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 in quantifying its value, bedload transport is essential for understanding 15 fluvial systems. In this study, we assessed different indirect bedload measurement techniques with a 16 reference direct bedload measurement in a reach of a large sandy-gravel bed river. Acoustic Doppler 17 Current Profiler (aDcp), Dune Tracking Method (DTM) and hydrophone measurement techniques were used 18 to determine bedload transport rates by using calibration with the reference method or by using empirical 19 formulas. This study is the first work which attempted to use a hydrophone to quantify bedload rates in a 20 large sandy-gravel bed river. Results show that the hydrophone is the most efficient and accurate method 21 for determining bedload fluxes in the Loire River. Although further work is needed to identify the 22 parameters controlling sediment self-generated noise, the calibration procedure adopted in this study 23 allows a satisfactory estimation of bedload transport rates. Moreover, aDcp and hydrophone measurement 24 techniques are accurate enough to quantify bedload variations associated with dune migration. 25


Introduction 26
Worldwide, rivers are in crisis (Vörösmarty et al., 2010). While changes in flow characteristics and fragmentation 27 are well known (Grill et al., 2019), the impacts of human activities on the sediment budgets are yet 28 underrepresented (Kondolf et al., 2018). The quantification of bedload transport is a key element to understand, 29 manage and restore the physical and ecological functioning of fluvial systems. It is a prerequisite to an accurate 30 estimation of global sediment budgets delivered by rivers to oceans (Syvitski and Milliman, 2007), to better 31 understand bedform dynamics in river channels (Best, 1988 In sandy-gravel bed rivers, the presence of bedforms is generally used to indirectly estimate bedload transport 52 (Simons et al., 1965). Single beam (Peters, 1978;Engel and Lau, 1980) or multibeam echosounders (Nittrouer et 53 al., 2008;Leary and Buscombe, 2020) are tools usually adopted to determine morphological parameters (such as 54 bedform height, wavelength and celerity) or to estimate sediment budget (Frings et al., 2014). These bathymetrical 55 surveys are often carried out simultaneously with sediment sampler measurements (Gaeuman and Jacobson, 56 6 V a proj = . cos ( . π) ; (3) 168 with wdir BT the flow direction with bottom track reference and bdir BT the boat direction with the bottom track reference 169 (in degree). Equation (3) gives a value of apparent bedload transport velocity for each time step (approximately 170 equal to 1 s) that was averaged to obtain a value for each sampling point. This method assumes that bedload is 171 orientated in the same direction as the main flow. According to Rennie et al. (2002), the bedload transport rate per 172 unit width (qs ADCP, g.s -1 .m -1 ) can be computed from two different kinematic models, the first of which is: 173 q s ADCP= 4 3 ρ s r V a proj ×10 3 ; (4) 174 where r =D50/2 is the particle radius, D50 is the median sediment diameter (m), ρ s is the sediment density (2650 175 kg.m -3 ). In this model, it is assumed the maximum bedload thickness is a single particle. The second model is: In order to evaluate the sensibility of the apparent bedload post-processing, the two kinematic models (Eq. 4 and 194 Eq. 5) were tested using raw apparent bedload velocity ( ) and projected apparent bedload velocity (V a proj ).

195
To assess the capability of the aDcp to detect bedforms through the evolution of apparent bedload velocity, 3 196 surveys were conducted by positioning the aDcp 0.6 m above the river bed. This experimental scheme was adopted 197

273
To evaluate the accuracy of a method against a reference, the discrepancy ratio is classically employed in the 274 literature (Van Rijn, 1984; Van den Berg, 1987; Batalla, 1997) and is defined as the ratio between the bedload rate 275 estimated with the indirect method and the bedload rate using BTMA. Computed bedload layer volume 276 concentration (Eq. 7) varies between 0.005 and 0.1 (0.03 in average). Bedload layer thickness ( ) (Eq. 6) ranges 277 between 1D50 and 7D50 (5D50 in average). Bedload rates computed using Eq. (5) underestimate BTMA bedload 278 rates with only 24% of the dataset with a discrepancy ratio between 0.5 and 2 ( Figure 4b). By considering apparent 279 bedload velocity without projection onto the flow direction, the kinematic model (Eq. 5) estimates satisfactorily 280 BTMA bedload rates with 41% of the dataset with a discrepancy ratio between 0.5 and 2. Conversely, using raw 281 apparent bedload velocity in Eq. (4), leads to only 33% of the dataset varying with a factor of 2 against 54% with 282 projected Va. According to these results, Eq. (4) better describes the sampler bedload rates with projected apparent 283 bedload velocity whereas raw apparent bedload velocity are preferred with Eq. (5). Some outlier data are observed 284 for BTMA bedload discharge lower than 0.1 g.s -1 .m -1 . These points correspond to low flow conditions for which 285 bedload samplers could under-estimate bedload fluxes (gap between the sampler mouth and the riverbed).

297
It appears difficult to estimate bedload rates only from dune celerity by assuming a direct relation between dune 298 celerity and bedload transport rates measured with BTMA. Estimation of bedload transport rates from dune 299 morphology has been performed by using empirical formula of Simons et al. (1965) (Eq. 13). The dataset is 300 composed of 49 DTM profiles with associated BTMA samples (Appendix C). The mean dune height and length 301 vary from 0.1 to 0.5 m, and 1.3 to 12 m, respectively. The median dune celerity varies between 13 and 61 m.d -1 . 302 According to Fig. 5a, bedload rates estimated with a discharge coefficient β = 0.33 are in agreement with BTMA 303 bedload rates with 67% of values in a factor of 2 of the perfect correlation compared with 49% of values for a 304 discharge coefficient of 0.57 (Fig.5a). The definition of the discharge coefficient proposed by Engel and Lau (1980)

316
Even if the statistical representativeness is lower than other methods (n=37, Appendix D), the RMA regression 317 between the acoustic power and BTMA sampling is better (R²=0.70) and 60% of values varying between a factor 318 2 (Fig. 5b). In consequence, new equation to estimate sediment transport from acoustic power is proposed: 319 P=6.6 ×10 10 q s 1.32 ; with Thorne's (1986) theory. The central frequency of the median spectrum of the Loire River is approximately 326 equal to 140 kHz. The frequency band of the bedload is shifted towards high frequencies due to finer grain size. 327 The acoustic power corresponding to the integration of the spectrum over a range of frequency is related to the 328 grain size (Thorne, 1985) and sediment kinematics (Gimbert et al., 2019). To analyse the effect of sediment mobility 329 on the acoustic power, the transport stage parameter (Van Rijn, 1984) is calculated. The power law adjusted 330 between these two parameters provides evidence for a positive evolution of the acoustic power with sediment 331 mobility (Fig. 6b). 332

336
The comparison can be performed between indirect methods to discuss the acceptability of the BTMA reference. 337 The apparent bedload velocity and the acoustic power are poorly correlated with mean dune morphological 338 parameters (Table 1).  The apparent bedload velocity estimated by aDcp is the velocity of the top layer velocity or dynamical active layer 346 (sediment being transported over a dune), whereas the dune celerity is the mobility of the exchange event active 347 layer, according to Church and Haschenburger (2017). It must be noted that apparent bedload velocity is higher 348 than dune celerity by a factor approximately equal to 100. On the other hand, the apparent bedload velocity is 349 positively correlated with the acoustic power. The COD of the RMA regression is equal to 0.76 (Fig. 7a). 350 Before focusing on the spatial distribution of unit bedload rates, total bedload rates are calculated by interpolating 351 unit bedload rates between sampling points on the cross section for each method. The COD of the RMA regression 352 established between BTMA bedload rates and water discharge is 0.71 ( Fig. 7b) with 77% of the values varying 353 within a factor of 2. The dispersion of bedload rates is higher for low water discharge (less than the mean annual 354 discharge of 680 m 3 .s -1 ). Bedload rates are estimated from Eqs. (13), (15) and (16), for the DTM, the aDcp and the 355 hydrophone, respectively. Both the hydrophone and DTM bedload rates are less scattered with 96% of values with 356 a discrepancy ratio between 0.5 and 2, compared with 82% for the aDcp.

Determination of bedload transport on a cross section using acoustics methods 362
To compare the spatio-temporal distribution of bedload transport rates, sediment transport sampling was performed 363 on the same cross section for all surveys and for various discharge conditions. Two surveys with contrasting 364 discharge conditions and different bed configurations are presented (

379
In May 2018, a bar (B1. Fig. 8a) was located just upstream of the sediment gauging section from the center to the 380 right part of the channel. In the left part of the channel, BTMA sampling was performed on the stoss side of another 381 bar (B2, Fig. 8a). Consequently, bedload rates gradually rose from the center of the channel (2 g.s -1 .m -1 , S4) to the 382 left part of the channel (15 g.s -1 .m -1 , S1) except for the DTM (Fig. 9a). The intensity of bedload transport rates was 383 evaluated for each acoustic signal from regression equations established above (Eqs. 13, 15 and 16, for DTM, 384 aDcp and hydrophone, respectively). The linear equation of aDcp calibration allow the calculation of negative 385 bedload flux for apparent bedload velocity below 0.0016 m.s -1 (Fig. 9a, S4). ADcp and hydrophone signals followed 386 the same trend as the BTMA measurement. In the right part of the channel, no reference measurements were 387 available (S5 and S6) but all acoustic signals followed the same trend (increasing bedload transport rates). The 388 bedload rates estimated with the DTM were lower than the reference in the left part of the channel. This can be 389 explained by the reduced number of dunes in this area that caused a higher uncertainty in dune celerity 390 determination. In the right part, the proximity of the bar front induced lower bedload transport rates measured with 391 aDcp and hydrophone. DTM integrates sediment dynamics over a longitudinal profile that does not necessarily 392 reflect the bedload transport conditions at a local scale. Due to the lee effect provided by the proximity of the bar 393 front, dunes were not present downstream of the bar and only dunes located on the stoss side of the bar were used 394 to calculate the mean dune celerity. ADcp underestimates whereas the hydrophone method overestimates the unit 395 bedload rate compared with BTMA measurements.

401
In December 2019 (Fig. 9b), the flow discharge was higher (2050 m 3 .s -1 ) than the value observed in May 2018 402 (Q=604 m3s-1) and measured bedload rates ranged between 32 and 120 g.s -1 .m -1 . Due to the bar migration, the 403 bed configuration was different. Bar B1 reached the sediment gauging cross section. As a consequence, sampling 404 points S3 to S6 were located on the stoss side of bar B1 (Fig. 8b). The sampling point S2 was located just 405 downstream of the bar front where the velocity and sediment transport rates were lower (Fig. 8b). The high spatial 406 resolution of the hydrophone measurements confirmed that the preferential bedload active width was located 407 between 250 and 450 m from the left bank (Fig. 9b). For this survey, acoustic signals (i.e. acoustic power, apparent 408 bedload velocity) followed the same evolution pattern as samplers along the cross section except for S3. Bedload 409 transport rates determined with the DTM did not follow the trend of bedload rates determined with aDcp and 410 hydrophone at the proximity of bar front and near the bank as in the previous survey (S2 and S6). The hydrophone 411 model overestimated the sediment transport in comparison with the BTMAs for S1, S3 and S5. 412

Sediment transport processes on bedforms analyzed from aDcp and hydrophone 413
The aDcp computed bedload rates evolved according to bedform location for fixed measurements performed on 414 dunes of height ranging between 0.05 m and 0.2 m ( Fig. 10a and 10b). Higher bedload rates were found on the 415 crest of the dune and lower values in the trough. The amplitude of bedload rates between crest and trough for low 416 flow conditions (Fig. 10b) ranged between 42 g.s -1 .m -1 and 67 g.s -1 .m -1 . For higher flow conditions, it varied between 417 45 g.s -1 .m -1 and 91 g.s -1 .m -1 (Fig. 10a). These values were extracted considering bedload rates in trough as equal 418 to zero (not negative). The aDcp linear regression (Eq. 15) did not allow the calculation of bedload transport rates 419 due to negative apparent bedload velocity. This is the case downstream the lee face of dunes (Fig. 10a,

427
Hydrophone drifts showed that the longitudinal evolution of acoustic power can be correlated with changes in 428 elevation of the riverbed due to dune and bar presence. For instance, in the presence of a 2 meter high bar front, 429 the bedload rate significantly decreased, illustrating the lee effect that is characterised by a decrease in bedload 430 sediment transport (Fig. 11a). This shows that the hydrophone is sensitive enough to detect this local phenomenon 431 induced by the presence of a bar front immediately upstream. The bedload rates range from about 8 g.s -1 .m -1 on 432 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). 433 According to flow velocity measurements, it appears that a 2 m high bar front can influence flow velocity and 434 bedload transport rates up to the reattachment point located approximately 100 m downstream. Downstream of the 435 bar front, the bedload transport rate increased at 11h06min (Fig. 11a) that would be in coincidence with the flow 436 reattachment point. Further downstream, the bedload transport rate increased from 8.5 to 23.4 g.s -1 .m -1 437 (representing respectively an acoustic power of 1.2×10 12 µPa² to 4.1×10 12 µPa²), where dunes exhibit a more 438 regular shape increasing their amplitudes from 0.02 m to 0.4 m, approximately. On the left part of the channel (Fig.  439 11b), the drift was located at the stoss side of a bar where larger dunes were observed (about 1 m in height) with 440 superimposed small dunes (height approximately equal to 0.3 m). The bedload transport rate calculated above 441 these bedforms increased near the crests of the large dunes (about 80 g.s -1 .m -1 ) and decreased in the troughs 442 (about 50 g.s -1 .m -1 ) where superimposed bedforms were smaller (Fig. 11b). This high spatial discretization makes the hydrophone functional over a wide range of discharges (even for low 474 water discharge, Fig. 6b) by catching the high spatial variability of bedload transport. It should be pointed that the 475 regression calculated in the present study (Eq. 16) is obtained from unit bedload rates (from several samples) and  (Rennie et al., 2017). Moreover, the accuracy of the 507 measurement on a single cross section depends on the water depth heterogeneity that in turn influences the aDcp 508 footprint and makes the aDcp method location sensitive when bedforms are present (Fig. 9b). Estimation of bedload 509 rates using empirical equations is limited by the number of variables that are difficult to measure in the field (e.g. Eq. (5) better estimates sampler bedload rates using the raw bedload velocity (Figure 4b). If we consider that cb 521 and ds are well estimated by van Rijn equations (Eqs. 6 and 7), these results confirm that the projection of the 522 apparent bedload velocity decreases the bedload velocity magnitude when the bedload direction differs from flow 523 direction (e.g. bed slope effects). The influence of bedload velocity projection appears to be important when 524 bedload are computed using kinematic models. Nevertheless, the calibration curve seems to be in agreement with 525 other studies. Although, the application domain of Eq. (4) does not correspond to the conditions in the Loire River, 526 the decrease of projected Va seems to compensate the overestimation of bedload rates when the raw apparent 527 bedload velocity is used. This is the opposite for Eq. an accurate method to estimate bedload transport in the Loire River (Fig. 6b) where dunes are present and high 544 enough (over the mean annual discharge). 545 As suggested by previous authors, both aDcp (Kenney, 2006) and hydrophone (Bedeus and Ivicsics, 1963) allow 546 a reliable representation of bedload fluxes on a cross section through the regressions with bedload rates obtained 547 using samplers. Fig. 9a and Fig. 9b highlight the benefits of the use of acoustic devices for the determination of 548 bedload transport rates in a large sandy gravel-bed rivers. In the present study, the time needed in the field to 549 complete the BTMA, DTM, aDcp and hydrophone methods (respectively the red, yellow, blue and black lines of 550 methods tested here seem to be able to quantify total bedload transport as efficiently as the direct method (Fig. 6b) 555 but special care should be taken with local estimation of bedload rates ( Fig. 9a and Fig. 9b). 556 Finally, regarding the correlation of aDcp and hydrophone with BTMA ( Fig. 3a and Fig. 5b), we can raise the 557 question of the reference method. Indeed, the regression between aDcp and hydrophone is more significant 558 (R²=0.76) and it could be the quality and the accuracy of BTMA sampling that reduce the quality of indirect 559 measurement regressions. increases from trough to crest of the dune and confirmed previous observations made with samplers (Kostachuck 566 and Villard, 1996;Carling et al., 2000). These observations were made on large dunes that migrate too slowly to 567 allow a continuous measurement along bedforms. Our study complements these observations by providing a fixed 568 and continuous measurement of apparent bedload velocity and providing bedload transport rate estimation based 569 on a calibration curve. The mean time between two subsequent crests (1 hour) shows that even for small bedforms 570 (HD = 0.05 to 0.2 m, Fig. 10a and Fig. 10b), the aDcp location significantly influences the bedload rates calculated 571 over a dune field (0.03 to 0.08 m.s -1 of difference between crest and trough). This suggests that care should be 572 taken using this method on river beds where large dunes are present but also when small dunes are migrating. 573 According to Rennie and Millar (2004), the sampling area diameter increases with the water depth and is 574 approximately equal to flow depth. Our protocol minimizes the water depth by submerging the aDcp and therefore 575 Supprimé: s 576 Supprimé: s 577 minimizes the beams sampling diameter, hence, minimizes the probability of sampling stoss or lee sides of the 578 same dune simultaneously. 579 In our study context, the acoustic power recorded by the hydrophone was not affected by the distance between the 580 hydrophone and the river bed. To our knowledge, there are no references mentioning investigations on bedload 581 transport rates associated with bedforms using a hydrophone. At a large time step (mean aDcp and hydrophone 582 samples), the apparent bedload velocity and the acoustic power did not follow the observed trend of mean bedform 583 characteristics derived from DTM measurement (dune celerity and dune height). This could be explained by the 584 difference of spatial scales between DTM and other methods. For a smaller time step, our results showed that 585 acoustic power is able to describe the influence of bars on bedload sediment transport (Fig. 11a). Moreover, as for 586 the aDcp, the hydrophone also detects the theoretical pattern of bedload transport rates associated with bedform 587 migration. As shown by Reesink et al. (2014), the lee effect generated by bar fronts influences the development of 588 dunes downstream. Specifically, the hydrophone is able to record the decrease of the acoustic power immediately 589 downstream of the bar front and its progressive increase downstream (translated by the development of dunes at 590 about 11h06, Fig. 11a). In the present study, dunes smaller than 0.4 m (Fig. 11a) were not high enough to allow 591 the observation of changes in the acoustic power along the bedform stoss sides. On the contrary, for higher dunes 592 (HD = 1 m, Fig. 11b) the bedload generated noise can be well recorded by the hydrophone. A hydrophone senses 593 all noises that are propagating in the water column. Therefore, the hydrophone can record noises that are far away 594 from its location. Noises are more and more attenuated with increasing distance (Geay et al., 2019). Particularly, 595 when there is few bedload noise close to the hydrophone, the hydrophone can sense the bedload noise that are 596 generated far away. This behaviour could explain why the hydrophone tends to overestimate bedload fluxes when 597 bedload fluxes are weak especially immediately downstream of a bar front (Fig. 9b). 598 Hydrophone lower detection limit was not reached during our study whereas the dispersion of bedload rates 599 measured with samplers for low apparent bedload velocity (Fig. 3) suggests that the lower detection limit of the 600 apparent bedload velocity by the aDcp seems to be about 1 cm.s -1 (Rennie et al., 2017). This lower detection limit 601 of the apparent bedload velocity should be reduced to the bottom track uncertainty by using our protocol with a 602 submerged and fixed aDcp device. 603

Conclusions 604
In this work, direct (BTMA samplers), active (aDcp and DTM) and passive (hydrophone) acoustic measurements 605 of bedload transport rates were compared in a large, sandy-gravel bed river characterized by the presence of bars 606 and superimposed dunes. Calibration curves between apparent bedload velocity measured using aDcp and 607 bedload rates measured using BTMA samplers were established but remain site-specific and dependent on grain 608 size. DTM seemed to be inappropriate where macroforms are present, as it influences the location and the size of