
behavior (see Figure 3.7). Also, the system constant values for the low concentrations
(0.02, 0.06g/l ) again seem to be too small (see Figure 3.8). Hence, only two profiles
obtained under concentrations 0.14g/l and 0.23g/l should be involved in the calculation.
The burst rms. signal profiles of 2.35MHz. transducer have not originated any other
problems different from those mentioned above, which is why the selection procedure for
that transducer is omitted here.








The values of the system constant determined for each TFACP transducer over the

distance ranges and concentration levels finally selected are reported in table 3.3.


Table 3.3. The system constant values of each TFACP transducer determined during the
calibration.
5.65MHz transducer 2.35MHz transducer 0.97MHz transducer

Distance range 0.306 0.603 0.506 0.699 0.506 0.706
selected, m (Bin #40 Bin #80) (Bin#67 Bin#93) (Bin #67 Bin #94)

Concentration levels 0.06 0.5 0.14 2.5 0.14, 0.23
selected, g/1

System constant, 0.3959 0.2752 3.7968
volt m2


As one can see from the previous discussion, the system constants of the TFACP
transducers have been determined only over quite narrow range of concentrations. That is
especially true for 0.97MHz transducer. It is hard to tell what caused the nontheoretical
behavior of the signal under the concentrations which are higher and lower than the ones
selected. It could be the instrument nonlinearity in the case of low concentrations and the
multiple scattering effect in the case of high concentrations, but both of them have not
been investigated and estimated. More detailed study of the instrument performance is
strongly required to answer this question. Finally, it should be mentioned that, although
the conditions created during TFACP calibration do not occur in nature, the results
obtained do demonstrate up to some extent what may happen in the real field conditions.





























I \ \\

1.5 -'\ \
'


0 I '
S. \ \\


~ \\ \

\ \ \
: , \\ "-_


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Distance from the transducer, m




Figure 3.2. The burst rms. signal profiles of 5.65MHz transducer. Different line styles
are used to indicate the concentration levels: solid 0.02 ...0.48g/l; dashed -
0.5...2.5g/1; dash-dotted 3.0...9.0g/l; dotted 11.0...30.0g/l.








































0.3 0.35 0.4 0.45 0.5 0.55 0.6
Distance from the transducer, m


Figure 3.3.


5.65MHz transducer calibration data versus equation (3.1).
symbols are used to indicate the concentration levels: 'x' -
'.' 1.0g/l; 'o' 1.5g/l; '+' 2.0g/l. The straight lines
best fit to equation (3.1).


Different
0.48g/l;
show the















S


0.35


0.4 0.45 0.5
Distance from the transducer, m


0.55


Figure 3.4. 5.65MHz-transducer system constant calculated for different concentration
levels: dotted line 0.02g/l; points 0.06-0.5g/1.


0.45 F


0.4 ,


0.35h


0.3F


0.25 F


0.2


0.15
0.3


:''''










4.5 I I


4 --.


3.5
.\ \ "': .
\\ \\ \. '

3- \ \
3o \m\ \,\ <' ,,

S \ \ :
2.5 -
0 I

2-


1.5 -










0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Distance from the transducer, m




Figure 3.5. The file rms profiles of 0.97MHz transducer. Different line styles are used to
indicate the concentration levels: '-' 0.02 ...0.48g/l; '--' 0.5...2.5g/;
S 3.0...9.0g/l; ':' 11.0...30.0g/l.


































Figure 3.6. The interaction of 0.97MHz transducer sound beam with the returning flow jet
in the calibration tank.












0



-0.2



S-0.4
c\i

0
* -0.6
:3
t'-
a)
-0.8
0



-1
-- -1.2


1.4


0.5


0.55 0.6 0.65
Distance from the transducer, m


Figure 3.7. 0.97MHz transducer calibration data versus equation (3.1). Different symbols
are used to indicate the concentration levels: 'x' 0.14g/l; '.' 0.23g/l;
'+' 0.5g/l; 'o' 2.5g/l. The straight lines show the best fit to equation (3.1).


_-1


O-- OOO0 OOO0eOoo eO00 0 00OO


xxxxxxxx XXX, VXX)

fi'


-



-

















4 o00000o


ooo0000


ooo00000


+
+


+ +
++fc++


X X XX
XX X


1.5F


XX
X


XXX


x
X X>

0.55 0.6 0.65
Distance from the transducer, m


0.7


Figure 3.8. 0.97MHz transducer system constant calculated for different concentration
levels: 'x' 0.02g/l; '+' 0.06g/l; '.' 0.14g/l; 'o' 0.23g/1.


mi,


c-*
C
0

E
a)
S2.5














CHAPTER 4

DUCK94 NEARSHORE FIELD EXPERIMENT


DUCK94 Nearshore Field Experiment was conducted in August October 1994 and
hosted by the US ARMY Engineer Waterways Experiment Station's Coastal Engineering
Research Center Field Research Facility (FRF) located in Duck, NC (see Figure 4.1). The
joint group of researchers from Coastal and Oceanographic Engineering Department of
the University of Florida and from the University of East Anglia (Great Britain) was
among the participants.


Figure 4.1. Location of the Field Research Facility [Birkemeir et al, 1985].










The underwater system of the instruments for multipurpose study of sediment
transport phenomena in the coastal zone has been deployed and operated by that group
during the experiment. The system consists of Three-Frequency Acoustic Concentration
Profiler (TFACP) described in Chapter 2, the pressure gauge, and the electro-magnetic
current meter. The underwater data logger equipped with the micro-computer and the
high capacity hard disk provides instrument control, data storage and data transfer to the
shore station through the underwater cable.
The system has been deployed in the vicinity of the offshore side of the nearshore
bar at 345 meters of longshore distance North of the FRF pier and 190 meters from the
shore. The sea bed at the site was composed by sand with mean size 0.148mm (see Figure
3.1). The instruments have been mounted on a vertical pole, which has been attached to
the horizontal frame jetted into the sea bed. Figure 4.2 shows the details of the
deployment.
The system has been operated in 'burst' fashion. It means that after continuous
collection of a certain amount of data the system is set into the 'sleep' mode (no data
collection) until the command starting the new burst comes from the shore station. The
instruments sample data with the same frequency so that a data point on the pressure
gauge (or current meter) record corresponds in time to one ensemble rms. signal profile of
TFACP transducer. The burst parameters have been varied during the experiment
according to the natural situations and goals of the research. Their typical values are
reported in Table 4.1.


Table 4.1. Typical values of the system burst parameters.

Burst duration, min. 23 31
Data sampling frequency Hz. 2

The number of data points (bins) in TFACP profile 90 100








SYSTEM LOCATION.

The system.


FRF Pier.


o0
/
/


INSTRUMENT MOUNTING.


TFACP orientation.

TJ 5.65MHz.

S 2.35MHz.

S 0.97MHz.


1 TFACP;

4 Instrument pole;


2 Current meter; 3 Pressure sensor;

5 Horizontal frame; 6 Data logger;

Figure 4.2. The system deployment.








The data collected in the particular burst are originally stored as a separate file into
the data logger hard disk Then, if the disk is full, those data files are transferred to the
shore station computer.
The system briefly described above allows one to obtain information about the
hydrodynamic conditions (waves, current, tide), the suspended sediment concentration,
and the sea bed dynamic(erosion, accretion). The information of waves, current and tide
is derived from the pressure gauge and current meter data by well-known spectral analysis
procedure. The sea bed location is determined from TFACP data (see Chapter 2). Since
the relative bottom position is measured and the distance between TFACP and the
pressure gauge is fixed, the water depth at the site can be calculated. The procedure
described in Chapter 2 allows inversion the TFACP transducer signal profiles stored in
the data files into suspended sediment concentration profiles under the assumption that
the size distribution of the sediment in suspension is the same as at the sea bed (constant
size assumption). Moreover, because of presence of three transducers with different
operational frequencies, there is a possibility of determination of sediment concentration
and size distribution parameters simultaneously. That possibility will be investigated in
Chapter 5.
The data were collected for about two months (from August 12th until October
16th). Three time periods, namely, August 20th August 28th, September 1st- September
9th, and October 9th October 15th can be considered as the most interesting ones
because of the significant natural events such as storms, and bed erosion or accretion
occurring in the coastal zone. Consequently, the further discussion will be concentrated
on them only. Figures 4.3 4.7 show the hydrodynamic conditions (water depth, waves
and current) and the sea bed evolution observed.
Figures 4.5, 4.6 clearly indicate two strong North-Eastern storms which occurred on
September 3rd September 5th and on October 12th October 16th. During the first
storm significant local bed erosion was observed at the site. In fact, the bed retreat has
been even larger than that shown in Figure 3.8. The bed has moved so far away from the
transducers that the bed location could not be detected because of TFACP hardware
limitations (the maximum possible number of bins in the profile 125), which is why the








data collection has been interrupted temporally in the morning of September 4th.
However, those changes have not resulted in the considerable net erosion. After the
storm, the bed has been detected just a few centimeters below its pre-storm position. On
the other hand, there was the large continuous bed accretion in the period October 12th -
October 16th, which was related to the offshore motion of the bar. This process finally
forced the researchers to stop the measurements completely and to remove the system
from the water. By that time the TFACP transducers had been almost buried into the
sand.
To obtain information of the sediment suspension under various hydrodynamic
conditions and to evaluate TFACP performance, the 'burst-averaged' suspended sediment
concentration profiles have been calculated for the entire set of data collected from each
TFACP transducer. That has been done by applying the basic inversion algorithm
described in Chapter 2 to the burst rms. signal profiles defined by equation (3.3). The bed
location has been determined by the position of the signal maximum in the burst rms.
profile. Unfortunately, there are some problems related to those results.
It should be pointed out that the concentration obtained from the burst rms. signal
profile is not the true mean over the burst. This is because the relationship between the
signal detected and the concentration is not linear (see equation (2.14)).
Also, there is an uncertainty about the exact bed location and about the
concentration values in the region close to the bed, which is caused by two factors. First,
TFACP creators argue that the bed location corresponds to the maximum of the signal in
the ensemble rms. profile. But Lee [1994] has demonstrated that, in general, the bed
location does not necessarily coincide with the position of the signal maximum. He also
has suggested that the complex of laboratory experiments helps to locate the bed in the
signal profile more precisely. However, such work has not been done in this study.
Second, the position of the signal maximum is different for each profile in the burst so
that the ensemble averaging in the region around the maximum positions, where the
signal gradients are very large, can result in an unrealistic shape of the burst rms. signal
profile. The variations of the maximum location inside the burst were about a bin (0.74
cm.). Also, the region of the sharp signal gradient typically has involved three bins (1.5










cm of the distance). So, the upper limit of the uncertainty region can be estimated as 2.5

cm above the bed location determined from the burst rms. signal profile.


E5F


LI


20 21 22 23 24 25
August


1 2 3 4 5 6
September


9 10 11 12 13
October


26 27 28


7 8 9


14 15 16


Water depth variations measured for three time periods: a) August 20th -
August 28th, b) September 1st September 9th, c) October 9th -
Octoberl5th Each point represents particular system burst in the real time
scale.


a

: :.
.* .


c
S* ". *** .***

i.- . *.. v **. ** .**. .. Ir *
\.' ***' *"* -'


Figure 4.3.


r\













E
S1.5
E
I 1


20 21 22 23 24 25 26 27 28


12-


8 -
20 21 22 23 24 25 26 27 28


Wave vector and Current(-.) Direction (Clockwise from the North)


20 21 22 23 24 25 26 27 28


Current Magnitude


20 21 22 23 24 25 26 27 28
August


Figure 4.4. Waves and current measured during DUCK94 field experiment.
August 20th August 28th.
Each point represents particular system burst in the real time scale.













E3
E2
r1


1 2 3 4 5 6 7 8 9


0-

5-
1 2 3 4 5 6 7 8 9


Wave vector and Current(-.) Direction (Clockwise from the North)


1 2 3 4 5 6 7 8 9


Current Magnitude


E-
E 0.4-
0.2
1


2 3 4 5 6 7 8 9
September


Figure 4.5. Waves and current measured during DUCK94 field experiment.
September 1st September 9th.
Each point represents particular system burst in the real time scale.

















9 10 11 12 13 14 15 16


9 10 11 12 13 14 15 16


Wave vector and Current(-.) Direction (Clockwise from the North)


300
_0200
100


9 10 11 12 13 14 15 16


Current Magnitude


9 10 11 12 13
October


14 15 16


Figure 4.6. Waves and current measured during DUCK94 field experiment.
October 9th October 15th.
Each point represents particular system burst in the real time scale.

















E














E
0


10 11 12 13
October


14 15 16


Figure 4.7. The burst averaged distance from TFACP down to the sea bed measured for
three time periods: a) August 20th August 28th, b) September 1st -
September 9th, c) October 9th October 15th Each point represents
particular system burst in the real time scale.


/U
a
65-.

60

55

50
20 21 22 23 24 25 26 27 28
August



80
b
75 -

70 .

65 - '- -

60
1 2 3 4 5 6 7 8 9
September





90-

80 .. ..
70- .

60 -
en I -il


E
0








It should be emphasized that the results obtained from burst rms. signal profiles
must not be considered as exact, but they do provide a preliminary estimation of the
concentration and can be used as an indicator of TFACP performance.
It has been found that the concentration values detected by 5.65MHz transducer are
always much lower than ones obtained from the other two TFACP transducers. This fact
is illustrated by Figure 4.8. Such constant discrepancy hardly can be explained by features
of the instrument or the inversion method. It may be suggested that the significant
difference of 5.65MHz data from the others could be caused by high concentration of an
organic material in the water. The presence of such a material can strongly increase the
attenuation of a high-frequency acoustic pulse and, therefore, reduce the value of the
signal detected. Since that effect has not been taken into account during TFACP
calibration, the data obtained from 5.65MHz TFACP transducer had to be discarded.
The other TFACP transducers (0.97MHz and 2.35MHz) show consistent results
under non-breaking waves (Figure 4.9), but the difference between them becomes
extremely large in the storm situation when breaking and broken waves are observed at
the site of instrument location (Figure 4.10). Also, the concentration profiles of 0.97MHz
transducer have an unrealistic shape. One can recall that during TFACP calibration
0.97MHz transducer has demonstrated very nontheoretical behavior under the
concentrations 0.48 g/1 and higher so that the discrepancy observed is not surprising.
Unfortunately, in this case, no clear explanation can be provided.
The concentration profiles detected by 2.35MHz transducer look reasonable under
the whole variety of conditions. Therefore, this transducer can be considered as the most
reliable data source. Figures 4.11 4.13 provide the overview of suspended sediment
concentration values observed during the experiment.


















25





20
E



E 15

0




5-
0












102 10 10 101
Concentration g/I





Figure 4.8. The burst averaged suspended sediment concentration profiles measured by
TFACP transducers. Burst 'ds05041' at September 3rd, 03:00. The solid
lane 0.97MHz transducer data. The dotted line 2.35MHz transducer data.
The dash-dotted line 5.65MHz transducer data.

















25


I I . . .. .


10-1
Concentration
Concentration


10-1
10


100
Concentration g/i


Figure 4.9. The burst averaged suspended sediment concentration profiles measured by
0.97MHz and 2.35MHz transducers. a) Burst 'ds05029' at September 2nd,
14:00 b) Burst 'ds05039' at September 3rd, 01:00. The solid lane -
0.97MHz transducer data. The dotted line 2.35MHz transducer data.


E
o 20
a)
.Q

0
t-
E 15


0
C

)10


OL
10












a


30 k


20


An


E
o
- 25
(D


E 20
0


r 15

Q3


10o


0
10-


100
Concentration g/i


100
Concentration g/l


Figure 4.10. The burst averaged suspended sediment concentration profiles measured by
2.35MHz and 0.97MHz transducers. a) Burst 'ds05050' at September 3rd,
12:00 b) Burst 'ds05067' at September 4th, 05:00. The solid lane -
0.97MHz transducer data. The dotted line 2.35MHz transducer data.


10l


10


"""" """'


I ..............~











Concentration @ 4cm above the bed


21 22 23 24 25 26 27 28
August


Concentration @ 10cm above the bed


21 22 23 24 25 26 27 28
August


Concentration @ 20cm above the bed


1U


10-2


21 22 23 24 25
August


26 27 28


Figure 4.11. Suspended sediment concentration values observed in the period
August 20th- August 28th. (2.35MHz transducer data).
Each point represents particular system burst in the real time scale.


100



110-1


1


202
20


100
100


101


10-2


10-3
20



o-1


S ~ S

*C I


10-4
2


.0











Concentration at 4cm above the bed


101


100


10
10-
10-2


2 3 4 5 6
September


7 8 9


Concentration at 10cm above the bed


10 1-1-1 1-1-1-1 1
1 2 3 4 5 6 7 8 9
September


Concentration at 20cm above the bed


100








10-5


2 3 4 5 6
September


7 8 9


Figure 4.12 Suspended sediment concentration values observed in the period
September 1st September 9th. (2.35MHz transducer data).
Each point represents particular system burst in the real time scale.


.
? *.


i i ii

+o

...


*


I


1











Concentration at 4cm above the bed


101



E)100
0



10,1





101

100
-1
10-2

10-3
10-3
9


3 14 15 16


Concentration at 10cm above the bed


10 11 12 13 14 15 16
October


Concentration at 20cm above the bed


10 11 12 13
October


14 15 16


Figure 4.13 Suspended sediment concentration values observed in the period
October 9th October 15th. (2.35MHz transducer data).
Each point represents particular system burst in the real time scale.


' c. '=~ ~ '~
.~ "'
e, .L
. )' =~C
''


10 11 12 1
October


)









r


* .- .*


101

100

10-


10-
10-3


r =' "- ." I* I "vI I
: *


9














CHAPTER 5

DETERMINATION OF THE SUSPENDED SEDIMENT
CONCENTRATION AND SIZE USING THREE-FREQUENCY
ACOUSTIC CONCENTRATION PROFILER


5.1. Theoretical Development


The governing Acoustic Backscattering Equation (2.14) contains information not
only about the suspended sediment concentration at certain location but also about the
sediment size distribution through the sediment backscattering factor (Fm) and sediment
attenuation coefficient (as) involved in the equation. The type of sediment size
distribution is assumed to be log-normal ( normal in phi-units ) so that the backscattering
factor and the sediment attenuation coefficient are only functions of two distribution
parameters ( g, mean value, o, standard deviation ) and the transducer operational
frequency Those functions have been described previously in Chapter 2. However, that
information cannot be obtained unless two additional equations which relate unknown
variables to each other are established. That can be done by operating simultaneously
three acoustic transducers with three different frequencies [ Hay and Sheng, 1992]. This
idea is a basis for determination of concentration and sediment size distribution using
Three-Frequency Acoustic Concentration Profiler (TFACP).
By writing Acoustic Backscattering Equation in discrete form (2.20) for each
TFACP transducer, the following set of equations can be generated:

Kj(i) = Fmj(i) exp(-2 Sr asj(i) C(i)) C(i);

Kj(i) = ( Vj(i)2 r(i)2 / Sysj ) exp(4 ((wj r(i) + Ij(i-1)) + 2 8r asj(i-1) C(i-1)); (5.1)
* j = 1, 2, 5. Subscript '1' stands for 0.97MHz transducer of TFACP; '2' for
2.35MHz transducer and '5' for 5.65MHz transducer;






50

* C(i), C(i-l) sediment concentration at the locations corresponding to bins # i and
#(i-l), kg/m3 ( or g/l);
* Fmj(i) sediment backscattering factor value ofj-th transducer at bin #i, m2/kg;

* Ij(i-1) the approximation of sediment attenuation integral value of the j-th transducer

(J sj(r) C(r) dr) at the distance corresponding to bin #(i-) ;
0
* r(i) distance from transducer corresponding to bin #i, m;
* Sr distance increment per one bin, m;

* Sysj the system constant of the j-th transducer, volt m2;

* Vj(i) the signal value of the j-th transducer at bin # i, volt;
* Xs(i), a(s(i-l) the sediment attenuation coefficient value of the j-th. transducer at the

locations corresponding to bins # I and #(i-l), m2/kg;
* aw the water attenuation coefficient value of the j-th. transducer, 1/m.

Hence, there are three equations, which in principle, may be solved for three

variables of interest ( C, gL a, ) provided that the transducers ensonify exactly the same

area or assume the distributions are the same in the ensonified volume, in other words
they must have identical scattering volume at the locations for which the calculation is
made. In practice, this requirement is hard to obey and it has not held for TFACP in this
study.
The scattering volume of the transducer at certain location (W(r)) is described by
equation (2.3):
W(r) = (1/8) cT (r 0 )2

* c speed of sound, m/s;

* r distance from the transducer, m;

* T acoustic pulse duration, s;

* 0 acoustic beam width, rad.

The pulse duration is the same for all TFACP transducers, but the sound beam width is
different. The 0.97MHz transducer has the widest beam, while the most narrow one
belongs to 5.65MHz transducer. That feature has appeared clearly in TFACP calibration.
Moreover, during the field experiment, the transducers have been separated from each








other in space by 5 cm. distance ( see Figure 4.3) so that the condition of identical
scattering volume obviously could not be satisfied in the entire region between the
transducer surfaces and the sea bed. However, at large distance from the transducers i.e.
in the near bed region, their sound beams could overlap each other.
Therefore, in order to use equations (5.1) for determination of sediment
concentration and size distribution parameters at certain location, one has to make the
assumption about uniform concentration and the unique size distribution in certain area
around that location. This area must be greater than the largest scattering volume of the
transducers. From the practical point of view, this implies time averaging of the original
signal for each bin along the sound path i.e. essentially the same process as the burst rms.
profile calculation applied to the TFACP calibration data ( see equation (3.3) ).
Additional possibility of fitting, at least partially, the identical scattering volume
condition is to set the starting point of calculation close to the sea bed i.e. in the region
where the sound beams overlap each other, but such an action can cause strong violation
of the basic assumptions which usually are made for the starting point. For example, the
assumption of negligible sediment attenuation is not obviously acceptable near the
bottom. It seems that the correct selection of the time scale of averaging and starting point
position can be made only under the knowledge of real situation which itself is the subject
of study. Hence, only 'trial error' approach is available at the present state of art so that
particular time scale and staring point position selected a priori do not necessarily
guarantee reasonable results in any case. However, let us continue the theoretical analysis
assuming that appropriate values of those parameters have finally been found.
It has been previously discovered that for operational frequencies about 1MHz the
sediment attenuation is negligible even under high concentrations ( up to 30 g/1) ( see for
example, [ Hay and Sheng, 1992]). This fact allows one to simplify corresponding
equation (5.1) by setting (s, and Ii(i-1) values to zero:

Kl(i) = Fmi(i) C(i);
Ki(i) = ( Vi(i)2 r(i)2 / Sys, ) exp( 4 awi r(i)); (5.2)








By solving equation (5.2) for the concentration and substituting that result into
equation set (5.1), the following system of two equations for two unknown sediment size
distribution parameters (g,, ) can be obtained:
In( K2(i) / K(i) ) = In( Fm2(i) / Fm(i) ) 2 K1 (i) 8r ( o2(i) / Fml(i) )

In( Ks(i) / Ki(i) ) = In( Fm(i) / Fml(i) ) 2 K1 (i) r (X ss(i) / Fml(i) ) (5.3)
Unfortunately, analysis of the data collected during the field experiment shows that
5.65MHz TFACP transducer did not perform properly (see Chapter 4 for details).
Therefore, the last equation of system (5.3) has to be discarded and simultaneous
determination of both distribution parameters becomes impossible. However, one can
obtain the estimation of the distribution mean from the first equation ,namely,
In( K2(i) / Ki(i) ) = In( Fm2(i) / Fm(i) ) 2 K1 (i) 8r ( as2(i) / Fmi(i) ) (5.4)

by assuming the standard deviation ( c,) at any particular location to be known and equal
to its value at the bed ('constant distribution width').
It is difficult to solve equation (5.4) directly even by using a numerical procedure,
because the unknown variable (g,) does not appear explicitly in it. Consequently,
additional assumptions have to be made about the quantities 'ln(Fm2(i)/Fmi(i))' and
'as2(i)/Fml(i)' which are implicit functions of the unknown size distribution mean and
known standard deviation. Those functions calculated over reasonable range of the mean
values for the standard deviation obtained from sieving analysis of the sand sampled at
the site of the instrument location ( o( = 0.34phi, see Figure 3.1 ) are plotted in Figures
5.1, and 5.2.
The functions shown in Figures 5.1, 5.2 can be approximated by polynomials of
some power to obtain explicit expressions for the unknown variable (j,). The third power
polynomial and the second power polynomial are the best fit to functions
'ln(Fm2(g,)/Fmi(g,))' and 'as2(Rp)/Fml(()' respectively, and, therefore, equation (5.4)
has, in general, three roots. Numerical experiments conducted with the field data have
demonstrated that two of those roots are not necessarily complex and, sometimes, they
can have reasonable values and they can be very close to each other so that, in order to
obtain the unique solution, one has either to establish a special 'right root identification'












3.2

3-

2.8

2.6

2.4

2.2

2-

1.8

1.6


2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8
The mean, phi-units


Figure 5.1. The quantity 'ln(Fm2/Fml)' involved in equation (5.4) versus the mean of the
size distribution (g,).


2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8
The mean, phi-units


Figure 5.2. The quantity 'as2/Fmi' involved in equation (5.4) versus the mean of the size
distribution (p,).
procedure, the criteria for which are not clear, or to use only the first power polynomial (a

straight line) for the approximation. The second choice has been taken in this study. As


.14R








one can see from Figures 5.3, 5.4, the straight line is not a bad approximation in this
particular case. Its parameters (gain and offset) obtained over range of the mean 2.25-
3.66phi are reported in table 4.1. Also, it is interesting to note that, according to Figures
5.3 and 5.4, some uncertainty occurred in determination of size distribution parameters at
the bed will probably not have a significant influence on the results.
After the mean of the sediment size distribution at the location given has been
determined, the sediment concentration (C) at that location is calculated from the first
equation (5.2), using the theoretical expression for the sediment backscattering factor

(Fm) presented in Chapter 2.


Table 5.1 The linear approximation parameters of the functions of equation (5.4)

Quantity in equation (4.4) Gain Offset

In( Fm2(Ji)/Fmi(g)) 1.1696 -1.0871

as2(Jt)/Fmi(R,) 1.0218 -0.1875


5.2. Field Results


The method for simultaneous determination of sediment concentration and the mean
of the size distribution from TFACP data has been described in the previous section. It
can be briefly summarized as follows:
* The size distribution is assumed to be log-normal (normal in phi-units).
* Only two transducers of TFACP ( 0.97MHz and 2.35MHz ) are used for that purpose.
* The standard deviation of size distribution (oY) is assumed to be constant at any

elevation and equal to its value at the sea bed, ao = 0.34phi (see Figure 3.1).

* The burst rms. signal profiles (see equation (3.3)) are utilized for the calculations.
* The mean of the size distribution at a certain location is determined from equation
(5.4), in which the quantities depending upon the distribution mean are approximated
by the linear functions (see Table 5.1).











* The sediment concentration is calculated by the first equation (5.2).

* The assumption of negligible sediment attenuation between the transducers and the

starting point is used for calculations at that point.

* The starting point has been placed at bin #70 (52.9 cm. from the transducer surface).

The method has been applied to TFACP data collected during three time periods:

August 20th August 28th; September 1st September 9th; October 9th October 12th.

(216 bursts). It should be mentioned that 0.97MHz transducer has been damaged at

October 13th so that application of the method to the rest of the data has not been

possible.


2.4 2.6 2.8 3 3.2
The mean, phi-units


3.4 3.6 3.8


Figure 5.3. Linear approximation of the quantity 'ln(Fm2/Fmi)' involved in equation
(5.4). The solid straight lane shows the approximation with parameters listed
in table 5.1. The other lines represent the actual quantity for various values of
the standard deviation of sediment size distribution: dotted a, = 0.34phi;

dashed a, = 0.3phi; dash-dotted o, = 0.39phi.


2.6

2.4


1.8


71' '


7 .... -

7 ... 7

.7



/ ...
///


/ .
/ .










3.6 ---






2.8





2.6-
2.4-




2.2- .

2
//




7 7






2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8
The mean, phi-units


Figure 5.4. Linear approximation of the quantity 'as2/Fml' involved in equation (5.4).
The solid straight lane shows the approximation with parameters listed in table
5.1. The other lines represent the actual quantity for various values of the
standard deviation of sediment size distribution: dotted C, = 0.34phi;
dashed o,=0.3phi; dash-dotted o( = 0.39phi.


Unfortunately, only in very few cases (12 bursts) the results can be considered as

reasonable. Many bursts have been discarded because of the spikes appearing in the

concentration and/or the mean size profiles, which can be caused by presence of a big

scatterer like a fish. The method also fails when the concentration becomes too high

(storm conditions) and too low (calm conditions). The nature of this failure is the same in

both cases, and it appears in increasing the mean sediment size with increasing the

elevation from the bed. Figures 5.5-5.8 show the examples. It can be seen from them, that

the failure is associated with discrepancy between 0.97MHz and 2.35MHz data obtained

under the 'constant size' assumption (0.97MHz transducer profile tends to be uniform). It

is hard to explain what exactly caused this failure but it can be noticed that during

TFACP calibration the transducers show the theoretical behavior only in the quite narrow

range of concentrations, it is especially true for 0.97MHz transducer (see Chapter 3). For

low concentrations, one may expect the influence of the instrument nonlinearity and, for








relatively high concentrations, the effect of multiple scattering may become significant.
Unfortunately, no specific work has been done on those issues in this study. Also, the
method fails in the region very close to the bed (below 2.5-3cm level). However, this fact
should be expected, because, as it has been mentioned in the previous chapter, the
ensemble averaging over the entire burst can produce unrealistic shape of the signal in
that region. Moreover, the concentration in the near bed region is usually very high so that
nontheoretical behavior of the transducers could also make the contribution.
The bursts, for which the results can be considered as reasonable, are listed in Table
5.2. They are organized according to the Mobility Number (M), which characterizes the
ratio between the disturbing hydrodynamic force (shear stress) and the stabilizing gravity
force acting on the sediment particle at the bed [Nielsen, 1992]:
M = Ub2 /(s 1) g d (5.5)
* M the mobility number;

* Ub maximum near bed horizontal wave velocity, calculated by linear wave theory

from the wave data measured (Hmo, Tp), m/s;
* s sediment specific gravity, s = 2.65;
* g gravitational acceleration, 9.81 m/s2;

* d sediment size, assumed to be equal to the mean size at the bed, d = 0.1476 mm.

The concentration and mean size profiles obtained for those bursts are shown in
Figures 5.9 5.20.


5.3. Discussion


As one can see from the previous section, the method developed provides

reasonable results only under a very limited range of hydrodynamic forcing conditions
(the Mobility number varies from 209 to 741) and the amount of data finally obtained is
quite small. However, some interesting and useful observations can be made regarding
suspended sediment concentration and size as well as the acoustic measurement
technique. Figures 5.21 and 5.22 summarize the results reported in the previous section.











Concentration
*''o ' "" '




S 0.









o
o







o
".0


121


Mean size

i




I\


I
i
/

/
/
/






1
/
/
/
/
/
/




!'


0.2 0.3
mm


0.4 0.5


Figure 5.5. Sediment concentration and mean size. Burst ds05010. September 1st, 19:00.
Waves with Hmo = 0.41m, Tp=12.8s. Water depth = 4.61m.
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.



As one can see, the mean size of the suspended sediment does differ from its value

at the bed (Figure 5.21). It is smaller. The averaged difference between the mean

sediment size at the bed and the mean sediment size in suspension calculated over whole

set of the results was 0.02mm (0.18phi). and the maximum value was 0.033mm

(0.29phi). These variations are much larger than the maximum variation of the mean size

appeared during the sieving analysis of different bottom sand samples (0.008mm /


E


S8
..,



E
0

6
0)
U)


*Jl----l--L. ,1, I, I i I 11----l--I >. >..> I in----l--' 1 r i i










O.O8phi). Therefore the difference between the mean sediment size in suspension and its

value at the bed should be considered as significant.


Concentration
14A, .


E
o10
-6
a)
.i3
-)
4-,
E 8
2
6-
a)
0

1 6


Mean size
141 1


0.12 0.14 0.16
0.12 0.14 0.16


Figure 5.6. Sediment concentration and mean size. Burst ds05017. September 2nd, 02:00.
Waves with Hmo = 0.96m, Tp=3.8s. Water depth = 4.91m.
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


0*



0.

0:
0:

OO









0



0
\

\

\


I
I
/

I


I

I


I
/


/


I
/
/


0.18


I ~~ ~ "


'











Concentration


10-1 100


Mean size
1,A4


E
o10
-6

Q)

E 8
0
L-
4-


(0


_.
0.12 0.14 0.16 0.18
mm


Figure 5.7. Sediment concentration and mean size. Burst ds05047. September 3rd, 09:00.
Waves with Hmo = 2.13m, Tp=6.ls. Water depth = 4.77m.
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


The mean size of the suspended sediment decreases quite rapidly from its bottom

value in the near bed layer (below 4.5cm level) and then varies just slightly so that it can

be considered as a constant. Also, there is a tendency that the mean size of sediment in

suspension increases as the result of increasing the hydrodynamic forcing. For the highest

values of the Mobility Number, it is close to the value at the bed (0.148mm). For the low


I
/
I

/


/



/
I



1



I







61

forcing conditions, the mean size of suspended sediment is considerably smaller (about

0.12-0.125mm).


Concentration


o
0:

0:


o:
0:


0o



0O


0O
0:
0:


0:

0


0'.
0.
0"


Mean size


E
0)

a10

E

a, 8
0
co
0
0


Figure 5.8. Sediment concentration and mean size. Burst ds05050. September 3rd, 12:00.
Waves with Hmo = 2.29m, Tp=6.7s. Water depth = 4.60m.
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


1I

/

/
/
/









I
I

i





I








Table 5.2. The bursts, which give the reasonable results for concentration and mean size.

Burst Start time Hmo, m. Tp, s. Depth, m M

da24118 8/23/11:18 2.09 10.7 5.30 741.6

da25126 8/23/16:51 1.99 9.8 4.90 717.3
da24117 8/23/11:02 2.08 10.7 5.42 716.1

da25128 8/23/17:55 2.05 9.8 5.23 706.1

da25134 8/24/10:36 1.97 9.14 5.34 621.0

ds05042 9/03 /04:00 2.07 6.1 5.49 510.7

da25132 8/ 24 /10:04 1.79 9.14 5.48 497.1
ds06083 9/06/16:00 1.51 11.6 4.58 464.0
ds05044 9/03 /06:00 1.99 5.6 5.49 428.6

ds05043 9/03/05:00 1.88 5.82 5.52 395.6

ds05037 9/02/23:00 1.64 4.7 4.38 335.3
ds05030 9/02/16:00 1.39 5.56 5.49 209.1


The concentration profiles obtained basically demonstrate the constant exponential
decay with height and they are not sensitive to the mobility number variations (Figure
5.22). The concentration values generally decrease from 0.25 0.4 g/1 at 3cm level down
to 0.13-0.25 g/1 at the elevation of 10cm above the bed.
Because the data scatter seems to be very high, no empirical expressions for the
suspended sediment size and concentration variations with the height and/or with the
hydrodynamic forcing can be drawn from that limited data set.
It can be noticed that the concentration profiles predicted under the 'constant size'
assumption almost coincide with those obtained by the method, which takes into account
the size variations, if the mean size of sediment in suspension is close to the value at the
bed. (see, for example, Figures 5.13, 5.15). On the other hand, such 'constant size'
concentration values are smaller than those determined by the method if the mean size in
suspension is smaller than at the bed (see, for example Figures 5.17, 5.20). This is so,
because the coarser sediment in suspension, which has been stated by the 'constant size'













Concentration


E

S8
C)

E
0

g 6
(0
"i


0.135


0.145


Figure 5.9. Sediment concentration and mean size. Burst da24118.
Started at August 23, 11:18. Burst duration: 936 s.
Waves with Hmo = 2.09m, Tp=10.7s., Water depth = 5.30m., M = 741.6
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption



assumption, implies the lower values of concentration for the same backscattered signal

detected. The facts just mentioned can be considered as an indirect verification of the

method developed. The concentration profiles obtained under the 'constant size'

assumption have basically the same shape as ones predicted by the method and, also, the

difference between 2.35MHz transducer profiles and the profiles predicted by the method

is very small even if the size variation is significant (see, for example, Figure 5.18).

Therefore, one may say that the 'constant size' assumption is not completely wrong. It


-O


.0
'0



-0


N
N
N.


/




/





I


Mean size


I










can provide good qualitative estimations, and in some cases, reasonable quantitative

results.


Concentration
12 . ...


10


E

S8
a)
E


O 6
Ca
1
Qv


Mean size


mm


Figure 5.10. Sediment concentration and mean size. Burst da25126.
Started at August 23rd, 16:51. Burst duration: 1872 s.
Waves with Hmo = 1.99m, Tp=9.8s., Water depth = 4.90m., M = 717.8
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


It is always worth-while to compare the results obtained with the similar work done

before by other researchers. However, in this case, there is almost nothing to compare

with. The paper of Hay and Sheng [1992], who were pioneers of this kind of

measurements, is only the material published about this issue. The most important

features of their work are briefly considered below.


0
0

0
o





o



0











Concentration
1--


E 10

E9
(D

E 8


7
(0
Q3 r


0.13 0.14 0.15 0
mm


Figure 5.11. Sediment concentration and mean size. Burst da24117.
Started at August 23th, 11:02. Burst duration: 936 s.
Waves with Hmo = 2.08m, Tp=10.7s., Water depth = 5.42m., M = 716.1
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


First, they have found that it was not possible to obtain the concentration and both

size distribution parameters i.e. the mean and the standard deviation, even if all three

transducers of the multyfrequency instrument have functioned properly. The reason for

that was related to the problem of multiple solution of the governing Acoustic

Backscattering Equation, which has been mentioned in section 5.1.

Second, they used a different method from than the one developed in this study.

Their technique involves all three transducers to determine the concentration and the

mean of size distribution. It is much more complicated and it seems to be more general


I






/


Sp

.0



b
0
'0
0

O
O



0
\


Mean size










and applicable to various conditions. However, their method could not be applied in this

study because only two transducers of TFACP have worked properly.


Concentration


Mean size


- -2 -
10-2 10
g/i


100 21
100 0.125


0.13 0.135 0.14
mm


Figure 5.12. Sediment concentration and mean size. Burst da25128.
Started at August 23rd, 17:55. Burst duration: 1872 s.
Waves with Hmo = 2.05m, Tp=9.8s., Water depth = 5.23m., M = 706.1
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.

The results reported by Hay and Sheng are shown in Figure 5.23. The mean size of

the sediment at the bed was 0.17mm and the data has covered the range of low values of

the Mobility Number (M = 28 215).


p


I






N









Concentration


0.145 0.15 0.155 0.16
mm


Figure 5.13. Sediment concentration and mean size. Burst da25134.
Started at August 24th, 10:36. Burst duration: 936 s.
Waves with Hmo = 1.97m, Tp=9.14s., Water depth = 5.34m., M = 621.0
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


In general, the their results look quite similar to those obtained in this study. The vertical

profiles of the mean sediment size seem to be uniform above 5-6cm level and its value

increases in the nearbed layer. However, it is strange that the mean size of the sediment in

suspension, even at quite high elevations is larger (0.18mm) than its value determined at

the bed. Hay and Sheng argued that this discrepancy is not critical because the random

variation of the results was significant (about 30%). It is interesting to note that Hay and

Sheng have faced the same problems as those that appeared in this study. For example,


- I


Mean size








68


one of the mean size profiles demonstrate increasing size with increasing elevation from

the bed.


14




12




S10


a)
.0


E 8




0
g


Concentration


Mean size


10-2 10-1 100 0.115


0.12
mm


0.125


Figure 5.14. Sediment concentration and mean size. Burst ds05042.
Started at September 3th, 04:00. Burst duration: 1775 s.
Waves with Hmo = 2.07m, Tp = 6.1s., Water depth = 5.49m., M = 510.7
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


:0

:o
I0
o


o
o

o

:0
10


.0



.0


0


/
/
/
/
I












Concentration


a


Figure 5.15. Sediment concentration and mean size. Burst da25132.
Started at August 24th, 10:04. Burst duration: 936 s.
Waves with Hmo = 1.79m, Tp=9.14s., Water depth = 5.48m., M = 497.1
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption


5- \



4 I


3-


2
0.14 0.145 0.15 0.155
mm


Mean size











Mean size
fIA


.12
0.12


0.16


Figure 5.16. Sediment concentration and mean size. Burst ds06083.
Started at September 6th, 16:00. Burst duration: 1688 s.
Waves with Hmo = 1.52m, Tp = 11.6s., Water depth = 4.58m., M = 464.0
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


:0



0
0

:0
0
0
0
:0



:0
.0


Concentration











Concentration


Mean size
1I


E
S10
-6
-o
0)

E 8
0



u) 6
i5


0.116 0.118 0.12 0.122
mm


Figure 5.17. Sediment concentration and mean size. Burst ds05044.
Started at September 3rd, 06:00. Burst duration: 1775 s.
Waves with Hmo = 1.99m, Tp = 5.6s., Water depth = 5.49m., M = 428.6
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


N




/
/












Concentration
14



i




0:
o

o
10-


o
*0





\0


6- o

:o
4o

4
o


Figure 5.18. Sediment concentration and mean size. Burst ds05043.
Started at September 3th, 05:00. Burst duration: 1775 s.
Waves with Hmo = 1.88m, Tp = 5.82s., Water depth = 5.52m., M = 395.6
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.


Mean size


/
I






N





/


/


0.118


0.12
mm


0.122


4 A












Concentration
A.


0.125 0.13 0.135 0.14
mm


Figure 5.19. Sediment concentration and mean size. Burst ds05037.

Started at September 2nd, 23:00. Burst duration: 1775 s.

Waves with Hmo = 1.64m, Tp = 4.7s., Water depth = 4.38m., M = 335.3
The circles stand for the concentration values obtained by the method. The

solid line 0.97MHz transducer under the 'constant size' assumption. The

dotted line 2.35MHz transducer under the 'constant size' assumption.


/




/



/


.o

:o
:o
.0

.0
.0

-o

.0
.0
0
.0


.0

"0

O0


Mean size


.,I f










Concentration











7-
o


6- o

:0
5-

0

40
6 0-, .. i -- . .


Mean size


0.117


Figure 5.20. Sediment concentration and mean size. Burst ds05030.
Started at September 2nd, 16:00. Burst duration: 1775 s.
Waves with Hmo = 1.39m, Tp = 5.56s., Water depth = 5.49m., M = 209.1
The circles stand for the concentration values obtained by the method. The
solid line 0.97MHz transducer under the 'constant size' assumption. The
dotted line 2.35MHz transducer under the 'constant size' assumption.







75





16


14



E


10


\ 8










0.11 0.12 0.13 0.14 0.15 0.16
Mean sediment size, mm


Figure 5.21. Vertical profiles of the mean size of the suspended sediment. The summary
of the data reported in section 5.2. Different line styles represent different
values of the Mobility Number (M): solid lines with crosses M=200-400;
dashed lines with circles M=400-600; solid lines with points M=600-800.














14


12
E




E S



o e
8-


6-

b4, 0b


0 0


102 101 100
Concentration, g/l


Figure 5.22. Vertical profiles of the suspended sediment concentration. The summary of
the data reported in section 5.2. Different line styles represent different values
of the Mobility Number (M): solid lines with crosses M=200-400; dashed
lines with circles M=400-600; solid lines with points M=600-800.















E
I--

k"





..
is ?Bi'l0- 2 3 67rT ,'io' i '


















130 155 180 205 230
D (um)



Figure 5.23. Vertical profiles of the sediment concentration (a) and the mean of sediment
size distribution (b) measured by Hay and Sheng[1992]. Different symbols
are used to distinguish the results obtained under different conditions
(different values of the mobility number (M)): the circles M=39.6; the
crosses M=28.5; the triangles M=67.2; the diamonds and pluses -
M=215.5.














CHAPTER 6

CONCLUSIONS


The objective of the study presented here was to obtain information about the
suspended sediment concentration and size from acoustic measurements of sediment
suspension in the coastal zone made during DUCK94 Nearshore Field Experiment by
using Three-Frequency Acoustic Concentration Profiler (TFACP).
It has been shown that it is theoretically possible to determine the concentration and
size distribution parameters of suspended sediment from backscattered acoustic signals of
three different frequencies, assuming the size distribution to be log-normal (normal in
phi-units). Three-Frequency Acoustic Concentration Profiler in general gives such a
capability, because it consists of three acoustic transducers (acoustic echo sounders),
which operate synchronically at three different frequencies 0.97MHz, 2.35MHz,
5.65MHz.
However, it has been found, that the original data collected from one of TFACP
transducer (5.65MHz) could not be utilized, because the acoustic signal has been strongly
distorted by the presence of organic material in the water and this effect has not been
taken into consideration during the instrument calibration. Consequently, the study has
been restricted to determination of concentration and the mean size of the suspended
sediment only.
The method, which allows to invert the original acoustic backscattered signals of
two TFACP transducers (0.97MHz and 2.35mhz) to be inverted to obtain vertical profiles
of suspended sediment concentration and mean size, has been developed and applied to
the data collected. This method implies the assumption that the standard deviation of the
size distribution is known, constant, and equal to its value on the sea bed. It should be
mentioned that this method does not pretend to be general and it can be considered as
applicable only for TFACP data collected during DUCK94 experiment.








Because of some problems related to the instrument performance, only in a few
cases (12 instrument bursts from 216 ones) the results obtained can be considered as
reasonable. They cover a very narrow range of hydrodynamic forcing conditions (the
Mobility Number varies from 209 to 742). The method fails when the suspended
sediment concentration becomes too high (breaking storm waves) or too low (long period
swell). The method also fails in the region very close to the bed so that the last point
closest to the bed, for which the reasonable results could be obtained was located at 3cm
level above the bed. This is because TFACP transducers, especially the lowest frequency
one, perform according to the governing equation, on which the method was based, only
in quite narrow range of concentrations. This fact has been discovered during TFACP
calibration.
The following essential features of suspended sediment concentration and size
profiles obtained can be pointed out:

* The mean size of the suspended sediment does differ from its value at the bed. It is
smaller.

* The averaged difference between the mean sediment size at the bed and the mean
sediment size in suspension calculated over the whole set of the results was 0.02mm
(0.18phi). and the maximum value was 0.033mm (0.29phi). These variations are
much larger than the maximum variation of the mean size appeared during the
analysis of different bottom sand samples (0.008mm / 0.08phi). Therefore the
difference between the mean sediment size in suspension and its value at the bed
should be considered as significant.

* The mean size of the suspended sediment decreases quite rapidly from its bottom
value in the nearbed layer (below 4.5cm level) and then varies just slightly so that it
can be considered as a constant.
* The mean size of sediment in suspension increases as the result of increasing the
hydrodynamic forcing and for the highest values of the Mobility Number it is close to
its value at the bed (0.148mm). For low forcing conditions the mean size of
suspended sediment is considerably smaller (about 0.12-0.125mm).








* The concentration profiles obtained basically demonstrate the constant exponential
decay with the height and they are not sensitive to the mobility number variations.

* The concentration values generally decrease from 0.25 0.4 g/l at 3cm level down to
0.13 0.25 g/1 at the elevation of 10cm above the bed.
* The data scatter seems to be very high so that no empirical expressions for the
suspended sediment size and concentration variations with height and/or with
hydrodynamic forcing can be drawn from this limited data set.
Also, it has been shown that for 2.35MHz transducer, the 'constant size'
assumption, which is used for the inversion of the single-frequency ACP signal into
suspended sediment concentration, does not result in significant error.
Finally, it can be mentioned that the simultaneous determination of suspended
sediment concentration and size from the acoustic measurements is a very complicated
problem in the theoretical as well as in the technical sense. Too many factors influence
the results. More theoretical study and practical attempts should be made to provide
significant improvement of the methodology and the instrumentation.













REFERENCES


Birkemeier W. A., H. C. Miller, S. D. Wilhelm, A. E. DeWall, and C. S. Gorbics,
1985. A user's guide to the Coastal Engineering Research Center's (CERC's)
Field Research Facility, Tech. Rep. CERC-85-1, U.S. Army Corps of Engineers,
Vicksburg, MS, 136pp.

Hay, A. E., 1983. On the remote acoustic detection of suspended sediment at long
wavelengths, J. Geophys. Res., 88(C12), 7525-7542.

Hay, A. E., and J. Sheng, 1992. Vertical profiles of suspended sand concentration and
size from multifrequency acoustic backscatter, J. Geophys. Res., 92(C10), 15,661-
15,667.

Hess, F. R., and K. W. Bedford, 1985. Acoustic backscatter system (ABSS): The
instrument and some preliminary results, Mar. Geol., 66, 357- 380.

Huff L., and D. C. Fisk, 1980. Development of two sediment transport instrument
system. in Proc. 17th Conference on Coastal Engineering, ASCE, New York, NY,
245-253.

Kennedy, S. K., R. Ehrlich, and T. W. Kana, 1981. The non-normal distribution of
intermittent suspension sediment below breaking waves, J. Sediment. Petrol., 51,
1103-1108.

Lee, T. H., 1994. Acoustic measurement and modeling of the vertical distribution of
suspended sediment driven by waves and currents, PhD dissertation, University of
Florida, Gainesville, Fl., 128pp.

Nielsen, P., 1992. Coastal Bottom Boundary Layers and Sediment Transport, Word
Scientific, Singapore, 324pp.

Nielsen, P., M. O. Green, and F. C. Coffey, 1982. Suspended sediment under waves,
Tech. Rep. 82/6, Coastal Stud. Unit, University of Sydney, Sidney, Australia,
157pp.

Thorne, P. D., 1993. Measuring suspended sediments using acoustics, Tech. Rep.
TR/092, Coastal and Oceanographic Engineering Department, University of
Florida, Gainesville, Fl., 25pp.






82

Thorne, P. D., C. E. Vincent, P. J. Hardcastle, S. Rehman, and N. Pearson, 1991.
Measuring suspended sediment concentrations using acoustic backscatter devices,
Mar. Geol., 98, 7-16.

Vincent, C. E., and M. O. Green, 1990. Field measurements of the suspended sand
concentration profiles and fluxes and of the resuspension coefficient y0 over a
rippled bed, J. Geophys. Res., 95(C7), 11,591-11,601.

Vincent C. E., D. M. Hanes, and A. J. Bowen, 1991. Acoustic measurements of
suspended sand on the shoreface and the control of concentration by bed
roughness, Mar. Geol., 96, 1-18.














BIOGRAPHICAL SKETCH


Konstantin Marusin was born on July 15, 1963, in the countryside of Central
Russia, but he has spent most of his life in Siberia. He graduated from Novosibirsk
Technical University (Russia) with an engineering degree in structural mechanics in
1985. He had changed a number of occupations before he finally got a position in the
Coastal Research Group of the Institute for Water and Environmental Problems (the
Siberian Branch of Russian Academy of Science) in 1990. Realizing the luck of the
required scientific background in coastal engineering, the author began constantly seeking
any educational opportunities. Fortunately, the best one he could ever expect occurred in
1993 when he was invited to study at the Coastal and Oceanographic Engineering
Department of the University of Florida. The author started his masters program in Fall
1993 and defended his thesis on May 17, 1995.




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