# In-situ characterisation of fluvial dune morphology and dynamics under limited sediment supply conditions, Seine River, France

Guillaume Michel, Sophie Le Bot, Julien Deloffre, Magalie Legrain, Romain Levaillant, Michel Simon, Bernadette Tessier, Sandric Lesourd

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## To cite this version:

Guillaume Michel, Sophie Le Bot, Julien Deloffre, Magalie Legrain, Romain Levaillant, et al. In-situ characterisation of fluvial dune morphology and dynamics under limited sediment supply conditions, Seine River, France. Geomorphology, 2023, 439, 10.1016/j geomorph.2023.108855. hal-04290099

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https://hal.science/hal-04290099v1

Submitted on 27 Mar 2025

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Distributed under a Creative Commons Attribution 4.0 International License
1 In-situ characterisation of fluvial dune

2 morphology and dynamics under limited

3 sediment supply conditions, Seine River,

4 France

5 Authors

6 Guillaume Michel¹, Sophie Le Bot¹, Julien Deloffre¹, Magalie Legrain², Romain Levaillant¹, Michel

7 Simon¹, Bernadette Tessier², Sandric Lesourd²

8 Corresponding author

9 Guillaume Michel, email : guillaume.mhl@gmail.com

10 Affiliations

11 1 Univ Rouen Normandie, Univ Caen Normandie, CNRS, Normandie Univ, M2C UMR6143, F-

12 76000 Rouen, France

13 2 Normandie Univ, UNICAEN, UNIROUEN, CNRS, M2C, 14000 Caen, France

14 Keywords

15 Bedform dynamics, morphology, limited sediment supply, dune tracking
## 16 Highlights

17 • Dune morphologies and shapes are constrained by sediment availability

18 • Limited supply of sediment restricts bedload transport associated with dune migration

19 • Differential bathymetry captures a portion of suspended bedload bypassing dunes

## 20 Abstract

21 Dune dynamics and associated sedimentary fluxes have been estimated over a period of a week in the river Seine characterized by limited sediment supply. Distributed into two corridors, typical medium and small dunes associated with fluvial environments have been characterised from multibeam data acquired on four dates, 23-29 March 2021, after a limited peak flood. Dune morphometric parameters have been quantified on cross-dune 1 m spacing of bed elevation profiles and dune migration rates have been calculated by analysing successive multibeam acquisitions. Evidence of limited sediment supply conditions have been recognized from areas uncovered by mobile sediment in the troughs between medium dunes. Under such conditions, bedload transport associated with dune migration has been estimated using three methods: differential bathymetry, dune tracking and the Van Rijn empirical formula using a correction factor accounting for limited sediment supply conditions. The three methods provide similar bedload fluxes (less than an order of magnitude difference), and the small differences are related to input data uncertainties and the capability of these methods to capture sediment transport processes, such as sediment bypassing dunes. Based on field observations, this paper brings new constraints to the relationships between dune morphological parameters, migration rates and sedimentary fluxes and environmental parameters (sediment grain size, flow velocity and water depth) under limited supply conditions in a real river.

## 37 1. Introduction

38 Fluvial bedform classification includes a large panel of shapes and dimensions, from bars to dunes and ripples (Ashley, 1990; Villard and Church, 2005). According to the classification of Ashley (1990), dunes occur as 2D and 3D forms with wavelengths greater than 0.6 m and height above 0.06 m, scaling with
41 water depth (Julien and Klaassen, 1995; Villard and Church, 2005; Yalin, 1964), although Bridge (2003) argued for a continuum of bedforms between ripples and dunes. Their morphological evolution and migration have long been considered to be strongly controlled by sediment transport. Grain size, flow velocity and water depth are also known to individually affect dune sizes and shapes (Bagnold, 1966; Best, 2005; Carling, 1999; Carling et al., 2000; Flemming, 2019; Kleinhans et al., 2002; Kostaschuk and Villard, 1996; McLean et al., 1999; van den Berg, 1987; Venditti et al., 2005).

47 Within rivers, sediment transport is divided into three modes with increasing flow velocity: rolling and sliding particles, saltating and jumping particles, and suspended particles (Gomez and Church, 1989; Van Rijn, 1993). As defined by Van Rijn (1993), there is no sharp limit between these modes of transport, but the bedload can be defined as the rolling and sliding particles in continuous contact with the riverbed and the suspended load as the sediment maintained in suspension by turbulence in the flowing water. The suspension number (Bagnold, 1966), defined as the ratio between the bed shear velocity and the particle fall velocity can be used to assess the relative importance of bedload transport to suspended load (Bagnold, 1966; Cheng, 2009; Van Rijn, 1984a, 1984b; Zomer et al., 2021) and the initiation of bed material into suspension. Studies have shown that a portion of the bedload transport may not participate in dune migration (Gaeuman and Jacobson, 2007; van den Berg, 1987) especially at the crest of the dune, where flow separation can occur and a portion of the bedload material becomes temporarily suspended (Best, 2005; Lefebvre et al., 2014; Paarlberg et al., 2007; van den Berg, 1987). Likewise, a portion of the suspended load can impact dune migration with the deposition of fine sediment within troughs between bedforms and contribute to sediment accumulation on the lee side (Kleinhans, 2001; Kostaschuk et al., 2009; van den Berg, 1987).

62 In rivers, parameters such as water depth and limited sediment supply are known to often prevent the dunes from reaching equilibrium (Carling et al., 2000; Claude et al., 2012; Kleinhans et al., 2002). In such cases, dune morphological parameters are modified, notably with a limited dune height and hence a relative elongation of the dune wavelength (Blondeaux et al., 2016; Mazzuoli et al., 2016; Vah
66 et al., 2020; Venditti et al., 2019). According to flume experiments and field observations, dune shape
67 is also influenced by the mobile sediment layer thickness, a consequence of the sediment supply
68 conditions (Kleinhans and Brinke, 2001; Tuijnder et al., 2009; Tuijnder and Ribberink, 2012; Vah et al.,
69 2020; Venditti et al., 2019). As such, Kleinhans et al. (2002) established a conceptual model from
70 experiments in a flume, based on the transport parameter (derived from grain size and flow velocity)
71 and mobile layer thickness. This model provides a qualitative description of the evolution of dune
72 shape with varying sediment supply. Moreover, on the basis of numerical models (Colombini and
73 Stocchino, 2011), experimental studies (Dreano et al., 2010; Tuijnder et al., 2009; Tuijnder and
74 Ribberink, 2012; Vah et al., 2020) and field case studies (Amos et al., 2004; Carling et al., 2000;
75 Kleinhans and van Rijn, 2002; van Landeghem et al., 2009), it has been shown that a limited sediment
76 supply directly affects sediment transport and dune migration.

77 To measure the bedload transport, different methods and techniques have been developed, from
78 direct sampling to empirical formulas (Claude et al., 2012; Conevski, 2020; Frings and Vollmer, 2017;
79 Hoekstra et al., 2004; Latosinski et al., 2017; Le Guern et al., 2020; Leary and Buscombe, 2020;
80 Liedermann et al., 2018; Mcelroy and Mohrig, 2009; Nittrouer et al., 2008; Recking et al., 2016).
81 Indirect methods have also been developed to estimate the bedload transport, using aDcp data (e.g.,
82 Conevski et al., 2019; Kostaschuk et al., 2009; Latosinski et al., 2017a; Le Guern et al., 2020; Rennie
83 and Church, 2010; Rennie and Millar, 2007; Villard and Church, 2005) or passive acoustic sensors (e.g.,
84 Barton et al., 2010; Goodwiller et al., 2019; Hilldale et al., 2015; Le Guern et al., 2020; Nicollier et al.,
85 2021). With the development of multibeam echosounders, indirect methods using the evolution of
86 dune shape also have been explored to estimate bedload transport (e.g., Claude et al., 2012; Hoekstra
87 et al., 2004; Leary and Buscombe, 2020; Nittrouer et al., 2008; Schmitt and Mitchell, 2014; Simons et
88 al., 1965; Wilbers, 2004; Zomer et al., 2021). Generally, indirect methods and empirical formulas are
89 considered less reliable than direct sampling (Claude et al., 2012). However, in comparison to direct
90 sampling methods that require numerous samples to be reliable (Claude et al., 2012; Gaeuman and
91 Jacobson, 2007; Kleinhans and Brinke, 2001; Vericat and Batalla, 2006), indirect methods and empirical
formulas are less time-consuming, technically easier to use and less expensive (Claude et al., 2012; Gaeuman and Jacobson, 2007). Several studies comparing direct, indirect and empirical formula based methods have been published in the past ten years (Cilli et al., 2021; Claude et al., 2012; Frings and Vollmer, 2017; Gaeuman and Jacobson, 2007; Le Guern et al., 2020; Leary and Buscombe, 2020; Recking et al., 2012), but the exploration of these methods rarely considered limited sediment conditions.

In the Seine River, the overall sediment dynamics remains poorly constrained, despite the importance of navigation traffic related to commercial activities that can be hindered by the development and migration of sandy bedforms (e.g., sandbars, dunes). In the estuarine section, suspended sediment fluxes have been studied both in the lower estuary (marine section) (Avoine, 1987; Brenon and le Hir, 1999; Dupont et al., 1994; Grasso and le Hir, 2019; Guézennec et al., 1999) and in the upper estuary (Deloffre et al., 2007, 2005; Verney et al., 2007, 2006), notably by focusing on fine-grained mud flats and their response to hydrodynamic forcing. However, bedload sediment fluxes have only been studied with observation and numerical modelling at the mouth of the estuary, at decadal and millennial timescales (Lesourd et al., 2003; Tessier et al., 2010; Waeles et al., 2007), while studies focusing on sand dynamics are lacking, both in the upper and fluvial estuary.

The main objective of this study is to highlight the characteristics of fluvial dune morphology and dynamics, as well as associated bedload sediment transport under established limited sediment supply conditions evidenced through field observations. Over a period of one week, both morphological evolution and migration rates of different categories of dunes are examined, as these parameters constitute good markers of active bedload transport. To estimate the bedload transport, three methods are compared: differential bathymetry, dune tracking and an empirical formula (Van Rijn, 1984b). Input data uncertainties that affect the unit bedload sediment transport estimations and the capability of these methods to capture sediment transport processes are discussed with regards to field observations.
## 2. Study Area

The Seine River is 774 km long with an outlet leading to the English Channel. It is located in the Seine Normandy Basin (France), which is characterised by a catchment area of 79,000 km² (Fig. 1a). The Seine River can be divided into two main sections, delimited at the location of the Poses Lock (Fig. 1b). The estuarine section located downstream from the Poses Lock corresponds to a macrotidal estuary influenced by tides and river flow. The fluvial section located upstream from the Poses Lock is only influenced by the river flow, with an mean annual flow of 410 m³.s⁻¹ and daily extreme values up to 2000 m³.s⁻¹ (measured at the location of the Poses Lock) (Deloffre et al., 2005). In 2021, the Seine mean annual flow reached 544 m³.s⁻¹ with 114 days of mean daily flows higher than the annual mean flow. The maximum daily flow of 1940 m³.s⁻¹ has been measured on the 8th of February 2021 (Fig. 1d) and a minimum daily flow of 220 m³.s⁻¹ on the 22nd of November 2021. These values have been recorded at the Vernon gauging station (station H320 0001 04 from Hydro.eaufrance.fr database) located 26 km upstream from the study area (Fig. 1b).

The study area is located 24 km upstream from the Poses Lock in the fluvial section (Fig. 1b) between kilometric navigation mark PK178 and PK179. The studied section is 1 km long and approximately 200 m wide, where the Seine River is 300 m wide. In this section, the Seine riverbed is incising old alluvial terraces (Bassompierre and de Mautort, 1967). The alluvial formations are located on top of locally outcropping limestones, from Turonian to Campanian age (Bassompierre and de Mautort, 1967). In the area, the navigation channel is restricted to the centre of the river. On the left side of the river, shoals are present with superimposed bedforms of tens of centimetres in height, wavelengths about 8 m and several metres-long crests, corresponding to dune morphologies (Ashley, 1990). All these features are monitored by recurrent bathymetric surveys from Voies Navigables de France (VNF), in charge of the Seine River navigation safety. Within this dune field, two areas of interest (ROI1 upstream and ROI2 downstream, see location on Fig. 1c) have been defined to perform very high-resolution analyses. Another set of morphologies have been evidenced in the centre of the river and
142 correspond to small dunes, with crest heights of about 0.15 m and wavelengths of about 4 m (Ashley, 1990). The third area of interest (ROI3) is located within the small dune field (Fig. 1c). The three ROIs have been chosen to cover both morphologies of dunes and small dunes, within sections where the morphologies have been clearly identified.

<figure><img src="image_3.png" /><figcaption>Fig. 1: Location maps of the Seine Normandy hydrographic basin and Seine River (a), the Seine River and hydrographic network, gauging station (HYDRO Eau France), Poses Lock and study area (b). Map of bathymetric dataset of the 29th of March 2021 and location of the aDcp profiles and grab samples stations (c) with map background sourced from IGN SCAN25®. Daily mean flow from the Vernon gauging station (d). The bold black segment corresponds to the survey period between the 23rd and the 29th of March 2021 (e). Zoom on the survey period displays the acquisition dates of the successive MBES datasets, grab samples and aDcp data.</figcaption></figure>
153 3. Materials and Methods

154 3.1. Field measurements

155 Multibeam echosounder (MBES) data, aDcp and grab samples used in this study have been collected
156 with a 7-m-long boat, over a period of a week, from the 23rd to the 29th of March 2021, just after a
157 short episode of limited flooding with flow peaking at 735 m³.s⁻¹ on the 22nd of March (Fig. 1). Over the
158 period of the survey, the daily mean flow decreased from 715 to 555 m³.s⁻¹ with an average mean flow
159 of 640 m³.s⁻¹.

160 3.1.1. Multibeam echosounder data

161 During the survey, four pole-mounted multibeam echosounder acquisitions have been performed: one
162 on the 23rd and the 29th and two on the 25th, one during the morning and the other one during the
163 afternoon. The time intervals between the acquisitions are of 45 h between the 23rd and 25th, 96 h
164 between the 25th and 29th, and 2h 20 min between the 25th morning and afternoon acquisitions.

165 Both bathymetric and bed backscatter data were simultaneously acquired by the MBES at a maximum
166 speed of 3 knots. The MBES used during this survey is a TELEDYNE® ODOM MB2© equipped with
167 attitude sensors POS MV Applanix® and connected to an external Trimble® 540TS GNSS receiver
168 mounted on top of the boat and receiving RTK corrections. The MBES was operated at a frequency of
169 400 kHz during the whole survey.

170 Bathymetric data have been acquired and processed by using the PDS® hydrography, Teledyne, vers.
171 4.4.3.4 software. Bathymetric processing includes: attitude correction, patch test correction,
172 automatic and manual filtering of the data. The bathymetric data are expressed as elevation over the
173 French Vertical reference system (NGF - IGN69). Both bathymetric and riverbed backscatter data have
174 been gridded to 0.15 m resolution, and then exported as GeoTiffs. Commonly, higher backscatter
175 values are associated to hard and/or rough sediment cover and low backscatter to soft sediments
176 (Lamarche et al., 2011; Lurton et al., 2015). It is known that intensity modulations caused by angle
177 dependence, i.e., the presence of morphologies at the riverbed, requires specific compensations
178 (Lurton and Lamarche, 2015). However, in the present study the orientation of the acquired swaths is
179 sub-parallel to the dune crests, limiting the effect of the morphologies onto the backscatter values.
180 Without calibration, absolute backscatter values cannot be used, but relative variations correlated to
181 sediment samples can be used confidently (Lamarche et al., 2011; Lurton et al., 2015). Backscatter data
182 have already been used in river environments to map sediment cover using advanced techniques (e.g.,
183 Buscombe et al., 2017; Eleftherakis et al., 2012). Within this study, backscatter data have been
184 interpreted to assess the percentage area of the riverbed uncovered by sediment within each ROI.
185 Here, the riverbed percentage area uncovered by sediment corresponds to the parameter p (Tuijnder
186 and Ribberink, 2012; Vah et al., 2020).

187 3.1.2. aDcp data and flow velocity values

188 On the 24th of March, a series of three aDcp profiles were acquired by using a dual frequency ROWE®
189 SEASEVEN® sensor simultaneously operated at 600 kHz and 1200 kHz. The aDcp acquisitions were
190 performed at a maximum speed of 1.5 knots, from the downstream limit of the survey area towards
191 the upstream one (Fig. 1c). From the left side of the river towards the centre of the river, the three
192 acquired profiles are 1143, 1048 and 941 m long, respectively.

193 The aDcp data were processed by using the PULSE® software with automatic application of attitude
194 and boat speed corrections. The aDcp profiles were exported as CSV files and exported as a matrix to
195 be post-processed and filtered (with columns corresponding to aDcp ensemble number, which
196 corresponds to 5 pings averaged by the software, and rows corresponding to bins). Matrix columns
197 with incomplete information (missing beam values or missing DGPS input correction) were dropped.
198 Once filtered, flow velocities were compiled by averaging all valid cell values of the matrix (each
199 column and each row, excluding cells with NaN values). For ROI1, 19 vertical velocity profiles were
200 averaged, 15 for ROI2 and 19 for ROI3.
201 **3.1.3. Sediment samples**

202 A total of 16 surface sediment samples has been collected on the 24th of March using a Van Veen grab
203 (25kg; 12L) (Fig. 1c). The location of each grab sample was automatically added to a Geographic
204 Information Software (GIS) project by connecting the Hemisphere VS100 Series Differential GPS (DGPS)
205 of the boat to a laptop. For each sample, the grab content was transferred to a plastic box. Supernatant
206 was removed after a short period of decantation and then the sediments were transferred to a plastic
207 bag and sealed.

208 Grain-size analyses were performed by mechanical sieving. The mechanical sieve used is a Retsch
209 AS300 control with 26 sieves with mesh size ranging from 20 mm to 63 µm, following a geometric
210 progression of ¹⁰V10 according to the AFNOR French Standards (AFNOR, 2000). Sediment mass density
211 was measured in the M2C sedimentology laboratory using a pycnometer according to the NF P 94-054
212 standards (NF EN ISO 17892-3).

213 The grain-size analysis results were processed by using GRADISTAT EXCEL spreadsheet (Blott and Pye,
214 2001) following the Udden (1914) and Wentworth (1922) sedimentological scales, Folk and Ward
215 (1957) for sediment parameters and Folk (1954) for sediment name classification.

216 **3.2. Dune mapping and characterisation**

217 Bedform morphological mapping, including dunes, is based on the bathymetric data, bathymetry
derivatives (i.e., slope and curvature) and Geomorphon index. Bathymetry derivatives were calculated
218 using QGIS® built-in tools. The Geomorphon index was produced using the Geomorphon tool (Stepinski
219 and Jasiewicz, 2011). Morphological classification of the study area includes bathymetric classification,
220 reclassification of the Geomorphon index and manual delineation of small-scale features.

221 The extraction of dune crests was performed within the three regions of interest (ROI) by manual
222 mapping based on slope and curvature data. Within each ROI, dune characteristics and migration rates
223 were compiled. Dune characteristics were extracted by using the BTT tool (Van der Mark et al., 2008),
224 which processes bed elevation profiles to identify bedforms and extract their characteristics after
225
226 detrending the profile from regional slope, based on the zero-crossing method (Fig. 2; Table 1). The 227 BTT script was compiled in MATLAB®2021 with application of a linear detrend. These bed elevation 228 profiles were automatically extracted using the QGIS and SAGA Cross Section tool, with a spacing of 229 1 m and a length corresponding to the longitudinal extent of each ROI. Values of each bathymetry 230 raster cell along the bed elevation profiles (BEP) was automatically extracted in QGIS and each profile 231 was exported as an individual CSV table. For ROI1, 23 bed elevation profiles were extracted, 19 profiles 232 for ROI2 and 23 for ROI3. A total of 6 BTT parameters (Fig. 2; Table 1) were extracted along each bed 233 elevation profile for each dunes within the three ROIs.

<figure><img src="image_4.png" /><figcaption>Fig. 2: Display of the BTT parameters (Van der Mark et al., 2008) extracted along one detrended BEP of the present study. See Table 1 for description of the parameters. The black box corresponds to the dune part which is used to determine the slope. Flow is from right to left.</figcaption></figure>

<table><caption>Table 1: Symbol and description of the morphological parameters processed using the BTT algorithm from Van der Mark et al. (2008).</caption><thead><tr><td>Symbol</td><td>Parameter (units)</td></tr></thead><tbody><tr><td>ηc</td><td>Crest elevation (m)</td></tr><tr><td>ηt</td><td>Trough elevation (m)</td></tr><tr><td>Δs</td><td>Height of stoss side (m)</td></tr></tbody></table>
<table><tr><td>Δl</td><td>Height of lee side (m)</td></tr><tr><td>λs</td><td>Length of stoss face (m)</td></tr><tr><td>λl</td><td>Length of lee face (m)</td></tr><tr><td>λc</td><td>Bedform length between crests (m)</td></tr><tr><td>λt</td><td>Bedform length between troughs (m)</td></tr><tr><td>λupcr</td><td>Bedform length between zero upcrossings (m)</td></tr><tr><td>λdowncr</td><td>Bedform length between zero downcrossings (m)</td></tr><tr><td>Sl</td><td>Mean slope lee face (°)</td></tr><tr><td>Ss</td><td>Mean slope stoss face (°)</td></tr></table>

241

242 Within the BTT software, the dune slope is calculated by dividing the vertical distance of the lee side by the horizontal distance, and this over a part of the dune lee side (black polygon in Fig. 2). The part of the dune lee side considered by the BTT software for slope calculation is displayed in Fig. 2. The dune length (L<sub>d</sub>) parameter was calculated for each dune by addition of the λs and λl BTT parameters (see Table 1).

243
244
245
246
247
248
249
250
251
252
253
An additional parameter, dune lee side maximum slope, was extracted from the slope raster derived from bathymetry (Fig. 3). To do so, slope raster values were extracted along the BEP (used for BTT processing) using the SAGA Toolbox in QGIS. Slope values along those profiles were plotted and peaks automatically detected using the Scipy Signal Python library (Fig. 3). Peak locations and associated slope values were manually reviewed by checking peak values and locations along the profile in GIS. For consistency with the other parameters, maximum slope values were averaged per ROI and per date.
<figure><img src="image_5.png" /><figcaption>Fig. 3: Slope raster on the 25th of March 2021 with location of the BEP used in BTT (spacing of 1 m) within the extent of ROI2 (a), and plot of the extracted slope values along one BEP (BEP17) with automated extraction of slope maximum values (red crosses) using Scipy Signal Python library.</figcaption></figure>

According to Carling et al. (2000), dunes with steepness greater than 0.06 are considered at equilibrium. For dunes characterised by steepness lower than 0.06, conditions such as limited water depth or limited sediment supply are considered as an environmental factor preventing the dune from reaching an equilibrium state (Carling et al., 2000; Tuijnder et al., 2009; Tuijnder and Ribberink, 2012). The dune steepness δ corresponds to the ratio between the dune height (Hd) and dune length (Ld) (Carling et al., 2000):

$$ \delta = H_d/L_d $$

Eq. (1)

The dune sinuosity corresponds to the ratio between the dune crest length and the shortest distance between the dune crest starting and ending points. As the sinuosity increases, dune shape transitions from linear to increasingly complex shape. As per example, sinuous dunes described by Venditti (2007)
and Venditti et al. (2005) are characterised by a sinuosity index of 1.3. Here, sinuosity values were calculated in QGIS using the field calculator within an attribute table. The following formula has been used to calculate the sinuosity:

$$ \text{sinuosity} = \frac{\text{length of dune crest}}{\text{straight line distance}} $$

Eq. (2)

where the length of dune crest and the straight line distance between the end points, both expressed in metres. Its expression as a GIS formula is:

$$ \text{sinuosity} = \frac{\text{length($geometry$)}}{\text{distance(start\_point($geometry$), end\_point($geometry$))}} $$

Eq. (3)

The term $geometry$ corresponds to each GIS feature, here the dune crest, onto which the formula has been applied.

Migration rates were compiled by extracting the distance between each manually delineated dune crest at two successive dates. The migration rates are expressed as metres per day (m.d⁻¹). Dune crests were digitised for each of the three bathymetric datasets using bathymetry data, bathymetry derivatives and Geomorphon classes in QGIS. The detailed workflow of the migration rate calculation is shown in Fig. 3.

Characteristics of the dunes within each ROI were averaged and the standard deviation of each parameter within each ROI was calculated.

287
<figure><img src="image_6.png" /><figcaption>Fig. 4: GIS workflow detailing the steps to perform the migration rates and sediment volume displaced estimations. Beside the step using SAGA GIS toolbox, all the steps have been performed in QGIS.</figcaption></figure>

### 3.3. Bedload transport assessment methods

Bedload transport is considered the main mechanism associated with dune migration (Hoekstra et al., 2004; van den Berg, 1987) and multiple methods have been compared to constrain the sediment fluxes associated with bedload discharge (e.g., Claude et al., 2012; Gaeuman and Jacobson, 2007; le Guern et al., 2020). In reality, there is no clear boundary between the bedload and suspended bed sediment transport (Van Rijn, 1993) and the separation between the two transport modes only exists for the purpose of mathematical representation. In this study, the bedload transport corresponds to the definition given by Van Rijn (1984b), which includes sediment particles rolling, sliding and saltating. To estimate the relative proportion of bedload transport and suspended bed material load, the suspension number (see Section 3.3.3) defined by Bagnold (1966) is used to estimate the dominant mode of transport (Bagnold, 1966; Van Rijn, 1984a, 1984b; Zomer et al., 2021).

Amongst the methods described within the literature for estimating bedload sediment transport within rivers, three different methods have been selected to compare values based on different input
304 data. The first one is based on differential bathymetry (Leary and Buscombe, 2020; Nittrouer et al., 2008), the second one, named 'dune tracking', is based on dune morphology metrics and dune migration rate (Claude et al., 2012; Engel and Lau, 1980; Leary and Buscombe, 2020; Mcelroy and Mohrig, 2009; Simons et al., 1965), and the last one is based on an empirical approach that estimates the bedload transport with an empirical formula (Van Rijn, 1984b). These methods have been chosen for the reliability of the results they already provided in other studies (Claude et al., 2012; Le Guern et al., 2020; Leary and Buscombe, 2020; Naqshband et al., 2016, 2014) and for the ease of their implementation. Namely, the required data input to estimate the bedload transport with these methods corresponds to standard data acquisitions for studies on sediment dynamics (e.g., bathymetry, flow velocities and grab samples).

### 3.3.1. Sediment flux from differential bathymetry

315 The first method used to estimate the sediment bedload is differential bathymetry. It is based on the integration of the sediment volume transported between two different bathymetric acquisitions. This method assumes that the volume eroded on the stoss side of a dune is deposited on the lee side, integrating bed material entering suspension (Claude et al., 2012; Gaeuman and Jacobson, 2007; Simons et al., 1965; van den Berg, 1987). Differential bathymetry between the 23rd and 25th of March and then between the 25th and 29th of March was calculated for both ROI1 and ROI2 areas. For ROI3 area, because of smaller bedforms with strong dynamics preventing feature tracking over several days, only the differential bathymetry between the 25th am and 25th pm was calculated. For each individual dune, the displaced sediment volume was calculated by integrating the difference between two DEMs along each migration segment, then integrated to 1 m sections along the dune crests (which corresponds to the spacing between migration segments) (Fig. 4). Bedload transport was then estimated by dividing the sediment volume by the time between the bathymetric acquisitions and multiplying the results by the sediment density. For this method, the main uncertainty corresponds to the bathymetric data, which includes the MBES precision and positioning errors, with both GPS precision and ship attitude (see Section 3.4). According to Nittrouer et al. (2008), when applying the
330 differential bathymetry method to estimated displaced sediment volumes, a portion of the sediment 331 displaced is not taken into account. The percentage of missed displaced sediment volume was 332 estimated using the Nittrouer et al. (2008) conceptual model, giving the missed percentage as a 333 function of the dune migration expressed in radians. Here, the missed percentage does not exceed 2% 334 of the displaced sediment volume captured by the differential bathymetry. 335

336 3.3.2. Sediment flux from dune morphology and migration rate

336 The second method used to assess bedload transport is the ‘dune tracking’ method (Claude et al., 337 2012; Engel and Lau, 1980; Hoekstra et al., 2004; Leary and Buscombe, 2020; Mcelroy and Mohrig, 338 2009; Schmitt and Mitchell, 2014; Simons et al., 1965). It relies on the morphological characterisation 339 of dune geometry and the migration rate of the dunes along the bed elevation profiles. The dune 340 tracking equation is:

341 $Qb_{DTM} = \rho_s \times \varepsilon \times f \times C_d \times H_d$

342 Eq. (4)

343 where $Qb_{DTM}$ is the sediment flux associated with the dune migration. It corresponds essentially to 344 bedload transport (kg.s⁻¹.m⁻¹); $\rho_s$ the sediment density (kg.m⁻³); $\varepsilon$ the sediment concentration assumed 345 to be equal to 0.65 for sands (corresponding to 1-porosity, assuming a sand porosity of 0.35) (Claude 346 et al., 2012); $C_d$ the dune migration rate (m.s⁻¹); $H_d$ the dune height (m); and $f$ the dimensionless shape 347 factor. The parameter $H_d$ corresponds to the height between the crest and the downstream trough of 348 the dune, which has been averaged for each ROI (Table 2). The $C_d$ parameter corresponds to the 349 migration distance averaged for each dune and then each ROI, over the time period between two 350 successive bathymetric acquisitions.

351 In the case of dune cross sections being perfectly triangular, the coefficient $f$ is equal to 0.5 (Claude et 352 al., 2012; Simons et al., 1965). However, to take into account the deviation of the bedform shape, this 353 shape factor has been adapted to be equal to the ratio between the cross-sectional area of a dune and
the cross-sectional area of a triangular dune with the same length and height (Hoekstra et al., 2004;

Schmitt and Mitchell, 2014):

$$f = \frac{V}{\lambda \times H_d}$$

Eq. (5)

where $\lambda$ is the dune wavelength (m) and $H_d$ the dune height (m). The parameter V corresponds to the

dune surface (m²), and is expressed as:

$$V = \frac{L_d \times H_d}{2}$$

Eq. (6)

where $H_d$ is the dune height (m) and $L_d$ the dune length (m). In this study, values for the coefficient f

range from 0.48 to 0.5. By applying this factor, the suspended bed material load bypassing dunes is

neglected (Claude et al., 2012; Le Guern et al., 2020; Mcelroy and Mohrig, 2009; Simons et al., 1965)

to only represent the sediment transport of the dune.

For both ROI1 and ROI2, bedload transport from the ‘dune tracking’ method was estimated between

the 23rd and 25th of March, and between the 25th and 29th of March. For ROI3, the bedload transport

was only estimated for the 25th of March, between the morning and the afternoon, since dune

migration for larger time periods is difficult to estimate (see remark in Section 3.3.1).

For the dune tracking method, uncertainties are essentially related to bedform morphology

measurements and also to the bedform migration celerity (see Section 3.4). All these parameters have

been averaged over the extent of the ROIs, which helps to smooth the effect of artefacts and manual

picking errors, but it also reduces the precision of the methods by excluding local variations of

transport.

Overall, uncertainties related to all measurements are difficult to constrain and quantify, but according

to other studies (Ancey and Pascal, 2020; Claude et al., 2012; Frings and Vollmer, 2017; Kleinhans and
Brinke, 2001; Rennie and Church, 2010), they are not the only source of errors. In fact, studies have highlighted that a portion of the bedload discharge corresponding to grains jumping from one dune to another is not taken into account by the dune tracking method (Claude et al., 2012; Gaeuman and Jacobson, 2007; Simons et al., 1965; van den Berg, 1987), which are also likely to affect the estimation of bedload transport (Gaeuman and Jacobson, 2007; Kostaschuk et al., 1989; van den Berg, 1987). However, based on laboratory (Simons et al., 1965) and field studies (Claude et al., 2012; Gaeuman and Jacobson, 2007; Villard and Church, 2003), the suspended-load transport participating in dune migration is usually considered as negligible.

### 3.3.3. Bedload sediment transport capacity from empirical formula (Van Rijn, 1984b)

Several empirical formulas were considered for this study. In the context of large sand and sand-gravel rivers, the steady flow formula from (Van Rijn, 1984b) for bedload transport provides accurate estimates (Claude et al., 2012; Kleinhans and van Rijn, 2002; Le Guern et al., 2020; Pinto Martins et al., 2009). This Van Rijn formula is described as suitable for sediment grain sizes ranging from 0.2 to 2 mm, which covers the median grain size ($D_{50}$) range of the sediment bed samples of the study area. Also, as this Van Rijn equation is one dimensional and non-linear, the use of local hydraulic parameters such as flow values is suitable.

The Van Rijn formula for estimating bedload transport capacity is:

$$Qb_{VR} = \frac{0.053 \times T^{2.1}}{D_{*}^{0.3}} \times [(s - 1)g]^{0.5} \times D_{50}^{1.5}$$

Eq. (7)

where $Qb_{VR}$ is the bedload transport (kg.s⁻¹.m⁻¹); $s$ the sediment density ratio derived from the sediment bulk density (Table 4) and water density (1000 kg.m⁻³); $D_{50}$ the median grain size (m) of the sediment bed sampled during this study (Table 4); $D^*$ the scaled particle diameter (Eq. (8)):
$$D_{*} = D_{50} \times \left( \frac{(s-1)g}{\vartheta^2} \right)^{\frac{1}{3}}$$

Eq. (8)

where g is the gravitational acceleration (9.81 m.s⁻²) and ν the water kinematic viscosity (1x10⁻⁶ m².s⁻¹).

The parameter T corresponds to the transport stage parameter, which is defined as:

$$T = \frac{u_{*}^{2} - u_{cr}^{2}}{u_{cr}^{2}}$$

Eq. (9)

where $u_*$ is the bed shear velocity (Eq. (10)) and $u_{cr}$ the critical bed shear velocity:

$$u_{*} = \frac{g^{0.5} \times \bar{u}}{C'}$$

Eq. (10)

where $\bar{u}$ is the flow velocity in m.s⁻¹, here averaged from all valid ADCP data bin velocities over a section corresponding to the extent of the ROIs; g the gravitational acceleration and C' is the Chézy coefficient related to grain roughness only, expressed as:

$$C' = 18 \times \log \left( \frac{12 \times Rh}{3 \times D_{90}} \right)$$

Eq. (11)

where Rh is the hydraulic radius corresponding to the water depth (m) when the river width is much higher than the water depth (Bjerklie et al., 2005; Wu et al., 2000); D₉₀ is the grain size for which 90% of the bed sediment particles are lower in size.

The effective Shields parameter θ is defined as follows (Kleinhans et al., 2002; Vah et al., 2020):
$$418 \qquad \theta = \frac{u_*^2}{(s-1) \times g \times D_{50}}$$

Eq. (12)

420 The critical bed shear velocity is defined from Shields (Van Rijn, 1984b) as:

$$421 \qquad \theta_{cr} = \frac{u_{cr}^2}{(s-1) \times g \times D_{50}}$$

Eq. (13)

423 and is used to define $u_{cr}^2$:

$$424 \qquad \theta_{cr} = 0.14 \times D_*^{-0.64} \quad \text{for } 4\<D_*\le10$$

Eq. (14)

$$426 \qquad \theta_{cr} = 0.04 \times D_*^{-0.1} \quad \text{for } 10\<D_*\le20$$

Eq. (15)

428 The bedload transport rates were estimated for each ROI on the 24th of March (in the first interval between the two first bathymetric acquisitions of the 23rd and 25th of March) with the ADCP flow velocity data collected.

431 According to a sensitivity analysis performed by Claude et al. (2012), only the flow velocity parameter is likely to sensibly affect the bedload transport estimation from the Van Rijn (1984b) formula. Since the input flow velocity corresponds to the averaged velocity over the whole water column and over each dune area (ROI1 to ROI3), uncertainties associated to local velocity variations are considered as negligible. Also, according to other studies in fluvial environments, assessment of flow velocity uncertainties mostly led to random errors that cannot be considered confidently in the bedload transport estimation (Claude et al., 2012; Rennie and Church, 2010).

438 The empirical formula used to estimate bedload transport capacity is established within a context of unlimited sediment supply. In the case of a limited sediment supply, a correction factor can be applied to the bedload transport rates according to Vah et al. (2020):
$$441 \qquad Qb_{VR}Corr = (1 - p) * Qb_{VR}$$

Eq. (16)

where *p* corresponds to the riverbed surface of non-mobile sediment (%) and $Qb_{VR}$ is the unit bedload transport rate for unlimited sediment supply.

Furthermore, to determine the relative importance of bedload transport to suspended load, the suspended number has been calculated (Bagnold, 1966; Zomer et al., 2021). It corresponds to the ratio of the bed shear velocity ($u_*$) and particle fall velocity (ws), which is defined as (Cheng, 2009; Zomer et al., 2021):

$$449 \qquad w_s = \sqrt{\frac{4}{3}(s-1)\frac{g \times D_{50}}{C_D}}$$

with $C_D$ as the drag coefficient (Zomer et al., 2021):

$$451 \qquad C_D = \frac{432}{D_*} (1 + 0.022 D_*^3)^{0.54} + 0.47(1 - \exp(-0.15 D_*^{0.45}))$$

According to Van Rijn (1984a), the initiation of suspension starts when $u_*/w_s \ge 0.4$. While this ratio is lower than 1, the bedload is the dominant transport mode (Zomer et al., 2021).

### 3.4. Semi-quantitative uncertainty assessment of field measurements and dune characterisation

Considering the challenge of assessing some error sources, such as the lag in GPS input corrections and uncertainties around acoustic velocity corrections for the input data, or parameter calculation for dune morphometry, a semi-quantitative error estimation was performed.

The horizontal accuracy of the Trimble® 540TS GNSS receiver with the integrated POS MV appliance is 0.02 m, with a vertical accuracy of 0.05 m. During periods of interrupted connection RTK correction (approximately less than 5% of survey time), the positioning system switched to DGPS mode, where the worse accuracies were 0.20 m horizontally and 0.50 m vertically.
According to the MBES datasheet, the Real Time Appliance synchronizes all the attitude measurements with accuracy of 0.10 m. The vertical accuracy of the MBES was estimated to be ±0.10 m. Controls were performed on fixed points (e.g., rock outcrops and mooring buoy) to assess the uncertainty of the bathymetry data at the different acquisition dates. The deviation varies in a range of +/- 0.05 m. Therefore, the uncertainty of bathymetry data is evaluated to be +/-0.15 m at maximum.

Regarding the aDcp data acquired with ROWE® SEASEVEN©, both 600 kHz and 1200 kHz beams have accuracies of ±0.002 m/s and a single ping precision of 0.035 m/s. Considering these values and the averaging of both pings and bins values over the different ROI, aDcp values uncertainties are relatively limited compared to the GPS uncertainties, which was used to correct ship velocity from the aDcp data.

Beyond uncertainties related to bathymetry data accuracy and precision, BTT parameter calculations are performed after slope detrending and consider dunes as continuous forms (Van der Mark et al., 2008) (i.e., the downstream foot of a dune coincides with the upstream foot of the next one), leading to possible uncertainties in the estimation of morphological parameter values. In particular, the BTT tool does not consider gaps in between dunes that may exist along the dune field, and may induce overestimation of dune lengths. To estimate uncertainties, morphological parameters (dune height, dune length and dune wavelength) using the detrended BTT profile were also manually calculated for the date of the 25th of March within ROI2, for one of every three profiles. Since the dune height, wavelength and length are used in the Dune Tracking formula (form factor), the propagated uncertainty on sediment fluxes values calculated from the Dune Tracking method was assessed. Results (morphological parameters and sediment fluxes) derived from the BTT extraction (for 27 dunes) are presented with the percentage of difference with the manually extracted and derived values.
485 **4. Results and interpretation**

486 **4.1. General morphology**

487 Within the centre of the river, the main riverbed corresponds to flat areas suited for navigation, while
488 shoals occur on both sides of the river (Fig. 5a). Depending on their morphology, irregular or smooth,
489 these shoals are interpreted as outcropping rocky basement (essentially on the right river side) or sand
490 bars (essentially on the left side of the river), respectively. On the southwestern corner of the study
491 area, along the left side of the river, a trough about 2.2 m deep is disconnected from the flat area by
492 shoals characterised by rough and irregular morphologies, interpreted as outcropping rocky basement
493 (Fig. 5a). The occurrence of outcropping basement is clearly evidenced on the right side of the river.
494 These basement outcrops are characterised by heights varying between 0.5 and 1 m and they are
495 characterised by rough contours and relatively flat tops. On the left side of the river (Fig. 5a), bedrock
496 outcrops are almost absent and mounds, smooth features different from outcropping rocky basement,
497 have heights between 0.3 and 1.1 m and diameters of 2.5 to 27 m. They are interpreted as formed
498 either by modern indurated clay or rocky basement outcrops (Bassompierre and de Mautort, 1967)
499 blanketed by sediments. Furthermore, two dune corridors have been recognised and extend from the
500 upstream to the downstream limit of the studied area.

501 **4.2. Dune morphologies and migration**

502 **4.2.1. Spatial distribution and morphometry**

503 In the study area, dunes are restricted to the left side of the river and centre of the river, and extend
504 along two corridors (Fig. 5a and b). The first corridor develops along the left riverbank, over a distance
505 of 940 m with a width varying between 12 and 50 m. Its connection to the riverbank is not mapped
506 because of navigation restrictions. The second corridor of dunes extends on the flat area near the
507 centre of the river. This corridor is narrower, with a width ranging between 8 and 30 m, but is longer
508 than the survey cover.
Within the corridor located along the left bank (Fig. 5a and b), the features have an average wavelength between 8.3 and 9 m, an average length between 8.8 and 8.3 m, and average heights of 0.2 to 0.3 m (Table 2), in ROI1 (Fig. 5d) and ROI2 (Fig. 5c), respectively. Comparing values obtained from the BTT tool and from manual extraction, the height and dune wavelength are consistent with an average error (difference from BTT values) of about 3%. However, those calculations highlight that the BTT tool overestimates the dune length by about 10% on average.

According to bedform orientation (orthogonal to river flow), geometry and dimensions (Ashley, 1990), these bedforms correspond to medium dunes (ROI1 and ROI2). On average, dunes are characterized by a steepness of 0.031 within ROI1, and of 0.027 within ROI2. Dunes from ROI1 and ROI2 show a similar average stoss side slope angle of 2.76° and 2.60°, respectively. However, dunes are different with regards to their lee side slope angle, with average slope angles of 6.12° for ROI1 and 4.62° for ROI2, and average maximum slope of 18.09° and 16.19°, respectively. The total crest length cannot be inferred because of the limited bathymetric cover close to the side of the river, which does not allow us to have the entirety of the features. However, sinuosity values have been calculated for the dune crest portions recognised on bathymetry data. Average dune sinuosity in ROI1 is about 1.05 and 1.1 in ROI2. Based on sinuosity values and visual observations, dune crest geometry changes upstream (ROI1) to downstream (ROI2), from a linear slightly irregular shape (Fig. 5d) to an irregular shape, locally sinuous (Fig. 5). The second corridor located in the centre of the river is interpreted as a sand ribbon with a length of 1233 m, width of about 8 to 30 m and height of about tens of centimetres. This sand ribbon is covered with bedforms oriented orthogonally to river flow and characterised by an average wavelength ranging from 4.5 to 5.4 m, average length between 4.4 and 5.4 m and average heights between 0.14 and 0.15 m (Table 2), corresponding to small dunes (Ashley, 1990). The small dunes are characterised by an average steepness of 0.031 and by an average crest sinuosity of 1.12. Between the different acquisition dates, the slope angles of the small dunes varies between 4.40° and 5.61° on the lee side, and between 2.78° and 3.31° on the stoss side, with the maximum slope varying between 13.49° and 15.02°. The relationship between the dune height and dune wavelength shows a consistent
general trend for three dates, but differences between the three ROIs occur. The small dunes are
535
clearly separated from the medium dunes, and the medium dunes within ROI2 displays lower heights
536
compared to ROI1, although having similar wavelength.
537

Within ROI2, local depressions have been evidenced within the troughs in-between dunes. These 538 depressions are sub-circular and are characterised by a deepening of about 0.1 m (Fig. 5c). This type 539 of features is also evidenced within ROI3 (Fig. 5e), in the trough in-between small dunes. There, the 540 depth of these incisions does not exceed few centimetres (0.02-0.05 m). 541

<figure><img src="image_7.png" /><figcaption>Fig. 5: Interpreted map of the studied Seine River section morphology with location of grab samples and associated sediment classes according to Folk (1954) (a). Bathymetric data zoom on the river section (b) where the three different ROI (1,2 and 3) and associated bathymetry have been extracted (c, d, e) for the analysis of dune morphometry and migration.</figcaption></figure>

542

543

544

545

546
547

Table 2: Summary of morphometric parameters (dune wavelength, dune height, dune length, dune lee side slope angle and dune stoss side slope angle) extracted with the BTT method (Van der

548

Mark et al., 2008) and averaged for each ROI, at the different date of acquisition. For dune maximum slope see Section 3.2. For average shape factor Eq. (4) and Eq. (5). For steepness and

549

sinuosity indexes see Section 3.2

<table><thead><tr><th rowspan="3">Parameter</th><th colspan="6">ROI2 (downstream)</th><th colspan="6">ROI1</th><th colspan="6">ROI3 (upstream)</th></tr><tr><th colspan="2">23-March</th><th colspan="2">25-March</th><th colspan="2">29-March</th><th colspan="2">23-March</th><th colspan="2">25-March</th><th colspan="2">29-March</th><th colspan="2">23-March</th><th colspan="2">25-March am</th><th colspan="2">25-March pm</th><th colspan="2">29-March</th></tr><tr><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>std</th></tr></thead><tbody><tr><td>BTT dune wavelength (m)</td><td>8.55</td><td>1.62</td><td>8.55</td><td>1.09</td><td>8.67</td><td>1.03</td><td>8.86</td><td>0.70</td><td>8.93</td><td>1.66</td><td>9.05</td><td>2.16</td><td>4.48</td><td>1.13</td><td>4.47</td><td>0.67</td><td>4.53</td><td>0.71</td><td>5.39</td><td>1.12</td></tr><tr><td>BTT dune height (m)</td><td>0.22</td><td>0.04</td><td>0.23</td><td>0.04</td><td>0.22</td><td>0.04</td><td>0.29</td><td>0.07</td><td>0.29</td><td>0.08</td><td>0.28</td><td>0.09</td><td>0.14</td><td>0.04</td><td>0.14</td><td>0.04</td><td>0.15</td><td>0.04</td><td>0.14</td><td>0.04</td></tr><tr><td>BTT dune length (m)</td><td>8.26</td><td>1.39</td><td>8.40</td><td>0.90</td><td>8.38</td><td>0.01</td><td>8.72</td><td>0.66</td><td>8.8</td><td>1.36</td><td>8.96</td><td>1.65</td><td>4.37</td><td>0.94</td><td>4.44</td><td>0.64</td><td>4.50</td><td>0.67</td><td>5.37</td><td>1.12</td></tr><tr><td>BTT slope lee side (°)</td><td>4.44</td><td>1.12</td><td>4.87</td><td>1.14</td><td>4.55</td><td>0.85</td><td>6.06</td><td>1.82</td><td>6.20</td><td>2.22</td><td>6.11</td><td>2.19</td><td>5.34</td><td>1.37</td><td>5.20</td><td>1.06</td><td>5.61</td><td>1.36</td><td>4.4</td><td>1.00</td></tr><tr><td>BTT slope stoss side (°)</td><td>2.62</td><td>0.56</td><td>2.62</td><td>0.52</td><td>2.57</td><td>0.42</td><td>2.8</td><td>0.41</td><td>2.79</td><td>0.32</td><td>2.70</td><td>0.43</td><td>3.31</td><td>0.60</td><td>3.26</td><td>0.62</td><td>3.29</td><td>0.77</td><td>2.78</td><td>0.62</td></tr><tr><td>Dune maximum slope (°)</td><td>15.12</td><td>4.88</td><td>16.64</td><td>4.67</td><td>16.8</td><td>5.08</td><td>17.92</td><td>6.25</td><td>17.96</td><td>6.72</td><td>18.39</td><td>6.84</td><td>13.57</td><td>4.34</td><td>14.51</td><td>3.91</td><td>15.02</td><td>5.05</td><td>13.49</td><td>4.65</td></tr><tr><td>Shape factor</td><td>0.48</td><td></td><td>0.49</td><td></td><td>0.48</td><td></td><td>0.49</td><td></td><td>0.49</td><td></td><td>0.50</td><td></td><td>0.49</td><td></td><td>0.50</td><td></td><td>0.50</td><td></td><td>0.50</td><td></td></tr><tr><td>Steepness index</td><td>0.027</td><td></td><td>0.027</td><td></td><td>0.026</td><td></td><td>0.033</td><td></td><td>0.033</td><td></td><td>0.031</td><td></td><td>0.032</td><td></td><td>0.032</td><td></td><td>0.033</td><td></td><td>0.026</td><td></td></tr><tr><td>Sinuosity</td><td>1.10</td><td>0.05</td><td>1.10</td><td>0.07</td><td>1.08</td><td>0.08</td><td>1.03</td><td>0.01</td><td>1.06</td><td>0.02</td><td>1.07</td><td>0.03</td><td>1.11</td><td>0.07</td><td>1.10</td><td>0.08</td><td>1.12</td><td>0.06</td><td>1.15</td><td>0.09</td></tr></tbody></table>

550

551
Over the period of survey, the general morphology of the medium and small dunes barely varied within each ROI. The height of the bedforms did not change significantly (approximately 2% of the height) and only their wavelength and length elongated slightly. Most of the wavelength variations are within the range, or below, the bathymetric grid resolution (0.15 m), and the dune height variations are systematically lower than the bathymetric vertical accuracy of 0.50 m. Hence, the dune morphological parameters are considered to not display temporal evolution at the scale of the 3-day study period.

<figure><img src="image_8.png" /><figcaption>Fig. 6: Comparison of dune parameters between ROI1 (blue), ROI2 (green) and ROI3 (yellow), for the three dates of acquisition, with display of dune height against dune wavelength scatter plot, dune sinuosity histogram and dune lee side max slope histogram.</figcaption></figure>

558

559

560

561
562

4.2.2. Migration rates

563

564

565

566

567

568

569

570

571

Over the three dates of bathymetric acquisitions, the migration of the dunes has been clearly evidenced, in both medium and small dune corridors (Fig. 7). The migration rates (Table 3) were calculated from dune displacements measured over the different periods. All displacements are significant enough, since they are greater than several times the resolution of the bathymetric grid (Fig. 7). However, regarding the migration of the small dunes (ROI3), the evolution of the features could only be analysed between the 25th morning and afternoon where it is possible to recognise each individual small dune. For the other longer periods, small dune displacement is too important, probably larger than a wavelength, and associated with feature merges and dissociations, which does not allow recognition of small dunes from one date to the other.

572

573

574

575

576

The dune migration between the 23rd and 25th varies between 1.97x10⁻¹ and 1.80x10⁻¹ m.d⁻¹ within ROI1 and ROI2, respectively (Table 3). This migration rate decreases between the 25th and the 29th to rates of 8.90x10⁻² m.d⁻¹ in ROI1 and 1.31x10⁻¹ m.d⁻¹ in ROI2, along with the river flow decreases. Within ROI3, the migration rate of the small dunes is of 2.04 m.d⁻¹, between the 25th am and 25th pm (Table 3).
Differential bathymetry

<figure><img src="image_9.png" /></figure>

Dune crests migration

<figure><img src="image_10.png" /><figcaption>Fig. 7: Digitized dune crests within ROI2 (a), ROI1 (b) and ROI3 (c), at the different date of acquisition, 23rd of March (blue), 25th of March (green) and 29th of March (red). For ROI3, digitized dune crests mapped on the 25th March morning are displayed in green and in yellow for the one mapped in the afternoon of 25th of March. Extracted bed elevation profiles (location on (b)) are displayed in (d).</figcaption></figure>

<table><caption>Table 3: Dune migration rate between the 23rd-25th of March, then 25th-29th of March for both ROI1 and ROI2, and between the 25th of March morning and afternoon for ROI3. Average, standard deviation, minimum and maximum values of the dune migration for each ROI and each time period are displayed in m.d⁻¹.</caption><thead><tr><th rowspan="2">ROI</th><th colspan="2">ROI2 (downstream)</th><th colspan="2">ROI1</th><th>ROI3 (upstream)</th></tr><tr><th>23rd-25th</th><th>23rd-25th</th><th>25th-29th</th><th>25th-29th</th><th>25th am - pm</th></tr></thead><tbody><tr><th>Period</th><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Average migration (m/d)</th><td>8,9E-02</td><td>2.0E-01</td><td>1,8E-01</td><td>1,3E-01</td><td>2.0</td></tr><tr><th>Maximum migration (m/d)</th><td>1.0</td><td>1.0</td><td>4.3E-01</td><td>6.0E-01</td><td>6.1</td></tr><tr><th>Standard deviation (m/d)</th><td>2.8E-01</td><td>2.6E-01</td><td>1.3E-01</td><td>1.7E-01</td><td>1.2</td></tr></tbody></table>
587 4.3. Hydrodynamics and sediment cover

588 Regarding hydrodynamics, mean flow velocities established from the ADCP profiles on the 24th of
589 March (Q=700 m³.s⁻¹) reaches 0.60 m.s⁻¹ and 0.59 m.s⁻¹ over ROI1 and ROI2, respectively. Over ROI3,
590 the mean flow velocities reaches 0.74 m.s⁻¹. The average flow velocity decreases from upstream (ROI1)
591 to downstream (ROI2) and increases towards the centre of the river section where small dunes occur
592 (ROI3). Following average flow velocities, depth values at the grab sample locations and sediment
593 grain-size parameters (Table 4), the parameter θ systematically exceeds the threshold of sediment
594 transport θcr (Table 4). The difference between them never exceeds 0.1, indicating that bedload is the
595 dominant transport mode (Tuijnder and Ribberink, 2012; Vah et al., 2020). The studied section is
596 characterised by five types of sediment (Table 4): gravelly sands, slightly gravelly sands, sands, slightly
597 gravelly sandy muds and muddy gravels (Folk, 1954) (Fig. 5 and Table 4). A general fining trend is
598 observed from upstream to downstream, with the most sandy samples located over the shoal
599 morphologies interpreted as sand bars (Fig. 5), while more muddy samples are located over the flatter
600 areas (Fig. 5). The small dunes corridor (ROI3) is characterised by a dominance of gravelly sands (within
601 ROI3) with the occurrence of a muddy gravel sample located downstream ROI3. Within the medium
602 dune areas (ROI1 and ROI2), the dominant sediment type corresponds to slightly gravelly sands with
603 one sand sample between ROI1 and ROI2 (Fig. 5) and a slightly gravelly sandy mud sample downstream
604 ROI2. The slightly gravelly sand sample, upstream, in ROI1, is slightly coarser (D50 = 545 µm) than the
605 one downstream in ROI2 (D50 = 367 µm) (Table 4). Between the small and medium dunes corridors,
606 the riverbed is also fining from upstream to downstream from slightly gravelly sand to mostly slightly
607 gravelly sandy mud. In muddy sediments (mud content up to 64%), the mud is compact with the
608 sediment being bimodal and poorly sorted (VEN1-2; Table 4). This tends to indicate a lag muddy
609 sediment partly covered with a fine layer of sands. Focusing on the mobile sediment cover (sand and
610 gravels), the grain of VEN1-2 becomes unimodal with a mode similar to that of sample VEN1-4. Grain-
611 size parameters of the mobile fraction (sands and gravels) evidenced the fining trend from upstream
612 to downstream with: (i) the gravel content decreasing downstream to the detriment of the sand
content, and (ii) D50 and D90 decreasing from 832.5 to 366.8 µm and from 1649.5 to 640 µm, respectively (Table 4).

615

Table 4: Summary table of the grain size analysis parameters and sediment classes from Folk (1954) for each sediment samples located within the ROIs. Sample VEN1-2 is located outside the ROI (cf. Fig. 5). The sediment densities (psed) have only been measured for the sediment samples used as inputs into bedload transport estimation equations. θ is the dimensionless effective Shields parameter (Kleinhans and van Rijn, 2002; Vah et al., 2020).

617

618

619

<table><thead><tr><th>Sample ID</th><th>VEN1-2 downstream ROI2</th><th>VEN1-4 in ROI2 (downstream)</th><th>VEN1-5 in ROI1</th><th>VEN1-13 in ROI3 (upstream)</th></tr></thead><tbody><tr><td>Water depth (m)°</td><td>4.9</td><td>4.4</td><td>3.8</td><td>4.8</td></tr><tr><td>Textural group</td><td>Slightly Gravelly Sandy Mud</td><td>Slightly Gravelly Sand</td><td>Slightly Gravelly Sand</td><td>Gravelly Sand</td></tr><tr><td>Sorting</td><td>Bimodal Extremely Poorly sorted</td><td>Unimodal Moderately Well Sorted</td><td>Unimodal Moderately Well Sorted</td><td>Unimodal Moderately Sorted</td></tr><tr><td>%Gr</td><td>0.8</td><td>1.6</td><td>4.3</td><td>6.9</td></tr><tr><td>%S</td><td>35.2</td><td>9.2</td><td>95.5</td><td>93</td></tr><tr><td>%M</td><td>64</td><td>0.2</td><td>0.2</td><td>0.1</td></tr><tr><td>D50 (µm)</td><td>9,245</td><td>366.8</td><td>545.2</td><td>832.5</td></tr><tr><td>D90 (µm)</td><td>360.8</td><td>640</td><td>929.5</td><td>1649.5</td></tr><tr><td>Mod 1 (µm)</td><td>357.5</td><td>357.5</td><td>565</td><td>715</td></tr><tr><td>Mod 2 (µm)</td><td>71.5</td><td>n.d.</td><td>n.d.</td><td>n.d.</td></tr><tr><td>psed (kg/m³)</td><td>n.d.</td><td>2380</td><td>2375</td><td>2440</td></tr><tr><td>ū (m.s⁻¹)</td><td>n.d.</td><td>0.60</td><td>0.61</td><td>0.74</td></tr><tr><td>θ transport</td><td>n.d.</td><td>0.110</td><td>0.085</td><td>0.084</td></tr><tr><td>θcr transport</td><td>n.d.</td><td>0.035</td><td>0.031</td><td>0.031</td></tr><tr><td>u*/w<sub>s</sub></td><td>n.d.</td><td>0.50</td><td>0.34</td><td>0.26</td></tr></tbody></table>

620

Considering the MBES backscatter data (Fig. 8), the sediment cover in the small dunes area (ROI3) is homogenous (Fig. 8c). While absolute backscatter values (range of values between 30 and 85 dB) cannot be use here because of artefacts, relative amplitude variations outside the nadir areas can be interpreted as sediment cover variations (see Section 3.1.1). In the medium dune areas (ROI1 and ROI2), bathymetric and backscatter profiles clearly evidence variations of backscatter values at the base of the lee side of the dune, with relatively higher backscatter values (+5-10%). This acoustic facies has also been evidenced downstream in the troughs between successive dunes (Fig. 8). There, the
backscatter values display a similar pattern of 10% higher amplitudes. Also, this acoustic facies has herein been sampled and is characterised by a sandy mud, where mud is plastic compacted (Fig. 8 and Table 4). Hence, this facies located in the dune troughs is interpreted as a compacted or even hard substrate, different from the gravelly sand constituting the dunes. Such compacted sediments can be considered as a lag non-mobile riverbed. This indicates that the mobile sediment cover (sand and gravels) is not complete in the study area (in ROI1 and ROI2 at least), and probably less complete downstream (e.g., in ROI2 compared to ROI1) given the sediment fining trend from upstream to downstream.

Areas uncovered by sands and gravels represent approximately 10% and 20% of the total surface within ROI1 and ROI2, respectively. The occurrence of areas uncovered by mobile sediment implies non deposition because of sediment bypass or sediment erosion, which suggests conditions of limited sediment supply. This observation is also supported by the fact that bedrock is exposed in many places of the study area, indicating areas deprived of recent sediment cover. Moreover, the increasing surface percentage uncovered by mobile sediment from upstream (ROI1) to downstream (ROI2) tends to evidence an increase of the limited sediment supply conditions down the river.
<figure><img src="image_11.png" /><figcaption>Fig. 8: Backscatter data of each ROI (a, b, c) with location of sediment samples and location of extracted bathymetric and backscatter profiles within ROI1 (d). Extracted backscatter along the profile (d) are displayed as raw data (dashed line) and as mobile average data (n=5) (plain line). Bathymetry data (e) and backscatter data (f) with location of the sediment sample VEN1-2 located downstream ROI2 (Fig. 5), with picture of the sample (g). Extracted bathymetry and backscatter data along the profile (e, f) are displayed in (h), with backscatter data displayed as raw data (dashed line) and as mobile average data (n=5) (plain line).</figcaption></figure>

## 4.4. Unit bedload transport

The unit bedload transport corresponds to the local bedload transport integrated along a 1-m section cross-sectionally. For the differential bathymetry, dune tracking and empirical formula methods were explored to assess bedload transport, the unit bedload was calculated by using the averaged sediment
volume displaced, migration values of the dune (Table 4), sediment grain size and the averaged flow velocities (Table 3).

### 4.4.1. Differential bathymetry

The unit bedload transport from the differential bathymetry method is displayed in Table 5. Between the 23rd and 25th, the transport rates are 0.94 g.s⁻¹.m⁻¹ for ROI1 and 0.64 g.s⁻¹.m⁻¹ for ROI2. For the period over the 25th and 29th, the transport rate is 0.42 g.s⁻¹.m⁻¹ for ROI1 and 0.49 g.s⁻¹.m⁻¹ for ROI2. Within ROI3, the transport rate from differential bathymetry reaches 4.22 g.s⁻¹.m⁻¹ between the 25th morning and 25th afternoon.

### 4.4.2. Dune tracking

From the dune tracking method, the unit bedload transport (Table 5) during the period of the 23rd to the 25th is 0.5 g.s⁻¹.m⁻¹ and 0.34 g.s⁻¹.m⁻¹ for ROI1 and ROI2, respectively. Between the 25th and 29th, the transport rates are 0.22 g.s⁻¹.m⁻¹ for ROI1 and 0.27 g.s⁻¹.m⁻¹ for ROI2. For ROI3, the transport rate reaches 2.55 g.s⁻¹.m⁻¹. Regarding uncertainties related to the morphological parameter extraction (see Section 3.4), the QbDTM value derived from manual extraction would be about 8.5% lower compared to values derived from BTT extraction.

### 4.4.3. Empirical formula

From the sediment and current data, u*/w_s values are always below the threshold of 1 (Table 4), indicating that bedload transport is the dominant mode of transport. This observation is consistent with the differences between θ and θ_c parameter values, less than 0.1 in our study, which indicate that the bedload is the dominant mode of transport (Tuijder and Ribberink, 2012; Vah et al., 2020). Regarding the suspension number (u*/w_s) threshold value of 0.4 (Van Rijn, 1984a; Zomer et al., 2021) for which suspension can be initiated, in our study the suspension number values only exceeds it in ROI2 (see Section 4.2 and Table 4). In this study, these observations allow us to validate the use of the Van Rijn formula for bedload transport solely.
The Van Rijn (1984b) empirical formula (Eq. (7)) gives estimation of the unit bedload transport capacity within a context of infinite sediment supply (Vah et al., 2020; Van Rijn, 1993). In this study, the dunes migrate in a context of partial mobile sediment cover over ROI1 and ROI2 (cf. Section 4.3). Therefore, the coefficient factor corresponding to the percentage of the riverbed surface uncovered by mobile sediment (p; Table 5) has been applied to the transport rate values obtained, as proposed by (Vah et al., 2020) (Eq. (16)). The percentages of the riverbed surface covered with mobile sediment (1-p) correspond to 90% and 80%, respectively, for ROI1 and ROI2 (see Section 4.3). Within ROI3, the mobile sediment layer covers 100% of the surface. Hence, no correction factor has been applied to the bedload transport capacity associated to the small dunes (ROI3).

The unit bedload transport capacity from the Van Rijn formula (Table 5) has been calculated for the 24th of March, day of the aDcp data acquisition. For ROI1, the unit bedload transport equals 0.82 g.s⁻¹.m⁻¹. In the ROI2, the unit bedload transport is equal to 0.92 g.s⁻¹.m⁻¹. Within ROI3, the unit bedload transport equals 2.33 g.s⁻¹.m⁻¹.

Table 5: Summary table of unit bedload transport estimation based on differential bathymetry, dune tracking method and empirical formulas. Unit bedload transport have been estimated between the 23rd-25th of March and 25th-29th of March for ROI1 and ROI2 and then between the 25th of March morning and afternoon for ROI3. The bed area percentage uncovered by mobile sediment (p) for each ROI is displayed above the unit bedload transport rate estimation and has been used as a correcting factor (cf. Eq. (16)) for the estimations from the empirical formula.

<table><thead><tr><th>Area</th><th colspan="2">ROI2 (downstream)</th><th colspan="2">ROI1</th><th>ROI3 (upstream)</th></tr></thead><tbody><tr><th>Period</th><td>23/03 - 25/03</td><td>25/03 - 29/03</td><td>23/03 - 25/03</td><td>25/03 - 29/03</td><td>25/03 am - pm</td></tr><tr><th>Time between acquisition (h)</th><td>45</td><td>96</td><td>45</td><td>96</td><td>2.3</td></tr><tr><th>Percentage area uncovered by mobile sediment (%)</th><td colspan="2">20</td><td colspan="2">10</td><td>0</td></tr><tr><th>QbDIFF (g.s<sup>-1</sup>.m<sup>-1</sup>)</th><td>0.64</td><td>0.49</td><td>0.94</td><td>0.42</td><td>4.22</td></tr></tbody></table>
<table><tr><td>QbDTM (g.s<sup>-1</sup>.m<sup>-1</sup>) (Eq. (4))</td><td>0.34</td><td>0.27</td><td>0.50</td><td>0.22</td><td>2.55</td></tr><tr><td>QbVR (g.s<sup>-1</sup>.m<sup>-1</sup>) (Eq. (7))</td><td>0.92</td><td></td><td>0.83</td><td></td><td>2.33</td></tr></table>

### 4.4.4. Comparison of the unit bedload transport values

Independently of the methods, unit bedload transport values decrease through time between the 23rd to 25th and then between the 25th to the 29th of March 2021 (Fig. 9) under decreasing river flow (Fig. 1). Moreover, unit bedload transport values are the highest (for all three methods) within ROI3 (up to four times higher than values in other ROIs for QbDiff; Fig. 9), which corresponds to the small dunes corridor located in the centre of the river, whereas unit bedload transport values are similar in ROI1 and ROI2.

Regarding the different methods, unit bedload transport estimated from the three methods show values of the same order of magnitude. However, in comparison with the dune tracking method, values from differential bathymetry are consistently higher with a factor 1.8, 1.9 and 1.65, respectively, for ROI1, ROI2 and ROI3 (Table 5 and Fig. 9). This difference is increased when considering the uncertainty related to the form factor of the dune tracking method (Sections 3.4 and 4.4.2). From the empirical formula, the difference with the two other methods is not consistent with QbVR being in between QbDIFF and QbDTM for ROI1, greater within ROI2 and lower within ROI3, but differences are small (factor 0.88, 1.44 and 0.55 compared to QbDIFF values).

From a spatial point of view, we observe higher transport estimations in ROI2 (downstream) than in ROI1 upstream for both periods with the van Rijn formula. With the two other methods (differential bathymetry and dune tracking methods), this trend is also observed between the 25th and 29th March. In contrast, these two methods indicate higher transport estimations in ROI1 between the 23rd and the 25th of March. This can be explained by a higher sediment transport during this period in ROI2 with higher bedload (cf. van Rijn estimations) and higher suspension (u*/ws > 0.4 in ROI2; see Table 4), and so sediment particles that can jump more from one dune to another and will not participate in dune
migration and are thus not taken into account in the Differential bathymetry and Dune Tracking methods.

<figure><img src="image_12.png" /><figcaption>Fig. 9: Histogram of the unit bedload transport values grouped by ROI for the different time periods and displaying the estimated values from differential bathymetry (black), dune tracking (dark grey), Van Rijn formula (light grey).</figcaption></figure>

721

722

723

# 5. Discussion

724

## 5.1. Dune morphology under limited mobile sediment cover

725

The medium and small dunes in the studied section of the Seine River correspond to typical bedforms developing in fluvial context (Allen, 1982; Coleman and Nikora, 2011; Kleinhans, 2001). Within this study, the relationship established between the dune length and dune height can be described by the following equation, $Hmean = 0.034\lambda^{0.9341}$ (with $\lambda$ corresponding to the dune wavelength in metres, $r^2=0.6$ for 176 values) (Figs. 6 and 10). On the basis of an extensive compilation of dune shapes from flume experiments and natural study cases from the tidal shelf to estuaries and rivers, Flemming (1988) have established equations to determine both $Hmax$ and $Hmean$. However, the equation defined in the present study differs from those two equations (Fig. 10), with a general downward shift of the dune height. The limited water depth in fluvial context compared to estuarine and marine ones could be an explanation to smaller dunes compared to Flemming's (1988) prediction. The equation established within the Seine River is more similar to the equation established by Francken et al. (2004) in the estuarine section of the Scheldt River (Fig. 10), where limiting factors such as the water depth,

726

727

728

729

730

731

732

733

734

735

736

737
738 grain size or limited sediment supplies (Carling et al., 2000; Claude et al., 2012; Kleinhans et al., 2002)

739 are mentioned.

<figure><img src="image_13.png" /><figcaption>Fig. 10: Log/log plot of the dune height as function of the dune wavelength for ROI1 (circles), ROI2 (squares) and ROI3 (triangles) at the different dates of acquisition, 23rd of March in white, 25th of March in grey and 29th of March in dark grey. For ROI3, dune parameters measured on the 25th of March morning are displayed in grey and in white for the dune parameters measured during the afternoon. Equations of the relationship equations between dune height and wavelength from (Flemming, 1988) are displayed in black (Hmax as plain line and Hmean as dotted line). The equation established by (Francken et al., 2004) is displayed as the dashed grey line. The relationship between the dune height and dune wavelength established within this study for the dunes mapped within the Seine River is displayed as the grey plain line.</figcaption></figure>

748

749 Following the dune steepness measured here and the equilibrium threshold of 0.06 established
750 (Carling et al., 2000; Yalin and Karahan, 1979), dunes and small dunes in the Seine River did not reach
751 an equilibrium state. At equilibrium, dune can reach a maximum height corresponding to
752 approximately 20% of the water depth (Kleinhans et al., 2002). In this section of the Seine River, the
753 dune height does not exceed 7% and 5% for the dunes within ROI1 and ROI2, and 3% for the small
dunes. Hence, water depth cannot be ruled out as a factor limiting the dune height.
754

755 In the study area, limited sediment supply conditions have been evidenced; rock outcrops, sand
756 ribbons and areas deprived of mobile sediment where compacted mud outcrops. The influence of
limited sediment supply is interpreted to have a larger impact in preventing the dune from reaching equilibrium. Interestingly, the development of dunes under limited sediment supply conditions has been described as leading to dunes with longer wavelengths than under unlimited sediment supply conditions in both experimental (Blondeaux et al., 2016; Vah et al., 2020) and numerical works (Mazzuoli et al., 2016). In fact, the dune wavelength increases under a limited sediment supply condition is more likely to be relative. In this study, the vertical shift displayed in dune height versus dune wavelength shows that the dunes are morphologically constrained by the limited sediment supply. Another morphological parameter displays an upstream to downstream evolution consistent with an accentuation of limited sediment supply: the crests of the most upstream dunes are slightly sinuous (1.03 to 1.07) but continuous (within ROI1 where percentage of the area uncovered by mobile sediment equals 10%), while the crests of downstream dunes are more irregular with an increased sinuosity (1.08 to 1.10) and locally discontinuous (within ROI2 where percentage of the area uncovered by mobile sediment equals 20%). These observations made on the dunes within the Seine River are consistent with conceptual model from Kleinhans et al. (2002) and observations from Venditti et al. (2019), linking the dune shape to limited sediment supply conditions (Carling et al., 2000; Cilli et al., 2021; Yalin and Karahan, 1979).

Furthermore, within ROI1 and ROI2, dune fields are characterised by the occurrence of depressed areas uncovered by mobile sediments within the troughs in-between the dunes. The sediment cover in those areas has been interpreted either as compacted mud (based on one sediment sample; Table 4) or as a hardened surface (grab sample refusal occurrences in dune troughs), which could be then interpreted as an immobile layer (Kleinhans et al., 2002; Venditti et al., 2019). The occurrence of such areas deprived of mobile sediment within dune fields has been related to limited sediment supply both in field and flume studies (Kleinhans et al., 2002; Kleinhans and van Rijn, 2002; Tuijnder and Ribberink, 2012; Vah et al., 2020). In flumes, it has been shown that the increasing surface area of an immobile layer uncovered by mobile sediment could be related to a decrease of the sediment supply (Tuijnder and Ribberink, 2012; Vah et al., 2020). As the surface of these areas increase from upstream (ROI1) to
783 downstream (ROI2) in the studied section of the Seine River, it is inferred that the volume of available
784 mobile sediment decreases from upstream to downstream. Within ROI3 where the sediment grain size
785 is coarser, the mobile sediment cover is apparently continuous. Nevertheless, these small dunes are
786 occurring as a narrow corridor in the centre of the river channel and could therefore correspond to
787 small dunes superimposed on top of a long sand ribbon, a bedform typically occurring in limited
788 sediment supply conditions. Therefore, ROI3 can also be considered as a limited sediment supply area.

789 Occurrence of erosional areas in the troughs between dunes could also be explained by the occurrence
790 of a Flow Separation Zone (FSZ) (Best, 2005; Lefebvre et al., 2014; Paarlberg et al., 2007). The FSZ
791 corresponds to an eddy generated on the lee side of the dunes because of a strong pressure gradient.
792 The FSZ only forms within the case of a lee side maximum slope angle greater than 10° (Lefebvre et al.,
793 2014; Paarlberg et al., 2007), a threshold value that has already been lowered compared to other
794 studies (Kostaschuk and Villard, 1996). In this study, the average lee side slope angle of the bedforms
795 does not exceed 6.2°, which is typical for dunes within rivers (Best, 2005), but maximum dune slope
796 values exceed the threshold of 10° at which a FSZ may occur (Kostaschuk and Villard, 1996). Therefore,
797 in the Seine River, a FSZ occurs and could further accentuate the surface of areas uncovered by mobile
798 sediment. While bedload is the dominant mode of transport (according to the suspension number (Van
799 Rijn, 1984a; Zomer et al., 2021) and the θ-θcr parameter (Tuijnder and Ribberink, 2012; Vah et al.,
800 2020)), a FSZ may cause sediment to jump from one dune to another (Kostaschuk et al., 2009;
801 Kostaschuk and Villard, 1996).

802 In the studied section of the Seine River, the sediment cover varies from gravelly sand to slightly
803 gravelly sand with the areas in between the dune troughs essentially characterised as slightly gravelly
804 sandy muds. The small dune corridor (ROI3) in the centre of the river is characterised by a coarser
805 sediment grain size (gravelly sands) that differs from the medium dune sediment (slightly gravelly
806 sands to sand) located along the left riverbank (ROI1 and ROI2). Within the medium dune field, the
807 sediment type and grain size follows a general fining trend from upstream to downstream.
808 Downstream at ROI2, the sediment sample (VEN1-2; Table 4) corresponds to a slightly gravelly sandy
809 mud, with the first sediment mod (357.5 µm) corresponding to the one characterising the mobile
810 sediment cover within ROI2 (VEN1-4; Table 4). This observation may indicate that the sand fraction
811 from ROI2, constituting the medium dunes, is exported downstream. However, the increasingly sparse
812 sandy and gravelly sediment cover indicates that the mobile sediment cover proportion decreases in
813 favour of the immobile sediment layer composed of compacted mud.

814 Considering this general trend in sediment grain size spatial variability between the different ROIs, the
815 apparently similar sediment transport potential (θ) for ROI1 and ROI3 can be explained by the higher
816 average river flow velocity in ROI3 (+0.13 m.s⁻¹ higher than in ROI1 and ROI2) at the centre of the river
817 channel. From ROI1 to ROI2, the increased θ parameter values are most likely explained by the fining
818 of the sediment grain size, as the average river flow velocity is almost identical (+0.01 m.s⁻¹ difference).
819 This translates as an increased potential sediment transport from ROI1 to ROI2, though no significant
820 difference between the bedload unit transport has been observed between ROI1 and ROI2. This could
821 be explained by the decreased volume of mobile sediment available within ROI2 compared to ROI1,
822 evidenced by the increase surface deprived of mobile sediment and lower steepness index than in ROI1
823 (0.005 lower).

824 The lower volume of sediment available downstream directly corresponds to a more limited mobile
825 sediment cover thickness. The concept of active layer may have several definitions (Church and
826 Haschenburger, 2017), but according to Kleinhans et al. (2002) the active layer thickness for triangular
827 dunes at equilibrium is defined as half the dune height (0.5Hd). By following this equation from
828 Kleinhans et al. (2002), the layer thickness is inferred to be about 0.14 m, 0.11 mm and 0.07 m in ROI1,
829 ROI2 and ROI3, respectively. Since the dunes do not reach equilibrium in the study area, the thickness
830 of the active layer cannot be assessed precisely, but is necessarily lower than 0.5Hd. If so, the method
831 from Kleinhans et al. (2002) only considers the small dunes superimposed onto the sand ribbon.
Based on transported sediment θ values and the TL* parameter (layer thickness predicted from dune height divided by water depth), Kleinhans et al. (2002) established a conceptual model for bedform occurrence in sand-gravel bed rivers. Observation of linear medium dunes within ROI1 and sinuous medium dunes within ROI2 are consistent with the shape prediction provided by the conceptual model from Kleinhans et al. (2002). For the small dunes in ROI3, the conceptual model predicts a point at the limit with small dunes, isolated bedforms and sand ribbons. From the in-situ observations in this study, it is inferred that the small dunes in the centre of the river may represent secondary bedforms, migrating faster on top of the sand ribbon. Such secondary bedforms are known to migrate faster and represent substantial bedload sediment transport (Carling et al., 2000; Venditti et al., 2019, 2005; Wilbers and Ten Brinke, 2003; Zomer et al., 2021), which is here consistent with the overall increase in bedload transport within ROI3, compared to the medium dunes along the left riverbank within ROI1 and ROI2.

844

<figure><img src="image_14.png" /><figcaption>Fig. 11: Conceptual model from Kleinhans et al. (2002) estimating dune shapes based on θ and TL* (dimensionless thickness) corresponding to the active layer thickness divided by the water depth. Thicknesses estimated for each ROI, using the method from Kleinhans et al. (2002), are displayed in the lower right corner.</figcaption></figure>

846

847

848
849

## 5.2. Migration rates and assessment of unit bedload transport estimation

850

Between the 23rd and 29th of March, the river flow decreased from small flood flow values (715 m³.s⁻¹)

851

to slightly above average river flow values (555 m³.s⁻¹). During this period, the unit bedload transport

852

values decreased, along with a decrease of dune migration. This relation between river discharge and

853

the decrease of bedload transport has already been evidenced for rivers under similar conditions

854

(Claude et al., 2012; Nittrouer et al., 2008; Rodrigues et al., 2015).

855

With maximum migration rates ranging from 1 m (ROI1 and ROI2) to 6 m (ROI3) per day, medium and

856

small dunes within the Seine River migrate slowly (Table 3). These migration rates are between 4 to 10

857

times slower than observations from Claude et al. (2012) in the Loire River and for similar river

858

discharge conditions. However, Lokin et al. (2022) have shown in the Waal River that dune migration

859

was related to river discharge and that dunes continued to migrate even at low flow, but at lower rates,

860

between 1.8 and 8 m per day. The migration rates observed in the Seine River, after a period of small

861

peak flooding with a decrease of the river discharge (Fig. 1), are consistent with the observations from

862

Lokin et al. (2022) and ascertain the limited dune migration in the Seine River during period of relatively

863

low flow (average river flow of 640 m.s⁻¹).

864

In comparison with studies in the Loire River (Claude et al., 2012; Le Guern et al., 2020; Rodrigues et

865

al., 2015) and under unlimited sediment conditions, the unit bedload transport estimated in the Seine

866

River is approximately ten times lower. As sediment grain size and hydraulic conditions in those studies

867

are close (e.g., D50 between 0.8 and 1.2 mm, with Q between 226 and 2410 m³.s⁻¹ in Le Guern et al.

868

(2020)) to the conditions observed in study area of the Seine River, such a difference is most likely

869

explained by the limited sediment supply conditions recognised here.

870

The estimated unit bedload transport values from differential bathymetry, dune tracking and empirical

871

formula methods are consistent, with less than one order of magnitude difference. Based on an

872

extensive quantitative comparison of empirical formulas, Recking et al. (2012) stated that a difference

873

with a factor lower than two is difficult to achieve considering uncertainties on input parameters.
Furthermore, in their in-situ study, Cilli et al. (2021) have observed discrepancy ratios between 1.65 and 16.7. Thus, bedload transport estimations in the Seine are considered to be reliable. However, uncertainties related to input measured parameters used here are significant enough to potentially explain variations in the estimation of unit bedload transport. The difference between morphological parameters extracted with BTT and manual calculations, which is highlighted in this study, is another factor to consider when using the dune tracking method. Looking at the differences in unit bedload transport estimation, it is known that application of a reasonably low uncertainty method is challenging (Claude et al., 2012; Le Guern et al., 2020; Leary and Buscombe, 2020; Recking et al., 2012).

Here, the suspension number values calculated within each ROI demonstrate that the bedload transport is the dominant mode of transport (values lower than 1) (Zomer et al., 2021). However, the suspended number also shows that sediment from ROI2 can enter suspension (values above 0.4), while within the other ROIs the suspension is not initiated (Van Rijn, 1984a; Zomer et al., 2021). Following Vah et al. (2020) and Tuijnder and Ribberink (2012), this observation of the sediment transport being dominated by bedload transport is supported by the parameter $\theta - \theta_{cr}$, being consistently above 0.1. This validates the use of an empirical bedload transport formula and can explain discrepancies with the differential bathymetry and the dune tracking methods that may include sediment deposited from suspension. Empirical sediment transport formulas predict transport capacities subsequently established for unlimited sediment conditions (Vah et al., 2020; Van Rijn, 1993, 1984b). Here, considering the evidence of limited sediment supply conditions, the application of a minor correction factor corresponding to the area effectively uncovered by mobile sediment (Tuijnder and Ribberink, 2012; Vah et al., 2020) provided more consistent bedload transport estimations when compared with differential bathymetry and the dune tracking methods. Furthermore, sediment transport empirical formulas intend to estimate bedload transport but there is no clear boundary between the bedload and suspended bed sediment transport (Van Rijn, 1993). Thus, a portion of suspended bed material, if any, may be integrated into this estimation.
Differential bathymetry, with the application of a correction factor (see Section 3.3.1), is supposed to integrate the entire volume of sediment displaced along the dunes (Leary and Buscombe, 2020; Mcelroy and Mohrig, 2009; Nittrouer et al., 2008). As eddies formed through the FSZ process (Best, 2005; Paarlberg et al., 2007) may occur in the Seine River (Section 5.1), these could favour sediment to jump from one dune to another and be deposited on the flanks of dunes located farther downstream (Kostaschuk et al., 2009). The differential bathymetry method is theoretically able to capture sediment redeposited on the dune flank after jumping from one dune to another (Mcelroy and Mohrig, 2009; Nittrouer et al., 2008). Conversely, dune tracking estimates bedload transport based on idealized dune shape (Claude et al., 2012; Hoekstra et al., 2004; Schmitt and Mitchell, 2014; Simons et al., 1965). Moreover, the application of the form factor in the dune tracking formula neglects the volume of sediment bypassing between the dunes (Le Guern et al., 2020; Mcelroy and Mohrig, 2009; Simons et al., 1965; Wilbers, 2004; Wilbers and Ten Brinke, 2003). This difference could explain why unit bedload transport estimated from differential bathymetry is consistently nearly twice higher (difference factor between 1.8 and 1.9) than unit bedload estimated with dune tracking. As the suspension number shows that the bedload transport is the dominant mode of transport (Van Rijn, 1984a; Zomer et al., 2021), with the suspension being initiated only in ROI2, sediment bypassing dunes because of FSZ (Best, 2005; Kostaschuk and Villard, 1996; Lefebvre, 2019; Lefebvre et al., 2014; Paarlberg et al., 2007) is considered as the most probable hypothesis. Higher resolution aDcp data would be required to quantitatively estimate the proportion of suspended bed material and FSZ occurrence.

Therefore, quantifying the effect of data uncertainties and the processes captured by the bedload transport estimation method is challenging. By averaging data along the aDcp sections, it is expected to limit the impact of noise and artefacts to get a representative value of the flow velocity (Conevski et al., 2019; Le Guern et al., 2020; Rennie and Millar, 2007). Still, uncertainties of flow velocity have a direct impact on the estimations with the Van Rijn formula (Van Rijn, 1993, 1984b) as the equation is very sensitive to it (Claude et al., 2012). For the differential bathymetry and dune tracking methods,
all the parameters are derived from the bathymetry data, so estimations from those methods are
conditioned by the precision and accuracy of these data (Section 3.4) (Huizinga and Survey, 2022;
Kaplinski et al., 2017). The differential bathymetry method is even more dependent on the precision
and accuracy of bathymetry data as it is the direct result of the comparison of two successive
acquisitions (Huizinga and Survey, 2022; Kaplinski et al., 2017; Nittrouer et al., 2008).

## 6. Summary and conclusion

Over a period of a week (23rd to 29th of March 2021), repeated multibeam data, along with sediment grab samples and aDcp profiles (24th of March), have been acquired in a fluvial section of the Seine River. Typical small and medium dunes associated with river environments have been mapped (Allen, 1982; Coleman and Nikora, 2011; Kleinhans, 2001) and characterised in terms of their morphology using BTT tool (Van der Mark et al., 2008), their migration rate, and associated sediment fluxes. Within the studied section of the river, medium dunes developed along the left riverbank and small dunes superimposed on a sand ribbon in the centre of the channel illustrates the variations of sediment cover grain size and thickness in a context of limited sediment supply conditions. These conditions have been evidenced because of the presence of rock outcrops and depressed circular areas in dune troughs where mobile sand and gravel sediment is eroded allowing compacted mud to outcrop, revealed by backscatter data and grab samples. These circular depressions, uncovered by mobile sediments in between the dune troughs, also demonstrate probable intermittent macroturbulences along the lee side of the bedforms related to flow separation processes (Lefebvre et al., 2014; Paarlberg et al., 2007).

No significant temporal variation in dune morphological parameters has been recognised, but spatial variations are associated with a fining of sediment grain size from upstream to downstream as well as an increase of the transport potential. Nevertheless, this increase in transport potential downstream is balanced by a more limited volume of available mobile sediment.

Dune steepness values (0.026 to 0.033) highlight the effect of limited sediment supply (Carling et al., 2000; Yalin and Karahan, 1979), preventing the dunes from reaching equilibrium. Following the
calculation of transport parameters and the estimation of dune layer thickness (Kleinhans et al., 2002),
more sinuous dune shapes (around 1.1 and up to 1.15) observed in the Seine River are consistent with
shapes recognised under increasingly limited supplies, in both flume experiments (Kleinhans et al.,
2002) and field observations (Venditti et al., 2019). The complete mobile sediment cover within the
small dune field has been interpreted as being related to the scale of observation. At the scale of the
small dunes, the mobile sediment cover is continuous but corresponds to a sand ribbon spatially
limited to the centre of the river channel, consistent with limited sediment supplies. In the context of
limited sediment supply, a new relationship between the dune wavelength and height has been
defined, showing an overall limited dune height in comparison to other studies (Flemming, 2000, 1988;
Francken et al., 2004).

Bedload transport rates associated with medium and small dunes observed over a period of a week
have been estimated by exploring three approaches. Two methods are based on bedform
morphometry and migration rates (differential bathymetry and dune tracking) (Mcelroy and Mohrig,
2009; Nittrouer et al., 2008; Simons et al., 1965). The third method uses an empirical formula for the
estimation of bedload transport (Van Rijn, 1984b), relying on the integration of parameters derived
from grain size and flow velocities. By using a correction factor related to areas uncovered by mobile
sediments (Tuijnder and Ribberink, 2012; Vah et al., 2020), the empirical formula has been corrected
to take into account the condition of limited sediment supply. Within the context of the Seine River,
bedload transport estimations from the three approaches show consistent values with less than one
order of magnitude difference. Nevertheless, differences between the three methods have been
related to both input data uncertainties (including uncertainties on morphological parameters) and
processes of integration. Furthermore, differences between bedload transport estimated by
differential bathymetry and dune tracking have been related to sediment bypassing between the
dunes. This portion of sediment, which may contribute to dune migration (Bagnold, 1966; Kostaschuk
et al., 2009; Kostaschuk and Villard, 1996), is indirectly evidenced here as it is captured by the
differential bathymetry while neglected by the dune tracking methods because of the application of
the form factor (Claude et al., 2012; Le Guern et al., 2020; Leary and Buscombe, 2020; Simons et al., 1965; Wilbers, 2004). By considering the suspension number indicating that bedload is the dominant transport mode, the proportion of bed material bypassing dunes is most likely explained by flow separation processes. These observations and associated conclusions stress the need of using several bedload transport assessment methods to capture all variations related to sediment transport processes.

## 7. CRediT authorship contribution statement

Guillaume Michel: Conceptualization, Investigation (data collection), Methodology, Software, Validation, Formal analysis, Investigation, Writing - Original Draft, Visualization. Sophie Le Bot: Conceptualization, Validation, Investigation, Writing - Original Draft, Supervision. Julien Deloffre: Conceptualization, Validation, Investigation, Writing - Original Draft, Supervision. Magalie Legrain: Resources. Romain Levaillant: Investigation (data collection). Michel Simon: Investigation (data collection). Bernadette Tessier: Writing - Review & Editing, Funding acquisition. Sandric Lesourd: Writing - Review & Editing, Funding acquisition, Project administration.

## 8. Funding

This work was supported by the Normandy Region as part of the RIN programme [award 18E01700/18P02973].

## 9. Acknowledgments

The authors are thankful to the public service Voies Navigables de France (VNF) for providing bathymetric data prior to the survey and for delivering authorisation and navigation notices. The authors are also thankful to the divers from the Fluvial Gendarmerie of Seine-Maritime, for their assistance in data collection. The writers thank the two anonymous reviewers for their valuable suggestions on improving the manuscript.
999 10. Software

1000 MBES data have been acquired and processed with PDS (©2002-2021 Teledyne RESON A/S, version 4.4.3.4). ADCP data have been acquired using ROWE (© 2011 Rowe Technology Inc.) Pulse Software (Version 4.13.5.1605) and processed using both Pulse software and Python scripts. All GIS mapping and analysis have been performed using QGIS 3.16. Bed elevation profiles have been extracted using SAGA in QGIS and processed in MATLAB 2021 by using the script from Van Der Mark et al. (2009).

1005 11. Appendix A

1006 $C_d$ dune migration rate (m.s⁻¹)

1007 CD drag coefficient

1008 C' Chézy coefficient related to grain roughness only (-)

1009 D50, D90 bed grain diameters such that 50 and 90% of the particles are finer (in metres in equations; microns in text and tables)

1010

1011 D* scaled particle diameter

1012 f dimensionless shape factor (-)

1013 g gravitational acceleration (=9.81 m.s⁻²)

1014 $H_d$ dune height (m)

1015 $L_d$ dune length (m)

1016 $p$ percentage of bed area devoid of mobile sediment (%)

1017 Q the river flow (m³.s⁻¹)

1018 $Rh$ hydraulic radius corresponding to water depth for steady flow (m)

1019 S sediment ratio (-)
<table>
  <tr>
    <td>1020</td>
    <td>T</td>
    <td>Transport stage parameter (-)</td>
  </tr>
  <tr>
    <td>1021</td>
    <td>ū</td>
    <td>mean flow velocity (m.s<sup>-1</sup>)</td>
  </tr>
  <tr>
    <td>1022</td>
    <td>u<sub>*</sub></td>
    <td>bed shear velocity (m.s<sup>-1</sup>)</td>
  </tr>
  <tr>
    <td>1023</td>
    <td>u<sub>cr</sub></td>
    <td>critical bed shear velocity (m.s<sup>-1</sup>)</td>
  </tr>
  <tr>
    <td>1024</td>
    <td>V</td>
    <td>dune cross sectional surface (m<sup>2</sup>)</td>
  </tr>
  <tr>
    <td>1025</td>
    <td>Qb<sub>DTM</sub></td>
    <td>unit bedload transport estimated from dune tracking method (kg.s<sup>-1</sup>.m<sup>-2</sup>)</td>
  </tr>
  <tr>
    <td>1026</td>
    <td>Qb<sub>VR</sub></td>
    <td>unit bedload transport estimated from Van Rijn formula (kg.s<sup>-1</sup>.m<sup>-2</sup>)</td>
  </tr>
  <tr>
    <td>1027</td>
    <td>Qb<sub>VR Corr</sub></td>
    <td>unit bedload transport estimated from Van Rijn formula with correction of limited sediment supply condition (kg.s<sup>-1</sup>.m<sup>-2</sup>)</td>
  </tr>
  <tr>
    <td>1028</td>
    <td>ε</td>
    <td>sediment concentration (1-porosity; =0.65)</td>
  </tr>
  <tr>
    <td>1030</td>
    <td>ps</td>
    <td>sediment density (kg.m<sup>-3</sup>)</td>
  </tr>
  <tr>
    <td>1031</td>
    <td>θ<sub>cr</sub></td>
    <td>dimensionless critical shear stress (-)</td>
  </tr>
  <tr>
    <td>1032</td>
    <td>v</td>
    <td>water kinematic viscosity (m<sup>2</sup>.s<sup>-1</sup>)</td>
  </tr>
  <tr>
    <td>1033</td>
    <td>w<sub>s</sub></td>
    <td>particle fall velocity (m.s<sup>-1</sup>)</td>
  </tr>
</table>

1034 12. References

1035 AFNOR, 2000. Granulométrie - 2 volumes. Paris.

1036 Allen, J.R.L., 1982. Sedimentary structures, their character and physical basis Volume 1. Elsevier.

1037 Amos, K.J., Alexander, J., Horn, A., Pocock, G.D., Fielding, C.R., 2004. Supply limited sediment transport

1038 in a high-discharge event of the tropical Burdekin River, North Queensland, Australia.

1039 Sedimentology 51, 145–162.
1040 Ancey, C., Pascal, I., 2020. Estimating Mean Bedload Transport Rates and Their Uncertainty. J Geophys

1041 Res Earth Surf 125. https://doi.org/10.1029/2020JF005534

1042 Ashley, G.M., 1990. Classification of large-scale subaqueous bedforms: a new look at an old problem;

1043 SEPM bedforms and bedding structures. J Sediment Petrol 60, 160–172.

1044 https://doi.org/10.1306/212f9138-2b24-11d7-8648000102c1865d

1045 Avoine, J., 1987. Sediment exchanges between the Seine estuary and its adjacent shelf. J Geol Soc

1046 London 144, 135–148.

1047 Bagnold, R.A., 1966. An approach to the sediment transport problem from general physics,

1048 Professional Paper. https://doi.org/10.3133/pp422I

1049 Barton, J.S., Slingerland, R.L., Pittman, S., Gabrielson, T.B., 2010. Monitoring coarse bedload transport

1050 with passive acoustic instrumentation: A field study. US Geol. Surv. Sci. Investig. Rep 5091, 38–

1051 51.

1052 Bassompierre, P., de Mautort, J., 1967. Carte géologique de la France (1/50 000), feuille Les Andelys (n

1053 216).

1054 Best, J., 2005. The fluid dynamics of river dunes: A review and some future research directions. J

1055 Geophys Res Earth Surf 110, 1–21. https://doi.org/10.1029/2004JF000218

1056 Bjerklie, D.M., Dingman, S.L., Bolster, C.H., 2005. Comparison of constitutive flow resistance equations

1057 based on the Manning and Chezy equations applied to natural rivers. Water Resour Res 41.

1058 Blondeaux, P., Vittori, G., Mazzuoli, M., 2016. Pattern formation in a thin layer of sediment. Mar Geol

1059 376, 39–50.

1060 Blott, S.J., Pye, K., 2001. GRADISTAT: a grain size distribution and statistics package for the analysis of

1061 unconsolidated sediments. Earth Surf Process Landf 26, 1237–1248.
1062 Brenon, I., le Hir, P., 1999. Modelling the turbidity maximum in the Seine estuary (France):
1063 identification of formation processes. Estuar Coast Shelf Sci 49, 525–544.

1064 Bridge, J.S., 2003. Rivers and floodplains: forms, processes, and sedimentary record. John Wiley & Sons.

1065 Buscombe, D., Grams, P.E., Kaplinski, M.A., 2017. Compositional Signatures in Acoustic Backscatter
1066 Over Vegetated and Unvegetated Mixed Sand-Gravel Riverbeds. J Geophys Res Earth Surf 122,
1067 1771–1793. https://doi.org/10.1002/2017JF004302

1068 Carling, P., 1999. Subaqueous Gravel Dunes Kuray Basin lake strandline palaeohydrology View project
1069 Glacial-Lake Outburst Floods in Chile: Impacts on Settlements, Infrastructure and Riverine
1070 Ecosystems View project. Article in Journal of Sedimentary Research.
1071 https://doi.org/10.1306/D4268A2C-2B26-11D7-8648000102C1865D

1072 Carling, P.A., Golz, E., Orr, H.G., Radecki-Pawlik, A., 2000. The morphodynamics of fluvial sand dunes
1073 in the River Rhine, near Mainz, Germany. I. Sedimentology and morphology. Sedimentology 47,
1074 227–252.

1075 Cheng, N.S., 2009. Comparison of formulas for drag coefficient and settling velocity of spherical
1076 particles. Powder Technol 189, 395–398. https://doi.org/10.1016/J.POWTEC.2008.07.006

1077 Church, M., Haschenburger, J.K., 2017. What is the “active layer”? Water Resour Res 53, 5–10.
1078 https://doi.org/10.1002/2016WR019675

1079 Cilli, S., Billi, P., Schippa, L., Grottoli, E., Ciavola, P., 2021. Bedload transport and dune bedforms
1080 characteristics in sand-bed rivers supplying a retreating beach of the northern Adriatic Sea (Italy).
1081 J Hydrol Reg Stud 37, 100894. https://doi.org/10.1016/J.EJRH.2021.100894

1082 Claude, N., Rodrigues, S., Bustillo, V., Bréhéret, J.G., Macaire, J.J., Jugé, P., 2012. Estimating bedload
1083 transport in a large sand-gravel bed river from direct sampling, dune tracking and empirical
1084 formulas. Geomorphology 179, 40–57. https://doi.org/10.1016/j geomorph.2012.07.030
1085 Coleman, S.E., Nikora, V.I., 2011. Fluvial dunes: Initiation, characterization, flow structure. Earth Surf
1086 Process Landf 36, 39–57. https://doi.org/10.1002/esp.2096

1087 Colombini, M., Stocchino, A., 2011. Ripple and dune formation in rivers. J Fluid Mech 673, 121–131.

1088 Conevski, S., 2020. Bedload Monitoring by means of Hydro - Acoustic Techniques.

1089 Conevski, S., Guerrero, M., Ruther, N., Rennie, C.D., 2019. Laboratory investigation of apparent
1090 bedload velocity measured by ADCPs under different transport conditions. Journal of Hydraulic
1091 Engineering 145, 4019036.

1092 Deloffre, J., Lafite, R., Lesueur, P., Lesourd, S., Verney, R., Guézennec, L., 2005. Sedimentary processes
1093 on an intertidal mudflat in the upper macrotidal Seine estuary, France. Estuar Coast Shelf Sci 64,
1094 710–720. https://doi.org/10.1016/j.ecss.2005.04.004

1095 Deloffre, J., Verney, R., Lafite, R., Lesueur, P., Lesourd, S., Cundy, A.B., 2007. Sedimentation on
1096 intertidal mudflats in the lower part of macrotidal estuaries: Sedimentation rhythms and their
1097 preservation. Mar Geol 241, 19–32. https://doi.org/10.1016/j.margeo.2007.02.011

1098 Dreano, J., Valance, A., Lague, D., Cassar, C., 2010. Experimental study on transient and steady-state
dynamics of bedforms in supply limited configuration. Earth Surf Process Landf 35, 1730–1743.

1100 Dupont, J.-P., Lafite, R., Huault, M.-F., Hommeril, P., Meyer, R., 1994. Continental/marine ratio changes
1101 in suspended and settled matter across a macrotidal estuary (the Seine estuary, northwestern
France). Mar Geol 120, 27–40.

1103 Eleftherakis, D., Amiri-Simkooei, A., Snellen, M., Simons, D.G., 2012. Improving riverbed sediment
classification using backscatter and depth residual features of multi-beam echo-sounder systems.
1104 J Acoust Soc Am 131, 3710. https://doi.org/10.1121/1.3699206

1106 Engel, P., Lau, Y.L., 1980. Computation of Bedload by Dune Tracking. ASCE Journal of the Hydraulics
1107 Division 106.
1108 Flemming, B.W., 2019. Ripples and dunes: do flumes tell the whole story? Marine and River Dune Dynamics 1–6.

1110 Flemming, B.W., 2000. The role of grain size, water depth and flow velocity as scaling factors controlling the size of subaqueous dunes, in: Marine Sandwave Dynamics, International Workshop. pp. 23–24.

1113 Flemming, B.W., 1988. Zur klassifikation subaquatischer, strömungstransversaler Transportkörper. Bochumer geologische und geotechnische Arbeiten 29, 44–47.

1115 Folk, R.L., 1954. The distinction between grain size and mineral composition in sedimentary-rock nomenclature. J Geol 62, 344–359.

1117 Folk, R.L., Ward, W.C., 1957. Brazos River bar [Texas]; a study in the significance of grain size parameters. Journal of sedimentary research 27, 3–26.

1119 Francken, F., Wartel, S., Parker, R., Taverniers, E., 2004. Factors influencing subaqueous dunes in the Scheldt Estuary. Geo-Marine Letters 24, 14–21. https://doi.org/10.1007/s00367-003-0154-x

1121 Frings, R.M., Vollmer, S., 2017. Guidelines for sampling bedload transport with minimum uncertainty. Sedimentology 64, 1630–1645. https://doi.org/10.1111/sed.12366

1123 Gaeuman, G., Jacobson, R.B., 2007. Field assessment of alternative bed-load transport estimators. Journal of Hydraulic Engineering 133, 1319–1328. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:12(1319)

1126 Gomez, B., Church, M., 1989. An assessment of bed load sediment transport formulae for gravel bed rivers. Water Resour Res 25, 1161–1186.

1128 Goodwiller, B., Wren, D.G., Surbeck, C.Q., 2019. Development and calibration of an underwater acoustic data collection system for monitoring coarse bedload transport. Applied Acoustics 155, 383–390.
1131 Grasso, F., le Hir, P., 2019. Influence of morphological changes on suspended sediment dynamics in a macrotidal estuary: diachronic analysis in the Seine Estuary (France) from 1960 to 2010. Ocean Dyn 69, 83–100.

1134 Guézennec, L., Lafite, R., Dupont, J.-P., Meyer, R., Boust, D., 1999. Hydrodynamics of suspended particulate matter in the tidal freshwater zone of a macrotidal estuary (the Seine estuary, France). Estuaries 22, 717–727.

1137 Hilldale, R.C., Carpenter, W.O., Goodwiller, B., Chambers, J.P., Randle, T.J., 2015. Installation of impact plates to continuously measure bed load: Elwha River, Washington, USA. Journal of Hydraulic Engineering 141, 6014023.

1140 Hoekstra, P., Bell, P., van Santen, P., Roode, N., Levoy, F., Whitehouse, R., 2004. Bedform migration and bedload transport on an intertidal shoal. Cont Shelf Res 24, 1249–1269. https://doi.org/10.1016/j.csr.2004.03.006

1143 Huizinga, R.J., Survey, U.S.G., 2022. Bathymetric and velocimetric surveys at highway bridges crossing the Missouri River near Kansas City, Missouri, August 2019, August 2020, and October 2020, Scientific Investigations Report. Reston, VA. https://doi.org/10.3133/sir20215098

1146 Julien, P.Y., Klaassen, G.J., 1995. Sand-dune geometry of large rivers during floods. Journal of Hydraulic Engineering 121, 657–663.

1148 Kaplinski, M., Hazel Jr., J.E., Grams, P.E., Kohl, K., Buscombe, D.D., Tusso, R.B., Survey, U.S.G., 2017. Channel mapping river miles 29–62 of the Colorado River in Grand Canyon National Park, Arizona, May 2009, Open-File Report. Reston, VA. https://doi.org/10.3133/ofr20171030

1151 Kleinhans, M.G., 2001. The key role of fluvial dunes in transport and deposition of sand-gravel mixtures, a preliminary note. Sediment Geol 143, 7–13. https://doi.org/10.1016/S0037-0738(01)00109-9
1154 Kleinhans, M.G., Brinke, W.B.M. Ten, 2001. Accuracy of cross-channel sampled sediment transport in large sand-gravel-bed rivers. Journal of Hydraulic Engineering 127, 258-269.

1156 Kleinhans, M.G., van Rijn, L.C., 2002. Stochastic prediction of sediment transport in sand-gravel bed rivers. Journal of hydraulic engineering 128, 412-425.

1158 Kleinhans, M.G., Wilbers, A.W.E., De Swaaf, A., Van Den Berg, J.H., 2002. Sediment supply-limited bedforms in sand-gravel bed rivers. Journal of sedimentary research 72, 629-640.

1160 Kostaschuk, R., Shugar, D., Best, J., Parsons, D., Lane, S., Hardy, R., Orfeo, O., 2009. Suspended sediment transport and deposition over a dune: R{\'i}o Paraná, Argentina. Earth Surf Process Landf 34, 1605-1611.

1163 Kostaschuk, R., Villard, P., 1996. Flow and sediment transport over large subaqueous dunes: Fraser River, Canada. Sedimentology 45, 849-863. https://doi.org/10.1111/j.1365-3091.1996.tb01506.x

1166 Kostaschuk, R.A., Church, M.A., Luternauer, J.L., 1989. Bedforms, bed material, and bedload transport in a salt-wedge estuary: Fraser River, British Columbia. Can J Earth Sci 26, 1440-1452.

1168 Lamarche, G., Lurton, X., Verdier, A.L., Augustin, J.M., 2011. Quantitative characterisation of seafloor substrate and bedforms using advanced processing of multibeam backscatter-Application to Cook Strait, New Zealand. Cont Shelf Res 31, 93-109. https://doi.org/10.1016/j.csr.2010.06.001

1171 Latosinski, F.G., Szupiany, R.N., Guerrero, M., Amsler, M.L., Vionnet, C., 2017. The ADCP's bottom track capability for bedload prediction: Evidence on method reliability from sandy river applications. Flow Measurement and Instrumentation 54, 124-135. https://doi.org/10.1016/j.flowmeasinst.2017.01.005

1175 Le Guern, J., Rodrigues, S., Geay, T., Zanker, S., Hauet, A., Tassi, P., Claude, N., Jugé, P., Duperray, A., Vervynck, L., 2020. Relevance of acoustic methods to quantify bedload transport and bedform dynamics in large sandy-gravel bed river. Earth Surface Dynamics Discussions 1-34.
1178 Leary, K.C.P., Buscombe, D., 2020. Estimating sand bed load in rivers by tracking dunes: A comparison of methods based on bed elevation time series. Earth Surface Dynamics 8, 161–172.
1179
1180 https://doi.org/10.5194/ESURF-8-161-2020

1181 Lefebvre, A., 2019. Three-Dimensional Flow Above River Bedforms: Insights From Numerical Modeling of a Natural Dune Field (Río Paraná, Argentina). J Geophys Res Earth Surf 124, 2241–2264.
1182
1183 https://doi.org/10.1029/2018JF004928

1184 Lefebvre, A., Paarlberg, A.J., Ernstsen, V.B., Winter, C., 2014. Flow separation and roughness lengths over large bedforms in a tidal environment: A numerical investigation. Cont Shelf Res 91, 57–69.
1185
1186 https://doi.org/10.1016/j.csr.2014.09.001

1187 Lesourd, S., Lesueur, P., Brun-Cottan, J.C., Garnaud, S., Poupinet, N., 2003. Seasonal variations in the characteristics of superficial sediments in a macrotidal estuary (the Seine inlet, France). Estuar Coast Shelf Sci 58, 3–16. https://doi.org/10.1016/S0272-7714(02)00340-2

1190 Liedermann, M., Gmeiner, P., Kreisler, A., Tritthart, M., Habersack, H., 2018. Insights into bedload transport processes of a large regulated gravel-bed river. Earth Surf Process Landf 43, 514–523.
1191

1192 Lokin, L.R., Warmink, J.J., Bomers, A., Hulscher, S., 2022. River dune dynamics during low flows. Geophys Res Lett 49, e2021GL097127.
1193

1194 Lurton, X., Lamarche, G., 2015. Backscatter mesurments by seafloor-mapping sonar Guidelines and Recommendations. Studies in Computational Intelligence 200p. https://doi.org/10.1007/978-3-642-01878-7_2
1195
1196

1197 Lurton, X., Lamarche, G., Brown, C., Lucieer, V.L., Rice, G., Schimel, A., Weber, T., 2015. Backscatter measurements by seafloor-mapping sonars Guidelines and Recommendations, Marine Geological and Biological Habitat Mapping. A collective report by members of the GeoHab Backscatter Working Group. Xavier Lurton and Geoffroy Lamarche (ed).
1198
1199
1200
1201 Mazzuoli, M., Kidanemariam, A.G., Blondeaux, P., Vittori, G., Uhlmann, M., 2016. On the formation of sediment chains in an oscillatory boundary layer. J Fluid Mech 789, 461–480.

1203 Mcelroy, B., Mohrig, D., 2009. Nature of deformation of sandy bed forms. J. Geophys. Res 114, 0–04. https://doi.org/10.1029/2008JF001220

1205 McLean, D.G., Church, M., Tassone, B., 1999. Sediment transport along lower Fraser River 1. Measurements and hydraulic computations. Water Resour Res 35, 2533–2548. https://doi.org/10.1029/1999WR900101

1208 Naqshband, S., Ribberink, J.S., Hurther, D., Hulscher, S.J.M.H., 2014. Bed load and suspended load contributions to migrating sand dunes in equilibrium. J Geophys Res Earth Surf 119, 1043–1063. https://doi.org/10.1002/2013JF003043

1211 Naqshband, S., van Duin, O., Ribberink, J., Hulscher, S., 2016. Modeling river dune development and dune transition to upper stage plane bed. Earth Surf Process Landf 41, 323–335. https://doi.org/10.1002/ESP.3789

1214 Nicollier, T., Rickenmann, D., Hartlieb, A., 2021. Field and flume measurements with the impact plate: Effect of bedload grain-size distribution on signal response. Earth Surf Process Landf 46, 1504–1520.

1217 Nittrouer, J.A., Allison, M.A., Campanella, R., 2008. Bedform transport rates for the lowermost Mississippi River. J Geophys Res Earth Surf 113.

1219 Paarlberg, A.J., Dohmen-Janssen, C.M., Hulscher, S.J.M.H., Termes, P., 2007. A parameterization of flow separation over subaqueous dunes. Water Resour Res 43, 12417. https://doi.org/10.1029/2006WR005425

1222 Pinto Martins, D., Bravard, J.-P., Stevaux, J.C., 2009. Dynamics of water flow and sediments in the upper Paraná River between Porto Primavera and Itaipu Dams, Brazil. Latin American journal of sedimentology and basin analysis 16, 111–118.
1225 Recking, A., Liébault, F., Peteuil, C., Jolimet, T., 2012. Testing bedload transport equations with consideration of time scales. Earth Surf Process Landf 37, 774-789.
1227 https://doi.org/10.1002/ESP.3213

1228 Recking, A., Piton, G., Vazquez-Tarrio, D., Parker, G., 2016. Quantifying the Morphological Print of Bedload Transport. Earth Surf Process Landf 41, 809-822. https://doi.org/10.1002/esp.3869

1230 Rennie, C.D., Church, M., 2010. Mapping spatial distributions and uncertainty of water and sediment flux in a large gravel bed river reach using an acoustic Doppler current profiler. J Geophys Res Earth Surf 115. https://doi.org/10.1029/2009JF001556

1233 Rennie, C.D., Millar, R.G., 2007. Deconvolution technique to separate signal from noise in gravel bedload velocity data. Journal of Hydraulic Engineering 133, 845-856.

1235 Rodrigues, S., Mosselman, E., Claude, N., Wintenberger, C.L., Juge, P., 2015. Alternate bars in a sandy gravel bed river: generation, migration and interactions with superimposed dunes. Earth Surf Process Landf 40, 610-628. https://doi.org/10.1002/ESP.3657

1238 Schmitt, T., Mitchell, N.C., 2014. Dune-associated sand fluxes at the nearshore termination of a banner sand bank (Helwick Sands, Bristol Channel). Cont Shelf Res 76, 64-74.

1240 Simons, D.B., Richardson, E. v, Nordin, C.F., 1965. Bedload equation for ripples and dunes, Geological Survey Professional Paper 462-H. USGS, Washington.

1242 Stepinski, T.F., Jasiewicz, J., 2011. Geomorphons-a new approach to classification of landforms. Proceedings of geomorphometry 2011, 109-112.

1244 Tessier, B., Delsinne, N., Sorrel, P., 2010. Holocene sedimentary infilling of a tide-dominated estuarine mouth. The example of the macrotidal Seine estuary (nw france). Bulletin de la Societe Geologique de France 181, 87-98. https://doi.org/10.2113/gssgbull.181.2.87
1247 Tuijnder, A.P., Ribberink, J.S., 2012. Experimental observation and modelling of roughness variation due to supply-limited sediment transport in uni-directional flow. Journal of hydraulic research 50, 506–520.

1250 Tuijnder, A.P., Ribberink, J.S., Hulscher, S.J.M.H., 2009. An experimental study into the geometry of supply-limited dunes. Sedimentology 56, 1713–1727.

1252 Udden, J.A., 1914. Mechanical composition of clastic sediments. Bulletin of the Geological Society of America 25, 655–744.

1254 Vah, M., Jarno, A., Le Bot, S., Ferret, Y., Marin, F., 2020. Bedload transport and bedforms migration under sand supply limitation. Environmental Fluid Mechanics. https://doi.org/10.1007/s10652-020-09738-6

1257 van den Berg, J.H., 1987. Bedform migration and bed-load transport in some rivers and tidal environments. Sedimentology 34, 681–698.

1259 Van der Mark, C.F., Blom, A., Hulscher, S.M.J.H., 2008. Quantification of variability in bedform geometry. J Geophys Res Earth Surf 113, 1–11. https://doi.org/10.1029/2007JF000940

1261 van Landeghem, K.J.J., Uehara, K., Wheeler, A.J., Mitchell, N.C., Scourse, J.D., 2009. Post-glacial sediment dynamics in the Irish Sea and sediment wave morphology: Data-model comparisons. Cont Shelf Res 29, 1723–1736. https://doi.org/10.1016/j.csr.2009.05.014

1264 Van Rijn, L.C., 1993. Principles of sediment transport in rivers, estuaries and coastal seas. Aqua Publications.

1266 Van Rijn, L.C., 1984a. Sediment Transport, Part II: Suspended Load Transport. Journal of Hydraulic Engineering 110, 1613–1641. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:11(1613)

1268 Van Rijn, L.C., 1984b. Sediment transport, part I: bed load transport. Journal of Hydraulic Engineering 110, 1431–1456.
1270 Venditti, J.G., 2007. Turbulent flow and drag over fixed two&hyphen; and three&hyphen;dimensional dunes. J. Geophys. Res 112, 4008. https://doi.org/10.1029/2006JF000650

1272 Venditti, J.G., Church, M., Bennett, S.J., 2005. On the transition between 2D and 3D dunes. Sedimentology 52, 1343–1359. https://doi.org/10.1111/j.1365-3091.2005.00748.x

1274 Venditti, J.G., Nittrouer, J.A., Allison, M.A., Humphries, R.P., Church, M., 2019. Supply-limited bedform patterns and scaling downstream of a gravel–sand transition. Sedimentology 66, 2538–2556. https://doi.org/10.1111/SED.12604

1277 Vericat, D., Batalla, R.J., 2006. Sediment transport in a large impounded river: The lower Ebro, NE Iberian Peninsula. Geomorphology 79, 72–92.

1279 Verney, R., Brun-Cottan, J.C., Lafite, R., Deloffre, J., Taylor, J.A., 2006. Tidally-induced shear stress variability above intertidal mudflats in the macrotidal seine estuary. Estuaries and Coasts 29, 653–664. https://doi.org/10.1007/BF02784290

1282 Verney, R., Deloffre, J., Brun-Cottan, J.C., Lafite, R., 2007. The effect of wave-induced turbulence on intertidal mudflats: Impact of boat traffic and wind. Cont Shelf Res 27, 594–612. https://doi.org/10.1016/j.csr.2006.10.005

1285 Villard, P. V., Church, M., 2005. Bar and dune development during a freshet: Fraser River Estuary, British Columbia, Canada. Sedimentology 52, 737–756. https://doi.org/10.1111/j.1365-3091.2005.00721.x

1288 Villard, P. V., Church, M., 2003. Dunes and associated sand transport in a tidally influenced sand-bed channel: Fraser River, British Columbia. Can J Earth Sci 40, 115–130.

1290 Waeles, B., le Hir, P., Lesueur, P., Delsinne, N., 2007. Modelling sand/mud transport and morphodynamics in the Seine river mouth (France): an attempt using a process-based approach. Hydrobiologia 588, 69–82. https://doi.org/10.1007/s10750-007-0653-2
1293 Wentworth, C.K., 1922. A scale of grade and class terms for clastic sediments. J Geol 30, 377-392.

1294 Wilbers, A.W.E., 2004. The development and hydraulic roughness of subaqueous dunes.

1295 Wilbers, A.W.E., Ten Brinke, W.B.M., 2003. The response of subaqueous dunes to floods in sand and gravel bed reaches of the Dutch Rhine. Sedimentology 50, 1013-1034.

1297 Wu, W., Wang, S.S.Y., Jia, Y., 2000. Nonuniform sediment transport in alluvial rivers. Journal of hydraulic research 38, 427-434.

1299 Yalin, M.S., 1964. Geometrical properties of sand wave. Journal of the Hydraulics Division 90, 105-119.

1300 Yalin, M.S., Karahan, E., 1979. Steepness of Sedimentary Dunes. Journal of the Hydraulics Division 105, 381-392. https://doi.org/10.1061/JYCEAJ.0005179

1302 Zomer, J.Y., Naqshband, S., Vermeulen, B., Hoitink, A.J.F., 2021. Rapidly Migrating Secondary Bedforms Can Persist on the Lee of Slowly Migrating Primary River Dunes. J Geophys Res Earth Surf 126, e2020JF005918. https://doi.org/10.1029/2020JF005918

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