{"@context":{"@language":"en","Affiliation":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","AggregatedSourceRepository":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","Campus":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","Creator":"http:\/\/purl.org\/dc\/terms\/creator","DateAvailable":"http:\/\/purl.org\/dc\/terms\/issued","DateIssued":"http:\/\/purl.org\/dc\/terms\/issued","Degree":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","DegreeGrantor":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","Description":"http:\/\/purl.org\/dc\/terms\/description","DigitalResourceOriginalRecord":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","FullText":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","Genre":"http:\/\/www.europeana.eu\/schemas\/edm\/hasType","IsShownAt":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","Language":"http:\/\/purl.org\/dc\/terms\/language","Program":"https:\/\/open.library.ubc.ca\/terms#degreeDiscipline","Provider":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","Publisher":"http:\/\/purl.org\/dc\/terms\/publisher","Rights":"http:\/\/purl.org\/dc\/terms\/rights","ScholarlyLevel":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","Title":"http:\/\/purl.org\/dc\/terms\/title","Type":"http:\/\/purl.org\/dc\/terms\/type","URI":"https:\/\/open.library.ubc.ca\/terms#identifierURI","SortDate":"http:\/\/purl.org\/dc\/terms\/date"},"Affiliation":[{"@value":"Applied Science, Faculty of","@language":"en"},{"@value":"Civil Engineering, Department of","@language":"en"}],"AggregatedSourceRepository":[{"@value":"DSpace","@language":"en"}],"Campus":[{"@value":"UBCV","@language":"en"}],"Creator":[{"@value":"Rennie, Colin D.","@language":"en"}],"DateAvailable":[{"@value":"2011-10-14T17:31:24Z","@language":"en"}],"DateIssued":[{"@value":"2002","@language":"en"}],"Degree":[{"@value":"Doctor of Philosophy - PhD","@language":"en"}],"DegreeGrantor":[{"@value":"University of British Columbia","@language":"en"}],"Description":[{"@value":"A new method for measurement of bedload transport velocity using an acoustic\r\nDoppler current profiler (aDcp) is evaluated. Conventional bedload sampling\r\ninvolves physical samplers that are notoriously inaccurate and of limited use for\r\ncharacterizing the spatial and temporal distribution of bedload. The new\r\ntechnique utilizes the bias in aDcp bottom tracking due to movement on the river\r\nbed. This bias can be determined by comparing the boat velocity by differential\r\nglobal positioning system (DGPS) and by bottom tracking.\r\nThe evaluation of the method had four components: field demonstration,\r\nlaboratory calibration, development of an error model to separate the bedload\r\nvelocity signal from the noise in the data, and use of the method in the field to\r\ncharacterize the spatial distribution of bedload transport velocity. The field\r\ndemonstration involved concurrent aDcp and physical sampler measurements of\r\nbedload transport at stationary sampling stations in the gravel-bed reach of Fraser\r\nRiver. Mean bedload transport velocities measured using an aDcp were shown to\r\ncorrelate with mean bedload transport rates estimated with the physical samplers\r\n(r\u00b2=0.93, n=9). The laboratory calibration involved the creation of a synthetic\r\nbedload by dragging small cobbles over an artificial river-bed in a towing tank.\r\nIt was shown that, despite high variability in the measurements that was due to\r\ninstrument noise, the aDcp can separately estimate the mean magnitude and\r\ndirection of the synthetic bedload velocity. However, due to excessive noise in\r\nindividual beam velocities that did not appear to be present in the field data, the bedload velocity in the direction of transport was underpredicted by 79% on\r\naverage. The error model is a new numerical method to probabilistically\r\ndeconvolve the bedload velocity signal and the noise in the data. For data from\r\nFraser River and from Norrish Creek, the probability density functions of the\r\nhighly positively-skewed bedload velocity signal and the acoustic noise were\r\nresolved. The bedload velocity signal could be modelled as either a compound\r\nPoisson-gamma distribution or a gamma distribution. The acoustic noise was\r\nnormally distributed and comparable to typical noise levels for aDcp water\r\nvelocity measurements. Finally, field measurements from a moving boat in a\r\nsand-bed reach and a gravel-bed reach of Fraser River were used to characterize\r\nthe spatial distribution of bedload transport velocity. The bedload velocity spatial\r\ndistribution was shown to be significantly correlated with the spatial distributions\r\nof near-bed water velocity and depth averaged water velocity. Smoothing was\r\nachieved by both block averaging and kriging, which revealed coherent patterns\r\nin the bedload velocity spatial distribution.","@language":"en"}],"DigitalResourceOriginalRecord":[{"@value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/37980?expand=metadata","@language":"en"}],"FullText":[{"@value":"Non-invasive measurement of fluvial bedload transport velocity using an acoustic Doppler current profiler by Colin D. Rennie B.Sc.(Eng.), The University of Guelph, 1995 M.A.Sc, The University of British Columbia, 1998 A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Faculty of Graduate Studies (Civil Engineering) We accept this thq\u00a3i) as qonfoi\/n)r$ to the required standard The University of British Columbia October 2002 \u00a9 Colin D. Rennie, 2002 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of cC\/'\">\/ ^>\\? \/Vi e
30 min ADP sample). Error bars represent precision (+ standard error), with standard error of bedload based on variability of VuV samples 57 Figure 1.9: Bedload transport rate versus mean primary bed speed for individual concurrent samples without sand transport 58 Figure 1.10: Mean primary bed speed versus shear stress (O, included in regression; \u2022 , outlier excluded from regression (see text)). Error bars represent precision (\u00b1 standard error), with standard error of shear stress based on standard error of u* from log-law fit 59 Figure 1.11: Influence of measurement depth on variance of va 60 Figure 2.1. Single ping measurements of apparent bed velocity (cm\/s) for a trial with expected bed speed of 6.5 cm\/s and expected direction of 180\u00b0 (Trial 12). Speed radii for 23, 47, and 70 cm\/s are shown 81 Figure 2.2. Measured versus expected apparent bed velocity: a) mean velocity component in direction of transport, b) mean magnitude of velocity vector. Precision bars indicate \u00b1 one standard error. Dashed line is perfect agreement. Solid line is best fit weighted regression. Symbols indicate orientation of transport with respect to the ADP x axis (see text), and if the artificial bed was present: \u2022 no transport, \u2022 180\u00b0 with bed, \u2022 0\u00b0 with bed, \u2022 198\u00b0 with bed, O 18\u00b0 with bed, \u2022 214\u00b0 no bed, A34\u00b0 no bed 82 Figure 2.3. Measured versus expected direction of transport. Precision bars indicate \u00b1 one standard error. Dashed line is perfect agreement. Solid line is best fit weighted regression. Symbols: + with artificial bed, X without artificial bed 83 Figure 2.4. Increasing standard deviation with increasing transport. Symbols: \u2022 measured standard deviation, O estimated instrument noise. Solid line is best fit regression to measured: ( y = 1.28x - 0.19; r2 =0.93). Dashed line is best fit regression to instrument noise: (y = 1.26x - 0.33; r = 0.91) 83 Figure 2.5: Running mean and coefficient of variation of the magnitude of the bed velocity vector for Trial 12 84 Figure 2.6: Running mean and coefficient of variation of the direction of the bed velocity vector for Trial 12 84 Figure 2.7: Probability density function and lognormal fit (smooth line) for magnitude of the bedload velocity vector for Trial 12 85 Figure 2.8: Probability density function for bedload velocity resolved in the direction of travel for Trial 11 85 Figure 2.9: Beam 1 velocity for a portion of Trial 11\/12. Expected beam velocity based on meanfm. 86 Figure 2.10: Beam 2 velocity for a portion of Trial 11\/12. Expected beam velocity based on meanfm 86 Figure 2.11: Beam 3 velocity for a portion of Trial 11\/12. Expected beam velocity based on meanfm 87 Figure 3.1: Model procedure and results for optimized compound Poisson-gamma fit to Fraser River data set 120 Figure 3.2: Deconvolved distribution of within beam spatial average bedspeed for the Fraser River and Norrish Creek data sets, using both an optimized compound Poisson-gamma and a gamma distribution. Both linear and log scales shown 121 Figure 3.3: Norrish Creek measured data and fitted model using optimized compound Poisson-gamma distribution 122 Figure 3.4: Comparison of measured distribution to gamma distribution for run L2 bedload transport rate of Kuhnle and Southard (1988) -; 123 Figure 3.5: Estimated gamma distributions of entrained particle velocities from cPg model for Fraser River and Norrish Creek data sets. Both linear and log scales shown 124 Figure 3.6: Spectral densities of primary bedload velocity and near bed water velocity components. Mean spectral density indicated by dashed line, and 95% confidence interval indicated by gray lines 125 Figure 4.1a: Sand bed reach depth (m), based on flow depth at beginning of data collection. Bed sediment sample locations marked with +, and labelled with d50.. 164 Figure 4.1b: Sand bed reach spatially block averaged depth average velocity in a) the first hour of measurement, and b) the second hour of measurement. Tail of vector arrow is centre of block 165 Figure 4.1c: Sand bed reach bed shear velocity (m\/s) distribution in first hour of data collection. Location of data collection points shown with small + symbols 166 Figure 4. Id: Sand bed reach raw bedload velocity (m\/s) from first hour of data collection, prior to stationary bedload sampling 167 xi Figure 4.1e: Sand bed reach block average bedload velocity (m\/s) in first hour of data collection overlain on depth (m) contours. Centre of vector arrow is centre of block. 168 Figure 4.1: f) Sand bed reach kriged bedload velocity distribution in first hour of data collection. Helley-Smith bedload sample locations marked with +, and bedload samples from second hour of data collection marked by * with value labeled, g) Sand bed reach kriged near-bed water velocity distribution for first hour of data collection 169 Figure 4.1.h: Sand bed reach (Sea Reach, Fraser River) bedload transport rate versus ADP bedload velocity calibration curve. Two outliers (denoted by O) were not included in the regression: it was presumed that these large bedload samples were due to bottom dragging of the Helley-Smith sampler 170 Figure 4.2a: Gravel bed reach depth (m) 171 Figure 4.2b: Gravel bed reach shear velocity distribution (m\/s). Location of data collection points shown with small + symbols 172 Figure 4.2c: Gravel bed reach spatially block averaged depth average water velocity (m\/s). Tail of vector arrow is centre of block 173 Figure 4.2d: Gravel bed reach raw bedload velocities 174 Figure 4.2e: Gravel bed reach block averaged bedload velocities (m\/s) overlain on depth (m) contours. Centre of vector arrow is centre of block 175 Figure 4.2: f) Gravel bed reach kriged bedload velocity distribution. Location of bedload sampling from 2000 freshet marked by + 176 g) Gravel bed reach kriged near-bed water velocity distribution 176 Figure 4.3a: Sand-bed reach June 22nd raw bedload velocities 177 Figure 4.3b: Sand-bed reach June 22nd kriged bedload velocities 177 Figure 4.3c: Sand-bed reach June 22nd kriged bedload velocity, with boat track shown by red + symbols: a) east component, b) north component 178 Figure 4.3d: Sand-bed reach June 22nd bedload velocity vector angle versus boat trajectory angle 179 Figure 4.3.e: Bedload velocity angle (counter clockwise angles with East at zero) versus ADP heading angle (clockwise angles with North at zero) 179 X l l Figure 4.3f: Sand-bed reach June 22nd bedload velocity vector angle versus boat trajectory angle after adjusting heading by -10\u00b0 180 Figure 4.3.g: Bedload velocity angle versus ADP heading angle after adjusting heading by-10\u00b0 180 Figure 4.3h: Sand-bed reach June 22nd kriged bedload velocities following -10\u00b0 rotation of raw velocities for ADP heading error 181 Figure 4.4.a: Minto side channel bedload velocity vector angle versus boat trajectory angle 182 Figure 4.4.b: Minto side channel bedload velocity vector angle versus boat trajectory angle after adjusting heading by -8.5\u00b0 182 Figure 5.1: Mean magnitude of bedload velocity vector versus mean bedload transport rate for Fraser River gravel reach data of Chapter 1 191 Figure 5.2: Standard deviation versus mean of primary bedload velocity for Fraser River gravel reach data of Chapter 1 192 Figure 5.3: Probability density function and beam gamma error model fit for bedload velocity resolved in the direction of travel for Trial 11 of Chapter 2 laboratory data. 193 Figure C. 1: Fraser River at Agassiz-Rosedale Bridge, facing upstream. Former WSC gauge site 08MF035. Width is 510 m. Described as a wandering gravel-bed river (D50,surf = 42 mm), with a slope of 4.8x10-4 (McLean et al. 1999). If bridge spans are numbered from left to right (facing upstream), the thalweg flows through span 5, and a shallow bar occurs at span 2. All 2000 freshet bedload sampling stations were downstream of the bridge at spans 3 and 4 (Chapters 1,3, and 4) 211 Figure C.2: a) ADP, b) Vi size VuV bedload sampler, and c) Helley-Smith bedload sampler 211 Figure C.3: Boat for Fraser River gravel-bed data collection (Chapters 1, 3, and 4).... 212 Figure C.4: Laboratory set-up for synthetic bedload. Note: an improved artifical bed was implemented for Trials 7, 8, 11, 12, 17, and 18. (Chapter 2) 212 Figure C.5: Norrish River at Hawkins Pickle Road Bridge, facing downstream from bridge, February 22, 2002. WSC gauge site 08MH058 (Chapter 3). River width at bridge is 28 m.. 213 Figure C.6: Norrish Creek on Feb 22, 2002. ADP securely mounted to bridge deck (Chapter 3) 213 X l l l Figure C.7: Boat for Fraser River sand bed Sea Reach data collection (Chapter 4) 214 Figure C.8: Fraser River sand bed Sea Reach, facing upstream (Chapter 4) 214 Figure D.l: Model procedure and results for estimated compound Poisson-gamma fit to Fraser River data set 216 Figure D.2: Model procedure and results for optimized compound Poisson-gamma fit to Fraser River data set 217 Figure D.3: Model procedure and results for beam gamma (spatially averaged bedload velocity within a beam area is gamma distributed) fit to Fraser River data set 218 Figure D.4: Model procedure and results for total gamma (linear combination of spatially averaged bedload velocity from each beam is gamma distributed) fit to Fraser River data set 219 Figure D.5: Model procedure and results for estimated compound Poisson-gamma fit to Norrish Creek data set 220 Figure D.6: Model procedure and results for optimized compound Poisson-gamma fit to Norrish Creek data set 221 Figure D.7: Model procedure and results for beam gamma (spatially averaged bedload velocity within a beam area is gamma distributed) fit to Norrish Creek data set.... 222 Figure D.8: Model procedure and results for total gamma (linear combination of spatially averaged bedload velocity from each beam is gamma distributed) fit to Norrish Creek data set 223 L i s t o f S y m b o l s The following symbols are used in this thesis: ADP = Acoustic Doppler Profiler; Ai = projected planar area of the z'th mobile grain; at = coefficient in error model; aDcp = acoustic Doppler current profiler; Bt = random variable for actual beam velocity for beam i; bi(t) = actual beam velocity for beam i; C = concentration; c = speed of sound; Ci = coefficient in error model; cPg = compound Poisson gamma distribution; cv = coefficient of variation; D = random variable for measured data; D = particle diameter; Di = particle diameter; DCh = characteristic particle diameter; DGPS = differential global positioning system; D# = #th percentile particle diameter by mass; 2>e,az = major, azimuthal diameter of individual beam sampling area; jbeilr = secondary, transverse diameter of individual beam sampling area; 14 = sampling area diameter; d = vertical distance between the bed elevation and the aDcp; dio = 50th percentile particle size of subsurface or of supply; da = depth of the active transport layer; dai - depth above the bed of the ith mobile grain; dr = distance from centre of rotation to transducer; F = acoustic operating (carrier) frequency; Fd = Doppler frequency shift; FR = Fraser River; \\f\\ = scattering form function; f# = probability density function for variable #; fm = percentage of the bed mobile within a beam; fmi = percentage of bed surface occupied by particle i; fR = received frequency; fs = sent frequency; {\/}\"* = n-fold convolution of random variables; Ga(u,a2) = gamma distribution with mean u and variance a 2 ; g - gravitational acceleration; gb = local bedload transport rate per unit width; HS = Helley-Smith bedload sampler; h = depth above the mean bed elevation; i = individual beam or individual particle; KS = Kolmogorov-Smirnov test of difference between distributions; ks = bed roughness; lp = bottom track pulse length; mi = mass per unit bed area of particle \/; N = number of pings; 2 2' N(p,,a ) = normal distribution with mean \\i and variance a ' NC = Norrish Creek; Nbi = random variable for random noise error in beam i; Np = number of particles within view of each aDcp beam; Ny = random variable for noise in the direction of transport; n = number of samples; n0i(t) = random noise error in beam i; 0(#) = of order #; PDT = Pacific daylight savings time; p = Tweedie parameter; p = probability r2= coefficient of determination; raDcP = horizontal distance from center of aDcp head to center of a transducer; n = particle radius; rt = transducer radius; SE = standard error of estimate; Ss = specific gravity of the sediment; std = standard deviation; t = time; T = pulse length; u = mean depth averaged primary water velocity; u5 = estimated mean primary water velocity at 5 cm above the bed; u* = shear velocity; V = random variable for spatially averaged bedload velocity; V = random variable for model of measured data; Vi - random variable for spatially averaged bedload velocity in beam i; Vt = volume of the bedload layer above the bed at the location of the z\"th mobile th (including the i particle volume); Vsi = volume of the z'th mobile grain; v = spatially averaged bedload velocity; va = apparent velocity of bedload; vad = mean bed speed resolved in the direction of particle movement; vm = the mean magnitude of the apparent bed velocity vector; vBT = boat velocity determined by bottom tracking; voi = beam velocity along beam i; v0i(t) = measurement of bedload velocity along beam i; VDGPS ~ boat velocity determined by use of DGPS data; VE = east velocity; ve = expected average bed velocity; v,- = actual spatial average bedload transport velocity within the ith beam; VAT = north velocity; vp = actual average bedload velocity; vPi = velocity of bedload particle i; vr = rotational velocity; = bottom track velocity error due to changing tilt; vv = virtual velocity of particle; vxi = velocity in x direction through beam i; vyi = velocity in y direction through beam i; vx = forward velocity; v = transverse velocity; XYZj = coordinates of impingement point for beam x = coordinate in forward direction; x = boat displacement; y = coordinate in transverse direction; z = coordinate in vertical direction; Az = depth cell size; a = variable in gamma distribution; a = significance level, probability of Type I error; a = roll angle; P = variable in gamma distribution; P = pitch angle; X = transducer pointing angle from the vertical; X2 = chai squared distribution; (j) = half beam width angle of central lobe; <|) = beam deflection angle from vertical; xix n = parameter in a Tweedie model; 9 = counter-clockwise angle from the x-axis to the direction of bedload transport (Chapter 3); cp = heading error counterclockwise to the true coordinate system when facing down (Chapter 1); K = von Karman constant; X = dune length; X = variable in Poisson distribution; Xa = porosity of the active transport layer; Xai = porosity of the bedload layer for the z'th mobile grain; (j. = mean; 6 = half-intensity (-3 dB) half beam width; Gexp = actual direction of transport; Qobs = observed mean direction of transport; p = correlation coefficient; p = density of water; ps = density of sediment particles; pv2 = correlation coefficient of vector fields of 2 dimensional vectors; Ey = 2x2 covariance or cross-covariance matrix of vectors \/ and j; a 2 - variance; CJD = standard deviation of measured va data; GINST = standard deviation of vfl due to instrument noise; XX vE (1.8b) where cp is the heading error measured counterclockwise to the true coordinate system when facing down, and VE and v# are the true east and north velocities A compass error of 2\u00b0 can produce a maximum bedload velocity component error of 3.5% of the magnitude of the bedload velocity vector. 1.3.6 Error due to dynamic instrument tilt In Rennie et al. (2002), we estimated an error due to rocking of the instrument during beam transmission or reception. We now believe that we were mistaken, as the instrument can measure instantaneous velocities only in the radial beam direction. The original description of error due to dynamic instrument tilt is given below, but further discussion is based on our new understanding. Rocking of the instrument during beam transmission or reception will impart an angular velocity to the beam that could be interpreted as a bottom track velocity. Assuming random fluctuations in the pitch and roll of the instrument, this will create random bottom track velocity errors that will depend on the angular velocity of the instrument and the range of the beam (i.e. the depth to the bed). The magnitude of these errors can be 19 approximated by determining the change in the XY coordinate of the impingement point of each beam due to the change in instrument tilt during an ensemble of measurements. Changes in the values of roll (a) and pitch (P) measured by the ADP from one ensemble to the next were used to estimate bottom track error due to dynamic instrument tilt. The ADP coordinate system follows a right hand rule, with the z-axis positive upwards and the x-axis positive in the horizontal direction of beam number one (Fig. 1.1). For a downward looking ADP, positive roll is defined as a clockwise rotation about the x-axis, and positive pitch is a counterclockwise rotation about the y-axis, when looking out from the origin. All the roll values were made negative to compensate for this irregularity. For each ensemble, the ADP provides estimates of the vertical depth for each beam (dj). Coordinates of the points where the beams impinged on the bed were found to be: d\\ tan(x) -d2tan(x) cos (60\u00b0) '- d3tan(x)cos(60\u00b0) XYZ] = 0 XYZ2 - d2tan(%)sin(60\u00b0) XYZ3 = - d3 tan(x)sin(60\u00b0,) ~d2 -d3 (1.9) Coordinates of the impingement points following the change in instrument tilt were found using a three-dimensional coordinate transform (Weisstein 1999, p.1580): XYZ, = 1 0 0 0 cos Act - sin Act 0 sin Act cos Act cos A P 0 sin A p 0 1 0 - sin A p 0 cos A P XYZ; (1.10) Values oiXi' and 7,-' were scaled by Z, \/Z,-assuming a flat horizontal bed surface. The change in X and Y divided by the ensemble time increment provides a first order estimate of the bottom track velocity error due to changing tilt (v,xi, v^ ,). However, each beam will 20 only sense the error component parallel to the beam. Equation 1.6 yields the sensed error in x and y due to tilt. In our measurements, estimated errors in x and y for individual sampling stations had standard deviations of about 1 cm\/s, with a maximum of 4.2 cm\/s. As expected, larger error is incurred for stations with greater depth. The estimate described above assumed that a ping acts as a single coherent pencil beam, and thus will be smeared through space as it is transmitted, reflected, and received from a dynamically tilting instrument. The assumption was that curving the beam due to dynamic tilt will result in an observable Doppler shift. In reality, the ping is a series of acoustic wavelets, each of which will act independently. If the instrument is dynamically tilting, each individual wavelet will have a rotational velocity with respect to the instrument. A simple analogy is a pitcher throwing a series of balls from a rotating pitching mound. In the frame of reference of a stationary observer, each ball will fly straight in a different direction than the preceding ball. In the frame of reference of the pitcher, each ball will curve due to a rotational velocity. For stationary scatterers on the river bed, the wavelet will reflect with zero Doppler shift. However, when the wavelet is received by the instrument in the reference frame of the instrument there is a rotational velocity of the backscattered wavelet. Considering rotation about the instantaneous axis of rotation, the rotational velocity (vr, in m\/s) will be the product of the angular rotation rate (co) and the distance from the centre of rotation to the transducer face (dr). The centre of rotation should be in the centre of gravity of the boat, assuming a rigid mount attaching the ADP to the boat. The instantaneous direction of vr will be perpendicular to dr. The magnitude of vr should be of 0(cm\/s): assuming co equals l\u00b0\/s i 21 and dr equals 2 m, vr will be 3.5 cm\/s. In effect, the magnitude of rotational velocity reflects the degree of translation of the transducer due to rocking of the boat. The question is whether this rotational velocity is parallel or orthogonal to the instantaneous beam axis. If it is orthogonal, then no Doppler shift will be recorded, and dynamic instrument tilt will not result in a bottom tracking error. Clearly, the direction of vr depends on dr, and thus, the relative locations of the ADP and the instantaneous centre of rotation of the boat. If the transducer and rotational centre are in line the rotational velocity will be perpendicular to the transducer face and there will be no Doppler shift recorded. We can not make precise estimates of the magnitude of potential errors due to dynamic instrument tilt, as we do not have information on the relative locations of the centre of rotation of the boat and the ADP. In future measurements, it would be worthwhile to note these locations. 1.3.7 Bedload transport rate Our conceptual model of bedload transport consists of an active transport layer of moving particles which is immediately above the static bed surface. Finer material travels in suspension in the water column above the bedload transport layer. Particles within the active transport layer move either by saltating (short hops) or rolling. Larger particles tend to roll and smaller particles saltate, depending on the dimensionless shear stress (Abbott and Francis 1977, Andrews and Smith 1992, Hu and Hui 1996a). Dimensionless shear stress is defined as: 22 where x is the bed shear stress, p is the density of water, g is gravitational acceleration, Ss is the specific gravity of the sediment, D is the particle diameter, and u* is the shear velocity (x = pw,2). See Equation 1.20 for a method to estimate u*. Andrews and Smith (1992) estimated theoretically that saltation should begin to occur once x* exceeds 0.06. Flume experiments by Hu and Hui (1996a) showed that 80% of particles roll when x* < 0.08, while they tend to saltate or suspend when x* > 0.2, and travel almost exclusively in suspension when x* > 2.8. Suspension occurs if the ratio of particle fall velocity to bed shear velocity is less than about 0.8 (Bagnold 1973). The Hu and Hui (1996a) transport mode criteria were based on measurements of shear velocity and transport mode of individual grains. Thus, effects of particle packing and bed morphology were not considered. Particle packing can increase the shear stress required to initiate motion, but may not effect the mode of transport once motion is initiated. However, increased bed roughness due to dunes or particle clusters will increase the total shear stress without a comparable increase in shear stress imposed on bed particles. Drake et al. (1988) used motion picture photography in a natural fine gravel-bed river to observe particle movements. Bed shear velocity at the time of measurement was about 0.078 m\/s. Particles smaller than 3 mm saltated (x* > 0.13). Particles greater than 3 mm usually rolled and particles greater than 7 mm always rolled (x* < 0.054). These observations are consistent with those of Hu and Hui (1996a), thus we will adopt the Hu and Hui criteria. We have observed u* in gravel bed rivers during bed mobilizing flows ranging from 0.1 to 0.2 m\/s. Thus, sands will saltate in the active transport layer of gravel bed rivers. Gravels will usually roll (D > 8 mm), but gravels may saltate in the highest imposed 23 flows (D < 30 mm). Materials finer than fine sands (D < 0.2 mm) will travel in suspension. Typical shear velocities we have observed in sand-bed channels during flood flows range from 0.04 to 0.08 m\/s. Kostaschuk and Villard (1996) reported u* values as high as 0.19 m\/s in the Main Channel of Fraser River. However, these values are for total bed shear velocity, including form resistance due to dunes. Segmentation of their velocity profiles suggests that grain shear velocity may have been about half the total shear velocity (Villard and Kostaschuk 1998). Using a range of u* from 0.04 m\/s to 0.08 m\/s and the criteria of Hu and Hui (1996a), particles finer than silts (D < 0.03 mm) will always, and fine sands may sometimes, travel in suspension. Sands will either saltate or travel in suspension, but will not roll. For bed slopes typical of natural streams, fluid momentum does not transfer below the bed surface, thus only surface particles are transported and the active transport layer is thin (Bagnold 1973). The depth of the active layer for rolling particles is one particle diameter. For bedload by saltation, the depth of the active layer is limited by the maximum height of saltation. Saltation trajectories have been observed to have heights ranging from 1.2 to 9.2 particle diameters, with a typical value of about 3 particle diameters (Abbott and Francis 1977, Lee and Hsu 1994, Hu and Hui 1996a, Lee et al. 2000). 24 In a sand-bed channel where transport is by saltation, the active layer depth should be about 3Dgo thus the active layer depth is of O(mm). D90 is defined such that 90% of a sample mass is comprised of particles smaller than the D90 particle size. During high transport rates in a sand-bed it is conceivable that particles below the initial surface are entrained following entrainment of a surface particle and prior to deposition of another particle. Thus, the active transport layer may consist of more than surface particles. Definition of the active bedload transport layer is complicated by the presence of a steep gradient in suspended sediment concentration within the water column. In practice, conventional measurements of bedload in sand-bed rivers have been conducted with samplers that have orifices of O(cm) depth . For example, a standard Helley-Smith sampler has a 7.6 cm by 7.6 cm square orifice. Thus, conventional sampling captures both bedload proper and near-bed suspended load. Drake et al. (1988) observed that saltating particle heights never exceeded the highest points of the poorly sorted gravel-bed surface. For a gravel-bed, it appears that the maximum depth of the active transport layer should approach the size of the largest particles on the bed (Andrews and Parker 1987), as the active layer thickness is determined by the size of the largest rolling particles. Thus the active layer depth is of O(cm). However, assessment of the active layer depth is complicated by spatial and temporal heterogeneity of transport. In a poorly sorted gravel-bed, the rate and calibre of bedload transport is non-linearly related to shear stress (Parker et al. 1982). For typical shear stresses in gravel bed channels only partial transport occurs (Wilcock and McArdell 1997), wherein only a portion of the bed surface is active at any one time. At low shear 25 stresses only the smallest particles are mobilized (Jackson and Beschta 1982). As shear stress increases larger particles are mobilized and a greater proportion of the bed surface is active instantaneously. At the highest flows the largest alluvial particles are mobilized, and the active layer depth approaches the depth of the coarse surface layer (about D9o), but the entire bed surface is still not simultaneously mobilized (Haschenburger 1999, Rennie and Millar 2000). Thus, the spatially averaged instantaneous active layer depth should always be less than D90. In gravel-bed channels bedload transport is further complicated by the degree of sediment supply. For low supply channels the bed surface will armour, wherein the bed surface is composed of coarser particles than the subsurface and the supply (Kellerhals 1967). Transport tends to occur as entrainment and transport of individual clasts. For higher sediment supply channels transport has been observed to occur as bedload sheets, which are low relief bedforms (amplitudes of 1 to 2 grain diameters) consisting of alternate congested (coarse) and smooth (fine) zones (Dietrich et al. 1989). The aDcp measures the spatially averaged velocity of the bed surface. For mobile grains, this will include both translational velocity and rotational velocity. For rolling particles, the surface velocity is equal to both the translational velocity and the rotational velocity, which are the same. Saltating grains, however, may have both a translational velocity and an independent rotational velocity. Drake et al. (1988) observed that saltating particles had a strong rotational velocity immediately following initiation of motion or impacts with the bed, but the rotational velocity quickly decayed and diminished to weak wobbling about randomly oriented axes. Thus, it appears that saltating grains do not have significant additional surface velocity due to rotation, and rotational velocity will not be considered further in this thesis. See Appendix A for further analysis of this issue. The aDcp provides an apparent bedload velocity (va), whereas a bedload transport rate often is required. If we assume that va is an unbiased measure of the actual spatially averaged bedload velocity (vp), then the local bedload transport rate per unit width (gb) can be calculated kinematically if the depth (da) and porosity (Aa) of the active transport layer are known (Haschenburger and Church 1998): * * = v , \u00ab \/ . ( l - A . ) p f (1.12) where ps is the density of the sediment particles. It is important to recognize that vp is a spatial average velocity, which depends on both particle velocities and the percentage of the bed surface that is mobile (see Equation 1.14). Application of (1.12) to sand-bed channels is relatively straightforward, wherein da is the depth of the bedload saltation layer that can be assumed to be about 3Z)po and (l - Xa ) is the sediment concentration within the bedload layer (see van Rijn 1984a, Villard et al. in press). Similarly, in gravel-bed channels (1.12) can be applied to time-integrated assessment of bedload transport (Haschenburger and Church 1998), wherein vp is the virtual velocity of the bedload (total travel distance divided by total time including rest periods), da is the time integrated mobilization depth of the bed sediments, and Xa is porosity of the static bed. However, (1.12) is problematic for instantaneous measurements of spatially averaged gravel-bed bedload transport. In this case the active 27 layer is the instantaneous bedload transport layer above the static bed. If bedload occurs as partial transport wherein much of the bed surface is inactive at any one time, it is difficult to estimate a depth or porosity of the active layer. Recall that the percentage of the bed surface that is instantaneously mobile is accounted for in vp. Thus, both da and Xa must be averaged by areal weighting over only the mobile grains: I dai A, da=- (1.13) i Z Ki Ai Xa=-i (1.13b) a V-V \u2022 Ki=-\u00b1TJL (i-i3c) i where dai is the depth above the bed of the z'th mobile grain, At is the projected planar area of the z'th mobile grain, Xai is the porosity of the bedload layer for the z'th mobile grain, Vsi is the volume of the z'th mobile grain, and Vt is the volume above the bed at the location of the z'th mobile grain (including the z'th particle volume). In practice, neither the depth nor the porosity of the active layer is known explicitly, but it should be possible to estimate da and Xa within acceptable bounds. The instantaneous da should range from about 3D 5 (saltating smallest grains) to Do0 (rolling largest grains). Thus da will range from a few mm to several cm, and can be assessed based on the proportion of each grain size in the bedload. The porosity of a layer with individual grain movements will range from Xa = 7\/^ = 0.78 (saltating spherical single grain with a saltation height of 3D) to 0.33 (rolling spherical grain). 28 Application of the kinematic model in this case is complicated. Alternatively, as will be shown, a calibration curve can be developed to relate gb to the measured va, provided that the transport rate has been independently sampled. Also, an alternative to the kinematic model can be developed to predict bedload transport rate from vp. Actual velocities of individual bedload particles (vpi) will vary, depending on particle size and shape, local bed roughness, and stochastic variability in fluid force. Furthermore, particularly in a gravel bed, some of the bed surface within the sampling area will be immobile. The actual average bedload velocity (vp) is a function of the actual particle velocities and the percentage of the bed surface occupied by each particle (fmi): v\u201e=2>\u201e.\/mi (1.14) Furthermore, a simple predictor of bedload transport rate is: gb =zZsbi = Z vPi m, (1.15) \/' i where m,- is the mass per unit bed area of particles size A moving with velocity vpi. Assuming spherical particles and that transported particles do not overlap vertically within the active transport layer, it can be shown that: mi = ri Ps fmi (1-16) where n is the particle radius (A\/2). Substituting (1.16) into (1.15) yields: Sb=%Ps }ZvPi fmi ri (1-17) i If the sediment is of uniform size such that r,- is constant, then from (1.14) and (1.17) gb=y3PsDvp (1.18) 29 where D is the uniform particle diameter. Thus, bedload transport rate can be estimated directly from the average bedload velocity i f the bedload particles are of uniform size. It may also be possible to define a \"characteristic\" particle size (DCh) for a poorly sorted bed. Comparison of (1.12) and (1.18) shows that, for transport of particles that do not overlap vertically in the active layer, Dch=l.5(l-Aa)da (1.19) 1.4 Methods 1.4.1 Study site We field-tested this technique during the 2000 freshet at the Agassiz-Rosedale bridge site of Fraser River in British Columbia, Canada (49.21\u00b0 N , 121.78\u00b0 W, Water Survey of Canada former gauge station 08MF035). The study site location is shown in Figure 1.4. The hydrology, bed material, and sediment transport characteristics of the site were described by McLean et al. (1999) on the basis of a 20-year program of sediment transport measurements carried out by the Water Survey of Canada. The river width is 510 m, and the channel gradient is 4.8X10\"4. The D50 and D90 of the surface sediment were reported to be 42 mm and 80 mm, respectively. The D50 and D90 of the subsurface sediment were 25 and 80 mm. The bed material is bimodal, mostly gravel-cobble with some sand. The thalweg flows along the left bank, and a shallow mid-channel bar occurs towards the right side of the channel. This bar is the tail of an upstream mid-channel island. Photographs of the site and sampling methods are provided in Appendix B and in Rennie and Millar (2001). 30 1,4.2 Apparent bedspeed Measurements were taken at flows ranging from 5600 m \/s to 6800 m \/s, which were less than the mean annual flood of 8800 m \/s, but greater than the 5000 m \/s threshold for gravel mobilization (McLean et al. 1999). The 1.5 MHz ADP, with internal compass and tilt meter, was deployed from a boat. The ADP was interfaced with the DGPS. Refer to Appendix B for the ADP operating parameters. Bottom track measurements occurred at 1 Hz, and ensemble averages were collected at 0.2 Hz. ADP and DGPS data were collected at 31 nearly-fixed locations for time periods ranging from 2 to 112 minutes. Positions were held either by motoring or by tying to the bridge, although there was some boat motion within a restricted area. Flow was steady during sampling at a station. Poor bottom track data quality eliminated eleven of the ADP stations: we were incapable of bottom tracking in depths less than 2 m or greater than 8 m, which limited good stations to the center of the channel. Presumably, the bottom track acoustic signal was excessively attenuated in the turbid Fraser River for depths greater than 8 m. Two bottom track data quality criteria were utilized. First, ensemble averages were accepted only if they had greater than 33% good pings (which guaranteed at least two good pings in an ensemble average) and if the recorded depth was reasonable (see below). Second, greater than 50% good ensemble averages were required in a time series. A bedload velocity vector was calculated for each ensemble, and resolved in the direction of the mean primary water velocity (Bathurst et al. 1977). Finally, an average apparent primary bedload speed was determined for each station. 31 1.4.3 Bedload Concurrent bedload samples were collected at 10 of the locations using a half-size VuV sampler (Novak 1957) for the coarse fraction (> 4.75 mm), and a Helley-Smith (HS) sampler (Helley and Smith 1971) for fines (>0.147 mm, < 4.75 mm). The aperture of the VuV sampler was 255 mm wide by 115 mm high, and the wire mesh gap of the sampler was 4 mm. The aperture of the HS sampler was 76 mm by 76 mm, with a collection bag mesh size of 0.2 mm. Typically, five 5-minute VuV samples and three 3-minute HS samples were collected over the course of about an hour at each station. HS samples were not collected at two stations, so HS samples from a similar station were used to estimate the fine fraction. The samplers were deployed from the bridge using a rope and pulley system. The shipboard ADP was positioned within a few meters downstream of the sampler. The samplers could not be deployed in the thalweg due to excessive depths and high velocities. Sampling efficiencies were assumed to be 0.33 for the VuV sampler (McLean et al. 1999) and 1.5 for the fine fraction from the Helley-Smith (Glysson 1993). Average fractional bedload transport rates were determined for each station by averaging the multi-sample transport within each size fraction, from which average cumulative particle size distribution curves were developed (Figure 1.5). We also examined individual VuV bedload transport rate samples and corresponding concurrent 5 minute ADP bedload velocity averages. 32 1.4.4 Shear stress A local mean bed shear stress was also calculated for each station by a log-law fit to the mean primary water velocity profile. It was necessary to correct the depth recorded by the ADP. It appeared that the estimated depth for each beam was not corrected for tilt of the instrument. The counter-clockwise values of roll (a) and pitch (P) measured by the ADP for each ensemble average were used to resolve a corrected depth for each ensemble. Coordinates of the points where the beams impinged on the bed in the tilted coordinate system were found using (1.9). Coordinates of the impingement points in the tilt-corrected coordinate system were found using (1.10). If an individual beam depth diverged from the mean depth for the beam by greater than 0.5 m, or a depth was not recorded, the beam depths for that ensemble were omitted. A mean depth for the ensemble was found by averaging Z, from the three beams. Finally, a mean depth for the station was found by averaging all the ensemble depths. Water column velocities were collected along three beams in bins vertically spaced 25 cm apart, with velocity in each bin based on backscatter from a 50 cm deep triangularly weighted window (SonTek 1998). The first good bin was centered > 0.25 m from the bed. An average water velocity was determined for each bin above the mean depth for the station. The average velocities for each bin were resolved in the primary direction for the mean profile by minimizing the depth averaged secondary mean velocity (Bathurst et al. 1977). Finally, the shear velocity (\u00ab\u00bb) and the bed roughness (ks) were estimated using the log-law with the slope and intercept of the least squares linear regression to the entire profile: 33 u = \u2014\u2014 ln{h) + \u2014 In K K \\ k s J (1.20) where K is the von Karman constant (0.41), and h is the depth of the bin above the mean bed elevation. The mean local bed shear stress (x) is simply pu,2, where p is the density of water. A standard error of each u* estimate was calculated based on the regression fit (Zar 1996,p.330). 1.5 Results The boat velocities determined by bottom tracking and by DGPS were used to estimate an apparent bedload velocity for each ensemble using Equation 1.1 (Figure 1.6a). The bottom track boat velocities were integrated to yield a boat trajectory (Figure 1.6b), which could be compared to the DGPS position fixes. A time series of va resolved in the direction of the primary water velocity was also constructed (Figure 1.7a). The bedspeed was resolved in the direction of the primary water velocity under the assumption that the bedload samplers aligned in this direction. In .most cases there was little difference between mean primary bedspeed and the mean bedspeed vector, as indicated by the small magnitude of the mean secondary bedspeed (Table 1.2). Figures 1.6 and 1.7 provide data from one, typical sampling station (sample 07132). Wide scatter was evident in estimates of va from the individual 5-second ensemble averages (Figure 1.6a). The coefficient of variation (standard deviation divided by the long-term mean) for va resolved in the direction of the average bedload speed vector 34 ranged from 0.9 to 6.4 for the 20 sampling stations. However, the long-term average for a station was consistently in the expected downstream direction. Similarly, the boat trajectory by bottom tracking ran upstream, in contrast to the essentially fixed position of the boat by DGPS. For sample 07132, bottom tracking falsely indicated that the boat moved upstream 290 m over the course of 1.5 hours, whereas the boat was essentially stationary and DGPS indicated that the boat remained within 2.4 m of the starting position (Figure 1.6b). The apparent boat trajectory indicated by bottom tracking reflects bias introduced by bed mobility. It is apparent that a large sample is required to estimate reliably the mean va. Both a running coefficient of variation (cv) (Kuhnle and Southard 1988) and a running average of the apparent primary bedspeed sequence were calculated to determine the duration of sampling required (Figure 1.7b). For each sampling station, a Monte Carlo process of 400 randomized sequences yielded an estimate of the number of 5-second samples required to achieve a reliable estimate within \u00b15% of the long-term mean or the long-term cv. A randomized sequence was used to ensure that any temporal trend in the data did not influence the result. For all of the stations with greater than 30 minutes of data, about 25 minutes of sampling was required to achieve stable estimates of the mean and the cv. Unfortunately, it appears that short-term sampling is not presently dependable due to excessive noise in the data. Similarly, assessment of temporal variability of at-a-station bedload for scales of seconds to minutes is not presently possible (however, see Chapter 3 for one such assessment). Quasi-periodic pulsing of bedload in plane-bed gravel rivers at periods ranging from 5 to 30 minutes is widely reported (see Gomez et al. 35 (1989) for review). The bedspeed time series of Figure 1.7a may display an irregular pulsing with a period of between 4 and 5 minutes. However, the trend is obscured by noise in the data. Spectral analysis of the bedspeed time series did not reveal any significant periodic or quasi-periodic pulsing. Again, noise in the data may have obscured temporal pulsing, but it could also be that the pulsing was not sufficiently periodic to emerge spectrally. Despite wide scatter in individual 5-second ensembles, the estimates of mean v0 appeared to be coherent when compared with bedload sampler data. The average apparent primary bedspeed was well correlated with mean bedload transport rate determined from-the bedload sampler data (Figure 1.8): Yb = 1.4 v~a- 0.046 (r2 =0.93, SE = \u00b10.0032, p< 0.0005 ) (1.21) Overbars indicate mean quantities, and units are SI. The linear regression was weighted (Montgomery and Peck 1982, pp. 362-363) by the reciprocal of the standard error of each v0 in order to account for the variable precision in va estimates, which was due to variable durations of sampling and increasing variance with increasing transport rate. SE is the standard error of estimate based on a weighted average va and a weighted sum of i residuals, andp is the probability that the slope is zero (i.e. zero correlation). We have plotted va on the abscissa in order that (1.21) is comparable to (1.12). It is apparent from (1.21) that a calibration curve can be developed for this site to relate va measured using an ADP to the mean bedload transport rate. The non-zero intercept of (1.21) will be discussed in Section 1.6.2. 36 The individual VuV bedload transport rate samples and corresponding concurrent 5 minute ADP bedload velocity averages displayed moderate correlation (Figure 1.9). It appears that relatively short sampling times of 5 minutes can produce useful data, although this correlation was heavily influenced by one high transport rate sample. One datum was deleted for which the sample was observed to fall out of the VuV sampler during retrieval. In this analysis we used only stations where sand was not measured in transport by the HS sampler, as the VuV sampler could not measure the sand fraction. For three of these stations we also compared the cv of the concurrent 5 minute ADP bedload velocity samples to the cv of the VuV bedload transport rate. The cv of va was consistently less than the cv of ga (Table 1.3), which suggests that the ADP bedload velocity is a more reliable measurement of bedload transport than conventional sampling. A significant correlation was also obtained for va versus mean bed shear stress (x) (Figure 1.10): ~a= 0.00128 X 1 ' 4 5 (r 2 =0.44, p< 0.0005 ) (1.22) The standard error of the exponent is 0.40, thus the shear stress exponent of 1.45 is the same as in the typical relationship between bedload transport rate and x 1 ' 5 (Yalin 1972). A power relation was achieved using a log transform of the data, which also helped reduce heteroscedasticity. One outlier with a low shear stress was neglected in the regression, which was justified as this station also had an unrealistic value of ks that cast doubt on the x estimate. 3 7 There is more scatter evident in Figure 1.10 than Figure 1.8, but this is expected as mean shear stress is merely a measure of mean flow competence, whereas bedload transport is also dependent on sediment supply, entrainability of the bed, and fluctuations in fluid force. Similarly, gb was not significantly correlated with x despite the fact that the mean velocity profiles displayed semi-log linearity, which suggests that x should have provided a reasonable estimate of mean local bed shear stress (cf. horizontal standard error bars in Figure 1.10). Tentatively, it appears that partial, patchy mean bedload transport rate can not be tightly predicted even with good measurements of mean local bed shear. 1.6 Discussion 1.6.1 Significance of a linear relation between bedload velocity and bedload transport rate Our results (1.21) indicated that apparent bedload velocity varied linearly with bedload transport rate, in accordance with the kinematic relation (1.12) if da (l - Xa ) was constant. This suggests that the depth and porosity of the active layer do not vary greatly, and the velocity of transport is the most important parameter in the kinematic equation. However, actual particle velocities do not necessarily increase linearly with transport rate, as the percentage of the bed surface that is mobile may also increase (1.14). 38 1.6.2 Influence of suspended sediment in the sample volume We are presently uncertain of the site specificity of (1.21). Possibly, variations in the bedload particle size distribution from site to site will alter the curve. It is noteworthy that (1.21) does not have a zero intercept. It appears that fine sand moving over the essentially stable bed created a velocity response at low mass transport rates. We suspect that bottom tracking was positively biased by suspended sediment near the bed (\"water bias\"), as well as by bedload proper. Fraser River is very turbid during freshet, with near-bed (15 cm above the bed) total fractional suspended sediment concentrations of 0(1000 mg\/L) at the location of our measurements (Environment Canada 1996). If water bias does influence the intercept of the calibration curve, then it is likely that variability from site to site in near-bed suspended load will make the calibration site specific. We roughly estimated the degree of backscatter from the average sampling volume that could be expected due to an estimated near-bed fractional suspended sediment concentration (Table 1.4). The suspended sediment concentration was estimated from previous observations (Environment Canada 1996) between 1968 and 1983 at a vertical 274 m from the right bank (i.e. the centre of the channel, near the location of our measurements). The vertical distribution of suspended sediment concentration for each size fraction was estimated from all available data for flows between 5000 and 8000 m3\/s. The fractional concentrations at 9 cm above the bed were estimated by extrapolating these curves (for each profile the measurement nearest the bed was 15 cm from the bed). The number of particles in the average sample volume during a ping was estimated for each size fraction using the concentration estimate at 9 cm above the bed. The average 39 sample volume depended on the depth and the pulse length (see Figure 1.2). The fractional mass was calculated by multiplying the fractional concentration by the average sample volume. The number of particles in a size fraction was determined by converting the fractional mass to a volume and dividing by the volume of a spherical grain with a diameter equal to the geometric mean of the size fraction. The total projected area from these grains was estimated, again assuming spherical particles. Literature values for form factors (|\/|) (Table 1.4) were used to modify the expected backscatter from the total projected area of each particle size. It appears that suspended sediment could have effectively covered up to 3 percent of the sampling area (depending on the flow depth). With an estimated typical near-bed (9 cm depth) velocity of 1.2 m\/s, near-bed suspended sediment may have contributed 3 cm\/s to the va signal, which agrees well with the intercept of (1.21). However, the Helley-Smith sampler should have collected most of the suspended sediment within 7.6 cm of the bed. In future experiments, concurrent measurements of near-bed fractional suspended sediment concentration would be useful. Assuming that suspended sediment introduced the same degree of bias for all sampling stations, then it may be reasonable to remove this bias as estimated by the regression intercept: gb =1.4v\u201e (1.23) where va =v.- 0.033 (1.24) is the corrected apparent velocity of bedload. 40 We should note that the form factors used in the analysis above depend on the acoustic wavenumber (k), and thus the operating frequency of the aDcp. We used a 1.5 MHz aDcp. The form factors would have been smaller for a lower frequency instrument, and thus suspended scatterers would have less of an impact on the bottom track velocity for an equivalent pulse length. Thus the calibration expressed in (1.21) is likely dependent on the acoustic operating frequency. This leads to an important question: where in the active bedload layer is the bottom track ping reflecting? It is well established that acoustic signal attenuation is inversely related to operating frequency. It may be that lower frequency instruments will penetrate through the mobile layer entirely to reflect off the solid, immobile boundary, with the result that no bedload velocity will be recorded (see, for example, Section 4.4.1). This will also depend on the size of the mobile particles, as particles for which krt>2 should influence the bottom tracking. Further, with a high frequency instrument and a high concentration of suspended scatterers, the bottom track pulse may be attenuated before it reaches the bedload layer. Presumably, in this case, the bottom would not be observable and the bottom tracking processing would not calculate a velocity. This likely occurred in our deep water measurements on Fraser River, where bottom tracking was not possible. 1.6.3 Measurement error The scatter in individual estimates of va was probably due to both measurement error and real temporal variability of bedload transport. It is difficult to quantify the relative importance of measurement error and real variability as contributors to the observed 41 variance in va (Figure 1.6a). However, real transport should only be in the downstream direction. The variance was nearly isotropic: the standard deviation of va in the transverse direction was consistently about 0.9 times the standard deviation in the vector direction (r =0.83). This variance in the transverse direction may have been a result of incorrect resolution of the bedload velocity vector due to sparse bedload transport, as outlined in Section 1.3.3. Furthermore, a large number of physically unrealistic negative apparent bedload velocities were recorded. Thus, it appears that the variance was largely due to measurement error. It is interesting to note that the variance of vfl appeared to depend on the measurement depth, with very high standard deviations observed at shallow depths of 2 m, and minimum standard deviation at about 3 m depth (Figure 1.11). Again, it is difficult to separate real variability from measurement error (see Chapter 3 for a method to do so), but it appears that the ADP worked best in depths of about 3 m. Real temporal variability would have been associated with stochastic variability in entrainment of individual or groups of particles and\/or quasi-periodic transport of bedload sheets (Gomez et al. 1989). The passage of large bedforms was not likely a factor: dune migration was not apparent in time series of individual beam depths, nor did spectral analysis of the bed speed time series reveal significant regular periodicity that would be expected with dune migration. Real temporal variability should be high for 5-second samples of bedload, even under steady flow and plane-bed conditions (Einstein 1937, McLean and Tassone 1987, Kuhnle and Southard 1988). A flume study by Kuhnle and Southard (1988) of statistically steady equilibrium bedload transport of a fine gravel mixture moving as bedload sheets provides a lower-bound estimate of the expected real 42 variability. The coefficient of variation decreased logarithmically with increasing sampling duration (their Figure 22). Extrapolating their result to a 5-second sampling duration produces a cv of 0.65 (for their run L2). Our measurements were collected during steady flow, but the steadiness of sediment supply was unknown. Furthermore, while the mean transport rate for run L2 (0.041 kg\/m\/s) was similar to our field results, the sediment was finer (D50 = 3 mm), thus transport in our measurements was probably more sporadic. It is likely that the real temporal variability of bedload transport would have produced a cv for our 5-second samples on the order of a value of one. The rest of \u2022 the variability in va can be attributed to measurement error. There are several methods to estimate the standard deviation of va due to measurement error (crf). First, a lower bound on ae can be crudely approximated by fitting a normal distribution, with a mean of zero, to the negative values of va. This assumes that the negative values are purely erroneous and do not include any positive signal. Second, if it is true that the coefficient of variation due to real variability equals one, then as should equal the measured standard deviation minus the mean. Third, a theoretical cr\u00a3 can be approximated by pooling (root sum of squares) the estimated errors due to instrument noise, dynamic tilt (assumed to be of 0(1 cm\/s)), heading error, and DGPS error described in Section 2.3. For our station data, all three estimates of ae equal each other on average. It is noteworthy that virtually all of the pooled error is due to instrument noise. This issue is explored further in Chapter 3. 43 1.6.4 Apparent bedload velocity The ADP yields a single estimate of bedload velocity, which we have termed the apparent bedload velocity (vfl). At the present time we do not know if va is a true measure of the actual average bedload velocity (vp), but it appears that v\u201e may have been an overprediction of vp. Use of (1.18) with observed va and gb consistently yielded a small \"characteristic\" bedload particle size (< D5 of the bedload, see Table 1.5). These values were an order of magnitude less than expected for DCh calculated using (1.19) and (1.13) from the observed fractional bedload transport rates (Table 1.5). The discrepancy may have been due to high values of va . Similarly, an attempt was unsuccessful to use observed va with the kinematic model (1.12) to predict the bedload transport rates measured with the samplers. Assuming an active layer porosity of 0.4, unrealistic values of da (about 0.3 mm, see Table 1.5) were required to match predicted to measured gb . Assuming a porosity of 0.78, which is typical of individual saltations, yields da equal to about 0.9 mm. These values for da are consistently less than estimated using Equation 1.13 and the observed fractional bedload transport rates. As mentioned above, va may have been positively biased by near-bed suspended sediment transport. If the corrected va is used, estimates of DCH and da are both about 0.8 mm (Xa = 0.4) or da of 2.4 mm (ka = 0.78). The estimate of da equal to 2.4 mm is comparable to the estimated da using Equation 1.13, and may be reasonable for saltating sand particles. It may be that saltating sand dominated the bedload velocity signal, or that va was an overprediction of vp. Controlled experiments were conducted in a laboratory towing tank to investigate vfl 44 systematically (Chapter 2). However, sand transport was not considered in the laboratory. 1.7 Conclusions A new technique has been presented for remote measurement of bedload transport. An acoustic Doppler current profiler was used to measure apparent bedload velocity. Mean apparent bedload velocity correlated well (r^ O.93) with mean bedload transport rates measured using conventional samplers. Thus, a calibration curve can be developed to relate apparent bedload velocity to bedload transport rate. A long sampling duration, on the order of 25 minutes, was required to achieve a reliable estimate of the mean apparent bedload velocity. Remote measurement of bedload transport using acoustic Doppler technology holds great promise, as measurements can be taken with relative ease and safety at channel-forming discharges throughout a study reach. This makes the technique especially favorable for measurement of bed movement in large rivers. Improvements to the technology may allow for collection of useful data with greater temporal resolution. 45 Table 1.1: Towing tank tests of single ping ADP bottom tracking tow velocity (m\/s) pulse length (cm) n X (m\/s) % error (%) std x (m\/s) cv y (m\/s) stdy (m\/s) -2.00 60 40 -1.985 -0\\8 0.083 0.04 0.010 0.050 -1.50 60 30 -1.488 -0.8 0.039 0.03 0.008 0.051 -1.02 60 56 -1.018 -0.2 0.029 0.03 0.004 0.031 -1.00 60 71 -0.992 -0.8 0.034 0.03 0.005 0.025 -0.50 60 96 -0.499 -0.2 0.015 0.03 <|0.001| 0.012 -0.30 60 122 -0.300 0 0.017 0.06 -0.001 0.014 -0.10 a 60 125 -0.098 -2.0 0.019 0.19 <|0.001| 0.005 -0.05 a 60 199 -0.049 -2.0 0.015 0.31 < 0.001 0.004 0 60 751 0 0.001 0.05 a 60 232 0.047 -6.0 0.016 0.34 <|0.00T| 0.005 0.10 a 60 122 0.096 -4.0 0.024 0.25 <|0.001| 0.006 0.30 60 121 0.298 -0.6 0.019 0.03 -0.001 0.013 0.50 60 93 0.495 -1.0 0.017 0.03 <|0.001| 0.015 1.00 60 67 1.002 0.2 0.022 0.02 0.004 0.023 1.02 60 55 1.012 -0.7 0.059 0.06 <|0.001| 0.031 1.50 60 35 1.500 0 0.049 0.03 0.021 0.055 2.00 60 49 1.981 -1.0 0.070 0.04 -0.006 0.070 -0.50 20 77 -0.501 0.2 0.018 0.04 0.002 0.016 0.50 20 76 0.496 -0.8 0.020 0.04 0.002 0.018 -0.50 b 60 108 -0.300 -0.6 0.017 0.03 0.497 0.016 0.50 b 60 110 0.003 -0.8 0.018 0.04 -0.496 0.018 a Tow carriage had trouble maintaining steady velocity in these runs (tow velocity appeared to be periodic about the expected velocity, with maximum error of about 0.01 m\/s). bADP was rotated 90\u00b0 such that motion was in y direction, % error and cv based on y component 06261 06301 06302 06303 06304 06305 06306 06307 07131 07132 07172 07173 07174 07181 07182 07183 07184 07261 07262 07263 Sample (1) W N) S O) CO O) O) 0 ) 0 - ' l\\5 A O M ( D W J i > I M M O ( O M - < 0 ) 0 ) 0 ) S U M ( D 0 ) - k J ( 0 - i U 0 ) ( f l 0 1 O 0 l > M O M - i M ^ < \u00bb N > C \u00bb 2.14 1.99 7.07 3.60 3.62 2.91 5.81 5.80 3.30. 3.41 2.81 2.56 2.18 2.08 2.32 3.21 2.60 3.02 4.50 5.11 Depth (m) (3) 0.114 0.134 0.033 0.080 0.066 0.133 0.129 0.136 0.104 0.120 0.120 0.121 0.172 0.129 0.129 0.112 0.117 0.107 0.106 0.099 0.005 0.026 0.003 0.006 0.008 0.009 0.005 0.008 0.005 0.005 0.006 0.015 0.030 0.002 0.006 0.004 0.007 0.004 0.004 0.004 0.034 0.075 2.5e-7 0.384 0.004 0.195 0.021 0.038 0.008 0.027 0.038 0.043 0.345 0.089 0.083 0.022 0.037 0.037 0.012 0.005 0.052 0.154 0.015 0.008 0.011 0.018 0.216 0.276 0.070 0.052 0.040 0.069 0.110 0.046 0.055 0.041 0.042 0.032 0.078 0.079 Prin (m mean (7) 0.239 0.429 i 0.135 0.125 0.123 0.081 0.224 0.254 0.174 0.135 0.136 0.160 0.291 0.305 0.207 0.120 0.141 0.152 0.188 0.158 Appare nary Is) st.dev (8) 0.009 -0.038 0.003 0.021 -0.020 0.006 -0.009 -0.006 -0.005 0.008 0.004 -0.010 0.040 -0.017 -0.004 0.000 0.004 0.004 0.007 -0.008 ;nt Bedsf Secoi (m mean (9) 0.224 0.444 0.138 0.097 0.115 0.098 0.152 0.181 0.154 0.126 0.123 0.112 0.222 0.282 0.187 0.120 0.136 0.146 0.165 0.168 )eed ndary Is) st.dev. (10) ro o s cs co o i A ^ K , cn o -\u00bb\u2022 _ ,\u201e ,\u201e _ , , ro U - ' O N O M U ^ U l O O l M M M O l - ' - ' U - 1 * \u2014 0.0344 0.0385 0.0863 0.0206 0.0125 0.0104 0.0067 0.0027 0.0735 Transpt (kg\/: mean (12) \u2014 0.0334 0.0103 0.0853 0.0147 0.0033 0.0101 0.0035 0.0001 0.0895 Drt Rate s\/m) st.dev. (13) 0.028 0.016 0.015 0.020 0.00045 0.009 0.00047 0.00034 0.050 3edload D50 (m) (14) ^ | u o i c n m s o i o i l col I 1 1 1 1 1 1 1 n VuV (15) w | W U U W C O M O J o | | | | | | | | | n HS (16) 3 CT\\ Table 1.3 Comparison of coefficient of variation of concurrent samples of ADP velocity (va) and VuV bedload transport rate (gb). Station cv of gb cv of V a n 07132 0.98 0.24 6 07183 1.62 0.46 5 07263 0.54 0.073 2 Table 1.4 Estimate of near-bed (9 cm above bed) fractional suspended sediment concentrations and form factors (k = 6300 m\"1) for calculation of proportion of va due near-bed suspended scatterers. D, mm C, mg\/L kri | \/ | 0.0020 60 0.0063 0.00014 a 0.0028 28 0.0089 0.00028 a 0.0057 51 0.018 0.0011 a 0.011 62 0.036 0.0045 a 0.022 66 0.070 0.017 a 0.044 77 0.14 0.068 a 0.088 127 0.28 0 .10 b 0.18 231 0.56 0 .18 b 0.35 212 1.1 0.50 b 0.71 58 2.2 1.0 b a From Medwin and Clay (1998), Rayleigh scattering, | \/ | = 24n{krif b From Thorne et al. (1995), Figure 9. 4 9 Table 1.5 Estimated characteristic particle diameter, active layer depth, and active layer porosity for bedload samples. All units in mm. Sample D5 D50 da* Aa* Dch b DChc da dae dal d g 07132 7.0 28 17 410 10 0.37 0.4 1.1 1.1 3.0 07173 0.31 16 3.1 710 3.3 0.32 0.4 0.7 1.0 1.8 07174 0.44 15 5.0 640 4.9 0.43 0.5 0.7 1.4 2.0 07181 0.29 20 3.3 710 3.6 0.15 0.2 0.8 0.4 2.3 07182 0.18 0.45 1.4 770 1.6 0.09 0.1 0.5 0.3 1.5 07183 0.25 9 1.8 750 2.0 0.27 0.3 1.9 0.9 5.2 07184 0.18 0.47 1.4 770 1.6 0.13 0.1 0.3 0.4 0.9 07261 0.16 3.4 1.1 780 1.3 0.05 0.05 - 0.1 -07263 8.5 50 24 380 13 0.47 0.5 0.8 1.4 2.3 a Calculated using Equation (1.13) with observed fractional gbi. This required estimation of the number of particles in transport in each size class and the projected planar area of a particle for each size class. Spherical particles with specific gravity of 2.6 were assumed. It was also assumed that particles smaller than 2 mm saltated with dt = 3* Dj and Xai =7\/9, and particles larger than 2 mm rolled with dai = A and A,ai = 1 \/3. b Calculated using Equation (1.19) and estimated da and Xa. c Calculated using Equation (1.18) with observed va and gb . d Calculated using Equation (1.12) with observed va and gb and assuming A\u201e = 0.40. e Calculated using Equation (1.12) with observed va and gb and assuming Xa = 0.40. f Calculated using Equation (1.12) with observed va and gb and assuming Aa - 0.78. 8 Calculated using Equation (1.12) with observed va and gb and assuming Aa = 0.78. O o \u00b0 p * CT CT p figs ) \u00ab )\u00a7Hs o o o o O O O cr CD Q 3 CO o Q o I 2.5 -2.5 -i 1 1 1 1 1 ; 1 1 1 1 1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 actual velocity, m\/s Figure 1.3: Towing tank test of ADP bottom tracking for 60 cm pulse length. 53 Figure 1.4: Study site locations. The study site for chapter 1 was the gravel study site on Fraser River. Also shown are the study sites on Norrish Creek (Chapter 3) and the sand bed Sea Reach of Fraser River (Chapter 4). 54 Sieve Size, mm Figure 1.5: Sampling station composite bedload cumulative grain size distributions. 55 East Bedspeed, m\/s -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 _50 -il 1 I i I i 0 50 100 150 200 250 East, m Figure 1.6: Sample 07132 (91 minute sample), a) Apparent bed velocity (+, individual five second ensemble average; 0, mean). Mean and [st. dev.] of East and North bed speeds are -0.053 [0.136] m\/s and -0.007 [0.126] m\/s, respectively, b) Boat trajectory by bottom tracking. Trajectory by DGPS nearly fixed at location (0,0). 56 Time, s 0 1000 2000 3000 4000 5000 i 1 1 1 1 1 \u2014 -0.05 J 1 1 1 1 1 \u2014 L 5 0 200 400 600 800 1000 K. Number of Five Second Samples Figure 1.7: Sample 07132. a) Time series of primary apparent bed speed, b) Running average (lower dashed line) and running coefficient of variation (upper solid line) of primary bed speed time series. Monte Carlo simulation (see text) suggests that 25 minutes of sampling is required for a reliable estimate of the mean. 57 Figure 1.8: Mean bedload transport rate versus mean primary bed speed ( \u2022 , 2 min ADP sample; O , > 30 min ADP sample). Error bars represent precision (\u00b1 standard error), with standard error of bedload based on variability of VuV samples. 58 0.25 Primary bedspeed from ADP, m\/s Figure 1.9: Bedload transport rate versus mean primary bed speed for individual concurrent samples without sand transport. 59 10 20 T , N\/m2 30 Figure 1.10: Mean primary bed speed versus shear stress (O, included in regression; \u2022 , outlier excluded from regression (see text)). Error bars represent precision (\u00b1 standard error), with standard error of shear stress based on standard error of u* from log-law fit. w 0.40 i E 0.0 2.0 4.0 Depth, m 6.0 8.( Figure 1.11: Influence of measurement depth on variance of va. 61 Chapter 2: Laboratory measurements of bedload transport velocity using an acoustic Doppler current profiler 2.1 Abstract A laboratory test was conducted to assess the accuracy and precision of bedload transport velocity measurement using acoustic Doppler current profiler (aDcp) bottom tracking. A synthetic bedload o f known velocity was created by dragging strings of stones over an artificial river bed in a towing tank. Trials were conducted at various particle speeds, percent mobile bed area, and aDcp orientation with respect to the direction of transport. Estimated apparent bed velocity (v a) vectors showed a large degree of scatter within a trial, and the bed velocity resolved in the direction of transport was biased toward zero. However, mean values of the magnitude and direction of v a predicted reasonably well the average bed velocity. The variance within a trial was due to three factors: 1) instrument noise, 2 ) variability in the percentage mobile bed area within a beam due to the large size of mobile particles with respect to the beam area, and 3 ) the inability of a three beam aDcp to resolve heterogeneous transport. We argue that instrument noise was the primary source of variance. 62 2.2 Introduction We are exploring the potential of acoustic Doppler current profiler (aDcp) bottom tracking for measurement of bedload velocity, with the goal of developing a non-invasive technique for gauging bedload transport. Refer to Section 1.3 for a review of the method. We have tested the method in the field, and found the measured mean apparent bed velocity to correlate with the mean bedload transport rate determined using conventional samplers (Chapter 1). However, in the field-testing we could not ascertain whether or not the measured va was an accurate measure of the actual average bed velocity. In this chapter we present laboratory tests in which we created a synthetic bedload of known velocity and compared the measured apparent bed velocity to the expected average bed velocity. 2.3 Methods We created a synthetic bedload by dragging strings of stones over an artificial river bed beneath an aDcp. We used a commercially available 1.5 MHz three beam Acoustic Doppler Profiler (ADP\u2122) made by SonTek to measure the apparent bed velocity. The tests were performed in a towing tank of painted concrete that is 60 m long, 12ft (3.66 m) wide, by 8 ft (2.44 m) deep. The width and depth appeared to be sufficiently large for the ADP bottom tracking to operate effectively, at least for static bed measurements (see Table 1.1 and Figure 1.3), although the bottom tracking pulse length had to be adjusted to 60 cm in order for the ADP to measure the depth accurately. Adjacent to the tank is a 63 track that runs two trolleys, which are pulled by a 25 hp motor via a cable system. As both trolleys are clipped to the same cable, they both move at the same velocity. Beams were cantilevered out over the tank from each trolley, and strings of stones were strung between the two trolleys. The trolleys were pulled back and forth, so that the stones were pulled back and forth through the sample area beneath the aDcp at an essentially steady, uniform velocity (see Figure C.4 in Appendix C). The velocity was varied between trials, ranging from 0 to 50 cm\/s. The aDcp was set at a depth of either 1.9 m or 2.0 m above the artificial river bed, which consisted of small river cobbles (b-axis diameters of 2 cm to 5 cm, rounded to sub-rounded) epoxied to 8 ft x 8 ft of V\" plywood sheeting. The artificial bed was used to ensure that the backscattering received by the aDcp was similar to the backscattering from the towed particles, and to improve simulation of a field condition. The area of the bed insonified (or \"seen\") by the aDcp bottom tracking depends on the distance between the aDcp and the bottom, the beam geometry, and the spread of each beam (Section 1.3.1). We used an aDcp with beams oriented at 120\u00b0 relative azimuth angles and projecting down at 25\u00b0 from vertical. We have assumed that the half-intensity beam width represents the beam spread. For a sampling depth of 2 m, the sample area consists of three quasi-elliptical areas, each with a major, azimuthal axis of 0.13 m, an area of 0.012 m2, and centred at 0.94 m along 120\u00b0 relative azimuth angles from the aDcp. The orientation of the aDcp beams with respect to the direction of particle motion was varied between trials. 64 The stone lines consisted of the same small river cobbles epoxied to 70 lb test nylon fishing line, with buttons strung along the strings providing the contact surface between the stone and the string. The rocks were spaced 10 cm apart, and each string had 50 stones, for a total of 5 m. The length of artificial river bed was 2.4 m, thus 2.6 m of sampling length was available with the artificial bed fully covered by a stone line. Strings were passed through the aDcp sampling area at 15 cm spacing for some trials and 10 cm spacing for other trials. String spacing was maintained by attaching the ends of each string with swivels to eyescrews spaced along wood boards that were in turn roped to the trolley beams. The strings were also passed through eyescrews spaced along wood boards weighted down on the tank bottom, to maintain line spacing and to ensure that the stones were dragged over the artificial bed rather than through the water column. Time series were collected for several particle speeds at each line spacing. We used an aDcp that sends and receives a bottom tracking signal once per second, and each traverse of the sample area produced only a few seconds of data (depending on the particle speed); thus time series were collected as aggregates of several traverses. Only data in which the stringed stones covered the length of the artificial bed were used. Time series were aggregated separately for traverses in the forward and backward directions. Three trials were also conducted without the artificial river bed. The expected average bed velocity (ve) was the product of the particle velocity (vp) and the percentage of the insonified bed surface that was mobile (fm): ve=vpfm (2.1) 65 The particle speed was well controlled, but the percent mobile bed area varied during a trial. In order to determine\/\u201e, a photograph of a sample of 72 stones was digitized: the mean and standard deviation of the projected surface area of the stones were 2.2x10\"3 m2 and 7.4x10\"4 m2, respectively. Similarly, a pebble count of 100 stones (a and b axes) yielded a mean and standard deviation of projected surface area (assuming an elliptical shape) of 1.9xl0\"3 m2 and 5.9X10\"4 m2, respectively. Using the estimate from digitization, an average stone occupied about 19% of the insonified area from a single beam. The small size of the insonified area may have been problematic: the percentage of the insonified area occupied by moving particles would have varied during a trial as particles moved into and out of the view of the beams. A Monte Carlo simulation was performed to estimate the variability of coverage within a beam, based on possible positions of the stones and the measured distribution of projected area of the stones. The stone areas were modelled as circles. The instantaneous mobile coverage for a single beam could have ranged from 0 to 48% with a mean and standard deviation of 14.5% and 8.5% for the 15 cm line spacing, and from 6% to 48% with a mean and standard deviation of 21.7%o and 6.1% for the 10 cm line spacing. In this chapter it has been assumed that fm equalled 14.5% for the 15 cm spacing and 21.7% for the 10 cm spacing when calculating the expected mean velocities. The effect of variable\/\u201e on the results will be discussed further below. 66 2.4 Results For each trial the va data were plotted in polar coordinates (for example from Trial 12 see Figure 2.1). Wide scatter was evident, with measurements from individual pings being completely unreliable. However, the measured apparent bed velocities tended to be in the direction of bed movement. The data sets for all the trials were summarized (Table 2.1). Comparisons between observed va and expected ve were plotted for both the mean bed speed resolved in the direction of particle movement (vad ) (Figure 2.2a) and the mean magnitude of the velocity vector (vav) (Figure 2.2b). The observed mean direction of transport (Qobs) was also compared to the actual direction of transport (Qexp) (Figure 2.3), with angles defined as counter-clockwise rotations (facing down) about the aDcp x axis (see Figure 1.1). The following regression equations were derived for Figures 2.2a, 2.2b, and 2.3: v~d = 0.21v -0.0060; ad e ( 2 2 ) SE = \u00b10.048 cm\/s, r2 =0.67 = 1.06 ve+0.15; (2.3) SE = \u00b10.1 lcm\/ s, r2=0.9\\ Qobs = 1.02 9^ + 4.6; SE = \u00b13.5\u00b0, rl = 0.97 (2.4) SE is the standard error of the estimate. The linear regressions of Equations 2.2, 2.3, and 2.4 were weighted (Montgomery and Peck 1982, pp. 362-363) by the reciprocal of the standard error of each mean in order to account for the variable precision in mean 67 estimates, which was due to variable durations of sampling and increasing variance with increasing va (Figure 2.4). It is encouraging that vad shows an increasing trend with ve (Figure 2.2a); however, vad tends to underpredict ve by 79%. Alternatively, vav displays much closer agreement to the expected ve (Figure 2.2b); and the mean direction of the va vector also tends to be reasonably well predicted (Figure 2.3). In other words, the measured magnitude and direction of va both tended to be distributed around their expected means. It appears that the aDcp predicted the mean magnitude of the bed velocity, and the mean direction of the bed velocity, but not the mean bed velocity component in the direction of transport. Thus, it may be necessary to estimate the mean ve using vav and the mean direction of va. There is a great deal of scatter in the measurements. About 2 minutes of data were required for stable estimates of the mean and cv of the magnitude of the bed velocity vector (Figure 2.5) and of the bed velocity vector direction (Figure 2.6). The coefficient of variation of the va vector magnitude was about 1.28 on average (Figure 2.4). Probability distribution functions of the va vector magnitudes were not significantly different from lognormal (Kolmogorov-Smirnov test) with means near the expected ve (Figure 2.7). Lognormal distributions indicate a combination of random terms by a multiplicative process, which seems reasonable for combination of error terms that produce instrument noise. The distribution of va(\/ for the same data set is shown in Figure 2.8, and will be discussed in Chapter 5 in the context of the error modelling presented in 68 Chapter 3. The thrust of the discussion will be that the lab data differ from the field data in their error structure, and the noise observed in the lab may have biased vact toward zero. The aDcp appears to measure smaller values of va when the transport is in the negative x direction than with positive x transport. The x direction is defined as the horizontal direction of the first beam. An aDcp is typically deployed with the flow, and thus the transport, in the negative x direction. The negative x direction corresponds to a transport direction of 180\u00b0 (solid symbols, Figure 2.2). Orienting the aDcp with transport in the negative x direction yielded a better estimate of ve for vav, but the converse was true for It appears that trials without the artificial bed yielded estimates of va in closer agreement to ve (triangles in Figure 2.2). Owing to the 25\u00b0 beam elevation angle from vertical, the backscattering from a smooth, flat bottom is probably less than from a rough bottom, as most of the acoustic pulse reflects away from the aDcp. Thus, it is reasonable to expect superior registering of mobile particles in the absence of the artificial bed, as backscattering from the immobile bottom is reduced. 2.5 Discussion 2.5.1 Measurement error The laboratory tests suggest that an aDcp can, on average, correctly resolve the magnitude and direction of bed velocity. However, it appears that vaa was biased toward 69 zero. The underprediction in the direction of travel was due to inability of the ADP to correctly resolve the direction of transport for individual pings. There are three conceivable sources of error that resulted in the scatter. First, due to imprecision in the system hardware or signal processing, the instrument may have incorrectly assessed the Doppler frequency shift in one or more of the beams. We will describe this as instrument noise. Second, variable percentage mobile area within a beam due to the large particle size and spacing would have produced temporal variability in va, despite the fact that ve was steady if measured over the larger scale of the artificial bed. Third, the same variability in percentage mobile area would have caused heterogeneous transport between the three aDcp beams, which, as will be explained below, would have produced erroneous va vectors. We will argue that instrument noise was the predominant source of scatter in the data. In particular, we will show that the inability to correctly resolve the direction of transport for individual pings was the result of large erroneous velocity measurements in individual beams. Error due to instrument noise for bottom tracking over solid, stable substrates is an order of magnitude less than error for water column velocity estimates (V. Polonichko, 2000, SonTek Inc., personal communication) because a strong backscatter signal is received from the solid boundary. The standard deviation of the horizontal water velocity measurements is reported to be (Theriault 1986a, SonTek 1998) 140 c ow = = (2.5) F Az V A where c is the speed of sound (nominal value 1500 m\/s), F is the acoustic operating frequency (1.5 MHz), Az is the depth cell size (0.25 m), and N is the number of pings. 70 The number of pings equals the averaging interval (Is) times the pinging rate (9 pings per second for the 1.5 MHz aDcp). Substitution of these values yields crw equal to 19 cm\/s, which suggests that the standard deviation of bottom tracking velocities due to instrument noise for a population of one-second ensembles should be on the order of 2 cm\/s. Bottom tracking tests in the towing tank with a mobile instrument showed that the standard deviation ranged from 2 to 8 cm\/s, with higher standard deviations observed for higher towing velocities (Table 1.1). However, bottom tracking error is greater when the bed is mobile, and the internal signal processing is not presently designed to resolve the velocity of a mobile bed. As a model of gravel transport in rivers, in our laboratory tests only a portion of the bed within each beam was mobile, while the majority of the area was stationary. The monofrequency sound pulse was likely reflected with two different frequencies: the original frequency for the portion insonifying the stationary bed, and a Doppler shifted frequency from the portion reflecting off mobile particles. The bottom tracking algorithm is proprietary, but it involves a pulse-to-pulse incoherent (\"narrowband\") technique (V. Polonichko, 2000, SonTek Inc., personal communication), thus probably a single, strong amplitude frequency is found and used to determine the Doppler shift (see Brumley et al. (1991)). It seems likely that the instrument would have more difficulty interpreting the received frequency spectrum of a mobile bed. Instrument noise can be attributed to two broad factors: 1) Doppler noise, which is uncorrelated from sample to sample; and 2) signal dwell time in the sample volume, 7 1 which is related to the pulse length (Lemmin and Lhermitte 1999, see Section 3.6.2). We suspect that the Doppler noise was high in the towing tank tests, although the ADP does not output signal to noise ratio for bottom tracking, which makes assessment of Doppler noise difficult. Signal to noise ratio is a measure of the power of the signal in the acoustic return versus the power of the background noise in the return. Doppler noise is proportional to the standard deviation of the backscattered Doppler spectrum, thus spectral broadening increases Doppler noise. Spectral broadening can occur when different scatterers in the sample volume have different velocities, as discussed above. This cause of random error tends to increase with higher particle velocities as a broader signal spectrum is required to account for velocities ranging from zero to the particle velocity. This may explain why we observed higher variance with higher mean velocities (Figure 2.4). Spectral broadening also occurs with receiver or backscatter noise, which may have occurred in the lab trials. It is useful to examine individual beam velocities when evaluating the noise. Theriault (1986b) presented equations to calculate the forward (vx) and transverse (v ) velocities given the velocity determined along each beam, assuming homogenous velocity in all three beams: 72 In this notation, beams are numbered counterclockwise when the aDcp is facing down, with the horizontal component of beam 1 parallel to the x-axis. The angle <|> is the beam deflection angle from vertical (denoted % in Chapter 1). Beam velocities were extracted from the data in xyz coordinates by solving (2.6): v M = vx sin(\u00a7) - v z cosfa) (2.7a) - vx sin(\u00a7) + V3 vy sinfa) - 2 v z cos(<\\>) vb2 = \u2014 (2.7b) - vx sin(<\\>) - S v y sinfa) - 2 vz cos(\u00a7) vb3 = (2.7c) In Figure 2.9-2.11 we present a short time series of the measured and expected vol, Vb2, and Vb3 beam velocities for Trials 11 and 12 (i.e. both forward and reverse directions). In general, along each beam the ADP was able to register zero velocity when the bed was immobile and register a velocity when the particles were moving. The direction of travel was aligned with the ADP x-axis (parallel to horizontal component of Vbi), and vb] shows the most coherence between observed and expected bedload velocity. We should acknowledge, however, that vw was underpredicted (Table 2.2). On the other hand, the Vb3, and the in particular, displayed large excursions from the expected velocity. Interestingly, vb2 was closer to the expected value than vbX or vb3 (Table 2.2). The expected beam velocities for Vbi and were only 1.4 cm\/s, which approaches the lower limit of velocity resolution for the ADP (measurements are recorded to the nearest mm\/s). This might explain the inability of the ADP to resolve the velocities in beams 2 and 3. We should note that the expected beam velocities in this case were similar to what might 73 be expected in a field condition of partial transport (Wilcock and McArdell 1997) of coarse gravel without fine material. Due to the three-beam geometry of the ADP, some measurement error inherently arises when bedload varies between the three beams. Consideration of the 3-beam geometry of the ADP, with beams separated by 120\u00b0 relative azimuth angles and slanted at fj> (25\u00b0) from the vertical, yields the measured beam velocities in terms of the x, y, and z bottom track velocity components in each beam: vb\\ = v\\x sin(\u00a7) - v u cosfo) (2.8a) vb2 = - v2x sin(30\u00b0)sin(\u00a7) + v2y cos(30\u00b0)sin(\u00a7)-v2z cos(\u00a7) (2.8b) vbi = - v3x sin(30\u00b0)sin(\u00a7)- v3y cos(30\u00b0)sin($)-v2z cos(\u00a7) (2.8c) Combination of (2.6) and (2.8), and assuming that all three viz are equal, yields predictors based on the forward and transverse velocities through each beam: v , = [2 vxl +0.5 (vx2 +VJ+0.866 ( v , 3 - v y 2 ) \\ \/ 3 (2.9a) v, = [0.5 (v , 3 -v x 2 )+0M6 (vy2 +vy3)]\/S (2.9b) When the percentage mobile bed area differs between the three beams, the direction and magnitude of the measured velocity vector will necessarily be wrong, due to the unequal weighting of vxi in the estimated vx. As discussed above, this may have arisen in our tests because individual particles were large with respect to the beam width, and occupied a substantial portion of a beam. The percentage of the bed mobile within a beam varied as particles moved through the beam. This error mechanism could have created variance in 74 the forward and transverse directions. In fact, if only one of beams 2 or 3 registered a velocity, then the direction of observed va would have been 60\u00b0 offset from the expected direction, which corresponds to several of the velocity vectors in Figure 2.1. The errors due to a large beam 2 or 3 velocity are as follows: However, based on Equation 2.9a if all vyi are zero, the magnitude of the observed va vector can not exceed the magnitude of the largest actual within-beam v&. Furthermore, direction errors can not exceed 60\u00b0. In Figure 2.1, some va vectors have magnitudes that exceed possible values of v0, even if the areal coverage within a beam was 48%. Also, some direction errors exceed 60\u00b0: the direction of the va vector had a standard deviation of about 97\u00b0 (Table 2.1). The observed data can only be explained if vy and\/or negative vx bedload velocity components were recorded. Examination of beam velocities showed that beam 2, in particular, had large positive and negative excursions in some trials (Figure 2.10). In our laboratory tests, there were no actual negative vx components, and only minimal actual vy components were caused by random jostling of the particles as they were dragged over the artificial bed. It appears then, that most of the variance was caused by instrument noise rather than real variability infm. Large value Direction of va vector Positive beam 2 Negative beam 2 Positive beam 3 Negative beam 3 -60\u00b0 120\u00b0 60\u00b0 -120\u00b0 Another possible explanation for the scatter in beams 2 and 3 is interference from side lobes or multiple scattering effects. Beams 2 and 3 were pointing partially toward the tank walls, and thus beam side lobes may have reflected off the tank walls. While side lobe interference was not observed for field tests or for mobile instrument towing tank tests (see Chapter 1), it is conceivable that side lobes reflecting off the tank walls or tank bottom contaminated the mobile bed towing tank tests. Side lobe interference, if present, would have been related to processing the signal from a partially mobile bed within the confines of the towing tank, and would have biased the beam velocities toward zero. In fact, beams 1 and 3 displayed more bias than beam 2 (Table 2.2). It would be desirable to evaluate the instrument noise independent of error due to unsteady percent mobile area within a beam. To this end, it would be useful to conduct further trials with a steady percentage of mobile bed area within beams. Alternatively, the expected variance in v\u201e due to unsteady percent mobile bed area and the corresponding heterogeneous transport can be determined using our estimates of the probability distribution of percent mobile bed area. Synthetic time series of values of vxj, vX2, and vX3 were created based on the estimated percent mobile area probability distributions. The distribution of actual ve was estimated by averaging instantaneous values of vxi from the three beams. The coefficient of variation (cv) of actual ve was 0.33 for 15 cm string spacing and 0.16 for 10 cm string spacing. Similarly, the distribution of expected measured va was derived using Equation 2.9, assuming vyi were zero. As expected, the maximum deviation from the expected direction was \u00b160\u00b0. The cv of expected measured vav was 0.41 for 15 cm string spacing and 0.19 for 10 cm string spacing, as compared to the measured cv of about 1.28 for all the trials (Figure 2.4). The 76 standard deviation due to instrument noise (Ginstrument) can be estimated assuming that the variance is pooled: \u00ae measured ~ \u00ae instrument ^\u00aeexpected (2-10) Equation 2.9 yields a cv of va due to instrument noise of about 1.26 (Figure 2.4), i.e. virtually all the measured variance was due to instrument noise. We considered the possibility that frequency tracking biased the measurements. Frequency tracking utilizes feedback from previous pings to narrow the passband of the instrument's noise filters (Chereskin et al. 1989, Chereskin and Harding 1993). This technique increases the signal to noise ratio by narrowing the search range for the Doppler signal, but can introduce bias if the filter passband is too wide or if it is not centered on the signal. However, SonTek ADPs do not use frequency tracking (C. Ward, 2002, SonTek Inc., personal communication). 2.5.2 Future Tests Further lab trials to test the precision and accuracy of the method may be unwarranted with the present instrument. Development of an improved bedload Doppler sonar prior to rigorous lab testing may be more fruitful. A full gamut of trials could be performed at various particle sizes, particle speeds, percent mobile bed area, and aDcp orientation with respect to the direction of transport. It would be possible to conduct multivariate analyses to determine if the aDcp is more capable of determining bedload transport velocity for certain particle sizes, transport rates, and aDcp orientations. It would also be possible to determine if the aDcp is more sensitive to increasing particle velocity or 77 increasing percent mobile bed area. The procedure would have to be modified in order to make the materials robust for such a large number of tests. The testing procedure was eventually abandoned due to breakage of strings. There were two major problems with the existing procedure: 1) the stones were large with respect to the beam area, which limited our ability to control the percent mobile bed area, and 2) the strings were easily tangled if lines were run close together within a beam area. It would also have been useful to use stones of perfectly uniform size, in order to control better the percent mobile bed area. A new method of conveying the stones should be used in any future trials. The problem is to ensure that not all the area insonified by a beam is mobile. Possible methods include attaching small stones to a net and dragging the entire net, and epoxying granules to thick ropes and dragging the ropes through the sample area. Alternatively, a calibration could be conducted in a mobile bed canal or flume of sufficient depth using underwater video to monitor particle velocities through the sample area. 2.6 Conclusions A laboratory test was conducted to evaluate the applicability of acoustic Doppler current profiler (aDcp) bottom tracking for accurate and precise determination of bedload transport velocity. A synthetic bedload of known velocity was created by dragging strings of stones over an artificial river bed in a towing tank. Trials were conducted at various particle speeds, percent mobile bed area within the aDcp beams, and aDcp orientation with respect to the direction of transport. Estimated apparent bed velocity (vfl) vectors showed a large degree of scatter within a trial, and va resolved in the direction of travel was biased toward zero, but mean values of the magnitude and direction of va predicted reasonably well the average bed velocity. The variance within a trial was due to three factors: 1) instrument noise, 2) variability in the percentage mobile bed area within a beam due to the large size and spacing of mobile particles with respect to the beam area, and 3) the inability of a three beam aDcp to resolve correctly heterogeneous transport (i.e., transport that varies between the three beams). Based on the estimated variability of percent mobile bed area within a beam during a trial, virtually all of the measured variance was due to instrument noise. Ul O l O l Ol o o o o 4^ O J w ro ro - i o o o o o o o o o ro ro \u2014*. \u2014x ro ro V i ro ro J>. 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CD \u2022 < ro bo J> ro o ro ->\u2022 o -\u00bb\u2022 ro CD ro J>. co ho ro p o o o o r o o o o CO co - s i o o CD 00 '->\u2022 q s 3 CD < . CO \" 3 CO o r* 3 a. E < CD O O O => o o q - i \"O co o \u2022S \u00a7 o ~ * 5-Table 2.2: Beam velocity statistics for Trials 11 and 12. All units cm\/s. Trial Beam Mean St. dev. Expected 11 V ; 0.1 1.7 2.8 11 v2 -1.4 7.3 -1.4 11 V3 0.1 2.6 -1.4 12 Vy -0.1 2.4 -2.8 12 0.8 4.5 1.4 12 VJ 0.1 4.2 1.4 Figure 2.1. Single ping measurements of apparent bed velocity (cm\/s) for a trial with expected bed speed of 6.5 cm\/s and expected direction of 180\u00b0 (Trial 12). Speed radii for 23, 47, and 70 cm\/s are shown. 1% CL L > 8. o 3 O cr CD CL TO' cr a 6. O g CD cr CD CL p \u2022a CD cn CD a a o >T3 O a cn g. N> CD CD \" cn < % 2_\u2022 CD 3 CD era' a* CD CL I-I CD CTQ >-t CD Cn cn S' 3 a cn CD X r 1 o w m y-En* 3' 9*. o' oo o o cr CD CL \u2022 o o O 3. 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CD CD CD o oo CD CL o a cr P a 3 + a* o p_ cr CD CL < CD !-| 00 . a 00 00 a - 3 CD DJ 224 Appendix E: Statistical comparisons of spatially block averaged bedload velocity The spatial block averages for bedload velocity were performed in a 5x5 grid. The blocks are numbered 1 to 25 in ascending columns, starting at the south-west block (ie. the north-west block is number 5 and the north-east block is number 25). The following tables describe the statistical comparisons between blocks for bedload velocity resolved in the downstream direction. Gravel-bed reach of Fraser River For the gravel bed reach, only block #6 was significantly different from the other blocks. blockprimbs Block N Mean Std. Std. Error 95% Confidence Minimum Maximum Deviation Interval for Mean Lower Upper Bound Bound 2 20 .210 .296 .066 .071 .348 -.032 1.368 3 39 .065 .143 .023 .018 .111 -.301 .509 4 17 .169 .215 .052 .058 .279 -.006 .774 6 14 .378 .521 .139 .077 .679 -.060 1.559 7 10 .188 .333 .105 -.050 .426 -.208 .907 8 19 .087 .146 .034 .017 .158 -.125 .318 9 26 .074 .286 .056 -.041 .189 -.229 1.199 12 16 .224 .337 .084 .045 .404 -.282 1.195 13 37 .132 .215 .035 .061 .204 -.150 .940 14 12 .001 .113 .033 -.071 .072 -.127 .197 18 36 .068 .252 .042 -.017 .154 -.384 .759 19 27 .055 .189 .036 -.019 .130 -.556 .493 20 13 .030 .167 .046 -.071 .131 -.128 .469 24 23 .057 .318 .066 -.081 .194 -.488 .862 25 86 .041 .240 .026 -.011 .092 -.477 .700 Total 395 .096 .260 .013 .070 .122 -.556 1.559 225 Sand-bed Sea Reach of Fraser River Descriptives prinibs, m\/s 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 84 .054 .120 | .013 .028 .080 | -.348 .381 ) 2 86 .061 .100 | .011 .040 .082 | -.206 .368 3 79 .096 .142 | .016 .064: .128 | -.385 .399 4 58 .226 .161 I .021 .184 .269 j -.111 .594 6 84 .466 .203 | .022 .422 .510 | -.110 1.181 7 69 .366 .268 I .032 .302 .431 | -.206 .943 8 81 .141 .247 | .027 .086 .196 | -.298 .937 9 53 .417 .241 I 0 3 3 .350 .483 | -.124 1.001 12 57 .484 .265 I .035 .414 .554 | -.150 1.130 13 124 .333 .293 I .026 .281 .385 | -293 1.178 14 139 .284 .303 I .026 .233 .335 j -.311 1.306 15 91 \\ .357 .286 | .030 .297 .416 | -.129 .969 19 101 .290 .316 | .031 .228 .353 | -.336 1.561 20 264 .238 .295 | .018 .202 .273 | -.227 1.304 25 129 .231 .274 I .024 .183 .279 | -.289 1.254 Total 1499 .261 .282 | .007 .247 .275 | -.385 1.561 Test of Homogeneity of Variances primbs, m\/s | Levene Statistic j df1 j df2 Sig. j | 12.7241 14 1484! .000! ANOVA primbs, m\/s Sum of Squares j df Mean Square F Sig. Between Groups 20.727) 14 1.480 22.316 .000 Within Groups 98.449 1484 6.634E-02 Total 119.176 1498 226 Post Hoc Tests Multiple Comparisons Dependent Variable: primbs, m\/s Mean Difference (l-J) Std. Error Sig. 95% Confidence Interval (1) BLOCK (J) BLOCK Lower Bound Upper Bound Tukey u c n 1 2 -6.55E-03 3.95E-02 1.000 -.14 .13. 3 -4.16E-02 4.04E-02 1.000 -.18 9.53E-02 4 -.17f) 4.40E-02 .008 -.32 -2.25E-02 6 -.41 (*) 3.97E-02 .000 -.55 -.28 7 -.310 4.18E-02 .000 -.45 -.17 8 -8.65E-02 4.01 E-02 .697 -.22 4.95E-02 9 -.360 4.52E-02 .000 -.52 -.21 12 -.43(*) 4.42E-02 .000 -.58 -.28! 13 -\u2022280 3.64E-02 .000 -.40 -.16 14 -\u202223(*) 3.56E-02 .000 -.35 -.11 15 -.30(*) 3.90E-02 .000 -.43 -.17 19 -.24(*) 3.80E-02 .000 -.37 -.11 20 -.18(*) 3.23E-02 .000 -.29 -7.39E-02 25 -.18(*) 3.61 E-02 .000 -.30 -5.43E-02 2 1 6.55E-03 3.95E-02 1.000 -.13 .14 3 -3.50E-02 4.01 E-02 1.000 -.17 .10 4 -.17(*) 4.38E-02 .013 -.31 -1.67E-02 6 -.41(*) 3.95E-02 .000 -.54 -.27 7 -.31 (*) 4.16E-02 .000 -.45 -.16 8 -7.99E-02 3.99E-02 .796 -.22 5.53E-02 9 -.36(*) 4.50E-02 .000 -.51 -.20 12 -.42(*) 4.40E-02 .000 -.57 -.27 13 -.27(*) 3.61 E-02 .000 -.39 -.15 14 -.22(*) 3.53E-02 .000 -.34 -.10 15 -.30(*) 3.87E-02 .000 -.43 -.16 227 19 -23C) 3.78E-02 .000 -.36 -.10 20 -\u20221&T) 3.20E-02 .000 -.29 -6.83E-02 25 -.17C) 3.59E-02 .000 -.29 -4.86E-02 1 4.16E-02 4.04E-02 1.000 -9.53E-02 .18 2 3.50E-02 4.01 E-02 1.000 -.10 .17 4 -.13 4.45E-02 .186 -.28 2.09E-02 6 -.370 4.04E-02 .000 -.51 -.23 7 -.27(*) 4.24E-02 .000 -.41 -.13 8 -4.49E-02 4.07E-02 .999 -.18 9.32E-02 9 --32H 4.57E-02 .000 -.48 -.17 o 12 --39C) 4.48E-02 .000 -.54 -.24 13 -\u202224C) 3.71 E-02 .000 -.36 -.11 14 -.19(*) 3.63E-02 .000 -.31 -6.47E-02 15 -.26(*) 3.96E-02 .000 -.40 -.13 19 -.19(*) 3.87E-02 .000 -.33 -6.33E-02 20 -.14(*) 3.30E-02 .002 -.25 -2.97E-02 25 --14D 3.68E-02 .019 -.26 -1.04E-02 1 .17(*) 4.40E-02 .008 2.25E-02 .32 2 \u202217(*) 4.38E-02 .013 1.67E-02 .31 3 .13 4.45E-02 .186 -2.09E-02 .28 6 -.24(*) 4.40E-02 .000 -.39 -9.10E-02 7 -.14 4.59E-02 .134 -.30 1.56E-02 8 8.52E-02 4.43E-02 .842 -6.51 E-02 .24 A 9 -.19C) 4.89E-02 .009 -.36 -2.46E-02 12 -.26(*) 4.80E-02 .000 -.42 -9.50E-02 13 -.11 4.10E-02 .364 -.25 3.21 E-02 14 -5.77E-02 4.03E-02 .984 -.19 7.88E-02 15 -.13 4.33E-02 .146 -.28 1.61 E-02 19 -6.44E-02 4.24E-02 .974 -.21 7.95E-02 20 -1.16E-02 3.74E-02 1.000 -.14 .12 25 -5.07E-03 4.07E-02 1.000 -.14 .13 6 1 .41 (*) 3.97E-02 .000 .28 .55 228 2 .41 n 3.95E-02 .000 .27 .54 3 \u2022370 4.04E-02 .000 .23 .51 4 \u202224(*) 4.40E-02 .000 9.10E-02 .39 7 .10 4.18E-02 .521 -4.18E-02 .24 8 33(*) 4.01 E-02 .000 .19 .46 9 4.96E-02 4.52E-02 .999 -.10 .20 12 -1.78E-02 4.42E-02 1.000 -.17 .13 13 \u202213(*) 3.64E-02 .020 9.83E-03 .26 14 \u202218(*) 3.56E-02 .000 6.17E-02 .30 15 .11 3.90E-02 .242 -2.27E-02 .24 19 \u202218C) 3.80E-02 .000 4.68E-02 .30 20 \u2022230 3.23E-02 .000 .12 .34 25 \u202224(*) 3.61 E-02 .000 .11 .36 1 .31 (*) 4.18E-02 .000 .17 .45 2 .31 n 4.16E-02 .000 .16 .45 3 \u202227(*) 4.24E-02 .000 .13 .41 4 .14 4.59E-02 .134 -1.56E-02 .30 6 -.10 4.18E-02 .521 -.24 4.18E-02 8 \u202223(*) 4.22E-02 .000 8.21 E-02 .37 9 -5.05E-02 4.70E-02 .999 -.21 .11 1 12 -.12 4.61 E-02 .400 -.27 3.85E-02 13 3.32 E-02 3.87E-02 1.000 -9.80E-02 .16 14 8.23E-02 3.79E-02 .686 -4.63E-02 .21 15 9.36E-03 4.11 E-02 1.000 -.13 .15 19 7.57E-02 4.02E-02 .863 -6.07E-02 .21 20 \u202213(*) 3.48 E-02 .018 1.03E-02 .25 25 .13(*) 3.84E-02 .034 4.70E-03 .27 8 1 8.65E-02 4.01 E-02 .697 -4.95E-02 .22 2 7.99E-02 3.99E-02 .796 -5.53E-02 .22 3 4.49E-02 4.07E-02 .999 -9.32E-02 .18 4 -8.52E-02 4.43E-02 .842 -.24 6.51 E-02 6 -\u2022330 4.01 E-02 .000 -.46 -.19 229 7 -.23H 4.22E-02 I 0 0 0 -.37 -8.21 E-02 9 -.28(*) 4.55E-02 | .000 -.43 -.12 12 -\u202234(*) 4.45E-02 I 0 0 0 -.49 -.19 13 -.19(*) 3.68E-02 | .000 -.32 -6.72E-02 14 -\u202214(*) 3.60E-02 I .006 -.27 -2.08E-02 15 -\u202222C) 3.93E-02 | .000 -.35 -8.24E-02 19 -\u2022150 3.84E-02 | .009 -.28 -1.93E-02 20 -9.68E-02 3.27E-02 | .170 -.21 1.42 E-02 25 -9.03E-02 3.65E-02 | .461 -.21 3.36E-02 9 1 .36(*) 4.52E-02 | .000 .21 .52 2 \u2022360 4.50E-02 j .000 .20 .51 3 \u2022320 4.57E-021 .000 .17 .48 4 \u2022190 4.89E-021 .009 2.46E-02 .36 6 -4.96E-02 4.52E-021 .999 -.20 I .10 7 5.05E-02 4.70E-021 .999 -.11 .21 8 \u2022280 4.55E-021 .000 .12 .43 12 -6.73E-02 4.91 E-02 I .990 -.23 9.93E-02 13 8.37E-02 4.23E-02J .811 -5.97E-02 .23 14 .13 4.16E-02J .091 -8.20E-03 .27 15 5.98E-02 4.45E-02 j .992 -9.11 E-02 .21 19 .13 4.37E-021 .202 -2.20E-02 .27 20 \u2022180 3.88E-021 .000 4.74E-02 .31 25 \u2022190 4.20E-021 .001 4.30E-02 | .33 12 1 \u202243(*) 4.42E-021 .000 .28 \u202258 2 \u2022420 4.40E-021 .000 .27 .57 3 \u2022390 4.48E-021 .000 .24 .54 4 \u2022260 4.80E-021 .000 9.50E-02 .42 6 1.78E-02 4.42E-02| 1.000 -.13 \u202217. 7 .12 4.61 E-02 | .400 -3.85E-02 .27 8 \u2022340 4.45E-021 .000 .19 .49 9 6.73E-02 4.91 E-021 .990 -9.93E-02 .23 13 \u2022150 4.12E-02J .020 1.12E-02 .29 230 14 \u202220C) 4.05E-02 .000 6.28E-02 .34 15 .13 4.35E-02 .185 -2.04E-02 .27 19 \u202219H 4.27E-02 .001 4.88E-02 .34 20 \u202225(*) 3.76E-02 .000 .12 .37. 25 \u202225(*) 4.10E-02 .000 .11 .39 1 .280 3.64E-02 .000 .16 .40 2 \u202227(*) 3.61 E-02 .000 .15 .39 3 \u202224(*) 3.71 E-02 .000 .11 .36 4 .11 4.10E-02 .364 -3.21 E-02 .25 6 -\u202213(*) 3.64E-02 .020 -.26 -9.83E-03 7 -3.32E-02 3.87E-02 1.000 -.16 9.80E-02 13 8 \u20221?(*) 3.68E-02 .000 6.72E-02 .32 j 9 -8.37E-02 4.23E-02 .811 -.23 5.97E-02 \\ 12 -\u202215(*) 4.12E-02 .020 -.29 -1.12E-02 14 4.91 E-02 3.18E-02 .970 -5.88E-02 .16 15 -2.38E-02 3.56E-02 | 1.000 -.14 9.67E-02 19 4.25E-02 3.45E-02 .997 -7.46E-02 .16 20 9.52E-02O 2.80E-02 .049 1.49E-04 .19 25 .10 3.24E-02 .105 -8.07E-03 .21 1 \u202223(*) 3.56E-02 .000 .11 .35 2 \u202222C) '3.53E-02 .000 .10 .34 3 .19(*) 3.63E-02 .000 6.47E-02 .31 j 4 5.77E-02 4.03E-02 .984 -7.88E-02 .19 6 -.18(*) 3.56E-02 .000 -.30 -6.17E-02 7 -8.23E-02 3.79 E-02 .686 -.21 4.63E-02 14 8 .14(*) 3.60E-02 .006 2.08E-02 .27 9 -.13 4.16E-02 .091 -.27 8.20E-03 12 -\u202220(*) 4.05E-02 .000 -.34 -6.28E-02 13 -4.91 E-02 3.18E-02 .970 -.16 5.88E-02 15 -7.30E-02 3.47E-02 .735 -.19 4.48E-02 19 -6.65E-03 3.37E-02 1.000 -.12 .11 20 4.61 E-02 2.70E-02 .931 -4.54E-02 .14 231 25 5.27E-02 3.15E-02 .942 -5.41 E-02 .16 1 \u202230H 3.90E-02 .000 .17 .43 2 \u202230(*) 3.87E-02 .000 .16 \u202243 3 \u2022260 3.96E-02 .000 .13 .40 4 .13 4.33E-02 .146 -1.61 E-02 .28 6 -.11 3.90E-02 .242 -.24 2.27E-02 7 -9.36E-03 4.11 E-02 1.000 -.15 .13 15 8 \u202222(*) 3.93E-02 .000 8.24E-02 .35 9 -5.98E-02 4.45E-02 .992 -.21 9.11 E-02 12 -.13 4.35E-02 .185 -.27 2.04E-02 13 2.38E-02 3.56E-02 1.000 -9.67E-02 .14 14 7.30E-02 3.47E-02 j .735 -4.48E-02 .19 19 6.63E-02 3.72E-02 .906 -5.99E-02 .19 20 \u2022120 3.13E-02 .012 1.29E-02 .23 25 \u202213(*) 3.53E-02 .028 6.04E-03 .25 1 \u2022240 3.80E-02 .000 .11 .37 2 \u202223C) 3.78E-02 .000 .10 .36 3 \u202219(*) 3.87E-02 .000 6.33E-02 .33 4 6.44E-02 4.24E-02 .974 -7.95E-02 .21 6 -.180 3.80E-02 .000 -.30 -4.68E-02 7 -7.57E-02 4.02E-02 .863 -.21 6.07E-02 19 8 \u2022150 3.84E-02 .009 1.93E-02 .28 9 -.13 4.37E-02 .202 -.27 2.20E-02 12 -.190 4.27E-02 .001 -.34 -4.88E-02 13 -4.25E-02 3.45E-02 .997 -.16 7.46E-02 14 6.65E-03 3.37E-02 1.000 -.11 .12 15 -6.63E-02 3.72E-02 .906 -.19 5.99E-02 20 5.28E-02 3.01 E-02 t .917 -4.94E-02 .15 25 5.93E-02 3.42E-02 .923 -5.68E-02 .18 20 1 .180 3.23E-02 .000 7.39E-02 .29 2 \u2022ISO 3.20E-02 .000 6.83E-02 .29 3 \u2022 140 3.30E-02 .002 2.97E-02 .25 232 4 1.16E-02 3.74E-02 1.000 -.12 .14 6 -\u202223(*) 3.23E-02 .000 -.34 -.12: 7 -\u2022130 3.48E-02 .018 -.25 -1.03E-02 8 9.68E-02 3.27E-02 .170 -1.42E-02 .21 9 -.18(*) 3.88E-02 .000 -.31 -4.74E-02 12 -.250 3.76E-02 .000 -.37 -.12 13 -9.52E-02(*) 2.80E-02 .049 -.19 -1.49E-04: 14 -4.61 E-02 2.70E-02 .931 -.14 4.54E-02 15 -.12(*) 3.13E-02 .012 -.23 -1.29E-02 19 -5.28E-02 3.01 E-02 .917 -.15 4.94E-02 25 6.54E-03 2.77E-02 1.000 -8.73E-02 .10 1 \u202218(*) 3.61 E-02 .000 5.43E-02 .30 2 \u202217(*) 3.59E-02 .000 4.86E-02 .29 3 .14(*) 3.68E-02 .019 1.04E-02 .26 4 5.07E-03 4.07E-02 1.000 -.13 .14 6 -\u202224C) 3.61 E-02 .000 -.36 -.11 7 -.13(*) 3.84E-02 .034 -.27 -4.70E-03 25 8 9.03E-02 3.65E-02 .461 -3.36E-02 \u202221 9 -\u202219(*) 4.20E-02 .001 -.33 -4.30E-02 12 -.25(*) 4.10E-02 .000 -.39 -.11 13 -.10 3.24E-02 .105 -.21 8.07E-03 14 -5.27E-02 3.15E-02 .942 -.16 5.41 E-02 15 -.13(*) 3.53E-02 .028 -.25 -6.04E-03 19 -5.93E-02 3.42E-02 .923 -.18 5.68E-02 20 -6.54E-03! 2.77E-02 1.000 -.10 8.73E-02 * The mean difference is significant at the .05 level. ","@language":"en"}],"Genre":[{"@value":"Thesis\/Dissertation","@language":"en"}],"IsShownAt":[{"@value":"10.14288\/1.0063896","@language":"en"}],"Language":[{"@value":"eng","@language":"en"}],"Program":[{"@value":"Civil Engineering","@language":"en"}],"Provider":[{"@value":"Vancouver : University of British Columbia Library","@language":"en"}],"Publisher":[{"@value":"University of British Columbia","@language":"en"}],"Rights":[{"@value":"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https:\/\/open.library.ubc.ca\/terms_of_use.","@language":"en"}],"ScholarlyLevel":[{"@value":"Graduate","@language":"en"}],"Title":[{"@value":"Non-invasive measurement of fluvial bedload transport velocity","@language":"en"}],"Type":[{"@value":"Text","@language":"en"}],"URI":[{"@value":"http:\/\/hdl.handle.net\/2429\/37980","@language":"en"}],"SortDate":[{"@value":"2002-12-31 AD","@language":"en"}],"@id":"doi:10.14288\/1.0063896"}