• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 List of symbols
 Abstract
 Introduction
 Principles of acoustic measurement...
 Inversion of acoustic data into...
 Implementation of acoustic measurement...
 Field measurements
 Vertical distribution of suspended...
 Conclusions
 References
 Biographical sketch






Group Title: Technical report – University of Florida. Coastal and Oceanographic Engineering Program ; 104
Title: Acoustic measurement and modeling of the vertical distribution of suspended sediment driven by waves and currents
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 Material Information
Title: Acoustic measurement and modeling of the vertical distribution of suspended sediment driven by waves and currents
Physical Description: xviii, 128 leaves : ill. ; 29 cm.
Language: English
Creator: Lee, Tae Hwan, 1956-
Publication Date: 1994
 Subjects
Subject: Coastal and Oceanographic Engineering thesis Ph.D
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1994.
Bibliography: Includes bibliographical references (leaves 124-127).
Statement of Responsibility: by Tae Hwan Lee.
General Note: Typescript.
General Note: Vita.
Funding: Technical report (University of Florida. Coastal and Oceanographic Engineering Dept.) ;
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Bibliographic ID: UF00075328
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Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: aleph - 002019431
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notis - AKK6872

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement 1
        Acknowledgement 2
    Table of Contents
        Table of Contents 1
        Table of Contents 2
        Table of Contents 3
    List of Tables
        List of Tables 1
        List of Tables 2
    List of Figures
        List of Figures 1
        List of Figures 2
        List of Figures 3
    List of symbols
        Section 1
        Section 2
        Section 3
        Section 4
        Section 5
    Abstract
        Abstract 1
        Abstract 2
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
    Principles of acoustic measurement of suspended sediment
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
    Inversion of acoustic data into suspended concentration
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
    Implementation of acoustic measurement system
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
    Field measurements
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
    Vertical distribution of suspended sediment
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
    Conclusions
        Page 120
        Page 121
        Page 122
        Page 123
    References
        Page 124
        Page 125
        Page 126
        Page 127
    Biographical sketch
        Page 128
Full Text




UFL/COEL-TR-104


ACOUSTIC MEASUREMENT AND MODELING OF
THE VERTICAL DISTRIBUTION OF SUSPENDED
SEDIMENT DRIVEN BY WAVES AND CURRENTS





by




Tae Hwan Lee


Dissertation


1994














ACOUSTIC MEASUREMENT AND MODELING OF THE VERTICAL
DISTRIBUTION OF SUSPENDED SEDIMENT DRIVEN BY WAVES AND
CURRENTS













By

TAE HWAN LEE


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1994














ACKNOWLEDGEMENTS


I wish to express sincere appreciation to my academic advisor and chairman of the

advisory committee, Dr. Daniel M. Hanes, for his support, constructive criticism and

encouragement at every stage of this dissertation. The research-related trips to Portland,

San Francisco, Vilano Beach and Amelia Island under Dr. Hanes' supervision allowed me

great opportunities to meet many leading authorities in the field and to see the territory. I

have learned from him an American way of life and business as well as the academic

matters.

I also would like to thank Dr. Robert G. Dean, Dr. Michel K. Ochi, Dr. Y. Peter

Sheng and Dr. Joann Mossa for serving as the members of my doctoral advisory

committee. I am grateful to Dr. Peter Thorne for the valuable discussions and advice on

acoustics. I am especially indebted to Dr. P. Nalin Wikramanayake who allowed me to

use his model.

I acknowledge the help I received from my fellow students and friends. Eric, Jingeol

and John were a great help with the instrumentation. Emre and Chris helped me with the

beach profile data. Lynda provided me with the detailed design of the facility for

measuring the settling velocity of sediment. Mike Krecic proofread this dissertation with

great patience. Special thanks are given to Mike and Pat Dombrowski for their friendship

and their cordial help to my family.

Thanks are due to staff members in the Coastal Lab for their assistance during the

field measurement and its preparation. I enjoyed not only their help but also the legendary

lunch-break volleyball. I also wish to thank the clerical and secretarial staffs for their

hospitality and professional assistance. Becky always helped me out even when matters










were not her own job. The archives will be remembered for their excellent service and

Helen's best-in-town cookies.

I owe Mr. Woo-Choong Kim, the Chairman of Daewoo Group, very special thanks

for giving me the opportunity to study abroad. I am also deeply indebted to Mr. Young

Soo Chang, the President of Daewoo Corporation, for his support and encouragement

during my stay while working on the Ph.D. program.

This research was sponsored by the Coastal Science Program, U.S. Office of Naval

Research. Their support is greatly acknowledged.

My final acknowledgment goes to my better half, Hyun Su Kim, for her love which

always let me stay in peace and happiness. Finally, I dedicate this dissertation to my late

parents, Byung Ik Lee and Bok Ryong Park. Their everlasting love and teaching has been

guiding me throughout my life.















TABLE OF CONTENTS

page

ACKN OW LED GEM EN TS .................................. .....................................................ii

L IST O F T A B L E S ........................................................ .......................................... vii

L IST O F F IG U R E S ....................................................... ........................................... ix

LIST O F SY M B O L S..................................... .................................................... xii

A B STR A CT ......... ............. .................. ........ ..... .. ...... .. ................ xvii

CHAPTERS

1 IN T R O D U C T IO N ........................................................ .......................................... 1

State-of-the-Art Review of Models and Measurement of Suspended Sediment.............. 1
M otivation and Outline of the Thesis ......... .................................... ...... ................. 7

2 PRINCIPLES OF ACOUSTIC MEASUREMENT OF SUSPENDED SEDIMENT.....9

The Outline of the Measurement Principles and the Forward Problem........................... 9
Backscattering by a Single Particle in Water ........................................................... 11
Acoustic Intensity of Spherical Waves in Homogeneous Medium ......................... 11
Attenuation of Acoustic Energy Intensity due to Absorption by Ocean Water.......... 13
B ack scattering ................................................ .................... .............. .. .............. 14
Backscattering by Mixture of Particles and Water...................................................... 16
Attenuation of Acoustic Energy Intensity due to Scattering by Particles ...... ......... 16
Scattered Volume and Its Effect on Bin vs. Distance Relationship ....................... 17
Scattered Volume and Concentration of Suspended Sediment.................................. 20
M easurem ent Lim its ....................................................... ..................................... 22
Spatial and Temporal Resolution ......... ....................... .................. 22
Limits on Measurable Particle Size and Concentration..........................................23
Limit on Measurement Range....................... ....................... .................. 24
Measurable Point Closest to Ocean Bed ............................................................ 24

3 INVERSION OF ACOUSTIC DATA INTO SUSPENDED CONCENTRATION..... 26

N ear Field Concentration.............................................................. .................. 27


I









F ar F field C concentration ............. .............................. ........................... .................. 30
Iterative Solution to Implicit Equation...................................... 30
Direct Solution to Explicit Equation..... .......................................... 31
Comparison of Solutions .................. ...... ............................... 33
Sensitivities of Inversion Process ....................................... .......... ........ .......... 34

4 IMPLEMENTATION OF ACOUSTIC MEASUREMENT SYSTEM ...... ........ 42

Description of the Measurement System........................................ 42
Location of Bottom Bin in Acoustic Intensity Profile ........................................... 45
Bin vs. Distance Relationship......................................... .......................... 49
Quantification and Elimination of System Nonlinearity.............................................. 52
C alib ratio n ......... ..... .............................................. ........... ... ................... 5 9

5 FIELD M EASUREM EN TS............................................................. .................. 67

Site.. ...................... ................................ .................. 67
General Description of the Site..................... ..................................................... 67
B each P ro file ............ ........................................... .......................... .................. 6 8
M easurem ent System .......................................................... ............................ 71
Configuration of the System .............................................................................71
Instrum ents .......................................................................... 73
Underwater Installation of the Instruments .................................. ................... 74
D ata File........................................................ ....... ......... ....... .......... 77
Bed Location and Concentration Profile of Suspended Sediment ................................ 78
Tides and W aves .................... ....................... ..... ............ ...... ... ....... 80
F luid V velocity ......................................... ........ .. ..... ............... ...... 80
Current and W ave V elocities ............................... .. .................... ................. ........ 80
Irregular W ave Velocity Near the Bed.................... ...............................................81
Prim ary W ave D direction ................................................... ................................. 83
P ore P pressure ................................................................ ........ ................ 86
Characteristics of B ed M aterial......................................................... .................. 86
W after T em perature ......................................... ..................................................... 90

6 VERTICAL DISTRIBUTION OF SUSPENDED SEDIMENT .................................. 91

Diffusion and Convection ............................................. .... .................. 92
R review of M models ........... .............. ..... ................. ........ .. ......................... 93
D iffusion M odel ................................. ...... ........ .... ............... ...... 93
C onvection M odel................................ ............. ............................. ............. 96
Combined Convection-Diffusion Model........... .......................... 98
Comparison of Model Results with Field Observations ........................................... 101
Field D ata ............................... ........... ...... ........................... 101
Estimation of Friction Velocities and Bottom Topography.................................... 102
Comparisons of Time Mean Vertical Distribution of Suspended Sediment ......... 105









Entrainment Probability Distribution Function.......................................................... 112
D discussion ................... ............................. .......................... 116

7 C O N C L U SIO N S ......................................................... ........................................ 120

R E F E R E N C E S ................................................................................. ..................... 124

BIOGRAPHICAL SKETCH ............................................................ ................... 128














LIST OF TABLES

Table page

3.1: C concentration Profiles. .................................................... .................................. 33

3.2: Comparison of Computation Time and Error of Inversion Methods......................... 34

3.3: Ratio of Error at 600 mm to the Initial Error............................................... 35

4.1: Specifications of Acoustic Concentration Profiler............................................ 43

4.2: Summary of the Profiles of Reflected Acoustic Intensity. ......................................47

4.3: Comparison of Predicted and Observed Bottom Bins............................................ 48

4.4: Actual Shape of Outgoing Acoustic Pulse. ........................ ...............................49

4.6: Input Voltage at the 5 MHz Transmitter ............................................................... 52

4.7: Vswith Values ........................................................................................ 56

4.8: Sum m ary of the Calibration D ata .................................................... ..................... 61

4.9: Summary of the Calibration Parameters............................................................. 65

5.1: Profile Survey D ata.................................................... ..... .......................... 70

5.2: Assignment of Channels in Data Logger, Tattletale VI........................................72

5.3: Elevation of Instruments above Bed................................................... .................76

5.4 : A C P data files .................... ................... ............................................ ..... 79

5.5: Gain and Offset at Channel 0'(High Resolution)................................................... 85

5.6: Sieve Analysis of Bed Material............................. ................... 86

5.7: Grain D iam eter and Fall V elocity. ............................................ ........................ 89









6.1: Parameters of the Data Files for Comparison.................................................. 101

6.2: Estimated Ripple Geometry and Friction Velocities ............................................. 105

6.3: Differences of the Diffusion and Convection Processes. ..................................... 119














LIST OF FIGURES


Figure pae

2.1: Form function. ...................................... ........ ....... ................. ......... ...... .. 15

2.2: Definition of scattered volume ..................................................... 19

2.3: M easurable point closest to ocean bed. .......................................... ................... 25

3.1: N ear field lim it .................................................................................................. 27

3.2: Concentration profiles to compare the inversion methods..................................... 37

3.3: Backscattered intensity profiles to compare the inversion methods.......................38

3.4: Error in concentration at 600 mm due to error in the initial concentration................ 39

3.5: Error in concentration at 600 mm resulting from error in caw................................... 40

3.6: Error in concentration at 600 mm resulting from error in cx ..................................41

4.1: Schematic of acoustic measurement system............................. ......................... 43

4.2: Sequence of data processing in the acoustic measurement system............................ 44

4.3 Experimental setup to measure the profile of the acoustic intensity reflected from the
b ed ...............................................................................................4 5

4.4: General shape of acoustic intensity reflected from the bed. ..................................... 46

4.5: Acoustic intensity profile measured in clear water. ............................................47

4.6: Experimental setup to measure the bin vs. distance relationship...............................50

4.7: Experimental setup to measure the system nonlinearity............................... 51

4.8: Response of acoustic measurement system to the incoming continuous acoustic wave
of different intensity ..................................................... ..................................... 53









4.9: Curve fits of the response of the acoustic measurement system at different bin number
..........................................................................................................55

4.10: Semilogarithmic plot of system output voltage before the elimination of system
nonlinearity ... .................................... .......... ......... ............................ ... 57

4.11: Semilogarithmic plot of corrected voltage after the reduction of system nonlinearity
.......................................................................................................... 5 8

4.12: Schematic of calibration tank. ........................................ ........................... 60

4.13: Determination of attenuation coefficients, aw and a .......................................... 62

4.14: Comparison of attenuation coefficient, a,, by experiment with model result based on
the assumption of spherical particles ................... ........................................63

4.15: Calculation of system param eter................................... ...................................... 64

4.16: Comparison of the calculated concentrations and input concentrations .................. 66

5.1: Orientation of shoreline longshoree current, wave and instrument frame ................ 68

5.2: B each profile .............................................................. ... ............. ...... 69

5.3: General setting of the measurement site ...............................................................71

5.4: Schematic of field measurement system..................................................72

5.5: Underwater deployment of the instruments. (April 1, 1992) ................................. 75

5.6: File nam e convention ................................................... .................................... 77

5.7: Calculation procedure of the irregular wave velocity near the bed ........................ 82

5.8: Error during FFT and inverse FFT ........................................... ....................... 83

5.9: Definition sketch of the primary direction.......................... ....................... 84

5.10: Size distribution of the bed material ................................................................... 87

5.11: Schematic of the facility to measure the settling velocity...................................... 88

5.12: D distribution of fall velocity............................................. ................................. 89

5.13: Grain diam eter and fall velocity.................................... ........................ ........... 90










6.1: Upward flux of the suspended sediment. ........................................ .............. 92

6.2: Profile of eddy diffusivity............................................94

6.3: Motion of a particle in convective process............................. ...................... 96

6.4: Distribution of suspended sediment under low wave energy condition................. 108

6.5: Distribution of suspended sediment under high wave energy conditions................. 110

6.6: Extrapolated and moving averaged concentration profiles (a0508m46).................. 112

6.7: Entrainment probability distribution function ....................................................... 114














LIST OF SYMBOLS

a Nondimensional fall velocity of sediment particle, wo/Kcu*w,

ao Radius of transmitter of sonar head

as Radius of scatterer

A Acoustic measurement system parameter

Ab Horizontal semi-excursion of orbital motion of fluid near the bed

B Constant related to the sound source strength

c Underwater speed of acoustic wave

C Concentration of suspended sediment

C Time mean concentration of suspended sediment

Ccalculated Calculated sediment concentration by inversion of acoustic data

Ci Concentration at location ri

Cinput Average concentration in a calibration tank

C, Sediment concentration at reference level

dso Median diameter of sediment particle

D Directivity of acoustic transducer

f Sound frequency in Hz

fpr Pulse repetition rate

f, Sampling rate

f2.5 Grain roughness friction factor with kb = 2.5 dso


I









F Probability distribution function of sediment entrainment

Fm Form function of scatterer

FFT{ } Fast Fourier Transform

g Gravitational acceleration

h Mean water depth

i f-i

I Acoustic intensity

lout Acoustic intensity after time varying gain

k Wave number

kb Equivalent Nikuradse roughness

N Number of particles in scattered volume

p Pressure

p Mean pressure

P Instantaneous sediment pickup rate at the sea bed

P Mean sediment pickup rate at the sea bed

qu Upward flux of suspended sediment

r Distance from the acoustic sensor to scatterer

ri Point where the initial concentration is prescribed

ro Acoustic near field limit

Re{ } Real part of complex quantity

s Specific gravity of sediment particle

Suu Power spectrum of wave induced fluid velocity in the primary wave
direction near the sea bed









S. Nondimensional sediment diameter defined by equation (6.37)

t Time

T Wave period
Water temperature

u, v Fluid velocity (horizontal components)

u, v Current velocity (horizontal components)

ui, v Wave velocity (horizontal components)

ub Wave velocity in the primary wave direction in the boundary layer

ud Complex defect velocity defined by the equation (6.30)

iip, i Wave velocities in primary wave direction and its normal direction

fi Amplitude of wave velocity near the sea bed

u*e Current friction velocity

u*cw Combined wave-current friction velocity

U, V FFT of i, i

V Scattered volume

Vin Input voltage

Vout Output from the acoustic measurement system

Vswitch Value of Vout at which the curve fitting formula is switched

we Convection velocity of sediment

wo Fall velocity of a sediment particle

z Vertical coordinate, upward positive from the bed

z, Sediment entrainment level defined in figure 6.3

Zp Elevation of pressure sensor









Zr Reference level (= 7 dso)

zo Bottom roughness, kb/30

zi Measurement point nearest to the sea bed

Z Nondimensional quantity defined by equation (6.37)

a Experimental free parameter (= 0.5)

as Attenuation coefficient due to scattering by particles

aw Attenuation coefficient due to absorption by water

6 Boundary layer thickness scale, Ku*,w/co

6r Spatial resolution of acoustic data

6 Ratio of current friction velocity to wave-current velocity, u*,/u*w,

6s Eddy diffusivity of suspended sediment

c)w Angle between the primary wave direction and the current

11 Displacement of water surface (Chapter 5)
Ripple height (Chapter 6)

K Von Karman constant

% Ripple length

v Kinematic viscosity

Vt Eddy viscosity

0 Width of acoustic beam in degrees (Chapter 2)
Rotation angle of coordinate system (Chapter 5)

Op Rotation angle of the coordinate system of the primary wave

Ow' Shields parameter based on wave skin friction velocity

02.5 Grain roughness Shields parameter









p Water density

t Duration of acoustic pulse

o Wave frequency in rad/sec

coo Mean zero-crossing wave frequency

T, Phase of sound wave emitted from the center of transmitter

F Phase of sound wave emitted from the edge of transmitter

SNondimensional vertical coordinate, z/6

CNondimensional reference level, zr/

Co Nondimensional bottom roughness, zo/6














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

ACOUSTIC MEASUREMENT AND MODELING OF THE VERTICAL
DISTRIBUTION OF SUSPENDED SEDIMENT DRIVEN BY WAVES AND
CURRENTS

By

Tae Hwan Lee

August, 1994

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

The principles, concepts and previous accomplishments associated with the acoustic

measurement of suspended sediment concentration are reviewed. The effects of sound

scattered from sediment in a scattered volume near the bed are investigated. The

algorithm for locating the sea bed from an acoustic intensity profile is developed and

works satisfactorily. The limitations of acoustic measurement of suspended sediment are

addressed.

An integral acoustic backscatter equation is solved analytically by converting it into a

nonlinear ordinary differential equation. The direct inversion of acoustic data into

sediment concentration based on the explicit analytic solution is significantly faster than

the conventional iteration method.

The sensitivity of the inversion process is tested with regard to the errors in

attenuation coefficients or errors in the near field concentration. Uniform concentration

profiles are very sensitive to those errors, but exponential concentrations are less sensitive.


xvii










The implementation and calibration of an acoustic measurement system is described.

A method of quantifying and reducing the system nonlinearity in the acoustic data is

developed. The data corrected with the method are practically free of the nonlinearity.

Currents, waves, pressure, sea bed location and profiles of suspended sediment

concentration are synchronously measured in the nearshore zone at Vilano Beach, Florida.

The data, instruments and the site are described. Also the method of calculating the

relevant quantities is described.

The mechanisms of sediment suspension under combined wave-current conditions are

reviewed. A pure diffusion model and a pure convection model are tested with the field

observations. The pure diffusion model predicts well the vertical distribution of sediment

suspension under high wave energy conditions but not under low wave energy conditions.

The pure convection model works well under low energy conditions but not under high

energy conditions.

A combined convection-diffusion model is developed using a time-invariant, vertically

varying eddy diffusivity profile and a probability distribution function of sediment

entrainment. Comparison with the field observations shows the combined model

predictions are in better agreement than diffusion or convection alone.

Uncertainties of the present studies are described. Recommendations on the future

studies are also given.


xviii














CHAPTER 1
INTRODUCTION


Shorelines, beaches and nearshore zones are valuable natural resources for residential

and commercial facilities such as harbors and shipbuilding yards and for recreational and

many other human activities. They also occupy one of the important elements of the

coastal ecosystem. It is not an overstatement that the prosperity of residents of countries

surrounded with long shorelines are heavily dependent on consistent management and

efficient development of these resources. Fulfillment of these conditions relies on the

understanding of mechanisms which govern the changes in the coastal environments.

The processes involved in the sediment phenomena of the coastal zone are
complicated and their interactions are usually nonlinear. It is hard to describe the

phenomena in analytical forms only. Experiments in laboratories and field measurements

are as essential as the theoretical studies. The progress in this research area has been

rather hampered by the lack of reliable data. In this chapter, the state of the art of

measurement and modeling of sediment suspension in unsteady flow is reviewed.



State-of-the-Art Review of Models and Measurement of Suspended Sediment

The changes of shoreline in planform are reasonably well studied in comparison with

the profile change. The time scale and length scale of the longshore processes are order of

several years and tens of kilometers, respectively. Longshore sediment transport models

based on wave energy flux have been well tested with field data by many authors such as

Inman and Bagnold [1963], Komar and Inman [1970], and Dean [1989]. Since Pelnard-

Considere [1956] introduced the one-line model, it has attracted many research efforts due










to its simplicity in mathematical formulation (e.g., Walton and Chiu [1979]). It has been

successfully used to predict the long term evolution of the planform of the natural

shoreline and nourished beach, and the effect of littoral barriers such as jetties and groins.

On the other hand, cross-shore processes in the coastal area are not understood as

well as the longshore counterpart. There are two different approaches to study the cross-

shore processes. The processes can be treated as approaching an equilibrium state

between constructive and destructive forces on a large scale without considering the

details of interaction of flows and moveable beds. Dean [1977] performed a very

comprehensive study on equilibrium beach profiles. This approach is very useful to

predict large scale responses of beach profiles to long term sea level rise or storm surge.

But the equilibrium beach profile model does not predict the details of profile changes

such as bar formation. The other approach is to describe the motions of fluid and

sediment in detail, and the interactions between them. This approach attracts many

researchers as new measurement techniques are developed. Studies on initiation of

motion, bed form, sheet flow and vertical distribution of suspended concentration under

wave and current belong to this category.

Grant and Madsen [1979] developed a boundary layer model under combined wave-
current condition using a time-invariant eddy viscosity profile. But this mixing length

model cannot reproduce the history effect of turbulence. Sheng [1982], for the first time,

solved the wave boundary problem with a higher order model of the Reynolds stress

instead of employing the eddy viscosity concept. Justesen [1988] applied the k-s model to

the turbulent oscillatory boundary layer.

Bed geometry is one of the problems which makes it difficult to predict the sediment

motion in oscillatory flow. Bagnold [1946] studied the details of size and shape of ripples

under waves. Hom-ma and Horikawa [1963] observed that lee vortices traveling upward

over rippled beds are very effective in carrying a large amount of sediment up to near the

water surface. And they also did a fairly thorough study on the relationship among ripple










height, ripple steepness and grain size Reynolds number. Nielsen [1981] compiled several

sets of field data and suggested empirical formulae for ripple height and length in terms of

mobility number. Wikramanayake [1993] introduced the ratio of skin friction Shields

parameter to nondimensional grain diameter in order to get more satisfactory formulae of

ripple height and steepness.

Sediment is transported primarily as bed load and suspended load. According to

Bagnold [1956], bed load is a part of the total load supported by intergranular forces.

Suspended load is supported by fluid forces. This is a theoretically beautiful definition;

however, it is extremely difficult to determine in which mode an individual particle near

the bed participates. Therefore, the classification is left to measurement techniques. The

question on the relative importance of different transport modes is also a matter of

measurement techniques. Use of instruments with high temporal or spatial resolution

gives answers to these long-time, unresolved questions. Komar [1978] suggested that bed

load transport was dominant in his study on longshore transport using dyed-sand tracer.

Hanes [1988], however, showed that the suspended mode is significant. This was

accomplished by using data acquired by optical and acoustical instruments, and

reinterpreting Komar's data with the concept of intermittent suspension.

Modeling the sediment suspension under natural conditions requires primarily two

tasks. One is to acquire sets of good data under various conditions. The other is to

choose the optimal number of mechanisms which are most responsible for the phenomena

of interest. A set of good data is one which is accurately measured, incorporated with

relevant data, and well documented. In reality, there are relatively many theories and

hypotheses, but not enough reliable sets of data, especially field measurements, to evaluate

them.

Laboratory measurements have some advantages over field measurements. It is easier

to measure the forcing and sediment motion in the laboratory. The entire procedure of

laboratory experiments is quite controllable and repeatable, but it is difficult to combine










waves and current in an oscillatory water tunnel. In addition, wave flumes usually have

scale problems. It is possible to employ a distorted or an undistorted Froude model for

experiments over a fixed bed. However, if we scale down the sediment size according to

the Froude model, the sediments become too fine and cohesive. Current can be

superimposed on wave motion in wave flumes, but the current created is always parallel

with the wave direction. The sediment motion in turbulent flow is governed by Reynolds

number. The only way to accommodate Froude and Reynolds similarities at the same time

is to use a prototype scale model. Hanes et al. [1994] did a series of laboratory

experiments on a prototype scale in the Supertank Laboratory Data Collection Project.

Sediment suspension and relevant data were acquired under various wave conditions. But

the water movement was two dimensional pure wave motion.

An accurate measurement in the field is a real challenge because the environment is

not controllable. The measurement methods of suspended concentration can be classified

into three categories: mechanical, optical, and acoustical measurements. The mechanical

measurement includes a sediment tube and a suction sampler. It is the most direct method

but lacks temporal and spatial resolution. An optical backscatterance sensor is a good

device to measure the time series of suspended concentration at a certain elevation. Its

response is very linear for a very wide range of concentrations; hence, its calibration is

simple and straightforward. One of the serious problems with mechanical or optical

methods is that any change in the distance from the bed due to erosion or deposition is not

accurately or synchronously measured. This can introduce significant errors in

measurement of suspended concentration near the bed where the concentration gradient is

very large. Besides, these methods disturb the hydrodynamic condition at and near the

measurement points. Local scouring near the instruments is another problem with the

optical or the mechanical measurement.

Acoustic measurement allows continuous measurement of the concentration profile of

suspended sediment with high resolution in time and space without disturbing the







5


measurement region. It is also possible to measure the change of the bed location

synchronously and continuously. Echo sounders, however, were originally developed to

detect underwater objects or to measure underwater bathymetry. For these conventional

applications, any signal originating from the points between the sounder and the objects of

interest is treated as noise. Therefore much effort is concentrated to filter out the effect of

suspended material along the sound path in the conventional applications. But the 'noise'

from the suspended particles becomes the signal of interest when it comes to the acoustic

measurement of particles in suspension. A new approach is required in this new

application of underwater sound.

Young et al. [1982], Tamura and Hanes [1986], Ludwig [1989], Sheng and Hay

[1988], Hay [1991], Libicki et al. [1989], and Thorn et al. [1991, 1993] are among those

who did experimental or theoretical work to develop a more accurate and practical

method of acoustic profiling of suspended concentration. However, the response of the

acoustic instruments is governed by the nonlinear acoustic backscatter equation. The

calibration of the acoustic measurement system and the inversion of its output into

suspended concentration are not straightforward. The method, by which the bed location

is determined from the profile of measured acoustic intensity, also should be established

with proper study. And all the valuable contributions from different authors need to be

incorporated into a comprehensive guide to the acoustic measurement of suspended

sediment in the field.

A model which fits data may be accepted as a good one. If the model fits data under

a wider range of conditions, it can be referred to as a better one. When a model fits a set

of data but does not fit another set of data under a different condition, simply adjusting the

parameters of or adding more degrees of freedom to the model may widen its apparent

validity. Some authors such as Hagatun and Eidsvik [1986], however, argue that apparent

data fit is not necessarily equivalent to model realism. It is probably necessary to evaluate










the validity of the mechanisms on which the model is based or to include other relevant

mechanisms to improve the model.

The model of suspended concentration profile can be divided into two modules:

reference concentration and vertical distribution. In oscillatory flow, the near bed

concentration does not vanish due to the sediment settling from a higher level even when

the near bed shear stress is zero. Van Rijn [1984] suggested the concept of pickup rate,

or vertical flux, for steady flow as an alternative. Nielsen [1992] showed that quasi-steady

modification of van Rijn's pickup function is a reasonable application to unsteady flow

condition. He also showed that the time averaged pickup rate is represented by reference

concentration multiplied by settling velocity when the process is stationary. The reference

level suggested by different authors ranges from zero to several centimeters above the bed.

Theoretically, the reference level should be the top of the bed load which thickness is on

the order of several grain diameters. That way, the reference level will be of order 1 mm if

the median grain diameter is of order 0.1 mm.

The vertical distribution of suspended concentration is the result of a balance between

upward sediment flux and settling of sediment particles due to gravity. Many of the

existing models employ the gradient diffusion process to describe the upward sediment

flux by turbulent mixing. The first model with eddy viscosity varying in time and space

was developed by Hom-ma and Horikawa [1963]. The time-varying concentration

profiles using that model were calculated later by Hom-ma et al. [1965]. Fredsoe et al

[1985] developed a combined wave-current model using eddy viscosity varying in time

and space. Their application was limited to co-directional flow over a flat bed.

Wikramanayake [1993] suggested a suspended sediment model using time-invariant eddy

viscosity. He modified the eddy viscosity profile of Grant and Madsen [1979]. His model

allows an arbitrary angle between currents and waves. Hagatun and Eidsvik [1986] used a

k-s model as a turbulence closure to describe suspended sediment concentration over a

flat bed.










Nielsen [1992] suggested a convection model to describe organized motions of

sediment on larger scales. A good example of this motion is the dense sediment cloud

moving upward trapped in lee vortices over a rippled bed. He also suggested a combined

convection-diffusion model to accommodate sediment mixing on both small and large

scales.



Motivation and Outline of the Thesis

The acoustic measurement provides high resolution in space and time and allows

synchronous measurement of bottom changes. There have been quite a few

accomplishments by different authors regarding many aspects of the acoustic

measurement. Yet, these accomplishments need to be rearranged around a specific goal:

implementation of the measurement system and correct interpretation of its data. There

are still some aspects to be clarified, for example, the exact location of bottom. And the

practical problems arising during the implementation should be investigated, too. I hope

that the first part of this dissertation fills the need for a practical and thorough guide of

acoustic measurement.

Turbulent diffusion is accepted to be responsible for the sediment mixing on a small

scale. But the vertical mixing of the sediment takes place on various scales. The question

is which mixing scale is dominant under which conditions. In this thesis, the acoustic

measurements of the time averaged concentration profile are compared with a pure

convection model and a pure diffusion model over rippled beds and flat beds.

In Chapter 2, the principles of acoustic measurement are presented. The equation

governing the acoustic backscatter is derived from the simplest case of a single particle in

water. And then, the effects of multiple particles in suspensions on the backscattered

acoustic intensity are discussed. The measurement limits are also studied.










In Chapter 3, the methods of inverting the measured acoustic data into suspended

concentration are investigated. The boundary condition near the sonar head is discussed.

A newly found analytical solution to the nonlinear acoustic backscatter equation is

presented. A direct inversion method using the analytical solution is compared to the

conventional iterative method. The sensitivities of the inversion procedure to parameters

of the governing equation are tested with different suspended concentration profiles.

In Chapters 4 and 5, practical problems of implementation and its application to field

measurement of acoustic system are studied. The method of locating the bottom bin in an

acoustic intensity profile is discussed in detail. The method to quantify and eliminate the

nonlinearities of the acoustic measurement system is developed. The field measurements

at Vilano Beach, St. Johns County, Florida are presented.

In Chapter 6, the vertical distribution of suspended sediment under combined wave-

current condition is investigated with the field data. Models of different mixing scale, i.e.,

a pure diffusion model and a pure convection model are compared with the measurements.

Also a combined convection-diffusion model is developed. The field condition ranges

from rippled beds to flat beds.

In Chapter 7, the summary of the results from the previous chapters and conclusions

are presented. Also recommendations on future study and field experiment are given.














CHAPTER 2
PRINCIPLES OF ACOUSTIC MEASUREMENT OF SUSPENDED SEDIMENT


The acoustic measurement of suspended sediment in ocean water consists of three

tasks: generation and transmission of a short acoustic pulse through ocean water,

reception or measurement of acoustic intensity backscattered by particles in suspension,

and inversion of the acoustic intensity into concentration of suspended particles. The

problem related to the transformation of underwater sound between transmission from and

reception by the transducer is called the forward problem. The procedure of interpretation

of backscattered acoustic intensity is the inversion problem. Design and calibration of the

measurement system belong to the implementation problem. In this chapter, the forward

problem and the limits of measurement are discussed.



The Outline of the Measurement Principles and the Forward Problem

When a short pulse of acoustic wave energy propagates through particles in

suspension, it continuously sends back a part of its energy which is scattered by the sand

particles. In this way, the acoustic energy of the short pulse is stretched in time. The

returned acoustic wave is not a short pulse but a continuous wave train, that is, a

continuous stream of returned pulses. During this stretching, the frequency remains

almost unchanged. The time delay between transmission and a certain point of the

received wave train is proportional to the distance from the sensor to sediment particles.

The propagation speed of sound underwater is approximately 1500 m/sec, whereas the

motion of sediment in suspension is of the order 1 to 100 cm/sec. This relatively faster

speed of underwater sound makes it possible to virtually freeze the sediment motion and










scan the particles in suspension along the sound path instantaneously. A time series of the

acoustic intensity profile can be generated by sending sound pulses repeatedly.

The amplitude of a returned sound wave train is changing with time although the

outgoing pulse has a constant amplitude. The envelope of the wave train has all the

information on the characteristics of the ocean water and the scatterers along the sound

path. There are a variety of mechanisms which affect the intensity of acoustic energy

when an acoustic wave propagates through the ocean water with particles in suspension.

The sound absorption by the ocean water and scattering by sediment particles are the most

important among the mechanisms. The amount of sound absorption is a function of water

temperature, salinity, viscosity, frequency of acoustic wave, and the traveled distance.

The energy loss due to scattering by suspended particles is determined by particle density,

size, shape, surface texture, the frequency of the acoustic wave, and the amount of

particles in suspension along the sound path. If the size of the sound source is small

enough to be assumed as a point, and if the sound is not confined by any means along its

sound path, there is an additional energy loss due to spherical spreading.

The acoustic measurement of suspended concentration is equivalent to filtering out all

the other information from the measured acoustic intensity in order to extract the one on

the concentration. In this following sections, the physical phenomena during sound

propagation are formulated in mathematical expressions. First, the backscattering by a

single particle in suspension is formulated with appropriate approximations. Next, the

formulation is extended to include the effect of the presence of multiple particles in

suspension. The final product of the formulation is the nonlinear acoustic backscatter

equation. The equation relates the acoustic intensity to the concentration of suspended

sediment.
During the formulation of the forward problem, all the relevant phenomena and

related research are discussed. The assumptions during the formulation are also discussed

with relation to possible error in field measurement. In addition, the factors affecting the






11


measurement limits are investigated. Understanding these factors is crucial for design and

implementation of the instruments by which the phenomena of interest can be measured

with desired accuracy.



Backscattering by a Single Particle in Water


Acoustic Intensity of Spherical Waves in Homogeneous Medium

First, let us consider an acoustic pressure wave originating from a point and

propagating in an open space of homogeneous medium. The pressure wave is governed

by the following spherical wave equation,


2p 42 ap _1 2p (2.1)
ar2 r r c2 at2

where r, t, p and c are the distance from the point, time and pressure at a certain distance,

and propagation speed of the pressure wave, respectively. Its solution is the sum of two

pressure waves propagating in opposite directions,



p(r,t) = Fdt +F (2.2)
r c) r \ c+

The first term on the right hand side of the equation (2.2), Fd/r, represents the pressure

wave diverging from the origin. The second term, FJr, represents the wave converging

toward the origin. The converging wave is not relevant to the acoustic measurement.

Only the first term will be considered.

If the diverging pressure wave is monochromatic, it can be expressed in the following

complex function,











B ( tr (2.3)
p(r,t) --exp t-
r c)


where B is a constant related to the source strength at the origin. The amplitude of the

pressure wave is inversely proportional to the distance from the origin. This solution is

not valid at the origin since it approaches infinity there.

Next, let us consider the motion of the fluid particle due to the propagation of the

diverging pressure wave. It is assumed that the displacement and velocity of fluid particles

are small. This assumption makes it possible to linearize the equation of motion by

neglecting the second order term. The fluid velocity, u(r,t), in the direction of wave

propagation can be described by the following equation of motion,

du _Qu 1 ap
dt at par
u(r, t) =1 ft p(r,r) dt
u(r,t) = a dt
p 0 9r (2.4)


where p is fluid density. By substituting the equation (2.3) into (2.4), we get the following

relationship between the pressure field and the velocity field,


1 c (2.5)
ur,t) 11-i- p(r,t) (25)
pcj wr)


The acoustic intensity of the spherical pressure wave, I(r), is defined by the following
expression,


1 T (2.6)
I = I f Re{p(r,t)} Re{u(r,t)} dt(


where Re{ } denotes the real part of the function inside the bracket. The equation (2.6)

can be evaluated by substituting the equations (2.3) and (2.5).











1 T B2 ( cos(o t -kr)sin(w t -kr)
I =- ,- cos2 -kr) +I-
T r 2pcL kr



II B2 1 (2.7)
r2 2pc )r2


where k is the acoustic wave number. The above equation shows that the acoustic

intensity is inversely proportional to the square of the distance from the origin. Equation

(2.7) is not valid at the origin. In application, the region where the spherical spreading of

acoustic energy is invalid is finite because the transmitter of the sonar head is not a point

but has a finite size. It is very important to know this limit in order to calibrate an acoustic

measurement system and interpret its data appropriately.

Attenuation of Acoustic Energy Intensity due to Absorption by Ocean Water

The pressure and fluid motion of an acoustic wave are attenuated during wave

propagation through ocean water. Rayleigh [1945] found that the shear viscosity of water
is one of the effects which causes this attenuation. According to his theoretical work, the

attenuation is a function of water density, shear viscosity, sound speed and frequency of

the acoustic wave. Later, it is found that the volume viscosity is also responsible for the

attenuation. The effect of volume viscosity is almost twice that of shear viscosity. The

salinity is a dominant factor for the attenuation of low frequency sound (Leonard et al.

[1949]). But the effect of salinity vanishes for frequencies higher than 1 MHz.

Tamura and Hanes [1986] explained this mechanism in an illustrative manner in their

report. This attenuation results in the exponential decay of pressure and fluid motion with

distance from the origin. When the absorption is taken into account, the equations (2.3)

and (2.7) are modified into the following,











p(r,t) -B e- expi t-8)
r C)




where aw is the attenuation coefficient due to absorption by water.

The effect of salinity is the most dominant cause of sound absorption for frequencies

below 100 kHz. Because most acoustic concentration profilers use frequencies higher

than 1 MHz, the effect of salinity on sound absorption is negligible for measuring

suspended sediment concentration. Thorne et al. [1991] recommends using Fisher and

Simmon's [1977] formula to find the attenuation coefficient. They rearranged the original

formula into the following form,


a, =(55.9 -2.37T +47.7 x10-2T2 -3.84 X10-4T3) X10-3f2 (2.10)


where T is temperature in degrees Celsius, f is sound frequency in MHz, and aw is in

Nepers/m. The attenuation coefficient becomes a function of water temperature only

when the working frequency of an acoustic instrument is given and is higher than

approximately 1 MHz.

Backscattering

When an acoustic wave is scattered by a suspended particle, part of the energy goes

back in the opposite direction of wave propagation. This is called backscattering. During

the round trip from the sound source to and from the suspended particle, the pressure and

acoustic intensity are spread spherically and attenuated twice by water, and backscattered

once by the particle. The backscattered pressure and backscattered acoustic intensity after

the round trip are described by the next equations,



















Fm


10-1





10-2
10-1 100 101 102
kas

Figure 2.1: Form function. Equation (2.13). The symbol k and a, denote the acoustic
wave number and the radius of the scatterer.




B -2 .(r* (2.11)
p(r,t) =aFBe exp t- (2.11)
r 2c

(r) 4e- F22 (2.12)



where a, is the radius of the particle, and Fm is the form function which describes the

scattering properties of the particle. The form function depends on the size, density,

surface texture and shape of the suspended particle, and on the frequency of the acoustic

wave.

Thorne et al. [1993] performed comprehensive studies on the form function. They.

proposed the following formula for irregularly shaped particles based on Sheng and Hay

[1988] and Hay [1991],











F. 1 -0.25exp (ka, -1.4)2I 7exp[ (ka -2.8)2 1. l(ka,)2 (2.13)
p 0.5 2.2 1 +1.1(ka,)2


Figure 2.1 shows the form function evaluated with equation (2.13). Actually the curve for
the form function of a single particle is very different from the figure. There are many
downward spikes due to the modal resonance. But use of the above curve can be justified
because we are not ultimately interested in an isolated particle but one of the particles in
suspension. The form function is strongly dependent on ka, in the Rayleigh region where
ka, is smaller than 0.5. But it is almost constant in the geometric region where ka, is larger
than 5. The particles in the Rayleigh region do not have a significant contribution to the
backscattered acoustic intensity because the form function decreases very rapidly with ka,.


Backscattering by Mixture of Particles and Water

Attenuation of Acoustic Energy Intensity due to Scattering by Particles
When an acoustic pressure wave propagates through a medium with particles
suspended, there is an additional attenuation of acoustic intensity due to scattering by the
particle along the sound path. This attenuation also results in an exponential decay of
pressure and acoustic intensity. The amount of the attenuation is closely related to the
concentration and the scattering characteristics of suspended particles along the sound
path. Because the effect of suspended particles accumulates along the sound path, the
concentration must be integrated along the sound path in order to formulate the effect
correctly. Therefore, the acoustic intensity scattered by one of the particles in suspension
is derived from the equation (2.12)











I(r) = 41 F2 i exp(-4aC(rAr))
r" 2pc(A-1OJ

I(r) = -4e (a2F B limexp- 4aC(r)Ar


S(r exp -4r- 4C(r')dr B2
r4 L a odrI])a 2pc (2.14)


where a, is the attenuation coefficient due to scattering by particles and C(r) is the

suspended concentration at distance r from the sound source. The coefficient, as, is a

function of the characteristics of the suspended particles such as the size, density, shape
and surface texture and has been assumed to be constant in this treatment. The procedure

of determining the coefficient is discussed in the section "Calibration" of Chapter 4.

Strictly speaking, the lower limit of integration is incorrect, since the equation is not

valid at the origin. The lower limit will be discussed in more detail later in the section

'Near Field Concentration" of Chapter 3. During the derivation of the above, it was
assumed that the scattering characteristics of suspended particles do not change along the

sound path. This assumption can cause an error in high elevations above the bed where

the size distribution of suspended particles might be different from that of the bed material.
But the error is probably small because the concentration of suspended sediment is usually

very low at high elevations. It was also assumed that there is no multiple scattering. This

assumption may not be correct if the concentration is very high. But the region of high

concentration is limited to the very thin layer near the bed. Therefore, the effect of

multiple scattering on the attenuation can be assumed negligible for the field

measurements.

Scattered Volume and Its Effect on Bin vs. Distance Relationship

So far we have considered acoustic intensity which is scattered by one of the particles

in suspension. But the acoustic backscatter, which is intensity detected at the transducer










at a certain time, is the sum of the contributions from the particles in a finite volume

because the acoustic pulse has a finite length and beam width. This is what is called

scattered volume.

Figure 2.2 illustrates the relationship among the scattered volume, the pulse length
and distance from the transducer. The sound speed and pulse duration are denoted by c

and r in the figure. In figure 2.2(a), two suspended particles are considered at distances r'

= r-cT/2 and r' = r from the transducer. If the acoustic pulse was fired from the

transducer at time t = 0, then the leading edge of the outgoing pulse will arrive at r' = r-

cz/2 r at time t = r/c-T/2. The time t here is the delay time since the pulse is fired The

leading edge of the same pulse will arrive at r' = r at the delay time t = r/c. For simplicity,

the delay time will be just called time herein.

Figure 2.2(b) shows the behavior of the two particles at r' = r-cr/2 and r' = r while

the acoustic pulse is propagating through those points. The suspended particle at r' = r-

ct/2 will begin scattering the acoustic wave or vibrating at time t = r/c-c/2 when the

leading edge of the pulse hits it, and continue vibrating till t = r/c +T/2, that is, during the

pulse duration. Another particle at r' = r will vibrate from t = r/c to t = r/c+T.

Figure 2.2(c) shows the detection by the transducer of the incoming pulses which are
scattered by the particles at r' = r-cT/2 and r' = r. The leading edge of a backscattered

acoustic pulse coming from r' = r-cT/2 will arrive at the transducer at t = 2r/c-T. The

backscatter acoustic intensity of the particle at r' = r-ct/2 will be detected until t = 2r/c,

that is, during the pulse duration. Similarly, the acoustic backscatter intensity of the

particle at r' = r will be detected from t = 2r/c to t = 2r/c+T. The particle at r' = r-cT/2 is

the nearest one of which the acoustic backscattered intensity can be detected by the

transducer at t = 2r/c. And the particle at r' = r is the farthest one. Therefore the

instantaneous acoustic backscatter intensity measured at t = 2r/c is the sum of the

contributions of the particles located between r' =r and r' = r-cT/2.










(a)



at t=r/c-T/2


at t=r/c


(b)



at r'=r-cT/2


at r'=r




(c)

from
r'=r-cT/2


from r'=r


r'=r-ct/2 r'=r


t=r/c-T/2 t=r/c+T/2


I l a,'ri/n I rat --o


t=r/c+T


uIFe ,u I time,t
t=r/c
""pulse duration time,t


t=2r/c-T t=2r/c


Ioulse duration -I


t=2r/c+T


SP TITF


tr2r/c

pulse duration I


r--
Transducer .... r.
----


- e -


Figure 2.2: Definition of scattered volume
(a) Location of acoustic pulse, (b) Timing of scattering at suspended particles
(b) Timing of detection of the returned pulse at transducer, (d) Scattered volume


ct/2
~I(i~


StImi


,


t I


I









Figure 2.2(d) shows the scattered volume. The beam width is denoted by 0. The

scattered volume can be calculated as a circular cylinder with base area t(rO)2/4 and height

ct/2 because the pulse length t is small compared to distance r except for the point near
the transducer and because the beam width is usually very small. The scattered volume is


S r ir(rO)2 (2.15)
2 4

where c, T and 0 are propagation of underwater sound, pulse duration, and beam width,
respectively. The transducer is thus assumed to have directivity herein.

As shown in figure 2.2(d), the center of the scattered volume is at r' = r-ct/4 when

the transducer detects the backscattered acoustic intensity at delay time t = 2r/c after the

pulse is fired. If the distance corresponding to the detected acoustic intensity is calculated

by dividing half of the delay time with the sound speed, then it will be cT/4 longer than the

distance to the center of the scattered volume. It is more reasonable to use the distance to

the center of the scattered volume as the distance of the measured acoustic intensity. This

difference is very important when the acoustic data are interpreted, because the
concentration gradient near the bed is very large. Any error related with the distance will
introduce a large error in the measurement of the sediment concentration near the bed.

Scattered Volume and Concentration of Suspended Sediment

If we assume that there are N number of suspended particles in the scattered volume

and that both of the source and target directivities are D, equation (2.14) can be modified

as the following one to include all the contributions from the suspended particles in the

scattered volume,


(r) =Bexp[-4wr -4C(r')dr' (2.16)
r4 K7~I~L *W Ja5 ~nm 2pc









where the subscript, n, is the index of individual particles and N is the total number of the
suspended particles in the scattered volume. It should be noted that the variable r in the
equation above is the distance from the transducer to the center of the scattered volume.

The average volumetric concentration of suspended concentration in the scattered
volume is defined as the following expression,


a, 1 32 a
C(r) 2
1 r2 3 crO
1 7rcTO2r2
8

By using the definition of the volumetric concentration, equation (2.16) is rewritten as
followings,


C(r) (r 302 42 2 i B24 (2.17)
I(r) = exp -4a r -4aC(r')dr' 2
r2 0 32 =a, 2pc


Equation (2.17) is expressed in the simpler form,


(r) =AC(r)rexp[-4awr -J4a,C(r')dr'] (2.18)


where A is what is called the system parameter,


3c2 aF B2 D4
32 a3 2pc


The above system parameter becomes constant when suspended particles of a particular
size distribution and backscattering characteristics are measured with a particular acoustic
system.










Now, we have the mathematical relationship between the suspended concentration

and the backscattered acoustic intensity with three parameters to be determined by

experiment. The three parameters, A, aw and as, in the acoustic backscatter equation

(2.18) should be determined when an acoustic measurement system is implemented and

deployed in a particular field condition. The method of determination of these constants is

discussed in the section "Calibration" of Chapter 4. The inversion procedure of the

backscattered acoustic intensity into the sediment concentration is a matter of mathematics

once the parameters and bin vs. distance relationship are determined by experiment in the

laboratory. Because the acoustic backscatter equation (2.18) is nonlinear and implicit, the

inversion procedure requires the use of some mathematical techniques. The inversion

procedure is discussed in Chapter 3.


Measurement Limits


Spatial and Temporal Resolution

The spatial resolution of the acoustic measurement of suspended concentration is

determined primarily by the sampling rate because the elapsed time between the
transmission and reception of the pulse is proportional to the distance from the transmitter

to the suspended particle. The spatial resolution is


br c(2.19)
2f,

where f, is sampling rate and c is the propagation speed of underwater sound which is

approximately 1500 m/sec. The number "2" in the denominator represents the round trip

of a sound wave to the measured suspended particles.

But the measured acoustic intensity is the sum of contributions from the particles in

the scattered volume. When the spatial resolution of the data, 6r, is smaller than half the










pulse length, cr/2, then the range represented by each measurement point will be

overlapped. The measurement becomes the moving average of the suspended

concentration with the spatial resolution determined by the sampling rate and with the

averaging range determined by the pulse duration, T.

The overlap of the measurements at each point can be made small by decreasing the

pulse length. But if the pulse length is too short, the pulse will have too small a number of

wave cycles. This may cause an error in measurement because the randomness of the

phase in an acoustic wave at each particle in the scattered volume decreases. Another

practical problem with too short a pulse length is the actual shape of the pulse. In reality,

acoustic pulses generated by a sonar head are not rectangular. It takes a finite period of

time for an acoustic pulse to reach its maximum constant intensity. It takes also a finite

period of time for the acoustic intensity of the pulse to decrease to zero. The pulse may

never have a chance to be flat for a long enough period of time if the pulse length is too

short. The acoustic intensity backscattered by too short a pulse may not represent the

average concentration of the particles in the scattered volume.

The temporal resolution profile measurement is determined primarily by the pulse

repetition rate. But the measured profiles usually have to be ensemble averaged to

produce statistically meaningful data. The ensemble averaging increases the randomness

of the phase and helps filter out irrelevant noises. If the pulse length is very short, the

number of profiles to be averaged should be increased to enhance the randomness of the

phase. Finally, the temporal resolution is the pulse repetition rate divided by the number

of profiles to be averaged.

Limits on Measurable Particle Size and Concentration

Given the frequency of the acoustic measurement system, it is more difficult to

measure the particles in the early stage of the Rayleigh range, see figure 2.1. The optimal

frequency is application specific. It is highly recommended that the frequency of the










acoustic system be chosen in a way that the particle sizes of interest are in the geometric

range.

The measurable concentration is also limited by the signal saturation level and the

ratio of signal to noise. The gain of the analog amplifier in the measurement system

should be adjusted so that the ratio of signal to noise is maximized but the signal level is

not saturated at the extreme level of the suspended particle concentration expected.

However, the system gain does not reduce the ambient noise originated from the

measurement field but the relative noise level in the system after the amplifier.

Limit on Measurement Range

The minimum distance, at which an acoustic system can measure the concentration of

the suspended particles, is the near field limit. The maximum distance is limited primarily

by the pulse repetition rate since the system measures the acoustic intensity between the

pulses.


c (2.20)
r-,
max 2 f
2fpr


where fp is the pulse repetition rate.

The measurable range can be extended at the expense of temporal resolution by

reducing the pulse repetition rate. But it is not always true because the maximum distance

is also limited by the ratio of signal to noise. The acoustic intensity drops rapidly with

distance. Time varying gains, are widely used to increase the range limit avoiding the

earlier saturation of signal level, since the acoustic backscatter intensity decreases with

time or distance due to spherical spreading and exponential attenuation.

Measurable Point Closest to Ocean Bed

When we acoustically measure the concentration profile of suspended sediment near

the ocean bed, there is a limit on the measurable point closest to the bed. This point is a









scattered
volume


incident T/2 scattered
pulse y... volume

cT incident \ ........cT/2
/ ipulse cT/4
reflected
bottom bottom t
pulse


(a) when t =0 (b) when t = T/2



Figure 2.3: Measurable point closest to ocean bed. T is the pulse duration.
(a) The location of the incident pulse and the scattered volume when the leading
edge of the incident pulse touches the ocean bed
(b) The location of the incident pulse, reflected pulse and the scattered volume,
half a pulse duration after the leading edge of the incident pulse touches the
ocean bed.


quarter of the pulse length, cr/4, above the bed. Below this point, the concentration can

not be measured because the acoustic intensity reflected at the bed predominates in the

region. The information on the concentration in measured acoustic intensity is

contaminated by the reflection of pulse at the bed.

Figure 2.3 illustrates this limit. The trailing edge of the scattered volume coincides

with that of the incident acoustic pulse. When the leading edge of the scattered volume

touches the bed, its trailing edge is coincident with the leading edge of the reflected pulse.

At this moment, the center of the scattered volume is ct/4 above the bed. After that, the

measured acoustic intensity becomes the sum of the contributions from the bed and the

suspended particles in the scattered volume. Therefore the point nearest to the bed, of

which concentration can be measured avoiding the effect of the bottom return, is a quarter

of the pulse length above the bed. This is consistent with the effect of the scattered

volume on the bin vs. distance relationship.














CHAPTER 3
INVERSION OF ACOUSTIC DATA INTO SUSPENDED CONCENTRATION


In the previous chapter, the forward problem was formulated mathematically. The

forward problem deals with the conversion of suspended concentration into backscattered

acoustic intensity. The final product of the mathematical formulation is the acoustic

backscatter equation (2.18) The task of finding the solution of the equation is called the

inversion problem because the acoustic intensity is inverted to the original quantity, the

concentration of the suspended sediment. The difficulties of the inversion mainly arise

from two facts: firstly, the equation is nonlinear and implicit, and secondly, the boundary

condition is not prescribed. A question related to the boundary condition regards the

location of the appropriate boundary.

In this chapter, the concept of near field limit and the location of the initial point are

discussed. The location of the boundary will be determined according to this concept.

And the procedure of finding the concentration of suspended particles at the initial point is

also discussed. The mechanism of scattering is complicated in the near field but the

concentration at the initial point can be found by simplifying the details of near field and by

putting the initial point outside the near field limit. This is equivalent to specifying the

boundary condition. Next, the equation (2.18) is solved by iteration successively along the

sound path. Also, an explicit form of the acoustic backscatter equation is developed and
solved directly, without iteration, and compared with the iterative solution. Also,

sensitivities of the inversion process to the calibration constants and to the error in the

boundary condition are investigated.









r +l/k


irregular wave I regular wave
transmitter
ro



near field transition far field
(Fresnel field) region (Fraunhofer field)



Figure 3.1: Near field limit. At the near field limit, the sound from the edge of the
transmitter is in phase with that from the center. The wave number of the sound wave is
denoted by k.




Near Field Concentration


The transmitter of acoustic pulse is usually a circular plate of finite radius. It does not

radiate like a point source at short distances. This region is called near field or Fresnel

field. In this field, the acoustic intensity is the sum of contributions from the different

parts of the transmitter surface. The acoustic pressure field is irregular. The interaction

between acoustic pressure field and suspended particles is also very complicated. The

equation (2.18) is not strictly correct in this field because it is developed for a spherical

acoustic wave field radiated from a point source.

Figure 3.1 illustrates the location of the near field limit. The near field limit, ro, is

defined as the first point along the axis of the sound path, where the distance from the

transmitter center is 1/k-th shorter than that from any point on the perimeter of the

circular surface of the transmitter. In this definition, k is the acoustic wave number. The

distance from the center of the transmitter to the near field limit is denoted by ro in the










figure. If the corresponding travel time of sound is denoted by to, then the sound phase at

the near field is


We =kro -w to


The sound from the edge of the transmitter travels the distance ro+l/k to the point at the

near field limit on the axis of the acoustic beam, and its phase at the point is


e =k(ro 1) -- 1 (ro )
k k

=k(ro -) -w (to +-)
k w
=kro -w to


Therefore the near field limit is redefined as the point where the acoustic pressure

transmitted from the center is in phase with that from any point on the edge of the

transmitter.

By trigonometry, the near field limit is expressed as follows:





ka2 1 ka2
0 2 2k 2 (3.1)

where ao is the radius of the surface of the transmitter. The second term of the equation is

negligible, since the value of k is of the order 106 for usual acoustic measurement systems

of suspended sediment.

In the far field or Fraunhofer field, the acoustic intensity is regular and falls off

smoothly with distance. All the formulae developed upon the assumption of a point sound

source are valid in the far field. There is a narrow transition region between the fields.

The calibration of the measurement system and the interpretation of its data should be










performed in the far field. Therefore the boundary for the acoustic equation should be

located just outside the transition region.

Since acoustic backscattered intensity at a certain point is a result of the accumulating

effect of spreading and attenuation along the sound path from the transmitter surface to

the point, the intensity in the far field is affected by the near field condition. The acoustic

wave field is very irregular in the near field, and the interaction between sound and

suspended particles is too complicated to be described in an analytical form. Downing et
al.[1993] proposed a formula to convert the near field acoustic intensity into the far field

equivalent, i.e., the spherical equivalent, so that concentration in the near field is found by

using the far field equation. This method moves the initial point inside the near field. But

the problem of finding the initial concentration remains.

In the field application, the usual purpose of acoustic profiling is to measure the

suspended concentration near the ocean bed which is in the far field. In this section, the

initial point is put in the far field but very close to the near field limit. Without considering

the details of the concentration in the near field, the suspended concentration at the initial

point is calculated assuming that the concentration is uniform from the transducer through

the point. This assumption is reasonable because the concentration decays exponentially

with distance from the bed under field conditions. The acoustic transducer is usually

located at least 1 meter above the bed where the suspended concentration is extremely low

and almost uniform. Now, the initial concentration can be found by iterative solution of

the following equation,


r2(r) (3.2)
C(r) =1 ) exp[ 4awr +4a,riC(r)] 32)
A

where ri is the distance from the transducer surface to the initial point, and C(ri) is the only
variable.









Far Field Concentration

Iterative Solution to Implicit Equation
Tamura and Hanes [1986] introduced the successive iteration method to solve the
acoustic backscatter equation. Equation (2.18) can be converted to the following
expression in a discrete form at r=rj and r=rj.1:



AC, =I,r,2 exp =[{4a, +2a,(C,_, C)}(ri -r_,)] (3.3)



AC,_, =I, _12exp -= 1 {4, +2a,(C,_ -+C,)}(r, --rj,)] (3.4)


where Cj and Ij are the suspended concentration and measured acoustic backscattered
intensity at r=rj, respectively.
By dividing equation (3.3) by (3.4), the concentration Cj at r=rj is implicitly
represented in terms of unknown Cj, known values of Cj-1, rj, rj-1, aw and a,, and the
measured values ofIj and Ij1,


r2 (3.5)
C, =CJ1 2 exp[{4a, +2a,(C,_, +C,)}(r, -1r_)]


The equation above is solved by iteration. The measured acoustic backscatter intensity
can be successively converted into concentration all through the water column once the
initial concentration is known. Note that the system parameter, A, is not involved during
the inversion process.
The method above may be simplified by assuming that the concentration gradient
between r=rj and r=rj.1 is not significant. Under this assumption, the term Cj in the right
hand side of the equation (3.5) can be replaced with Cj-. And the equation is simplified
into the following form.











r2 (3.6)
C, =CJ 2 exp[(4ca +4a,Cj,_)(r, -r,-)]
1-10 -1

Equation (3.6) is explicit and does not need iteration to be solved. But the solution still
must be found successively through the sound path because Cj is expressed in terms of C3-

1.

Direct Solution to Explicit Equation

As an alternative to the method just described, equation (2.18) can be directly solved

in the following fashion. By taking the logarithm of equation (2.18) and solving for I(r),

we get the following equation,


In[r2I(r)] =(lnA +lnC(r)) -4f [a, +a,C(r')] dr' (3.7)


Taking the derivative of both sides of the above equation with respect to r yields the

following equation,


rl' +21 C' (3.8)
= --4(aw +otC)
rl C

where I'=dl/dr and C'=dC/dr. We get the following Bernoulli-type nonlinear ordinary

differential equation by rearranging the equation above,


4 rl +21C = (3.9)


The above differential equation has the following analytical solution,


I(r)r2 exp(4awr)
C(r) -r (3.10)
y -4a, I(r')r'2 exp(4ar')dr' (3.10)
ori









where y is an integration constant, and ri is the point where the initial concentration is
prescribed. If the concentration at r=ri is known, then


I(ri )ri exp(4ari)
C(r,)

Finally, we have an explicit expression for concentration.


I(r)r2 exp(4aowr)

C (r,) ,r.
I(r.)ri2 exp(4ar,7) ...,4rI(tr 2(4I'dt (3.11)


Since the above expression is explicit, the measured backscatter intensities may be
converted into suspended sediment concentration at any elevation without iteration or
successive calculations. The equation above is discretized for computation as follows,


G,
CJ GI G- (3.12)
C, -2a, G.=,+,(G-tG,_a,)(rj -rj_,)


where


G, =,r,2 exp(4a r) and C, =C(r,)

It should be noted that the development of the explicit solution is a mathematical
technique only; the physics of the scattering processes are assumed to be the same.
Therefore, the solution obtained using equation (3.12) is the same as the solution obtained
using equation (3.7). The advantage of the explicit method is primarily an improvement in
computational time, as will be shown below. Since this solution does not need successive
calculation, it is possible to get the concentration profile near bed without calculating










concentrations at higher elevations. Also note that equation (3.12) does not contain the

system parameter, A, explicitly but does require the initial concentration, Ci.

Comparison of Solutions

Six different profiles of suspended sediment concentration will be used as examples to

compare the solutions and to investigate the sensitivity of the inversion process. The

profiles are shown in figure 3.2 and their details are listed in table 3.1.

The profiles of backscattered intensity signal for those six concentration profiles are

calculated with equation (2.18). The constants, A, aw and aw are assumed to be 2 x 10s,
4.65 x 10-4 Nepers/mm and 8.17 x 10-7 Nepers/mm/(mg/l), respectively. Spatial resolution

was set to 3 mm. The initial point was assumed to be approximately 123 mm from the

transducer. Figure 3.2 shows the signal level profiles calculated with equation (2.18).

The signal level is defined as the square root of the measured intensity because the

transducer actually measures the pressure and converts it into voltage.


Table 3.1: Concentration Profiles.
profile number profile
ul C(r)=50 mg/1, 0 u2 C(r)=500 mg/1, 0< r<600 mm
u3 C(r)=1000 mg/1, Or <600 mm
el C(r)=50exp[0.02(r-600)] mg/1, 0 e2 C(r)=500exp[0.02(r-600)] mg/1, 0 e3 C(r)= 1000exp[0.02(r-600)] mg/1, 0< r 600 mm


The inversion times for the three inversion methods are compared using a uniform

concentration profile (u2: 500 mg/1) with superimposed random fluctuations. The

maximum amplitude of the random fluctuation is 30 mg/l. An i486-based personal

computer with clock speed of 50 MHz was used for these calculations. The inversion

programs for equations (3.5), (3.6) and (3.12) were written in Matlab version 3.5k. The

input concentration value of table 3.1 was used for the initial concentration, hence, no










error at the initial point is introduced during the inversion. The inversion range is 123-600

mm. The Matlab command 'fsolve' ,which is based on a modified Newton's method, was

used to obtain the iterative solution of equation (3.5). The concentration at the adjacent

point closer to the sensor was used as an initial guess for the iteration process.

The results are summarized in table 3.2.. The inversion by the direct method is the

fastest of the three. It is approximately 1000 times faster than the successive iteration

method and approximately 5 times faster than the successive method. The rms. errors for

all three inversion methods are also given in Table 3.2. In general, these errors are small.

The direct method provides fast inversion with virtually no additional error. This is of

practical importance because the size of an acoustic data set is usually quite large.


Table 3.2: Comparison of Computation Time and Error of Inversion Methods
inversion method computation time rms. value of relative error equation
successive iteration 37.75 sec 3.0 e-5 % (3.5)
successive 0.27 sec 2.0 e-2 % (3.6)
direct 0.04 sec 7.5 e-5 % (3.12)


Sensitivities of Inversion Process

The sensitivities of the inversion methods to various parameters were compared for

the six concentration profiles. For this purpose, the successive method by the equation

(3.6) was not considered since it has no advantage over the direct method in terms of

accuracy or computation time.

The error at r=600 mm introduced by the miscalculation of the initial concentration

was investigated. The inversions are started with incorrect values of the initial

concentration, with relative errors ranging from -20 % to 20 %. The error in

concentration at a range of 600 mm is plotted against the initial error in figure 3.4a for

uniform concentration profiles and in figure 3.4b for exponential profiles. The error does

not increase significantly along the sound path in case of exponential profiles; however, it










grows fast in the case of uniform profiles. Table 3.3 shows the ratio of the error at 600

mm to initial error. Both inversion methods result in nearly the same errors, so in Figure

3.4 the solid lines (direct method) and the dashed lines (iteration method) lie on top of one

another. For the cases of uniform concentration, overestimates of the near field

concentration cause larger errors at 600 mm than are caused by underestimates of the

near field concentration. In contrast to the high sensitivity for uniform profiles, the

inversions of the exponential profiles are not as sensitive to errors in the initial

concentration. Figure 3.4b illustrates that the error in the near field concentration results

in a roughly equivalent error in the concentration estimate at a range of 600 mm.

Figure 3.5 shows the error in concentration at 600 mm due to the error in estimation

of the attenuation coefficient by water,aw.. Such an error might result from not accurately

knowing the water temperature. Again the two methods give essentially the same results

with the inversion of the uniform concentrations showing more sensitivity to aw than the

inversion of the exponential profiles.

Figure 3.6 shows the error in concentration at r=600 mm due to error in estimation of

attenuation coefficient by suspended particles, a,. The error is more than 300 % for the

uniform profile, u3, with only 20 % error in a,. However, the error is less than 4% for

the exponential concentration profiles when the error in as is 20 %. The error at r=600

mm due to an error in as is enhanced for greater concentrations because the loss of sound

is related to the product of concentration and as.



Table 3.3: Ratio of Error at 600 mm to the Initial Error
concentration ratio of error at 600 m t the initial error
profile when initial er or is (-) 20 % when initial rror is 20 %
direct method iteration method direct method iteration method
ul 1-06 1_06 1 10 1_10
u2 1.77 1_77 2_86 2_86
u3 273 2_73 20.01 20-01
el 1 01 1 _01 1 01 1 _01
e2 1 07 1.07 1 10 1.10
e3 1,14 1.14 1 ____.22 1 22






36


The inversion of the uniform concentration profile, which is usually created in the

laboratory for calibration, is extremely sensitive to errors in estimation of attenuation

coefficients and initial concentration. However, with the exponential concentration, which

is commonly found in sediment suspension phenomena, the inversion is only weakly

sensitive to attenuation coefficients. The errors in the estimation of initial concentration

result in commensurate errors throughout the range of the exponential profile.

Therefore, any errors in calibration are significantly reduced during the field measurement.
























_ 1000 I I I I ii I I i
Sa00
E

o 800 -



0
L /





g 4 0 0 ........................... ........................... .............................................
un u k
S















and e3, respectively.
c n

-o i i i i i

0 --- -- i ----- --i -- ---- --_- __.. .... 4 -.'-- -e... -__ --_-o---'--
0 100 200 300 400 500 600

distance from sensor [mm]

Figure 3.2: Concentration profiles to compare the inversion methods. Solid lines with 'o',
'x' and '+' mark represent uniform concentration profiles, ul, u2 and u3, respectively.
Dashed lines with 'o', 'x' and '+ mark represent exponential concentration profiles, el, e2
and e3, respectively.





















3000



2500



2000
-o


1500
-5
01
1000



500


0-1 -------- --=-b- -- -I -- --- --l -----B-- - I---I i
100 150 200 250 300 350 400 450 500 550 600

distance from sensor [mm]

Figure 3.3: Backscattered intensity profiles to compare the inversion methods. Symbols
are as in figure 3.2.






































-15 -10 -5 0 5


10 15 20


-15 -10


-5 0


10 15 20


error in nearfield concentration [%]

Figure 3.4: Error in concentration at 600 mm due to error in the initial concentration.
Marks on the lines are as in Figure 3.2. Solid and dashed lines represent the direct and
iteration method, respectively. The different inversion methods are not distinguishable.
(a) Results for uniform concentration profiles;
(b) Results for exponential concentration profiles.


-100L
-20
) 30-


-300
-20








- --........................... ...................... ... .------. -. .


..... ................- --i... .. .........



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


----- -,-- -- -- t-



----------!----------- -----?












(a)






E
E
o
0
(0
4-*
0
o

0
L-

C
U
O
U

L)







(b)






E
E
0
o
0
cD
4.,


O
C-
0


a
L
C
1-

U
C

0
L-
0U


10 15 20


-15 -10 -5 0 5 10

error in estimation of attenuation coefficient of water


15 20


[%]


Figure 3.5: Error in concentration at 600 mm resulting from error in tw Symbols and line
patterns are as in Figure 3.4. Different inversion methods are not distinguishable.
(a) Results for uniform concentration profile;
(b) Results for exponential concentration profile.


-15 -10 -5
I


-40'
-20

25


20 -


15


10


5


0


-5


-10


-15


-20
-20







41


(a) 350


3 0 0 .............................. ............................... ..................................................................... .................................. .............. .. ...... ... .. .................... .... ... ...... ............. .
300


E 250





E ) 40 --------------................................................. ............ .......-------------------..........-....-.........-......-
.. .-- ---- -...
2 100




.--50
0
C










0)
0 -



0.)























_4------------i ------ "------------i------------* ------i- i---------------i-------
-503





















-20 -15 -10 -5 0 5 10 15 20

error in estimation of attenuation coefficient of sand [%]


Figure 3.6: Error in concentration at 600 mm resulting from error in a,. Symbols and line
patterns are as in Figure 3.4. Different inversion methods are not distinguishable.
(a) Results for uniform concentration profiles;
(b) Results for exponential concentration profiles.
E





4 -








-4
-20 -15 -10 -5 0 5 10 15 20

error in estimation of attenuation coefficient of sand [1]

Figure 3.6: Error in concentration at 600 mm resulting from error in a,. Symbols and line
patterns are as in Figure 3.4. Different inversion methods are not distinguishable.
(a) Results for uniform concentration profiles;
(b) Results for exponential concentration profiles.














CHAPTER 4
IMPLEMENTATION OF ACOUSTIC MEASUREMENT SYSTEM


The attenuation coefficients and system parameter of an acoustic system can be

determined in a laboratory by creating uniform concentration profiles of known values

with specific sand samples. However, the acoustic measurement of concentration profiles

requires a fast sampling rate to accomplish the high resolution in time and space. Besides

that, many of the systems use time varying gains to enhance the ratio of signal to noise

over the measurement range. The result is that the acoustic system is usually loaded with

lots of sophisticated electric components and has a certain degree of system nonlinearities.

These nonlinearities should be removed before any laboratory calibration of laboratory

data or interpretation of field data is done.

In this chapter, an acoustic measurement system which was developed for a field data

collection project is described. The procedure of determining the relationship between the

distance and bin number in profile data is explained. Next, the method of quantification

and elimination of system nonlinearities is developed. Also, the methods of determining

the attenuation coefficients and system parameter are described.



Description of the Measurement System

The acoustic measurement introduced here was developed by the Coastal and

Oceanographic Engineering Department, University of Florida, and deployed at Vilano

Beach, St. Johns County, Florida. The field measurement is described in the next chapter.

The system configuration is shown in figure 4.1. It consists of three parts: acoustic

concentration profiler, underwater package, and shore station.






















Underwater
Shore Station Package

Figure 4.1 Schematic of acoustic measurement system.




Table 4.1: Specifications of Acoustic Concentration Profiler.
Model Simrad Mesotech Model 810
Acoustic pulse Excitation frequency : 5 MHz
Duration : 10 p.sec
Repetition rate : 100 Hz
Time varying gain (dB) 20 log1i (7) +20, r is range in mm
Output signal 455 kHz amplitude modified


The acoustic concentration profiler, Simrad Mesotech Model 810, is a transceiver

which transmits and receives 5 MHz underwater sound. The sound pulse is generated

every one hundredth second. The nominal pulse duration is 10 Psec which corresponds to

7.5 mm of radial dimension of scattered volume. The acoustic energy is scattered back to

the transceiver by the suspended particles and converted into voltage. The voltage is

proportional to the square root of the energy intensity. The profiler employs a time

varying gain which compensates for the spherical spreading of acoustic intensity. The

output from the profiler is 455 kHz of amplitude modified analog signal of which envelope

represents the backscattered acoustic pressure at the transceiver surface. Table 4.1 is a

summary of the specifications. The diameter of the transducer is 0.32 cm. The theoretical











AA A ,ACP AA
SV (TVG)

5 MHz 455 kHz
acoustic wave amplitude
modified




rectified pass \sample data
pasfilter I hold logger
digitized
data

interface board (ensemble
mean & rms)

Figure 4.2 : Sequence of data processing in the acoustic measurement system. ACP
and TVG stand for acoustic concentration profiler and time varying gain, respectively.


near field limit calculated with (3.1) is 10.7 cm. But Hay [1991] found that the actual near

field limit is 10.3 cm.

The underwater package consists of a data logger (Tattletale VI) and an interface

board. The data logger executes the control program, which is loaded in the EPROM, and

stores data digitized by the interface board. The data logger has a 200 Mb hard disk drive.

The interface board rectifies and filters the analog signal from the profiler, and digitizes it

at the sampling rate of 250 kHz, which corresponds to 3 mm of spatial resolution. The

board also processes the digitized signal to get the ensemble mean and ensemble rms.

value before sending it to the data logger. It also controls the time delay between the

firing of a pulse and the beginning of the sampling. The sequence of the data process is

illustrated in fig 4.2.

The shore station has a personal computer, a storage device and a power supply. The

computer communicates via a cable with the data logger in the underwater package. It

monitors the measurement system offloadss the data from the data logger before the hard









upward slope plateau downward slope
width width width






bottom bin



total width


Figure 4.4: General shape of acoustic intensity reflected from the bed.



concentration will result. It is essential to locate the ocean bed accurately and know

where to stop the inversion process in an acoustic intensity profile.

Figure 4.3 shows the experimental setup to measure the return signal reflected from

the bottom. The acoustic concentration profiler is firmly attached to the vertical rod

which is in turn inserted into the center of the steel tripod. The distance from the

transducer surface to the bottom is adjustable. The plastic cylinder was filled with water

so that the transducer surface is submerged. At first, the acoustic intensity reflected from

the plastic bottom was measured. Next, the plastic bottom was covered with a steel plate,

and the reflected intensity was measured. After that, sand was spread evenly at the

bottom in a thick layer, and the intensity was measured. The distance from the transducer

to the bottom was 283 to 290 mm. The distance was increased by 1 mm for each

measurement.

The acoustic intensities reflected from different materials were identical in their

shapes. Figure 4.4 shows the general shape of reflected acoustic intensity profiles. It

consists of an upward slope, a plateau and a downward slope. Table 4.2 is the summary

of the dimensions of the reflected acoustic intensity profiles. The upward slope widths are

































Figure 4.3 Experimental setup to measure the profile of the acoustic intensity reflected
from the bed.



disk drive of the data logger gets full, and saves them on the storage devices. The power

supply is also connected by armored cable to the underwater package. The batteries in the

package are continuously charged.



Location of Bottom Bin in Acoustic Intensity Profile

Once an acoustic measurement system and the inversion method are implemented, we

are almost ready to measure the concentration profile of suspended sediment at a field.

But it is very important to know accurately which bin corresponds to the ocean bed in an

acoustic intensity profile. If it is attempted to invert the acoustic intensity, which was

reflected at the bed, into suspended concentration, profiles of unrealistically high









3 bins with two exceptions of eight. The total widths are 8 bins with only one exception
of eight.


0 20 40 60 80 100


bin number


Figure 4.5: Acoustic intensity profile measured in clear water. The first peak represents
the outgoing pulse. The second one is the reflected pulse from the bottom.


Table 4.2: Jummary of the Profiles of Reflected Acousti .


The numbers in () are the travel time of the acoustic pulse for the correspondent bin
number


Range Total Width Upslope Width Plateau Width Downslope Width
283 mm 8 bins (32 gsec) 3 bins (12 gtsec) 3 bins (12 pisec) 2 bins ( 8 psec)
284 mm 8 bins (32 pisec) 3 bins (12 psec) 3 bins (12 psec) 2 bins ( 8 pisec)
285 mm 9 bins (36 psec) 4 bins (16 ptsec) 2 bins ( 8 psec) 3 bins (12 psec)
286 mm 8 bins (32 psec) 3 bins (12 psec) 2 bins ( 8 gpsec) 3 bins (12 pisec)
287 mm 8 bins (32 psec) 3 bins (12 psec) 3 bins (12 psec) 2 bins ( 8 gpsec)
288 mm 8 bins (32 psec) 4 bins (16 p.sec) 2 bins ( 8 ptsec) 2 bins ( 8 psec)
289 mm 8 bins (32 psec) 3 bins (12 psec) 3 bins (12 psec) 2 bins ( 8 psec)
290 mm 8 bins (32 ptsec) 3 bins (12 plsec) 3 bins (12 pisec) 2 bins ( 8 psec)
Typical
value 8 bins (32 p.sec) 3 bins (12 pisec) 3 bins (12 psec) 2 bins ( 8 ptsec)










The location of the maximum acoustic intensity is random in the plateau. The

variation of the intensity over the plateau is less than 250 bits. However, the upward slope

width is very regular and consistent, and the slope is very sharp. The intensity goes up to

4000 bits from almost zero over a 4 bin wide upward slope. Figure 4.5 shows an example

of the measured acoustic intensity profile. The first peak on the left-hand side represents

the outgoing pulse, the second one on the right-hand side is the reflected pulse from the

bottom.

With the facts presented above, the algorithm of locating the bottom bin in a acoustic

intensity profile is developed. At first, locate the point of maximum acoustic intensity in

the plateau. Next, determine the plateau width by searching for the points which values

differ from the maximum intensity by no more than 300 bits. And then, take the first point

of the plateau width. That is, find the starting point of the plateau and the ending point of

the upward slope. Finally, predict the bottom bin by subtracting the typical upward slope

width, 4 bins, from the starting point of the plateau.


Table 4.3: Comparison of Predicted and Observed Bottom Bins.
Range Observed Bottom Bin Predicted Bottom Bin
283 mm 90 90
284 mm 90 90
285 mm 90 91
286 mm 91 91
287 mm 91 91
288 mm 91 92
289 mm 92 92
290 mm 92 92



In table 4.3, the predicted bottom bins are compared with observed ones. There are

only two mispredictions out of eight. Besides that, the error is only one bin, that is,

approximately 3 mm. This error occurs primarily because the resolution of the experiment

is 1 mm whereas the spatial resolution of the acoustic system is approximately 3 mm. This

acoustic measurement system locates the actual bottom to within 3 mm resolution.










The starting point of the upward slope is the one where the reflected acoustic

intensity begins to affect the backscatter intensity profile. This is the point where the

leading edge of the reflected acoustic pulse coincides with the trailing edge of the

scattered volume (see figure 2.3). If the inversion process is terminated at the starting

point of upward slope, the effect of the bottom return on the acoustic intensity can be

effectively excluded. This means, however, that the points closer than ct/4 to the bottom

are not measured.


Table 4.4: Actual Shape of Outgoing Acoustic Pulse.
Nominal Actual Shape
Pulse Width Total Width Upslope Width Plateau Width Downslope Width
10 sec 32 Psec 6 6tsec 16 tsec 10 gsec


In table 4.4, the actual shape of the transmitted acoustic pulse is summarized. The

455 kHz amplitude modulated output from the acoustic concentration profiler was

measured with an oscilloscope (see figure 4.2). The nominal pulse duration is 10 gpsec,

but the measured duration was 32 ptsec. Therefore, this system actually measures the

suspended concentration at elevations higher than 12 mm above the ocean bed, i.e.,


1 (1.5 x106 mm2)(32 X10-6 sec) =12mm.
4 4



Bin vs. Distance Relationship

The distance between two adjacent data points in a profile, i.e., the spatial resolution

can be estimated with equation (2.19). But the actual resolution and the offset in bin vs.

distance relation should be determined experimentally. The experimental setup is shown in

figure 4.6. A long water tank was used to accommodate the moving target and the

acoustic concentration profiler. The acoustic concentration profiler was placed










underwater in a horizontal orientation. The underwater target plate made of Plexiglas was

mounted on a trolley which moves horizontally over the tank. The acoustic backscattered

intensity was measured with the profiler and recorded on the hard drive of PC, and the

actual distance from the transducer surface to the target surface was accurately measured

with a steel tape measure.




pc ------------- ---
PC
SACP water
------ --.........................

data acquisition
package

Figure 4.6: Experimental setup to measure the bin vs. distance relationship.



The bin number which corresponds to the target surface was determined from the

profile shape of the measured acoustic intensity in the same manner as the bottom bin in

the previous section. The offset and spatial resolution in the bin vs. distance relationship

was determined with a least-square method. However, the bin vs. distance relationship

determined in the clear water should be adjusted in order to be used for sediment

suspension. Since the observed bottom bin in a mixture of sand and water is actually cr/4

above the real bottom due to the effect of the scattered volume, the distance determined in

the clear water must be reduced by that amount, i.e.,

distance = bin number x 6r + offset ct/4 (4.1)

where 5r is the experimentally determined spatial resolution, c is propagation speed of

underwater sound, and t is the actual pulse duration measured. The actual bin vs. distance

relationship of the system implemented in this chapter is


distance [mm] = bin number x 3.0019 mm + 12.8874 mm 12 mm


(4.2)

















5 Mhz continuous wave


5 Mhz
transmitter




clear
water
















5Mhz
AdP


It
I'
I '

I I
I I
I I
I I
I I
I I


I I


Figure 4.7: Experimental setup to measure the system nonlinearity. The function
generator drives the transmitter with a stable 5 MHz continuous wave. The excitation
level is monitored with an oscilloscope. The excitation level is incremented from 0.04 volt
through 10.8 volts. The incoming acoustic intensity is continuously measured by the
acoustic system.









Quantification and Elimination of System Nonlinearity


The acoustic measurement system may have some nonlinearities. The measured

acoustic intensity profiles must be free of the system nonlinearity when used for laboratory

calibration of attenuation coefficients and system parameter, or inversion of field

measurement. The quantification and removal of system nonlinearities is one of the most

essential procedures in the implementation of the inversion algorithm.

The nonlinearity can be analyzed electronically step by step at each analog component

of the system. This is not only time consuming but also can result in accumulation of error

from each analysis step. And the nonlinearities of interest are not those of the individual

components but the total nonlinearities of the system which are involved from the initial

detection and the final digitization ofbackscattered acoustic intensity.


Table 4.6: Input Voltage at the 5 MHz Transmitter
Input Number of Input Number of
Voltage Measurements Voltage Measurements
0.04 V 1 1.20 V 2
0.08 V 1 1.40 V 2
0.12 V 1 1.60 V 2
0.16 V 1 2.00 V 2
0.20 V 1 2.50 V 1
0.25 V 1 3.00 V 4
0.30 V 1 4.00 V 2
0.35 V 1 5.00 V 3
0.40 V 1 6.00 V 2
0.50 V 2 7.00 V 4
0.60 V 2 8.00 V 5
0.70 V 2 9.20 V 1
0.80 V 3 10.00 V 1
1.00 V 3 10.80 V 1


An alternative to quantify the system nonlinearity is the acoustic method. The

experimental setup is shown in Figure (4.7). The 5 MHz acoustic concentration profiler

was put at the bottom of a cylinder facing upward. The cylinder was filled with clean























1000


500


0 100 200 300 400 500 600

bin

Figure 4.8: Response of acoustic measurement system to the incoming continuous
acoustic wave of different intensity. The first peak corresponds to the outgoing pulse
from the system. The second one is the pulse reflected at the air-water interface. Each
curve represents a different input voltage at the transmitter. The input voltage ranges
from 0.04 to 10.8 volts. The higher the input voltage, the steeper the curve.



water. Another 5 MHz transmitter was put near the water surface facing downward. The

transmitter was driven by a stable 5 MHz continuous wave which was generated by a

function generator. The acoustic intensity was measured by the profiler, and digitally

stored on the hard drive of data acquisition package. The measurement was done with

various excitation levels at the transmitter ranging from 0.4 to 10.8 volts. The excitation

level was measured by an oscilloscope. Some of the excitation levels were repeated. The

excitation level and the number of repetitions are summarized in the table 4.6.

The system response to the incoming continuous acoustic wave is shown in figure

4.8. Each curve represents the system response to an input voltage. The steepest curve

corresponds to the response to a 10.8 volt input. The mildest one is the response to a










0.04 volt input. The first and the second peaks are the outgoing pulse from the system

and the incoming pulse reflected at the air-water interface, respectively. The digitized

signal level of the curves increases with the bin number due to the time varying gain. The

signal level was saturated and cut off at bit 4095 because the interface board uses 12 bit

data. The signal level here is proportional to the square root of the measured acoustic

intensity because the transducer detects the acoustic pressure instead of the energy

intensity and converts it into voltage.

There are two nonlinearities observed in figure 4.8. The time-varying gain shows

nonlinear behavior near the saturation level for a given input voltage. Another

nonlinearity is seen at a low bin number. The latter is the more important of the two,

because the inversion of the signal to suspended concentration needs initial condition at a

low bin number. The nonlinearity near the saturation level is not of practical importance

since the system is usually designed to avoid saturation levels under the field condition of

interest.

The quantification and elimination of the system nonlinearity from the data is

equivalent to finding the acoustic intensity, which is originally detected at the surface of

the sensor, from the data digitized by and stored in the system. Therefore, the output

from the system, i.e., the received signal becomes the independent variable, and the input

voltage at the 5 MHz transmitter becomes the dependent variable during the analysis of

the system nonlinearity.

In figure 4.9, the input voltage is plotted against the system output at certain bin

numbers. The symbols, 'o', '+', '*' and 'x', represent the system responses at bin number

40, 60, 80 and 100, respectively. The solid lines are the curve fits of the data at the bin

numbers. Three different types of truncated Laurent series were used. Specifically, two

truncated series with different order were used to fit the data at each bin number between

40 and 58. The coefficients of each truncated Laurent series varies with bin number. The

reason is that the characteristic of the response is varying with bin number both














E

N
I 4





10-
0



0 50 100 150 200 250 300 350 400

digitized system output [bit]

Figure 4.9: Curve fits of the response of the acoustic measurement system at different bin
number. Symbols 'o', '+', '*' and 'x' indicates the system response at bin number 40, 60,
80 and 100, respectively. The solid lines are the curve fits of data with the truncated
Laurent series.



qualitatively and quantitatively as shown in figure 4.9. The following equations are the

three types of truncated Laurent series used in the curve fit,


Cl,bVout,b +C0,b +-,bVoutb ,for Vo,b
Vin,b Cl,Vou,b C,b C1,bVout,b 2,bVoutb ,fr Vout,b switch,b, b <8 (4.3)
C3,bVo3utb +C2,bVout.b +1,bVou,,b +COb +C-1bVoutb +C-2,b Vob ,for b >59


where Vi is the input voltage at the 5 MHz transmitter, Vout is the output from the system,

and Vswitch is the output value at which the power series should be switched to the other.

The second subscript 'b' indicates the bin number. The values of Vswitch are listed in table

4.7.
























The original data, before the correction by the equation above, was amplified with the

time varying gain by the system. As listed in the table 4.1, the time-varying gain

compensates the spreading loss of the acoustic energy. The effect of the time-varying gain

is equivalent to multiplying the measured intensity with the distance squared and a
constant as in the following equation,


Iu, (r) r
101og10I =201og1o +20
I(r) 7

Io(r) = 10 r2i(r) (4.4)
49

where I(r) and Iout(r) are the measured acoustic intensities before the time-varying gain and

the final output of the system after the gain, respectively. By substituting equation (4.4)

into (2.18), and using the fact that Iout is proportional to Vout squared, we get the following

equation,


V2 (r) =AC (r)exp[ -4a wr -f 4aC(r')dr, (4.5)


If the concentration is uniform, then the equation above can be rewritten as followings


Table 4.7: Vswitch Values
Bin Number Vswith Bin Number Vswitch
40 123 50 203
41 132 51 212
42 137 52 220
43 146 53 231
44 153 54 241
45 162 55 250
46 170 56 258
47 177 57 266
48 187 58 276
49 195__

































150 200 250 300 350 400

distance from the transducer, mm

Figure 4.10: Semilogarithmic plot of system output voltage before the
system nonlinearity. The concentrations are uniform, 20 mg/l to 20 g/l.
amplified with time-varying gain.


VO2(r) =ACexp[-4(ai, -a,C)r]


1
In V(r) =-In AC -2(a,, +aC)r
2


450



elimination of
The output is


(4.6)


(4.7)


Therefore, when the concentration is uniform, the system output after the time-varying

gain must be represented by lines of different slopes, decreasing with distance in a

semilogarithmic scale if there is no system nonlinearity present.

Figure 4.10 shows the actual output of the system with uniform concentrations. The

concentration range is from 20 mg/1 to 20 g/1. The method of creating the uniform

concentration is explained in detail in the next section entitled "calibration." As shown in


I I


~C= =............. --------- ---------_;~ _
.. ...... -----------





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

























1Q4 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ .... --- ---- i -------- -------- 1 ---- --------

104
150 200 250 300 350 400 450
distance from the transducer, mm

Figure 4.11: Semilogarithmic plot of corrected voltage after the reduction of system
nonlinearity. The concentrations are uniform, 20 mg/l to 20 g/l. The corrected voltage,
Vi, was multiplied with distance from the transducer because the time-varying gain was
also removed during the elimination of the nonlinearities.



the figure, many of the curves are not straight. Some of them are even increasing with

distance at the beginning. There are surely system nonlinearities involved.

The data after the correction by equation (4.3) is not only reduced in the system

nonlinearity but also deprived of the time-varying gain because the equation finds the

values before the time-varying gain. But the ratio of signal to noise enhanced by the time-

varying gain is kept intact during any digital processing. The corrected value, V1i, was

multiplied by distance and plotted against the distance from the transducer in a

semilogarithmic scale in figure 4.11. All the plots now become nearly linear, decreasing

with distance. The system nonlinearities were almost eliminated from the original data.

The output from the acoustic measurement system should be corrected to be free of









system nonlinearities before being used for calibration or inversion. The method

developed in this section works satisfactorily.


Calibration

The attenuation coefficients, as and aw can be determined with uniform concentration

created in the laboratory. Figure 4.12 shows the calibration facility. The facility consists

of a cylinder and a circulating system. The cylinder is made of Plexiglas, and has four jet

holes on the wall at its top, and a funnel at its bottom. The circulating system consists of a

centrifugal pump, circulation tube and four jets. The pump circulates the sand-water

mixture to create as uniform a sand concentration in the cylinder as possible. The jets help

make the concentration more uniform. The funnel prevents the sand from accumulating at

the bottom. The acoustic concentration profiler is put on the top of the cylinder. The

transducer is just below the water surface and just above the water jet holes. The data

acquisition package and a PC are connected to the profiler.

The total volume of water in the cylinder and the circulating system is 44.33 liters.

The water temperature was 22 C. Sand was sampled from the location of instruments.

The description of the site and the characteristics of the sand are presented in Chapter 5.

The sand is dried and sifted from shell fraction with a number 20 sieve. The dried and

sifted sand is weighed and added to water while the circulating system is running. The

uniform concentrations are created from low to high. The mixture is circulated at least for

5 minutes and then measured by the profiler for 2 to 4 minutes at each concentration.
The pulse repetition rate is 100 Hz and the sampling starts 20 Ptsec after the

transmission of the pulse. The profiles are ensemble averaged for 2 seconds. The data

acquisition system stores ensemble means and ensemble rms. values. The ensemble rms.

values are used to calibrate the system. The reason for that is the acoustic system

measures the pressure wave but the concentration of suspended sediment at a certain































Pump

Figure 4.12: Schematic of calibration tank.



distance is proportional to the pressure squared. The rms. of the rms. profiles is taken to

reduce the profiles into one profile for each concentration. The profile shapes measured

are shown in figure 4.10. They are affected by the system nonlinearities.

The system nonlinearities are removed from each profile as explained in the previous

section. The corrected profiles are shown in figure 4.11. The corrected profiles in the

figure were multiplied by distance. The corrected profiles multiplied by distance can be fit

by straight lines in semilogarithmic scale as described by the equation (4.8).


InV(r) =A, -A2r (4.8)


where
A1 =-lnAC and A2 =2(a, +a,C)
2










The attenuation coefficients, aw and a, are found from the slopes of the straight lines,

A2's. The concentrations used to find the attenuation coefficients are 40 to 3500 mg/l.

For high concentrations, only part of each profile is used because the signal drops rapidly

to noise level due to scattering.


Table 4.8: Summary of the Calibration Data
Input Number of rms. First Bin Last Bin Slope by Least
Concentration Profiles to be Number Number Square Fit:
(mg/1) averaged -2(aw+asC)
40 41 35 400 -0.001019
80 60 35 400 -0.001085
160 51 35 400 -0.001299
250 60 35 400 -0.001509
500 120 35 400 -0.002117
1000 70 35 400 -0.003205
1500 70 35 310 -0.004185
2000 70 35 270 -0.005110
2500 80 35 250 -0.006063
3000 51 35 210 -0.006804
3500 70 35 205 -0.007489



In table 4.8, the number of rms. profiles, and the first and the last bin numbers are

listed, which are used to find the slope by least-square fit for each concentration. The first

bin number is set to 35 which is located just outside the near field limit. The last bin is the

point where the signal drops to noise level. In figure 4.13, The values of A2 are plotted

against the input concentrations, Ciput. The solid line is the least-square fit of A2'S. The

slope of the line is the attenuation coefficient due to scattering by suspended particle, as.

The intercept of the line on the vertical axis is the attenuation coefficient due to absorption

by water, aw.

The calibrated coefficient, aw, is compared with the value given by the equation

(2.10). The value by the calibration is 5.434x10"4 Nepers/mm, and the one by the

equation is 5.689x10"4 Nepers/mm with the water temperature 22 oC. The prediction









x10-3
8
A2 = 2*(ALPHAw + ALPHAs*C)
7 .............. ALPHA ..=-5.434070e-04 Nepers/m m ..............................
ALPHAi = 9.611361e-07 Nepers/mm/(mg/I)
..... .. .. ... .................. ...................... ...... ..................................... .........










1 ..............--......... -.. -..................-........ -.....--- -------...---- -I---------------.....-.... -........-.-.-.---------- ---------------.....................

1 IS
0 500 1000 1500 2000 2500 3000 3500

Cinput [mg/I]

Figure 4.13: Determination of attenuation coefficients, a, and a,. The asterisks represent
the A2 values by equation (4.8). The solid line is the least-square fit of the data. The
intercept on the vertical axis and the slope of the solid line correspond to aw and as,
respectively.

error of the equation is 4.7 %. The value by the calibration is not actually used in field

measurements because the water temperature at the field is different from that of

laboratory experiments. Instead, equation (2.10) is used. The prediction error by the

equation may be smaller than 4.7 % because the water temperature was changing slightly

due to the heat flux from the pump during the experiment.

The calibrated coefficient, a,, is compared with the value given by the formula of

Sheng and Hay [1988] to see if the calibrated value is in a reasonable range. They

suggested the following formula for the attenuation coefficient, as, under the assumption

of spherical particles,










x 0-7


2.5



2

csas
1.5


1I


0 1


2 3 4 5 6 7 8 9


Ka.


Figure 4.14: Comparison of attenuation coefficient, a,, by experiment with model result
based on the assumption of spherical particles. The model is described by equation (4.9).


(4.9)


0.1771(ka,)4 0.002 65
1, -+0.2361(ka,)4 (ka,)2 1000 +0.001.65
\ ~/ J2.65)


where as is the particle radius, and k is the acoustic wave number. The last factor in the

right hand side of the equation above is the conversion factor from volumetric

concentration to mg/l unit. The unit of cca, is Nepers/(mg/l).

The value of as by the calibration is 9.611x10"7 Nepers/mm/(mg/l), and the one by

equation (4.9) is 1.068x10-7 Nepers/mm/(mg/l) with the median grain radius, a,=0.144

mm. The value under the assumption of spherical particles is 11. 1 % larger than the one

by the experiment. The calibrated coefficient is in a reasonable range compared with the


-


...................... ------ ----- -----



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



. . . . . . .



. . . . . . ------------------- . .



. . . . . . . - - - - -


Sheng & Hay t1988]
- Vitano sand (Seng & Hay model) ................
a Vilano sand (experiment)

I I I I I






64

x1013 bin #35-40
2.5


A (by least square fit) = 6.895446e+09
2 .



1.5

ACinput




0.5



0 500 1000 1500 2000 2500 3000 3500

input concentration, Cinput [mg/I]

Figure 4.15: Calculation of system parameter. The symbol '+' represents the ACmput
values calculated by equation (4.10). The solid line is the least-square fit of the data. The
slope of the solid line is the system parameter, A.



existing formula. In figure 4.14, the formula of Sheng and Hay [1988] is plotted in

comparison with the calibrated ocas.

The system parameter is calculated with equation (3.2) and the calibrated values of aw

and as. The equation can be rewritten as followings,


AC,,,, =rVexp[ 4(a, +a,Cu,,)r] (4.10)


where Ciput is the known uniform concentration created in the calibration cylinder. The

ACinput values are calculated for Cinput values of 40 to 3500 mg/1 and from bin number 35

to 40. The input concentrations are the same as those in table 4.8. In figure 4.15, the

ACinput values are plotted against Cinput. The symbol '+' represents the ACiput values










calculated with equation (4.10). The solid line is the least-square fit of the data. The

slope of the solid line is the system parameter. Its value is A=6.895x 109.

The concentrations at bin numbers 35 and 40 are calculated with the calibration

constants A, aw and a, and compared with the input concentrations. The concentrations

are calculated by the iteration method with the equation (3.2). The results are shown in

figure 4.16. The dashed lines represents Coalculated = Ciput. The solid lines are the

calculation results based on the calibration of the parameters. They reproduce the input

concentration very well.

Table 4.9 is the summary of the calibration of the parameters. The parameter, aw, is

only valid for the water temperature during the calibration, which was 22 C. The value

aw for the inversion of the field data should be calculated by equation (2.10) with the

water temperature measured at the field. The 'digitized intensity level' in the unit of the

parameter, A, is the square of the digitized level of the output voltage of the measurement

system. But in this table, the meaning of the digitized level is different because the

digitized signal was processed during the elimination of the system nonlinearity.
















Table 4.9: Summary of the Calibration Parameters.
Parameter Calibrated Value Unit
aw_ 5.434x10-4 Nepers/mm
s, 9.611 x 107 Nepers/mm/(mg/l)
A 6.895xl09 digitized intensity level. mm2/(mg/l)


































0 500 1000 1500 2000 2500 3000


3500


3000


2500


2000


1500


1000


500


0 500 1000 1500 2000 2500 3000 3500

C input [mg/I]

Figure 4.16: Comparison of the calculated concentrations and input concentrations.
Equation (3.2) and the calibration parameters in table 4.9 were used to calculate the
concentration. The dashed lines represent CinputCcalculated. The solid lines represent the
calculation
(a) Comparison at bin number 35
(b) Comparison at bin number 40.


. ................... .......................... ................. .. ..... ........... -- -------- --------... ..................;... .......... ........ ... ...





. .................. ................ ------------....................; ................... ..................... ........... .


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


3500














CHAPTER 5
FIELD MEASUREMENTS


The concentration of suspended sediment and the relevant physical quantities were

measured in the nearshore zone of Vilano Beach, St. Johns County, Florida from March

22 to April 9, 1992. The objective of the measurements is to obtain comprehensive sets of

data on the small scale mechanisms of sediment suspension under a variety of combined

wave and current conditions. The acoustic measurement system implemented in the

previous chapter and other instruments including an electromagnetic current meter, a

pressure sensor, a pore pressure sensor, and two optical backscatterance (OBS) sensors

were deployed.

In this chapter, a description of the site is given. The measurement system and the

instruments are also described along with the measurements taken. The methods of

finding irregular wave velocity near the bed and the primary wave direction are suggested.

Also the analyses of the characteristics of the bed material are presented.


Site


General Description of the Site

The measurement site is accessed by state road A1A. The road runs parallel to the

coast line. The beach is on the long, narrow spit which is surrounded by Atlantic Ocean to

the east, Intracoastal Waterway to the west, and St. Augustine Inlet to the south. There

are many houses on the sand dune. The sand dune is well-developed and has a height of

approximately 3 m. The face of the dune is well covered with vegetation. The beach is

accessible by car. The area is a good place for recreational activities. There is no shore






68


Shoreline N



Instrument
frame

Beach

Primary wave direction


Longshore current


Figure 5.1: Orientation of shoreline longshoree current, wave and instrument frame. The
orientation of the shoreline and the cross bar of the instrument frame are approximately
21 0 and 28 counterclockwise from north, respectively. See figure 5.5 for the details of
the instrument frame.



protection structure or littoral barrier at the site. The orientation of the shoreline is

approximately 21 0 counterclockwise from the north (see figure 5.1). The beach material

contains 1 to 2 % shell fraction by weight. There are well-developed beach cusps on the

beach face with a 20 to 30 m regular spacing.

The primary direction of incident waves was from the northeast during the

experiment. The rms. wave height ranges approximately from 0.4 m for calm conditions

to 1.2 m for rough conditions. The direction of longshore current was mainly from north

to south during the field measurement. The tide is semi-diurnal. Its range is

approximately 1.4 m. The current magnitude was 0.1 to 1.4 m/sec. There was no rip

current observed at the site during the measurement. The water temperature was

approximately 16 to 19 "C. The visibility near the instruments was less than 3 m.

Beach Profile

The profile of the site consists of a sand dune, a narrow berm, a fairly steep beach

face and an offshore bar. The figure 5.2 is the plot of beach profile. The profile was










5,~--~-- i ---- ---- --- i --- i --- i ------- i------.- i-- --|
4 .. ......................... .-... ......... .... ...... .... ........ ........... ............... ... .............. ..................... ..... ............... ........ .. ............ ......... .... ...... ...............
5 r







-2


Instrume ts
-3

-4
0 20 40 60 80 100 120 140 160 180 200

distance from bench mark [m]


Figure 5.2: Beach profile. The distance was measured from the bench mark at the bottom
of the stair of the beach house which corresponds to the foot of the sand dune.



surveyed from the foot of the sand dune to the location of the instrument on April 10,

1992. The distance was measured from the bench mark at the foot of the sand dune.

There is a 10 m wide berm at the foot of the sand dune. The berm is covered with

vegetation. The beach face is fairly steep. The average slope over the distance from the

offshore end of the berm and the deepest point before the offshore bar is 5.9 %. The

offshore bar is located just outside the surf zone.

Eight screw anchors and two wooden stakes were installed in a straight line between

the berm to the offshore bar. The elevation was measured at and between the stakes and

the screw anchors with a level and a staff. The distance was measured with a range finder.

The survey data are summarized in table 5.1. The bench mark at the stair of the beach

house corresponds to the foot of the sand dune.















.Table 5.1: Profile Survey Data
Distance [m] NGVD [m] Remark
0.00 4.068 Bench mark at the stair of the beach house
8.27 4.308
10.97 3.503
15.77 2.758 Wooden stake #1
22.02 1.728 Wooden stake #2
26.67 1.288
31.97 0.898
36.37 0.568
40.37 0.338
44.62 0.158
48.82 -0.002
54.87 -0.222
58.87 -0.392
62.17 -0.552 Water line 9:20,4/10/92
65.77 -0.662 Screw anchor #1(bottom)
75.97 -1.182 Screw anchor #2(bottom)
83.67 -1.642 Screw anchor #3(bottom)
94.37 -1.872
103.97 -1.992
108.37 -1.672 Screw anchor #4(bottom)
121.37 -1.292 Screw anchor #5(bottom)
128.87 -1.442 Screw anchor #6(bottom)
139.37 -1.812 Screw anchor #7(bottom)
145.87 -2.022 Screw anchor #8(bottom)
149.07 -2.162
155.47 -2.402
167.37 -2.722
179.17 -3.072
194.77 -3.272









shore station

vegetation power &
communication
cable






instruments &
data logger

Figure 5.3: General setting of the measurement site.





Measurement System


Configuration of the System

The instruments were deployed at the offshore slope of the offshore bar as shown in

figure 5.3. The distance of the instruments from the bench mark was 192.8 m. The water

depth at the instruments was approximately 2.6 to 4.0 m. They were supplied with power

and controlled through cables from the shore station. The station was installed at a beach

house on the sand dune. The length of the cables was approximately 300 m. The

measurement was continuous except when the data were offloaded.

Figure 5.4 shows the overall configuration of the field measurement system. The

configuration is exactly the same as the one in figure 4.1 except for the additional

instruments which are directly connected to the data logger, Tattletale VI. One pressure

sensor, one pore pressure sensor, one electromagnetic current meter (EMCM) and two

OBS sensors were added to the acoustic measurement system which was developed in

Chapter 4. The additional sensors are synchronized with the acoustic concentration

profiler (ACP).









Shore Station


Underwater
Package


Sensors


Figure 5.4: Schematic of field measurement system.


The software in the data logger controls the ACP through the interface board and the

other instruments directly. The analog signal from the ACP is digitized by the interface

board (see figure 4.2). The signals from the other instruments are digitized by the data

logger, Tattletale VI. The channels assigned to the instruments are listed in table 5.2.


Table 5.2: Assignment of Channels in Data Logger, Tattletale VI.
Channel Instrument
0 Pore Pressure Sensor (High Resolution)
1 Pressure Sensor
2 EMCM (Longshore Direction)
3 EMCM (Cross-shore Direction)
4 OBS Sensor (Serial # 053)
5 OBS Sensor (Serial # 057)
6 Battery Voltage
7 Pore Pressure Sensor (Low Resolution)
Note: The signal from one pore pressure sensor is digitized on two channels with different
gains.


The continuous measurements are divided and stored into consecutive data files. The

size of one data file is limited to 1 Mb. The software generates the file identifier, and

names the data files with it automatically. The digitized data, its file identifier, and the

start time and end time are stored together in a data file on the hard drive of the data










logger. All the instruments and the data logger are powered by rechargeable batteries.

The batteries are charged continuously through the cable from the shore station. The

voltage of the batteries is monitored at the shore station.

All the measurement activities are monitored and controlled through the PC at the

shore station. The software in the data logger stops and resumes running according to

commands from the PC. The data files stored on the hard drive of the data logger are

offloaded to the magneto-optical disk, which is connected to the PC at the shore station,

once or twice a day before the hard drive becomes full.

Instruments

The ACP is the Simrad Mesotech Model 810. The specifications and the calibration

parameters of the ACP are listed in Tables 4.1 and 4.9, respectively. The bin vs. distance

relationship is described by equation (4.2). The dimension of the instrument is 89 mm

square and 203 mm long. Its submerged weight is 1.2 kg.

The EMCM is the Marsh-McBirney Model OEM521. It mainly consists of an AC

electromagnet within a 1.5 inch ball and two pairs of electrodes. The water flowing past

the ball interacts with the magnetic field generated by the magnet, and produces a voltage

that is proportional to the velocity of the water. The two pairs of electrodes detect the
voltage and resolve the velocity vector into two components.
The OBS sensor is the D & A Instrument Co.'s Model OBS-3. This sensor consists

of a high intensity infrared emitting diode (IRED), a detector (four photo diodes), and a

linear, solid state temperature transducer. The IRED produces a beam with half-power

points at 50 o in the axial plane of the sensor and 50 o in the radial plane. The detector

integrates IR scattered between 140 o and 160 o. The integrated intensity is linearly

proportional to the sediment concentration in the vicinity of the sensor. This sensor

measures the time series of sediment concentration at one level. The nominal

measurement range is 2 mg/1 to 100 g/1 of sand, and 0.1 mg/1 to 5 g/1 of mud. The










diameter and length of the instrument is 31 mm and 180 mm, respectively. Its submerged

weight is 70 g.

The pressure sensor is the Trans Metrics P21. It is a bonded strain gauge type. It

measures absolute pressure. The bonded strain gage transducer measures the pressure by

introducing a fluid into a low volume chamber where it acts against a diaphragm. The

stress of the fluid against the diaphragm causes a resistance change in strain gages located

on the opposite side of the diaphragm. The resistance change is proportional to the

applied pressure.

The pore pressure sensor is Druck's miniature pore water pressure transducer type

PDCR 81. It is a wet-dry differential pressure gauge with a porous ceramic filter plate at

the wet end to resist the effective stress of bed soil. The wet end is exposed to bed soil

and the dry end is kept dry in the housing. A back pressure is established by compressing

the dry air in an underwater housing with a miniature latex balloon, which is installed

inside the housing and inflated by hydrostatic water pressure. The strain of the diaphragm

caused by the difference in pressure between the ends is detected by strain gauges. The

measurement range is 5 psi. The signal from the transducer is amplified with two different

gains. The measurement resolution is 0.7 mm of water at channel 7 and 0.14 mm of water

at channel 0. The diameter of the wet end is 0.256 inch.

Underwater Installation of the Instruments

The frame and mountings for the instruments are shown in figure 5.5. They are made

of stainless steel and aluminum. Several things were taken into consideration during the

design and installation of the frame and the mountings. The frame should be stiff enough

to withstand extreme flow conditions. The flow condition and ocean bed must be

disturbed as little as possible by the instruments or the frame. All the instruments should

be adjustable to be aligned in a vertical line as much as possible. This ensures that the

instruments are in the same phase of the wave motion. But the instruments must be out of










the beam width of the ACP. Underwater installation and removal of the frame and the

instruments should be easy.


cross bar


data
acquisition
packsge


Figure 5.5: Underwater deployment of the instruments. (April 1, 1992)
(a) Plan view.
(b) Front view. Seen toward the ocean from the shore.










The following features were implemented to accommodate the requirements above.

Three vertical stainless steel posts were water-jetted 6 feet into the bed. Each post has

three triangular wings at their bottom ends for security and easy jetting. The three posts

were connected with two cross bars and universal joints, the one below the bed and the

other at top of the posts. The three posts were not aligned. This helped withstand the

back and forth motion of waves. All the mountings and clamps for the instruments were

given as many degrees of freedom as possible. All the instruments were hung from the

cross bar to avoid local scouring of the bed. The ACP was attached to the cross bar

facing downward. The EMCM was put on the ACP mounting. The other instruments

were mounted on a vertical telescopic pipe which was attached to the crossbar. The

telescopic pipe was approximately 30 cm away from the axis of the acoustic beam of ACP.

Therefore the measurement field was almost undisturbed by the frame or instruments. The

data acquisition package was also buried below the bed to minimize the disturbance. The

pore pressure sensor was installed on a separate stainless steel pipe jetted below the bed.


Table 5.3: Elevation of Instruments above Bed.
Instrument Elevation above Bed
EMCM 57 inches
ACP 40 inches
OBS Sensor (Serial # 053) 32 inches
Pressure Sensor 29 inches
OBS Sensor (Serial # 057) 12 inches
Note: Measured on April 1, 1992.


The orientation of the cross bar was 28 0 counterclockwise from the north as shown

in figure 5.1. The elevations of the instruments above the bed are listed in table 5.3 They

were measured on April 1, 1992. The elevations are not constant because the bed location

changes due to erosion or deposition; however, the relative distances among the

instruments are constant. The instantaneous elevation of the ACP can be found as

explained in the section entitled "Location of Bottom Bin in Acoustic Intensity Profile" in













seperator

serial number of measurement
burst

'm' for ACP
's' for the other instruments

start hour of the particular
continuous measurement

date

'a' for April
'm' for March





Figure 5.6: File name convention



Chapter 4. The instantaneous elevation of the other instruments are found with that of the

ACP and the relative distances. The pore pressure sensor was buried approximately 6

inches below the bed surface. During the first week the pore pressure was not deployed.

The data acquisition package was buried under the bed on April 1, 1992. It was on the

bed before that date.



Data File


The continuous measurement is divided into consecutive measurement bursts which

size are limited to 1 Mb. Each measurement burst consists of two files: one for ACP data

and one for the other instruments. The ACP data file contains the ensemble mean and the

ensemble rms. value of acoustic intensity profile. The data file of the other instruments










contains the time series of the pressure, the pore pressure with two different resolutions,

the OBS intensity at two elevations, and the 2 horizontal components of fluid velocity.

The file name convention is illustrated in figure 5.6 The first letter denotes the month,

"a" for April and "m" for March. The next two digits indicate the date. The following

two digits represent the starting hour of the particular continuous measurement. The

following letter indicates the instruments, "m" for ACP and "s" for the other instruments.

The last two digits correspond to the serial number of the measurement burst. The

extension of the files is always "mat" which means the file is in Matlab format.



Bed Location and Concentration Profile of Suspended Sediment


The bed location and the concentration of suspended sediment are found with the

ACP data as explained in Chapter 4. The ensemble rms. values of the acoustic intensity

profiles are used to obtain them. The spatial resolution is 3.0019 mm. The temporal

resolution is 1 sec to 1 min. The number of the data points per an acoustic intensity

profile is 310 to 512.

The procedure of data processing is as the follows. The instantaneous distance

between the ACP and the bed is found with the raw rms. data. Then, the raw data are

corrected with equation (4.3) to eliminate the system nonlinearities. The near field

concentration is calculated at bin number 40 with an iterative solution to equation (3.2).

The corrected acoustic intensity profile is inverted into the concentration profile of the

suspended sediment with the direct method described in equation (3.12). The ACP files

are summarized in table 5.4. The exact same sets of files exist for the data of the other

instruments.













Table 5.4: ACP data files.
Deployment Average Data Files Filename
Points
per
Profile
1 sec 512 21 m2212m03-12, m2215m13
points m2216m14-23
400 50 m2517m92-21, m2613m22-41
Package 380 30 m2506m62-91
on the seabed 360 20 m2411m35-54
5 sec 380 5 m2560m57-61
Without 15 sec 360 2 m2416m55-56
pore pressure sensor 350 1 m2311m27
340 6 m2318m29, m2320m30-34
310 1 m2314m28
30 sec 380 1 m2218m24
350 2 m2222m25-26
1 sec 400 90 m2807m51-70, m2921m01-30
Package ___ m3021m33-72
on the seabed 15 sec 400 21 m2712m43-46, m2722m47-50
m2816m71-73, m2822m74-77
With m3017m31-32, m3109m73-74
pore pressure sensor ___ m3115m75-76
30 sec 400 2 m2908m78-79
1 sec 400 31 a0120m79, a0208m80-09
380 90 a0508m41-60, a0513m61-00
Package buried ___ a0612m01-30
beneath the seabed 350 20 a0310m14-33
5 sec 380 5 a0714m31-35
10 sec 380 7 a0608m01-03, a0814m38-41
With 15 sec 400 5 a0111m78, a0223m10-13
pore pressure sensor 380 19 a0807m36-39, a0900m42-56
60 sec 380 7 a0320m34-39, a0416m40
total number of files __436_
Note: The data files of the other instrument are exactly the same as the ACP files in the
above table.









Tides and Waves


The tide or mean water depth is found by converting the time mean pressure to the

height of the water column. The gain and the offset are 8.327x10-3 and -10.77,

respectively. The unit of the calibrated quantity is meters of water. The mean water depth

is


S_ (5.1)
P9
pg


where p/pg is the instantaneous value of the calibrated pressure data, and the overbar

denotes the time mean. The distance of the pressure sensor above the bed, z = Zp, is

determined by the instantaneous elevation of the ACP above the bed and the relative

distance of the pressure sensor from the ACP, which is available in table 5.3. The vertical

coordinate is positive upward from the bed.

The displacement of the water surface due to the wave motion, 1, is found by linear

wave theory.


_p-p coshkh (5.2)
pg cosh(kzl




Fluid Velocity


Current and Wave Velocities

The current velocity is the time mean of the time series of the calibrated EMCM data.

The difference between the calculated current velocity and the time series of the calibrated

data corresponds to the time series of the wave velocity.


(5.3)


u(z" 0 ='U(z,) Ffi(z,,t); V(Z"Ot ==V(Z') +(Z,,j)










where u and v denote the cross- and longshore components of the calibrated fluid velocity,

respectively. The elevation of the EMCM, z,, is found in the same manner as that of

pressure sensor, zp. The overbar and the tilde indicate the time mean and oscillating

components of the fluid velocities, respectively.

The unit of the calibrated quantities is m/sec. The gain and offset are 1.861x10-3 and

-3.81, respectively. The positive directions of the longshore and the cross-shore

components of the calibrated EMCM data are 28 and 118 counterclockwise from the

north, respectively.

Irregular Wave Velocity Near the Bed

The wave velocity near the bed can be calculated with the wave velocity at z = zc by

using linear wave theory. If the wave motion is monochromatic sinusoidal, then the free

stream wave velocity near the bed is


(O,) i(zt) (z ,t) (5.4)
iu(O,t) ; (0,t) =
cosh kz' cosh kze


The irregular wave motion must be decomposed into sinusoidal components before

the equation is applied to it. This task can be done by using FFT and inverse FFT. Figure

5.7 illustrates the procedure. At first, the time series of the wave velocity at the elevation

of the EMCM is transformed by FFT into the quantity on the frequency domain.


U(z,w) =FFT(i(ze,t)}; V(zw) =FFT({(z,,t)} (5.5)


where U and V are complex quantities.

The wave number of each frequency component is calculated with the dispersion

relationship. The quantity near the bed on the frequency domain is found with equation

(5.6),




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