We analyze the hydrodynamics and sediment transport on a mudflat in Willapa Bay, Washington State, United States. Velocity profiles and suspended sediment concentrations were simultaneously measured for 46 days in a major flow-through channel, in a dead-end tributary channel, on the channel bank, and on the adjacent tidal flat, encompassing periods with and without wind waves. A lateral circulation, perpendicular to the direction of the main channel, is observed to be associated with high sediment discharge directed from the channel to the tidal flat at the beginning of flood. This sediment discharge is able to explain the turbid tidal edge, which is a common feature of many tidal flats. An analytical model describing the lateral circulation and a conceptual model describing the sediment spillover from the channel are proposed. According to the model, the tidal flat sediment dynamics are strongly influenced by the sediment input from the main channel during fair weather, a process that is often overlooked in simplified models of tidal flat morphodynamics.
 Intertidal areas are characterized by extensive tidal flats incised by a network of channels. The sedimentary dynamics of these systems is governed by a variety of processes, which take place at different temporal and spatial scales [de Swart and Zimmerman, 2009]. The main processes triggering sediment transport are tides, stratification and density-driven circulation, wind waves and wind-induced currents, and drainage processes [Eisma, 1997; Le Hir et al., 2000; Friedrichs, 2012].
 Tidal asymmetries, generated by the distortion of the tidal wave during its propagation in shallow water, result in a residual sediment transport. Analytical models suggest that high friction promotes flood dominance and hence landward transport, while an extensive intertidal storage area, such as tidal flats and salt marshes, promotes ebb dominance and hence seaward transport [Speer and Aubrey, 1985; Friedrichs and Aubrey, 1988]. In addition, the phase of the principal tidal constituents can generate tidal asymmetries in the absence of any internal distortion [Hoitink et al., 2003], which, for example, results in ebb-dominated tides along the Pacific coast of the United States [Nidzieko, 2010].
 River discharge often induces density-driven flow and stratification of the water column. Strain-induced periodic stratification (SIPS) [Simpson et al., 1990] influences the structure of the bottom boundary layer and can generate a landward net transport [Geyer, 1993; Stacey and Ralston, 2005].
 Transport of fine sediments, which takes place predominantly in suspension, is largely affected by settling lag [Postma, 1961; Pritchard, 2005]. In addition, because of asymmetry in vertical mixing induced by flocculation, larger flocs are transported at different water depths and velocities during ebb and flood [Winterwerp, 2011]. Both settling lag and internal tidal asymmetry results in a net landward transport.
 This work will focus on another important process that is often overlooked in simplified tidal flat models [e.g., Roberts et al., 2000; Pritchard, 2005]: the sediment exchange between channels and tidal flats. Because of the higher current velocity, tidal channels are often characterized by higher suspended sediment concentration than tidal flats during fair weather [Allen and Duffy, 1998; Ridderinkhof, 2000; Janssen-Stelder, 2000]. Therefore, channels are a potential source of sediments for the flat, provided that a transport mechanism between them is present. Indeed, lateral circulation, i.e., the water fluxes between large channels and adjacent shoals, has been observed and explained with analytical models [Uncles et al., 1986; Li and O'Donnell, 1997; Li and Valle-Levinson, 1999; Li and O'Donnell, 2005]. This circulation is characterized by the divergence of water from the channel during flood and a convergence during ebb. In addition, salinity gradients can establish a lateral baroclinic circulation between channels and shoals, with water moving out of the channel near the bed and converging at the surface [Lacy et al., 2003; Ralston and Stacey, 2005].
 A number of authors observed sediment transport from high- to low-energy environments driven by tidal dispersion. Yang et al.  found that during calm weather, sediments are preferentially resuspended in subtidal channels and are advected landward by tidal currents. Ridderinkhof et al.  argued that horizontal transport processes can explain some of the observed sediment patterns of the Ems-Dollard Estuary in the Netherlands [see also Dyer et al., 2000], by causing an exchange of sediments between the channels and the mudflat. Black  concluded that sediment advection from deep and energetic regions of the Humber Estuary in the United Kingdom can explain the high sediment concentration measured on the mudflat at the beginning of the flood, which is often referred to as turbid tidal edge. These sediment pulses were also detected in the Gradyb tidal area of the Wadden Sea [Pejrup, 1988] and in the mudflat of the Tavy Estuary in the United Kingdom [Uncles and Stephens, 2000].
 The turbid tidal edge on a small mudflat in San Francisco Bay was explained by Talke and Stacey  by considering the propagation of a salinity front: sharp horizontal density gradients are capable of trapping sediments and advecting them without significant dispersion [Ralston and Stacey, 2005]. Warner et al.  measured a similar turbid tidal edge in San Francisco Bay associated with strong barotropic gradients from the channel to the tidal flat. Both the flood pulse and the barotropic gradients were reproduced with the numerical model Regional Ocean Modeling System (ROMS) [Song and Haidvogel, 1994] without introducing stratification, suggesting that, in this case, the turbid edge was not associated with frontal processes. The model's results showed that the flood pulses were associated with a net accretion on the tidal flat. However, the authors did not specify whether the turbid tidal edge was produced by local erosion or by advection. Similarly, Christie et al.  measured a net increase of bed elevation just after the sediment flood pulses. These results indicate that the turbid tidal edge is a key process for the accumulation of sediment on tidal flats.
 In this paper, we investigate the mechanisms producing sediment exchange between channels and tidal flat in Willapa Bay, Washington State, United States. The data set consists of velocity profiles and suspended sediment concentration simultaneously measured in a main flow-through channel, in a small tributary channel, on a channel bank, and on the adjacent tidal flat. The data set spans 46 consecutive days of measurements during spring and neap tides, as well as during periods with wind waves.
 Our measurements show a distinct transverse circulation characterized by a high-velocity flow spilling from the channel at the beginning of the flood, similar to those measured [Collins et al. 1998; Le Hir et al., 2000; Friedrichs, 2012] and simulated [Warner et al., 2004] in various tidal flat-channel systems. The purpose of this paper is twofold: to introduce a simple analytical model for channel hydrodynamics that explains the observed transverse circulation, and to propose a conceptual model, named herein the channel spillover mechanism, which describes the sediment exchange between channels and tidal flat, thus offering an explanation for the turbid tidal edge.
2. Study Site
 Willapa Bay, Washington State, United States, is a mesotidal embayment, with mixed-semidiurnal tides having a mean tidal range of 2.7 m [Hickey and Banas, 2003]. The bay is located on the North Pacific coast of the United States, and it is protected by a sand barrier peninsula on the seaward side aligned along the N-S direction (Figure 1a). The bay has approximately a rectangular shape, 8 × 40 km, with a single inlet on the north side. The tide enters the bay through the inlet and propagates in the N-S direction. Four main rivers discharge in the bay: the North and Willapa rivers in the upper part, the Naselle River in the middle part, and the Bear River in the lower part of the bay. Of the four major rivers entering the bay, the Willapa and North rivers account for 70%–80% of the freshwater delivered to the bay [Banas et al., 2004]. These two rivers are located very close to the inlet and therefore have only a minor effect on the southern part of the bay. The Naselle River accounts for about 20% of the total freshwater input. The Bear River discharge is estimated to be 17% of the Naselle River (D. J. Nowacki and A. S. Ogston, Water and sediment transport of channel-flat systems in a mesotidal mudflat: Willapa Bay, Washington. submitted to special issue, Tidal Flats, of Continental Shelf Research, 2011), which translates to about 3% of the total freshwater input. The Bear River discharges in the Bear River channel, which is one of the major tidal channels within the bay (Figures 1a and 1b). We will herein refer to the Bear River channel as the BR channel.
 The southern part of the bay is characterized by extensive mudflats, incised by channels of a wide range of dimensions (Figure 1b). The mudflat substrate has a high concentration of silt and clay sediments [Peterson et al., 1984]. Sediments in the channels and on the flat are compositionally similar and are characterized by flocs ranging from 0.16 to 20 μm (B. A. Law et al., Flocculation on a muddy intertidal flat in Willapa Bay, Washington, Part I: A regional survey of the grain size of surficial sediments, submitted to special issue, Tidal Flats, of Continental Shelf Research, 2011). Our study focuses on the upper part of the BR channel and its adjacent mudflat (Figure 1b). The BR channel is oriented along the bay major axis (N-S) and is about 100–200 m wide and 2–3 m deep with respect to Mean Lower Low Water (MLLW) (NOAA nautical chart 18504, 1998). At this location, the mudflat is drained by a series of small tributary channels, oriented W-E, spaced approximately 200 m, and connected to the BR channel (Figure 1c). The mouth of these channels is about 1 m deep and 10 m wide; the channels are about 500 m long and shoals until reaching the tidal flat elevation. According to the classification of Ashley and Zeff , the BR channel constitutes a flow-through channel, while the tributary channels on the mudflat are dead-end (drainage) channels.
 Five acoustic Doppler current profilers (ADCPs) were deployed for 46 days (from 21 February to 9 April 2010) for a total of 90 tidal cycles. Two ADCPs were placed on the tidal flat (TF1, TF2), one at the mouth of a dead-end channel, one inside the BR channel, and one on the tidal flat next to the BR channel (channel bank) (Figure 1c). The ADCPs were deployed directly on the bed surface in the upward looking configuration. Near the bank site, the BR channel bifurcates in two branches, which reconnect after 1 km. The east branch is about 60 m wide and 2 m deep with respect to the tidal flat, and the west branch is about 80 m wide and 3 m deep. The ADCP in the BR channel was deployed in the east branch (see Figure 1c). Finally, an optical backscatter sensor (OBS) was deployed with the ADCP in the dead-end channel at 20 cm from the channel bottom.
 A topographic survey reveals that the mudflat is approximately flat along the N-S direction, at the spatial scale of the tidal flat width (500 m). A bottom slope is present in the W-E direction, but only within the last 250 m close to the landward boundary, varying gradually from 0.1% to 1% (Figure 1e). The mudflat is placed 0.7 m below mean sea level, and its elevation is set herein equal to zero in a local coordinate system. The two instrument sites on the tidal flat are placed at the same elevation; the bottom of the dead-end channel is 1 m below the tidal flat, the bank site (low tidal flat) is 0.3 m below the tidal flat, and the site in the BR channel is 1.4 m below the tidal flat elevation.
3. Data Collection and Analysis
3.1. Tidal Currents
 Velocity profiles u(z) were measured with the ADCPs at 2 Hz every 30 min, averaging over 60 s, with a vertical cell size of 10 cm and a blanking distance of 10 cm. Water depth (d) was calculated using the pressure measured by the ADCP piezometers and by assuming a constant water density ρ equal to 1025 kg/m3. The pressure was corrected with the atmospheric pressure measured at the NOAA station at Toke Point (station 9440910). The water level was obtained by adding the bed elevation (measured during the survey) to the water depth.
 Water discharge per unit of width (simply referred to as discharge) was calculated by integrating the velocity profiles over the vertical: q = ∫u(z)dz. Depth-averaged speed U was calculated by dividing discharge per unit of width by the water depth: U = q/d.
 Current-induced bed shear stress was calculated from the depth-averaged speed as
where CD is the drag coefficient. In order to use the depth-averaged velocity, rather than a velocity at a fixed water depth, the drag coefficient is the chosen variable with water depth, and it is computed with the Manning's formula
where g is the gravitational acceleration. The choice of the Manning's coefficient n will be discussed in the results section.
 At every location, a wave burst of 512 points was sampled hourly at 2 Hz. The surface elevation energy spectrum Sη was reconstructed from each wave burst using the standard linear wave theory [Tucker and Pitt, 2001]. The multiplying factor to account for the reduction of pressure with depth was limited to 10, to avoid injecting noise into the reconstruction of the surface spectrum [Gibbons et al., 2005]. For frequency corresponding to a multiplying factor greater than 10, we assumed that the energy spectrum is proportional to f−4, a characteristic function of the tail spectrum in shallow water [Bouws et al., 1985].
 The significant wave orbital velocity at the bed Ubs was calculated from the surface elevation energy spectrum using the linear wave theory as follows [Wiberg and Sherwood, 2008]
where ω is the angular frequency and k is the wave number. The wave-induced bed shear stress, τwave, was computed as
 Suspended sediment concentration (SSC) was estimated using the backscatter signal of the ADCP and the turbidity value measured by the OBS when present. The OBS turbidity signal was calibrated against SSC measured in a laboratory tank, using sediments collected on the tidal flat. The linear regression between the OBS signal and the measured SSC had a correlation coefficient, r2 = 0.97. The OBS was present only at the dead-end channel site.
 At every location, suspended sediment concentration at the bottom of the water column (SSCb) was estimated using the first bin of the ADCP's backscatter signal [Gartner, 2004; Hoitink and Hoekstra, 2005]. The sonar equation can be written as [Deines, 1999]
where R is the distance along the beam (in m), A is the sum of the water absorption coefficient and the sound attenuation due to sediments (in db/m), E is the echo strength (in counts), Er is the received signal strength (the echo baseline when no signal is present), Kc is the received signal strength indicator scale factor, and a is a constant parameter. The factor Ψ describes the departure from spherical spreading of the backscatter signal, calculated from the formula of Downing et al.  as
with Rcr defining the transition between far and near field, calculated as Rcr = πat2/λ, where at is the transducer radius (1 cm) and λ is the acoustic wavelength.
 For each ADCP, Er was set equal to the recorded minimum value of the echo strength. The values of a and Kc (equation (5)) were calibrated using the SSC computed with the OBS signal at the dead-end channel site (Figure 1d). For the sites where the OBSs were not present (tidal flat, BR channel, and bank), the same values of Kc and a were used.
 The SSC vertical distribution SSC(z) was computed assuming a Rouse profile
where zr is the reference elevation, equal to the height of the first ADCP bin (0.2 m); and Ro is the Rouse number, defined as ws/Ku*, where ws is the settling velocity, u* is the friction velocity, and K is the von Karman's constant (0.4). The friction velocity was calculated from the total mean bed shears stress, computed with the nonlinear combination of τwave and τcurr [Soulsby, 1997]: . The settling velocity was estimated from the exponential decrease in SSC after the flood peak currents at all sites. Given the restricted range of SSC (0–0.8 kg/m3), we found that a constant settling velocity is appropriate (mean equal to 0.34 mm/s, with a standard deviation of 0.18 mm/s). The term SSC will herein refer to the depth-integrated SSC. Finally, suspended sediment discharge per unit of width was calculated by integrating over the vertical the product of the velocity profiles and the SSC profile.
3.4. Error Analysis
 The nominal accuracy for the ADCP is ±0.5 cm/s plus 1% of the measured value. The accuracy of the pressure transducer (and hence water depth) is 2.5 cm. The error of the water discharge calculation depends on both velocity and water depth and is on the order of a few percent. The nominal accuracy of the OBS is 0.5 g/m3. The high correlation of the OBS calibration curve obtained in the laboratory (r2 = 0.97) suggests a high accuracy of the SSC measured in the field. SSC computed with the acoustic backscatter of the ADCPs presents instead a very large error. The low correlation (r2 = 0.55) between the SSC measured with the OBS and the acoustic backscatter at the dead-end channel can be explained by three factors. First, even if the average over the three acoustic beams of the instrument is performed, the backscatter signal is measured as an integer number of counts, which spans a limited range (around 50 units). Second, the variability in sediment composition, especially the amount of sand, could significantly change the calibration curve of the acoustic backscatter. However, field surveys showed that the sediment composition is uniform in the studied mudflat and contains a very small amount of sand (Law et al., submitted manuscript, 2012, and T. J. Hsu et al., On the landward and seaward mechanisms of fine sediment transport across intertidal flats in the shallow water region: A numerical investigation, submitted to special issue, Tidal Flats, of Continental Shelf Research, 2011). Finally, the sonar equations introduce further approximations. Adding all these uncertainties, we roughly estimate that the accuracy of the SSC measurements obtained with the backscatter is on the order of 50%. On the other hand, the very recursive SSC patterns observed among different tidal cycles indicates that the precision of the measurements with the backscatter signal is on the order of 10%, in agreement with the precision estimated by Gartner . Several successful applications [Gartner, 2004; Hoitink and Hoekstra, 2005; Fagherazzi and Priestas, 2010; Sommerfield and Wong, 2011; Hsu et al., submitted manuscript, 2011] suggest that the acoustic backscatter can be used to quantify SSC with enough accuracy to detect sediment transport processes.
3.5. A Simple Model for Barotropic Lateral Circulation
 We consider a rectangular geometry, with the x axis along the longitudinal direction of the main channel and the y axis lying along the channel cross section. The cross-section bed elevation, described by the function zg = zg(y), varies laterally, but it is constant along the x axis.
where the subscripts denote the components along x and y directions, ξ is the water level, and d is the water depth, equal to ξ − zg. The Coriolis term is neglected, and the friction term is expressed with the Manning formula, as in equation (2).
 Similarly to Li and Valle-Levinson , we assume that the water level is uniform along the cross section (y axis). The validity of the assumption is supported by a scale analysis of the terms in equation (9). We introduce a scale D for water depth, a scale ωT for the tidal angular frequency, and a scale for the across-tidal flat length, Ly, and for the along-tidal flat length, Lx. Following the nondimensional analysis presented by Fagherazzi et al. , we can write
where the variables with an asterisk are nondimensional. The equations (10)–(12) thus become
with the introduction of three nondimensional parameters
 The representative parameters are Ly ∼ 500 m (width of the tidal flat at the measurement site), Lx ∼ 5000 m (length of the tidal flat and main tidal channels in the Southern part of Willapa Bay), ωT = 1.4 10−4 S−1 (semidiurnal tide), and n = 0.016 s m−1/3 (see section 4.3). Water depth discriminates when the parameters γ and Λ are small. For a water depth of 0.2 m, corresponding to the minimum depth for the ADCP velocity measurements, γ is 0.25 and Λ is 26.
 The parameter ε2 is small (∼0.01), and therefore we can neglect the terms in equation (13) multiplied by ε2, as long as the parameters γ and Λ are less than O(102). We can also neglect the term in γ in equation (12), so that equations (12) and (13) become
Equation (16) states that the advection and the local acceleration terms can be neglected in the momentum equation in the x direction [see also Friedrichs and Madsen, 1992]. Equation (17) states that, at a first approximation, the water surface is flat in the y direction and, therefore, ξ = ξ(x, t). For water depths smaller than 0.2 m, the friction term becomes gradually important, and the assumption of constant water level along y is no longer valid.
 Introducing the discharge per unit width qx = Uxd and qy = Uyd and recasting equations (14), (16), and (17) in terms of dimensional variables (equation (11)), we obtain
We assume that the Manning coefficient n is a function of y but not of x, i.e., that the bottom friction can vary only between channel and tidal flat. For simplicity, we drop the absolute value and the sign operator in equation (18). Taking the derivative of equation (18) over the x direction, we obtain
so that the system (19)–(20) can be rewritten at every location x as
where α and β are coefficients that depend on the longitudinal barotropic gradient, which is a function of x but not of y.
Equations (21) and (22) are our simplified model of lateral circulation on a small tidal flat flanking a long channel. Note that if α and β are known, the flow velocity can be computed along the width y of the tidal flat, since all the other terms in equations (21) and (22) are independent of x. Therefore, the model is a useful tool for studying the lateral circulation in a channel-flat system without solving the tidal propagation along the channel. According to equation (21), the highest divergence in the discharge along the x direction takes place in the portion of the cross section with the greatest water depth and the lowest value of n, i.e., in the channel. The lateral circulation stems from the difference in discharge divergence between channel and tidal flat in the along-channel direction, combined with the constraint of a constant water level. Basically, the tidal channel fills much faster than the tidal flat so that some water must move from the channel to the flat to maintain the water level constant along the transverse direction.
 The two coefficients α and β can be evaluated exactly by computing the propagation of the tidal wave along the longitudinal direction and obtaining the corresponding barotropic gradients [e.g., Friedrichs and Madsen, 1992]. However, these coefficients can be estimated by introducing an additional equation. Integrating the continuity equation along the y direction, and imposing a zero lateral velocity at the boundaries of the cross section, we derive
where L is the width of the cross section. Equation 23 gives an integral constraint that can be used to estimate the unknown parameters α and β in equations (21) and (22). For simplicity, we will consider the two extreme cases: α ≫ β and α ≪ β. Any other relationship between α and β would give a solution that is bounded by the solutions of these two end-members. The choice between the two extreme cases does not change the qualitative result of equation (21) (greater longitudinal discharge divergence for greater water depths) but affects only the exponent of the power law relationship in equations (21) and (22) (5/3 for α ≫ β and 2/3 for α ≪ β). Once equations (21) and (22) are solved, the lateral discharge is computed by integrating the divergence of transverse lateral discharge, and the transverse velocity is calculated dividing the transverse discharge by the water depth.
 According to this simple formulation, the lateral circulation depends on the water level displacement, the cross-section geometry, and the friction coefficient. Because of the integral constraint in equation (23), the role of equation (21) is only to redistribute the total longitudinal discharge divergence within the cross section. As a consequence, the lateral circulation depends on the ratio between the friction coefficient in the channel and on the tidal flat, but not on its absolute value.
4. Hydrodynamic Results
4.1. General Water Circulation
 At high tide, the entire tidal flat is submerged below 2–3 m of water, while it emerges at low water (Figure 2a). The site in the BR channel is always submerged, even during the lowest tide (−1 m below tidal flat level), while the site at the mouth of the dead-end channel is exposed at very low water levels. The depth-averaged velocity U is projected along the BR channel (160°N) and is perpendicular to the channel (70°N), a direction that coincides with the dead-end channel axis (Figure 1c). We will refer to the former as axial velocity and to the latter as transverse velocity. The velocity is considered positive during flood, i.e., when the two components are directed toward 160°N and toward 70°N.
 At all sites, the flow pattern is variable within a tidal cycle but similar between different tidal cycles. The velocity magnitude is greater during spring tides than during neap tides, but the qualitative pattern remains the same. Therefore, we will describe only a characteristic tidal cycle, considering separately the axial velocity and the transverse velocity.
4.1.1. Axial Velocity
 In the BR channel, on the bank, and on the tidal flat, the flow is primarily along the axial direction for most of the tidal cycle. Axial velocities at the two tidal flat sites (TF1, TF2) are very similar, both varying between −0.3 and 0.3 m/s (Figure 2c). For simplicity, we will refer to the velocity on the tidal flat as the average velocity between the two locations. On the tidal flat, the phase lag between water level and axial velocity fluctuation, calculated as the time lag that maximizes the correlation between the two curves, is −90°. The tide is oscillating as a standing wave, with the velocity peaking when the water level is around mean sea level.
 In the BR channel, the axial velocity is higher than on the tidal flat (maximum velocity around 0.5 m/s); the phase lag between water level and velocities is −78°, representative of a partially progressive wave (Figure 2b). The peak flood velocity in the BR channel is reached 1.5 h earlier than on the tidal flat, while the peak ebb velocity is reached 1 h later than on the tidal flat. Therefore, the peak velocity in the BR channel always occurs at a lower water level than on the tidal flat.
 On the bank site, the axial velocity is similar to that on the tidal flat, with the peak velocity reached at the same tidal stage (Figure 2b). However, while the flood peak velocities are almost identical between the two sites, the peak ebb velocity on the bank is 30% higher than on the tidal flat. The axial velocity at the dead-end channel, computed by averaging only the portion of the velocity profile above the tidal flat elevation, is similar to that at the bank (Figure 2b).
4.1.2. Transverse Velocity
 In general, a positive transverse flow (directed toward the tidal flat) is detected during flood, while a negative flow (from the tidal flat to the BR channel) is detected during ebb.
 The transverse velocity on the bank shows a clear peak at the beginning of the flood (up to 0.4 m/s), when the water inundates the tidal flat (Figures 2d and 3a). After the peak, the velocity slows down to around 0.1 m/s. The inward velocity lasts until 2 h after high slack water; then the transverse flow reverses, and a steady velocity around 0.1 m/s directed toward the channel takes place. Finally, when the ebbing flow has almost drained the tidal flat, the transverse velocity peaks again to 0.2–0.3 m/s.
 The transverse velocity in the dead-end channel mimics the one on the bank, with a peak at the beginning of the tidal flat inundation (Figures 2d and 3b). Flood velocities are slightly weaker than on the bank, while the opposite holds for ebb velocities. In addition, the dead-end channel shows a very strong transverse ebb velocity when the water levels drops below the tidal flat elevation (up to 1 m/s, depending on tidal amplitude, Figure 3b). This ebb peak was measured by Mariotti and Fagherazzi  and explained as the drainage of the mudflat through lateral runnels.
 On the tidal flat, a similar pattern is also detected: the velocity is directed toward the tidal flat during flood and toward the BR channel during ebb (Figure 2e). In this case, the magnitude of the transverse flow is about half that on the bank, and the peaks are less evident.
4.2. Model Results
 The lateral circulation model is applied to the study case, considering the cross-section geometry in Figure 4a, by imposing the water level measured in the BR channel. We consider a case with constant value of the Manning coefficient in both channel and tidal flat and a case in which the coefficient on the tidal flat is 1.41 the value in the channel. The two cases yield almost identical results (Figures 4c and 4d), indicating that the variation in water depth between the channel and the tidal flat is more important than a possible variation in bottom frictions.
 The model reproduces the peak velocity at the beginning of the flood. The peak velocities are greater at the bank (around 0.3 m/s, Figure 4c) than on the tidal flat (around 0.1 m/s, Figure 4d), in accordance with the measured values. The model anticipates the timing of these peak velocities at both locations. This deviation from the measured data is probably caused by neglecting the lateral barotropic gradient, which tends to delay the propagation of the water from the BR channel.
 For both the bank and the tidal flat sites, the same qualitative pattern is obtained assuming α ≫ β and α ≪ β. In the former case, the magnitude of the velocity is greater than in the latter case, because the asymmetry in axial discharge divergence between tidal flat and channel is higher. After the flood peak, the velocity decreases, remains low (<0.1 m/s), and finally grows and peaks again toward the end of the ebb (reaching a value around 0.2 m/s at the bank and 0.1 m/s on the tidal flat). The model also shows that the lateral discharge is always greater at the bank than on the tidal flat (Figures 4e and 4f).
 The model does not capture the transverse velocity during the last stage of the flood. A possible explanation is that, at higher water levels, the flow is no more affected by the BR channel, but instead is controlled by the large-scale circulation driven by the complex basin geometry. The model suggests that the observed lateral fluxes at the beginning of the tidal flat inundation and at the end of the tidal flat drainage are generated by the difference in discharge divergence between the main channel and the tidal flat and by the constraint of continuity (equations (21) and (22)).
 In the rest of this paper, we will investigate how sediment dynamics are affected by this lateral circulation. However, we will first analyze the structure of the vertical velocity profile in order to assess the role of stratification.
4.3. Stratification and Drag Coefficient
 In this section, we evaluate the possible effects of stratification and estimate the friction coefficient in equation (2). Stratification, and, in particular, SIPS [Simpson et al., 1990], is able to influence the structure of the bottom boundary layer and hence turbulence mixing and bed shear stress [Stacey and Ralston, 2005]. Therefore, the analysis of stratification is important in order to understand the patterns of current induced bed shear stress during ebb and flood.
 No direct measurements of salinity were performed during the survey. However, the freshwater input of Bear River can be used to qualitatively estimate the importance of stratification. The measuring period was characterized by low river discharge: the mean discharge from Bear River (estimated as 20% of the Naselle River discharge, U.S. Geological Survey (USGS) station 12010000) was 2.6 m3/s, with a peak of 5.2 m3/s (Figure 5c). As a reference, the tidal prism in the southern Willapa Bay tidal flat is about 45 106 m3, which gives a mean tidal discharge of 2 103 m3/s. The low river discharge suggests that stratification was low during the sampling period. In fact, during the same period, Nowacki and Ogston (submitted manuscript, 2011) measured vertical variation of salinity on the order of a few practical salinity units in a nearby tributary channel.
 Velocity profiles were analyzed to infer the structure of the bottom boundary layer and to detect the presence of stratified flows. In order to reduce the scatter on the velocity measurements, the profiles were ensemble averaged based on water level, tidal phase (ebb or flood), and tidal range (Figure 6). First, a tidal range was assigned to each velocity profile, calculated as the difference between the closest high and low slack water levels. Distinction was made between flood profiles (mean velocity < 0) and ebb profiles (mean velocity > 0). Finally, within each class of tidal range (1.5–2.5, 2.5–3.5, and 3.5–4.5 m), all the velocity profiles corresponding to a water level between −0.25 and 0.25 m were averaged together to produce one profile; this was repeated in intervals of 0.5 m from −0.25 to 2.75 m.
 A qualitative observation of the velocity profiles (Figure 6) indicates that the bottom boundary layer extends over most of the water column, at least for water depths smaller than 2.5 m, which are associated with the highest velocities. The profiles do not show apparent differences between ebb and flood, for each class of tidal range and water level. In particular, no middepth maxima in the velocity profiles, characteristic of stratification and baroclinic circulation, are evident [Ralston and Stacey, 2005; Lacy et al., 2003].
 Bed roughness was estimated fitting a log linear profile distribution to all the profiles with a mean velocity greater than 0.2 m/s [Soulsby and Dyer, 1981]. The estimated bed roughness shows a large variability, ranging from 0.3 to 46.8 mm, with a mean of 5 mm. No clear differences between ebb and flood, between accelerating and decelerating flow, and between BR channel and tidal flat were detected.
 An independent estimation of the bed roughness was done using the mean sediment diameter D: zo = D/30 [Nikuradse, 1933]. The mean floc size of the sediments is 16 μm in the channels and 20 μm on the mudflat (Law et al., submitted manuscript, 2011), which gives a very low bed roughness (0.006 mm). However, the high value of zo estimated from the velocity profiles can be explained by the presence of bed forms [Ke et al., 1994]. In situ observations confirm that the tidal flat is incised by ubiquitous runnels and small creeks. Because these bed forms are related to the drainage of the tidal flat at a very low water level [Williams et al., 2008; Carling et al., 2009], they lack any prevalent orientation with respect to the main flow, and they cannot be directly compared to dunes and ripples found in fluvial environments [e.g., Best, 2005].
 Assuming that the bed form-related drag is not contributing to the shear stress responsible for sediment transport [van Rijn, 2007], we choose a single coefficient in the Manning formula (equation (2)), constant for all sites and tidal phases. We take this coefficient equal to 0.016 s m−1/3, which, for a water depth equal to 1 m, gives CD = 0.0025, a value commonly used in muddy tidal environments [Whitehouse et al., 2000]. This value corresponds approximately to a bed roughness of 0.2 mm.
5. Sediment Dynamics
 SSC is highly variable within the tidal cycle, among different tidal cycles, and among different locations (Figure 5). During periods without waves, SSC in the BR channel is greater than on the tidal flat for the entire tidal cycle (Figures 5f, 5g, and 7). On the contrary, during periods with wave activity, SSC is greater on the tidal flat than in the BR channel (Figures 5f, 5g, and 7), in agreement with the higher shear stress induced by waves on the shallow tidal flat (Figures 5d and 5e). Here we will focus on the sediment dynamics without waves (Hs on the tidal flat < 0.1 m). The role of wave-induced resuspension will be considered in the Discussion.
5.1. Suspended Sediment Concentration During Fair Weather
 SSC shows a recursive pattern between different tidal cycles. For simplicity, we describe a single tidal cycle, representative of all tides during periods without waves and rainfall.
 In the BR channel, higher values of SSC (Figure 8a) are found in correspondence with higher axial velocities, which trigger higher shear stresses (Figure 8b). Considering only tidal stages with water level above the tidal flat, SSC in the BR channel correlates well to the current shear stress during both ebb and flood (Figure 9a).
 SSC at the bank site peaks at the beginning of the flood (Figure 8a, stage F1), in correspondence with high transverse velocity (Figures 2d and 8c). At this stage, SSCs on the bank and in the BR channel are similar. After this peak, SSC decreases following a reduction of transverse flow (Figures 2d and 8c, stage F2). This decrease in SSC is not present in the BR channel. After 1 h, SSC peaks a second time, reaching a value close to the SSC in the BR channel (stage F3). This second peak is associated with the maximum longitudinal velocity on the bank. SSC on the bank maintains the same value as the SSC in the BR channel for the rest of the flood and the initial part of the ebb. Toward the end of the ebb, SSC on the bank increases again in correspondence with higher shear stresses (Figure 8a, stage E1) and decreases in correspondence with the ebb peak in transverse velocity (Figures 2d and 8c, stage E2).
 SSC in the dead-end channel shows a very similar pattern: a first peak at the beginning of the flood, followed by a decrease in SSC and then by a secondary peak. In this case, the secondary peak is lower than on the bank. During the last stage of the ebb, SSC increases again to values similar to the bank. Finally, a very high peak of SSC (up to 1 kg/m3) is found in correspondence with the ebb peak velocity when the tidal flat is exposed [see Mariotti and Fagherazzi, 2011]. Because the ADCPs on the tidal flat were placed at a higher elevation than on the bank, measurements during the transverse flood peak are not present. The first two measurements of SSC on the tidal flat are always very high (Figure 8a, stage F1-F2) and represent the propagation of the peak of SSC during flood (turbid tidal edge). The turbid tidal edge takes place about 0.5 to 1 h after the sediment discharge peak measured at the bank location. At this stage, the SSC on the tidal flat is nearly equal or higher than on the bank but lower than in the BR channel. After the initial peak, SSC on the tidal flat decreases slowly and steadily, without displaying a secondary peak found at the bank and dead-end channel (stage F3). SSC increases again toward the end of the ebb, in correspondence with higher shear stresses on the tidal flat (stage E1).
 The relationship between SSC and current shear stress on the tidal flat shows an asymmetry between ebb and flood (Figure 9b). During ebb, the SSC remains low for shear stress below 0.15 Pa and then increases fast. Assuming that the low values of SSC (<0.05 kg/m3) are the background value always present (e.g., wash load), the values of 0.15 Pa indicate approximately the critical shear stress for erosion on the tidal flat. In situ measurements of critical shear stress produced similar values (P. L. Wiberg et al., Seasonal variations in erodibility and sediment transport potential in a mesotidal channel-flat complex, Willapa Bay, Washington, submitted to special issue, Tidal Flats, of Continental Shelf Research, 2011). On the contrary, during the initial stage of the flood (water depth on the tidal flat <1 m), elevated SSCs are found in correspondence with very low shear stresses (<0.1 Pa). A similar decoupling between shear stress and SSC was observed in a nearby region of the southern Willapa Bay tidal flat and was explained by advection of sediment from the adjacent channel (P. S. Hill et al., Flocculation on a muddy intertidal flat in Willapa Bay, Washington, Part II: Observations of suspended particle size in a secondary channel and adjacent flat, submitted to special issue, Tidal Flats, of Continental Shelf Research, 2011).
5.2. Transverse Suspended Sediment Discharge
 The sediment flux from the BR channel is similar to the propagation of a sediment-laden salinity front in San Francisco Bay described by Ralston and Stacey  and by Talke and Stacey . At our site, however, we found advection of sediment that was not associated with a salinity front. A major difference between the two results is that the site in San Francisco Bay was a very small and enclosed tidal flat, with a direct freshwater input from two major tidal creeks. Instead, the lower Willapa Bay is an open tidal flat with low freshwater input, at least during our measurements, which is more similar to the site of Warner et al. . Therefore, our observations suggest that the advection of sediment from the channel is not associated with the propagation of a salinity front, as also indicated by Warner et al. .
 From continuity, the water flowing on the bank in the transverse direction originates from the BR channel, which is characterized by an elevated SSC. Therefore, the high sediment flux on the bank during the early flood stage (Figure 8c, stage F1) is explained by advection of sediment from the BR channel. The fact that SSC on the bank is almost identical to SSC in the BR channel (Figure 8a, stage F1) suggests that erosion and deposition on the bank are close to a dynamical balance during the water spilling.
 There is strong evidence that sediment resuspension from the tidal flat is small compared to the advective flux of sediment from the BR channel. First, laboratory erosion measurements using a gust chamber showed that sediment erodibility is higher in the channels than on the tidal flat (Wiberg et al., submitted manuscript, 2011). Second, because of the increase of sediment resistance caused by dewatering during aerial exposure [Amos et al., 1988; Tolhurst et al. 2006b], sediment erodibility on the tidal flat is expected to be low at the beginning of the flood inundations.
 Finally, a consideration about the role of dead-end channels in the sediment budget is made. Transverse sediment discharge in the dead-end channel is greater than that on the bank (Figures 8c and 8d). However, dead-end channels constitute less than 10% of the boundary between the BR channel and the tidal flat. Assuming that the measurements in the dead-end channel and on the bank are representative of these two elements, the width-integrated sediment discharge in the dead-end channel is small compared to that on the bank. Therefore, the flux of sediment on the tidal flat during flood is influenced more by the fluxes on the bank than the fluxes in the dead-end channels. The flux of sediment in the dead-end channel becomes instead significant during the last stage of the ebb, when the tidal flat emerges.
6.1. Channel-Tidal Flat Sediment Exchange
 The first measurement on the tidal flat at the beginning of the flood (Figure 8a, stage F1) shows a distinct turbid tidal edge. SSC decreases after the initial peak, even if the local bottom shear stress increases (Figures 8a and 8b). Similarly, there is a low correlation between SSC and shear stress during flood (Figure 9b). Local resuspension is not a likely cause of the turbid tidal edge during flood, in agreement with the finding of Black  and Talke and Stacey .
 We suggest that the transverse sediment discharge coming from the BR channel is contributing to the formation of the turbid edge on the tidal flat. The sediment discharge peak measured at the bank location takes place around 0.5 to 1 h before the SSC peak on the tidal flat, which is approximately the time needed for a current of 0.3 m/s to reach the distance between the BR channel and the tidal flat sites (500 m). A simple mass balance reveals the contribution of the lateral discharge to the sediment budget on the tidal flat. We isolate a strip of tidal flat with 1 m length along the BR channel direction. Considering a turbid tidal edge equal to 0.3 kg/m3, a water depth of 0.3 m, and a tidal flat width equal to 500 m, the amount of sediment in suspension over this strip of tidal flat is 45 kg. At the beginning of the flood (Figure 8c, stage F1), the peak transverse flux from the bank is 0.05 kg/s, which multiplied by a time step (0.5 h) gives 90 kg. Therefore, the amount of sediment transported by the transverse flow is more than sufficient to explain the turbid tidal edge and additional sedimentation on the bank and tidal flat.
 The secondary peak of SSC on the bank during flood (Figure 8a, stage F3) is explained by the peak in longitudinal velocity, provided that erodible material is present. The high velocity is probably caused by turbulent transport of momentum, as the water level increases and the bank becomes part of the BR channel. The transverse sediment discharge during the secondary peak (Figure 8c, stage F3) is comparable to that observed during the first peak (stage F1). However, because of the greater water depth and smaller transverse velocity, SSC does not significantly increase on the tidal flat (Figure 8a).
 The transverse velocity during the secondary SSC peak is probably associated with the large-scale tidal circulation in the bay. At high water levels, such as during the stage F3, the flow is less channelized and, hence, the velocity direction is more affected by the shape of the tidal basin than by the channel's orientation. As a result, our analytical model is not able to capture this flow that strongly depends on the overall morphology of the basin. Finally, during ebb, SSC on the tidal flat remains low for most of the time, increasing only toward the end following an increase in shear stress. As suggested by the SSC-shear stress relationship (Figure 9b), local resuspension seems the most probable source of sediment. During ebb, SSC in the BR channel is equal to or greater than on the tidal flat, and the transverse sediment discharge is oriented toward the BR channel. Therefore, even if the BR channel is a potential source of sediment, the advective mechanism acts in the opposite way: relative low SSC water is transported from the tidal flat to the BR channel.
6.2. The Channel Spillover Mechanism
 The simplified analytical model used herein shows how barotropic lateral circulation determines the pattern of transverse velocity observed on the bank and on the tidal flat. According to the model, the maximum lateral discharge takes place when the water level is just above the tidal flat elevation. This phase corresponds to the higher SSC in the BR channel and, therefore, to the phase when the BR channel is a potential source of sediment for the tidal flat.
 We delineate a specific process for asymmetric sediment flux on the tidal flat, which we will refer to as channel spillover mechanism. The conceptual model is based on the following assumptions.
 1. Currents, and hence shear stresses, are higher in the flow-through channel than on the tidal flat.
 2. Because of the higher shear stresses, SSC in the flow-through channel are higher than on the tidal flat, during both ebb and flood. This assumption requires that bottom erodibility in the channel is equal to or greater than that on the tidal flat, as in our study site (Wiberg et al., submitted manuscript, 2011).
 3. The transverse barotropic flow is directed from the flow-through channel to the tidal flat during flood and in the opposite direction during ebb.
 Given these constraints, relatively high SSC water is brought from the channel to the tidal flat during flood (Figure 10, stage F1), while relatively low SSC water is brought from the tidal flat to the flow-through channel during ebb (Figure 10, stage E2). The role of the channel bank during flood is neutral, i.e., water coming from the channel to the tidal flat does not change its SSC. This asymmetric pattern results in a net sediment transport from the channel to the tidal flats.
 The role of concentration gradients driving sediment across mudflats via tidal dispersion has been already emphasized [Roberts et al., 2000; Prichard et al., 2002; Friedrichs, 2012]. The novelty of our conceptual model is to show that this sediment transport mechanism is associated with a specific lateral circulation between a channel and its adjacent tidal flats.
 The proposed mechanism presents some similarities with the scour and settling lag mechanism [Postma, 1961]: both processes are due to spatial (or Lagrangian) asymmetries [for a review, see Friedrichs, 2012]. Settling lag results from the combination of the delay in sedimentation after the velocity has diminished to the point at which particles can no longer be held in suspension, plus one of the following: (1) tidal velocities decreasing landward, (2) water depth decreasing landward, and (3) high slack water period greater than the low slack water period (for a review, see Pritchard ). The channel spillover mechanism stems from a difference in the boundary condition of SSC and from lateral circulation. This mechanism is present even without (1) variations in velocity along the direction of sediment transport, (2) variations in water depth along the direction of sediment transport, and (3) slack water duration asymmetries.
 An additional difference is that the settling lag effect is dominant around high slack water, after sediment erosion generated by peak currents. Instead, the channel spillover mechanism is dominant at the beginning of the flood, when the water inundates the tidal flat (Figure 9b, water depths < 1 m). The proposed mechanism is analogous to the transport of sediment on fluvial floodplains. In both cases, sediment is transported in the main channel, where velocities are higher, and advected on the adjacent areas, characterized by lower velocities that favor sediment settling.
 The channel spillover mechanism proposes an alternative explanation of the turbid tidal edge. Cross-sectionally integrated models for axial sediment transport showed that the turbid tidal edge stems from local flow convergence, which tends to accumulate suspended sediment [Friedrichs et al., 1998; Pritchard et al., 2002; Pritchard, 2005]. Our model instead suggests that the turbid tidal edge on the tidal flat is formed by transport from a source of elevated SSC, i.e., it is driven by tidal dispersion. The two processes do not exclude each other, and it is plausible that both contribute to the formation of the turbid edge.
 The channel spillover mechanism does not require tidal asymmetries, but does not preclude their presence. The mechanism works for both symmetric and asymmetric tides provided that two main processes are present: SSC is higher in the channel and water discharge is directed from the channel to the tidal flat during flood and in the opposite direction during ebb.
 During wave events, bottom shear stresses are larger on the tidal flat than in the BR channel, leading to higher SSC on the flat surface (Figures 5f, 5g, and 7). Therefore, wave activity reverses the direction of the channel spillover mechanism. Indeed, several authors [Yang et al., 2003; Ridderinkhof, 2000; Janssen-Stelder, 2000] observed higher SSC on tidal flats and sediment flux directed toward subtidal channels during stormy weather.
 Finally, the contribution of the dead-end channel flow to the width-integrated transverse sediment discharge is small with respect to the contribution of the overbank flow. The contribution of the dead-end channel is significant only during the very last stage of the ebb, when the water level drops below the tidal flat elevation and the bank is exposed. The ebb pulse in the dead-end channel is associated with extremely shallow drainage [Mariotti and Fagherazzi, 2011] and produces a net export of sediment from the tidal flat.
 We measured a lateral circulation between a large flow-through channel and the adjacent tidal flat in Willapa Bay, Washington State, United States. The lateral velocity is higher at the beginning of the tidal flat inundation and at the end of the tidal flat drainage. A simplified barotropic model suggests that this lateral circulation is generated by the difference in discharge divergence between the main channel and the tidal flat along the channel direction. This model allows estimating the lateral circulation by continuity arguments only, without solving the propagation of the tidal wave in the longitudinal and lateral directions.
 The lateral circulation is characterized by a flux of sediment directed from the BR channel to the tidal flat during flood. This flux likely originates from the elevated SSC in the BR channel and is transported across the bank without significant change. The advection of sediment from the BR channel contributes to the formation of the turbid tidal edge measured on the tidal flat. Even though observations suggested the importance of sediment advection from channels [e.g., Ridderinkhof et al., 2000], this process has never been emphasized and described in detail, nor associated with a specific lateral circulation, nor related to the formation of the turbid tidal edge.
 We propose a simple mechanism, called herein channel spillover, that stems from two conditions: (1) higher SSC in the main channel than on the tidal flat and (2) water diverging from the channel during the early phase of the flood and converging during the late stage of the ebb. According to the channel spillover mechanism, sediments are brought from the main channel to the tidal flat during flood, but not during ebb, generating a net accumulation on the tidal flat.
 This mechanism can either occur independently or interact with other sedimentary processes acting on tidal flats. Tidal asymmetries in duration, velocity, or stratification are not altering the spillover mechanism, provided that conditions (1) and (2) are present. However, the presence of wind waves increases SSC on the tidal flat more than in the BR channel, reversing the channel spillover mechanism. Therefore, it is clear that a complete understanding of the tidal flat sediment dynamics requires the coupling between all these processes.
 This research was supported by Office of Naval Research awards N00014-10-1-0269 and N00014-07-1-0664, Department of Energy NICCR program award TUL-538-06/07, and VCR-LTER program award GA10618-127104.