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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 ACKNOWLEDGMENTS............................................................... ..........................iii LIST OF TABLES ......................................... ............................ vi L IST O F FIG U R ES ..................................................................... ................................vii KEY TO SYMBOLS ............................................................................ .................. x A B ST R A C T ................................................................................... ............................ xiv 1 INTRODUCTION .................................................. ........................................ 1 2 SYSTEM DEVELOPMENT................................................... ........................ 4 Instrum ents ................................................................ .......................................... 5 System D em hands ....................................................................... ....................... 8 System A architecture ................................................................ ............................ 11 Software and Algorithms.................................... ...................... 16 S um m ary ......................................................................... ......................................23 3 ACOUSTIC BACKSCATTER CONVERSION TECHNIQUE.............................. 25 T heory........................................................ ............................... ................... 28 D evelopm ent..................................... ..............................................................31 Concentration inversion ......................................................... ..................... 31 Size determ ination.............................................. ......................................... 35 Verification of Technique......................................................... 39 S um m ary ............................................................................ ................................... 45 4 SUSPENSION TIME SCALES.......................... ..................... .....................46 T he SIS96 Project.............................................. ............................................. 47 Size D term nation ............................ .......... ........................... ...................... 53 Dominant Frequency Band of Suspension Events ................... ........... .......... 59 Correlation with Velocities..................... ........... .......................71 Discussion of Results ................... ........................................................... 81 5 CONCLUSIONS......................................... ...................................................87 iv A ACOUSTIC PARAMETERS ................... .. .. ........................91 Lognorm al D istribution........................................................... ...................... 91 S system C o instant ......................................................................... .......................... 9 1 W after A ttenuation.................................................................... ............................. 9 1 Sedim ent A ttenuation .............................................. ....................................... 92 B ackscatter.......................................................... .................................................. 94 N earfield C correction .................................................................. ..................... 95 B LIST O F V EN D O RS .............................................................. ......................97 C MONLOG 1.0 PROGRAM LISTING......................................... 99 R E FE R E N C E S ............................................................................. ....................... 147 BIOGRAPHICAL SKETCH.................................................... 150 LIST OF TABLES Table oage 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 Fiure 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 MHz 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/l contour for whole time series of run 18................................62 411 Plot of the 1 g/1 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 Tso indicating less lower frequency (high period) relevance with increased distance from bed ................. ....... ... ........................................................ 70 418 Surface displacement time series with envelope determined by Hilbert tran sform ............................................ ....................... ............... ....................... 7 1 419 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 Magnitude of transfer function for run 18 ........................... .......................80 424 Results from run 23......................................... ............................................... 82 425 R results from run 25................................................................. ....................... 83 426 R results from run 27................................................................. ....................... 84 A1 Normalized total scattering cross section....................................... ....................93 A 2 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; Neper/ c Sound speed in water; m C(z) Mass concentration; or kg/ Co Concentration of suspended sediment at range zo; I or k 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 f, Acoustic frequency; MHz I Integrating factor used in finding explicit concentration solution I Discrete form of integral i Index (chapter 2 table element; chapter 3 transducer number) j Index bin number K, Constant in form function; K = 1.14 for noncohesive sedimentary material K, Constant in normalized total scattering crosssection; K, = 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; mm p(Z) Coefficient in Bernoulli equation (substitution) p Coefficient in Bernoulli equation (substitution); p Q(Z) Coefficient of inhomogeneous term in Bernoulli equation (substitution) Coefficient of inhomogeneous term in Bernoulli equation (substitution); Q R, ith element in RMS lookup table S Acoustic transducer system constant; S ,,S,,. Energy spectra; (time series units)2 xs T Temperature; C t Substitution in Bernoulli equation solution; C' V(z) Output voltage from acoustic transducer; V Vo Output voltage at range z0; V x Dimensionless particle radius x,,x2 Empirical constants in form function; x, = 1.4, x2 = 2.8 Z, Cumulative variance function z Range from transducer; m z( Range to first point in analysis; m z. Theoretical nearfield limit; m a (z) Sound attenuation due to sediment; Nepers /m a Sound attenuation in water; Neper/ Y 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; (NepersXm r, ,r42 Empirical constants in form function; I, = 0.5,1r2 = 2.2 Pc Mean concentration across transducers; g or k/3 I / m p0 Mean grain diameter in phi vI,v, Empirical constants in form function; v = 0.37,v2 = 0.28 P, Sediment density; kg/ or2 Variance oc Standard deviation of concentration across transducers; g or kg Ca Standard deviation of grain diameter in phi T Acoustic pulse width; s 0 Logarithmic grain diameter; 0 = log2 d X Normalized total scattering cross section 4 (z) Nearfield correction parameter /0 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 I 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 I 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 Beach S.te 'B... ^  ...... c StShore System cmpu ,i B V TV? 505 camera OBS Offshore Package \MTA's Fs 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 .ii.. Iihl rli er., 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)= {P(Z) Z e4( ,) (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 O, 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 120 points sampled at 100 kHz 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 (MONLOG10.C) TPU timing diagram TCR 1 1 MHz  Base r equency /16 .... TPU channel 14 1 A to conve ter riggerj .. TPU channel 9  100 Hz z1n F3 interrupt TPU channel 10  100 Hz : U F1 interrupt TPU channel 11 _ 100 Hz n HI interrupt TPU channel 13 I Hardware trigger s u, TPU channel 12  100 Hz Hardware sync pulse I I i i I I I i l s I 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 TBAaSE FlBUM OT40TX4 FFio ummllon memory F u 1 I.umem to mmor FSR F2 xcmma nomemor For use in data processing no Sn included in MAT lie. FaSUM 0NPPa 8*NOSP+24'NPP+32768 3FasF i unnapn men ory SPSOR [i NO Bor SPi = iummpnmon imiory F1HED i i NO eP '4 e FF Mat ab dae haadsr F1 RMS profile l.m" xlef FHED NppNFi TA12 variab N PH TTMA128 variable SM ib It. ft, Stored as snglae data Wle on TT SPMEN 26 S MTAianaha NFP'(NPP'6+NOSP*2)+ MTtBAs 26 MTA NUMSCANS'152+ MIAED 11 1 26*9+24 MT21EDs MTANUMSCANS77 MTA 123 L lme Ie M.IMI, TIm M I F 2MBA o ounieiyn e olr OFFENoo rl Dumeoyoiablespce PAD var able I 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: Ro =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. ;Initialize RMS routine for F nidxres move.l _flsqr,a0 move.l _tflbas,al move.l _rtbase,a2 ;RMS routine Fl avloopfl move.l (a0),d0 move.l #0,(aO)+ 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 #1,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 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 27 Theoretical voltage from concentration; 5 MHz 2.5 iiii 2 1.5 Dashed: 2 cm, max at 9.2 g/l 0) Dotted: 16 cm, max at 1.3 g/l 1 Solid: 31 cm, max at 0.7 g/l 0.5 0 1 2 3 4 5 6 7 8 9 10 Concentration (g/l) Figure 31. Expected voltage for given concentrations, 5 MHz transducer. 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). VYz =(S2cT.) F(z)C(z)e 4z,+, sinhB )v2'Wz) B (31) a, = 1J(Z)C(Z)dZ (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 r = acoustic pulse width (s) i = 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,+ (z)C(z)) zo = range from transducer at which first concentration and size is evaluated. 4 = 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, a, = 0.25. Note these parameters are given in units of phi, defined as 0 = log, 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% 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/1) sinh 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: Vz = AF(z)C(z)e .") (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 ()z2 exp(4z(a, +a,(z))) AF(z)C(z)= V2(z2 exp j4(a, +(. "k .(. k (35) Following the LH95 derivation, first, the natural logarithm of the equation is found InA+lnF+lnC=21n(Vz)+ (4a, +4C)di (36) and then the derivative, denoted by ('). F' C V'z +V += 2[1 I+4a, +4C (37) Upon arranging the terms of equation (37), a nonlinear differential equation of the Bernoulli type results. C+F'2( +V 4a, ]C= 4C2 (38) Rewriting in standard form, equation (38) becomes the following: C' + p (z) )C" (39) with F' V'z+V P(z)= F 2 4(4a (310) Q(z)= 4 (311) n = 2. (312) Following the standard method of solution for a Bernoulli equation, the following substitutions can be made: (313) t=C'"=C1; C=t1 dC dC dt t t' dz dt dz (314) These substitutions result in a readily solved first order linear inhomogeneous differential equation. tt'+ pt = Qt2 (315) t'+ t t= (316) Where, in equation (316), the following apply: p=p S=Q (317) Solution to equation (316) is found by first determining the integrating factor. I=exp(q dz) (318) jPdz=f F'_ 2V+V 44a z=InF+4az+21n(Vz) (319) (Vz )2 I =exp(21n(Vz)+4,z In F)= Z exp(4a z) (320) F After multiplying the equation by the integrating factor, an exact differential results, which can then be integrated for solution. d (Vz)2 exp(4az)t 4 (V exp(4az) (321) dz F F (VF exp(4az)t =j 4 exp(4,2)d+y (322) Equation (322) is then solved fort, and then finally for the concentration, C. Equation (322) is then solved for t, and then finally for the concentration, C. y 4.(W) exp(4a, )d t= (323) v exp(4a z) F (Vz exp(4a.z) C=t 2 (324) tyJ4(F exp(40 *, Next, the boundary conditions (325) are applied for solution of the integration constant. C = Co V=V o at z (325) F=Fo Y = exp(4azo) (326) F,,Co The concentration Co at the nearfield limit z,, 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 (Vzo)2 e4,(.+c) (327) C F(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 (z 4) (3ei C= 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+l bins outside the nearfield region of each transducer. ( jexp(4a,,) (329) F, i = 1,2,...,m Ii j=1,2...,n In the denominator of this expression, I is the discrete form of the integral, given by the following: I", =2 '(Vz exp(4ak)+ ., ( k exp(4a, k ) (330) The integration constant is defined again at point zo. y= (z exp(4a,,zo) (331) FoCs,0 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 zo 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 = (Z (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/1. Should the transducer be located a half meter from the bed, concentrations above 1.6 g/l 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 4 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. Pc =Yl C, (333) C = (l (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) 0 004 o 0 02 0 an 0 0 0 0 01 02 03 00 0 0 08 00 I (c) 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/1, and the grain size distribution was assumed to have a median grain diameter yi. = 2.66 and a standard deviation t, = 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) 0Ii 0 01 02 03 o4 o( m)o0 o07 0 0 01 a.? 04 0 0a 07 o0 00 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 41 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 Thome's (1997) simulations, and size in the majority of the cases. This test does illustrate the (a) (b) DIstanc0 00) 0 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. 01 2 04 0 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. co" co to to 01 02 01 O1 OI DS ol 00 118 Diaun(m) i   i! '" ,, ,, ,, O1 02 03 o DI OB Oi 08 08 OMnalmi 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 p = 2.66 and a standard deviation a = 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 (a) (b) 2 0 1 7 02 03 04 os 00 O 0s 0 0 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)  j Of 05 OB 07 OB 00 4 05 o.0 0o7 .B 0 0 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 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 reconfiguring 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 IF i Figure 42. Instrumentation used in project. Table 41. Calibration constants for instruments used in present analysis. Instrument Gain Offset System constant Pressure sensor 8.35 x103 mout 6.77 m /count (salt water) (salt water) CurrentX 1.187x10 count 2.457 m/ Current Y 1.203 x10 m count 2.492 / OBS 1.409x10 count 01649/ 2.25 MHz ACP 11 mV 0.464 5.00 MHz ACP 2 mV 0.929 51 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 4 I 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) 2.2SMHZ S0.44 DC= 11ol 5.0 MHz S09.g2 DCo.02 vot I o  0 0 04 0 OA OS o.7 o Range (m) oangs (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 0 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 07 05 L0.4 03 02 0.1 0 05 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. (a) (b) i I 140 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 7 6 5 CUi5 a3 2 C2 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 6   I   i i E 03 4 21 I I.. . 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Elapsed time (s) Figure 47. Change in bottom location due to settling of instrument framework. 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 20 1t 21o 221 a 2 2.2 2z 2 2 222 1o 0 0 RuHW13l 1; \ 004(3,00000) b i 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. io' la' id" 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 dso Depth (EDT) (MM:SS) (m) (gim) (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 Hno Tpeak 8pek Iu direction Ir npp, ) nppl (m) (s) () (cm/s) () (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 J.3 3 2.5 0 E2 Co 1.5 0.5 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 3 0 200 400 600 800 1000 1200 1400 1600 1800 Elapsed time (s) Figure 410. Plot of the 100 mg/l contour for whole time series of run 18. 1 1 111 0 200 400 600 800 1000 1200 1400 1600 1800 Elapsed time (s) Figure 411. Plot of the I g/l contour for whole time series of run 18. 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/1 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 0.6 00r 1 1 1 1 .20.21 I 1200 1300 1400 1500 11 ~L 600 1700 11 S1200 1300 1400 1500 1600 1700 Elapsed seconds (s) Figure 412. Time series of the squared bottom velocity magnitude and vertically integrated concentration. ' .''V 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 6 o) 03 52 01 0 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 Z,, indicates at a particular frequency the portion of the total variance accounted for by lower frequencies. In analytical form, Z, is given by the following expression: f Jsf f')df' Z,(f)= I = S(f')df' (41) S (f ')df ' 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 12 1c 10 6 a) 4I 2 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 0.9 0.8 a0.7 '0.6 0.5 0.4 0 S0.3 LL 0.2 0.1 Frequency (hz) 0 0.05 0.1 0.15 0.2 Frequency (hz) Figure 415. Cumulative variance functions from concentration and bottom velocity spectra for run 18. 0.25 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. 0.9 ,0.8 / S0.7 / S0.6 0.5  F 0.4 Concentration (5 cm) 03  Surface elevation 2 0.3  uL 0.2 0.1 0 0 0.05 0.1 0.15 0.2 0.25 Frequency (hz) 0.9 _ 0.8  0.7  5 0.6 0.5  0.4  0.3  L 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 Ts5 therefore indicates that the low frequency variation prevails over the higher frequencies in the suspension time series. A plot of T.0 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 .. . 0.4 0.3 0.4 CL 0 0.2 0.3 0.4 0.5 500 550 600 650 700 750 800 850 900 950 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. r = a cos(kx ot) + acos(k2x 2t) (42) The wave numbers and angular frequencies alternatively can be represented by the following: Ak k = k 2 Ak (43) k2 =k+ 2 and Ao ,=o 2 SAC (44) o,=ff+ 2 Substituting these expressions and simplifying gives (Ak A (45) r7= 2acos xxt cos(x t) Squaring this expression and simplifying shows each interaction term. l + cos(Akx AI)+cos(2(x tr))+ cos((2 + Ak)x (2 + Acr)t) (46) 772 = a 2 + a cos((2k Ak)x (2 Aa)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((k, k, )x (ao )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((k, +k,)x (o + o,)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: tcos(2kx 2oct) (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 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 I 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. S{C, (o } + {Q, (4)} (410) s ())s,, (o) In this expression, S. and Sy, are the autospectral densities of the respective signals, and C,y 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 0.9 0.8 0.7 0.6 s0.5 00.4 0 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 1.2 Z0.8 S0.6 0 0 0.2 o 1 I 0o '~L 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(o)= X ()H () (411) The transfer function, H(w), is simply a function which relates a linear system's input, X()), the square of the bed velocity magnitude in this case, to the system's output, Y(m), 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. 0 0.05 0.1 0.15 0.2 Frequency (Hz) Figure 422. Phase of transfer function for run 18. Negative phase indicates concentration lags square of velocity magnitude. 0.25 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/l 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 FW.0 (0 1 Frq 5 02 025 F MyH2 S 005 01 F 0. 02 025 Figure 424. Results from run 23: (a) bottom velocity spectrum; (b) concentration spectrum; (c) coherence; (d) transfer function phase; (e) transfer function magnitude. 0 01 FI,, 1 Br~' l gh) A OiL o o or olr or ozi o7 OS : 0 oo 01 015 o02 05 FtqU an CyHl Figure 425. Results from run 25: (a) bottom velocity spectrum; (b) concentration spectrum; (c) coherence; (d) transfer function phase; (e) transfer function magnitude. 6se6% 0gh0c0twrnc D Fr 01 (0) i, olr (a) (a) III ________________ n B. I a i" I,", oo o.05 015 2 FrIiy (? jo:  S F0 r 0 q O.5 0. 2 Figure 426. Results from run 27: (a) bottom velocity spectrum; (b) concentration spectrum; (c) coherence; (d) transfer function phase; (e) transfer function magnitude. ', V N r FrttU.roy (05) which can propagate down through the profile didn't have far to propagate. Analysis of the concentration spectrum shows that low frequency variation is as well represented as variation in the incident wave band. Failing to account for the low frequency variation in concentration will result in neglecting a large percentage of the variation. Considering that the surface elevation spectrum and near bed velocity spectrum show no infragravity component, the sediment suspension was not driven by long waves. The frequencies of the variation coincide well with the incident band frequencies and the resulting frequencies from interactions between components of the incident band. This indicates that the groupiness of the waves is responsible for the low frequency variations in concentration. Physically, several explanations are possible. Sediment may be more readily suspended after several consecutive large waves than after only a single large wave, perhaps due to group enhanced fluidization of the bed. Possibly the time required for the sediment to settle introduces a sort of memory effect, such that each consecutive large wave of a group will add more sand to that currently suspended. Likewise, turbulence generated at the bed may build, changing the boundary layer structure and the settling properties of the sediment. Linear coherence between the square of the velocity and the near bed concentration is found across most of the frequency spectrum. Because many attempts at modeling sediment transport treat the wave conditions by a single representative wave height and period, no low frequency components from interactions will result. Not surprisingly, there has been little success in predicting an instantaneous concentration time series. Should linear interactions between spectral components be considered, the present results seem to indicate prediction of the concentration time series is promising. 
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