UFL/COELTR104
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 researchrelated 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
lunchbreak 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 bestintown cookies.
I owe Mr. WooChoong 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
StateoftheArt 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 ConvectionDiffusion 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 semiexcursion 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 fi
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 wavecurrent 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 wavecurrent 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 zerocrossing 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 wavecurrent 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 convectiondiffusion model is developed using a timeinvariant, 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.
StateoftheArt 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 oneline 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, crossshore 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 timeinvariant 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 ks 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. Homma 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 longtime, unresolved questions. Komar [1978] suggested that bed
load transport was dominant in his study on longshore transport using dyedsand 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 quasisteady
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 Homma and Horikawa [1963]. The timevarying concentration
profiles using that model were calculated later by Homma et al. [1965]. Fredsoe et al
[1985] developed a combined wavecurrent model using eddy viscosity varying in time
and space. Their application was limited to codirectional flow over a flat bed.
Wikramanayake [1993] suggested a suspended sediment model using timeinvariant 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
ks 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
convectiondiffusion 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 convectiondiffusion 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) 11i 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 t8)
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 x102T2 3.84 X104T3) X103f2 (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
101
102
101 100 101 102
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(A1OJ
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'
= rcT/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/cT/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' = rcr/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/cc/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' = rcT/2 and r' = r. The leading edge of a backscattered
acoustic pulse coming from r' = rcT/2 will arrive at the transducer at t = 2r/cT. The
backscatter acoustic intensity of the particle at r' = rct/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' = rcT/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' = rcT/2.
(a)
at t=r/cT/2
at t=r/c
(b)
at r'=rcT/2
at r'=r
(c)
from
r'=rcT/2
from r'=r
r'=rct/2 r'=r
t=r/cT/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/cT 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' = rct/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/kth 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 Cj1, rj, rj1, 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,)]
110 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 Bernoullitype 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.=,+,(GtG,_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 104 Nepers/mm and 8.17 x 107 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(r600)] mg/1, 0
e2 C(r)=500exp[0.02(r600)] mg/1, 0
e3 C(r)= 1000exp[0.02(r600)] 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 i486based 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 123600
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 e5 % (3.5)
successive 0.27 sec 2.0 e2 % (3.6)
direct 0.04 sec 7.5 e5 % (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 106 1_06 1 10 1_10
u2 1.77 1_77 2_86 2_86
u3 273 2_73 20.01 2001
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
01  =b  I   l B  II 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.)
_4i  "i* i ii
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 lefthand side represents
the outgoing pulse, the second one on the righthand 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 X106 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 leastsquare 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 airwater 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 airwater 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 timevarying 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 +C1bVoutb +C2,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 timevarying gain
compensates the spreading loss of the acoustic energy. The effect of the timevarying 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 timevarying 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 timevarying 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 timevarying
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 timevarying 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 timevarying gain because the equation finds the
values before the timevarying 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 sandwater
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 leastsquare 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 leastsquare 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
x103
8
A2 = 2*(ALPHAw + ALPHAs*C)
7 .............. ALPHA ..=5.434070e04 Nepers/m m ..............................
ALPHAi = 9.611361e07 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 leastsquare 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 07
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 1.068x107 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 #3540
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 leastsquare 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 leastsquare 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_ 5.434x104 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 welldeveloped 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 welldeveloped 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 semidiurnal. 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 (Crossshore 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 magnetooptical 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 MarshMcBirney 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 OBS3. 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 halfpower
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 wetdry 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 waterjetted 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 m2212m0312, m2215m13
points m2216m1423
400 50 m2517m9221, m2613m2241
Package 380 30 m2506m6291
on the seabed 360 20 m2411m3554
5 sec 380 5 m2560m5761
Without 15 sec 360 2 m2416m5556
pore pressure sensor 350 1 m2311m27
340 6 m2318m29, m2320m3034
310 1 m2314m28
30 sec 380 1 m2218m24
350 2 m2222m2526
1 sec 400 90 m2807m5170, m2921m0130
Package ___ m3021m3372
on the seabed 15 sec 400 21 m2712m4346, m2722m4750
m2816m7173, m2822m7477
With m3017m3132, m3109m7374
pore pressure sensor ___ m3115m7576
30 sec 400 2 m2908m7879
1 sec 400 31 a0120m79, a0208m8009
380 90 a0508m4160, a0513m6100
Package buried ___ a0612m0130
beneath the seabed 350 20 a0310m1433
5 sec 380 5 a0714m3135
10 sec 380 7 a0608m0103, a0814m3841
With 15 sec 400 5 a0111m78, a0223m1013
pore pressure sensor 380 19 a0807m3639, a0900m4256
60 sec 380 7 a0320m3439, 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 8.327x103 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.
_pp 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 1.861x103 and
3.81, respectively. The positive directions of the longshore and the crossshore
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),
