Relevance of acoustic methods to quantify bedload transport 1 and bedform dynamics in a large sandy-gravel bed river 2

14 Despite the inherent difficulties to quantify its value, bedload transport is essential to understand fluvial 15 systems. In this study, we assessed different indirect bedload measurement techniques with a reference 16 direct bedload measurement in a section of a large sandy-gravel bed river. Acoustic Doppler Current 17 Profiler (aDcp), Dune Tracking Method (DTM) and hydrophone measurement techniques were used to 18 determine bedload transport rates using calibration with the reference method or using empirical formula. 19 Results show that the hydrophone is the most efficient and accurate method to determine bedload flux in 20 the Loire River. Even though parameters controlling self-generated noise of sediments still need to better 21 understood, the calibration determined in this study allows a good approximation of bedload transport 22 rates. Moreover, aDcp and hydrophone measurement techniques are both able to continuously measure 23 bedload transport associated to bedform migration. 24


Introduction 25
Worldwide, rivers are in crisis (Vorösmarty et al., 2010). While changes in flow characteristics and fragmentation 26 are well known (Grill et al., 2019), the impacts of human activities on the sediment budgets is yet underrepresented 27 (Kondolf et al., 2018). The quantification of bedload transport is a key element to understand, manage and restore 28 the physical and ecological functioning of fluvial systems. It constitutes a prerequisite to the accurate estimation of 29 global sediment budgets delivered by rivers to oceans (Syvitski and Milliman, 2007), to better understand bedform 30 dynamics in river channels (Best, 1988  (2) 111 where VGPS and VBT are respectively the boat velocity according to GPS reference and bottom track. When the 112 GPS signal was poor or missing, the apparent velocity was considered directly equal to the boat velocity according To avoid compass and GPS issues, and to eliminate the effect of residual lateral displacement of the anchored 118 boat, the apparent bedload velocity was projected onto the flow direction using: 119 (3) 120 with wdir GPS the water direction with GPS reference and bdir BT the boat direction with the bottom track reference (in 121 degree). Eq. (3) gives a value of apparent bedload transport velocity for each time step (about 1 s) that was 122 averaged to obtain a value for each sampling point. According to Rennie et al. (2002), the bedload transport rate 123 per unit width (qs ADCP, g.s -1 .m -1 ) can be computed from two different models: 124 q s ADCP= 4 3 ρ s r V a ×10 3 ; (4) 125 q s ADCP= V a d s (1-λ)ρ s ; (5) 126 In Eq. (4), r =D50/2 is the particle radius and the active layer thickness (ds) is considered as a constant, with D50 is 127 the median sediment diameter (m), ρ s is the sediment density (2650 kg.m -3 ). In Eq. (5), λ is the porosity of the 128 active transport layer considered as a constant and equal to 0.35, and the van Rijn (1984) formulation was adopted 129 to compute the active layer thickness as a function of the hydraulic condition and sediment grain size: where T is the transport stage parameter that reflects the sediment mobility, u * ' is the bed shear velocity related to 134 the grain (m.s -1 ), d is the mean water depth (m), D90 is the 90 th percentile of the sediment grain size (m), , u ̅ is the 135 mean water velocity measured from aDcp (m.s -1 ) and u *cr is the critical bed shear velocity (m.s -1 ) calculated from 136 the Shields curve (Van Rijn, 1984) and function of grain size through the scaled particle parameter D*: where g is the acceleration of the gravity (m.s -²), ν the kinematic viscosity (m 2 .s −1 ) and s the sediment density ratio. 139 For the range of grain size of this study, u *cr is computed as follows: 140 To assess the capability of the aDcp to detect bedforms through the evolution of apparent bedload velocity, 3 143 surveys were conducted by positioning the aDcp 0.6 m above the river bed. This experimental scheme was adopted 144 to avoid lateral movements of the boat, to be as close as possible to the river bed, and to reduce the space between 145 beams. This configuration permitted to fix the insonified surface for each beam to about 0.0046 m² and a distance 146 of 0.56 m between opposed beams, and could allow a better understanding of the apparent bedload velocity 147 gradient along bedforms. These surveys were performed during several hours (from 2.1 h to 4.7 h) to see more 148 than one dune lee side pass under the device. The value of apparent bedload velocity was smoothed by using a 149 moving windows with an average of 500 points (approximately 500 seconds) to remove the noise from the raw 150 dataset. In the present study, all negative values were excluded from the comparison with BTMA measurements 151 (16% of apparent velocity values). Lau, 1980) following the dune crests between two subsequent bathymetric surveys for a mean interval time equal 159 to 40 minutes. The interval time needs to be adjusted with discharge because of the dune celerity variation from 160 one survey to another. The determination of a proxy to evaluate sediment transport directly from DTM 161 measurements is difficult. A semi-empirical equation was used to compare bedload transport rates with the 162 reference measurement. The computed dune parameters were used to calculate the unit bedload transport rate 163 (q s DTM, g.s -1 .m -1 ) using the formula by Simons et al. (1965): 164 where H D is the mean dune height along the profile (m), C D is the median dune celerity (m.s -1 ) and β is the bedload 166 discharge coefficient equal to 0.5 for a perfect triangular dune shape. The β coefficient neglects the volume of 167 bypassing material from previous dunes or exchanges between bedload and suspended load (Wilbers, 2004). Due to its large variability (Van den Berg, 1987;Ten Brinke et al., 1999;Wilbers, 2004), the sensibility of the bedload 169 transport rate was assessed for β=[0.33; 0.57], as proposed in the literature (Engel and Lau, 1980;Wilbers, 2004). 170 Considering the accuracy of the bathymetrical echosounding and the representativeness of dune celerity, only 171 profiles with a mean dune height of 0.1 m and more than 10 dunes are considered. 172

Hydrophone and acoustic power 173
Passive acoustic monitoring was performed with a Teledyne RESON Hydrophone TC4014-5 (sensitivity of -180 174 dB) plugged into an EA-SDA14 card from RTSYS Company. This device has a large frequency range from 0.015 175 to 480 kHz, with a linear response until 250 kHz (±3dB). The hydrophone has been deployed following the protocol 176 (13) 184 The minimum frequency was chosen to avoid hydrodynamic and engine noises, while the maximum frequency was 185 set by the upper limit frequency of the device and was adjusted related to PSD. Finally, the nearest hydrophone 186 drift for each BTMA sampling point was selected. Several tests were carried out to ensure that these acoustic 187 power variations were not related to the distance between the hydrophone and the river bed. As no theoretical 188 formula has been developed to estimate bedload rates from hydrophone measurements, only the calibration 189 approach was implemented.

Comparison between acoustics and direct bedload transport rate measurements 192
The BTMA dataset is composed of 135 unit bedload rates calculated from 2628 individual sediment sampling. That 193 represents an average of 19 samples on each sampling point to compute unit bedload rates (minimum of 5 and 194 maximum of 57 samples). Bedload rates measured using the BTMAs ranged between 0.01 and 268 g.s -1 .m -1 . The 195 standard deviation of unit bedload rates increased with discharge with a mean value of 33 g.s -1 .m -1 . This illustrates 196 the spatio-temporal variability of sediment transport induced by bedform migration.
The aDcp dataset is composed of 98 simultaneous measurements of apparent bedload velocity and BTMA 198 samplings (Fig. 3a). The mean apparent bedload velocity is 0.022 m.s -1 and the maximum value was 0.11 m.s -1 . A 199 Reduced Major Axis (RMA) regression has been computed between these two variables with a coefficient of

212
Bedload transport rates were calculated considering the concentration and the thickness of active layer as constant. 213 In order to evaluate the accuracy of a method against a reference, the discrepancy ratio is classically employed in 214 the literature (Van Rijn, 1984; Van den Berg, 1987; Batalla, 1997). This ratio is defined as the ratio between the 215 bedload rate estimated with the indirect method and the bedload rate using BTMA. Approximately 57% of the 216 computed bedload transport rate (Eq. 4) is within the discrepancy ratio (Figure 3b), while only 14% when using the 217 Van Rijn definition of the active layer thickness (Eq. 5). According to these results, considering the active layer 218 thickness proportional to the median sediment grain size seems to be a good approximation to determine bedload 219 rate, especially for bedload rate greater than 1 g.s -1 . 220 It appears difficult to estimate bedload rates only from dune celerity by making a direct relation between dune 221 celerity and bedload transport rates measured with BTMA. Estimation of bedload transport rates from dune 222  The acoustic power corresponding to the integration of the spectrum over a range of frequency is related to grain 242 size (Thorne, 1985) and sediment kinematics (Gimbert et al., 2019). To analyze the effect of sediment mobility on 243 the acoustic power, the transport stage parameter (Van Rijn, 1984) is calculated. The power law adjusted between 244 these two parameters evidences a positive evolution of the acoustic power with sediment mobility (Fig. 5b). 245 https://doi.org/10.5194/esurf-2020-77 Preprint. Discussion started: 7 October 2020 c Author(s) 2020. CC BY 4.0 License.

250
The comparison can be made between indirect methods to discuss the acceptability of the BTMA reference. The 251 apparent bedload velocity and the acoustic power are not well-correlated with mean dune morphological 252 parameters (dune celerity and dune height). The aDcp method is measuring the apparent velocity of the grain being 253 transported from the stoss to the lee side of a dune. It must be noted that apparent bedload velocity is higher than 254 dune celerity with about a factor 100, whereas the grain size (D50) is smaller than dune height with the same order. 255 Therefore, sediments that are 100 times smaller than dune height allows the dune migration with a celerity 100 256 times smaller than their own celerity. On the other hand, the apparent bedload velocity is positively correlated with 257 the acoustic power. The RMA regression model explains 76% of the dataset dispersion (Fig. 6a). 258 Before focusing on the spatial distribution of unit bedload rates, total bedload rates are calculated by interpolating 259 unit bedload rates between sampling points on the cross section for each method. The RMA regression established 260 between BTMA bedload rates and water discharge explain 71% of the dataset dispersion ( Fig. 6b)

Determination of bedload transport axes on a cross section using acoustics methods 270
To compare the spatio-temporal distribution of bedload transport rates, sediment transport gauging was performed 271 on the same cross section for all surveys and for various discharge conditions. Two surveys with contrasting 272 discharge conditions and different bed configurations are presented to illustrate the capacity of acoustics methods 273 to determine bedload axes in a river reach characterized by the presence of macroform and superimposed 274 mesoforms (sensu lato, Jackson, 1975).

279
In May 2018, a bar (B1. Fig. 7a) was located just upstream the sediment gauging section from the center to the 280 right part of the channel. In the left part of the channel, BTMA sampling was done on the stoss side of another bar 281 (B2, Fig. 7a). Consequently, bedload rates were gradually rising from the center of the channel (2 g.s -1 .m -1 , S4) to 282 the left part of the channel (15 g.s -1 .m -1 , S1) except for the DTM (Fig. 8a). The intensity of bedload transport rates 283 a b a b was evaluated for each acoustic signal from regression equations established above (Eq. 12, Eq. 14 and Eq. 15, 284 for DTM, aDcp and hydrophone, respectively). ADcp and hydrophone signals followed the same evolution as the 285 BTMA measurement. In the right part of the channel, there was no reference measurements (S5 and S6) but all 286 acoustic signals followed the same trend (increasing bedload transport rates). The bedload rates estimated with 287 the DTM were lower than the reference in the left part of the channel. This can be explained by the reduced number 288 of dunes in this area that caused a higher uncertainty in dune celerity determination. In the right part, the proximity

297
In December 2019 (Fig. 8b), discharge was higher (2050 m 3 .s -1 ) and measured bedload rates ranged between 32 298 and 120 g.s -1 .m -1 . Due to the bar migration, the bed configuration was different. Bar B1 migrated on the sediment 299 gauging cross section. As a consequence, sampling points S3 to S6 were located on the stoss side of bar B1 (Fig.  300   7b). The sampling point S2 was located just downstream the bar front where velocity and sediment transport rates 301 were lower (Fig. 7b). The high spatial resolution of the hydrophone measurements confirmed that the preferential 302 bedload axis was located between 250 and 450 m from the left bank (Fig. 8b). For this survey, acoustic signals 303 (i.e. acoustic power, apparent bedload velocity) followed the same evolution pattern as isokinetic samplers along 304 the cross section except for S3. Bedload transport rates determined with the DTM did not follow the trend of bedload 305 rates determined with aDcp and hydrophone at the proximity of bar front and near the bank as in the previous 306 survey (S2 and S6). The hydrophone model overestimated the sediment transport in comparison with the BTMAs 307 for S1, S3 and S5. 308 a b

Sediment transport processes on bedforms analyzed from aDcp and hydrophone 309
The aDcp computed bedload rates evolved according to bedform location for fixed measurements performed on 310 dunes of height ranging between about 0.05 m and 0.2 m (Fig. 9a and 9b). Higher bedload rates values were found 311 on the crest of the dune and lower values in the trough. The amplitude of bedload rates between crest and trough 312 for low flow conditions (Fig. 9a) ranged between 42 g.s -1 .m -1 and 69 g.s -1 .m -1 . For higher flow conditions, it varied 313 between 43 g.s -1 .m -1 and 111 g.s -1 .m -1 (Fig. 9b). The aDcp power regression (Eq. 14) did not allow the calculation 314 of bedload transport rates due to negative apparent bedload velocity. This is the case downstream the lee face of 315 dunes (Fig. 9a, between 19

321
Hydrophone drifts showed that the longitudinal evolution of acoustic power can be correlated with changes in 322 elevation of the riverbed due to dune and bar presence. For instance, in the presence of a 2 meter high bar front, 323 the bedload rate significantly decreased, illustrating the lee effect that is materialized by a decrease in bedload 324 sediment transport (Fig. 10a). This, showed that the hydrophone is sensitive enough to detect this local 325 phenomenon induced by the presence of a bar immediately upstream. The bedload rates range from about 8 g.s -326 1 .m -1 on the bar crest to 376 g.s -1 .m -1 in the bar trough (1 10 12 µPa² to 1.7 10 14 µPa² of acoustic power, respectively). 327 According to flow velocity measurements, it appears that a 2 m high bar front can influence flow velocity and 328 bedload transport rates up to the reattachment point located approximately 100 m downstream. Downstream the 329 bar front, the bedload transport rate increased from 11h06min (Fig. 10a) that would be in coincidence with the flow 330 reattachment point. Further downstream, the bedload transport rate increased from 8.5 to 23.4 g.s -1 .m -1 331 (representing respectively an acoustic power of 1.2×10 12 µPa² to 4.1×10 12 µPa²), where dunes exhibit a more 332 regular shape increasing their amplitudes from 0.02 m to 0.4 m, approximately. In the left part of the channel (Fig.  333 10b), the drift was located on the stoss side of a bar where larger dunes were observed (about 1 m in height) with 334 a b superimposed small dunes (height approximately equal to 0.3 m). The bedload transport rate calculated above 335 these bedforms increased near the crests of the large dunes (about 80 g.s -1 .m -1 ) and decreased in the troughs 336 (about 50 g.s -1 .m -1 ) where superimposed bedforms were smaller (Fig. 10b).

Relevance of acoustics for computing bedload transport rates 344
Despite their lack of accuracy and their low spatial representativeness, isokinetic samplers allow a direct 345 measurement of bedload and represents. To this date, measurement based on isokinetic samplers is the only 346 technique used to compare or calibrate another bedload sediment gauging method in large rivers. The presence 347 of bars affect sediment transport locally and make sampling method very sensitive to the location of the sampling 348 point. For low water discharge (below mean annual discharge, 800 m 3 .s -1 ), bars are emerged and reduce 349 considerably the width where sediment transport occurs. The number of sampling points decrease with discharge 350 (because bars were not flooded) leading to a higher bedload rates variability (Fig. 6b). Moreover, for these hydraulic 351 conditions, bedload transport occurs over a very low thickness reducing the efficiency of the sampler (initially 352 calibrated to 50%, Eijkelkamp, 2003). The presence of dunes influences the performance of the sampler by 353 preventing the exact positioning of sampler mouth on the river bed. 354 The use of hydrophones to estimate bedload transport in a lowland sandy gravel-bed river constitutes a new 355 research topic. As discussed by several authors, the use of hydrophones was so far restrained to gravel-bed rivers 356 2.5% and channel width ranging between 8 and 60 m. In these mountainous environments, the median grain size 361 ranged between 0.9 and 62 mm (n=582 samples). In our study, the downstream reach of the Loire River shows 362 smaller slope (S=0.02%), a wider channel (W=500 m), and a median grain size ranging between 0.3 mm to 3.1 363 mm (n=450 samples). The hydrophone is an efficient tool for sediment transport gauging, allowing the 364 measurement of numerous sampling points (average of 17 sampling points) during few time (an hour). This high 365 spatial discretization makes the hydrophone functional over a wide range of discharges (even for low water 366 discharge, Fig. 6b) by catching the high spatial variability of bedload transport. It should be pointed that the 367 regression calculated in the present study (Eq. 15) is obtained from unit bedload rates (from several samples) and heterogeneity that influences the bottom track sampling area of beams and make the aDcp method location 385 sensitive when bedforms are present (Fig. 8b). When negative values of apparent bedload velocity are measured, 386 the value is considered as null and interpolated over a width that is probably wider than the effective width where 387 bedload transport is null. In consequence, total bedload transport rates estimated with Eq. (14) lead to an 388 underestimation of BTMA bedload transport rates, especially for low water discharge (Fig. 6b)  Contrarily to the aDcp, the DTM allows the investigation of "event active layer" (Church and Haschenburger, 2017). to estimate bedload transport in the Loire River (Fig. 6b) where dunes are present and high enough (over the mean 414 annual discharge). 415 As suggested by previous authors, both aDcp (Kenney, 2006) and hydrophone (Bedeus and Ivicsics, 1963) allow 416 a reliable representation of bedload fluxes on a cross section through the regressions with bedload rates obtained 417 using samplers. Fig. 8a and Fig. 8b highlight the benefits of the use of acoustics devices for the determination of 418 bedload transport rates in a large sandy gravel-bed rivers. In the present study, the time needed in the field to 419 complete the red, yellow, blue and black lines of Fig. 8b (BTMA, DTM, aDcp and hydrophone methods, 420 respectively) are about 1 day, 4 hours, 1.5 hours and 45 minutes, respectively. This underlines the high potential 421 of hydrophones to quantify bedload in large rivers with high spatial variability of sediment transport and map 422 bedload sediment fluxes at a large scale as proposed by Williams et al. (2015) using the aDcp. Moreover, all indirect 423 methods tested here seem to be able to quantify total bedload transport as efficient as the direct method (Fig. 6b) 424 but special care should be taken to local estimation of bedload rates (Fig. 8a and Fig. 8b). 425 Finally, regarding the correlation of aDcp and hydrophone with BTMA ( Fig. 3a and Fig. 5a), we can raise the 426 question of the reference method. Indeed, the regression between aDcp and hydrophone is more significant (R²=0.76) and it could be the quality and the accuracy of BTMA sampling that reduce the quality of indirect 428 measurement regressions. 429

Hydrophone and aDcp sensibility to bedform observations 430
Passive (hydrophone) and active (aDcp) acoustic devices are rarely used for analysis of bedload transport rates 431 associated with bedforms in relatively large lowland rivers. Several studies mention differences in apparent bedload  Fig. 9a and Fig. 9b), the aDcp location significantly influences the bedload rates calculated 440 over a dune field (0.03 to 0.08 m.s-1 of difference between crest and trough). This suggests that care should be 441 taken using this method on river beds where large dunes are present but also when small dunes are migrating. 442 According to Rennie and Millar (2004), the sampling area diameter increases with flow depth and is more or less 443 equal to flow depth. Our protocol minimizes flow depth by submerging the aDcp and therefore minimizes the beams 444 sampling diameter, hence, minimizes the probability to sample stoss or lee sides of the same dune simultaneously. 445 In our study context, the acoustic power recorded by the hydrophone was not affected by the distance between the 446 hydrophone and the river bed. To our knowledge, there are no references mentioning investigations on bedload 447 transport rates associated with bedforms using a hydrophone. At a large time step (mean aDcp and hydrophone 448 samples), the apparent bedload velocity and the acoustic power did not follow the observed trend of mean bedform 449 characteristics derived from DTM measurement (dune celerity and dune height). This could be explained by the 450 difference of spatial scales between DTM and other methods. For a finer time step, our results showed that acoustic 451 power is able to describe the influence of bars on bedload sediment transport (Fig. 10a). Moreover, as for the aDcp, 452 the hydrophone also detects the theoretical pattern of bedload transport rates associated with dune migration. As 453 shown by Reesink et al. (2014), the presence of bars influences the development of dunes downstream and the 454 distance between bar crest and dune initiation point increases with flow velocity. Specifically, the hydrophone is 455 able to record an increasing acoustic power assumed to be associated with the increasing dune height downstream 456 of the bedform initiation point (about 11h06, Fig. 10a). In the present study, dunes smaller than 0.4 m (Fig. 10a) 457 were not high enough to allow the observation of changes in the acoustic power along the bedform stoss sides. 458 Hydrophone lower detection limit was not reached during our study whereas the dispersion of bedload rates 461 measured with samplers for low apparent bedload velocity suggests that the lower detection limit of the apparent 462 bedload velocity by the aDcp seems to be about 1 cm.s -1 (Rennie et al., 2017). This lower detection limit of the 463 apparent bedload velocity should be reduced to the bottom track uncertainty by using our protocol with a 464 submerged and fixed aDcp device. 465

Conclusions 466
In this work, direct (BTMA isokinetic samplers) with active (aDcp and DTM) and passive (hydrophone) acoustic 467 measurements of bedload transport rates were compared in a large, sandy-gravel bed river characterized by the 468 presence of bars and superimposed dunes. Calibration curves between apparent bedload velocity measured using 469 aDcp and bedload rates measured using BTMA samplers were established but remain site-specific and strongly 470 correlated to grain size. DTM seemed to be inappropriate where macroforms are present, as it influences the 471 location and the size of superimposed mesoforms. The calculation of bedload rates with empirical formulas is 472 sensitive to bedload discharge coefficient for DTM and to thickness and concentration of active layer for aDcp. 473 These parameters remain always difficult to measure in the field. The use of the hydrophone to monitor bedload 474 transport rates is for the moment mainly limited to gravel-bed rivers. Results presented in this study highlight the 475 potential of this technique for the quantification and mapping of bedload transport rates in relatively large river 476 channels where migrating bedforms are present. This study consolidates a previous recent study (Geay at al.,477 2020) by extending a general calibration curve to large sandy-gravel bed rivers. The hydrophone global calibration 478 curve allows a good representation of the bedload fluxes evolution through a cross section. The method is cheaper 479 to implement and more efficient than the reference method. This might allow mapping bedload transport rates by 480 interpolating acoustic power along several cross sections performed on a large sandy gravel bed river. Moreover, 481 acoustic devices (aDcp and hydrophone) are able to catch the evolution of bedload signal along bedforms stoss 482 and lee sides with some limitation of bedform size for the hydrophone and signal noise for the aDcp. Regarding 483 results of the comparison between bedload velocity and acoustic power, the association of aDcp and hydrophone 484 could be an efficient way to control the quality of both devices. However, additional measurements need to be done 485 to explore the quality of the regression in other river environments (different grain sizes, river-bed slope or 486 propagation effect). Finally, the lack of post-processing open access tools for these surrogate technologies slow 487 the development and use of these devices to bedload rates determination.