G Antoine

B Camenen
email: benoit.camenen@inrae.fr

M Jodeau

J Némery

M Esteves

Downstream erosion and deposition dynamics of ne suspended sediments due to dam ushing

Keywords:

Fine sediment dynamics downstream dams is a key issue when dealing with environmental impact of hydraulic ushing. This paper presents an analysis of six eld campaigns carried out during dam ushing events (in June 2006(in June , 2007(in June , 2009(in June , 2010(in June , 2011(in June , and 2012) ) in the Arc-Isère river system in the Northern French Alps. Suspended sediment concentrations (SSC) and discharges were evaluated using direct measurements or/and 1D hydraulic modelling at up to 14 locations along the 120 kilometres-long river channel.

The total suspended sediment ux (SSF) is analysed along the Arc and Isère rivers for each Arc dam ushing event. Uncertainties were quantied based on a propagation method of both measurement and modelling errors. The resulting condence interval provides elements of discussion on the signicance of the sediment mass balance between two consecutive measurement sites. Whereas the discharge time-series of each ushing event is roughly the same, the quantity of ne sediments removed from the reservoirs varied from 10,000 tons in 2007 to 40,000 tons in 2006. Also, a signicant erosion is observed in the river system for some events (20,000 tons in 2007) while the SSF barely varied for other events (in 2009 and 2011). This detailed data set allows to identify specic locations in the river network where deposition or erosion occurred. This dynamics is closely related to both the hydrology in the upper Isère River and the morphology of the Arc and Isère rivers, which have been aected by the 2008 and 2010 oods.

Introduction

About 1% of the total storage capacity in the world's reservoirs is lost each year due to sedimentation [START_REF] Mahmood | Reservoir sedimentation: Impact, extent, and mitigation[END_REF][START_REF] Yoon | The state and the perspective of the direct sedimentation removal methods from reservoirs[END_REF][START_REF] Vörösmarty | Anthropogenic sediment retention: major global impact from registered river impoundments[END_REF]. This sedimentation rate depends mainly on the size of the reservoir relative to the amount of sediment owing into it. Since the construction of new dams is rather dicult in developed countries due to stricter environmental regulations and the lack of suitable sites, procedures have been established to sustain the storage capacity of existing reservoirs. In numerous cases, hydraulic ushing has been used successfully to restore lost reservoir storage capacity [START_REF] Kondolf | Sustainable sediment management in reservoirs and regulated rivers: Experiences from ve continents[END_REF]. The ushing process consists in opening dam outlet gates to produce ows with velocities high enough to ush away the sediments accumulated in the reservoir. Theoretical and numerical studies [START_REF] Chang | Numerical modeling for sediment-pass-through reservoirs[END_REF][START_REF] Olsen | Two-dimensional numerical modelling of ushing processes in water reservoirs[END_REF][START_REF] Liu | Environmental impacts of coordinated sediment ushing[END_REF][START_REF] Khosronejad | Three-dimensional numerical modeling of reservoir sediment release[END_REF][START_REF] Ji | Sediment ushing at the Nakdong River estuary barrage[END_REF], laboratory experiments [START_REF] Lai | Flushing sediment through reservoirs[END_REF][START_REF] Campisano | Experimental and numerical analysis of the scouring eects of ushing waves on sediment deposits[END_REF][START_REF] Campisano | Laboratory investigation on the eects of ushes on cohesive sediment beds[END_REF], and eld observations [START_REF] Jansson | Measurement and quantication of a sedimentation budget for a reservoir with regular ushing[END_REF][START_REF] Rayan | Eects of ushing of two reservoirs in Spain[END_REF] have shown that under appropriate conditions, hydraulic ushing can remove both ne (with cohesive material) and coarse (sands and gravels) sediments.

Flushing operations can have a signicant impact on the morphology and ecology of the downstream part of a river system [START_REF] Collier | Eects of ow regulation and sediment ushing on instream habitat and benthic invertebrates in a New Zealand river inuenced by a volcanic eruption[END_REF][START_REF] Chung | Eect of reservoir ushing on downstream river water quality[END_REF][START_REF] Crosa | Eects of suspended sediments from reservoir ushing on sh and macroinvertebrates in an alpine stream[END_REF][START_REF] Bilotta | Developing environment-specic water quality guidelines for suspended particulate matter[END_REF][START_REF] Alcayaga | Predicting the geomorphological responses of gravel-bed rivers to ow and sediment source perturbations at the watershed scale: an application in an alpine watershed[END_REF]. As an example, [START_REF] Crosa | Eects of suspended sediments from reservoir ushing on sh and macroinvertebrates in an alpine stream[END_REF] observed a drop in trout density as high as 73% a ushing operation performed in 2006 in an alpine reservoir. In this case, high suspended sediment concentrations (SSC) were measured in the downstream part of the river (peak values up to 80 g/l and event-averaged value equal to 4 g/l). On the other hand, when limits for SSC are adopted, [START_REF] Peteuil | Sustainable management of sediment uxes in reservoir by environmental friendly ushing: the case study of Gènissiat dam on upper Rhône River (France)[END_REF]; [START_REF] Espa | Downstream ecological impacts of controlled sediment ushing in an alpine valley river: a case study[END_REF][START_REF] Espa | Tackling reservoir siltation by controlled sediment ushing: Impact on downstream fauna and related management[END_REF] demonstrated that environmental degradations can be signicantly reduced. Also, several studies have focused on the morphological eect of ushing waves on the river bed, which mainly concerns coarse sediments [START_REF] Kondolf | The ushing ow problem: Dening and evaluating objectives[END_REF][START_REF] Wohl | Sediment deposition and transport patterns following a reservoir sediment release[END_REF][START_REF] Brandt | Classication of geomorphological eects downstream of dams[END_REF][START_REF] Petts | Dams and geomorphology: Research progress and future directions[END_REF][START_REF] Petticrew | Evaluating ne sediment mobilization and storage in a gravel-bed river using controlled reservoir releases[END_REF]. These studies identied the direct link existing between the intensity of the ushing operations and the downstream erosion of the river bed (gravel bars or main channel).

However, ne sediments transported by ushing ows can also have a morphological impact on the downstream river system [START_REF] Smart | Barrage ushing implications (monitoring sediment releases from the Rangipo hydro barrage)[END_REF][START_REF] Van Maren | Predicting the morphodynamic response of silt-laden rivers to water and sediment release from reservoirs: Lower Yellow River, China[END_REF]. Following a ushing event, [START_REF] Brandt | Sedimentological and geomorphological eects of reservoir ushing: The Cachi reservoir, Costa Rica[END_REF] measured an increase of mean bed elevation of 10 centimetres due to the deposition of ne sediments over a 30 kilometre-long reach downstream of the Cachi dam, in Costa Rica. As an exacerbating factor, vegetation grows more easily on ne deposits, and provides optimal conditions for new deposition of ne sediments due to the local decrease of ow velocities [START_REF] Newcombe | Eects of suspended sediments on aquatic ecosystems[END_REF][START_REF] Murle | Eects of experimental ooding on riverine morphology, structure and riparian vegetation: The river spol, swiss national park[END_REF][START_REF] Asaeda | The impacts of sediment released from dams on downstream sediment bar vegetation[END_REF][START_REF] Jourdain | The role of hydrology on vegetation removal in a heavily managed gravel bed river: the Isère, Combe de Savoie, France[END_REF]. Finally, ne sediments can be the vectors of propagation for particulate pollutants, and the residence time of the contaminated particles in the river channel is an important parameter to evaluate the vulnerability of a system [START_REF] Frémion | Inuence of dams on sediment continuity: A study case of a natural metallic contamination[END_REF].

Fine sediment deposition uxes often represent a small part of the total suspended sediment ux (SSF) in embanked alpine river for high ow conditions. They have been observed as non-negligible for small braided systems only [START_REF] Navratil | Assessment of intermediate ne sediment storage in a braided river reach (southern french prealps)[END_REF][START_REF] Misset | An attempt to link suspended load hysteresis patterns and sediment sources conguration in alpine catchments[END_REF], where exchanges with the bed can be of the same order of magnitude than upstream input. Therefore, the quantication of the mass of ne deposited sediments, its spatial distribution and its temporal dynamics during one event is rather dicult to assess for large embanked systems. Bathymetric surveys performed before and after a ushing event are expensive, time consuming and highly exposed to uncertainty measurement regarding the possibly small thickness of ne sediment deposits. Some aerial photograph analysis provided an estimate of the deposits but limited to surface measurements and dicult to apply to long reaches [START_REF] Camenen | Estimate of ne sediment deposit dynamics over a gravel bar using photography analysis[END_REF][START_REF] Camenen | Estimation of the volume of a ne sediment deposit over a gravel bar during a ushing event[END_REF]. Furthermore, the measured bed evolution provides an estimation of the volume of sediments deposited or eroded. To be compared to sediment uxes, an additional hypothesis on the sediment mixture and porosity of the bed is needed to convert the dierential volume into a sediment mass.

The method based on SSF consists in estimating the dierence between event-integrated SSF for two consecutive positions of the river reach. Such method only provides a reach-averaged behaviour that could be dicult to interpret if the distance between two positions is long. Moreover, the uncertainty is sensitive to the temporal frequency of measurements, and can sometimes become too high to give relevant conclusions [START_REF] Garcia | Sedimentation engineering: processes, measurements, modeling, and practice[END_REF]. This explains that few studies have focused on ne sediment budgets based on SSF measurements, especially for long embanked systems [START_REF] López-Tarazón | The sediment budget of a highly dynamic mesoscale catchment: The River Isábena[END_REF]. None of these studies quantied precisely or examined critically their results with respect to uncertainty values. As an example, the work of [START_REF] Tena | Suspended sediment dynamics during ushing ows in a large impounded river (the lower river ebro, ne iberian peninsula)[END_REF] on the Ebro River improves the understanding of the spatial and temporal dynamics of suspended sediment transport during ushing ow but it did not address the issue of ne sediment deposition in the river.

In this paper we raise the following questions: what is the downstream dynamics of SSF during dam ushing events in an impounded river system?

Regarding the uncertainty on SSF estimated from a detailed data set, what is the signicance of local mass balance between two consecutive measurement sites? How to explain these mass balances with erosion and deposition processes on the river bed? To answer these questions, we analysed the propagation of SSF along the Arc and Isère river system following six hydraulic ushing events of the Upper Arc dams in June 2006June , 2007June , 2009June , 2010June , 2011June , and 2012. For these six ushing events, measurements of discharges and SSC were performed at fourteen sites along 120 kilometres of the river downstream of the ushed reservoirs [START_REF] Antoine | Dynamique des matériaux en suspension le long de rivières aménagées de montagne[END_REF].

In the rst part of this paper we describe the eld campaigns performed to measure water discharges and SSC at dierent sites of the river system as well as the method developed to explore this detailed data set. The obtained instantaneous values of SSF are integrated over the ushing time period, in order to compute the local mass balances between two consecutive measurement sites. Then, a model of uncertainty propagation is proposed to estimate the signicance of these local mass balances. In the second part of the paper, a global analysis of discharge, SSC and SSF values is provided at the river scale. Also, a discussion is provided on the links between local mass balances and site morphologies and history.

Material and method

Study site

The Arc-Isère river system is a typical example of impounded Alpine river system largely inuenced by river management and dam management.

The Arc-Isère River system

The Isère River and its tributary, the Arc River, are located in the Northern French Alps. The respective surface areas of the catchments are 1950 km 2 and 5570 km 2 for the Arc River and the Isère River upstream of the city of Grenoble (Figure 1). Both catchments are characterized by a nival hydrological regime, with an annual mean water discharge of 30 m 3 /s for the Arc River at Pontamafrey and 177 m 3 /s for the Isère River at Grenoble.

In the second part of the 20 th century, three dams, with a storage capacity of 0.8 Mm 3 , were built on the middle section of the Arc River: the Freney dam, the Pont-des-Chèvres dam and the Saint-Martin-la-Porte dam (SMLP dam). Compensation water ows along more than 50% of the total length of the Arc River due to the water intakes used for hydropower generation. Nevertheless, tributaries of the Arc and Isère rivers can be very dynamic, and strong seasonal discharge variations occur in both rivers during the year: in the middle of summer, the mean monthly discharges on the lower Arc River can reach 50 m 3 /s, and 250 m 3 /s on the Isère River. In winter, mean monthly discharges are 10 m 3 /s on the Arc River and 150 m 3 /s on the Isère River. Natural oods usually occur at the beginning of summer and in autumn. Dams are opened during large oods and have no impact on the ood dynamics in the downstream part of the valley because of their low storage capacities [START_REF] Marnezy | L' Arc et sa vallée: Anthropisation et géodynamique d' une rivière alpine dans son bassin versant [The Arc River system: anthropisation and geodynamic of an alpine river system[END_REF]. The discharge for the 10-years ood on Arc River (Pontamafrey) is estimated at 180 m 3 /s, and 900 m 3 /s on the Isère River (Grenoble).

Because of continuous embankments, the Arc River is strongly constrained laterally and the mean slope of the river bed varies from 1% at Saint-Jeande-Maurienne to 0.2% just upstream of its conuence with the Isère River.

The slope can be locally steeper and supercritical ows are frequently observed on some parts of the river's course. The slope of the Isère River is smaller, with values from 0.2% close to the conuence to 0.09% at the end of the study site. Both Arc and Isère river beds are mainly made of gravels with a poorly sorted grain size distribution. Both rivers are characterized by systems of alternate bars that are often vegetated in the Isère River [START_REF] Serlet | Biomorphodynamics of alternate bars in a channelized, regulated river: An integrated historical and modelling analysis[END_REF]. They are also exposed to snow-melt oods, debris ows and are greatly aected by deposits of ne sediment on vegetated banks. This paper focuses on the Arc-Isère river system, from the SMLP dam to the city of Grenoble. The locations of the measurement sites are dened in this paper as the distance of the site from the conuence (sites on the Arc River have negative positions and sites on the Isère River have positive positions).

Flushing of the Arc dams

To maintain storage capacity and electric power production, the three dams of the middle Arc River (Figure 1) are ushed yearly at the beginning of June, except if a larger ood occurs before the planned hydraulic ushing. For example, no ush was performed in 2008 because a 15-years ood occurred in May. During the ushing operation, the successive openings of the dam outlet gates (see Figure 2a) are dened precisely to optimize the hydraulic eect of the ush. As dam operators follow a project hydrograph, similar discharge time series were observed for every ushing event (see Fig- ure 2b) although some dierences can be observed because of the natural ow in the Arc and Isère rivers. At the SMLP dam, the dierent dam opening phases correspond to the following parts of the hydrograph in the Arc River:

1. rst a warning wave (for fauna and hydraulic safety precautions) of about 20 m 3 /s is generated by an overow of the clear water; 2. then a discharge step is performed, providing a discharge amplitude of approximately 90 m 3 /s for 3 hours; 3. water is provided by larger reservoirs on the upper Arc watershed (Bissorte and Mont-Cenis dam reservoirs mainly, see Fig. 1) to maintain the water discharge value and increase it to its maximum value (from 130 to 150 m 3 /s) for about 4 hours. The maximum discharge value corresponds to a one-year ood on the Arc River; In 2012, an additional peak up to 175 m 3 /s arose during the rst discharge step. It resulted from some unexpected problems in the gate management.

SSC and discharge measurements

To evaluate the suspended load propagation along the reach resulting from dam ushing events, high frequency measurements were performed during June 2006June , 2007June , 2009June , 2010June , 2011June , and 2012 events. These measurements were anticipated and organization was facilitated by planning the dam ushing several weeks in advance. Measurements consisted in gauging discharges and performing SSC monitoring at several locations along the river reach (Figure 1).

SSCs were estimated from samples taken from surface water (bucket samples from a bridge) or at the riverside (ISCO 4230 automatic sampler) at 14 measurement sites (Figure 1). The samples were ltered and weighed following the ISO 11923 protocol. SSC estimation was also performed thanks to turbidimeters (Hach Lange Solitax SC-Line TS 50 g/l) installed at four monitoring stations [START_REF] Thollet | Measurements of the ne sediment uxes in the arvan, arc, and isère rivers [suivi du transport sédimentaire sur les rivières arvan, arc et isère[END_REF]. In these cases, water samples were used to establish a relation between the measured turbidity and the eective SSC.

As a consequence, it is important to note that the present study excludes coarse particles such as sand since it is poorly measured from surface and/or riverside samples and turbidity. In addition, samples were taken in main tributaries (Arvan, Glandon, Isère restitution, Isère River) to verify that their concentrations were negligible throughout the ushing events. Therefore, the only eect of these tributaries was to decrease the SSC through dilution.

Discharges were estimated at ve sites along the Arc-Isère system (A7, A5, A2, I3, and I1) where a hydrometric station is present. At these sites, water level was measured and the discharge was obtained using well documented rating curves and additional discharge measurements (using a classical current meter, LSPIV image analysis technique and/or ADCP measurements [START_REF] Jodeau | Application and evaluation of LS-PIV technique for the monitoring of river surface velocities in high ow conditions[END_REF][START_REF] Dramais | Advantages of a mobile LSPIV method for measuring ood discharges and improving stage discharge curves[END_REF]. In addition, pressure gauges (autonomous Diver type and bubbler system pressure gauges) were used to measure water level variations at several locations, giving information on the transfer time of the ushing waves.

One dimensional hydraulic model was built for the whole river system to complete the discharge data set. The 1D hydraulic numerical code Mascaret (Goutal and Maurel, 2002, part Table 1 summaries the measurement methods used at each measurement site for each ushing event. The position of each measurement site is given by its distance from the conuence (see also Figure 1). Both SSCs and water discharge time series are thus available at 14 measurement sites for the ve ushing events.

SSC Q SSC Q SSC Q SSC Q SSQ Q SSQ Q A10 -50.

Suspended Sediment Fluxes

Instantaneous Suspended Sediment Fluxes

At each measurement site located at the position X i , instantaneous ux values φ are computed using a linear interpolation of both discharges and SSC values:

φ(X i , t) = Q(X i , t) × SSC(X i , t) (1)
Due to a lack of data, three data sets were excluded: site I4 in 2006 and 2007 and site A1 in 2007. SSC data were measured at site A2 with an automatic sampler. However, since this site is located 500 m downstream the outlet channel of the Randens hydro-power plant, an incomplete lateral mixing was suspected. SSC measurements were performed at several points throughout the river in 2010; the results presented a standard deviation up to 40% due to incomplete lateral mixing, even under low SSC conditions.

Consequently, no SSC measurement is made at this site since 2011, and the data from this site will be excluded from the ux estimations.

Suspended Sediment Fluxes integrated over the ushing event

The instantaneous ux computed using Eq. 1 can be integrated over the time period of the event T event , which varies from 12 hours in the Arc River to 16 hours in the Isère River, due to dispersion processes:

Φ(X i ) = Tevent φ(X i , t)dt (2)
This temporal integration provides the global mass of suspended sediment Φ transported through a measurement site located at position X i . A formalism was also introduced to study the temporal dynamic. A cumulative transported mass was calculated as a function of the percentage t% of T event :

Φ % (X i , t%) = t%×Tevent φ(X i , t)dt (3)

Local mass balance

The detailed spatial proles of the total mass transported at the fourteen measurement sites are used to estimate a local mass balance. This local mass balance ∆Φ between two consecutive measurement sites located at positions X i and X i+1 ,respectively, is expressed such as:

∆Φ(i → i + 1) = Φ(X i+1 ) -Φ(X i ) (4)
This integrated approach could mask successive deposition or erosion phases during one event. Then, it is possible to obtain a dynamic local mass balance value using Eq. 3, i.e. a mass balance between two consecutive measurement sites after t% of T event :

∆Φ % (i → i + 1, t%) = Φ % (X i+1 , t%) -Φ % (X i , t%) (5) Note that Φ(X i ) = Φ % (X i , 100%) and ∆Φ(i → i + 1) = ∆Φ % (i → i + 1, 100%).
2.4. Uncertainty in the integrated ux estimations

Uncertainty propagation model

As the instantaneous SSC and discharge values are obtained separately, the relative variance of the instantaneous SSF can be expressed as the sum of the relative variances σ 2 Q and σ 2 SSC of these variables:

σ φ = σ 2 Q + σ 2 SSC (6)
According to the methodology developed in the GUM (Joint Committee for Guides in Metrology, 2008), the same decomposition of each relative variance σ Q and σ SSC is performed to take into account all signicant sources of uncertainty. In the proposed error propagation model, σ Q and σ SSC are assumed time-averaged.

Uncertainty of the discharge values

Uncertainties in the discharge values of the data set come mainly from three sources: the measurement method (σ Q,M eas ), the numerical model (σ Q,M od ) and, eventually the temporal linear interpolation (σ Q,Int ).

σ Q = σ 2 Q,M eas + σ 2 Q,M od + σ 2 Q,Int (7)
Measurement method (σ Q,M eas ). The same measurement method is used at the four measurement sites where discharge values are available. These measurements are performed using the velocity-area method, which consists in sampling ow velocity and depth across the cross-section for the discrete integration of the discharge. Using these isolated measurements, a rating Numerical modelling (σ Q,M od ). For each ushing event, the simulated instantaneous discharges were compared to those observed on the four measurement sites. The time transfer of the water wave is well reproduced by the model for each ushing, as are the maximum discharge values. The standard deviation between the measured and modelled discharge was estimated systematically using the following equation:

σ M i = 1 N N j=1 Q mod (j) -Q meas (j) Q meas (j) (8)
The σ M i -values vary from 2% to 7% with an averaged value around 5%.

Larger values correspond generally to low ow discharges, which are not as accurately modelled. However, these low ow discharges are not signicant in term of overall uxes.

Eect of temporal sampling frequency (σ Q,Int ). Water levels are measured continuously or calculated numerically with a small time step, so the temporal eect of the linear interpolation (used to compute the instantaneous suspended sediment ux at every time step) is neglected for the discharge values. As this assumption is not correct for the SSC measurements, this source of uncertainty is taken into account in the following part.

Uncertainty of the SSC values

Four main sources of uncertainty are identied concerning the SSC values:

the vertical (σ SSC,V H ) and transversal heterogeneity (σ SSC,HH ) of the SSC in a river cross-section, the dierent measurement methods used (sampledltered-wetted (σ SSC,Spl ), or from turbidity measurement (σ SSC,T u )) and the eect of linear interpolation (σ SSC,Int ).

σ SSC = σ 2 SSC,HH + σ 2 SSC,V H + σ 2 SSC,Spl + σ 2 SSC,T u + σ 2 SSC,Int (9)
Spatial heterogeneity (σ SSC,HH and σ SSC,V H ). SSC values are measured assuming a homogeneity throughout river cross-section. Vertical homogeneity depends on the degree of turbulence of the river ow, the grain size distribution of the suspended sediments and the geometry of the river bed. Some studies [START_REF] Ryan | Incomplete mixing in a small, urban stream[END_REF][START_REF] Horowitz | Variations in suspended sediment and associated trace element concentrations in selected riverine cross sections[END_REF] Using the numerical hydraulic model to estimate u * , the maximum value of the Rouse-Schmidt number calculated is thus Z = 3 × 10 -2 , which yields theoretically a relative standard deviation of 3% from the mean value on the SSC prole. As a consequence, we assume hereafter that σ SSC,V H = 3%. It should be noted that this value would be higher while including the sand fraction.

Lateral homogeneity is mainly function on the lateral variability in turbulence, and so on the lateral variability in bed roughness. It was studied during the ushing of 2006 [START_REF] Némery | Carbon and suspended sediment transport in an impounded alpine river (Isère, France)[END_REF] on the Isère River at site I1,

where the river slope is the mildest (0.1 %) and the river cross-section is the widest (100 meters). The measurements were performed at three sampling positions at the surface (left, middle and right side of the section). The average value of the standard deviation was σ SSC,HH = 5% between the middle of the section and the left and right sides, and the error occurred mainly during the lowering phase of the ushing event.

These two values (σ SSC,V H = 3% and σ SSC,HH = 5%) are used at every measurement site, for every ushing event. These uncertainty values may be locally higher near conuences. Indeed, in case of a conuence, the lateral homogeneity also depends on the longitudinal mixing and the distance to the conuence. However, since all measurement sites are far enough from conuences (except A2, which has been skipped), this local eect is neglected.

Measurement method (σ SSC,Spl and σ SSC,T u ). The SSC measurement method plays a key role in error production. For this study, two dierent methods were used to measure the SSC: a direct method, using automatic or manual samples, and an indirect method, using a turbidimeter.

The error produced by the rst method was studied in laboratory [START_REF] Mano | Processus conditionnant les apports de sédiments ns dans les retenues -Optimisation des méthodes de mesure et modélisation statistique [Fine sediment supply processes in dam reservoirs: statistic modelling and optimization of measurement method[END_REF]. The repeatability of the measurement was tested 40 times on several samples, over a range of SSCs from 0.02 to 1 g/l. This experimental study showed that the relative standard deviation decreased rapidly with SSCs from 20.1% to 5.5%. Another experiment was performed with higher concentrations (about 10 g/l), and conrmed the decrease of the mean standard deviation to 2.5%. Since most of the measured concentrations during a ushing event vary from 1 to 30 g/l, the relative standard deviation from the direct sampling method was assumed equal to σ SSC,Spl = 2.5%. and the time period T event of the ushing event. Finally, the relative standard deviation resulting from the interpolation can be expressed for a whole instantaneous SSC signal of N values as:

σ SSC,Int = 1 N N i=1 |SSC i -SSC i+1 | × ∆t T event × SSC i +SSC i+1 2 (10)
As observed in Figure 3, σ SSC,Int decreases with the number of sampled SSCs during the event. This result allows dening a sampling strategy during the ushing event. This indicator varies from about 0.004% for a very high frequency signal (turbidimeter) to 24% for a low frequency signal (manual sampling with a frequency lower than one sample per hour). Whatever the case, uncertainties due to sampling frequency become negligible as soon as there is at least one sample every 30 mn (σ SSC,Int ≈ 3%). The high frequency obtained thanks to turbidimeters is therefore not so benecial in terms of overall uncertainty since σ SSC,T u = 10%.

Signicance of the local mass balance

Knowing the uncertainty in the integrated ux estimations, the signi- cance of the local mass balance ∆Φ(i → i + 1) can be evaluated regarding the condence interval of the integrated uxes calculated at two consecutive measurement sites. The condition for a signicant erosion or deposition rate between two consecutive measurement sites is thus the following :

|Φ(X i+1 ) -Φ(X i ))| > σ Φ (X i+1 ) + σ Φ (X i ) (11)
3. Results

Total uxes and global uncertainty

The calculated values of Φ(X i ) and their associated relative uncertainties σ Φ are presented in the Table 2. Measurements were not achieved every year at the 14 sites generally due to experimental diculties.

The uncertainty values of the integrated uxes vary between 9.2% and 25.9%, with a mean and median values of 11.5% and 10.7% respectively.

Φ σ Φ Φ σ Φ Φ σ Φ Φ σ Φ Φ σ Φ Φ σ Φ A10 - -

Spatial evolution of total uxes

As the rst measurement site A10 is located only one kilometre downstream to the SMLP dam, it gives the mass output from the three Arc River dams. In Figure 5, we can see that this total input of sediment from dams varied from 12, 000 tons in 2007 to 40, 000 tons in 2006 (at A9) and 52, 000 tons in 2012 . These variations in the storage and removal of ne sediment from the reservoirs depend on the upstream watershed incomes and dam management operations during the year separating two consecutive ushing events. It should be noted that in Figure 5, a decrease (respectively increase) in Φ(X i )

indicates deposition (respectively erosion). For the 2012 ushing event, a larger erosion was observed due to the much larger discharge during the rst step of the ushing event that led to a much signicant erosion of the dam reservoirs.

- Over the whole river system, the values of Φ(X i ) vary widely depending on the ushing event with some clear dierence on the Arc and Isère rivers, respectively:

-On the Arc River, between A10 (-50 km) and A1 (0 km), Φ(X i ) was conserved in 2006, 2009, and 2010, whereas This indicates that the river bed responds dierently to very similar ushing hydrographs depending on the year. A more detailed analysis of the Φ spatial evolution shows that even if the value Φ(X i ) remained the same, conserved or increased along the entire studied area, specic local variations may occur especially around St-Jean-de-Maurienne (X ≈ -40 km) and in the Isère River straight after the conuence with the Arc River (0 < X < 15 km).

Strong positive or negative gradients of Φ(X i ) can be observed, which indicate potentially strong local deposition or erosion processes.

Local mass balance

Regarding the condence interval, some local variations of Φ(X i ) appear to be not signicant. As an example, the magnitude of the local variations observed between A4 (X = -24 km), A5 (X = -33 km) and A6 (X = -38 km) is not high enough to be signicant regarding the condence interval for most ushing events. Fig. 4b shows on the opposite a strong positive variation between I3 (X = 14 km) and I2 (X = 27 km) in 2010, which is signicant regarding the condence interval.

Table 3 presents the values of the local mass balance ∆Φ(i → i + 1) (expressed in 10 3 tons) along the study area. If ∆Φ(i → i + 1) > 0, this means that resuspension occurs between two consecutive measurement sites located at positions X i and X i+1 . If ∆Φ(i → i + 1) < 0, this means that deposition occurs between the two consecutive measurement sites. The local mass balance values which are conrmed by the condence intervals are given in bold font in Table 3 following Eq. 11. It should be noted that depending on the year, some intervals have been aggregated due to the absence of data in some sites. It does not aect the results since the condition proposed (Eq. 11)

does not depend on the distance between the two consecutive measurement sites.

A3-A4

+3.1 -0.1 +1.9 +2.1 +18.7

A2-A3

+1.2 +13.9 -0.5 -0.8 +7.4 -6.3 2006 and 2007 (group 2). The dierence observed between the mass balance distributions of groups 1 and 2 is particularly evident for upstream sites in the Arc River, where the slope of the river bed is high: for example, high erosion of the bed was observed between measurement sites A8 and A7 before the year 2008, whereas systematic deposition was observed after this year.

A1-A2 I4-A1 +3.3 -1.0 +0.1 -11.3 +14.0 I3-I4 +4.4 I2-I3 +19.8 +0.4 -11.5 I1-I2 +16.4 -6.3 +1.8
The same behaviour was observed between sites A5 and A4, whereas the opposite was observed between sites A6 and A5. The two groups of ushing events were separated by a major event: in May 2008 a natural ood owed from the upper Arc catchment (15-year return period). Regarding previous results, the bed changes due to this ood signicantly modied the local mass balance distribution. [START_REF] Jaballah | Alternate bar development in an alpine river following engineering works[END_REF] showed evidences on these large eect of the 2008 ood on the river morphology on a 5 km long reach (located between A6 and A5), which conrms its impact on SSF dynamics. The ood that occurred in May 2010 (the second highest in intensity during the study period), and which aected in similar proportions all the sub-catchments of the Isère watershed, did not change this local mass balance distribution. The dierence of behaviour between ushes could also be partly explained by the settling properties of sediments that can change depending on the storage duration in dam reservoirs [START_REF] Legout | Assessment of erosion and settling properties of ne sediments stored in cobble bed rivers: the Arc and Isère alpine rivers before and after reservoir ushing[END_REF]. Indeed, most deposits in dam reservoirs form during the spring period. Depending on the exact date of the dam ushing, their storage duration can vary from a few days to a few months depending on the hydrology.

Discussion

Spatio-temporal dynamics of discharge and SSC

The analysis of SSC and discharge signals gives information on their variability along both rivers and could provide some clues about the dierences in ux dynamics from one ushing event to another. In Figure 6, the discharge and concentration measurement are presented for the dam ushes of 2007 and 2009 at Pontamafrey (A7) and Grenoble (I1), respectively.

On site A7, the SSC patterns resulting from the 2007 and 2009 ushing events dier in shape and magnitude. In 2007 the peak SSC value (16.7 g/l)

was measured during the rst discharge step of the ushing hydrograph, whereas the peak value of the 2009 SSC signal (10.9 g/l) appeared during the second discharge step. These dierences may be explained by the availability of the ne sediments and the erosion processes in the three dam reservoirs of the Arc River. In 2007, the SSC peak value corresponds to sediments that are easily removed from the reservoirs, while the second part of the SSC signal is related to sediments removed due to higher bed shear stresses (higher As a consequence, the sediment input is highly function of the hydrology during the months preceding the ushing event, and so the accumulation of fresh ne sediments in dam reservoirs during the spring period. On site I1, the SSC signals are smoothed, because of the long distance travelled along the river and the dispersion processes; the dierences between the SSC peak values are attenuated. One should note that the SSC peak is measured systematically after the discharge peak of the hydrograph since the ood wave travels faster than ow velocity.

Hydrology inuence on SSC dynamics

In order to understand the possible inuence of the hydrology on the ne sediment dynamics, we dene an average discharge for the spring season before the ushing event Q m,spring (i.e. from the 1st April to the day before the ushing event) at both A7 and I1 location, as well as a base discharge Q m,base during the ushing event on the Isère River at I1 location (averaged discharge on the day before the ushing event). Indeed, the Q max values are almost the same whatever the event on the Arc River; they increase only with the input from tributaries, i.e. at the Isère restitution (X = -8 km), the Isère conuence (X = 0 km), and at the Cheylas restitution (X = +20 km).

Results are presented in Tab. 4 together with the concentration peak values measured at A7 location for both discharge step.

Table 4: Mean discharges at Pontamafrey (A7) and Grenoble (I1) during the spring period before ushing events (Q m,spring ) and at the restitution near A2 site (Q m,rest ), peak concentrations for the rst (C p1 ) and second (C p2 ) plateau of the event, and cumulative SSF (Φ tot,spring ) measured at site I1 during the 3 months preceding each ushing event.

Site A7 A2 I1 In general, the second peak of concentration during the 2nd plateau is higher than the rst one since bed shear stresses are higher in the dam Φ < 20, 000 tons. The initial total ux from dam reservoir is thus function of the duration without dam operation. On the other hand, the hydrology during the spring period does not appear to inuence signicantly the amount of ne sediment to be eroded. No correlation could be found between the average ow Q m,spring on the two month prior to the ushing event and the initial total ux. Also, we note that erosion generally occurred in the Isère River when the base discharge Q m,base in the Isère River is the highest (2006, 2010, and 2012).

Q m,spring C p1 C p2 Q m,rest Q m,spring Q m,
This could be explained as the gravel bar were then ooded and ne sediment stocks over gravel bars could be resuspended. However, for the 2012 event, which reached the largest discharges (close to 500 m 3 /s), highest vegetated part of gravels bars have been ooded and have enhanced deposition. We expect to relate erosion on the downstream part of the Arc River observed in 2007, 2011, and 2012 with the additional ow discharge coming from the restitution (Q m,rest ). However, no clear correlation could be made. In any case, the sediment mass transported during a ushing event does not represent more than 5% of the annual suspended sediment mass transiting at site I1. These results corroborate previous estimations of the contribution of hydraulic ushes to annual SSF of the Isère River [START_REF] Némery | Carbon and suspended sediment transport in an impounded alpine river (Isère, France)[END_REF].

Our results conrm the importance of the suspended sediment dynamics before the event (during the spring period). Indeed, the spatial distribution of sediment deposits strongly aects the possible resuspension of sediment during the ushing event. Some studies [START_REF] Droppo | The eect of depositional history on contaminated bed sediment stability[END_REF] have shown the eect of sequential bed depositions under several ow conditions in the bed erosion process, especially if the proportion of cohesive sediments in the total suspended load is non-negligible.

Dynamic mass balance

Table 3 gives spatial information on the local mass balances per river reach. For example, the river bed between the two consecutive measurement sites A4 and A3 was systematically eroded as was the river bed between A3 and A1. Furthermore, the lengths of these two reaches are almost equal (≈ 12 km). However, the values of the dynamic and time-normalized mass balance ∆Φ % (i → i + 1, t%) (Eq. 5) on these parts of the river bed show very dierent mass transport dynamics during the ushing events. In Fig. 7 c andd, the values of ∆Φ % (A3 → A1, t%) and ∆Φ % (A4 → A3, t%), respectively, are plotted as a function of the time made dimensionless with the duration of the event T event . Although the two reaches of the river were globally eroded at the end of the ushing event, the A3-A1 reach endured rst some large erosion and then some deposition. This succession of erosion and deposition could be explained by an easily erodible mass of sediment on the river bed that was removed by the rst discharge step of the ush hydrograph. During the second discharge step, the water level became high enough to ow on gravel bars implying signicant deposition. On the other hand, the A4-A3 reach endured successively considerable deposition and then even larger erosion during the same event (Fig. 7 d). On this reach, two large, easily submersible banks and a small dam reservoir were the only remarkable sites.

They could indeed explain the following mass balance dynamics from 2009 to 2011 events: before the rst discharge step, the reservoir was emptied, removing a small proportion of the ne deposited sediments. This rst release generated nevertheless a SSC peak at a relative low discharge value and did not inuence the global mass balance value. The rst discharge step led to considerable deposition on the easily submersible banks which were eventually easily re-suspended by the second discharge step. Furthermore, the second discharge step involved suciently high water levels to remove the upper layer of sediment deposited in the small reservoir. The global mass balances calculated for all the events were in this case not representative of the temporal dynamics of this reach, where the exchange processes with the river bed were signicant. The four examples presented in Figure 7 show that the river reaches have not the same ability to recover the prior-ood equilibrium : reaches like the ones between A5 and A4 or A3 and A1 show in 2011 very similar dynamics than the one observed in 2007. For the two other reaches, the prior dynamics were still not recovered in 2011. It also shows the dominating inuence of river morphology on SSF dynamics.

Physical characteristics of the transported sediments

Sediments parameters like grain size and/or settling velocity but also suspended concentration are fundamental for predicting deposition processes [START_REF] Legout | Assessment of erosion and settling properties of ne sediments stored in cobble bed rivers: the Arc and Isère alpine rivers before and after reservoir ushing[END_REF]. Their variability could also explain observed dierences between ushing events or river reaches [START_REF] Garcia | Sedimentation engineering: processes, measurements, modeling, and practice[END_REF]. In 2011, grain size distribution (GSD) have been measured for every sediment samples at A5, A1 and I1 sites. Grain size characteristics, averaged over the ushing period, are presented in Table 5. These grain size measurements show that few dierences are observed between the three measurement sites for this event even if a small ning In 2011, the ux was globally transferred between A5 and A4 with a rst period of deposition followed by a period of erosion. In this case, one can conclude that the freshly deposed sediments during the rst part of the event have been re-suspended during the second part of the event explaining the constant GSD. However, between A3 and A1, the opposite behaviour is observed. Previous sediments deposits on the river bed were replaced by the suspended sediments coming from upstream. However, a similar GSD is observed indicating a certain consistency of the long term dynamics of the ne deposits in these reaches.

Conclusion

Six eld campaigns were analysed to evaluate the impact of dam ushing events on suspended sediment dynamics downstream of the dams. SSC and discharge measurements were performed on the Arc and Isère Rivers, France, at 14 sites in June 2006June , 2007June , 2009June , 2010June , 2011June , and 2012. These intensive measurement campaigns allowed an estimation of suspended sediment uxes along the reaches of both rivers as well as the local mass balance.

To estimate the signicance of the observed local variations, a propagation model for the uncertainty on the global ux was built, taking into account the main sources of error for both SSC and discharges. The mean calculated uncertainty value was σ Φ = 11.5%. These uncertainty values conrm the global tendency of suspended sediment ux propagation, whereas only 14 out of 52 local mass balances between two consecutive measurement sites were signicant. Also, a dynamic time-normalized method was developed to evaluate and discuss temporal variations of the mass balance during one ushing event.

Even if the dam ushing operating protocol was identical over the years (except for 2012), the suspended sediment mass removed from the reservoirs varied from 10,000 tons in 2007 to 40,000 tons in 2006. The hydrology on the Upper Arc River during the previous spring period signicantly aected the eciency of these ushing events. On the other hand, the global ne sediment mass balance along the studied river segment varied from zero in 2011 and 2009 to 30,000 tons in 2007 indicating also a strong eect of the initial state: stock of ne sediments in the river but also river geometry.

We showed that the bed morphology signicantly modied the ne sediments dynamics. Indeed, the May 2008 ood, a 15-year return period ood on the Arc River that largely modied both Arc and Isère river morphologies yielded major changes in ne sediment dynamics during ushing events. Indeed, opposite behaviour were observed for many reaches in terms of global mass balance (after the ushing event) but also in terms of temporal dynamics during the event (erosion followed by deposition or the opposite).

Another point to be addressed is the quantity and quality of the ne sediment stocks in the river bed, i.e. surface deposits and stocks inltrated in the bed matrix. Indeed, our knowledge of the stocks remains very limited.

It would be important to evaluate the quantity of available sediments as deposits but also stocked in the river bed that could be re-suspended as soon as coarse particles are mobilized [START_REF] Navratil | Assessment of intermediate ne sediment storage in a braided river reach (southern french prealps)[END_REF][START_REF] Misset | An attempt to link suspended load hysteresis patterns and sediment sources conguration in alpine catchments[END_REF].

More continuous monitoring of SSF, but also direct measurements on the river bed and in dam reservoirs are necessary to estimate the initial state of the river bed and the availability of the ne sediments in reservoirs.

To better predict the eect of dam ushing, investigations must now focus on combining the analysis of local morphodynamics and global hydrological aspects more in detail. It could be eventually made in the future thanks to repeated Lidar surveys, assuming that topographic changes are only due to ne sediment dynamics and only occur on gravel bars. An important issue is the sand fraction. It corresponds indeed to approximately 50% of the deposit volume [START_REF] Camenen | Estimation of the volume of a ne sediment deposit over a gravel bar during a ushing event[END_REF] whereas sand ux are not captured by the turbidimeters nor by the surface sampling network. Also, the use of a numerical model to calculate downstream sediment propagation would help dam operators to optimize dam ushing scenarios.

Figure 1 :

 1 Figure 1: Map showing the location of the Arc and Isère catchments and measurement sites.

Figure 2 :

 2 Figure 2: Photo of the SMLP dam outlet gates during a ushing event (a), and discharge time series of the six studied ushing events at Pontamafrey (b).

  of the open-source TELEMAC-MASCARET system) was used for this study. The model geometry was built using topographical data from several river cross-section surveys conducted between 2004 and 2007 on the Arc and Isère Rivers. 56 river cross sections were available to build the Arc River bed, giving an average prole density of about 1 cross section per kilometre. On the Isère River, this density was higher (about one prole every 200 meters). Because local slopes can be very steep, the calculation mesh was xed at spatial resolution of 20m. Calibration of the Strickler coecients was performed by comparing measured and computed water level and discharge values. Strickler friction coecients used to calibrate the model vary from 20 m 1/3 /s in the upstream part to 45 m 1/3 /s in the downstream part.The upstream boundary condition was built from the most upstream discharge time-series measured on the river (A7, Figure1) using a time shift based on pressure gauge measurements. The downstream boundary condition is a free water ux boundary condition. Three main water inputs were set at Randens (10 km upstream the Arc-Isère conuence; turbinated water from the Aigueblanche reservoir), at the conuence (upstream part of the Isère River), and at Cheylas (30 km downstream the Arc-Isère conuence; turbinated water from the Flumet reservoir).

  4 --M.S. 1D M.S. 1D M.S. 1D M.S. 1D M.S. 1D A9 -48.5 M.S. 1D M.S. 1D -.7 M.S. 1D M.S. 1D M.S. 1D M.S. 1D M.S. 1D --A7 -40.0 M.S. H.S. Tu. H.S. Tu. H.S. Tu. H.S. Tu. H.S. Tu. H.S. A6 -37.9 M.S. 1D M.S. 1D M.S. 1D M.S. 1D A.S. 1D --A5 -33.1 M.S. H.S. Tu. H.S. Tu. H.S. M.S. H.S. M.S. H.S. M.S. H.S. A4 -24.0 --A.S. 1D A.S. 1D A.S. 1D A.S. 1D A.S. 1D A3 -12.2 A.S. 1D A.S. 1D A.S. 1D A.S. 1D A.S. 1D A.S. 1D A2 -9.2 A.S. 1D A.S. 1D A.S. 1D A.S. 1D -H.S. -H.S. A1 -0.3 A.S. 1D A.S. 1D A.S. 1D A.S. 1D Tu 1D Tu 1D I4 3.6 A.S. 1D A.S. 1D A.S.

  curve is extrapolated to transform the continuously measured water levels into discharge values. The uncertainties resulting from this method are entirely site dependant. Le Coz et al. (2012) proposed a method to estimate the uncertainty of this measurement method at site A2 during dam ushing in 2011. Using these results, the value σ Q,M eas = 7% was chosen. It is of the same order of magnitude of the uncertainty estimated by Olivier et al. (2008) from well documented rating curves of several mountainous discharge stations.

  have shown that the homogeneity of suspended sediment is highly site dependant. Vertical SSC distribution has never been estimated on the Arc and Isère Rivers, because of the high ow velocities during ushing events. However, the Rouse-Schmidt number Z = W s /(κu * ) (with W s : settling velocity of the suspended sediments, κ = 0.41: Von Karman constant, and u * : friction velocity) gives information on the potential vertical heterogeneity of the suspension (Garcia, 2008). Very low values of the Rouse-Schmidt number (Z 1) indicate that the suspended sediments are well distributed over the vertical dimension of the river cross-section. Such vertical homogeneity was also veried on a secondary channel of the Arc River (Camenen et al., 2018). Antoine et al. (2012) measured the settling velocity of suspended sediments during the ushing event of 2011 and observed a maximum value W s = 2 mm/s.

Figure 3 :

 3 Figure 3: Interpolation error for the SSC as a function of the number of sampled data.

   shows an example of the global uncertainty prole for the 2010 dam ush, with the SSC, discharge and global uncertainty proles (Figure4a), and the resulting condence interval Φ(X i ) ± σ Φ (X i ) (Figure4b). The global uncertainty stems in almost equal proportions from the uncertainties on discharge and SSC. The results are similar for the other ushing events, except for the case of very scattered SSC samples. In these cases the contribution of the SSC uncertainties is predominant (e.g. in 2006).

Figure 4 :

 4 Figure 4: Spatial variation of the uncertainties in ne sediment concentration, discharge, and ne sediment ux estimations for the 2010 dam ushing event (a) and condence interval resulting from the estimation of global uncertainties (b).

Figure 5 :

 5 Figure 5: Spatial proles of the integrated suspended sediment uxes Φ(X i ).

Figure 6 :

 6 Figure 6: Water discharge and concentration time-series at sites A7 (Pontamafrey, a and c) and I1 (Grenoble, b and d) for the 2007 (a and b) and 2009 (c and d) ushing events.

  reservoirs. However, in 2007, a lower value is observed indicating a smaller stock of ne sediments in the reservoirs. It could be explained by the ood event in September 2006 (Q max ≈ 150 m 3 /s). Only two other signicant oods, for which dam gates were opened, were observed during the period between 2005 and 2012: the May 2008 ood (Q max ≈ 450 m 3 /s) and the June 2010 ood (Q max ≈ 160 m 3 /s). Similarly, the following ushing event in 2009 and 2011 yielded a low total ux Φ just after dam reservoirs, i.e.

4. 3 .

 3 Initial quantity of erodible sediments in the river bed Continuous SSF measurements at site I1, which integrate the whole study area, are available over the whole period of the study (with a sampling step of 30 minutes). More specically, the cumulative SSF measured at site I1 during the 2-3 months preceding each ushing (from 1st April) event showed large variations as a function of the event (Tab. 4): from 125,000 tons in 2011 to 1,000,000 tons in 2010. The large amounts of sediment mass in 2006 and 2010 were mostly due to a very active spring period but also due to some engineering works on the Isère dikes in 2010. Also, a large compensation reservoir directly connected to the Arc River just upstream A7 (X = -40 km) was cleaned out over a three month period in 2010 and 2011. In 2006 and 2010, the 2-month integrated SSF at I1 reached very large values that have potentially led to large deposition over gravel bars. Signicant re-suspension have been observed on the Isère River during the ushing events performed these two years, and on the Arc River during the 2006 event, which appears consistent with the hydrology during the spring period. The cleaning of the compensation reservoir in 2011 could also explain the large re-suspension observed in the Arc River during the following ushing event, just upstream the conuence with the Isère River.

Figure 7 :

 7 Figure 7: Dynamic cumulative mass balance between A8 and A7 (a), A5 and A4 (b), A4 and A3 (c) and A3 and A1 (d) (a positive value means erosion whereas a negative value means deposition).

  is observed. Only the percentile D 90 changed signicantly between A1 and I1. In 2011, one observed a signicant local erosion between A5 and A1 and a signicant local deposition between A1 and I3 this year. The local deposition between A1 and I3 could be related to the decrease of D 90 values with a position of the coarsest particles downstream the conuence with the Isère River. During the ushing event of June 2011, the additional discharge coming from the upper Isère River was low, and the ow velocity could have decrease signicantly downstream the conuence where the river width is larger. Despite the signicant local erosion observed between A5 and A1, no change were measured in terms of grain size distributions. Fig. 7 b, c and d shows the local dynamics of erosion and deposition between A5 and A1.

Table 1 :

 1 Summary of the methods used for discharge and concentration measurements (Site: code of the measurement point located at the distance D from the conuence). Three methods were used for the concentration values (A.S.: Automatically Sampled, M.S.: Manually Sampled, Tu: Turbidity measurements) and two methods were used for the discharge values (H.S.: Discharge values from Hydrometric Stations, 1D: Discharge values computed with the 1D model).

	Site X	2006	2007	2009	2010	2011	2012
	[km]

  [START_REF] Navratil | Global uncertainty analysis of suspended sediment monitoring using turbidimeter in a small mountainous river catchment[END_REF] gave a global uncertainty value resulting from the turbidimeter sampling method. The authors estimated a relative standard deviation of 5% at high concentrations (more than 10 g/l) and 10% at lower concentrations (between 1 and 10 g/l). In the data set presented in Table1, most of the SSC values obtained from a turbidimeter were lower than 10 g/l.Thus the relative standard deviation is xed at σ SSC,T u = 10%. However, for the specic cases of ushing event, turbidity measurements were generally combined with regular ISCO sampling; as a consequence, we reduced the error to 5%.

Eect of temporal sampling frequency (σ SSC,Int ). The term σ SSC,Int has to be estimated due to the heterogeneity of the sampling frequencies for the SSC measurements. A simple formula is proposed to estimate this term: between two measured SSC values SSC i and SSC i+1 separated by the time interval ∆t, the local relative error could be estimated as the product |SSC i -SSC i+1 | × ∆t, normalized by the averaged SSC value (SSC i + SSC i+1 )/2

Table 2 :

 2 Summary of the global uncertainty σ Φ (in %) associated with the ux Φ at the 14 sites (in 10 3 Tons).

	Site	2006	2007	2009	2010	2011	2012

Table 3 :

 3 Local mass balance (∆Φ(i → i + 1), in 10 3 tons) distribution in the Arc-Isère river system for the six studied dam ushing events (bold values correspond to signicant values regarding the global uncertainty value, positive values correspond to erosion whereas negative values correspond to deposition).

	Reach	2006	2007	2009	2010	2011	2012
	A9-A10 -A8-A9 -2.9	+4.8 +4.8	+4.7	+7.2	+3.5	+5.9
	A7-A8 +7.8	+0.8	-7.9	-11.1 -3.3
	A6-A7 +19.1 +1.4 A5-A6 -24.5 -5.1 +1.5 +3.3	+7.0 +1.4	+4.5 +0.2	-9.1
	A4-A5 -0.1	+3.3	-4.2	-1.7	-0.2	+4.8

Table 3

 3

	indicates that only 14 of the 52 local mass balances are signi-
	cant for the proposed uncertainty model propagation: 5 of the 19 negative
	mass balances, and 9 of the 33 positive mass balances. However, signicant
	local mass balances highlight dierent behaviours of the river bed evolu-
	tion: in 2010, a signicant deposition is observed just upstream a strong
	re-suspension, even if the two successive river reaches (separating A8, A7
	and A6) have almost the same mean slopes (about 1%) and reach lengths
	are smaller than 5 kilometres. More generally, we can see that ushing events
	produce signicant dynamics in terms of exchange with the river bed, with
	values of re-suspension or deposition of ne sediments up to 20,000 tons .
	Despite this relatively low signicance of the local mass balance values,
	meaningful tendencies may explain why local variations can be signicant for
	one ushing event but not signicant for the next one. More generally, the
	responses of the river bed can be divided into two groups: the river bed gave
	similar responses for 2009, 2010 and 2011 (group 1), and similar responses for

  base Φ tot,spring : a third intermediate peak concentration at 20 g/L was observed because of the unexpected peak discharge in the middle of the rst plateau.

	Year	m 3 /s	g/l g/l	m 3 /s	m 3 /s	m 3 /s	10 3 tons
	2006	30.0	9	24	83	246	229	950
	2007	33.5	17	8	56	208	232	400
	2009	36.0	1	10	52	210	201	430
	2010	35.5	3	12	98	209	368	1,000
	2011	33.5	5	13	33	116	165	125
	2012	27.0	12 * 42	55	261	444	650

*

Table 5 :

 5 Time-averaged values of D 10 , D 50 and D 90 (µm) measured at sites A5, A1 and I1 during the 2011 ushing event.

	Site 2011 ushing event
		D 10 D 50	D 90
	A5 3.4 16	51
	A1 3.4 17	54
	I1	3.1 14	39

Acknowledgements

This work has been partially supported by the French National Research Agency (ANR) under the grant ANR-18-CE01-0020 (DEAR project). The study took place on an experimental site of the ZABR (Zone Atelier du Bassin Rhône) which is a CNRS-labelled site. We would like to thank all the persons from INRAE (River hydraulic team of RiverLy, Lyon), IGE (Hydrimz team, Grenoble) and EDF (DTG, Grenoble) who produced all the eld data used in this study.