A NEW METHOD FOR THE MEASUREMENT OF BEDLOAD TRANSPORT USING TIME SEQUENCED BATHYMETRIC DATA. David Daniel Abraham

Transcription

1 A NEW METHOD FOR THE MEASUREMENT OF BEDLOAD TRANSPORT USING TIME SEQUENCED BATHYMETRIC DATA by David Daniel Abraham A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Civil and Environmental Engineering in the Graduate College of The University of Iowa May 2009 Thesis Supervisor: Professor A. Jacob Odgaard

2 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL PI-I.D. THESIS This is to certify that the Ph.D. thesis of David Daniel Abraham has been approved by the Examining Committee for the - thesis requirement for the Doctor of Philosophy degree in Civil and Environmental Engineering at the May 2009 graduation. \Vi1Jiam A. Thomas

3 Copyright by DAVID DANIEL ABRAHAM 2009 All Rights Reserved

4 ACKNOWLEDGMENTS This trek has been arduous at times, but mostly interesting and challenging. At the present time the rewards of such an endeavor have been realized in the solution of a technical problem. But for me personally, a far greater and unexpected reward has been the interaction with all the gracious colleagues and friends and family members who contributed in so many different ways. Some contributed with technical prowess, some with simple suggestions, and almost all with encouragement to pursue the matter to its logical end. I have attempted to do so and hope that the result will find application in real world problems, which will be an additional reward down the road. I gratefully acknowledge and thank Professor Odgaard for being the Thesis Supervisor as well as an advocate and friend throughout. Likewise for each of the other committee members, Bill Eichinger, Roger Kuhnle, Marion Muste, Thanos Papanicolou and Tony Thomas. Here at WES, Ron Copeland, Brad Johnson, Ronnie Heath, Gary Brown, Jarrell Smith and Thad Pratt bore the brunt of sometimes long discussions pondering the work, and so deserve special mention. However that is not to take away from all the others too numerous to mention who listened, added ideas, operated boats, and set up flumes and instruments. In the COE and FISP, Jon Hendrickson, Kevin Landwehr, Ken Stark, Jeff Waters, Dan Eng, Clarence Thomas, Brod Davis and the CHL-IRIP not only added encouragement, but funding through various ways and means. I especially thank all my family members, scattered about as we may be, for all your love and encouragement. Finally, in whatever benefits might come forth from this work, I do believe that each of you deserves a share of the credit. Something like this is never done in a vacuum, and never accomplished by only one person. 11

5 ABSTRACT Vessel mounted Multibeam depth sounders can be used to map the bathymetric features of rivers, including sand waves. This research has shown that it is possible to use two sequential bathymetric surfaces which contain sand wave profiles to determine bed load transport. Starting with the well known bed-load equation for translating bed forms, analytic and geometric considerations are presented which establish a relationship between the rate of scour on the eroding side of a sand dune and the average transport in the same dune, for certain ideal conditions. It is further shown that the rate of scour is twice the average transport. Using these two pieces of information, bedload transport can be computed from the scour rate obtained from the difference of two surfaces acquired over a fmite time interval. To test the new method, three data sets were acquired. Two of these sets were obtained in flumes under controlled conditions. This provided a measured value of a bedload to which the value computed by the new method could be compared. Computed results show very good agreement with measured data, having average values that were 30% and 8% greater than the measured value for sets 1 and 2 respectively. The third data set was from Mississippi River bathymetry. Computations were made on 5 large sand waves for which sequential data were available over a range of time intervals. Although no measured value was available to compare to, the results were consistent within a given wave. All indications are that the method is repeatable and consistent when reliable bathymetric data are available. Instrument resolution was considered, and will play an important role in determining a minimum time interval between sequential profiles. At this time the method is limited to use on large sand bed rivers in which lower regime sand waves (no antidunes) are present and in which measurements can be made. For optimal data collection efficiency, some knowledge of dune size and wave speed is necessary. Ill

6 TABLE OF CONTENTS LIST OF TABLES... vi LIST OF FIGURES... vii PREFACE... ix CHAPTE.R 1 INT.RODUCTION Defmi tions The Need for and Historical Background of Bedload Measurement Physical Sa.mplers Analytic Measurement Techniques Combination Bedload Measurement Methods Purpose of Research Layout of the Dissertation Innovations and Contribution of the Research... 9 CHAPTER 2 THEORETICAL BASIS FOR THE NEW BEDLOAD MEASUREMENT METHOD Sand Transport in a Translating Bedform Some Analytic Considerations Some Geometric Considerations A New Conceptual Bedload Measurement Method CHAPTER 3 BEDLOAD COMPUTATIONS FOR FLUME DATA SET Collection of Data Equipment and Procedure: Total load (gs) Equipment and Procedure: Suspended Load (gss) Equipment and Procedure: Bedform Load (gsbi) Data Processing and Analysis Results for Flume Data Set CHAPTER 4 BEDLOAD COMPUTATIONS FOR FLUME DATA SET Collection of the Data Equipment and procedure: Total Load ( qs) Equipment and Procedure: Bedform Load ( qsbi) Processing and Analysis of the Data Results for Flume Data Set CHAPTER 5 BEDLOAD COMPUTATIONS FOR MISSISSIPPI RIVER DAT A Collection of the Data Equipment and Procedure Processing and Analysis of the Data Results for Mississippi River Data lv

7 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS Conclusions Recommendations REFERENCES v

8 LIST OF TABLES Table Table 1. Variability of Transport in Different Wave Forms Table 2. Raw Data and Computed Transport Table 3. Comparison of Hydraulic Parameters and Wave Speed...40 Table 4. TNP-6 run Table 5. Transport Results TNP Table 6. Data Collection Times and Time Steps Table 7. ISSD0Tv2 Computations Using 4 Time Steps Table 8. ISSD0Tv2 Computations Using 3 Time Steps Vl

9 LIST OF FIGURES Figure 1. Definitions of Total Sediment Load Helley-Smith Bedload Sampler Delft-Nile Bedload Sampler Triangular Approximation of a Typical Sand Wave Method off orward Motion of a Sand Wave Example off orward Motion of a Sand Wave in a Flume Flow Characteristics Over Sand Dunes Schematic Definition for the terms of Equation Relationship Between Scour and the Product of V s and H Triangular Wave Translating to the Right with Constant Velocity Comparison of Area Movement for Rectangular and Triangular Waves Variation of Area Transport for Different Geometric Shapes Demonstration of 2: 1 Ratio of Scour and Transport View of Experimental Flume Looking Upstream Schematic of Experimental Flume Density Cell Connected to Return Slurry Pipe Isokinitic Sampling of Suspended Sediments Accoustic Sensor Banks of 8 Transducers Each Locations of Longitudinal Profiles Example of an Extracted Longitudinal Profile Surface Difference for the Last Wave as a Time Series Surface Difference for the Last Wave vs. Position Sample of Sand Dunes formed in the 1.22m Wide Flume Dune Profile Measurement Technique Using Two Acoustic Transducers Vll

10 25. Acoustically Measured Sequential Dune Profiles Example of Sequential Dune Profile from Flume Data First 3 Waves of 3-d Surface for Profile TNP Difference Plot for First 3 Waves oftnp ISSD0Tv2 Computed Versus Measured Transport Values Swath of Bathymetric Data 76m Wide and 5.8 km Long Survey Vessel 'Boyer", St. Louis District USACE Selected Study Area Showing 5 Well Defined Dunes Difference Plot Showing Scour and Deposition Vlll

11 PREFACE This author has pursued the measurement of bedload transport moving in sand waves of large sand-bed rivers for some years now. The idea was conceived of sometime in 1998 when the Engineering Research and Development Center - Coastal and Hydraulics Laboratory (ERDC-CHL) field measurement group began plotting out bathymetric data obtained using high resolution multibeam depth sounding equipment. This equipment was vessel mounted and allowed the acquisition of sufficient data points to resolve the bathymetric features of the sand waves and even ripples on the river bed. Considering that the vertical resolution was sufficient, it was postulated that by taking successive bathymetric measurements of the same location at two or more different times, the differences of surface elevations that would occur during this time interval should allow the computation of the bed-materialload transported in the sand waves. By 2003, using data collected at Pool 8 of the Upper Mississippi River, a methodology for computing bedload transport had been developed. It was initially called Integrated Surface Difference Over Time (ISDOT), see Abraham and Pratt However, the name did not emphasize that numerous cell computations were being added up over a river cross section, so the name was changed to Integrated Section, Surface Difference Over Time (ISSDOT), see Abraham and Hendrickson During this time period it was realized that the method as used at that time was not computing the transport, but the change in transport during the time interval. Thus it was acknowledged that the method could be used to show relative changes of transport, but not the absolute value of transport at a given location. For a discussion of the implications of that fact, see Abraham et al 2006, page 19. In 2007, funding was received to further the research and resolve, if possible, the outstanding issues of the ISSDOT methodology. The funding was provided by the ERDC-CHL Internal Research and Improvement Program (IRIP), and the Regional Sediment Management (RSM) program. The work was carried out at. IX

12 the University of Iowa, Iowa Institute of Hydraulic Research (IIHR) and at ERDC-CHL in the later half of An investigation into the bed continuity equation (generally referred to as the Exner Equation), and translating geometric wave forms was part of the work performed to establish a more fmn analytic understanding and foundation for the method. This analysis showed that a modified version of the original ISSDOT method should provide a way to compute the absolute value of the bedload transported in the moving sand waves. Modifications were made and by summer's end it had become clear that the method could in fact provide very good estimates of bedload transport. This was determined by using several sets of bathymetric data obtained in flume studies and computing the bedload transport using the modified ISSDOT method. Computed values compared well with the measured values. This thesis is not intended to look back on previous versions of the method, but rather documents the most recent work on the ISSDOT method and is intended to show its validity and how it can be used. For clarity and to differentiate the older concept of ISS DOT from the present version, the newer modified method will be referred to in this document as ISSDOTv2. X

13 1 CHAPTER 1 INTRODUCTION 1.1 Defmitions Bedload transported in sand waves, is the subject of this research. In this dissertation the terms sand waves, dunes, sand dunes, or bedforms all mean the same thing and are used interchangeably when discussing the various aspects of bedload transport. An appropriate departure point for this subject matter is to make some basic definitions. The material that exists in the bed of a river can be transported both in suspension and in migrating waves, or dunes, as well as in flat beds or antidunes depending on flow and sediment conditions on the bottom of the channel. Making a distinction between suspended sediment transport and bedload transport comes about because of the different physical processes that characterize them. These differences are so large that it becomes necessary to develop quite different techniques to measure them, and thus also differing ways of defining each. Figure 1 is a diagram which helps in understanding the different defmitions. Einstein (1950) defmed bedload as "bed particles moving in the bed layer. This motion occurs by rolling, sliding and, sometimes, by jumping". He further defmes a bed layer as, "a flow layer, 2 grain diameters thick, immediately above the bed. The thickness of the bed layer varies with the particle size". This defmition most closely refers to the 'bed' in the left column of Figure 1. Bedload is defmed by Emmett (1980) as "that sediment which is carried down a river by rolling and saltation on or near the streambed." He further adds the stipulation that it is the part of the sediment load supported by frequent solid contact with the unmoving bed. According to this definition, it could refer to the transport in the 'bed' as in the left column of Figure 1, or it could be a portion of the 'unmeasured' bed material in the right column. Suspended load on the other band is defined as that portion of the bedmaterialload in which a particle has no contact with the bed. Thus suspended bed

14 2 material can be the 'suspended' material in the left column, the 'wash' load and a portion of the 'bed material' in the middle column, and the 'measured' and a portion of the 'unmeasured' bed material in the right column. Figure 1. Definitions of Total Sediment Load These examples illustrate the necessity of clearly defining what portion of the total sediment load a researcher is interested in. In the case of large sand dunes, the bed material transported in the translating dune will certainly be as described by Einstein. But it can also have a portion of particles that jump higher than 2 grain diameters and remain suspended for distances greater than 100 grain diameters, yet never permanently go into suspension and always fall back down on the same dune due to its relatively large size. These particles will fall into Emmett's defmition of bedload. Since the subject of this research is quantification of bedload being transported in large sand dunes, it appears that both definitions apply. Therefore when bedload is referred to in this document it will be understood to encompass the 'bed' load of the 'mode of transport' column, and a

15 3 portion of the 'unmeasured' load of the 'mode of measurement' column of Figure 1. Finally, washload is ignored in this study. Thus the total sediment discharge is considered to comprise the suspended load and the bedload, both of which originate from the bed-material. Since the bedload is only a portion of the total bed-material load, and suspended and total bed-material are also discussed in this work, the following nomenclature is used to stay as close as possible to the defmitions in ASCE Manual 54 Appendix III. gs is total sediment discharge per unit width, [M/TL] gss is suspended sediment discharge per unit width, [M/TL] gsb is bedload sediment discharge per unit width, [MITL] qs is total sediment discharge in volume per unit width, [L 2 /T] qss is suspended sediment discharge in volume per unit width, [L 2 /T] qsb is bedload sediment discharge in volume per unit width, [L 2 /T] 1.2 The Need for and Historical Background of Bedload Measurement Measurement of bedload transport is important for numerous reasons. Some of the most important are: Area. research. For the determination of dredging requirements. Predicting depositional effects on entrances to harbors, locks and dams. Predicting the useful life of sediment detention basins. Predicting the loss of storage capacity of reservoirs over time. Sediment management for environmental concerns. Sediment management with respect to land subsidence as in the Louisiana Coastal To help determine actual ratios of bedload to suspended load, and other related

16 4 To develop sediment rating curves, that is, establish relationships of flow versus bedload transport for local areas in which sedimentation problems have been identified. To provide a proven and accurate measurement of bedload that could be used by researchers to improve analytic methods. Attempts to measure suspended load are well defmed and documented. See for example, St. Paul U.S. Engineer District (1941), Davis (2005), and Gray et al. (2008). However, suspended sediment samplers typically can not sample any closer to the bed than the distance from their bottom to the nozzle. This distance is usually somewhere between 3 to 5 inches, depending on the size of the sampler. They normally are not able to sample any of the material rolling and saltating along the bottom of the river, and thus miss most or all of the bedload. Thus bedload cannot be measured by these samplers Physical Samplers Bedload samplers of the pressure difference kind, Helley and Smith (1971), on the other hand sit on the bottom of the river and capture most or all the Sample bag Figure 2. Helley-Smith Bedload Sampler

17 5 bedload. However, they might also capture some of the suspended load. Many other bedload samplers have been devised, such as bags, boxes and traps, see Hubbell (1964), Leopold and Emmett (1976), and Kuhnle (2008). The different methods described by these authors met with varying success depending on the size of the river and the type of bed material, that is, whether it was cobbles, gravel, or sand. Yet for whatever successes could be mentioned for small to medium sized streams, there was no method or sampler developed that could sample the bedload of large sand-bed rivers. In this case, a large sand bed river is meant to be applied to rivers such as the Mississippi, Columbia, Missouri, and Ohio. The spatial variability of transport and the flow depths make physical sampling of these rivers especially problematic. One of the few samplers that might be used to attempt measurements on such rivers is the Delft-Nile sampler, see Gaweesh and van Rijn (1992), and Figure 3. This sampler has been used on the Nile River in Egypt and the Rhine River in Holland as described in Gaweesh and van Rijn Figure 3. Delft-Nile Bedload Sampler

18 6 (1994). It was also used on the Mississippi River just south of Vicksburg in November of 2002 with some success. However, the depth of the river, number of samples required and other logistical considerations make the use of this sampler and any like it very labor intensive and somewhat problematic on large rivers at the present time. Thus physical sampling of large sand bed rivers to determine bedload transport remains elusive to the present time Analytic Measurement Techniques Analytic methodologies have also been attempted. These methodologies are usually one of three basic types; deterministic, probabilistic, or empirical; or even a combination of these. The earliest researcher normally mentioned who attempted an analytic method to determine bedload transport is DuBoys (1879), who envisioned bedload transport as layers of sand sliding over one another. In modem times, H.A. Einstein (1942,1950), Meyer Peter and Muller (1948), Bagnold (1956), Colby (1957), Yalin (1963, 1972), Engelund and Fredsoe (1976), van Rijn (1984, 2007), Cheng (2002}, and others have all presented methodologies by which bedload can be computed. Other researchers have made comparisons of the various methods and/or compiled guidance lists for the best application of them; see Stevens and Yang (1989), Nakato (1990), Molinas and Wu (2001), and Thomas, Copeland and McComas (2002), Garcia et al appendix D (2008). Despite the many analytic transport functions and physical sampling methods described above, there is still no standard methodology that provides an undisputed 'best estimate' for bedload transport in large sand bed rivers. To emphasize this consider a quote from Leopold and Emmett (1997), 'It would be highly desirable to have direct measurements of the bed-load transport in a natural river and of the concomitant hydraulic characteristics of the flow. The problem has been particularly

19 7 intractable, because no sampling device has been available that would provide reliable and repeatable measurements of the debris load moving along the bed of the river.' Combination Bedload Measurement Methods Other than direct measurement and/or analytic equations, several other methods of determining bedload transport are commonly considered. One such method is dune tracking, which uses a combination of analytic considerations and field data. With some basic assumptions which shall be considered later, it is stated that all or some portion of the bedload moves in the sand waves, or dunes. Thus if one can measure some properties of the moving dunes, then one can compute the bedload transport. A landmark paper was written by Simons and Richardson (1965) describing the process. Crickmore (1970) and Engel and Lau (1980), also pursued bedload quantification using similar considerations. The basic premise is that by knowing the wave speed and dune geometry, one can compute the bedload transport in the dune. The different researchers acquired flume data to validate the results. Their computed values of bedload compare well with measured values and the analytic formulation is sound for the conditions set forth. However difficulties arise in applying the method to dunes in natural channels. The spatial variability and temporal instability of the dunes as they move cause the determination of their geometry and celerity to be problematic. Cross correlations of dune geometry statistics must be performed on at least two dune profiles taken at different times for one sample point. This point is again an average over some time and space. Wilbers (2004) had some success employing a method like this using multibeam bathymetric data. However, field data of bed load transport from independent methods is either marginal or nonexistent, and thus results obtained using these methods are difficult to verify in the field. Thus the need still stands as lamented by Leopold above, '... no sampling device has been available that would provide reliable and repeatable measurements of the debris load [bedload] moving along the bed of the river'. If such a device or methodology

20 8 existed, it could become a standard by which these other methods might be evaluated. Such a method must be tested against known values. This can be most readily done in a flume in which the various parameters of sediment transport can be controlled and/or measured to some know extent. The International Bedload Surrogates Monitoring Workshop organized by the Bedload Research International Cooperative (BRIC) in April of 2007 provided an excellent forum for presentation and initial testing of new measurement techniques. This method was not submitted at that time. Hopefully further collaboration with the BRIC will be possible in the future. For more information on the BRIC see Gray, Laronne and Marr (2007). Hamaori (1962), and Willis and Kennedy ( 1977) presented methods which used dune profiles and statistical considerations to determine transport in controlled flume conditions. Finally, Jain (1992), Rennie et al (2002), and Papanicolaou (2009) have presented particle movement methodologies by which to estimate bedload transport. 1.3 Purpose of Research This research effort was initiated to help resolve some of the problems enumerated above regarding the measurement of bedload transport. It is a methodology which uses a combination of analytic considerations and modem measurement techniques. It will be shown that, under certain ideal conditions, the bedload moving in a translating dune has a set relationship to the amount of material being removed on the upstream side of the dune, which we will call the scour rate. This is, that the scour rate occurs at a ratio of 2: 1 to the average transport in triangular dunes. An important part of the research consists of substantiating this relationship. Knowing that this relationship exists allows one to use two sets of spatially concurrent bathymetric data taken at two separate points in time to determine the bedload transport. Another important part of the research is to verify the outcome of the new method computations with measured data.

21 9 1.4 Layout of the Dissertation In the chapters that follow a theoretical basis for the new measurement technique will be presented. Then several data sets will be shown from which bedload computations were made. Where available, the computations will be compared with measured values. Discussion of results will then be made and finally, a chapter on concluding remarks. 1.5 Innovations and Contribution of the Research It has not been noted in the literature that anyone has identified this unique relationship between bedload transport in a waveform and the scour rate. If it is known, then it has not been used in this manner to determine bedload transport. So both of these facts if not new, are certainly new uses of that information. Nittrouer et al (2008) have recently published a paper on the subject of using bathymetric data for determining bedload transport. One major and significant difference between their work and this is that they have not identified nor used the scour rate to bedload ratio in their computations. Also, they choose to use the depositional changes in the bedforms rather than the scour, and thus their method might be more applicable to alluvial fans where deposition occurs. Other than Nittrouer (2008), previous methods described above all require that wave celerity and dune statistics be determined in order to find the bedload. Such computations result in an averaged value of dune geometry and wave speed over some time interval and spatial domain. An innovation of this method is the direct computation of the bedload transport value from the measured data, which directly estimates the transport in a given dune. Further, all the other methods perform computations along longitudinal transects. Thus the average values computed are valid only for the transverse position in the cross section from which the profile was obtained. This method can and is intended to be

22 10 used from bank to bank if the waves permit and thus can also be used to determine lateral variations across the section. This should be possible with other methods as well, but not without more extensive computations, averaging and/or sampling. It is intended to use the new method to literally integrate over a cross section using the actual dunes by superimposing a grid over a 3-d surface. This will be shown in more detail in the chapter on field data. Finally, the new method has the potential to greatly improve the accuracy, and decrease the uncertainty of bedload measurements because the number of intermediate calculations and averaging performed on the raw data can be greatly reduced and/or eliminated compared to some of the other referenced methods. Unfortunately, at this early time in the development of this method, no comparisons have been with other field methods. This method is not without its limitations. These are discussed in the 'Conclusions' section of this document.

23 11 CHAPTER2 THEORETICAL BASIS FOR THE NEW BEDLOAD MEASUREMENT METHOD 2.1 Sand Transport in a Translating Bedform Riverine bedforms are wave shaped sediment undulations on the bottom of the river formed by the moving water above them. They can exist in various shapes and dimensions, such as ripples, dunes, plain bed, anti dunes, and some combinations of these. See for example Graf(1984, p. 277). Since the scope of this research necessarily deals only with dunes and ripples, the other bedforms will not be discussed t Typical Sand Wave or Bedform From Flume Run TNP Triangular Approximation 0.08 ~ '----, , ' Figure 4. Triangular Approximation of a Typical Sand Wave Figure 4 shows actual data taken in the Agricultural Research Service National Sedimentation Lab (ARS-NSL) flume in Oxford Mississippi. A typical sand wave is graphed from the data in the magenta colored data series. The wave is about 1.3 m ( 4.3 ft) long and 0.1 m (.33ft) high and was produced with a flow of m 3 /sec (10.67 cfs), a flow depth of0.366 m (1.2 ft) and a Froud Number of In this case, the length to height aspect ratio is about 13:1. However, this can vary considerably depending on flow and sediment characteristics. For a more thorough discussion of the

24 12 relationships between sediment, dune dimensions and flow characteristics, see Kennedy and Odgaard ( 1991 ). With regards to this new method of computing bedload transport in the sand dunes, considerations of geometry are important. That is because the geometry of the translating waves, and intervening time intervals, are used as a basis of determining the bedload transport. In the theoretical discussion that follows, it will be necessary to model the dunes in some quantitative manner. As shown in Figure 4 the general shape of dunes and ripples can be approximated by long low triangles. In fact, any triangular shape can be used as an analytic model. In general, the mode of movement of the sand wave is as shown in figure \ \ \ \ \ \ \ Deposition \ Figure 5. Method of Forward Motion of a Sand Wave In this figure, the brown shaded area represents the stoss, or scouring side of the sand wave. Individual sand grains are removed from a thin surface layer and are moved up the slope by a process of skipping, hopping and saltation. These particles are deposited on the downstream face (lee [or sheltered] side) of the wave as shown by the green shaded area. In this manner, the bedform creeps forward to the right in the figure. Although the figure is idealized, the mechanism of removal from the stoss side and concurrent deposition on the lee side is a correct description of the process by which sand waves

25 13 move forward. Figure 6 was made from video footage of a translating sand dune as viewed through a window in the ARS-NSL flume. The black line represents the initial position of the wave. After successive intervals of 5 seconds each, the video was stopped and each outline of the wave sketched. Although the outlines of the wave are not perfectly parallel and somewhat irregular, the process of scour and deposition as the mechanism of forward movement is clearly shown. Figure 6. Example of Forward Motion of a Sand Wave in a Flume Bedload transport (gsb) as defined in the Introduction, is non-uniform and variable over the surface of most sand waves. In general gsb will have a value of zero near the trough of the wave, and some maximum value near the crest of the wave. The variability of transport is highly influenced by the flow over the dune or bedform. In general, flow moves over the dune as shown in figure 7. At the crest, there exists a flow-separation,

26 14 resulting in a separation zone as indicated. Within this zone the flow actually moves in an upstream direction, thus influencing the deposition on the lee side. The flow reattaches at a point usually downstream of the trough. As the flow moves past the point of re-attachment, that is as flow begins to move up the slope, turbulent flow structures are the more dominate flow characteristic. Flow Separation Separation Zone Flow Re-attachment Figure 7. Flow Characteristics Over Sand Dunes Continuing up the slope, at a point somewhere near the midpoint between the trough and crest of the stoss side, the re-attached boundary layer flow begins to dominate the turbulent flow structures and critical shear stress occurs. From this point, the shear stress continues to increase, until at the crest it reaches a maximum value. The implications of these observed flow characteristics over the face of the dunes with regards to sediment transport on the stoss side of the dune are the following. From the reattachment point to the point of critical shear, a combination of turbulence and bed shear entrain and transport sediment up the dune face. Past the point of critical shear stress mean temporal bed shear stress is the dominant cause of entrainment and transport. On the lee side, flow separation at the crest facilitates cascading of sediment layers down that

27 15 face, as well as the possibility of partial suspension of some of the bedload in the eddy. Whether the partially suspended bedload continues in suspension, deposits in the trough, or deposits on a downstream dune, helps to determine the morphology of the sand wave. Volumes have been and are being written regarding the numerous aspects of flow over dunes and its hydraulic and sediment transport implications. For the purposes of this research no further investigation into these details is deemed necessary or required. However, for those interested in further details and discussion see for instance, Raudkivi, (1963); Nelson, McLean and Wolfe (1993); Bennett and Best (1995); Wilbers (2004); Best (2005); and Stoesser et al (2008). 2.2 Some Analytic Considerations Bedload transport (gsb) in moving sand waves, or bedforms, has been described by numerous researchers. Some basic considerations are reiterated here. Garcia et al (2008) gives a through description of the conservation of sediment mass for the bed sediments to include the interaction of sediments in the water column that erode from or deposit onto the bed. Equation 1 is a slightly modified version of Garcia's mathematical statement for the conservation of mass in a bedform. (1) In this case 'x' is the streamwise direction and 'y' is the cross-channel direction (into the page in this description). 'A is the bed sediment porosity, 11 is the bedform surface elevation referenced to some arbitrary datum, H is the dune crest height from the trough, qsb is the bedload transport, t is time, E is the erosion rate out of the bed, and D is the deposition onto the bed. Figure 8 shows a schematic definition of the terms of the equation. The erosion rate E is the product of the fall velocity ( w) of the sediment particles in suspension and a dimensionless sediment entrainment rate Es.

28 16 E=wE, T) r.. - T H ~ X Figure 8. Schematic Definition for the Terms of Equation 1 The deposition rate is the product of the fall velocity and the near bed volumetric sediment concentration Cb (volume of sediment per volume of water-sediment mixture). The erosion and deposition rates have units of length per time, which is consistent with the other terms. Equation 1 states that the time rate of change of the bed elevation is equal to or determined by the net flux ofbed material into and out of the control volume (the black dashed lines in Figure 8). The flux of material can be the bedload saltating along the bottom, but also can be suspended material being entrained or deposited. When only the streamwise (x-axis) direction is considered and no bed material goes into suspension or is deposited, equation 1 becomes equation 2. (2) This is the familiar, Exner (1925), equation. In this form it has been simplified to a! dimensional bed sediment continuity equation for the conservation of mass. Starting with this equation Simons, Richardson, and Nordin (1965), Crickmore (1970), Engel and Lau

29 17 (1980), and Wilbers (2004), show the development of an equation for the computation of bedload transport in triangular sand waves based on an average forward wave speed or celerity (vs), and dune crest height, (H). (3) This equation expresses the sediment discharge as a volume per unit width, [L 2 /T] or area per time. Equation 3 is beguilingly simple. It is this simplicity which makes the equation especially attractive for use in the computation of bedload transport in dunes and ripples, providing that the wave speed and height can be adequately determined. However, the simplicity also makes the equation subject to abuse and misuse. In reality, to make use of the formula numerous factors have to be accounted for. Wilbers (2004) in section has clear explanations of five possible factors that must be considered in using the bedform equation. The following short discussion relates to Figure 9, and provides a connection between the bedload equation and the geometry of two sequential bedform profiles. Considering again equation 3 the most direct procedure to determine qsb is to measure dune height Hand the velocity of the dune crest Vs (the average distance that the 11 A Br vs _...;, ~, l \ l \ F E D c X T H Figure 9. Relationship Between Scour and the Product of Vs and H

30 18 crest travels in a given period of time). The equation shows that qsb is obtained as the product ofvs and H multiplied by Y2(1-A.). In Figure 9, the product ofvs and His indicated as area ABCD. By geometry, this area equals area ABEF. It follows that an alternative to measuring Vs and H is to measure the amount of scour on the upstream face of dunes occurring over a given period of time. Practically, with the recent advances in bathymetry measurements, this approach shows the potential to be more accurate than one based on measurements ofvs and H. This geometric approach is the basis of the ISSD0Tv2 method, which is a large part of the subject matter of the next section. 2.3 Some Geometric Considerations In section 2.2 the analytic basis for computing bedload transport from sand dunes was discussed. In this section, the geometric considerations that allow for the usage of incremental movements of a bedform for the computation of bedload transport are more thoroughly discussed. This discussion is necessary because ISSDOTv2 uses only two types of empirical data. These are bathymetric elevations (geometry) and the time difference between two surface data sets (time). The discussion in this section is intended to further explore the relationship between incremental movement of sand waves, and the bedload equation. Note that in using only geometry and time, knowledge of the wave speed Vs is not necessary. This is by design, see Abraham and Pratt (2002) and Abraham and Hendrickson (2003). Sand wave velocities or celerity, are very difficult to determine in field conditions. This prompted a search for a methodology that could circumvent the necessity of determining wave speeds for individual waves throughout a measured river bed region and yet allow accurate measurement of the bedload transport. It is noted that knowledge of wave speed is still desirable for efficient usage of the method in large field applications, but not necessary in the bedload computations. In the discussion that follows regarding translating waveforms, the following conditions are applied.

31 19 The mechanism of movement is scour on the left and deposition on the right. The waveform moves with constant velocity v 5 The wave shape does not change. Stoss-side scour is equal to lee-side deposition. Porosity of the sediment mixture is neglected. These conditions imply that none of the bed material being transported in the wave goes into suspension. Consider the idealized triangular bedform shown in Figure 10. This wave moves to the right with velocity v 5 of 1 unit per minute. In the triangle outlined in the red dotted line, the tan shaded area on the left-hand side of the triangle has an area of 6 units and represents the unit-volume scour over the interval of 1 minute. Thus the scour rate is 6 units per minute. However, because of its triangular shape, the bedload in the moving waveform is by inspection, not H * v 5, but, one half of the product ofh and v s The value of 12 is introduced as a result of the triangular wave geometry. = 1 SO. Unit Time in minutes = : -... Wave soeed 'v"' ' = 1 unit oer minute H = 6 Units 0 L = 10 Units Figure 10. Triangular Wave Translating to the Right with Constant Velocity

32 20 If equation 3 is applied to the wave in figure 10, the bedload transport is found to be Y2*6* 1, or 3 units per minute. This can also be seen by considering the movement of the entire wave. The area of the triangle is 30 square units. As shown in the figure it takes 10 minutes to move the triangle's total area (30 square units) past its original position to its final position outlined in green. Thus the total volume moved in the waveform is or 3 units per minute. This is consistent with the bedload transport value determined by using the bedload equation. The point in this discussion is to note the difference between the scour rate on the stoss side of the waveform and the average bedload transport ( qsb) in the translating wave. The scour rate was noted above as 6 units per minute, while qsb is shown to be 3 units per minute. Thus qsb is found to be Y2 the scour rate. Figure 11 is an excellent geometric H = 6 Units Time in minutes = ,,,,,,, ' Wave sneed 'c' = 1 unit ner minute : ~,_ ,'I'. ' ' I ','. ', I ',. ',! ',,' I ',. I L = 10 Units ' ' ' ' ' ' ' ' Figure 11. Comparison of Area Movement for Rectangular and Triangular Waves

33 21 tool to visually see why this statement is true. Consider the case in which for both shapes the rate of scour on the stoss (left) side is 6 units per minute and the same material is deposited on the lee (right) side causing the wave form to move to the right. When the rectangle is moved 5 units to the right in 5 minutes its entire area of 30 square units (the shaded rectangle) has been moved past the point x= 10 for an average qsb of 6 units per minute. In this case qsb is simply the product of H*v s However when the triangle is moved 5 units to the right in 5 minutes only Y2 of its area (15 square units, Y2 of the shaded triangle) has moved past x= 10, for an average qsb of 3 units per minute. Both have the same scour rate, but qsb for the triangle is clearly Y2 the scour rate. Although not earth shaking in magnitude, the implications of this statement are very important in the implementation of the ISSDOTv2 methodology, or any method similar to it which uses sequential bathymetric data for the determination of bedload transport. The reason for this will become apparent in the next section. But frrst, two questions need to be examined. 1. Is this statement true for any triangular waveform? 2. What might be the physical explanation for the factor of2? Regarding the first question, refer to Figure 12. In the figure, each triangle and the trapezoid have a height of 6 units and an area of 30 square units. The blue shaded region on the left of each waveform represents the scour unit-volume (6 square units) that is eroded in one minute as the waveform moves one unit to the right. Each waveform starts with its rightmost extremity at the location x= 10, and for purposes of this analysis is allowed to move 5 units to the right in 5 minutes (vs = 1 unit per minute). The waveform outlined in the green dashed line shows the wave's location at this time. Analysis of the waveforms at this location reveals some interesting facts, which are here described and tabulated in Table 1. The scour rate, or volume removed from any waveform in one minute, is 6, and thus in 5 minutes 30 square units will scour. This volume of scoured material is deposited and shown as a granular shaded area to the right of each waveform.

34 22 Rig}lt Trimgle 30SU N:>n Synnretric Triangle ~ ~ ~~~ ~~~.,... ~,~ ~., ~~~, J.J.JJ SU Trnpez.oid 30SU SU =sqmreunits Figure 12. Variation of Area Transport for Different Geometric Shapes

35 23 Therefore, the area of each granular shaded region must also be equal to 30 square units, which is verified in the sketch. One might intuitively think therefore that the transport in the waveform is also 30 square units in 5 minutes, or 6 square units per minute, but, that is not the case, as mentioned earlier. To see this, consider the area enclosed by the red solid lines to the right of x= 10 for each waveform, which represents the amount of material in that waveform that was transported past the position x= 10 during the 5 minute interval. For the rectangular waveform (not shown in this figure, but can be easily inferred from Figure 11, 30 square units were indeed moved past x=10. Therefore the transport rate in that waveform is 30 square units in 5 minutes, or 6 square units per minute, and thus equal to the rate of scour on the upstream side of the waveform. However, by inspection, for the trapezoid and any triangle, the red outlined area (unit volume) is not 30 square units. By simple geometry the areas are found to be, 24, 22.5, 21, and 15 square units respectively for the trapezoid, right triangle, non- symmetric triangle and symmetric triangle. Note that the symmetric triangle is not shown in Figure 12, but its value of 15 is easily inferred from Figure 11.. Thus the average transport rates in each of those waveforms during the 5 minute interval are, in the same order, 4.8, 4.5, 4.2, and 3 square units per minute, see Table 1, row four. These values are NOT equal to the scour rate of 6. In fact, the point where the left end of the waveform has just passed x=10 (waveform shown as the solid green line) is the point in time and space where each waveform fmally moved al130 units of its area (unit volume) past the starting point. For the triangles this takes an additional5 minutes of time (vs=1 unit per minute) compared to the rectangle and thus the average transport rate in each triangle is 30 square units in 10 minutes or 3 square units per minute. The trapezoid is somewhat more efficient with a rate of30 square units in 7 minutes, or about 4.3 square units per minute.

36 24 Table 1. Variability of Transport in Different Wave Forms Different Wave Forms (WF) Rect Trap R. Tri. N.-Symm. Tri. Symm. Tri.. 1 Scour unit-vol. per minute Minutes to move WF 5 units Unit-vol. in WF moved past x= 1 0 in 5 minutes 4 Avg. Trans. ( qsb) after 5 min qsb after WF passes x= 1 0 6A c 3c 3c A Rectangle needs 5 minutes to move its 30 units past x=10. (30/5 = 6) B Trapezoid needs 7 minutes to move its 30 units past x=10. (30/7 = 4.3) c Triangles require the full10 minutes to move their 30 units past x=10. (30/10 = 3) 2.4 A New Conceptual Bedload Measurement Method The result of this finding (for triangles) is very important because it verifies by geometry the results obtained by analytic considerations in chapter 2.3. That is, that the average transport in the waveform is 3 square units per minute. We would normally not care about the geometric consideration because the analytic description, and others like it, has already been validated through experimentation. The value in the whole exercise is related to the blue shaded area on the left of each waveform. Recall that this research involves determining bedload transport only from geometry and time. The scour region is the area (unit volume) that is directly measured when two sequential bathymetric surveys are made over the same bedform. If the time between the surveys is known, then

37 25 the scour rate can be determined for that bedform. The value of the geometric consideration has been that it illustrates clearly the direct relationship that exists between the eroding section of a triangular dune and the average transport in the same dune.,,,.,' J", _ 30SU Right "" Triangle ~ ~ '~ Non- Symmetric, ' Triangle '~,,_ ~,, 30SU Synunetric Triangle,, ~,,,, su SU =square units Figure 13. Demonstration of 2:1 Ratio of Scour and Transport Further that this relationship is two to one in numerical value for any triangular waveform. Thus for the limitations stated at the beginning of this section, one only needs

38 26 a set of sequential bathymetric waveform profiles to determine bedload transport. The computations can be done on 2-d profiles, or using three-dimensional surfaces as well. The real value of the methodology will probably be in its application to 3-d surfaces. Another value of the geometric consideration is that it allows one to see clearly the reason for the two to one relationship between scour and transport rates for triangles. Recall the second question posed above 'what might be the explanation for the factor of 2?'. Figure 13 clearly shows what happens. In order to move the material in the browndashed-line triangle to the green solid-line triangle, the space between them was filled and emptied during the 10 minute time interval. This space can be seen as a dot-filled triangle of the same dimensions as the other two triangles but inverted between them. Thus all the material in the original triangle had to be moved two times before arriving at its fmal position; once out of the original triangle and once through the inverted triangle. A total of 60 square units had to be moved in the process of moving any of the triangles through its full length. Sixty square units moved in 10 minutes implies that the volumetric rate of removal (scour rate) had to be 6 square units per minute, yet average transport in the waveform is clearly 30 square units per minute, and thus the two to one ratio of scour rate to average transport. The previous discussions have shown that it should be possible to determine the bedload transport in a moving bedform of triangular shape by quantifying the scour rate on the stoss-side of a sand dune. The scour rate can be directly computed by quantifying the area between two successive profiles of a 2-dimensional plan-view bedform, or the volume between two successive 3-dimensional surface plots. In either case, the measured value that is obtained must then be divided by two. The units will be volume per time, [L 3 /T] or can also be expressed as volume per time per width of channel [area per time or unit volume]. When multiplied by the density of the water sediment mixture, [MIL 3 ] the transport rate in the wave is obtained as mass per time. In common usage transport rates

39 27 are normally expressed as tons per day in field conditions and lbs per foot per second (or kilograms per meter per second) in experimental work. The next three chapters show the method applied to several sets of data. Two of the data sets were taken in flumes for which a measured value of bedload transport was available to compare to. The third data set was from field data obtained on the Mississippi River.

40 28 CHAPTER3 BEDLOAD COMPUTATIONS FOR FLUME DATA SET Collection of Data A flume study was conducted at the USDA-Agricultural Research Service, National Sedimentation Laboratory (ARS-NSL) in Oxford Mississippi from December 2002 to February The purpose of the flume study was to test the ISSDOT concept for measuring bed-load transport. As mentioned earlier, the method depends on being able to accurately measure or map the surfaces of sand waves at two different times. In the flume, it was possible to measure the suspended bed material (g 55 ) as well as the total bed-material load (gs). When the suspended is subtracted from the total, the remainder should be the bed material that is moving in the sand waves, gsb This presupposes that there is no wash-load, which was indeed the case in these flume runs. When the bed material moving in the sand waves was independently measured at the same time by the ISSD0Tv2 method, which we will call gsbi, then gsbi can be compared to, and should approximate gsb The foregoing discussion is shown by Equation 4. g s - g ss = g sb "" g sbi (4) Figure 14 shows the flume that was used to collect this data set. This flume was 30.5 m (1 00 ft) long, 1.2 m ( 4 ft) wide and 0.6 m (2 ft) deep. The sediment-water mixture is recirculated from downstream to upstream via a return pipe running under the flume. Figure 15 shows a schematic diagram (not to scale) identifying the major features of the flume. To reduce clutter in the figure, the head bay, flow diffuser, pump, viewing window and other details are not shown.

41 29 Figure 14. View of Experimental Flume Looking Upstream Measurement of &bi ~ Measurement of &s r I I ~--- ~ I Q ~.,., ~ ~ ' -.., Slurty Return Pi For measuring gs 100Ft ~ Figure 15. Schematic of Experimental Flume

42 Equipment and Procedure: Total load (gs) The total bed-material load (gs) was measured by a procedure that was for all practical purposes the same as in the experiments conducted by Kuhnle and Derrow (1994) in the same flume. The procedure is repeated here verbatim since hardly anything needs to be either added or taken away from that description. Total sediment load was measured using a density cell to determine the density of a fraction of the sediment water mixture from the return pipe of the flume. The pressure difference across the pump was used to drive flow through a 1.27 em diameter sampler nozzle through tubing to the density cell and back through tubing to a tap just upstream from the pump. The sampling system is similar to that used by Willis and Kennedy (1977). The density cell consisted of a vibrating U-tube in which vibrational amplitude/frequency changes associated with density changes in the U-tube generated proportional changes in voltage. The output voltage of the density cell was read by a personal computer. The difference of the output voltage and the voltage at zero sediment concentration of the density cell was proportional to the sediment concentration in the water. The density cell was calibrated using the bed sediment over the full range of sediment concentrations encotmtered in the experiments before the investigation began. During data collection periods the voltage output of the density cell was read at 1-second intervals. At periods of approximately one hour, a valve in the density cell sampler line was closed and the voltage of the density cell at zero sediment concentration was recorded for several minutes. Sediment concentrations were calculated for every 1-s interval of sampling as the difference between the logged voltage and the linearly interpolated zero voltage taken just before and after the concentration data was taken. Mean transport rates were calculated from the approximately 7 hr of transport data collected in each of the experiments." The only adjustments to this description are that density cell readings were taken at 4 second intervals in the present study, and that the duration of density cell data collection was 2.7 hours. The density cell is shown in Figure 16 as the reddish brown vertically oriented cylinder on the right side of the photo.

43 31 Figure 16. Density Cell Connected to Return Slurry Pipe Equipment and Procedure: Suspended Load (g~ The suspended sediment (gss) data were collected using a combination of acoustic and isokinetic physical samplers. The upper 6. 7 em of the flow depth was measured using a sampler with 4 equally-spaced nozzles. These 4 nozzles collected samples isokinetically simultaneously at 4 positions in the vertical, and are shown in Figure 17 along with the acoustic sensor. The flow depth below the 6.7 em was "sampled" using acoustic basckscattering. The acoustic data and the lowest physical sample overlapped and were used as a calibration point for the backscatter data. These measurements were collected at 9 equally-spaced verticals in the cross-s ection of the flume. The data was used to calculate mean concentrations of suspended sediment at each of the 9 locations. The values obtained at these 9 locations were then used to calculate a mean cross-section average of suspended sediment concentration. This value was multiplied by the flow rate

44 32 to give a rate of sediment being transported as suspended load. [Kuhnle, personal communication] t Figure 17. Isokinitic Sampling of Suspended Sediments Equipment and Procedure: Bedform Load (gsbi) In order to determine (gsbi) using the ISSD0Tv2 method, it was necessary to map the moving sand waves. This was done with special sensors manufactured by SeaTek Instrumentation and Engineering ( which are shown in Figure 18. Each sensor bank consisted of 8 transducers for which the acoustic operating frequency was 5 MHz. A signal processing electronics package was also supplied to allow communication with a PC via a RS232 communications port. The electronics package is capable of nmning up to 32 transducers, and sampling up to 2 external analog channels.

45 33 Three methods were used to test how well the sensors recorded the distance to the bottom. The results of these tests determined the instrument resolution and error. Figure 18. Accoustic Sensor Banks of 8 Transducers Each The tests consisted of the following scenarios; multiple depth measurement samples using stationary sensors in still water, two sensors each taking one sample at the same location in still water, and moving sensors in still water. The maximum average error of the eight sensor pairs was found to be about 2.2 mm. Additionally, the tests indicated that the speed at which the sensor banks traversed the flume did not influence the measurement error. Data to compute the bedload moving in the sand waves (gsbi) was collected by mapping the surface of the dunes. This was originally accomplished by creating transverse swaths across the flume seven inches wide using the SeaTek acoustic instruments previously described. At the time the data were taken, it was not considered

46 34 necessary to capture entire wavelengths of the dunes, and therefore the swaths were narrow and obtained at varying times and speeds. In arriving at the ISSDOTv2 modified Longitudinal A Profiles A I A A I I I I I A A A A y =.304 y =.912 X =.178 y =.684 X Transducer sweep direction ~ Flow y X - 0,------~~~~ \ Flume Walls I Figure 19. Locations of Longitudinal Profiles method it was determined that, at a minimum, a partial dune-length from trough to crest was necessary to compute absolute value of transport. The only way that could be done with the existing data set was to extract an elevation-time-series for various spatial locations in the flume. This was possible because every data point in the original files contained an x-y position, an elevation (Z) [same as 11 in previous discussions], and an

47 35 associated time (t). Thus programs were written to extract all elevations and times for selected transverse positions in the flume. This was done for x locations at y=.304 m (1ft) to y=.912 m (3 ft) by increments of.076 m (.25ft), which is shown in Figure 19. Examples of the extracted longitudinal profiles are shown as the brown dashed lines in the figure, which are not necessarily in the exact positions or to scale, but close enough for the purposes of the discussion. By using the data obtained from the two transducers initially positioned at x=o, and x=.l78 m (.58ft) it was possible to obtain two sequential profiles at each x location. The time lag between the two positions was enough to allow sufficient translation of a given dune to defme the scoured area. Recall that scour area and time are the required data to make the bedload computations. An example of one of the time series is shown in Figure 20. Extracted Time Series Longitudinal Profile for y =.684 m (2.25 ft) E -;; iu 0.35 ~ jjj ~ ~ ~... --trans119 x= trans 8/16 x=o.o ~... ~ ~ ~.L ~ ~ ~ Time (seconds) Figure 20. Example of an Extracted Longitudinal Profile The irregularity of spacing of the data points along the horizontal axis was expected, and is due to the varying times between the transverse sweeps of the transducer banks and also the varying speeds of each sweep. In reviewing this profile and others like it at the different y locations, it was decided that the very last wave on the right would be used to

48 36 make the transport computations. This was because in all of the plots a reasonable estimation of the trough and crest of the dune could be made. Additionally, this wave showed a minimal change in shape during the measurement interval, and thus comes closest to meeting the criteria laid out in section 2.3. In the next section the methodology for analyzing this waveform is discussed. 3.2 Data Processing and Analysis The data for the last wave of each profile described above was extracted and plotted. From this data it was possible to determine the area between the two profiles and the time (DT) which it took the wave to move from the initial to fmal position. Figure 21 shows the plotted data for an example profile. The transport unit volume computation Longitudinal Profile at y=2.25 for the last Wave I,;_ I I I I I I I... -u.. c x=.58 N x=o.o Linear (x=o.o) 0.9 Linear (x=.58)., 0.8 I I I I ' Time (seconds) ~... Figure 21. Surface Difference for the Last Wave as a Time Series required a length of the wave as well as the height (DZ) and the time (DT) between the profiles. DZ was computed by subtracting the pairs of data points (12 pair in this case) and taking the average of these differences. This value was found to be about.0165m (.0545 ft). The time for the wave recorded by the downstream transducer at x =.178 to

49 37 Longitudinal Profile at y=2.25 for the Last Wave c: 1.1 N x=.58-4-x=o.o -Linear (x=.58) Linear (x=o.o) I I I I I I ~ 2.3 I I I. 3.3 Position (x) in ft Figure 22. Surface Difference for the Last Wave vs. Position scour down to the elevation of the wave recorded by the upstream transducer is the wave speed. Another way to think of this is the time required for the blue profile to move to the left in the figure until it is close to being superimposed over the magenta profile. For example the blue profile was at elevation 1.2 at about 7020 seconds while the magenta profile was at elevation 1.2 at about 6880 seconds. For this data point, the two profiles are separated in time (DT) by about 140 seconds. By selecting several elevations and computing DT in a similar manner, an average DT between the waves was determined. Since the distance between the downstream and upstream recording transducers was m (0.58 ft), the wave speed could be found as 0.178/DT (0.58/DT). For this wave the average DT was about 135 seconds and thus the average wave speed was found to be about m/s ( ftls). To fmd the length of the wave, the times of each profile were normalized and then the differences recorded between each data point and zero. These times were then multiplied by the wave speed to give a distance or position. This is simply converting the elevation versus time profile to an elevation versus position profile. The resulting graph is shown in Figure 22. From this graph the wavelength can be read as about 0.836m (2.75ft) minus 0.152m (.5 ft) or 0.684m (2.25 ft). The

50 38 horizontal distance read off the graph is considered sufficiently accurate due to the very low slope-angle of the sand wave with the horizontal. With the information gathered above the bedload transport in this translating wave can be computed via the proposed modified ISSDOTv2 method. The scour mass per time should be equal to the unit area (wavelength multiplied by DZ) divided by the time (DT) and multiplied by the sediment-water density, which is here taken as kg/m 3 (96lbs/ft 3 ). For the sample profile and using values determined above this should come out to be about lbs per second per foot of flume width. Recall that the scour rate on the eroding side of the waveform is twice the average transport in the waveform, so the computed value has to be divided by two. Thus the average bedload transport in the moving bedform is estimated to be kg/m/sec ( lbs/ft/sec) as determined from the profile at y=.684 m (2.25 ft). This computation was made on a per-unit length of flume-width basis. The validity of this result will be discussed in the next section. Before showing the results, it is necessary to mention the analysis of the total bedload and suspended load. The analysis of the total bed material load involved the measurements taken with the density meter in the return slurry pipe as described in section The results showed a value of kg/sec/m ( lbs/sec/ft). The measured suspended load yielded a value of which was approximately 58.6% of the total load. Thus the amount that must have been moving in the sand dunes would be 41.4% of the total load, or kg/sec/m ( lbs/sec/ft). This the measured value of the bedload to which the value computed using the ISSD0Tv2 method can be compared. 3.3 Results for Flume Data Set 1 The computations made for the example profile discussed in section 3.2 were also made for eight other profiles. The nine profiles were spaced m (0.25 ft) apart and covered the middle half of the flume width as shown in Figure 19. All the data required to make bedload computations are shown in Table 2 for each x-axis lateral position.

51 39 They are computed as in the example in section 3.2. The results shown in column six (US Customary Units) and column seven (SI Units) are the computed bedload transport gsbi using the ISSDOTv2 method. Recall that gsb is the bedload derived from subtracting the measured suspended sediment discharge gss from the measured total sediment discharge gs. So value of gsbi computed from geometry (sequential bedform profiles) and time must be compared to the value of gsb, which was kg/sec/m ( lbs/sec/ft). Table 2 column 6 and 7 shows that the method provided very reasonable estimates of the bedload moving in the dunes. The results in column 9 show values that ranged from 44 to 228 percent of the 'measured' value. The average was 137 percent. Table 2. Raw Data and Computed Transport y Wave Scour Mass Transport Transport Dune Wave %of Lateral Length DZ DT per Time q sbi q sbi Speed Measured Position l(ft) l(ft) (sec.) lbs/sedft lbs/sec/ft kg/sedm ft/sec Value Averages For sediment transport measurements this is a remarkably good estimate. Some confidence was provided to the analysis by the fact that dune wave speeds were backcalculated from the existing data. This was accomplished by knowing the distance (0.176m or 0.58 ft) between transducers 1 and 8 and time (DT) it took for a wave to move from transducer 8 to 1. The wave speed was the distance divided by DT, and was computed for each wave. These are shown in column 8 of Table 2. The average value

52 40 was fps. As can be seen in Table 3, dune speeds from Willis and Kennedy (1977) for runs 21 and 29 were very similar, for comparable values of water depth, average velocity and Froude number. Table 3. Comparison of Hydraulic Parameters and Wave Speed sediment Q Depth Avg Vel Froude# Dune wave sized-50 cfs ft fusee speed fps [(mm) ARS K & W-77 run run Even though the wave speed consideration provided yet another element of credibility to the analysis, the small amount of data used to compute gsbi, (only 9 profiles for one wavefonn) was considered smnewhat 'weak' evidence for a proof of concept. Also, because the suspended load had to be measured and subtracted form the total load, an additional element of uncertainty was added to the experimental procedure. Thus additional data were searched for by which ISSD0Tv2 might be tested. The additional data were found in a data set which came from a different and older ARS-NSL flume study. That data set and the analysis of it is the subject of Chapter 4.

53 41 CHAPTER4 BEDLOAD COMPUTATIONS FOR FLUME DATA SET Collection of the Data The second data set used to validate the ISSD0Tv2 method was acquired during flume experiments carried out in December of 1993 and January of 1994 at the ARS NSL. The purpose of those experiments was to test a methodology to determine bedload transport by the wave celerity method using bedform profiles obtained by a newly Figure 23. Sample of Sand Dunes formed in the 1.22m Wide Flume

54 42 developed (at that time) set of acoustic probes. Six experimental runs were made, identified as TNP-1 to TNP-6. Flow rates varied from m 3 /sec (7.16 cfs) to m 3 /sec ( cfs) and Froude Number varied from to In those experiments, sand with a median diameter of mm was used. The experiments were designed such that the sand was of a size such that no material would go into suspension. By doing so, no suspended material measurements would be required. The total sediment discharge was measured in the return flow pipe could be used as a direct comparison to ISSDOTv2 measurements of the bed load. One data set from each experiment was used in this computational effort. A sample of the variability of sand waves produced in the flume is shown in Figure Equipment and procedure: Total Load (q 5 ) All experiments were conducted in the same flume described in 3.1 The measurement of the total sediment discharge g 5 was obtained by the same equipment and methodology as described in section Equipment and Procedure: Bedform Load (qsbi) In order to measure the changing bedform profiles over a period of time, two acoustic probes were mounted on a common platform and track, and separated by a distance of3.179 m (10.43 ft) as shown in Figure 24. The assembly was moved in a direction parallel to the flow in the center of the channel by a precisely controlled stepper motor at speeds varying from m/sec (0.041 ft/sec) to m/sec (0.125 ft/sec). The transducers were moved quickly relative to the speed of the sand waves in the downstream direction, with each one mapping the same wave in a short period of time. In this manner a time series of two sequential wave profiles were obtained. An example of the two sequential profiles is shown in Figure 25. With respect to their sequential nature, these profiles were very similar to those extracted from data set 1 in Chapter 3, and thus lend themselves well to bedload computations via ISSDOTv2.

55 43 1,1;1 Instrument Carriage Acoustic loj.ttrans ~PN. 1- _ ~ '~ 2.., 1 ""'... R '1 at on top o ffl umew ,_ '... all ---,..- '..,_,., Q r..-,.. Figure 24. Dune Profile Measurement Technique Using Two Acoustic Transducers However, these wave profiles were considered superior to those in data set 1 in that they contained complete wave profiles with multiple waves in each experimental run. They also were obtained over a broad range of flow conditions and thus serve to check the method's robustness regarding sensitivity to widely varying flow conditions. Wave recorded at time I by transducer I. Wave recorded at time 2 by transducer 2.,... ' ' \ Figure 25. Acoustically Measured Sequential Dune Profiles

56 Processing and Analysis of the Data A typical plot of the data acquired by the methodology described in is shown in Figure 26 which was from experiment TNP-6, run As can be seen in the figure, most of the waves moved to the right a sufficient distance in the time interval to allow application of the method. In applying the conditions stated in section 2.3, two waves were not used in the computations for this example run. These were the waves between x to 6.2, and x tolls. As can be seen, these waves changed their shapes significantly during the time interval. TNP E 0.3, ,------r "1 -Series1 o.2s , Series : , J o+---~---~---~--~---~---~--~----r Longitudinal Position in Flume (m) Figure 26. Example of Sequential Dune Profile from Flume Data To compute bedload from a profile as in Figure 26 using a surface difference method, consider the first full wave on the left. During the incremental movement of the wave from the blue line to the magenta line, the area between the lines is the unit volume

57 45 of scour that occurred in the interval ~t. Recall from the analytic and geometric discussion that the scour rate was shown to be related to the average bedload transport in a wave by a value of two to one. Thus to compute transport, (gsbi) one needs to quantify the unit volume scour rate, divide it by two, and multiply by the sediment-water-mixture density (p ). The unit volume scour rate is the area between the lines divided by the time interval ( -I ~t). This relationship can be expressed as in equation 5. p gsbl = 2 ~t (5) To determine the unit volume of scour for any wave in Figure 26, the 2-d profile for sensor 1 (the blue line) was repeated at 0.25m intervals over a width of lm in the graphic user interface SMS (Surface-Water Modeling System). This created a 3-d surface as shown in Figure 27. Figure 27. First 3 Waves of 3-d Surface for Profile TNP6-1532

58 46 The same procedure was repeated for sensor 2 (the magenta line). Then the surface created from sensor 1 was subtracted from that for sensor 2. This is the same procedure that will be used with bathymetric surfaces obtained from sequential multibeam field surveys. The difference plot in Figure 28 shows the areas of scour (red) and deposition (blue) that occurred for each wave in the time interval of 84 seconds. In the SMS program a scour depth is calculated for each node, and thus an actual scour volume can be computed Figure 28. Difference Plot for First 3 Waves oftnp for each cell. The total volume under a given area can be obtained when the user simply selects those cells. When all the red cells for a given wave are selected, the sum is the total scour volume ( JL) for that wave. This procedure allows for very accurate volume determinations. Table 4 shows the computed volumes for each wave in TNP The volumes and time step of 84 seconds were then used in equation 2 to compute gsbi for

59 47 each wave, which is also shown in Table 4. The arithmetic average and standard deviation were then computed for all seven waves. Table 4. TNP-6 run 1532 Transport computations TNP-6 run 1532 Wave No. Vol. mj 9sbl avg stdev This procedure was repeated for one run in each experiment, TNPl to TNP 6. The results are discussed in the next section. 4.3 Results for Flume Data Set 2 The results for the computations carried out on selected data sets from the six experiments are shown in Table 5. Values of bedload transport computed by ISSD0Tv2 are compared with the values measured by the density cell. The right hand column shows the computed value as a percentage of the measured value. In Figure 29 the straight line shows the line of perfect agreement between measured and computed values of bedload transport. The diamonds represent the values of gsbi computed using ISSD0Tv2. As can

60 48 be seen, they fall very close to the line of perfect agreement. This is very compelling evidence of the capability of the method to measure the absolute value of bedload transport. Table 5. Transport Results TNP 1-6 Sed transport rate, Sed trans %of density rate, from measured Exp# cell ISSDOTv2 value i(kg/s m) (kq/s m) TNP TNP TNP TNP TNP TNP ave stdev The only subjective part of the analysis is in the selection of which waves in any series will be used. In the present case the condition of minimum change of wave shape guided the selection of waves for a given run. Other than that there are no 'user adjustable' inputs, and thus minimal chance for user error or bias. The verification of the factor of two is also important to consider in looking at the computational results. Does the data in fact verify the analytic and geometric conclusion that the scour rate is twice the average transport? To show this, the factor of2 was left out of a second set of transport computations which are indicated in the legend as 'No Div by 2'. These data points are shown as the triangles in Figure 29. As can be seen, they are not in good

61 49 agreement with measured data. The importance of this factor becomes more apparent at higher transport rates. Computed vs Measured 9sbl / / ~ / - c::n /. Computed Value... c» ::I computed=., / en measured c» / No Div by 2 "C L ::E , A ~ Computed 9sbl Figure 29. ISSDOTv2 Computed Versus Measured Transport Values For the results of this data set in general, it must be remembered that the computations were made from a single 2-d profile (in the longitudinal and vertical plane). This single profile was 'stretched' left and right to form a laterally-uniform 3-d wave from which surface difference volumes could be obtained. This would ignore the inherent lateral variation of the waves themselves as shown in Figure 23, as well as sidewall effects of the flume. Yet in spite of these two factors, the computed bedload values are very close to the measured values. This is probably not an indication that the lateral variation over the small distance of 1.22m ( 4 feet) of flume width can be neglected in an average sense, but rather that since numerous waves were used, the transport in the

62 50 different sizes of waves provided an accurate average value. Although this could be a valid consideration in this flume study, it should not automatically follow for field conditions. That is because in the flume, most of the waves moved with a constant and similar velocity. In a field condition, the dune wave speeds will vary considerably from left bank to right bank. Thus their morphology and resulting transport rates will also vary. It is shown in the next chapter that ISSD0Tv2 should be able to account for the lateral variation because with actual field data complete waves are mapped in all three dimensions.

63 51 CHAPTERS BEDLOAD COMPUTATIONS FOR MISSISSIPPI RIVER DATA 5.1 Collection of the Data Fifteen data files were obtained from New Orleans District. The data in these files were collected by the Corps of Engineers StLouis District Hydrographic Survey Team in March of2001. The location was on the Mississippi River between River Mile (RM) to RM The data in file 1 c7_1702.xyz was taken on 7 Mar 2001 starting at 1702 hours. The data in files lc8_0838.xyz through lc8_1647.xyz were taken Table 6. Data Collection Times and Time Steps Date Time DT DT min seoonds 7-Mar Mar on 8 Mar 2001 starting at 0838 hours and ending sometime after 1647 hours the same date. The last four digits of each file indicate the time of day that each swath was begun. For purposes of using ISSDOT as a method of computing bed-load transport in sand

64 52 waves it is important that the data are collected with known times and concurrent spatial locations. Also, the direction of vessel travel and rate of travel should be as consistent as possible from data set to data set. As per personal communication with Mr. Joe Burnett of the St. Louis District these criteria were met in these data sets. A list of all the data sets and their starting times are shown in Table 6. Also shown in the table are the time differences in minutes and seconds between each pair of files. This is a Typical Contoured File There are 15 Such Data Sets Direction of Boat Travel The Selected Study Area Figure 30. Swath of Bathymetric Data 76m Wide and 5.8 km Long A plan view of the bathymetric features of a typical data set is shown in Figure 30. These swaths of data are about 76 m (250 feet) wide and nearly 5.8 km (3.6 miles) long. The boat moved from the top-right of the figure to the bottom-left, or from the Northeast to the Southwest. Visual observations of all of the data sets indicated that the data are much more dense in the longitudinal center and less dense toward the edges. This makes sense as the beam angle increases from zero directly below the vessel, to some larger angle left and right of the vessel. It was noticed from the data sets that at

65 53 about river mile (RM) to there were some very distinct sand waves that might lend themselves well to ISSDOTv2 computations. This series of waves is shown in the figure as 'The Selected Study Area'. It was from these waves that computations were made to show the validity of the ISSDOTv2 method and how it can be applied to field data Equipment and Procedure The bathymetric data were collected by a vessel mounted multibeam acoustic sounding device. Figure 31 shows a photo of the vessel Boyer which served as the data collection platform on which the multibeam sensors were mounted. Figure 31. Survey Vessel 'Boyer", St. Louis District USACE The bathymetric data acquisition unit was a Reson SeaBat 8101 Multi beam Echo sounder with 101 beams, beam angle of 1.5 degrees and an operating frequency of

66 khz. The resulting swath coverage is 150 degrees nominal. Some of the more important questions that might be raised regarding the performance characteristics of the boat and multibeam sensor are addressed by the following correspondence with those who acquired the data. Prior to using the data, several questions were asked of Mr. Joe Burnett, St. Louis District boat operator and Geodesist who was responsible for the data collection. Of the questions asked, numbers 3, 4 and 5 were: 3. Type ofgps system used? 4. Data compensation for boat pitch, heave and roll? 5. Estimate of the horizontal and vertical resolution? His verbatim answers to these questions in the same order were: 3) A Differential GPS-aided Inertial Navigation System. This is an Inertial Block that uses motion to calculate in movement in a 3-dimensional plane, but gets its initial position from an internal Differential GPS System. Every 1 second update, that is received from the internal DGPS, is sent to the Inertial Block, and the Inertial Block uses a Kalman Filter to determine the best possible position from the motion that it encountered and the new position from the DGPS. The Inertial System can generate up to 200 positions per second, instead of the 1 per second that a standard DGPS System can generate. This in tum, allows for more accurate positioning of the soundings that are being collected. 4) Because the Inertial System calculates motion in a 3-dimesional plane, it also records Heave, Pitch, Roll, and Heading. It can generate all four of these up to a rate of 50 times per second, for each. It uses a two antenna system to get its initial Heading Azimuth, then again, the Inertial Block calculates its 3- dimensional motions and checks the DGPS (for Heading and Position) every second. 5) This question is more complex than you can imagine. Because Hydro surveying is basically an open-ended traverse that does NOT come off of any TRUEL Y known XYZ coordinate, I honestly can't tell you how accurate my Horizontal and Vertical accuracies are. And anyone who tells you differently, must have sold ice to eskimos. I have conversed with my counterparts and they agree. What I can say, is that because I used the same equipment for this entire survey, and I calibrated and

67 55 checked it to the best that can be done, my PRECISION or Repeatability is very good. Why, because compared to itself, any errors, discrepancies, etc. are all relative, therefore, they cancel each other out. So, I would feel safe in saying that my resolution from one pass to the next is within just a few tenths of a foot, if not better. 5.2 Processing and Analysis of the Data The data sets for the 'study area' shown in Figure 32 were extracted from the larger data files to make them more manageable in the post processing software. As can be seen in figure, the waves are very well defined and thus provided a good data set for computations in that they meet the criteria established in section 2.3. Figure 32. Selected Study Area Showing 5 Well Defmed Dunes A grid of3.04 square meter (10 foot square) cells was overlaid on the waves between the lines shown in the figure. This formed the computational mesh by which to compute volumes as in section 4.2. The SMS software was again used to interpolate the xyz

68 56 bathymetric data points to the mesh. This was done for the data set collected at 1420 hours on 8 march 2001, as well as those for 1345, 1311, 1237 and 1157 hours. The result was five interpolated meshes at the five respective times. Then the surface for the mesh at 1157 was subtracted from that at 1420, resulting in a difference plot with a ~t of 143 minutes or 8580 seconds. This plot is shown in Figure () Figure 33. Difference Plot Showing Scour and Deposition The red cells show the areas of the waves that scoured and the blue shows the areas which were depositional. Similarly the meshes of 1237, 1311 and 1345 were also subtracted from that at These three additional difference plots resulted in decreasing ~t's of 103, 69 and 35 minutes respectively. This allowed a sensitivity check on the values of computed transport for different values of ~t. The difference plots were then used to determine the volume of scour that occurred in a given wave during the time

69 57 interval. This was done by using the program SMS to select all the red cells in a given wave, which represents the scour volume. Equation 5 was then applied with p = kg/m3 and the appropriate ~t for the given difference plot. In this case, the value obtained by Equation 5 was then divided by 54.86, which was the width of the computational mesh in meters. This provided the output in a per-unit-width format. Each difference plot contained 5 distinctive sand waves and the computations were made for four separate difference plots. Thus 20 different transport values were computed in this analysis. The reason for selecting progressively shorter time intervals between the successive bathymetric surfaces was to test the effect of varying ~t on computational output. From previous versions ofissdot it was noted that as ~twas decreased, transport, or change in transport, became larger. See Abraham et al2006 for a short discussion of this matter. As noted in the references, this was not an expected result if the sand waves remained constant in shape and all other hydraulic factors were constant during the measurement interval(s). For such conditions, the sediment transport in the waves should be relatively constant in value as well. If the ISSDOTv2 method is robust, then when varying the time interval (~t) between reasonable limits, the computed transport values should not change significantly. The results of these computations are discussed in the next section. 5.3 Results for Mississippi River Data The analysis of the pervious section provided 20 separate transport computations. These are shown in Table 7 with four computations for each wave. Wave 1 is the top right wave in Figure 33, wave 2 is the next one down and so on. The difference-file from which the data came, the time difference in minutes and seconds, the scour volume in cubic meters, and finally, the transport gsbi in metric units are listed in columns for each wave. The scour volume in cubic feet is also shown because it is the raw data in which the volumes were obtained from the computational meshes. Within a given wave all four

70 58 Table 7. ISSDOTv2 Computations Using 4 Time Steps ISSDOTv2 computations for RM to usinq four time steps. Difference Time (ot) Time (Dt) Scour Vol 9sbi Scour Vol 9sbi File minutes seconds m3 ko/m/s ft;j lbs/ft/s Wave S S S38 0.8S SO E 3S S avq Std Dev Wave S S S S1S 0.8SS S S E S avg Std Dev 0.1S3 Wave S S S S S S6.91S S S avo Std Dev Wave S S SS E 3S S3 927S avo 1.82S Std Dev WaveS S S S S SO E 3S 2100 S avg Std Dev Summary by wave Avg. 9sbi (kq/m/s) Std Dev C.O.V. Wave S2862 Wave S Wave S06 Wave4 1.82S WaveS O.S2S32S computations should yield similar values of transport for the different time intervals if all conditions as in section 2.3 were true. Thus all four values should ideally be exactly the

71 59 same. However, because some or all of the stated conditions are violated to varying degrees due to the inherent stochastic nature of river hydraulics and sediment transport in general, the results are expected to have some variability as well. This can be seen in the computed values for any wave. No single wave has the same computed value of transport for all four difference plots. By inspection of the computed values for each wave, it becomes clear that the greatest difference in transport from the mean is found in the shortest time step of 35 minutes, with the exception of wave number 4. This raised concern about how short of a time step can be used. One consideration in limiting the time step is measurement error, or instrument resolution. In the case of this data set, instrument resolution was stated as approximately between m (0.1 feet) and m (0.2 feet). When random nodes from the same wave, but at different time steps were sampled, it was found that a significant number of nodes at the 35 minute time step had a change in elevation that approached the instrument resolution. This indicated that these measurements could be spurious and so seems to indicate that data from this time step should not be used. Nevertheless, for the sake of comparison, the 35 minute time step was used in the summary of this table. The summary shows an average value of transport and the standard deviation for the four computations made for each wave. The coefficient of variation (C.O.V. = [Std Dev/Avg]), is a non-dimensional measure of dispersion or variability, and for any wave is shown to be less than 0.23 except for wave 5 where it is about Because of the instrument resolution discussed above, the 35 minute time step was left out of a second set of computations, the results of which are shown in Table 8. The same computations are shown in the table as before, but with those for L\t =35 minutes set to zero. Only time steps of 69, 103 and 143 minutes were considered. The summary results show significantly smaller C.O.V. 'sin all cases except wave 4, which is essentially unchanged. Thus it can be reasonably concluded that removing the short time step did in fact reduce the variability in the computed results for each wave. It also points

72 60 Table 8. ISSDOTv2 Computations Using 3 Time Steps ISSDOTv2 computations for RM to usin_g_ three time steos. Difference Time {Cl) Time (Dt) Scour Vol 9 sbl Scour Vol 9 sbi Wave 1 File minutes seconds m3 kg/m/s cu ft S S S38 0.8S SO S avg Std Dev Wave S S S S1S 0.8SS S S S avg Std Dev Wave S S S S S S6.91S S avg Std Dev O.OS8 Wave S S SS S ayg_ Std Dev Wave S S S S S SO S avg Std Dev Summary by wave Avg. 9 sbi (kg/m/s} Std Dev C.O.V. Wave Wave Wave O.OS S Wave WaveS to the fact that the instrument resolution might be a very useful tool to estimate the minimal time step between sequential measurements. This could be done by using only

73 61 data for which average depths of scour exceed the instrument resolution by some value greater than one. The overall results shown in Table 8 indicate that the ISSD0Tv2 method can be applied to field data and will yield results that are repeatable, and consistent. Computed values of transport for a given wave exhibit expected randomness about some mean value with changes in ~t, but do not become asymptotic to any value as in the previous method computations. This is a good indicator of a sound theoretical basis of the methodology and its robustness when applied to field data.

74 62 CHAPTER6 CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions The measurement of bedload transport in large sand bed rivers has proven over the years to be a very difficult task. The numerous and various attempts that have been made in the past added to the body of knowledge regarding bedload transport, and obtained varying degrees of success. Yet until the present time there was still no method that was proven and accepted in the engineering community to provide accurate estimates of bedload transport in these large rivers. In this document, a new method (ISSDOTv2) has been introduced and described which is capable of providing measurements of the bedload in moving bedforms. This is accomplished by non-invasive measurement of the elevation differences of time sequenced bathymetric data. The theoretical basis for the method has been thoroughly presented and shown to be sound. This was accomplished by using pertinent analytic and geometric considerations and examples. To prove the concept, the method was applied to three different sets of data. Two of these data sets were obtained in flume experiments under very controlled conditions. The experiments were performed at the ARS NSL in Oxford, Mississippi. The third data set consisted of bathymetric data obtained by vessel mounted multi beam acoustic transducers. Those measurements were made by the USACE St. Louis District on the Mississippi River south of Baton Rouge, Louisiana in the spring of In the flume experiments the bedload transport was determined by direct measurement and thus provided a reliable value against which to compare the results of the new measurement technique. In these same experiments sequential bathymetric data were available for obtaining ISSDOTv2 bedload computations. The results of ISSDOTv2 for the first flume data set showed that the average of the transport computations was 137% of the measured values (approximately 37% greater). However, because of the relatively small amount of data available in that flume study, a more

75 63 comprehensive data set was obtained and used as well. The results of ISSDOTv2 for the second flume data set showed that the average of the transport computations was 108% of the measured values (approximately 8% greater). These results show by the very good agreement with measured data that the new method has the potential to return highly accurate estimates of bedload transport. The confidence in these results is aided by the number of wave profiles used, the varying hydraulic conditions (Froude numbers from 0.2 to 0.5), and the fact that large enough sand was used in the experiment to preclude the occurrence of suspended bed-material. In data set three, the field data, there is no measured value to compare to. The main purpose of presenting the field data in this document was to verify that the method can be used with actual field data, and to show the some details of how that might be done. These two goals were accomplished. Sequential bathymetric field data were analyzed in a manner consistent with the methodology used in and proven by the flume experiments. One important criterion that needed to be checked was whether or not ISSDOTv2 would provide similar transport values in a given sand wave for varying time steps. The results clearly showed that computed bedload transport values for a given wave were relatively uniform regardless of the time step for elevation differences greater than the instrument resolution. In these cases, (see Table 8) the greatest transport variability for a given wave was in wave number 5, having a C.O.V. of The coefficient of variation (C.O.V. = [Std Dev/Avg]), is a non-dimensional measure of dispersion or variability. An interpretation of this is that the standard deviation of the three measurements is no greater than 28% of the average value for that wave. The C.O.V. 's for waves 1 to 4 are in order, 0.08, 0.02, 0.04, and These values indicate relatively tight fits about the mean value, and accordingly, relatively small variability. These results show that ISSDOTv2 can be used on field data to produce consistent and repeatable results. ISSD0Tv2 will advance the state of the art with regards to the measurement of bedload transport because of its robustness and improved accuracy. This

76 64 is because previous methods using dune measurements like those described in chapter one all require that the wave celerity and dune statistics be determined and arithmetically manipulated in order to find the bedload transport in the waveform. When computations are complete, one basically has an averaged value over some time and space. Besides the error in the measurement of the waves themselves, additional uncertainty is added by the manipulations of the data. It is intended to use the new method to literally integrate over a cross section using the actual dunes by superimposing a grid over a 3-d surface like the one shown in Figure 32 and computing the scour volume during the time interval. Thus an innovation of this method will be that the averaging of dune geometry statistics and wave speeds will not have to be made. The values of computed transport will come directly from the measured scour volumes, and thus directly represent the transport in a given dune. The result will be a more accurate estimate of bedload transport. Further, all the other methods perform computations along longitudinal transects. Thus the average values computed are valid only for the transverse position in the cross section from which the profile was obtained. The new method can take into account the lateral variability of transport in a cross section. That is because the surface difference plots isolate the scour and deposition in the waves and thus allow one to move across any section selecting only the cells of a given wave. For lack of data that was not possible to demonstrate in this study with numerical values. It has not been noted in the literature that anyone has identified this specific relationship between qsb and the scour volume. If it is known, then it has not been used in this manner to determine qsb. So both of these facts if not new, are certainly new uses of that information. Regarding the uniqueness of this of this methodology, with the exception ofnittrouer (2008), there does not appear to be any other researchers attempting to measure bedload transport in a similar manner.

77 65 Regarding any restrictions or limitations on ISSDOTv2, the method is certainly limited by the consistency of the data collection vessels and instrumentation. Although the multibeam instrument resolution can be cited as extremely important in the determination of the time step, it must be remembered that every aspect of the data collecition platform (boat and associated equipment and instruments) must be properly operating in order to acquire usable data for this method. Thus the method must be considered as the sum of the data collection process and the ensuing computational methodology. The number of survey boats available for such data collection activities are necessarily limited due to their cost and complexity. Thus the ability to field and use such specialized equipment is in a sense a limitation of the method. Another limitation is related to the rivers themselves. If there are no moving sand dunes, obviously the method cannot be used. Such conditions do exist at extremely low flows, and at upper regime high flows that produce anti dunes. Yet the in-between range of flows at which dunes are formed is sufficiently wide such that the transport rates associated with them are of keen interest to river managers. Finally, the superposition of smaller dunes or ripples on the very large dunes will present a limitation of sorts. The solution of this dilemma will probably be found in the time interval that is allowed to elapse between successive measurements. Longer time increments will allow the larger dune to move sufficiently such that the scour volume for the entire wave will be measurable. 6.2 Recommendations In the course of this study there were numerous questions that arose that deserve consideration but were beyond the scope of what could reasonably be accomplished in the present work. These are mentioned here for completeness and as proposals for future investigations. The time steps to be used in collecting the data are important. Chapter five showed clearly that the time step (~t) should not significantly affect the transport rate if

78 66 the waves move with constant velocity and do not change shape during the interval. However, if the time step is too short or too long, the transport values could be compromised. When dt is too short, instrument resolution becomes an issue. Thus investigations into the data collection boat and its instrument capabilities as related to the data collection interval and rates of scour or deposition is an area of future research that will help to define a low end of the time step. When ~t becomes too long, it is possible that both scour and deposition could have occurred at a single location. In such a case the determination of change in volume could be affected by both, and thus is indeterminate for either. The superposition of scour upon deposition and visa-versa occurs continuously at the crest and trough respectively of all translating sand waves. Thus as any wave moves forward there theoretically should be cells at these locations which are removed from the computations. However, with minimal movement and change of shape, these effects could cancel one another out. Thus values computed from trough to crest without any adjustments could still be valid. Additional research is thus needed to verify if such an error is produced. If it is, then a revised computational procedure and/or optimal time step to minimize such an error should be investigated. The details of determining how to use ISSDOTv2 with full compliments of field data have yet to be worked out. It must be remembered that the methodology is not just a computational procedure on field data, but includes a method of collecting the field data which minimizes total field data collection activity, and maximizes output results. This will require more specific research campaigns with collaboration between the engineers and data collection boat operators. Before each campaign discussions of instrument resolution, numbers and locations of swaths, and timing based on known or estimated dune speeds should be discussed. Such discussions should result in campaigns for which the collected data will be valid over a range of flow conditions and for various sizes of swaths and time steps. When verifiable and consistent results are obtained, written guidelines can be produced.

79 67 As the ISSDOTv2 matures, another aspect of the overall methodology that should receive consideration is the computational hardware and software on the boat. At the present time, the bathymetric data is simply stored on a computer on the boat at the time it is acquired. It is later transferred to lab computers where it must be post processed. After post-processing, the data can then be used by someone applying the ISSD0Tv2 method for bedload computation. That process requires triangulating, grid interpolation, surface differencing, cell selection, and fmally volume and transport computations. At present many of the steps have to be done manually. However, many of these processing steps could be automated to various degrees. Thus it is conceivable that an on-board person could be viewing data as it is collected, making the necessary decisions regarding wave selections, and having computed output results before the boat ever docks. This could approach 'real time' bedload data collection, for which other data are also concurrently known, such as flow, water depth and slope. Uses for such an assemblage of data are numerous, not the least of which is the preparation of bedload discharge rating curves that could be prepared after campaigns made at differing river flows. Finally, ISSD0Tv2 should be considered as a research tool for future investigations into bedload transport in both flume and field studies. For instance it has already been proposed by a prominent researcher in sediment transport studies that the relationship between the transport values computed by ISSDOTv2 and the reference concentration Cb be investigated. Cb is used in the Rouse Equation for suspended sediments, see Garcia (2008) page Ill, and is normally estimated by physical samples and other empirical means. If its value could be more accurately determined or shown to have some clear and predictable relationship to the bedload values computed by ISSDOTv2, then that value could be used to greatly increase the accuracy of the predicted suspended sediment profiles made using the Rouse equation. Another research venue will involve sediment transport functions. These transport functions vary widely when applied to field conditions. If ISSD0Tv2 can be verified in field conditions, then it

80 68 could become a yardstick by which to evaluate the performance of the various transport functions. This is an area rich in research potential that would also have wide applicability in practical applications.

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