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 The morphology of dunes in rivers and estuaries often lags behind changes in river discharge and neap-spring tides. This study extends previous research by examining the response of large subtidal dunes in the Fraser Estuary, Canada, to changing flow conditions over a semidiurnal tidal cycle. An acoustic Doppler current profiler (ADCP) is used to measure three-dimensional velocity profiles and estimate sediment transport and a digital echosounder to measure bed profiles and dune characteristics. Mean flow velocity accelerates from 0.60 to 1.99 m/s and mean flow depth decreases from 15.1 to 12.2 m on the falling tide, followed by a decrease in mean velocity to 0.25 m/s and an increase in depth to 15.25 m on the rising tide. Estimates based on ADCP bottom-tracking and backscatter, and the sediment transport model of van Rijn (1984a, 1984b, 1984c), indicate that bed-material sediment transport generally follows the pattern of mean velocity over the tidal cycle. Dune length does not change significantly over the survey period. Changes in dune height, steepness and leeside slope angle precede changes in flow velocity, increasing early in the tidal fall because of scour in dune troughs that is likely caused by increased turbulence resulting from development and expansion of the flow separation/deceleration zone. Erosion of dune crests increases as peak velocity is approached near low tide, resulting in a decrease in dune height. Concentrations of sand in suspension also increase with mean velocity, leading to deposition in troughs and a further reduction in dune height and leeside slope angle. Sand falls out of suspension and drapes the dunes as high tide approaches. Dune length is not in equilibrium with the flow whereas dune height is in equilibrium with the strongest flows that occur around low tide. A comparison of bed-material transport based on dune migration and the model of van Rijn (1984a, 1984b, 1984c) suggests that the model provides reasonable estimates of bed load in the Estuary, although the model must be used with caution because deposition from suspension also contributes to dune migration.
 Dunes are ubiquitous features in sand-bed rivers and estuaries and play an integral role in the relationships between boundary layer flow structure and sediment transport [American Society of Civil Engineers, 2002; McLean et al., 1994, 1999; Nelson et al., 1995]. Many of the relationships developed between dunes and their controlling environmental variables have been established in laboratory flumes with unidirectional, steady, uniform currents [e.g., Bennett and Best, 1995; Best and Kostaschuk, 2002; McLean et al., 1994; Nelson et al., 1999], which are conditions that rarely apply to dunes in natural settings. This is particularly true in estuaries where dunes are affected by temporal and spatial variability in flow resulting from changing fluvial and tidal conditions. Several studies have shown that large, subtidal dunes lag behind seasonal [e.g., Gabel, 1993; Julien et al., 2002; Kostaschuk et al., 1989a; Wilbers, 2004; Wilbers and ten Brinke, 2003] and tidal [e.g., Kostaschuk and Ilersich, 1995] changes in flow, resulting in hysteresis in dune properties. However, instruments that lack the temporal and spatial resolution required to examine detailed process-response relationships, including hysteresis, have limited studies of subtidal dunes over single tidal cycles. The present study uses instruments that have this capability, namely an acoustic Doppler current profiler and digital echosounder, to study the changes in dune morphology that occur over a semidiurnal tidal cycle in the Main Channel of the Fraser River estuary, British Columbia, Canada (Figure 1).
2. Study Area
 Discharge in the Fraser River is characteristically highest during the spring and early summer when warmer temperatures and spring rains result in the annual snowmelt freshet. Discharge at Hope (150 km upstream of the study reach) during the spring freshet ranges between 6000 and 12,000 m3/s. The Fraser is a relatively large river and discharge does not vary significantly over daily timescales. The Main Channel flows into the Strait of Georgia, a semi-enclosed, high-energy marine basin. Tides are mixed, mainly semidiurnal with a mean range of 3 m near the mouth of the Main Channel and 5 m during spring tides. Over one semidiurnal tidal cycle (approximately 13 hours), river discharge remains relatively constant and tidal movement controls the variation in flow within the estuary. A salt-wedge intrusion extends into the lower Main Channel, with its position being determined by river discharge and tidal height [Kostaschuk and Atwood, 1990]. The salt-wedge is flushed downstream during falling semidiurnal tides and flow at low tide is unstratified throughout much of the estuary during high river discharge.
 Surveys were conducted from a launch using an Ocean Data Equipment Bathy1500 200 kHz digital survey echosounder (DES) and a SonTek 1500 kHz 3-beam acoustic Doppler current profiler (ADCP). The ADCP was used to measure three-dimensional velocity profiles and estimate sediment transport as bed load and suspended load. Both instruments were tied to a Trimble AgGPS122 differential global positioning system (DGPS), which uses a differentially corrected signal from a navigation beacon located nearby, allowing for a measured spatial precision from the moving launch of around 0.1 m. Under the conditions of this study, the manufacturers estimate a precision of ±0.02 m for the DES and ±0.01 m/s for the ADCP.
 Velocity and depth data were collected along a survey line in the center of the Main Channel line during 7–20 June 2000 (Figure 1). Dune transects were made over tidal cycles (tidal fall and rise) on several days, but strong winds resulted in a reliable set of transects only on 20 June, and these data are presented herein. A total of 17 transects were measured along the survey line between 0727 local time (LT) and 1951 LT on 20 June. River discharge was declining in June (Figure 2) but was high on 20 June (8 050 m3/s). High tide (3.8 m) was at 0605 LT, low tide (1 m) at 1325 LT and the second high tide (4.5 m) at 2105 LT (Figure 2). A series of seven large dunes, located near the downstream end of the survey line, were selected for analysis on the basis of reliable identification of individual dunes between surveys. A post-survey analysis of transect positions showed that all transects were within a 60 m wide band along the centerline of the channel and most were within 30 m.
 The DES employs a bottom-finding algorithm for flow depth that works well when suspended sediment concentrations are low but provides “false bottoms” when concentrations are high. Contaminated DES measurements during high sediment concentrations were thus replaced by estimates obtained from a “digital paper trace” record.
 The ADCP utilizes an internal compass to define flow direction and a tilt sensor to correct for vessel pitch and roll, while velocity measurements are corrected for vessel motion using DGPS positions. The three transducers of the ADCP are set at 25° from the vertical axis and are equally spaced in the horizontal (120°), producing different orientations relative to the flow. The static diameter of the ADCP sampling area increases with depth to a maximum of 0.93 of the depth at the bed, which means that the velocity measurements nearest the bed in the dune troughs are unreliable because the three ADCP beams will encounter the bed at different depths. Kostaschuk et al.  suggest that a mean bed position from ADCP data can be determined by a sharp increase in echo intensity. Since the inflection point above the maximum echo intensity represents the transition between the bed and the water column, the ADCP bin above the inflection point can therefore be used to define the lower limit of uncontaminated velocity measurements. These procedures were followed in this study. Kostaschuk et al.  also found that a sampling interval of 5 s and a vertical resolution of 0.25 m provided the best combination of low signal:noise ratio, stable velocity measurements, good spatial resolution over dunes and reliable positions from the DGPS. These settings were also used in the present study.
 The bottom tracking capability of an ADCP, which involves measurement of the Doppler shift of an independent acoustic echo from the bed, can be used to estimate bed load transport [e.g., Kostaschuk et al., 2005; Rennie et al., 2002; Villard et al., 2005]. Bottom tracking is designed to measure boat velocity over an immobile bed, and thus in cases where the bed is mobile, the bottom tracking Doppler shift is a function of both the velocity of the boat and the velocity of the mobile bed. The velocity of the mobile bed is therefore related to the difference between (1) the “apparent” boat velocity with respect to the bed measured with ADCP bottom tracking (Ubtk) and (2) the “actual” boat velocity measured with a DGPS (UDGPS). High suspended sand concentrations can result in the bottom-track pulse “seeing” a false bed and registering sediment transport velocities that reflect sand transport in suspension rather than sand transported as bed load [Kostaschuk et al., 2005].
 The strength of an ADCP acoustic return from the water column, or backscatter (B), is a function of both instrument and sediment properties and has been used to estimate the concentration of suspended sediment in a wide range of flows [e.g., Alvarez and Jones, 2002; Kostaschuk et al., 2005; Reichel, 1998]. Instrument response is a function of ADCP frequency, transmit power, receiver sensitivity and distance to the measurement volume, while the size, type and concentration of suspended sediment are the most important sediment properties. Acoustic frequencies have different sensitivities dependent on particle size, and, at a single frequency, backscatter strength is a function of particle size, type and concentration. For a constant type and size of particle, scattering strength is thus theoretically directly proportional to concentration. However, it is important to note that, in practice, it is not possible to distinguish between the effects of suspended sediment concentration and particle size on the acoustic backscatter [Reichel, 1998], and calibration with known values of concentration is therefore required for absolute ADCP-based estimates of concentration. However, since a particular calibration is only valid if the size distribution does not change, and direct measurements of concentration were not possible herein, the ADCP backscatter cannot be calibrated in this study.
 Sediment transport rates over the tidal cycle were estimated using the “simplified” model of van Rijn [1984a, 1984b, 1984c, 1993]. Although there is a wide range of models that can be used to estimate sediment transport rates, the van Rijn model has been shown to provide reasonable results in a variety of environments [e.g., Chandler and Kostaschuk, 1994; van den Berg, 1987]. The simplified model uses mean velocity and does not require water surface slope or shear stress measurements, and so it is applicable to the tidal flows in the present study. Volumetric (per unit channel width: m2/s) bed load (qb) and suspended bed-material load (qs) are predicted from
where U is mean depth-averaged flow velocity over the survey line, Ucr is the critical depth-averaged entrainment velocity, s is the density ratio ρs/ρ, ρs is sediment density (assumed = 2650 kg/m3), ρ is water density (assumed = 1000 kg/m3), d50 is the median bed-material size (here = 0.32 mm), h is mean flow depth over the survey line, d90 is the coarsest ninetieth percentile of bed-material size (here = 0.45 mm), g is the acceleration of gravity, and ν is kinematic viscosity (assumed = 1 × 10−6 m2/s).
Figure 3 provides examples of ADCP velocity records taken at the downstream end of the survey line (Figure 1) early in the falling tide (0727 LT; Figure 3a), around low tide (1347 LT; Figure 3b) and late in the rising tide (1930 LT; Figure 3c), while Figure 4 shows mean velocity profiles for the same transects. The 0727 LT record is the only transect with stratified flow, with velocities in the intrusion being weak and directed upstream. Upper layer velocities in the river flow above the salt-wedge are higher and directed downstream, with a well-defined top to the saline intrusion being visible (∼12 m, Figure 3a). The salinity intrusion has been flushed seaward of the measurement reach by 0815 LT and all flows were downstream-directed throughout the remainder of the tidal cycle. Velocity at 1347 LT (Figure 3b) is high, reflecting the dominance of the river flow and also showing the topographic forcing of flow by the dunes with higher velocities over crests than over troughs. Velocity at 1930 LT (Figure 3c) is low but still directed downstream.
Figure 5 shows mean flow depth and mean velocity spatially averaged over each transect. Mean depth and velocity display inverse patterns over the tidal cycle and both change more slowly on the falling tide (0727–1347 LT) than on the rising tide. The Froude number, Fr, is given by
and is plotted in Figure 6 over the tidal cycle, although the 0727 LT transect was not used in these calculations because the flow was stratified. Values of Fr are all sub-critical and very low, generally following the pattern of flow velocity. Values of Fr around low tide are comparable to other values reported from the Fraser Estuary by Kostaschuk and Villard  and Best and Kostaschuk . Discharge per unit channel width (Uh) shows a similar pattern to Fr, except that Uh is relatively higher during the falling tide.
 Mean bed load velocity (Ubed) and acoustic backscatter (B) measured with the ADCP vary in a similar fashion over the tidal cycle (Figure 7) and follow the pattern of mean flow velocity. Bed load velocities are close to zero at high tide but are very high and comparable with mean flow velocity (compare Figures 5 and 7) around low tide. Such grain velocities that are comparable with the flow velocity are likely to represent sediment in suspension, and reflect the bias of bottom tracking to sand suspended in the flow. Indeed, the bed detection revealed by bottom tracking shows a bed position about 5 m from the flow surface around low tide (the actual mean depth from the DES is 12.2–12.6 m), reflecting the high concentrations of suspended sand and bias of the bottom tracking toward sediment suspended within the flow. Values of backscatter intensity tend to increase more rapidly and decrease more slowly than bed load velocity (Figure 7). Since backscatter is likely more sensitive than bottom tracking to fine sediment in suspension [e.g., Kostaschuk et al., 2005; Rennie et al., 2002], this may produce a response that is tempered by permanently suspended fine sediment within the flow. Variations in the predicted bed load and suspended load, based on the model of van Rijn (equations (1)–(5); Figure 8), show both to vary with velocity over the tidal cycle, peaking around low tide. Figure 8 also illustrates that much more sand is transported in suspension compared to bed load, particularly around low tide.
Figure 9 provides examples of echosounding profiles at the first high tide (0727 LT), just before low tide (1228 LT), and just before the second high tide (1852 LT). The “planed-off” crests on the 1228 LT profile are due to contamination of the DES record from high suspended sediment concentrations; calculations of dune properties on this and other contaminated records were based on digital paper traces. Although there have been changes in the shape of some dunes (e.g., Figure 9: dune B), the seven dunes can be identified over the tidal cycle.
Figures 10 and 11 show variations in the mean and standard deviations (error bars) of dune height, length, steepness (height/length) and leeside slope angle over the tidal cycle, as quantified from the seven dunes (A–G) identified on Figure 9. The error bars suggest that interpretations of changes in dune characteristics over the tidal cycle must be treated with some caution. This is especially true for dune length where, except for the survey at 1003 LT, there is considerable overlap in error bars and changes in the time series are not significant. There is less overlap in the error bars for height, indicating that the changes are significant, particularly during the tidal fall. Considerable overlap in error bars also occurs for steepness and leeside slope angle, but these are related to changes in dune height so their patterns are examined further. In general, height, steepness and leeside slope angle increase on the tidal fall and decrease on the tidal rise.
 Some of the variability in the shapes of the dune profiles (Figure 9) and in dune characteristics (Figures 10 and 11) may be due to deviations in the positions of survey lines (Figure 1). For example, recent work by D. R. Parsons et al. (The morphology and flow fields of three-dimensional dunes, Rio Paraná, Argentina: Results from simultaneous multibeam echo sounding and acoustic Doppler current profiling, submitted to Journal of Geophysical Research, 2005) (hereinafter referred to as Parsons et al., submitted manuscript, 2005) using a multibeam echosounder in the Rio Paraná, showed that there was considerable variability in dune height even along laterally continuous crestlines. Parsons et al. (submitted manuscript, 2005) found that this variability was most pronounced in areas of strong planform crestline curvature. Although the present study has no direct data on dune planform shape, previous research in the Fraser [Kostaschuk and MacDonald, 1988; Villard and Church, 2003] suggests that, during high river discharge, dunes are primarily 2-dimensional in shape with gentle crestline curvature. Villard and Church  found that dunes display relatively linear crests across the channel and concluded that mid-channel profiles, such as those used in the present study, reasonably represent the dune geometry within the channel.
Figures 12–14 present phase diagrams for relations between sediment transport, dune geometry and flow velocity. Although the relations are complex and subtle in some cases, clockwise hysteresis loops predominate for bed load velocity, dune height, dune steepness and dune lee slope angle, indicating that changes in these properties generally precede changes in mean velocity. The hysteresis loops for bed load velocity and dune height are very tight, suggesting a relatively direct response to velocity. A counterclockwise loop predominates for backscatter and dune length, so that these changes lag behind velocity. The hysteresis loop in dune length is controlled mainly by the decrease in length revealed in the 1003 LT survey (Figure 10a) early in the tidal fall, with the remaining surveys suggesting little response to changes in flow velocity. The decrease in length at 1003 LT could also reflect a slight deviation in the survey line toward the edge of the channel that may possess slightly shorter dunes. Additionally, the lag in backscatter values may reflect enhanced turbulence and sediment suspension produced during adverse pressure gradients generated on the rising tide [Kostaschuk et al., 1989b].
 Echosounding records show that the rapid increase in dune height early in the tidal fall (Figure 5: 0700–1200 LT) is due to scour in the dune troughs, which leads to an associated increase in leeside slope angle (Figure 11) and possibly a decrease in dune length at 1003 LT (Figure 10a). This scour is likely due to increased turbulence in the troughs caused by development of the flow separation/deceleration zone on the lee side, such as that measured in flume experiments [e.g., McLean et al., 1994; Bennett and Best, 1995; Best and Kostaschuk, 2002] and in the field [Kostaschuk, 2000]. Sediment deposited during the previous tidal rise settles directly out of suspension during low flow velocities at high tide and thus should be relatively loose and easy to entrain during this period of falling stage and increasing flow velocities. The changes in leeside slope angle that occur here (<10° to >20°) suggest significant flow separation would be generated that would thus increase leeside shear layer development and the generation of large-scale turbulence [e.g., Best and Kostaschuk, 2002; Kostaschuk, 2000], which further contributes to trough scour. The increasing presence of large-scale turbulence during this period is witnessed on the flow surface by the greater development, in size and frequency, of surface eruptions or “boils,” which are a manifestation of turbulence generated in the leeside [Kostaschuk and Church, 1993; Best and Kostaschuk, 2002; Best, 2005]. As peak velocity is reached late in the tidal fall and early in the tidal rise (Figure 4: 1200–1700 LT), the velocity profile is fully developed and shear stresses increase over dune crests, as suggested from field studies by Smith and McLean  and Kostaschuk and Villard , resulting in crestal erosion and a decrease in dune height. Smith and McLean  and Kostaschuk and Villard  also found that sand suspension increases with mean velocity and speculated that this leads to deposition in troughs and a further reduction in dune height and leeside slope angle. Additionally, the role of increased sediment concentrations in the near-bed zone at higher flow velocities may lead to the suppression of large-scale turbulence which may further decrease the dune height [Best, 1996; Bridge and Best, 1988; J. L. Best, The fluid dynamics of river dunes: a review and some future research directions, submitted to Journal of Geophysical Research, 2005]. The lag in backscatter (Figure 12), together with numerical simulations by Johns et al.  and flume experiments by Hand and Bartberger , also support this interpretation. As flows decelerate and then increase slightly later in the rising tide (Figure 4: 1700–2000 LT), sand falls out of suspension [e.g., Kostaschuk et al., 1989b] and “drapes” the dunes without causing any further large-scale change in dune geometry.
 Previous research has shown that dunes in the Fraser River are in “disequilibrium” with seasonal river flows and bi-weekly tidal variations [Kostaschuk and Ilersich, 1995; Kostaschuk et al., 1989a; Villard and Church, 2003]. The present study indicates that the relations between dune morphology and semidiurnal variations in flow are also indirect, suggesting that disequilibrium also exists at the semidiurnal timescale. This hypothesis can be tested by comparing changes in dune height and length over the semidiurnal tidal cycle with predictions obtained from equilibrium dune models. Several models are available, ranging from purely empirical relations developed from flume and field data [Allen, 1968] to the more theoretically based method of van Rijn [1984a, 1984b, 1984c]. However, since the theoretical model of van Rijn requires measurements of hydraulic variables that cannot be reliably obtained in the present study, the present analysis is restricted to use of the model proposed by Allen , which requires only flow depth (m), as a basis for comparison,
Equations (7) and (8) were based on data obtained in flow depths from 0.6 to 40 m [Allen, 1968]. Figure 10 shows that the dune lengths measured in the present study are all well below the predictions from equation (8), whereas dune heights are similar to the predictions from equation (7) during the period around low tide (1100–1600 LT). This comparison suggests that dune height is in equilibrium with the strong downstream flows around low tide but dune length is not. Studies of both ripples [e.g., Baas, 1994, 1999] and dunes [e.g., Wilbers and ten Brinke, 2003] have shown that a greater volume of sediment must be transported to influence dune wavelength, and hence dune length requires longer to respond to changing flow conditions as compared to dune height. The measurements of dune length herein therefore may reflect dunes adjusted to earlier conditions in the channel and a hysteresis related to seasonal changes in river discharge or spring-neap tidal conditions [Allen, 1973; Kostaschuk et al., 1989a; Kostaschuk and Ilersich, 1995; Villard and Church, 2003].
 The dunes examined in the present study (Figure 9) have migrated between 9.1 and 19.2 m downstream over the tidal cycle, values that are comparable to measurements by Kostaschuk and Ilersich  for the period around low tide when dunes are actively migrating. The sediment transported per unit channel width within the migrating dunes over the semidiurnal cycle, qd (m2), can be estimated from
where β is the dune “shape factor” and C is the distance that the dunes have migrated. Wilbers  conducted extensive tests and found that β = 0.57 was the best estimate for most cases and this value is adopted herein. Application of equation (9), using a tidal-cycle average of H for each dune, results in a total sediment transport (± standard error) over the tidal cycle of qd = 9.71 ± 1.42 m2. Integrating the predictions from the model of van Rijn over the tidal cycle (Figure 8) yields estimates of bed load qb = 10.1 m2 and suspended load of qs = 61.3 m2. The value of qd is nearly identical to qb; Villard et al.  compared the full van Rijn model with Helley-Smith measurements of bed load over dunes in another channel of the Fraser Estuary and also found a good correlation. The remarkable agreement between qd and qb in the present study must, however, be treated with considerable caution because the contribution to dune migration made by deposition from suspension [e.g., Johns et al., 1990; Kostaschuk and Ilersich, 1995] remains poorly understood.
 Previous research has shown that dunes in rivers and estuaries often lag behind changes in river discharge and neap-spring tides. This study extends that research by examining the response of large subtidal dunes in the Fraser Estuary to changing flow conditions over a much shorter semidiurnal tidal cycle. Measurements of three-dimensional velocity profiles and estimates of sediment transport are made with an acoustic Doppler current profiler together with bed profiles and dune characteristics that are measured with a digital echosounder.
 Mean flow velocity increases and mean flow depth decreases on the falling tide, followed by a decrease in mean velocity and an increase in depth on the rising tide. Estimates based on ADCP bottom-tracking and backscatter and the sediment transport model of van Rijn [1984a, 1984b, 1984c] indicate that bed-material sediment transport generally follows the pattern of mean flow velocity over the tidal cycle. Changes in dune length are not significant over the tidal cycle but dune height, steepness and leeside slope angle precede changes in flow velocity. Scour in dune troughs occurs early in the tidal fall owing to increased turbulence in the flow separation/deceleration zone, resulting in an increase in dune height, steepness and leeside slope angle. Dune crests are eroded as mean velocity peaks near low tide, resulting in a decrease in dune height. Deposition in troughs and a further reduction in dune height and leeside slope angle occur around low tide because concentrations of sand in suspension also increase with mean velocity. As high tide approaches, sand falls out of suspension and drapes the dunes. Dune height is in equilibrium with the strongest flow velocities that occur around low tide but dune length is not in equilibrium with the flow. An estimate of bed-material transport based on dune migration suggests that the van Rijn [1984a, 1984b, 1984c] model provides reasonable estimates of bed load in the Estuary, although deposition from suspension also contributes to dune migration and thus this result must be treated with caution.
 The present study illustrates that it is vital to quantify and incorporate the effects of temporal discordance in dune dynamics throughout the tidal cycle into models that predict sediment transport and flow resistance within tidal estuaries. However, this study and others like it are commonly limited by a lack of detailed data on three-dimensional bed geometry, such as those described in the multibeam surveys of Parsons et al. (submitted manuscript, 2005). Considerable progress has been made in measuring flow and sediment transport over dunes using instruments such as ADCPs, but these data must be linked to full quantification of the three-dimensional dune geometry to enable further progress in understanding dune dynamics.
 Special thanks are owed to Jason Blair and Paul Villard for field assistance, Mike Church for his ongoing support and Arjoon Ramnarine for piloting the launch. Some of the data used in this paper are from Blair's  unpublished M.Sc. thesis. The Natural Sciences and Engineering Research Council of Canada and the Natural Environment Research Council of the United Kingdom provided funding. J. B. is grateful for award of a Leverhulme Trust Research Fellowship that aided the completion of this paper. The comments of two referees and JGR Editors Bob Anderson and Suzanne Hulscher greatly sharpened the focus of the paper.