UFL/COELTR/116
DEVELOPMENT AND FIELD APPLICATION OF A
LITTORAL PROCESSES MONITORING SYSTEM FOR
EXAMINATION OF THE RELEVANT TIME SCALES OF
SEDIMENT SUSPENSION PROCESSES
by
Eric D. Thosteson
Dissertation
1997
DEVELOPMENT AND FIELD APPLICATION OF A LITTORAL PROCESSES
MONITORING SYSTEM FOR EXAMINATION OF THE RELEVANT TIME
SCALES OF SEDIMENT SUSPENSION PROCESSES
By
ERIC D. THOSTESON
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
1997
In loving memory of
H. Dale Henderson and Lois W. Heaster.
ACKNOWLEDGMENTS
To the Coastal Sciences Program of the US Office of Naval Research, I wish to
express my appreciation for providing the financial support for this research. For their
unique ability to teach the practical aspects of coastal engineering on a day to day basis
despite neverending demands, constant criticism, and meager rewards, I wish to thank
Sidney Schofield, Chuck Broward, Vernon Sparkman, Victor Adams, and Jim Joiner.
Their expertise, dedication, and never ending assistance and good humor have been as
rewarding as any course offered during my academic career. I sincerely appreciate the
freedom, trust, and friendship granted to me while pursuing my research interests from
Dan Hanes, the chairman of my graduate committee. To the remainder of my graduate
committee, chosen for their love for the science of coastal engineering, which is apparent
in their teaching and unending assistance, I wish to express my gratitude.
For their constant support and encouragement, I am forever grateful to my mom,
Karen Thosteson, my brother, Pete Thosteson, and my sis', Melanie Bleigh. Additional
thanks go to Chris and Monica for their friendship and free food, the DogBoy for
providing the foreground music while I worked on this dissertation in the background,
and to all of the great friends I've made in this endeavor.
TABLE OF CONTENTS
page
ACKN OW LED GM ENTS..................................................................................................iii
LIST OF TABLES .............................................................................................................vi
LIST OF FIGURES ........................................................................................................... vii
KEY TO SYM BOLS .................................................................................................... x
ABSTRACT ..................................................................................................................... xiv
1 INTRODUCTION ................................................................................................. 1
2 SYSTEM DEVELOPMENT................................................................... 4
Instrum ents .............................................................................................................. 5
System Dem hands ................................................................................................... 8
System Architecture ................................................................................................... 11
Software and Algorithm s....................................................... ........................... 16
Sum m ary..................................................................................................................... 23
3 ACOUSTIC BACKSCATTER CONVERSION TECHNIQUE.............................. 25
Theory......................................................................................................................... 28
Develop ent.................. ......................................................................................... 31
Concentration inversion ..........................................................................................31
Size determ ination................................................................................................... 35
Verification of Technique................................................ ..... ................................ 39
Sum m ary..................................................................................................................... 45
4 SU SPENSION TIM E SCALES..............................................................................46
The SIS96 Project .............................................................................................. ...... 47
Size Determ nation ............................................................................................... 53
Dominant Frequency Band of Suspension Events ......................................... .... 59
Correlation with Velocities......................................................................................... 71
D discussion of Results ................................................................................................. 81
5 CON CLU SIONS....................................................................................................... 87
iv
A A COU STIC PARA M ETERS ............................................................. .................. 91
Lognorm al D istribution............................................................................................. 91
System Constant................................................................................................. 91
W after A ttenuation....................................................................................................... 91
Sedim ent A ttenuation............................................................................................... 92
Backscatter.................................................................................................................. 94
N earfield Correction ............................................................................................. 95
B LIST OF VEN D ORS ........................................................................................... 97
C MONLOG 1.0 PROGRAM LISTING.......................................... ..... ............99
REFEREN CES ................................................................................................................ 147
BIO GRA PH ICA L SKETCH ........................................................................................... 150
LIST OF TABLES
Table page
31 Values of sinh(B)/B for extreme concentrations ................................... ............ 30
41 Calibration constants for instruments used in present analysis ............................... 50
42 Conditions at the measurement site during experiments examined in this study...... 60
LIST OF FIGURES
Figure page
21 External components to acquisition system........................................... .............. 5
22 Realtime processing of collected backscattered signal profiles............................ 10
23 Block diagram of internal system components...................................... ........... 12
24 TPU timing in synchronized pulse width modulation mode ................................. 14
25 Memory map of data memory on the model 7..................................................... 18
26 68000 series assembly necessary for binary search algorithm ................................23
31 Expected voltage for given concentrations, 5 MHz transducer............................... 27
32 Significance of sinh(B)/B term in acoustic backscatter equation............................ 30
33 Numerically generated profiles for (a) 1.0, (b) 2.25, and (c) 5.0 MHz transducers ..40
34 Resulting (a) concentration and (b) median grain sizes from inversion technique
using 2.25 and 5.0 M Hz profiles ...................................... ................................ 40
35 Resulting (a) concentrations and (b) median grain size from inversion technique
using 1.0 and 2.25 M Hz profiles ................................... ................................. 41
36 Resulting (a) concentrations and (b) median grain size from inversion technique
using 1.0, 2.25, and 5.0 M Hz profiles ................................... .................................41
37 Comparison of known and calculated concentrations (a) shown at distinct
concentrations and ranges, and (b) shown as the mean error of all concentrations
w ith range ............................................................................................................ 43
38 (a) Comparison of known and determined median grain size and (b) the resulting
error w ith range.................................................................................................... 43
41 Sensor Insertion System (SIS) ............................................................................. 48
42 Instrumentation used in project.................................................................................. 50
43 Calculated concentration profiles from (a) 2.25 MHz and (b) 5.00 MHz
calibration data using optimum system constant and DC offset versus known
concentration............................. ........................................................................... 52
44 Best fit normal cumulative distribution function to sieved grain size data; sample
taken at location of and prior to run 18................................................................. 52
45 (a) Profile taken from pier on north and south side with superimposed
experimental water depths and (b) corresponding sieved median grain size ...........53
46 Multiple roots in variancesize relation ................................................................ 54
47 Change in bottom location due to settling of instrument framework ...................... 56
48 Perceived median grain size profiles from run 19 and run 20 and corresponding
near bed concentration profiles......................................... ............................. 58
49 Surface elevation spectrum for run 18 with 80% confidence intervals ................... 61
410 Plot of the 100 mg/1 contour for whole time series of run 18................................ 62
411 Plot of the 1 g/l contour for whole time series of run 18 ....................................... 62
412 Time series of the squared bottom velocity magnitude and vertically integrated
concentration ...................................................................................................... 63
413 Concentration spectrum for run 18 ............................................................... 64
414 Bottom velocity spectrum for run 18............................................... ................ 66
415 Cumulative variance functions from concentration and surface elevation energy
spectra......................................................................................................................... 67
416 Cumulative variance functions from concentration and surface elevation energy
spectra..................................................................................................... .................. 69
417 T50 indicating less lower frequency (high period) relevance with increased
distance from bed ................................................................................................ 70
418 Surface displacement time series with envelope determined by Hilbert
transform ................................................... ........................................................ 71
419 Spectrum of envelope ......................................................................................... 74
420 Coherency function between square of bed velocity magnitude and near bed
concentration for run 18 ...................................................................................... 76
421 Concentration spectrum with areas of coherence > 60% indicated....................... 77
422 Phase of transfer function for run 18 ................................................. ............. 79
423 M agnitude of transfer function for run 18 .......................................... .......... ... 80
424 Results from run 23............................................................................................ 82
425 Results from run 25............................................................................................ 83
426 Results from run 27............................................................................................ 84
Ai Normalized total scattering cross section........................................... ............. 93
A2 Form function...................................................................................................... 95
ix
KEY TO SYMBOLS
A Acoustic transducer system constant
a,a, Sediment particle radius (as determined by sieve analysis); mm
Radius of acoustic transducer's piezoelectric crystal; m
a,
B Total local attenuation of sound; Nepersm
m
c Sound speed in water; m/
C(z) Mass concentration; or kgm
o Concentration of suspended sediment at range z0; g or km
Co Empirical relation in form function
d Grain diameter (as determined by sieve analysis); mm
F(z) Backscatter function
Fo Backscatter function at range Zo
f Form function
f Frequency; Hz
fM Acoustic frequency; MHz
I Integrating factor used in finding explicit concentration solution
Iij Discrete form of integral
i Index (chapter 2 table element; chapter 3 transducer number)
j Index bin number
K, Constant in form function; Kf = 1.14 for noncohesive sedimentary
material
Ka Constant in normalized total scattering crosssection; Ka = 0.18 for
quartz sediment
ko Thorne's (1993) acoustic transducer system constant;
m Number of acoustic transducers
N Number of elements included in RMS calculation
n Highest bin number (n +1 total bins)
n Power of inhomogeneous term in Bernoulli equation
P(z) Backscattered pressure; Pa
p(a) Probability distribution of sediment radii; Ym
mm Coefficient in Bernoulli equation (substitution)
p() Coefficient in Bernoulli equation (substitution); p
Q() Coefficient of inhomogeneous term in Bernoulli equation (substitution); p
Qz) Coefficient of inhomogeneous term in Bernoulli equation (substitution)
Coefficient of inhomogeneous term in Bernoulli equation (substitution);
Q
Ri ith element in RMS lookup table
S Acoustic transducer system constant;
Sxx, S, Energy spectra; (time series units)2 s
T Temperature; C
t Substitution in Bernoulli equation solution; C'
V(z) Output voltage from acoustic transducer; V
Vo Output voltage at range zo; V
x Dimensionless particle radius
xI, x2 Empirical constants in form function; x, = 1.4, x2 = 2.8
Zx Cumulative variance function
z Range from transducer; m
Zo Range to first point in analysis; m
z, Theoretical nearfield limit; m
a, (z) Sound attenuation due to sediment; Nepers
m
aw Sound attenuation in water; Nepersm
7 Constant of integration in explicit solution for concentration. Evaluated
using known values at zo
E Empirical constant in nearfield correction relation; E = 2
S(z) Local sediment attenuation proportionality; (NepersXm2)
771,772 Empirical constants in form function; 77, = 0.5,772 = 2.2
P c Mean concentration across transducers; or kgm
Uo Mean grain diameter in phi
V, ,v2 Empirical constants in form function; v, = 0.37,v2 = 0.28
P, Sediment density; kg/m
72 Variance
a7
c Standard deviation of concentration across transducers; or km
a7 Standard deviation of grain diameter in phi
T Acoustic pulse width; s
0Logarithmic grain diameter; 0 = log2 d
X Normalized total scattering cross section
Z (z) Nearfield correction parameter
0o Nearfield correction parameter at range Zo
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
DEVELOPMENT AND FIELD APPLICATION OF A LITTORAL PROCESSES
MONITORING SYSTEM FOR EXAMINATION OF THE RELEVANT TIME
SCALES OF SEDIMENT SUSPENSION PROCESSES
By
Eric D. Thosteson
December 1997
Chairman: Daniel M. Hanes
Major Department: Coastal and Oceanographic Engineering
A microcontrollerbased system of oceanographic instrumentation providing a
comprehensive set of measurements relevant to sediment transport processes has been
developed. Analysis of the data provided by the system yields time series of vertical
profiles of mean sediment size and concentration, horizontal profiles of bedform
geometry, and single location measurements of flow velocity, pressure, turbidity, and
water temperature. Details of the system architecture, including capabilities provided by
both hardware and software contained within the system are given.
An improved method for the determination of suspended sediment size and
concentration from the system's acoustic backscatter intensity measurements is
presented. By retaining the size dependence throughout the derivation for an explicit
solution for concentration, a new explicit solution to the acoustic backscatter equation
results. This new concentration solution improves the technique for determining median
sediment size by incorporating sediment attenuation in the calculation. Because this new
technique relies on the minimization of the variance in concentration as determined by
different frequency transducers, the previous technique of pairing transducers of different
frequencies is replaced by a technique making use of any number of different frequency
transducers. The new size/concentration inversion technique is tested using both
simulated and laboratory data. Numerical precision is shown to be the only source of
error with the use of simulated data. Laboratory tests result in less than 20% error in the
determination of both concentration and size over a range of nearly one meter.
Finally, suspended sediment concentration data from the nearshore region
obtained from an experiment performed in Duck, North Carolina, are examined to find
the relevant time scales of sediment suspension. In this location, low frequency forcing
mechanisms are as significant in suspending sediment as the incidentband wave forces
typically used to model suspension. Like wave groups, this low frequency forcing results
from the linear superposition of velocity components in a narrow band of frequencies.
When these frequency interactions are considered, coherence greater than 60% is found
between the velocity squared and the nearbed concentration across most of the spectrum.
CHAPTER 1
INTRODUCTION
With continuing coastal development, the need for proper coastal planning and
management of its resources grows. Towards meeting this need, several models of beach
evolution are currently used as tools for predicting shoreline change and for design of
coastal structures. Improving these models requires a better understanding of the
underlying physical processes of sediment transport. The capability of a theory to
describe the basic physics of a process is dependent on the accuracy of measurements of
the process. Refinement of the theory of the basic mechanics of sediment transport thus
depends upon improved measurements of the processes.
Developments in computers and instrumentation have not only improved the
capability of measurement of sediment transport phenomena in the laboratory, but have
made possible field measurements not possible a decade ago. While the control and
repeatability of laboratory experimentation is appealing, there are factors which influence
sediment transport in the field, which are neglected in laboratory studies. The evidence
of this is the disagreement often encountered between results from laboratory and field
experiments. Thus, it is desirable not only to verify laboratory results in the field, but
also to improve field experimentation apparatus and technique such that other elements
influencing the motion of sediment can be found.
In this dissertation, a new system of instrumentation developed for field
measurement of smallscale sediment transport and the associated hydrodynamics is
1
presented. Chapter 2 begins the presentation with details of the instrumentation and
architecture of the most recently developed system. This system was developed after
several refinements of earlier systems. Each refined system was developed in response to
newly discovered limitations of the prior system. Improvements from earlier versions
include new and better instrumentation, faster communications, and less restrictive data
storage requirements. In all, five systems were developed, beginning with the system
used in the Supertank project (Hanes et al., 1993; Thosteson, 1995). Subsequent systems
were used for the Vilano Beach project, the Duck94 project, and the SIS95 and SIS96
projects. During the writing of this text, the latest system is being used in the
SandyDuck97 project. In later chapters, the data presented are not that from the system
described in Chapter 2, but instead are from the next most recent version of the system.
In an effort to present the reader with the most recent and useful information, Chapter 2
presents the newer system. The overall architecture has changed little since the version
used in the Duck94 experiments, but the reader will be alerted to differences in the
systems when appropriate.
Perhaps the most powerful instrument and certainly the most demanding
computationally on the system is an acoustic backscatter system, used for obtaining high
resolution measurements, both spatially and temporally, of suspended sediment
concentration and size. Recent improvements to the technique of determining
concentration from the measured backscattered intensities are further extended in chapter
3 to include determination of the mean grain diameter of particles in suspension. The
new technique presented removes attenuation assumptions previously required in order to
determine the particle size and reduces the computational effort in determination of both
concentration and size. Also, this technique allows more than two unique frequency
transducers to be used in a single computation. This reduces the possibility of obtaining
multiple solutions for size, which can arise when only two unique frequencies are used,
and again reduces computational effort.
In chapter 4, the field experiments performed the fall of 1996 at the SIS96 project
are reviewed and the analysis of the resulting data is covered. Field application of the
acoustic analysis techniques presented in chapter 3 for determination of suspended
sediment size will be investigated. The remainder of the analysis is centered on
determining the frequency ranges in which sediment suspension is most prevalent. It is
seen that often the most dominant suspension events occur with a frequency much lower
than the frequencies of the incident waves, though very little energy is found in the
spectrum within the infragravity band. A coherency function analysis with the square of
the bottom velocity shows that the low frequency forcing responsible for the sediment
suspension results from the interaction between frequencies in the incident band of the
spectrum. Interaction between frequency components is reviewed, showing that the
resulting low frequency forcing is caused by wave groups. In chapter 5, conclusions
from this research and suggestions for future research will be presented.
CHAPTER 2
SYSTEM DEVELOPMENT
With more sophisticated oceanographic instrumentation comes the need for more
advanced data acquisition and instrument control systems. Evolving from acquisition
systems used in several earlier experiments, a new system has been developed for use in
the SandyDuck97 project, held at the Field Research Facility (FRF) in Duck, North
Carolina in late 1997 (Hanes et al., 1993). This new system delivers highly accurate
measurements of both the hydrodynamics and the resulting sediment processes with high
temporal and spatial resolution. The focus during the development of this system has
been on the ability to collect an unbroken record of data, consisting of highly
synchronous data from all instruments attached to the system, with duration of several
days. Such a record allows the investigators to utilize standard time series analysis
techniques to examine sediment processes on time scales ranging from seconds to days
without making assumptions typically required to account for gaps between data records.
In its current form, outlined in figure 21, the system utilizes a three frequency acoustic
backscatter system (ABS), two acoustic Doppler velocimeters (ADVs), three multiple
transducer arrays (MTAs), an optical backscatterance sensor (OBS), a pressure sensor, a
compass, a tilt meter, an external temperature sensor, and an underwater video camera.
Internal monitoring includes leak detection, internal temperature, unregulated and
regulated shore supplied voltages, and the internal battery voltage. This chapter
Figure 21. External components to acquisition system.
describes the system architecture, essential algorithms responsible for data collection and
processing, and the system's capabilities.
2.1. Instruments
The choice of instrumentation used by the current system was made to most
accurately record as many parameters relevant to sediment suspension processes as
possible with minimal flow obstruction. Waves and currents are measured using a
Transmetrics pressure sensor and Sontek threeaxis acoustic Doppler velocimeters
(ADVs). ADVs were chosen due to their ability to provide highresolution velocity
measurements for long periods of time without the zerodrift difficulty associated with
electromagnetic devices an important consideration with the long records which will be
collected with this system. Tilt and compass transducers will ensure accurate positioning
of the ADVs and monitor any frame motion or failure. For a combined concentration and
turbidity measurement, a single D&A Instruments OBS is utilized. Three Seatek MTAs,
two operating at 2.00 MHz and the third at 5.00 MHz, are used for bottom bedform and
slope measurements. MTAs are linear arrays of acoustic transducers which provide high
resolution measurements of bedforms and the local slope of the seabed. The 5.00 MHz
unit contains 32 transducers spaced 1.5 cm apart, making it ideal for measurement of
smallscale bedforms (wavelengths of order 5 to 50 cm). Each 2.00 MHz unit contains
16 transducers spaced 6 cm apart, providing excellent measurement of larger scale
bedforms (wavelengths of order 20 to 200 cm). To this point in time, all three MTAs
have been used together to form a single 2.5 m array, giving bedform measurements
ranging from small to large scale (Jette and Hanes, 1997). Since orientation of bedforms
can not be determined when the MTAs are used in this manner, orientation is determined
from video observations with a DeepSea MicroSeaCam 1050 when turbidity is low and
from an independent Simrad Mesotech model 900 rotating scanning sonar system, not
described in this text. Profiling for suspended sediment size and concentration is
accomplished using an acoustic backscatter system (ABS) made by the Centre for
Environment, Fisheries and Aquaculture Science (CEFAS, formerly known as The
Fisheries Laboratory), a description of which follows. Finally, to determine speed of
sound and acoustic attenuation parameters for use in evaluating data from the acoustic
instruments, water temperature is measured. Further information on the instrumentation
vendors is found in appendix B.
Simultaneous operation of multiple acoustic concentration profilers at different
frequencies has successfully provided measurements of profiles of both sediment
concentration and mean sediment size (Hay and Sheng, 1992). The present system
includes an ABS utilizing 1.0, 2.2 and 5.0 MHz transducers. Sync and trigger lines
provide precise control over selection and firing of the transducers. A single analog
signal line returns the envelopes of the backscattered analog voltages. Upon receipt of a
pulse on the sync line, the ABS begins a cycle such that the first pulse on the trigger line
fires the first transducer and switches the signal line to transmit data from the first
transducer to the acquisition system. The next pulse on the trigger line causes the second
transducer to be fired and switches the signal line to transmit the second transducer's
voltage envelope. The cycle continues with the third pulse selecting the third transducer.
Additional pulses on the trigger line restart the cycle, beginning again with the first
transducer.
Of the instruments listed above, the system is responsible for analog to digital
conversion and subsequent storage of the data from all but the MTAs and the video
camera. Responsibility of the system to the MTAs is limited to setting acquisition
parameters and collecting data through a digital serial connection shared between all
three MTAs and the main system. The video camera is switched on and off and provided
power by the system. The video signal simply enters the underwater package and exits
immediately through the shore cable. Of the remaining instruments, all but the ABS are
instruments that collect data from a single point in space only. For this reason, they will
henceforth collectively be referred to as the single point instruments (SPIs). The system
has been designed to provide data at a maximum rate of four final measurements per
second. Signals from each of the SPIs are passed through twopole, linearphase, anti
aliasing filters with a cutoff near 10 Hz. This filter, combined with oversampling of the
SPIs at 100 Hz and subsequent averaging to the desired final measurement rate,
eliminates the possibility of aliasing and minimizes signal degradation due to the
frequency response of the filter.
2.2 System Demands
Fundamental to the design of this system is the desire to minimize the travel
distance of analog signals from the instruments. The purpose of this is to minimize
filtering effects, both in amplitude and phase, and reduce the introduction of additional
signal degradation caused by the otherwise necessary modulation and demodulation of
the raw highfrequency signals. We therefore place the system offshore, which results in
new design demands related to power consumption, size, storage requirements, and
system monitoring functions. We also desire that the system be fairly selfcontained,
requiring only minimal external equipment support and userintervention. User
intervention consists of configuring sampling schemes before data collection and
offloading of any data residing on the system after collection is complete. Finally, given
the specific modes of operation of the instruments to be used in the study as well as any
other demands imposed by them, synchronous measurements from all instruments is of
the utmost importance.
Ideally, each of the three ABS transducers should measure the identical profile at
the same instant in time, giving three coincident and collocated measurements of acoustic
backscatter. In practice, this is difficult for several reasons. First, physical limitations
due to the size of the transducers and the acoustic beams from the transducers prevent
achieving measurements from perfectly overlapping profiles. Second, to statistically
reduce the random fluctuations in the backscattered signal due to coherence of the
returned signal, for each transducer, single profiles of the mean power are constructed
from several consecutive profiles. It is important to realize that the mean power must be
used rather than the mean voltage, as the concentration of suspended sediment is
proportional to the power of the backscattered signal. This is shown by the acoustic
backscatter equation written in terms of the mass concentration, C (Thorne et al., 1991).
C(z)= Z e4y (a,+a,) (21)
In this equation, P is the backscattered pressure (proportional to the voltage measured at
the crystal), z is the distance from the transducer, V is a function describing nearfield
characteristics of the transducer, ko is the system constant, and aw and a, are water and
sediment attenuation parameters respectively. The system constant characterizes specific
physical and electrical properties of a particular transducer. These parameters and the use
of the acoustic backscatter equation are examined in more detail in chapter 3 and
appendix A. Since the sediment size and concentration profiles are in general functions
of time, additional fluctuations in the backscattered signal due to random reconfiguration
of the particles in the ensonified volume and due to changing sizes and concentrations
certainly result. To account for these limitations, several conditions shall be imposed on
the acquisition system. Profiles must be acquired at a high enough rate such that the
changes with time in size and concentration profiles are small. Within this period, a
sufficient number of profiles need to be collected such that a representative average will
statistically minimize the fluctuations. Finally, the ensemble of samples from any one
transducer should be well distributed over this entire period.
Acoustic concentration profilers very quickly produce large volumes of data. To
meet the three conditions imposed above, the current system collects 100 profiles per
second from each of the three transducers on the ABS. Each individual profile consists
of up to 120 12bit samples from the analog signal, sampled at 100 kHz. For ease of
processing and storage, each 12bit sample, hereafter referred to as a bin, is stored in a
zeropadded 16bit word. As each profile is collected, the squared value of each bin is
calculated using a highly efficient tablelookup algorithm. This squared value is then
added to a running sum of squares, such that for each bin in the profile, the root mean
squared (RMS) value can be calculated after a specified number of profiles have been
collected. Again in the interest of minimizing computational time, RMS values are
calculated from the sums through the use of a binary search method through a previously
calculated table of sums. Figure 22 outlines the entire reduction procedure for the case
of computing RMS profiles of 120 points from 23 consecutive profiles a common
4 .. .
E, F:R return ds
120 points sampled at 100 kHz
i square d:. '
profiles ...
23 profiles collected at 100 Hz
Figure 22. Realtime processing of collected backscattered signal profiles.
configuration of this system. Algorithms for computing the square and the RMS will be
detailed later in this text. The final outcome of this onthefly processing of the
backscattered signal profiles is a set of statistically meaningful profiles requiring
significantly less storage space and significantly less communications bandwidth to
transmit realtime digital data from the system.
2.3 System Architecture
To meet the control, communications, synchronization, processing, and data
collection requirements given, a lowpower Onset Tattletale model 7 data logging engine
is employed. The model 7 provides 512 kilobytes of flash EEPROM storage and 256
kilobytes of static RAM for system and application software, as well as an additional 2
megabytes of pseudostatic RAM for data storage. In addition, it includes 28 digital I/O
lines, a 4 channel analog to digital converter, a parallel I/O port, RS232
communications, a realtime clock, and 500 megabytes of hard drive storage. Central to
the model 7 is the Motorola 68332 microcontroller. The 68332 incorporates the CPU32
central processing unit executing a superset of MC68000 instructions. For use in the
present system, the microcontroller operates at 16 MHz. Also, the 68332 incorporates a
time processing unit (TPU), which is essentially a special purpose slave processor that
controls two timers and sixteen I/O lines. In the present system, this TPU is
indispensable for handling synchronization as well as hardware and software triggering.
Figure 23 outlines the additional interfacing made to the model 7 in the system.
Additional information and descriptions follow.
Further extending the features of the model 7 is a Daedulus Research MUX32
board. This board further multiplexes each of the four analog to digital channels by
eight, allowing the model 7 to sample up to 32 analog signal lines. These 32 channels
will be referenced by a port, numbered 0 to 3, corresponding to the original channel
number on the analog to digital converter, and a channel number numbered 0 to 7, now
referring to one of the newly multiplexed lines. Besides increasing the number of analog
lines, the MUX32 also buffers the 16 TPU digital I/O lines and replaces the model 7's
analog to digital reference with a voltage reference of higher precision.
Figure 23. Block diagram of internal system components.
Interfaced to the model 7 is a filter board, which provides the antialiasing for the
analog signals, as previously mentioned, a power board, and several communications
components. On the shore end, the DC voltage supplied to the package is such that 30 V
is input to the system package offshore with all instruments turned on. For example, if
the resistance in 500 meters of cable is such that 15 V is lost due to this resistance, 45 V
would be supplied from shore. Given 30 V input, the power card regulates power for all
components of the system in addition to providing power switching for each of the
instruments independently. Also, the power card keeps 24 V of NiCd batteries charged,
for use in supplying short bursts of high current to power the model 7's hard disk drive.
These batteries also can power the system for a short time in the event the power
connection from shore is compromised. Communications from the package to shore is at
57.6 kilobaud through two 50 ohm coaxial cables using RS422 transceivers on both ends
of the connection. Such a connection has been shown in previous experiments to be
reliable through 500 meters of coaxial cable. For reasons discussed shortly, RS232
communications from the model 7 go through an Onset Tattletale model 8. Between the
model 7 and model 8, serial communications are at 38.4 kBd. The serial communications
path then goes from the model 8's 57.6 kBd RS232 connection to the RS422 transceiver
on the communications card.
By default, the main clock, TCR1, on the TPU of the 68332 runs at one fourth of
the CPUs clock frequency. Instead, with a CPU clock frequency of 16 MHz, TCR1 is set
during system initialization to operate at 1 MHz due to the range of clock frequencies that
must be generated by the TPU. Without making this change, the risk of losing
synchronization between channels because of counter overruns within the TPU increases.
MonsterLog 1.0 (MONLOG1O.C) TPU timing diagram
TCR 1 
1 MHz
Base frequency/16
TPU channel 14 
100 kHz
A to D converter trigger
TPU channel 9 
100 Hz
F3 interrupt
TPU channel 10 
100 Hz
F2 interrupt
TPU channel 11 
100 Hz
F1 interrupt
TPU channel 13 
400 Hz
Hardware trigger
TPU channel 12 
100 Hz
Hardware sync pulse
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E 
C Ci C i 4 C ; q "t C C C 6 i
C C C C d S 5
Figure 24. TPU timing in synchronized pulse width modulation mode.
TPU channels are used in the present system for hardware synching and triggering of the
ABS, hardware triggering of the analog to digital converter, and for generation of the
interrupts necessary for the triggering of software exceptions used for data acquisition.
By using a mode of operation on the TPU known as synchronized pulse width
modulation, several TPU lines are set to run continuously as perfectly synchronized
clocks. Figure 24 illustrates the clock rates, pulse widths, and timing between channels.
Once these clocks have been started, they will run continuously and perform their
associated tasks without any intervention from the CPU. Analog signals are continuously
sampled, so the program simply decides which samples to keep. Data acquisition is
performed entirely within exceptions, described in more detail later, so it can be started
by simply enabling the interrupts generated by TPU channels 9 through 11.
Since both ACP profiles and SPI data are collected at 100 Hz and subsequently
processed down to the desired final data acquisition rate, at some instant immediately
after processing, a large burst of data is both saved to the data memory within the model
7 and output from the model 7. This burst of data, up to approximately 1000 bytes of
data, must be transmitted from the model 7 within roughly 10 ms to prevent interfering
with the timing of the data acquisition. Rather than complicating the communications
requirements by use of a MBd serial line, these data are simply output to the existing
parallel port on the model 7 into a FIFO buffer and then into the model 8 mentioned
above. By continuously monitoring the parallel and serial connections to the model 7, the
model 8 buffers all communications and allows the use of a single, 57.6 kBd, serial
connection to the package. This 57.6 kBd line is sufficient to allow transmission four
times per second of 120 point profiles from each of the three ACPs and the additional 14
channels of interest.
2.4 Software and Algorithms
A program called Monlog 1.0 controls the system. Monlog is written mainly in
C, with additional assembly coding of the actual data acquisition and data processing
routines for speed. Most of the code handles userinterface functions, such as creating
menus, handling user I/O, setting the time, setting record numbers, defining the sampling
scheme, and offloading stored data records. The algorithms necessary to handle these
functions are trivial and will not be covered in this text, although a full listing of the
program is given in appendix C.
Typical operation of the system begins at powerup. The system software handles
initialization of the core components of the Model 7. To customize specific portions of
the initialization, such as the necessary modification of the TPU configuration register to
establish the TPU's 1 MHz clock rate, the contents of the Model 7's serial EEPROM are
modified. Immediately following the system initialization, control is given to Monlog.
Monlog starts with system specific initialization, enabling charging of the system
batteries and ensuring that all interfaced instruments are started in a known state.
Communications baud rates are established and system variables initialized. The TPU
channels are set up and started as was shown in figure 24, with the interrupts they
generate initially disabled, and appropriate default values are set to govern data
acquisition. Finally, the internal monitoring channels are sampled, and the results, along
with the main system menu are displayed to the user.
Once the main menu is displayed, several options are available to the user. A
standard input routine is used throughout the program, such that a timeout feature can be
utilized at each opportunity for input. This guarantees that any involuntary selections,
such as could be caused by line noise, will not leave the program in an indeterminate
state. Upon any timeout, the program returns control to the main menu routine,
maintaining original values for any values that may have inadvertently been changed.
Included in the main menu are options that allow the user to power each of the
instruments interfaced to the system individually and to subsequently test them in an
interactive test mode, displaying results to the user in real time. Additional options are
used to offload data resident on the systems hard drive to shore using the Xmodem data
transfer protocol and to define the sampling scheme and system modes of operation.
An emergency stormmode can be enabled from the mainmenu. When enabled,
Monlog will detect loss of communications while in the main menu routine, and should
such a condition be detected, the program will begin acquiring data using a conservative
predefined acquisition scheme. Since loss of communication most likely will coincide
with loss of shoresupplied power, this scheme is defined for collection of short data files
at regularly spaced intervals in an attempt to conserve battery power for a time period
roughly equal to that of a storm.
Preparation for acquisition begins with the user setting the time and date and
defining the sampling scheme. Parameters such as the number of points per ABS profile,
number of profiles to include in an ensemble RMS profile, final sampling rates for the
ABS, SPIs, and MTAs, and sampling durations are all defined by the user. Based on this
information, Monlog allocates all available data memory and sets up pointers to
18
appropriate memory locations to create data headers, store data, create lookup tables for
use by the squaring and RMS algorithms, and temporarily store sums during data
acquisition. Figure 25 shows the structure of these pointers in memory based on values
determined from the user configuration. Note that the ranges labeled TMU and PAD
together form a Mathwork's Matlab data file in the memory of the model 7. Such
Monster Package memory map & setup
SOBASE
x' lookup table
RTBASE 4096x4
RMS lookup table
F1SUM 4096x4
F1 summation memory
F1SQR NPP'4
F1 XF summation memory
F2SUM NPP'4
F2 xsummation memory For use in data processing not
F2S0R NPP'4
6 1   Nincluded in MAT file.
F3SUM 2 NPPs mo 8*NOSP+24'NPP+32768
F3 summation memory
F3SQR NPP'4
F3 X summation memory
SPSUM NPPO4
SPI x summation memory
SPSQR NOSP'4
SPI x' summation memory
F1HED NOSP'4
F1 Matlab data header
FIRMS 26
F1 RMS prolilie tim nes
F2HED NPP'NFP'2
F2 Mallab data header
F2RMS 26
F2 RMS profile lime series
F3HED NPP.NFP'2 TMA128 variable
F3 Mallab data header Stored as single data file on TT
F3RMS 26
F3 RMS profile time series
SPHED NPP'NFP'2
SPI Mallab header
SPMEN 26
SPI time series
MT1HED NOSP'NFP'2 TMU variable
S MTA # Matlab header NFP*(NPP'6+NOSP*2)+
MT1BAS 26 MTA NUMSCANS*152+
MTA #1 profile time series 26*9+24
MT2HED MTA NUMSCANS72
MTA #2 Matlab header
MT28AS 26
MTA #2 profile time series
MT3HED MTA_NUMSCANS'40
MTA #3 Matlab header
MT3BAS 26
MTA #3 profile time series
TMHED MTA NUMSCANS'40
Matlab Time header
TMBAS 26
Data ile start/end times
DMHED 24
Matlab Dummy header
DMBAS 26
OFFEND+1 Dummy variable space PAD variable
Figure 25. Memory map of data memory on the model 7.
compact structuring beforehand allows one to offload the entire range of memory
sequentially to the shorebased computer and immediately load the data record into the
analysis software for data inspection and processing. Note also that although the MTA
data are not collected directly by the model 7, space is allocated within the data file for
each of the MTAs. MTA data are offloaded from each of the MTAs after the rest of the
data file has been filled. This data format is convenient since the data from all of the
instruments are stored in the same file along with both the starting and ending times and
dates of the collection. In prior systems, all data collected by the system resided in these
data files. With the added ability to collect unbroken data files of length greater than
what could possibly be stored in this memory segment, only the first portion of the
collected data, whatever portion will fit within the 2megabyte limit, is stored in this
format.
After the dynamic memory configuration, all that remains for Monlog to do is
enable the interrupts generated by the TPU channels and monitor the acquisition. Four
exception routines handle all of the data acquisition. Outside of these four exceptions,
the main process (that process running prior to the CPU's receipt of any interrupt)
monitors the progress of the exception routines and at the appropriate time, performs the
data analysis and storage. Following the timing diagram shown in figure 24, the order of
events following the memory initialization is as follows:
1) Interrupts generated by TPU channels 9 to 11 are set to execute the same
exception routine, entitled NOTHING.
2) Interrupts are enabled.
3) Upon identifying an interrupt from TPU channel 9, that interrupt associated with
the acquisition of transducer F3, the NOTHING routine reassigns each interrupt
its own exception routine. This insures that a profile from transducer Fl will be
the first to be sampled.
4) A hardware sync pulse is sent from TPU channel 12 to the ABS, effectively
resetting the ABS to sample transducer Fl on the next received trigger pulse.
5) A hardware trigger is sent from TPU channel 13 to the ABS, triggering transducer
Fl.
6) Shortly after sending the trigger to the ABS, TPU channel 11 generates an
interrupt, which starts the exception routine responsible for sampling transducer
Fl.
7) As data are continuously being sampled from the analog to digital converter in
relation to the triggering from TPU channel 14, each sample is acquired from the
converter, squared by use of a previously calculated lookup table, and added to a
running sum appropriate for the location in the profile.
8) Transducer Fl's exception routine completes and acknowledges the interrupt,
returning control back to the main process, which to this point, continues to
monitor the progress of the exceptions.
9) The above process repeats with TPU channel 13 triggering transducer F2, and
TPU channel 10 generating the interrupt that executes transducer F2's sampling
routine.
10) Channel 10's interrupt is acknowledged, again returning control to the main
process.
11) Again, the process repeats, with TPU channel 13 triggering transducer F3, and
TPU channel 9 generating the interrupt that executes transducer F3's sampling
routine.
12) This sampling routine additionally selects and samples each SPI attached to the
system, adds the result to an appropriate running sum for the particular SPI, and
decrements the counters being monitored by the main process.
13) Once the main process has detected that the appropriate number of profile
acquisitions have occurred, it again reassigns the interrupts to execute the
NOTHING exception routine. This routine has the task of keeping a tally of the
number of times TPU channel 9 interrupts occur. After a designated number of
occurences, this routine reassigns the interrupts to again sample analog data.
14) Immediately following the reassignment of the interrupts to the NOTHING
exception, the main process performs data processing and storage. Note that the
NOTHING exception will be called a sufficient number of times to allow the data
processing and storage tasks to complete before data sampling resumes.
This process continues until the time limit specified in the sampling scheme definition is
surpassed.
To this point, the details of the data analysis have been neglected. The first
analysis algorithm in need of description is the lookup table used to square the incoming
samples from the ABS. Normal multiplication is far too costly in processing time, so a
table lookup algorithm is employed. This table is simply a 4096 element (corresponding
to each possible value from the 12bit analog to digital converter) list of squared values.
Given a value to be squared, this value is used as an index into the list, or table. The
value located at the given index is the square of the index. Next, the second algorithm is
responsible for providing the RMS value from a given running sum of squared values.
Again, standard algorithms involving multiplication and division demand too much
processor time, so an alternative approach is used. Since the number of elements used in
the calculation of the RMS value is known in advance in the given situation, a table of
sum of square values can be calculated prior to data acquisition. If N elements are to be
used, then the value in the table corresponding to the ith index is given by the following:
R, =N(i+0.5)2 (22)
By finding the lowest number in the table greater than a given running sum of squares
value, the resulting index to that element of the table is a very close approximation to the
RMS value for the given sum. For example, if an RMS value is to be determined from 23
elements, a table of borderline sums of 23 squared values can be generated. The first
element in the table, corresponding to index 0, would be as follows:
R0 = 23x(0.5)2 = 5.75 (23)
If a given sum of squares, after 23 samples have been added to it, is less than this value,
than the RMS value is closely approximated by the index into the table. Finally, since the
elements of the table are ordered by value, rather than searching each of the 4096
elements of the table for the first value greater than that given, a binary search algorithm
is utilized. The search begins at the center of the table, and the values are compared.
Based on the results of this comparison, the next comparison will be with the value
centered in either the upper or lower portion of the table. With each successive
comparison, the number of table elements remaining to compare is cut in half. Since all
divisions are by 2, binary shift operations are used to perform the division. For a 4096
element table, only 12 comparisons need to be made. The assembly code used for this
comparison is shown in figure 26. Note that the variables used in the beginning of the
routine as memory pointers were initialized prior to this segment of code.
routine for F1
nidxres move.l _flsqr,a0
move.l _tflbas,al
move.1 _rtbase,a2
;RMS routine Fl
avloopfl move.l (a0),d0
move.l #0,(a0)+
move.l #$0800,dl
move.l #$0400,d4
move.l #0,d3
move.l #0,d2
sredofl lea ($0000,a2,dl.w*4)
TABLE[TEST]
cmp.l (a5),d0
bge felsefl:
Y>=TABLE[TEST]
move.w dl,d2
bra dunfl:
felsefl move.w dl,d3
dunfl move.w d4,d5
or.w d3,d5
move.w d5,dl
Isr.w #l,d4
bne sredofl:
bcs sredofl:
move.w d2,(al)+
;Set base of Fl's sum(x^2)
;Set base of Fl's RMS storage
;Set base of rms table
;get byte from sum(x^2)
;initialize sum(x^2) storage
;initialize TEST
;initialize HALF
;initialize BASE
;initialize ANSWER
,a5 ;location of
;branch to else portion if
;ANSWER=TEST
;skip else portion
;BASE=TEST > else portion
;WORK=HALF
;WORK=HALF or BASE
;TEST=HALF or BASE
;shift HALF right 1 bit
;branch back 10 times
;branch back 1 final time
;store rms value
Figure 26. 68000 series assembly necessary for binary search algorithm.
2.5 Summary
In this chapter, a system of oceanographic instrumentation capable of providing a
broad set of measurements relevant to sediment transport processes is presented. All
;Initialize RMS
24
instruments are in close proximity to the data system, maximizing data integrity.
Extremely efficient analysis algorithms written in C and assembly language provide data
processing and reduction during collection. Use of multiple processors allows
measurements to be both stored internally on the systems internal storage and exported to
shore during collection through serial communications. Data stored on the system are
offloaded using an error correction protocol to a compact, binary data file that can be
immediately viewed and interpreted by analysis software.
CHAPTER 3
ACOUSTIC BACKSCATTER CONVERSION TECHNIQUE
Use of a high frequency underwater acoustic transducer to profile the vertical
distribution of sediment concentration has been demonstrated under both laboratory and
field conditions by several investigators (Hanes et al., 1988; Hanes et al., 1993; Hay and
Sheng, 1992; Thorne et al., 1991; Green and Vincent, 1991). Basically, profiles of the
intensity of backscattered sound from suspended sediment are collected, and this intensity
is related to the suspended sediment concentration at each point in the profile. A typical
technique for determination of concentration from acoustic backscatter data requires
inversion of the acoustic backscatter equation for concentration, which yields an implicit
equation needing an iterative technique for solution. In order to obtain profiles of
concentration from a single transducer operating at a fixed frequency, knowledge of the
sediment grain size distribution is required prior to applying the inversion procedure. In
addition, the assumption that this size distribution either remains constant with range or
with a predetermined form at all ranges is required, as the scattering and absorption
properties of the sediment are dependent upon grain size (Thorne, 1993). Recently,
several investigators have demonstrated effective measurement of both the profiles of
sediment concentration and of the median grain size of the distribution (Hay and Sheng,
1992; Crawford and Hay, 1993). The technique requires the use of multifrequency
acoustic transducers. Since the absorbing and scattering properties of sediment depend
on both the grain size and upon the frequency of the incident sound, each unique
25
frequency transducer provides an independent measurement of the backscattered intensity
profile. Hence, each point in the profile can be described by a number of independent
equations equal to the number of coincident and collocated measurements of unique
frequency. Typically, three transducers of unique frequency are used to collect
coincident intensity profiles. Although in theory, use of three frequencies suggests that at
each measured point, concentration and two parameters of the grainsize distribution can
be determined, typically, only concentration and one parameter of the distribution are
obtained. The sensitivity of the equations to small variations in intensity and also the
nonlinearity of the sediment size response functions are responsible for this limitation.
Lee and Hanes (1995) presented an explicit solution for concentration, to be
referred to in this paper as LH95, from the acoustic backscatter equation, significantly
reducing the computational effort by removing the need for iteration. An added benefit
derived from use of the explicit solution is removal of the ambiguity in concentration
solutions obtained by the iterative solution to the implicit equation. Figure 31 shows the
relation between concentration and transducer voltage (proportional to the square root of
intensity) as calculated by the acoustic backscatter equation (32) assuming a constant
concentration profile. From this figure, it is apparent that a single voltage value from the
transducer may result from two different concentrations. Physically, this can be
described with the following argument. At low concentrations, the sound attenuation due
to sediment in the sound path is low, resulting in an increase in the intensity of the
backscattered sound with increasing concentration. As this attenuation becomes more
dominant, the intensity of the backscattered sound begins to decrease with increased
concentration. So, from the two concentration solutions obtained from the implicit
Theoretical voltage from concentration; 5 MHz
0 1 1 
0 1 2 3 4 5 6 7 8
Concentration (g/l)
Figure 31. Expected voltage for given concentrations, 5 MHz transducer.
9 10
equation, the choice of the correct solution depends upon the magnitude of the
attenuation. The explicit solution for concentration yields only one concentration, as this
dependence on attenuation is accounted for by integration of the intensity profile.
In spite of the benefits presented by use of the LH95 explicit solution, it is
restricted in its use to concentration only. Its use requires that the grain size distribution
be known and constant with range. Holdaway and Thorne (1997) extended the
functionality of the solution by allowing the size distribution to vary but to retain a
predetermined form with range from the transducer. In the following derivation, a
similar explicit solution for concentration retaining the dependence on the grain size
distribution is found by following the LH95 development. Based on this explicit form,
the methods used for evaluating parameters of the grain size distribution are reexamined,
and an improved method, at least in computational effort, is introduced. In addition, the
existing method for evaluating the grain size parameters by pairing ACPs of different
frequencies is extended to utilize an arbitrary number of unique frequency transducers.
3.1 Theory
The equation that relates the intensity of the backscattered acoustic signal to the
concentration and size distribution of the scatterers in suspension is referred to as the
acoustic backscatter equation. This equation has been presented in several forms, each
nearly equivalent. Presented here is a general form of the equation, based jointly on the
form presented by Hay (1991) and Thorne (1993).
2 2 ( 2B (31)
Zo
aS Z )C(2)d2 (32)
The variables in equations (31 to 32) are defined as follows:
V = voltage read from transducer
z = distance from transducer
S = system constant
c = speed of sound, assumed constant with distance
T = acoustic pulse width (s)
fy = nearfield correction term (see appendix)
F = backscatter parameter (see appendix)
C = mass concentration, (sediment density in F)
a, = water attenuation parameter (see appendix)
a, = sediment attenuation parameter
B =(a, +C(z)C(z))
zo = range from transducer at which first concentration and size is evaluated.
( = local sediment attenuation proportionality constant (see appendix)
The nearfield correction term, y is included here for completeness, and it can easily be
included in the following derivation by temporarily absorbing it in the backscatter
parameter. Since it is simply another function of z, it does not complicate the derivation.
It has not been included in the following derivation, because it was not used in the
subsequent numerical simulations or laboratory tests. The complete solution, including
this term, is presented in the appendix.
In equation (31), the final term on the right side of the equation, (sinh B)/B,
presents difficulty when trying to obtain an explicit solution for concentration. This term
accounts for the difference in the magnitude of the sediment attenuation from the portion
of the ensonified volume closest to the transducer to the portion furthest from the
transducer. Figure 32 shows the magnitude of this term versus the term B, and table 31
shows the magnitude of this term for several cases using a distribution of quartz sand
with median grain diameter, u, = 2.65 and standard deviation, oa = 0.25. Note these
parameters are given in units of phi, defined as 0 = log2 d where d is the grain
diameter in mm. The transducer frequencies listed in table 31 are the highest
frequencies used in this study. A 30 g/l mass concentration corresponds to roughly a 1%
1.07
m
c
r
"' 1.03
0 0.1 0.2 0.3 0.4 0.5 0.6
B value
Figure 32. Significance of sinh(B)/B term in acoustic backscatter equation.
Table 31. Values of sinh(B)/B for extreme concentrations.
Transducer Concentration (g/l) sinh B
B
B B
frequency (MHz)
5 30 0.5591 1.053
5 5 0.0994 1.002
2.25 30 0.0956 1.002
2.25 5 0.0172 1.000
concentration by volume, the approximate upper limit of concentration before multiple
scattering must be considered, and the 5 g/1 concentrations are the highest tested in this
study. From these results, it can be seen that for the highest concentrations for which the
present theory applies, this term can be significant when the highest frequency
transducers are used. When operating transducers of lower frequency with suspensions
of lower concentration, this term is very close to unity. Additionally, since the sediment
attenuation term within the exponential function is an empirically determined parameter,
determination of its value without including the (sinh B)/B term may compensate for its
absence. So, for the remainder of this text, the acoustic backscatter equation will be
approximated by the following expression:
v2z2 = AF(z)C(z)ez4,a+a()
(33)
In equation (33), the system sensitivity constant, S, the speed of sound, c, and the pulse
width, r, have been combined into a single system constant, A. The system constant can
be later separated back into these constituents in order to correct for sound speed
variations.
3.2 Development
3.2.1 Concentration inversion
Beginning with the general form of the acoustic backscatter equation (34), the
concentration dependence is removed from the sediment attenuation term, a,, giving a
form in which the multiple term dependence on concentration is more obvious (35).
AF(z)C(z)= V2 (z)z2 exp(4z(a, +a,(z)))
(34)
AF(z)C(z)=V2(z)z2 exp 4(aw + (2)C(2))d
ZOJ
Following the LH95 derivation, first, the natural logarithm of the equation is found
In A+ln F +lnC= 2ln(Vz) + J (4a, + 4C)d
(36)
and then the derivative, denoted by (').
F' C V+V
+=2 + 4o, + 4C
F C Vz
(37)
Upon arranging the terms of equation (37), a nonlinear differential equation of the
Bernoulli type results.
C'[+ F_2V+V 4a, C= 4C2
(38)
Rewriting in standard form, equation (38) becomes the following:
C'+ p(z)C = Q(z)c
P(z=[ F' 2(Vz+V 4,,]
p(z) LF 2 Vz
Q(z)= 44
n=2.
(39)
(310)
(311)
(312)
Following the standard method of solution for a Bernoulli equation, the following
substitutions can be made:
t=C" = C1; C =t1
with
(35)
(313)
dC dC dt
dz dt 2 d
dz dt dz
(314)
These substitutions result in a readily solved first order linear inhomogeneous differential
equation.
 t2t + pt1 = Qt2
t' + pt =Qt
t+ fit =
(315)
(316)
Where, in equation (316), the following apply:
p=p
Q=Q
(317)
Solution to equation (316) is found by first determining the integrating factor.
I=exp(q dz)
SPdz=~ F 2( Vz+V 4ad z=InF +4az +21n(Vz)
I =exp(21n(Vz)+4azzlnF)= exp(4atz)
F
(318)
(319)
(320)
After multiplying the equation by the integrating factor, an exact differential results,
which can then be integrated for solution.
d (Vz)2 exp(4a = 4 exp(4taz)
dz F ) F
()2 exp(4,zz)t = 4( exp(4a,w)di~ + y
F F
Zo
(321)
(322)
Equation (322) is then solved for t, and then finally for the concentration, C.
yz 4( W exp(4a,2)di
t = zo (323)
(Vz) exp(4a,z)
F
(Vz)2 p(4
1 F exp(4alz)
C t z(V,, (324)
t y 4 exp(4a,)d2
Zo
Next, the boundary conditions (325) are applied for solution of the integration constant.
C=Co
V = Vo at z = zo
V a (325)
F=Fo
Y= F Cexp(4ao) (326)
The concentration Co at the nearfield limit z0, which is the closest point to the transducer
not in the nearfield, may be estimated in many applications by assuming the
concentration and size are constant within the nearfield. With this assumption, the
implicit form of the acoustic backscatter equation, equation (35), simplifies somewhat,
giving equation (327).
Co (Vz0)2 e4Z+) (327)
AF
This can be solved iteratively for concentration for a given grain size, using a zero
sediment attenuation form of the equation for an initial estimate.
C(Vzo)2 e4o.
Co e (328)
AF
3.2.2 Size determination
The technique originally introduced by Hay and Sheng (1992) for determining the
median size of particles in suspension involved first approximating the acoustic
backscatter equation (35) by neglecting the sediment attenuation. In this way ratios
could be constructed from the approximate equations for any pair of unique frequency
transducers. Since the concentration dependence of the attenuation is removed by
neglecting the sediment attenuation, the remaining concentration terms in the equation
cancel in the formation of the ratio. Hence, the only remaining unknowns in the ratios
are functions of the size distribution of the suspended particles. By assuming the particle
size can be described by a twoparameter distribution, the lognormal distribution, and by
further assuming one parameter is constant, the ratios can be evaluated over a range of
the other parameter. The standard deviation is the parameter assumed constant and the
ratios are determined over a range of median particle sizes. Median particle size is then
found by minimizing the difference between the ratios and its known value with respect
to the median particle size. Crawford and Hay (1993) improved the technique by solving
the approximate equations first for those terms that are not functions of the size
distribution or transducer frequency. These terms are equal in all of the equations,
regardless of transducer frequency, so equating the remaining terms in the other
equations eliminates the concentration dependence. Again, the minimization technique is
applied as before to determine the median particle size.
First by solving each transducer's equation only for concentration, and then by
minimizing the variance in the concentrations predicted by any number of transducers
with respect to median sediment size, Crawford and Hay's technique is here slightly
modified. By using the explicit solution for concentration, (324), there is no longer the
need to neglect the sediment attenuation. In addition, once the median particle size is
found by the minimization technique, the mean concentration is readily computed from
the existing concentration solutions. The exact procedure is as follows.
The explicit solution for concentration derived above is discretized to represent
each frequency of m transducers with n+1 bins outside the nearfield region of each
transducer.
(V exp(4a,iz) (329)
SF.j i = 1,2,..., m
iligj j = 1,2,..., n
In the denominator of this expression, I is the discrete form of the integral, given by the
following:
Iij = 2 i,k exp4ak ik exp(4aiZk,1 k1) (330)
k=1 Fi .k F'k
The integration constant is defined again at point zo.
i = (V,0 exp(4a,zo) (331)
It should be mentioned that zero concentration in suspension, which results in zero
voltage read at the transducer, will result in an indeterminate value of the integration
constant. The location of z0 should thus be set at the first range with nonzero
concentration, determined by the following iterative technique.
The initial concentration in the profile, located at the first point outside all of the
transducer nearfields, is found for each transducer by the former iterative technique.
Co =(Vz)2 e4zo(a+co) (332)
AF
Two considerations should be taken when determining this initial concentration.
First, because of attenuation, the magnitude of the voltage read from the transducer is
limited in magnitude from the above expressions, as is apparent in examination of
figure 31. Due to the statistical fluctuations in the backscattered signal and also to
instrument noise, it is possible that the actual signal is higher in magnitude than this
theoretical limit. In such cases, the iterative technique will not converge to a solution. A
simple divergence test in the iteration algorithm will reveal this condition. Minimization
of the difference between the initial concentration guess and that returned by equation
(332) will produce a good concentration approximation in such cases. Second, it is
important to realize that equation (332) will produce two concentration solutions for the
reasons discussed previously. For the lowest frequency transducers typically used, the
higher magnitude solution is regularly above the expected range of applicability of the
present theory, and can safely be ignored. For the higher frequency transducers, the
decision of which concentration to use must be based on physical arguments or by
comparison with the results from lower frequency transducers. In field measurement of
suspended sediment, the transducer is usually a sufficient distance from the bed, such that
the higher magnitude solution is again outside the expected range and can be safely
ignored. For example, a typical 5.0 MHz transducer with a 16 cm nearfield will give two
solutions at zo = 16 cm. As seen in figure 3.1, the lower magnitude solution will fall
between 0 g/1 and 1.6 g/l, and the higher above 1.6 g/l. Should the transducer be located
a half meter from the bed, concentrations above 1.6 g/1 will not likely be found at zo = 16
cm (34 cm above the bed), and the lower magnitude solution is the most probable
concentration.
The complete technique for solution is as follows. Equation (332) is solved
iteratively for the initial concentration for each transducer over a range of median grain
diameters. Note that both F and are functions of the grain size distribution, typically
assumed to be lognormal. Calculation of these parameters first requires one to
determine the distribution based on the given median grain diameter. The form of the
lognormal distribution is given in the appendix. The standard deviation of the grain size
distribution is assumed constant and is determined by other physical arguments. In the
case of field measurement of sediment suspension, the standard deviation is generally
assumed equal to that of the distribution of sediment in the seabed below the transducer.
For each median grain diameter, the mean concentration and the variance in the
concentration between transducers is calculated.
1 2
cm. (333)
2 1 = i (334)
The median grain diameter is recognized as that with the minimum concentration
variance, and the concentration is given by the corresponding mean concentration. If
only two transducers are used, more than one solution for the median grain diameter is
possible. In this case, determination of size is still possible if the range of grain sizes is
restricted and appropriate transducer frequencies are selected in advance.
After the initial concentration is found, the integration constant, y, can be found
for each transducer from equation (331). The solution for the remainder of the bins in
the profile proceeds by solving equation (329) for each transducer for a range of median
grain diameters, and then by selecting the correct grain diameter by minimization of the
concentration variance between transducers, given by equation (334). Again, the
concentration is given by the corresponding mean value from all transducers.
3.3 Verification of Technique
As an initial test of the calibration technique, ideal voltage profiles for 1.0, 2.25,
and 5.0 MHz transducers were simulated using the acoustic backscatter equation (34)
(a) (b)
0.7 6, 1.42
0.5
504 0o8
> 0.3 >0.6
0.2 0.4
0. 02
0 01 02 0.3 04 0 06 07 08 0.9 1 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9
Distance (m)
2.5
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distane (m)
Figure 33. Numerically generated profiles for (a) 1.0, (b) 2.25, and (c) 5.0 MHz
transducers.
with a predetermined lognormal distribution. For simplicity, the generated profiles
contained no nearfield, or in other words, the acoustic backscatter equation is assumed to
be valid at the face of the transducer and beyond. Figure 33 shows these numerically
generated profiles. The concentrations used were 0.01, 0.02, 0.04, 0.08, 0.16, 0.32,
0.63,1.25, 2.5, and 5.0 g/l, and the grain size distribution was assumed to have a median
grain diameter /. = 2.66 and a standard deviation o = 0.25. Since in the absence of
attenuation, the voltage read from the transducer increases with increasing suspended
particle concentration, the concentrations are easily distinguishable at zero distance.
Higher attenuation with higher operational frequency and with higher concentration is
apparent from the figures. Particularly, the profiles from the highest concentrations in the
5 MHz simulation are attenuated so heavily that away from the transducer little, if any,
signal remains.
a) b)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0. 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Distance (m) Distance (m)
Figure 34. Resulting (a) concentration and (b) median grain size from inversion
technique using 2.25 and 5.0 MHz profiles. Asterisks indicate known values.
Shown in figure 34 are the concentration and size profiles resulting from
applying the new technique using double precision calculations (64 bit) with only the
10,
10 
o!10
10o'
104 H
~_ I
2.25 and 5.0 MHz voltage profiles from figure 33. Since only two frequencies were
used in this test, the range of median grain sizes was restricted within +/ 2 standard
deviations of the initial known distribution. In figure 34b, the size profiles overlap for
all cases except the cases involving the highest two concentrations. Not surprisingly, the
technique accurately produced the initial concentration, as in Holdaway and Thorne's
(1997) simulations, and size in the majority of the cases. This test does illustrate the
(a) (b)
102 250
10 200
10 150
0 00
102 50
0 0.1 02 03 0.4 0.5 0.6 0.7 08 0o9 0 0.1 0.2 0.3 014 0.5 0.6 0.7 0.8 0.9
Distance (m) Distance (m)
Figure 35. Resulting (a) concentrations and (b) median grain size from inversion
technique using 1.0 and 2.25 MHz profiles. Asterisks represent known values.
(a) (b)
102 250 .
10o 20D
O .01o o  *3 150
10 150
10 100
10"2 I 501
0 0.1 0o2 0!3 0.4 0.5 06 07 0.8 09 1 0 0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance (m) Distance (m)
Figure 36. Resulting (a) concentrations and (b) median grain size from inversion
technique using 1.0, 2.25, and 5.0 MHz profiles. Asterisks represent known values.
difficulty though in using the highest frequency transducer through significant ranges of
high concentrations. As noted before in figure 33, at the highest concentrations, the high
sediment attenuation results in large signal loss away from the transducer. In figure 34,
the error induced in evaluating the concentration and size from this small signal is
apparent. Figure 35 shows the results from use of the 1.0 and 2.25 MHz signals. The
results in this test showed excellent agreement with both the original size and
concentrations, even through a onemeter range of relatively high concentration. The
final inversion, shown in figure 36, uses all three of the simulated signals. Again,
because of the signal loss in the high concentration 5 MHz data, the results exhibit similar
behavior to those in figure 34. For this reason, it is important to be aware of signal loss
when working with the highest frequency transducers, such that this can be considered in
the inversion algorithm.
Laboratory tests were performed in a recirculating calibration chamber which
produces a suspension of sediment of approximately constant concentration and constant
grain size distribution (Hanes et al., 1988). Transducer frequencies of 1.0, 2.2, and 5.0
MHz were used for the measurements. Backscattered intensity signals were collected at
100 Hz with each transducer, and the ensemble RMS was determined from 1 minute's
data for each concentration. As in the numerical simulations, the distribution parameters
for the sediment were a median grain diameter y. = 2.66 and a standard deviation cr =
0.25. The concentrations used were 0, 0.1, 0.2, 0.3, 0.4, and 0.5 g/l. Figure 37 shows
the agreement between the known concentration and that determined with the new
inversion technique. Several factors explain the form of the error curve with range. First,
concentrations in the chamber were determined by adding calculated dry masses of
43
(a) (b)
0.6 20
Is
+ 18
0.5 o
16
10
03.4 104
o 12
0.3 0.1 0 03 0.4 0. 05 06 0.7 08 0
0.2
x 6
4
0.1
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.4 0.5 0.6 0.7 0.8 0.9
Known concenlraion (01) Distace (m)
Figure 37. Comparison of known and calculated concentrations (a) shown at distinct
concentrations and ranges of (*) 40 cm, (o) 50 cm, (x) 60 cm, and (+) 70 cm; and (b)
shown as the mean error of all concentrations with range.
(a) (b)
200 20
190 18
1801
16
170
S160  
& I12
150
10
140
130 8
.4 0.5 0.6 0.7 0.8 0.9 .4 0.5 0.6 0.7 08 0.9
Distance (m) Distance (m)
Figure 38. (a) Comparison of known (broken line) and determined (solid line) median
grain size and (b) the resulting error with range.
sediment to the known volume of water. Due to hindered settling within the funnel at the
base of the chamber, actual concentrations in the tube may be slightly lower than those
calculated. Next, the initial concentration measurement is located 40 cm from the
transducer face due to both nearfield effects from the transducers and from complications
introduced by amplifier saturation at shorter ranges. Determination of the initial
concentration must therefore be done with a signal that has already experienced 40 cm of
water and sediment attenuation through significant concentrations. The sensitivity of the
concentration measurement to attenuation increases the likelihood of error, particularly
for high concentrations, long attenuation paths, and high operational frequencies.
Finally, for calibration of the acoustic transducers, the error between known and
calculated concentrations was minimized in the range from 40 cm to 90 cm. In this
minimization technique, approximately half of the calculated concentration profile
typically falls below the known value and half above. This effect is apparent in the error
profile of the present concentration evaluation, Figure 37b, which shows the best
agreement in the center portion of the profile. If the transducer calibration were
performed at just a single range, as is often described in the literature, and the
measurements presented in this text evaluated using the single point calibration
information, the error in the determination of concentration is less than 5%.
Figure 38 compares the known median grain size with that measured in the
circulation chamber. Again, if the calibration is performed at a single range and the size
determined from the single point calibration, the error in evaluation of median grain size
is less than 10%. Even in this case, the evaluated median grain size is slightly higher
than the known value. Errors result in this evaluation from use of somewhat low
concentrations for determination and from differences in various sediments not accounted
for explicitly in the empirical form function. Use of low concentrations was made
necessary by operation of the 5.0 MHz transducer with an initial concentration evaluation
point located a significant distance from the transducer. Presently, one form function is
said to describe noncohesive quartz sediment (see appendix), but it is expected that grain
properties of a given sediment sample will modify the form function slightly. Empirical
evaluation of the form function for a given sediment type would likely improve the error
in determination of the median grain size.
It should be noted that evaluating concentration and size with a constant
concentration profile is actually a more demanding application of the technique and
system than is typically experienced in field measurements, due to the propagation of
error through the profile. In measurements of sediment suspension above the seabed, the
transducer is typically far enough from the seabed such that the concentrations near the
transducer are low.
3.4 Summary
A new technique of determining both concentration and the median grain
diameter of suspended particles has been presented. The significant advantage of the
technique is that by using an explicit solution for concentration, the median grain
diameter can be found without having to neglect sediment attenuation. In addition,
because incorporating the correct median grain diameter in the explicit solution will
produce an identical concentration regardless of the operational frequency of the
transducer, the concentration variance between any number of transducers can be
minimized to find the median grain diameter. Numerical simulations show the technique
produces both the expected concentrations and grain diameters. In addition, laboratory
results from a recirculating calibration chamber verify that the technique applies well in
determining sediment size and concentration from measurements of backscattered
acoustic intensity.
CHAPTER 4
SUSPENSION TIME SCALES
In the previous chapters, a new system of instrumentation capable of accurate
depiction of sediment suspension processes with high spatial and temporal resolution has
been described. In addition, a new, robust process of data conversion from
multifrequency acoustic backscatter data to concentration and median sediment size has
been introduced. In the fall of 1996, a system similar to that described in the first chapter
was deployed from the Sensor Insertion System (SIS) at the Army Corps of Engineers
Field Research Facility (FRF) in Duck, North Carolina. In this chapter, the time series of
concentration profiles obtained from the acoustic backscatter measurements collected at
this project are examined in relation to the instantaneous hydrodynamic measurements.
It is common in the study of sediment suspension in a wave environment to
decompose the concentration into steady and fluctuating components (Nielsen, 1992).
The significance of each component in a sediment transport calculation depends on the
relative importance of the two transport mechanisms: transport by currents or transport by
waves. In the longshore direction, the sediment flux computed from the product of the
mean concentration and steady current velocity has been used successfully for
determining the mean longshore rate of transport (Hanes and Huntley, 1986). In general,
determination of the mean vertical suspended sediment concentration profile typically
involves computation of the near bed concentration by use of a reference concentration
model and computation of concentrations above by a vertical distribution model. Of the
46
many models of reference concentration, a simple linear relation between the bed shear
stress and reference concentration is shown to work best (Smith and McLean, 1977;
Thosteson, 1995). The mean vertical concentration distribution is best described by a
model incorporating both turbulent diffusion and vertical convection due to vortex ripples
(Nielsen, 1992; Lee, 1994). In examination of crossshore transport, the fluctuating
component of concentration becomes more important (Huntley and Hanes, 1987).
There is significant evidence of the importance of low frequency water wave
motion in the process of crossshore sediment transport (Huntley and Hanes, 1987; Beach
and Sternberg, 1991; Osborne and Greenwood, 1992). This has been attributed to the
fixed phase difference between the components of velocity and concentration, where the
low frequency velocities result from free and groupbound infragravity waves. Low
frequency variation in concentration has been shown to be associated with wave groups
(Hanes, 1991). The aim of the present investigation is to examine the significance of the
concentration variation at various frequencies and to further examine suspension by wave
groups. It is hoped that this will aid in development of future models that predict the
fluctuating components of concentration.
4.1 The SIS96 Project
Shown in figure 41 is the SIS on the FRF's pier. All instrumentation is deployed
from the SIS, which consists of a crane mounted on tracks that extend along the length of
the pier. Instruments attached to an arm (called the "bah") at the end of the crane's boom
can be positioned with reasonable precision at locations near the seabed. Four bayonets
located at the end of arm closest to the pier are forced into the seabed by the weight of the
crane to stabilize the bah. Crossshore movement of the SIS allows data collection to be
.4.  ." C*C c ~ 
Figure 41. Sensor Insertion System (SIS)
performed in areas with varying sediment composition and wave conditions. The
bulkiness of this arrangement immediately suggests that the framework will interfere
with the processes to be measured. While there is certainly an effect from the presence of
the structure, precautionary measures are taken to minimize this impact. The arm itself
consists of pipe of smaller diameter than the main structure, and is just massive enough
not to flex by wave forcing. Next, the arm is distanced as far from the bed as possible
considering the range limitations of the acoustic instruments. Orientation of the arm is
longshore, such that it will have the minimum influence in the vertical and crossshore
directions. In the presence of longshore currents, measurements are taken on the
appropriate side of the pier to be upstream of the pier and the main structure of the crane.
Finally, the instruments themselves are located at the end of the arm farthest from the
main structure and pier. Though these measures minimize the influence of the supporting
structure and the pier itself, it is expected that some influences endure. This is accepted
as a tradeoff for the ease of repositioning the test site and recohfiguring instrumentation.
It should be mentioned that even after the longest deployments of the instrumentation
(approximately 1 hour), no scour hole could be seen with the MTA measurements,
suggesting that the influence of the arm itself was minimal.
As mentioned previously, the system of instrumentation used in this project was
slightly different from that described in chapter one. In fact, this project inspired many of
the new features of the newer system. The fundamental limitation of the system
deployed in this project was the constraint on the duration of data collection. As will be
recognized later, the analysis of the data from these experiments indicates that long
records of suspension must be examined to capture low frequency events that can
dominate the record. The other difference in the systems is in the instruments utilized.
Figure 42 shows the instruments as they were positioned on the arm of the SIS during
the project. Of the instruments shown in figure 42, the following instruments were a
part of the system and used in this investigation: 2 Simrad Mesotech model 810 ACPs, 1
Sontek ADV, 1 TransMetrics P21LA25 PSIS pressure sensor, 3 Seatek MTAs, 1
DeepSea MicroSeaCam 1050, and 1 D&A OBS 3. The remaining instruments shown in
the figure were owned and operated by the FRF. Note that two individual Simrad
Mesotech ACPs with frequencies of 2.25 and 5.0 MHz were used instead of the ABS
system described in the previous chapters. As will be seen later, this introduced
complication into trying to determine size from the backscatter data.
50
SIS96 Instrument Arrangement
View from South
when on pier
h 35 i
CJ
Figure 42. Instrumentation used in project.
Table 41. Calibration constants for instruments used in present analysis.
Instrument Gain Offset System constant
Pressure sensor 8.35x103 mount 6.77 m
(salt water) (salt water)
Current X 1.187 x103 ms count 2.457 m/
Current Y 1.203x103 count 2.492 m/
scount /s
OBS 1.409 x 103 ,count 0.164/ 
2.25 MHz ACP 11 mV 0.464
5.00 MHz ACP 2 mV 0.929
Calibration of the instruments which measure from only a single point in space,
termed single point instruments (SPIs), is straight forward. Hydrostatic measurements
are used for calibration of the pressure sensor, and the ADVs are calibrated using a
moving cart in a tank of still water. The OBS sensor is calibrated in a sediment
recirculating calibration tank with the ACPs. Table 41 shows the calibration constants
for the various instruments. As described in the previous chapter, the only undetermined
parameter for the ACPs is the system constant. Due to a slight DC offset in the output
signals from the ACPs, table 41 also lists the optimum offset for each transducer. An
optimization process is utilized to determine both the system constant and DC offset
which produces the concentration profiles closest to the known concentrations in the
sedimentrecirculating tank. The predicted concentration profiles versus the known
values of concentration for the two ACPs are shown in figure 43. Across all locations
and concentrations, the mean errors for the 2.25 MHz and 5.0 MHz transducers are 8.8%
and 17.9% respectively.
(a) (b)
2.25 MHz S=0.464 DC=O.011 volts 5.0 MHz S=0.929 DC=0.002 volts
10o 100
o o
10, 
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Range (m) Range (m)
Figure 43. Calculated (solid lines) concentration profiles from (a) 2.25 MHz and (b)
5.00 MHz calibration data using optimum system constant and DC offset versus known
concentration (dashed lines).
For four days, from October 29 until November 1, 1996, experiments were
performed from various locations on the pier, ranging from water depths of 1.4 to 7.0
meters. Measurements were attained with wave conditions ranging from H,,= 0.35 to
1.0 m, due to the capability of moving the SIS. Waves were a mixture of locally
generated seas with peak periods near 6 seconds and an underlying swell component near
11 seconds. The local component was most prevalent at the start of the week, with the
swell component becoming more dominant in the latter days. Grab samples of sediment
were collected at the start of each data collection run, and sieve analysis indicated the
median grain sizes ranged from 120 to 200 microns (3.06 and 2.32 respectively on the <
scale). Sieve analysis also indicated that the grain size distributions of the samples from
the runs investigated in the present study (identified in section 4.3) were described well
by the lognormal distribution. Shown in figure 44 is the best fit normal cumulative
distribution function to the sieve data from run number 18. Figure 45 shows the
Mean phi= 2.242 Std. dev. = 0.4482
0.9 
0.8
0.7
i 0.6
S0.5
0.4
0.3
0.2
0.1
0
0 0.5 1 1.5 2 2.5 3 3.5
Phi
Figure 44. Best fit normal cumulative distribution function to sieved grain size data;
sample taken at location of and prior to run 18.
53
(a) (b)
I 210 x
x
6 200.
4 190 xc
2 1180
2 I160
._.8
4. 150
6 140
8 ~ 130
10c '1 O 120 v
0 100 200 300 400 50S 600 0 100 200 300 400 500 600
Pier location (m) Pier location (m)
Figure 45. (a) Profile taken from pier on north (solid) and south (dashed) side with
superimposed experimental water depths (*) and (b) corresponding sieved median grain
size.
variation of the median sediment grain size with pier location and the beach profile as
taken over the edge of the pier with a plumb bob. Elevation in this figure is relative to
the mean water level at the time of the survey. Jette presents additional information
regarding the SIS96 project (1997).
4.2 Size Determination
As described in the previous chapter, the median grain diameter of the particles in
suspension can be determined by computing the concentrations from each frequency
transducer over a range of sizes. Again, the size is determined to be that which
minimizes the variance in the computed concentrations across transducers.
Determination of size from field data is complicated by several factors that sometimes act
in conjunction. These complicating factors include the following: multiple zeros in the
variance versus size relation, poor measurement resolution, statistical fluctuation in the
backscattered signal returns, and spatially separated acoustic beams.
Because of the nonlinearity of the form function, it is possible that the variance is
zero at more than one grain size. Increasing the number of unique sound frequencies
decreases the likelihood of the variance having multiple roots. In this project, only two
transducer frequencies were used, making the determination of the correct root difficult at
times. It is not uncommon to obtain a variance versus size relation as that shown in
figure 46. In such a case, a physical argument based on the sizes that a bed sample
contains is used to choose the more likely sediment size. If the backscattered signal is
mainly from a washload component in the suspended sediment (small suspended particles
x 108
6
4 \
._
I
CO
02
02
1
0
80 100 120 140 160 180 200 220 240 260 280
Median grain diameter (microns)
Figure 46. Multiple roots in variancesize relation.
not found locally, but instead advected from another region), than certainly this choice
will be in error.
Next, resolution of the transducers and sampling resolution must be considered.
For instance, in the present experiments, the transducers are sampled with a 12bit analog
to digital converter. At small amplitudes, a onecount change in the measured
backscattered signal can result in a change of order in determined concentration. Since
ultimately it is the difference in concentration measurements across transducers which
determines the median sediment size, this large change in concentration drastically
changes the resulting size evaluation. For this reason, a minimum value of the
backscattered signal strength is required before the size evaluation can be trusted. In
practice, only sizes obtained from concentrations greater than 50 mg/l are used.
Because the measurement of the returned signal from suspended sediment is a
random process, many instances or profiles must be collected to obtain statistically
meaningful results. As described in chapter 2, the root mean square (RMS) of a
predetermined number of profiles is generated by the acquisition system. The number of
profiles included in this RMS profile is chosen such that the error in the concentration
measurements, proportional to the reciprocal of the square root of the number of profiles,
is minimal. Again, because of the sensitivity of the size evaluation to small concentration
differences, a small error in concentration may result in a relatively large error in the
evaluation of size. For this reason, an RMS computed from a significant number of
measured signals (averaging of the measured intensities) must be used in order to obtain a
reliable size evaluation. It is essential that the sea bottom location in the profile be
determined prior to the RMS process, since movement of the bottom with time will make
it difficult to determine its location from an RMS profile. For this same reason, with
regard to bed location, the closest reliable size estimate is that just above the highest bed
location over the averaging period. In the present experiment, there was significant
movement of the bed location in the profile, as indicated in figure 47. The change in bed
location was due not to accretion, but instead to settling of the framework into the seabed.
This was verified by examination of the MTA bottom profile, which showed a uniform
movement of the profile with little change in the ripple field.
Bottom location relative to that at start
Rr
0 I I II I
0 200 400 600 800 1000 1200 1400 1600 1800 2(
Elapsed time (s)
Figure 47. Change in bottom location due to settling of instrument framework.
000
uhirfill H I
A
Finally, it is often difficult in the field to obtain acoustic backscatter
measurements from transducers with collocated beams. Physical restrictions due to the
size of the transducers require that the beams be spatially separated. Since a significant
amount of temporal averaging is performed before the analysis, this introduces no
difficulty should the seabed be flat. If ripples exist, as they did in nearly every
experiment in this project, then it is likely that one transducer will receive backscatter
from a concentration profile which is higher or lower spatially. This spatial separation
corresponds to the transducers being positioned above different areas of the ripple
wavelength. In such a case, the differences in concentrations between the two
transducers results not only because of sediment size variations, but also because the
measurements are located at different elevations from the bed. Away from the bed, the
resulting error in size is probably small, as advection and mixing will remove horizontal
gradients in concentration. However, near the bed, the comparison of concentrations
measured from different elevations from the bed will result in notable error in the size
evaluation. The backscatter profiles can be aligned based on bed elevation as opposed to
alignment by transducer face locations, but this will result in the neglect of any
differences in the true vertical concentration and size profiles over a ripple wavelength.
Despite careful consideration of each of the above complexities, a consistent
estimate of the median sediment size could not be obtained from the data collected in this
project. In figure 48, the resulting size profiles from two separate data runs are shown
together with completely different results. The data for both runs were collected at the
same location, with one hour between the start times of the runs. Both size profiles result
from RMS profiles of the entire 16 minute runs. Inspection of the time series of the bed
58
(a) (b)
5 5
2 1.4 221.6 221.8 222 222.2 222.4 222.6 222.8 120 130 140 IS0 160 170
Sao (micons) Size (micrn)
RUm#19 Rmn#20
K K
S4 4
11
K K
0 0   
221.4 221.6 221.8 222 222.2 222.4 222.6 222.8 120 130 140 150 160 170 11
Size (microns) Size (microns)
Run #19 Run 820
1 10 10 105 1 1
Concentraion (g/) Concetration (g4)
Figure 48. Perceived median grain size profiles from (a) run 19 and (b) run 20 and
corresponding near bed concentration profiles.
elevations from each transducer indicates the bottom location was the same for each
transducer. A sediment sample taken from the bed indicates a median grain diameter of
200 microns was present at this location. Although neither of the results seems
unreasonable, examination of the concentration variance across transducers indicates
agreement in concentration is never achieved. Over the entire range of the trial grain
sizes, selected to be from plus or minus three standard deviations of the local median
grain size, no applied size will result in equal concentration readings across transducers.
As to which transducer yields the higher concentration, there is no consistency. Either
transducer is just as likely to respond with a higher concentration measurement.
Recall that the beams of the two transducers used in this project were close
together (within 4 inches of one another) but not collocated. For this reason, it is
possible, and the results seem to indicate that a horizontal gradient in concentration exists
between the transducers. Although this result seems unlikely with time averaged data,
the likelihood of occurrence increases if the time series of concentration is dominated by
a few infrequent suspension events a hypothesis which is verified by the following
analysis. Furthermore, this result indicates the importance of having truly collocated
beams if an evaluation of median grain size is to be performed.
4.3 Dominant Frequency Band of Suspension Events
In order to study the most dominant time scales of sediment suspension, four runs
of the 30 runs collected will be examined. The investigation is limited to these four runs,
because these were the only runs of sufficient length to provide confidence in the low
frequency portions of the spectral analysis to be presented. Recall that in the system used
for this project the duration of data collection is limited by the available memory in the
data logger, unlike the newer system described in chapter 1. Table 42 shows the
conditions under which the experiments were performed. In this table, the wave height is
determined by correcting the pressure time series for depth attenuation using linear wave
theory and is then verified using that obtained by correcting the velocity time series,
again using linear wave theory (Dean and Dalrymple, 1984). In this calculation,
contributions from wave periods less than 3 seconds and greater than 20 seconds are
removed, albeit examination of the spectra prior to removal shows little energy in these
Table 42. Conditions at the measurement site during experiments examined in this
study.
Run Date Time Duration Pier side Location d50 Depth
(EDT) (MM:SS) (m) (4m) (m)
18 10/31/97 12:39:36 32:14 South 207 211 2.41
23 11/01/97 09:01:08 43:44 South 226 194 3.09
25 11/01/97 10:57:54 37:56 North 226 187 3.20
27 11/01/97 12:35:24 37:56 North 238 194 3.60
Run Hmo Tpeak Opeak I U direction 11 ripple ripple
(m) (s) (0) (cm/s) (0) (cm) (cm)
18 0.53 10.0 97 16 350 0.5 13
23 0.57 10.9 88 10 11 0.5 15
25 0.39 11.7 88 9 3 1.5 14
27 0.51 10.1 88 5 5 1.2 11
portions. The angles given are in a reference frame so 0 is directed longshore to the left
of an onshore observer looking out at sea, and they increase in the clockwise direction.
Wave direction is found using the maximum entropy method with the pressure and
horizontal velocity data, and is given as the direction from which the waves propagate.
In all cases listed, the instruments were placed offshore of the breakpoint such that the
instruments remained submerged for the duration of each run. In addition, collection
away from breaking waves avoids contamination of the concentration measurements by
bubbles. Due to the difficulties mentioned above in evaluating the grain size profiles, the
assumption of constant grain size is utilized in the conversion from the backscattered
signal to concentration. The grain size used in the analysis is that obtained from a grab
61
3.5,
3 
2.5
0. !
2
03
1
0.5 i
0 0.05 0.1 0.15 0.2 0.25
Frequency (Hz)
Figure 49. Surface elevation spectrum for run 18 with 80% confidence intervals.
sample taken in the vicinity of the instruments prior to data collection. Figure 49 shows
the surface elevation spectrum from run number 18. In this case and in each case that
follows, the spectrum is found using the entire record of surface elevation. A Bartlett
spectral window is then used to smooth the spectrum, resulting in a spectral estimate with
approximately 6 degrees of freedom. Note that the most significant portion of the energy
is found in the incident band of the surface elevation spectrum. Also, note the lack of
energy in the lowest frequency band that at the extreme left in the figure. Logged
observations indicate that the waves consisted of swell from an offshore lowpressure
II ~II~ i I
J~ ~
III I Ii 1b I I II I
0 200 400 600 800 1000 1200 1400 1600 1800
Elapsed time (s)
Figure 410. Plot of the 100 mg/1 contour for whole time series of run 18.
I I I I I I
Figure 411. Plot o
200 400 600 800 1000 1200 1400 160(
Elapsed time (s)
f the 1 g/l contour for whole time series of run 18.
0 1800
1 1 1 1 11 1~ III1 __,_A
1I11 I1I
u I
mal ill halu l
m
" ''Y'UI"
system with little or no locally generated wind waves, in agreement with the measured
spectrum.
A qualitative observation of the concentration profile time series indicates that
suspension events in general tend to be intermittent with only infrequent occurrences of
highconcentration events, as described by Hanes (1988). This can be seen in figure 4
10, where the 100 mg/l contour as determined from the 2.25 MHz transducer is plotted.
For comparison, the same time series is shown in figure 411, but the one gram per liter
contour is instead plotted. Inspection of figure 411 shows that the high concentration
events are indeed less frequent than the lower concentration events seen in figure 410.
 0.8 
2 0.6
gc0.4
. 0.2
01
1200 1300 1400 1500 1600 1700 1800
E 15
C.
E
C
. 10
aU
o
o 5
0
U)
U)
I I II
S1200 1300 1400 1500 1600 1700 1800
Elapsed seconds (s)
Figure 412. Time series of the squared bottom velocity magnitude and vertically
integrated concentration.
In addition, these infrequent high concentration events stay confined to the region very
close to the bed. Although these high concentration events are few in number, they
generate concentrations which greatly outweigh the typical concentrations found between
events. The infrequency of the high concentration events is again apparent in the bottom
time series of figure 412. Shown in the upper time series for comparison is the square of
the bottom velocity magnitude. This comparison will be examined in more detail in
section 44.
Next, the concentration time series is brought into the frequency domain by use of
the Fast Fourier Transform (FFT). Transformation of the concentration time series to the
^5
6
2
04
0)4
Ca
C,
.2 2
r
0
o
0 0.05 0.1 0.15 0.2 0.25
Frequency (hz)
Figure 413. Concentration spectrum for run 18.
frequency domain results in what will be termed the concentration spectrum. This
concentration spectrum reveals the relative importance of each frequencies contribution
to the total variation in concentration. Based on the observations just made, the lowest
frequencies should show the highest contribution to the total variation in concentration.
In figure 413, the concentration spectrum is plotted from the time series of vertically
integrated concentration profiles of run 18, so the relative magnitudes of the total
concentration contributions at each frequency can be examined. As expected, the largest
portion of the suspended sediment concentration fluctuation, or variance, is accounted for
by variation at the lowest frequencies.
In order to examine this further and to look at the significance of this outcome at
different elevations from the bed, the cumulative variance function (CVF) is introduced.
The CVF, denoted by Za, indicates at a particular frequency the portion of the total
variance accounted for by lower frequencies. In analytical form, Zx is given by the
following expression:
I
jS.(f')df f
z, (f )= =1 j (f')df' (41)
fIS,(f')df' o
0
In discrete form, the lower limits of integration are replaced by the lowest resolvable
frequency, 1/T where T is the record duration. Likewise, the upper limit in the
expression in the denominator is replaced by the Nyquist frequency. For both the
concentration spectrum and the bottom velocity spectrum, the CVF is determined, and in
each case, the percentage contribution to the total fluctuation overeach band is easily
determined. Since the concentration can be expected to be more closely related to the
C\1 10
E
V i
8
(D
6
S4 i
2 
0
0 0.05 0.1 0.15 0.2 0.25
Frequency (Hz)
Figure 414. Bottom velocity spectrum for run 18.
near bed velocity than to the surface elevation, the bottom velocity spectrum, shown in
figure 414, is used instead of a surface spectrum. It is found by attenuating the
measured velocity spectrum to the bed by use of linear wave theory (Dean and
Dalrymple, 1984). A comparison of the CVFs generated for the bottom velocity in figure
414 and the concentration spectrum from figure 413 is shown in the first plot of figure
415. In addition, the second plot makes the same comparison, but with the CVF
generated from the concentration time series measured 1 cm from the bed. Because the
highest concentrations are found near the bed, the integrated concentration is dominated
by the contribution from the near bed concentrations. So, it comes as no surprise that the
0 0.05 0.1 0.15 0.2 0.25
Frequency (hz)
1
0.9
:0.8 '
S0.7 
5 0.6 
0.5
S0.4 Concentration (1 cm)
c  Surface elevation
" 0. 
0.1
0
0 0.05 0.1 0.15 0.2 0.25
Frequency (hz)
Figure 415. Cumulative variance functions from concentration and bottom velocity
spectra for run 18.
two plots indicate nearly the same behavior for the integrated and nearbed
concentrations. In both cases, a significant portion (nearly one third) of the total variation
in concentration is accounted for in the low frequency band. In comparison, very little of
the energy of the surface spectrum, figure 49, or the bottom velocity spectrum, figure
414, is found at low frequencies. In order to clearly show the significance of lower and
incident frequencies, the plots are cut off at 0.25 Hz. Within the frequency range from
0.25 to 1.00 Hz, the variation in velocity and in concentration is uniformly distributed.
These results indicate the nearbed suspended sediment concentration time series
has a very significant lowfrequency component. Furthermore, the forcing mechanism is
not apparent at the low frequencies, since this region is poorly represented in the surface
elevation spectrum. Although figure 415 indicates that the depthintegrated suspended
sediment concentration has similar behavior to, and is likely dominated by the nearbed
concentration, it is still instructive to examine the behavior further from the bed. Figure
416 makes the same comparison as in figure 415, but instead uses concentrations
measured 5 and 10 cm from the bed. Note that the low frequency contribution diminishes
and the variation in concentration is more uniformly distributed across the spectrum.
Also, with increasing height from the bed, the contribution to the total concentration
variation by frequencies greater than 0.25 Hz becomes more relevant. This and the
diminishing low frequency contribution both indicate that the variation becomes more
uniformly distributed with frequency as the distance from the bed increases. Above 10
cm, the concentration variation becomes still more uniform with frequency, but the
concentrations become so small that signal to noise ratio of the concentration
measurement becomes too low.
69
0.9 
>0.8 8 '
F
S 0.7
05 0.6
0.5 I "
. 0.3
u 0.2 
0.1
0
0 0.05 0.1 0.15 0.2 0.25
Frequency (hz)
1
0.9 
0.8 
0.7 
/
65 0.6 /
0.5
0.4 /
O 0.3
Lu 0.2 Concentration (10 cm)
/ , Surface elevation
0.1
0
0 0.05 0.1 0.15 0.2 0.25
Frequency (hz)
Figure 416. Cumulative variance functions from concentration and bottom velocity
spectra for run 18.
0 2 4 6 8 10 12 14 16 18 20
T50 (s)
Figure 417. Tso indicating less lower frequency (high period) relevance with increased
distance from bed for run 18.
To further examine this dependence on the distance from the bed, the frequency at
which the CVF of the concentration spectrum is equal to 0.5 is determined at each
measurement elevation above the bed. The corresponding period is that at which 50% of
the variation in concentration occurs above and below, and is designated by Ts0. A high
value of To therefore indicates that the low frequency variation prevails over the higher
frequencies in the suspension time series. A plot of Ts0 shown in figure 417 reinforces
previous observations showing the diminishing contribution to the total concentration
variation by lower frequencies with distance from the bed.
4.4 Correlation with Velocities
Long waves have been shown to drive sediment transport in the nearshore
environment (Beach and Sternberg, 1991). In the present experiments, the bottom
velocity spectrum and the surface elevation spectrum show very little energy at the low,
or long wave, frequencies where significant concentration variation exists. In this case,
the mechanism resulting in the low frequency concentration variation is not apparent.
Simple examination of the wave energy spectrum from a wave record can reveal the
frequency components contributing to the sea state, but will not provide information on
0.5 i i
0.4
0.3
0 .2 :: : .
0.1
Co
0.2
0.3 
500 550 600 650 700 750 800 850 900 950 1000
Elapsed time (s)
Figure 418. Surface displacement time series from run 18 with envelope determined by
Hilbert transform.
amplitude modulation resulting from the interaction of waves at various frequencies. The
interaction between components at the surface results in low frequency amplitude
modulation of the wave record, termed 'groupiness' due to the 'groups' of waves formed.
By use of the Hilbert transform, the envelope of the wave record can be found (Haller
and Dalrymple, 1995). Such an envelope is shown superimposed on a portion of a
surface elevation time series in figure 418. Wave groups are generally believed to
contribute to the forcing of long waves (LonguetHiggins and Stewart, 1964) and the
suspension of sediment in the nearshore region (Hanes, 1994). Because visual
observations at the time of the experiments indicated that wave groups were present, it is
speculated that the same interactions that result in wave groups result also in the low
frequency suspension events seen in the previous section. In the following, the source of
these interactions is examined.
Begin by considering the sum of only two components of slightly different
frequency.
77 = a cos(k,x aot) + a cos(k2x a2t) (42)
The wave numbers and angular frequencies alternatively can be represented by the
following:
k, =k 
2
2 Ak (43)
k =k+ +
2
and
SAC
,=a 2
SA (44)
2
Substituting these expressions and simplifying gives
Ak AC _(45)
r= 2aco Axt cos(kx t)45)
Squaring this expression and simplifying shows each interaction term.
2 1 + cos(Akx ACr)+ cos(2(kx t))+ cos((2 +Ak)x (2 +A+)t) (46)
[+ cos((2k Ak)x (21 Ao)t)
Examining the terms within brackets one at a time, the first term, being independent of
frequency, is simply a 'DC' offset. The second term, of greatest interest in this study, can
be rewritten as
cos((k2 k,)x(2 a)t) (47)
which clearly shows this term results from the the difference of the original frequency
components. Similarly, the second and third term can be rewritten as
cos((k2 + k,)x (2 + )t) (48)
which again clearly shows this term results from the sum of the original frequency
components. The final two terms are harmonics of the two original frequency
components, respectively, as can be seen by rewriting the fourth term as follows:
cos(2k2x 22t) (49)
Of the four components mentioned above, the frequency difference between components
results in wave groups. In order to examine the frequencies of the wave groups, the
envelope presented in figure 418 is transformed into the frequency domain,
0.18
0.16
0.14
e 0.12
>, 0.1
0.08
u 0.06
0.04
0.02
0 I I
0 0.05 0.1 0.15 0.2 0.25
Frequency (hz)
Figure 419. Spectrum of envelope from run 18.
resulting in the envelope spectrum shown in figure 419. From figure 419, it is apparent
that the frequencies best represented in the envelope spectrum are the same as those
represented in the lowest portion of the concentration spectrum, figure 413. Re
examination of figure 413 also reveals an active range of concentration variation at
frequencies higher than the incident wave frequencies. The components in this range
likely result from the harmonics and the frequency sum terms discussed above. This
further supports the conjecture that interaction terms contribute significantly to sediment
suspension.
Considering that all of the interactions are seen in the concentration variation, it is
worthwhile to examine the relation between the square of the bed velocity magnitude and
the near bed concentration. As before, the bed velocity magnitude is determined by
combining both horizontal velocity components, which are found by attenuating the
velocity measurements using linear wave theory. Concentration measurements made 1
cm above the bed are utilized in the following analysis. To this point, the results shown
in the figures have been restricted to those from run 18 for clarity. It should be noted that
the results from the other 3 runs used in this investigation show still greater significance
in the lowest frequencies of the concentration spectra. Application of the following
methods of analysis will verify this, and this analysis' results from data runs 23, 25, and
27 will be shown in figures 424 through 426 respectively.
In order to examine the relation, the coherency function is utilized. The
coherency function indicates whether one signal can be expressed as a linear function of
another signal. It is calculated by performing auto and crossspectral analysis over
sections of the signals, and then determining the linear relation between sections.
{c,o (04)} + {Q", (0)} (410)
(oM)S,, (O)
In this expression, Sx and Syy are the autospectral densities of the respective signals, and
Cy and Qy are the cospectrum and quadrature spectrum the real and imaginary
components of the crossspectral density function. Ochi (1990) provides thorough
explanations concerning the development and application of each of these functions as
well as the additional spectral analysis techniques presented in this dissertation. If the
same linear relation holds between various sections, the coherency function will return a
value of one. If the sections are related by nearly linear relations, the coherency function
will still return a value close to one. Should the sections have completely different linear
relations or should no linear relation exist for certain sections, the coherency function will
be zero. Ideally, the signal should be broken into as many sections as possible,
providing many degrees of freedom in the analysis. In addition, it is desirable to obtain
good frequency resolution at the lower frequencies in the spectral analysis, requiring that
the sections be sufficiently long. In the present case the length of the data files was
limited by the available memory in the data logger. Consequently, the number of degrees
of freedom in the analysis is limited to approximately 10, which allows a maximum
period of 3 minutes to be resolved. Coherency function values of better than 60% were
found in most of the comparisons between the square of the velocity and the near bed
a 0.5
(D
O 0.4
0
0.3
0.2
0.1
0.05 0.1 0.15 0.2
0.25
Frequency (Hz)
Figure 420. Coherency function between square of bed velocity magnitude and near bed
concentration for run 18.
concentrations, particularly at the lowest frequencies in the spectrum, as seen in figure
420 and plot (c) of figures 424 through 426. There is significant variation in the
magnitude of the coherency function across frequencies, due, in part, to the limited
degrees of freedom in the analysis. In addition, it is difficult to determine a linear
relation in the regions of the spectra in which there is little energy, due to limited
instrument resolution. Therefore, the value of the coherency function in these regions is
not as meaningful. For this reason, the results of the coherency analysis are presented in
another form. In figure 421, the concentration spectrum for the nearbed concentration is
shown. The curve is shown as solid in those regions in which the coherency function,
Nearbed concentration vs velocity magnitude squared
0.8
"'
t"
C
0.6
C"
0
o
.m 0.4
o
o
o
0 0.05 0.1 0.15 0.2 0.25
Frequency (Hz)
Figure 421. Concentration spectrum (dotted) with areas of coherency function > 60%
indicated (solid) for run 18.
determined from the near bed concentration and square of the bed velocity magnitude,
returned a value greater than 60%. These marked regions are the most dominant regions
of the concentration spectrum, covering a total of 76% of the total variation of the
spectrum. This indicates that a linear relation between the velocity squared and near bed
concentration is likely. In each of figures 424 through 426, plot (b) verifies this result,
showing high coherence in the portions of the spectrum with the highest magnitudes of
variance. Though only run 18 showed significant variation in concentration at incident
wave band frequencies, it should be noted that significantly higher coherence was found
in this region as the number of degrees of freedom in the analysis was increased. Since
increasing the number of degrees of freedom simply means increasing the number of
instances used in the evaluation, this could suggest that the statistical means of the
processes are linearly related at these frequencies. More runs with significant variation in
this frequency band need to be analyzed to confirm such a hypothesis.
Since the coherency analysis indicates a linear relation exists between the square
of the bed velocity magnitude and the near bed concentration, it is interesting to examine
the transfer function.
Y(w)= X((o)H(o) (411)
The transfer function, H(o), is simply a function which relates a linear system's input,
X(o), the square of the bed velocity magnitude in this case, to the system's output, Y(o),
the near bed concentration (Ochi, 1990). In the frequency domain, the input signal
multiplied at each frequency by the transfer function produces the output signal.
Considering that the input and output signals can vary in both magnitude and phase, the
transfer function evaluated at a particular frequency in general produces a complex
number. The phase variation is indicative of the time lag between the processes. Figure
422 shows the phase of the transfer function calculated for run 18. Examination of
figure 422 and plot (d) of figures 424 through 426 show a relatively small, and
typically negative, transfer function phase. There is a slight trend to decrease in phase as
frequency increases in the lowfrequency band of the relation. Such a trend indicates that
the time lag between the signals is nearly constant. It is expected that this time lag is
related to the upward sediment flux from mixing and to the fall velocity of the sediment.
Future investigations which include measurements of sediment size will aid in verifying
such a relation.
20 .
0
20 :
S40
0) I"
60
80
100 i
0 0.05 0.1 0.15 0.2 0.25
Frequency (Hz)
Figure 422. Phase of transfer function for run 18. Negative phase indicates
concentration lags square of velocity magnitude.
0 0.05 0.1 0.15 0.2 0.25
Frequency (Hz)
Figure 423. Magnitude of transfer function for run 18.
Finally, in figure 423 and in plot (e) of figures 424 through 426, the magnitude
of the transfer function is shown. For each particular run, the magnitude of the transfer
function at the frequencies in which the coherence was high varies little with frequency.
The relative difference in the transfer function magnitudes for different runs is attributed
to the difficulty in quantifying the bed location in the concentration profiles. In other
words, because the spatial resolution of the concentration measurement was limited to
0.75 centimeters by the sampling rate of the system, so was the resolution in determining
the bed location. With an exponential height variation in concentration, a small error in
determining the bed location can result in a significant change in concentration. For
example, referring back to figure 48, the concentration changes from 1.5 g/1 at the
closest measurement to the bed to approximately 0.5 g/l at the next closest measurement
0.75 cm higher. Regardless, it is promising to see that the value is nearly constant across
frequency for a particular run, and that this value is of similar magnitude between runs. It
is expected that this parameter too is related to sediment parameters and local
hydrodynamic conditions, such as bed roughness or bedforms. In relation with the
calculation of the time mean reference concentration, future research could attempt to
relate the magnitude of the sediment resuspension coefficient, since a linear relation
seems likely (Smith and McLean, 1977; Thosteson, 1995).
4.5 Discussion of Results
Although nearly every possible complexity preventing accurate evaluation of the
median grain diameter of suspended sediment was considered there were insurmountable
difficulties in determining grain size from the data collected in this experiment.
Horizontal gradients in concentration between measurements are believed to be
responsible for the difficulties in determining grain size. Vortex ripples were measured
in every data run, and may be responsible for this horizontal variation in concentration.
Because of the difficulties encountered, the constant grain size assumption was made in
the remainder of the analysis. Concentration measurements from the 2.25 MHz
transducer were used as opposed to those from the 5.0 MHz transducer, since for the
grain sizes encountered in the region, the 2.25 MHz unit shows less sensitivity to grain
size. It should be noted that errors resulting from this assumption are likely small in the
present analysis, because the active portion of the profile remained small. Namely, the
concentration profile stayed confined to the area very close to the bed, so analysis errors
82
(a) (b)
3.5
41.89% high cohefnce
3
2.5
13
2
05
0 0.05 01 0.15 0.2 025 0 0.05 0.1 0.15 02 0.25
Frequency (Hz) Frequency (Hz)
(c) (d)
S* I 200
0.9 :
0.850
100
0.7
0.4 / v 501 .P 1. ": .. : :
100
02
0.1 150
0 0.05 0.1 0.15 0.2 0.25 0.05 0.1 0.15 0.2 0.25
Frequency (Hz) Frequency (Hz)
(e)
2.5
2
0.5
0 0.05 0.1 0.15 0.2 0.25
Frequency (Hz)
Figure 424. Results from run 23: (a) bottom velocity spectrum; (b) concentration
spectrum; (c) coherence; (d) transfer function phase; (e) transfer function magnitude.
83
(a) (b)
3i 25
2.5
i20
2 .66.6% high cohrenc.
~1.515
1 5
10
C '^ f ^   ..' ' ^  I  i  *** **.*  
0 0.05 0.1 0.15 0.2 0.25 0.05 0.1 0.15 02 0.25
Frequency (Hz) Frequency (Hz)
(c) (d)
1 200
0 9 1 0
008
100
07
0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.( 0.15 0.2 0.25
0.6
04
0.3
Frequency (Hz) Frequency (Hz)
(e)
10
02
20
0 0.05 0.1 0.15 02 0.25
Frequency (Hz)
Figure 425. Results from run 25: (a) bottom velocity spectrum; (b) concentration
spectrum; (c) coherence; (d) transfer function phase; (e) transfer function magnitude.
0.05 0.1 0.15
Frequency (Hz)
0 005 0.1 0.15
Frequency (Hz)
02 0
100
50
100
150
/
0 0.05 0.1 0.15 0.2 0.2
Frequency (Hz)
0.2 0.25
Figure 426. Results from run 27: (a) bottom velocity spectrum; (b) concentration
spectrum; (c) coherence; (d) transfer function phase; (e) transfer function magnitude.
K.
PA
lil ~ .... 1_ 
~C~C
0
i
