Denudation systematics inferred from in situ cosmogenic 10 Be concentrations in fine (50–100 µm) and medium (100–250 µm) sediments of the Var River basin, southern French Alps

Marine sedimentary archives are well dated and often span several glacial cycles; cosmogenic 10 Be concentrations in their detrital quartz grains could thus offer the opportunity to reconstruct a wealth of past denudation rates. However, these archives often comprise sediments much finer (<250 µ m) than typically analyzed in 10 Be studies, and few studies have measured 10 Be concentrations in quartz grains smaller than 100 µm or assessed the impacts of mixing, grain size and 5 interannual variability on the 10 Be concentrations of such fine-grained sediments. Here, we analyzed the in situ cosmogenic 10 Be concentrations of quartz grains in the 50–100 and 100–250 µm size fractions of sediments from the Var basin (southern French Alps) to test the reliability of denudation rates derived from 10 Be analyses of fine sands. The Var basin has a short transfer zone and highly variable morphology, climate and geology, and we test the impact of these parameters on the observed 10 Be concentrations. Both analyzed size fractions returned similar 10 Be concentrations in downstream locations, 10 notably at the Var’s outlet, where concentrations ranged from (4.02 ± 0.78) × 10 4 to (4

Second, the most distal samples in this study are still taken from the channel.As such, they have not undergone long-shore transport, mixing, bioturbation, density flows, etc. that characterise many offshore environments.I would recommend that the authors rephrase this slightly.
We agree that such processes can affect the 10 Be signal and alter its interpretation in sediments archives.We thus have reworded the abstract and the conclusion to mention this caveat and meet the Reviewer 1's recommendation: page 2, line 17: Our results demonstrate that fine-grained sediments (50-250 µm) may return accurate denudation rates and are thus potential suitable targets for future 10 Be applications, such as studies of paleo-denudation rates using offshore sediments.page 11, line 8: "Our results demonstrate that fine-grained sediments (50-250 µm) may return denudation rates similar to those of coarser sediments typically used in 10 Be studies (250 µm to 1 mm) and are thus potential suitable targets for future 10 Be applications, such as studies of paleo-denudation rates using offshore sediments.However, marine sedimentary dynamics such as long-shore transport, mixing, density flows and sea level changes, might alter the validity of this statement.Hence, an additional test will be to analyze 10 Be concentrations in both fine and coarse sand subaliquots of marine core samples." Their work does demonstrate that fine-grained quartz can be used over short transport distances and in a fairly complex geomorphic setting.This is significant, even without an offshore connection.The authors do a good job of reviewing Alpine denudation studies and placing their work in this context.I appreciated the quick overview offered by figure 4.

Thank you.
It is interesting that the 10 Be results are similar to the modern sediment flux despite the different timescales and spatial averaging.I am somewhat surprised that the limestones would be eroding at an equivalent rate (especially since they would be undergoing relatively more chemical weathering than the quartz bearing regions).Are there any sediment flux data for subcatchments that are predominantly quartz?That might help pull this apart more convincingly.This is a good point but as far we know no sediments flux data from carbonate lithology exist in the studied region.Nevertheless, we added a reference to a paper by Thomas et al. (2016) where the authors use 36 Cl to measure denudation rates on carbonates rocks near (100 km) the Var catchment.page 7, line 19: "Given different lithologies may have different erodabilities, this observation might be questionable.Thomas et al. (2017) measured 36 Cl derived denudation rates in carbonates rocks located about 100 km from the Var basin.
They obtained denudation values ranging between 0.10 mm yr -1 and 0.20 mm yr -1 , comparable to those of the quartz bearing rock of the lower Var catchments, which have similar climatic and geomorphologic settings." The lack of an interannual signal, despite significant torrents, is also a bit surprising given previous examples of this (i.e.Kober et al., 2005, etc.).
We agree with Reviewer 1 and we believe that temporal variations are more prone to be observed in small and upper catchments, such as we do observe with proximal samples VAR-16-2 and VAR-17-2 (see discussion in section 4.5) but are buffered downstream.This behavior has already been observed in different settings (e.g.Lupker et al., 2012).To better discuss this point we add the following sentence to the main text: page 10, line 32: "This scale effect on the 10 Be signal buffering -larger watershed reducing the temporal stochasticity -has already been observed in other settings (e.g.Lupker et al., 2012)."I would have liked to have seen a more developed discussion of grain size dependence of cosmogenic nuclide data.The authors do note that some have reported trends and some not and provide a few examples of drivers.Since this is a fairly short manuscript, there is space to expand this to discuss when we might expect a grain size dependence and why (i.e.Lukens et al., 2019, etc.).This could be incorporated into a broader summary of the development of the method presented here.Following Reviewer1's wishes we added a paragraph regarding grain-size dependent 10 Be concentrations processes in the introduction part.page 3, line 22: "Furthermore However, grain size distributions are not always uniform across continental basins (Lukens et al., 2016), and 10 Be concentrations in fine sands and silts at river outlets may not be representative of their entire drainage area.Furthermore, since the production rate of in situ 10 Be is depth-dependent, any vertical variations of the granulometric distribution may induce a grain size control on the measured 10 Be concentrations.Several geomorphological processes are potential controls of such grain-size dependence (Aguilar et al., 2014;Attal et al., 2015;Brown et al., 1998;Carretier et al., 2015;Codilean et al., 2014;van Dongen et al., 2019;Lukens et al., 2016;Puchol et al., 2014;Riebe et al., 2015): landslides can bring 10 Be-poor coarse material to the surface that is then mixed with fluvial sediments (Aguilar et al., 2014;Attal et al., 2015;Belmont et al., 2007;Brown et al., 1998;Carretier et al., 2015;Puchol et al., 2014).The basin slope and precipitation also exert a control on the thickness of mixed soil on hillslopes, as well as the depth of erosion process, which all may impact the relationship between grain-size and the 10 Be concentrations (van Dongen et al., 2019).At last, the sediment transport time, which may differs for coarse and fine grains, as well as attrition, may both yield a grain-size effect control on 10 Be concentrations (Attal et al., 2015;Belmont et al., 2007;Carretier et al., 2015;van Dongen et al., 2019;Lukens et al., 2016;Matmon et al., 2003).It is worth noting that most of the studies investigating grain-size dependent 10 Be concentrations processes do so using medium sand grain-size to pebble-sized sediments (125 µm to > 1 mm).There is only one study presenting data on a fraction smaller than 125 µm (Brown et al., 1995)."page 8, line 41: "In the Var basin, we observe no systematic impact of grain size on the 10 Be concentration (Fig. 2).All but two samples have similar 10 Be concentrations for the 50-100 and 100-250 µm size fractions."
Denudation is the combined effect of physical erosion and chemical weathering processes, and may vary with time.Because climate exerts a strong control on denudation (Molnar, 2004;Yanites and Ehlers, 2012;Zhang et al., 2001), it is important to predict how landscapes will respond to the large and rapid climate changes expected in the future.Terrestrial cosmogenic nuclides (TCNs) in river sediments provide a means to determine denudation rates at the basin scale (Bierman and Steig, 1996;Brown et al., 1995;Granger et al., 1996;von Blanckenburg, 2005).Thus, for decades, TCN (mostly 10 Be) concentrations have been measured in present and past river sediments across a wide variety of climatic and geological contexts to quantify denudation rates (see review by Portenga and Bierman, 2011) over different time scales (Bekaddour et al., 2014;Charreau et al., 2011;Granger and Schaller, 2014;Grischott et al., 2016Grischott et al., , 2017;;Marshall et al., 2017;Puchol et al., 2017;Schaller et al., 2002).However, although offshore marine sedimentary archives are well dated and often record several glacial cycles, they have remained unused for reconstruction of paleo-denudation rates, mainly because their grain sizes are too fine to facilitate standard in situ 10 Be analyses in quartz.Indeed, typical cosmogenic dating samples have grain sizes of 250 µm to 1 mm.In deep (>200 m water depth) marine environments, sediments of such grain sizes are restricted to submarine canyons in which the stratigraphic record is poorly preserved.Thus, analyzing TCNs in fine sand fractions (50-100 µm) is prerequisite to reconstructing past denudation rates from marine sediments because this granulometric range often dominates in offshore, turbidite-rich sedimentary cores (Bonneau et al., 2014;Jorry et al., 2011).Furthermore However, grain size distributions are not always uniform across continental basins (Lukens et al., 2016), and 10 Be concentrations in fine sands and silts at river outlets may not be representative of their entire drainage area.
Furthermore, since the production rate of in situ 10 Be is depth-dependent, any vertical variations of the granulometric distribution may induce a grain size control on the measured 10 Be concentrations.Several geomorphological processes are potential controls of such grain-size dependence (Aguilar et al., 2014;Attal et al., 2015;Brown et al., 1998;Carretier et al., 2015;Codilean et al., 2014;van Dongen et al., 2019;Lukens et al., 2016;Puchol et al., 2014;Riebe et al., 2015): landslides can bring 10 Be-poor coarse material to the surface that is then mixed with fluvial sediments (Aguilar et al., 2014;Attal et al., 2015;Belmont et al., 2007;Brown et al., 1998;Carretier et al., 2015;Puchol et al., 2014).The basin slope and precipitation also exert a control on the thickness of mixed soil on hillslopes, as well as the depth of erosion process, which all may impact the relationship between grain-size and the 10 Be concentrations (van Dongen et al., 2019).At last, the sediment transport time, which may differs for coarse and fine grains, as well as attrition, may both yield a grain-size effect control on 10 Be concentrations (Attal et al., 2015;Belmont et al., 2007;Carretier et al., 2015;van Dongen et al., 2019;Lukens et al., 2016;Matmon et al., 2003).It is worth noting that most of the studies investigating grain-size dependent 10 Be concentrations processes do so using medium sand grain-size to pebble-sized sediments (125 µm to > 1 mm).There is only one study presenting data on a fraction smaller than 125 µm (Brown et al., 1995).
Several studies have suggested that sediment mixing is not always efficient in mountainous environments (Binnie et al., 2006;Savi et al., 2014), which would further bias interpreted denudation rates.Finally, 10 Be concentrations integrate the denudation signal over time periods dependent on the denudation rate that correspond to the time needed to erode 60 cm of rock (Lal, 1991).Perturbations in the sedimentary routing process, such as human-induced erosion or stochastic events like landslides or flash floods, can potentially affect 10 Be concentrations over much shorter time scales and therefore bias the interannual consistency of the 10 Be signal (Dingle et al., 2018;Lupker et al., 2012;Sosa Gonzalez et al., 2017).
The effects of spatial mixing, grain size and temporal variability on TCN concentrations have mostly been tested on sand fractions coarser than 125 µm.With the exception of Brown et al. (1995Brown et al. ( , 1998)), who investigated grain sizes as small as 63 µm, these processes remain largely unexplored in fine size fractions <125 µm.Therefore, it is critical to understand how fine sediments capture denudation rates in onshore basins and if these processes alter the observed TCN concentrations.
Here, we measured in situ 10 Be concentrations in the 50-100 and 100-250 µm size fractions of modern present-day quartz sediments of the Var River.The Var drains a mountainous basin in the southern French Alps, is characterized by a steep mean slope of 23°, and its small alluvial plain limits sediment storage (Bonneau et al., 2017).The Var sedimentary system responds quickly (i.e.within 1000 yr) to climatic forcings, and is thus an ideal setting to test the suitability of fine-grained sediments to record paleo-denudation rates (Bonneau et al., 2017).We analyzed multiple samples within the Var basin to assess the spatial variability of denudation rates across a high diversity of geomorphic and climatic contexts.We then traced the upstream to downstream evolution of 10 Be concentrations in both analyzed size fractions to monitor the impact of grain size on the observed 10 Be concentration, the sediment mixing efficiency at major fluvial junctions, and the interannual variability of the denudation signal.

The Var basin
The Var and its main tributaries (Vésubie, Tinée, Estéron and Coulomp Rivers) drain a mountainous basin of 2800 km 2 in the southern French Alps (Fig. 1).This steep basin is characterized by a mean slope of 23° and elevations ranging from 0 to 3143 m above sea level with a mean elevation of 1200 m (Fig. 1).The Var basin can be divided into two main geological regions: crystalline basement in the north and sedimentary terrains in the south.In the northern and highest part of the basin, the Mercantour-Argentera Massif comprises migmatites, gneiss and granite (Fig. 1) inherited from the Paleozoic Hercynian orogen (El Bedoui et al., 2011).The late Paleozoic to Cenozoic sedimentary cover of the southern and western parts of the basin mainly comprises Mesozoic marls and limestones (Kergkhove and Montjuvent, 1977;Roure et al., 1976).These sediments also include Permian pelites and sandstones (locally overlain by Cenozoic marls, limestones and sandstones) at the southern edge of the Mercantour-Argentera Massif and in the inner part of the Var basin (Fig. 1).In the southernmost part of the basin, the Pliocene to Quaternary Gilbert delta developed after sea level rise in the Mediterranean Sea following the Messinian salinity crisis (Mulder et al., 1996).
Stochastic erosional processes such as landslides -the most studied being La Clapière landslide in the Tinée valley (El Bedoui et al., 2009;Casson et al., 2003) -and screes occur in the steepest part of the basin (Julian, 1977).Four hydropower dams have been built in the upper part of the basin (Fig. 1), but only the Lac Long dam (2500 m elevation) has a significant water storage capacity (4 700 000 m 3 ).Nine sedimentary dams were built in the lowest part of the basin in the 1970s to enhance sediment deposition and protect the city of Nice (Anthony and Julian, 1999).The climate in the Var basin is mostly controlled by elevation and is thus highly variable, from a Mediterranean climate in the south to a mountainous climate in the north.Between 1981 and 2010, the mean annual temperature and mean annual precipitation recorded at Nice (2 m above sea level; Fig. 1) were 16 °C and 733 mm yr -1 , respectively, and those at Guillaumes (790 m above sea level; Fig. 1) were 10.7 °C and 910 mm yr -1 , respectively (Meteo France database; https://donneespubliques.meteofrance.fr).

Sampling and 10 Be analyses
We collected eleven sediment samples (2 kg each) from active riverbeds of the Var River and its main tributaries (Vésubie, Tinée, Estéron and Coulomp Rivers) in November 2016.Sampling locations were carefully selected to avoid any humaninduced perturbations in the basin, such as dams (Fig. 1).The Tinée and Vésubie Rivers were each sampled at two locations: one within the crystalline massif (TIN-16-2 and VES-16-1) and one just upstream of their junctions with the Var River (TIN-16-1 and VES-16-2) (Fig. 1).The Coulomp and Estéron Rivers were each sampled upstream of their junctions with the Var River (COU-16-1 and EST-16-1).The Var River was sampled at five locations throughout the basin: one upstream of the Tinée confluence (VAR-16-2), one upstream of the Vésubie confluence (VAR-16-3), one upstream of the Estéron confluence (VAR-16-4) and two at the river outlet near the Mediterranean Sea (VAR-16-5A and VAR-16-5B).In November 2017, we resampled three of the rivers in four of the same locations: VAR-17-2, VAR-17-5B, VES-17-1 and TIN-17-2.We sieved the samples to obtain 50-100 and 100-250 µm grain size fractions.Quartz grains were isolated from both fractions by magnetic separation and successive HCl + H 2 SiF 6 baths following the standard procedure.For the fine-grained fraction (50-100 µm), samples were first decanted during few minutes, then the supernatant was carefully removed.The pure quartz grains were then leached three times in HF to dissolve 30 % of the total weight of quartz and eliminate meteoric 10 Be contamination (Brown et al., 1991).We then spiked the purified quartz samples with 0.3 mg of the Centre de Recherches Pétrographiques et Géochimiques (CRPG) 9 Be carrier solution (concentration of 2020 ± 83 ppm, corresponding to ~2.25 × 10 9 atoms 9 Be).The spiked quartz samples were then completely dissolved in 48 % HF; beryllium was separated using anion and cation exchange columns and pH-sensitive precipitations before being oxidized to BeO, mixed with Nb powder and loaded into targets for measurement of 10 Be/ 9 Be ratios using the ASTER accelerator mass spectrometer at Centre Européen de Recherche et d'Enseignement des Géosciences de l'Environment (CEREGE).

Calculation of denudation rates
In situ cosmogenic 10 Be is produced by cosmic rays in minerals such as quartz within the uppermost layer of Earth's surface (Lal and Peters, 1967).The 10 Be concentration in quartz depends directly on the time spent near the surface and, thus, on the denudation rate (Lal, 1991).Therefore, the average denudation rate at the basin scale can be derived from the 10 Be concentrations measured in detrital quartz exported by fluvial sediments and sampled at the outlet of the studied basin (Brown et al., 1995).Assuming that denudation is steady-state and the 10 Be decay constant is negligible (von Blanckenburg, 2005), the spatially averaged denudation rate of a basin is inversely proportional to the 10 Be concentration in sediments (Brown et al., 1995;Granger et al., 1996).The basin-averaged denudation rate can thus be calculated as: where i refers to the different 10 Be production pathways and associated particles (n for neutron,  for slow muons and  for fast muons). ! are the mean basin-wide 10 Be production rates, computed from the arithmetic mean of spallogenic and muogenic production using specific scalings for each production pathway as a function of elevation and latitude: P n = 4.11 ± 0.19 atoms g -1 yr -1 , P µs = 0.011 ± 0.001 atoms g -1 yr -1 and P µf = 0.039 ± 0.004 atoms g -1 yr -1 (Braucher et al., 2011;Martin et al., 2017). ! are the attenuation lengths for each particle: Λ n = 160 g cm -2 , Λ µs = 1500 g cm -2 and Λ µf = 4320 g cm -2 (Braucher et al., 2011).Finally,  is the mean density of the eroded material (2.7 g cm -3 ) and  is the 10 Be concentration measured in the fluvial sediments collected at the basin outlet.
We calculated basin-averaged 10 Be production rates for each production pathway and each studied subbasin using the Basinga GIS tool (Charreau et al., 2019), based on the Lal-Stone time-dependent scaling model (Lal, 1991;Nishiizumi et al., 1989;Stone, 2000), and using up-to-date worldwide production rates computed by the Cosmic Ray Exposure program online calculator (https://crep.otelo.univ-lorraine.fr/;Martin et al., 2017).We accounted for basin topography using a cellby-cell approach based on the 5 m resolution digital elevation model "RGE ALTI" produced by the French Institut National de l'Information Géographique et Forestière.Denudation rates were corrected for paleomagnetic variations that occurred during the integration time and topographic shielding (Charreau et al., 2019).Topographic shielding factors were calculated using the ArcGIS toolbox of Codilean (2006), which computes both self-shielding and shading.Quartz-free areas were excluded from the basin-averaged production rate calculations based on 1:50 000 and 1:250 000 scale French Geological Survey geological maps (Bigot et al., 1967;Campredon et al., 1980;Faure-Muret et al., 1954, 1957;Gèze et al., 1969;Ginsburg et al., 1980;Kergkhove and Montjuvent, 1977;Kergkhove and Roux, 1976;Kergkhove and Thouvenot, 2010;Roure et al., 1976).Quartz-bearing zones comprise 730 km 2 , corresponding to 26 % of the total surface area of the Var basin.We calculated denudation rates for each of the Var's subbasins using the measured 10 Be concentrations and Eq. ( 1) (Table 1).We also calculated effective denudation rates and 10 Be concentrations in the downstream part of three basins by correcting for the contribution of upstream nested subbasins (Table 2, Fig. S1) (see Granger et al., 1996 and Portenga et al., 2015 for methods).

Results
The raw 10 Be concentrations of the sediment samples are reported in Supplementary Data.Blank-corrected 10 Be concentrations are reported in Table 1 and summarized in Figure 2 for the 2016 sampling.We obtained twenty 10 Be measurements from the eleven samples collected in 2016; concentrations were measured in both the 50-100 and 100-250 µm grain size fractions for all samples except VAR-16-4 and TIN-16-2, which did not yield sufficient amounts of quartz in the 50-100 µm fraction.We obtained five 10 Be measurements from the four samples collected in 2017; both grain size fractions were measured for VAR-17-2, only the 50-100 µm fraction was measured for VAR-17-5B and only the 100-250 µm fraction was measured for VES-17-1 and TIN-17-2.Measurement blanks accounted for, on average, 11 ± 7 % of the measured 10 Be/ 9 Be ratios.Native 9 Be amounts have been measured in three samples (VAR-16-5B 100-250 µm, TIN-16-2 100-250 µm and VES-16-1 100-250 µm).All three samples have been found to have negligible amounts of native 9 Be, accounting for at most 0.3 % of the 9 Be carrier added to each sample.Most samples had similar 10 Be concentrations within uncertainties for the 50-100 and 100-250 µm grain size fractions (Table 1 and Fig. 2).VES-16-1 and VES-16-2 are two exceptions because they yielded different 10 Be concentrations in each size fraction: for both samples, the 50-100 µm fraction had higher 10 Be concentrations than the 100-250 µm fraction.Importantly, the most distal samples collected at the outlet of the Var River (VAR-16-5A and VAR-16-5B) had undistinguishable 10 Be concentrations in both size fractions, ranging from (4.02 ± 0.78) × 10 4 atoms g -1 to (4.40 ± 0.64) × 10 4 atoms g -1 .We also note a decrease of the variability of the 10 Be concentration from upstream to downstream (Fig 2 .).Sediments resampled in 2017 (VAR-17-2, VAR-17-5B, VES-17-1 and TIN-17-2) had concentrations similar within uncertainties to the 2016 samples (Table 1); only the 50-100 µm fraction of VAR-17-2 had a significantly lower 10 Be concentration compared to the same size fraction of the 2016 sample.

Comparison of 10 Be-derived denudation rates with the modern sediment flux
To validate the use of 10 Be-derived denudation rates obtained from fine-grained sediments, we compare the denudation rates obtained at the outlet of the Var River (samples VAR-16-5A and VAR-16-5B) to previous results for the Var basin.Both the denudation rates derived from the 100-250 µm (0.24 ± 0.03 mm yr -1 ) and 50-100 µm fractions (0.25 ± 0.04 mm yr -1 ) at the Var outlet are in remarkable agreement with the denudation rate of 0.22 mm yr -1 calculated by Bonneau et al. (2017) based on modern Var River sediment fluxes estimated by Mulder et al. (1996).This demonstrates that fine-grained sediments can accurately preserve and transport the 10 Be-derived denudation signal across the Var basin.Furthermore, because the 10 Bederived denudation rate was calculated solely for quartz-bearing rocks whereas the sediment flux-based estimate includes all lithologies, the agreement between the two methods suggests that quartz-bearing rocks are eroded at the same rate as other rock types in the basin.Given different lithologies may have different erodabilities, this observation might be questionable.
Thomas et al. ( 2017) measured 36 Cl derived denudation rates in carbonates rocks located about 100 km from the Var basin.
They obtained denudation values ranging between 0.10 mm yr -1 and 0.20 mm yr -1 , comparable to those of the quartz bearing rock of the lower Var catchments, which have similar climatic and geomorphologic settings.We note that the integration time of the 10 Be signal at the outlet (VAR-16-5A and VAR-16-5B) is between 2.3 and 2.6 kyr (Table 1), whereas the modern sediment flux was estimated over a 20 year period (between 1974 and1994;Mulder et al., 1996).The agreement of the two methods thus suggests that denudation rates in the Var basin have been stable over the last 2.6 kyr.

Comparison with previously published 10 Be studies across the Alps
In this subsection, we compare the Var basin denudation rates with other studies reporting 10 Be-derived denudation rates in similar environments of the Alps.It is notably important to verify that the variability of the 10 Be signal carried by finegrained sediments follows the same trend as larger grain sizes.Multiples studies have explored the relationship between denudation and landscape parameters such as topography and climate at a global scale (e.g.Portenga and Bierman, 2011) and at the scale of the Alps (Delunel et al., 2010;Dixon et al., 2016;Molliex et al., 2016;Norton et al., 2011;Wittmann et al., 2007).The two most frequent parameters used in correlation with denudation rates are the average slope (Dixon et al., 2016;Portenga and Bierman, 2011;Wittmann et al., 2007) and average elevation of the basin (Delunel et al., 2010;Molliex et al., 2016;Wittmann et al., 2007).Figure 4 compares the 10 Be-derived denudation rates of each subbasin with its mean slope and elevation.We calculated subbasin effective denudation rates by excluding nested upstream subbasins for three subbasins (VAR-16-2, TIN-16-1 and VES-16-2) following the method of Portenga et al. (2015) (Table 2) to account for the local parameters of each subbasin.Furthermore, Figure 4 compares our data from the Var basin with previously published 10 Be-derived denudation rates across the Alps, as available in the OCTOPUS Database (Codilean et al., 2018).We selected 133 basins with drainage areas comparable to the Var basin and its subbasins, i.e. ranging from 10 to 10 000 km 2 (Fig. 4).
Alpine denudation rates range from 0.01 ± 0.01 mm yr -1 (Buechi et al., 2014) to 2.83 ± 0.93 mm yr -1 (Norton et al., 2010) for grain sizes ranging from 63 to 1000 µm, consistent with the overall variability of denudation rates across the Var basin (Fig. 4).It is worth noting that the Octopus database takes into account all lithologies when calculating morphometric values (such as mean elevation and mean slopes as shown in Fig. 4); whereas in this study all metrics have been calculated on quartz bearing surfaces only.
In Figure 4, we classified 10 Be-derived denudation rates for the Alps into three granulometric groups: <250, 250-500 and >500 µm, and we note several key observations.First, the maximum grain size analyzed does not seem to induce a strong control on the 10 Be-derived denudation rates at the scale of the Alpine belt.Second, the mean slope of the basin does not exert a linear control on denudation rates because the highest denudation rates are not observed on the steepest slopes (Fig 4. a); denudation rates on average slopes of 23-32° are characterized by the highest average values, but are highly variable.In the Var basin, denudation rates increase nonlinearly with subbasin slope, as observed in mountainous basins elsewhere (Binnie et al., 2007;Dixon et al., 2016;Montgomery and Brandon, 2002;Roering et al., 2001;Wittmann et al., 2007).This nonlinear relationship has been interpreted as the result of a change from diffusive to non-diffusive transport dynamics above a given slope angle, variously reported to be between 22° and 30° (Binnie et al., 2007;Montgomery and Brandon, 2002;Roering et al., 2001).This slope threshold is about 30° in the Var basin.On average slopes of 16-30°, denudation rates in the Var basin are rather restricted, from 0.10 ± 0.01 mm yr -1 (COU-16-1, 100-250 µm) to 0.22 ± 0.04 mm yr -1 (VAR-16-2, 100-250 µm).Denudation rates increase on the steepest average slopes (>30°), with values ranging from 0.20 ± 0.04 mm yr - 1 (VES-16-2, 50-100 µm) to 0.83 ± 0.28 mm yr -1 (TIN-16-1, 100-250 µm) (Table 2; Fig. S1).The hillslope transport model of Montgomery and Brandon (2002), based on the model of Roering et al. (1999), can explain the nonlinear relationship between average slope and denudation rate observed in our data (Fig. 4a).We explain the nonlinear relationship between average slope and denudation rate observed in our data using the hillslope transport model of Montgomery and Brandon (2002), based on the model of Roering et al. (1999), (Fig. 4a).In this model we assume a chemical weathering rate of 0.023 mm yr -1 for the Var (the mean value between spring and winter from Donnini et al., 2016), a critical slope of 33° (similar to Ouimet et al., 2009) and diffusivities (K) of 0.001 m yr -1 and 0.008 m yr -1 , which are within the range of global values complied by Hurst et al. (2013).Third, it has been shown that elevation exerts a positive control on denudation rates across the Alps (Fig. 4b), either due to frost cracking (Delunel et al., 2010), the impact of U-shaped glacial morphologies (Molliex et al., 2016) or greater uplift rates in higher regions (Wittmann et al., 2007).In the Var basin, the relationship between elevation and denudation appears rather weak, notably because the Tinée subbasin (sample TIN-16-1, 100-250 µm) presents the highest denudation rate (0.83 ± 0.28 mm yr -1 ) although situated at a relatively low elevation (1486 m).The high denudation rate in this area is most likely the result of the steep average slope (~32°) (Table 2; Fig. 4; Fig. S1).In the Alps, slope and elevation display a nearly linear relationship for slopes lower than ~20°, but the two variables are much more scattered for slopes steeper than 25° (Fig. 4c).
Overall, the 10 Be-derived denudation rates we obtained from fine-grained sediments (50-250 µm) in the Var basin are in the range of previously reported rates in the Alps.Our rates are also similar to those inferred from a wide range of grain sizes (63-1000 µm) at various slopes and elevations.This result suggests that denudation rates derived from 10 Be concentrations in fine-grained sediments (50-250 µm) properly record denudation in this region, with slope being the dominant control on denudation rates.This conclusion is further supported by the similar 10 Be concentrations of the 50-100 and 100-250 µm size fractions throughout the basin, the notable exception being the steep upstream Vésubie subbasin (VES-16-1, Fig. 5), discussed in Sect.4.3.

Impact of grain size on 10 Be concentrations
In the Var basin, we observe no systematic impact of grain size on the 10 Be concentration (Fig. 2).All but two samples have similar 10 Be concentrations for the 50-100 and 100-250 µm size fractions.In the Vésubie subbasin, the 10 Be concentrations of the two size fractions did not overlap within uncertainties (Table 1; Fig. 5).To understand this discrepancy, following previous studies (van Dongen et al., 2019;Lukens et al., 2016;Riebe et al., 2015) we investigated the potential controls of topographic and climatic parameters on the 10 Be concentrations of the sediments (Fig 5).For basins with nested upstream subbasins (VAR-16-2 and VES-16-2), we calculated subbasin 10 Be concentrations by removing the contribution of their upstream subbasins (COU-16-1 and VES-16-1, respectively; Table 2, Fig. S1) following the method of Portenga et al. (2015).It is thus apparent that above 2000 m elevation in the upper Vésubie (VES-16-1), sediments of the 50-100 µm size fraction have significantly higher 10 Be concentrations than those in the 100-250 µm fraction, whereas the two fractions have relatively similar concentrations in the downstream subbasin (VES-16-2; Fig. 5a).Because mean annual temperature is a function of elevation, it is tempting to propose that the main control on this discrepancy is climatic (Fig. 5b).A plausible temperature-altitude control could be related to frost cracking, an erosion mechanism enhanced by cold conditions.Indeed, in the nearby Ecrins Pelvoux massif (~120 km north of the Var basin), Delunel et al. (2010) found a positive correlation between elevation and 10 Be-derived denudation rates.It has been previously shown that frost cracking, an erosion mechanism enhanced by cold conditions, can be the principal driver of 10 Be-derived denudation rates in the nearby Ecrins Pelvoux massif (~120 km North of the Var basin) (Delunel et al. 2010).However, more data are required from different settings to thoughtfully document the influence of a potential frost cracking impact on a grain size dependent erosion rate.
An alternative possibility is that the slope of the subbasin affects the contributions of different grain sizes to the observed 10 Be concentration (Fig. 5c).Steeper areas are characterized by a larger contribution of sediments from deep-seated landslides, which are typically coarser sediments (Attal et al., 2015) with lower 10 Be concentrations (Puchol et al., 2014).
The mixing of landslide-derived material with finer hillslope surficial sediments will thus produce sediments with different 10 Be concentrations in the fine and coarse fractions (Fig. 5c), which is in line with the global compilation by van Dongen et al., (2019) where average basin slope has been found to be the primary driver of grain-size-dependent 10 Be concentrations.
Additional data are necessary to distinguish between the effects of climate and landslides in generating the observed discrepancy between the 50-100 and 100-250 µm fractions in the upper Vésubie subbasin.However, we stress that this grain size effect is limited to the Vésubie upstream subbasin and is not observed in larger subbasins below 2000 m elevation.
Importantly, we observe no effect of grain size on the measured 10 Be concentrations at the outlet of the Var basin (Fig. 2).

Sediment mixing
To determine if the 10 Be concentrations measured at the river outlet are representative of the entire basin, it is critical to assess whether the sediments are well mixed throughout the basin (Bierman and Steig, 1996;Binnie et al., 2006).This is of increased importance in the Var basin due to the heterogeneous distribution of quartz-bearing rocks.Because the basinaveraged denudation rate integrates surfaces of variable denudation rates, the average rate will not reflect the correct repartition of source areas if sediment mixing is inefficient, leading to erroneous denudation rates.Therefore, we here investigate the efficiency of sediment mixing by calculating the expected 10 Be concentration of sediments downstream of a particular junction, C calculated , as the 10 Be concentration of sediments from each tributary weighted by the sedimentary fluxes upstream of the junction (Binnie et al., 2006;Clapp et al., 2002;Matmon et al., 2003;Neilson et al., 2017;Savi et al., 2014): where subscripts 1 and 2 denote the two upstream subbasins,  ! and  ! are the 10 Be concentrations of their respective sediments measured upstream of the junction,  ! and  ! are their denudation rates, and  ! and  ! are the surface areas comprising quartz-bearing rocks in each subbasin.If sediment mixing is efficient, the calculated concentrations will be similar to that measured downstream of the junction.
We calculated mixed concentrations at the Var-Tinée (VAR-16-3, junction I), Var-Vésubie (VAR-16-4, junction II) and Var-Estéron junctions (VAR-16-5A/B, junction III) (Fig 6 .).We used the 10 Be concentrations measured in both size fractions for junction I, but only those of the 100-250 µm fractions (the only available data) in junctions II and III.At junction I, the calculated 10 Be concentrations for both grain sizes are in agreement with the measured 10 Be concentrations.
Similarly, at junction II, the expected and measured 10 Be concentrations are compatible within uncertainties.At junction III, the difference between the measured and expected 10 Be concentrations is greater, though they are compatible within uncertainties (C measured = 4.07 ± 0.74 atoms g -1 vs C calculated = 3.55 ± 0.50 atoms g -1 ).This discrepancy may be due to the 16 km distance between the Var-Estéron junction, where the mixed 10 Be concentration is computed, and the downstream sampling location, VAR-16-5A/B.Indeed, between these two points, the basin is developed over quartz-rich Pliocene conglomerates (Fig. 1) whose contribution may slightly modify the observed 10 Be concentrations.Finally, the presence of sedimentary dams in this area does not strongly affect the observed 10 Be concentrations of the sediments.Consequently, the fluvial dynamic of the Var basin efficiently mixes the sedimentary material transported by each major tributary.This confirms that the overall decrease of 10 Be concentrations from upstream to downstream (Fig. 2) is due to the efficient mixing of sediments across the basin.This behavior has previously been observed in other basins with much larger floodplains such as the Po (Wittmann et al., 2016) or the Ganga (Lupker et al., 2012).

Interannual variability of 10 Be concentrations
As in most mountainous areas, the discharge regimes of the Var River and its upstream tributaries (Tinée and Vésubie) are characterized by erratic and torrential behavior (Anthony and Julian, 1999).Therefore, it is important to assess whether extreme rainfall events, which are frequent in the study area (Anthony and Julian, 1999) and generate floods with high sedimentary loads (Mulder et al., 1996), affect the observed 10 Be concentrations.In November 2016, heavy rainfall induced multiple high discharge events in the Tinée, Vésubie and upstream Var (Fig. 7b).Consequently, the discharge at the outlet of the Var increased to over 200 m 3 s -1 seven days before sampling.Conversely, 2017 was characterized by more moderate rainfall and the discharge at the Var outlet was around 10 m 3 s -1 during sampling.Despite these differences, the 10 Be concentrations measured in 2016 and 2017 are in agreement (Fig. 7a), with the exception of the finer sediments (50-100 µm) in the upstream Var, which yielded statistically different 10 Be concentrations in 2016 and 2017 (samples VAR-16-2 and VAR-17-2).This difference may have resulted from a stochastic event (e.g.landslide) that locally modified the 10 Be concentrations.Such perturbations are rarely buffered in such a small subbasin (the VAR-2 subbasin has a quartz-bearing surface area of only 83.3 km 2 ) (Niemi et al., 2005;Yanites et al., 2009).However, upstream valleys (i.e. the Tinée and Vésubie) are the most subject to such events (Anthony and Julian, 1999), but do not show any interannual variations.Most importantly, the fine sediment (50-100 µm) samples at the Var outlet (VAR-16-5B and VAR-17-5B) were remarkably similar between the two years (Table 1, Fig. 7a).This scale effect on the 10 Be signal buffering -larger watershed reducing the temporal stochasticity -has already been observed in other settings (e.g.Lupker et al., 2012).Thus, despite highly variable discharge and the occurrence of stochastic events, the integrated 10 Be concentrations of sediments exported by the entire Var basin are not affected by a detectable interannual variability.

Conclusions
We documented modern millennial denudation rates in the Var basin (southern French Alps) using 10 Be concentrations measured in quartz grains in the 50-100 and 100-250 µm size fractions of detrital river sediments. 10Be-derived denudation rates range from 0.10 ± 0.01 mm yr -1 to 0.57 ± 0.09 mm yr -1 within the basin and the average denudation rate obtained at the Var outlet is 0.24 ± 0.04 mm yr -1 , in remarkable agreement with the denudation rate of 0.22 mm yr -1 determined based on the Var River sediment flux (Bonneau et al., 2017).The spatial variability of denudation rates within the Var basin is on the same order of magnitude as other 10 Be studies across the Alps.The dominant control on denudation rates in the Var basin appears to be the average slope of the subbasin, consistent with previous published studies.The 10 Be concentrations of the two analyzed size fractions were different only in the upper and steeper parts of the basin, but were similar at the Var outlet.
By comparing the expected and measured 10 Be concentrations at three tributary junctions, we demonstrated that sediment mixing is efficient throughout the basin.We investigated the interannual variability of 10 Be concentrations in sediments under different discharge regimes during wet and dry years (2016 and 2017, respectively); we observed local variations, but concentrations at the outlet were similar each year.Our results demonstrate that fine-grained sediments (50-250 µm) may return denudation rates similar to those of coarser sediments typically used in 10 Be studies (250 µm to 1 mm) and are thus potential suitable targets for future 10 Be applications, such as studies of paleo-denudation rates using offshore sediments.
However, marine sedimentary dynamics such as long-shore transport, mixing, density flows and sea level changes, might alter the validity of this statement.Hence, an additional test will be to analyze 10 Be concentrations in both fine and coarse sand subaliquots of marine core samples.

Data availability
A raw data table including all samples is available in supplement.

Authors contributions
AM, PHB and JC designed the study.AM, PHB, JC and CP collected the samples for analysis.AM prepared the samples for 10 Be analysis and the ASTER Team measured the 10 Be/ 9 Be ratios using the French Service National AMS ASTER.AM, PHB, JC and SM analyzed the data.AM wrote the initial manuscript, PHB, JC, CP and SM commented and contributed to the final version.

Figure 1 :5
Figure 1: Geological setting of the Var basin and its subbasins.Geological data are from the French Geological Survey (see text for references).White lines delimit the sampled subbasins, colored squares represent sampling points and red hashed areas indicate the presence of quartz-bearing rocks.Hydrological station data are from the HYDRO database (www.hydro.eaufrance.fr):I, Villneuve d'Entraunes station; II, Nice, Pont Napoléon station; III, Saint Sauveur sur Tinée station; and IV, Utelle station.5

Figure 2 :Figure 3 :
Figure 2: 10 Be concentrations in quartz from river sands of the Var basin plotted against the distance to the estuary (km).Data are available in Table 1.Symbol shape reflects the analyzed grain size and colors indicate the subbasin.The dashed line corresponds to the mean concentration of all samples, excluding the four outlet samples.Error bars represent 1 sigma uncertainties.

Figure 5 :Figure 6 :Figure 7 :
Figure 5: Differences in 10 Be concentrations of the 50-100 and 100-250 µm size fractions as a function of (a) elevation, (b) mean annual temperature and (c) average subbasin slope.Mean elevation and temperature were calculated for quartz-bearing surfaces only using a 5 m resolution DEM from the Institut National de l'Information Géographique et Forestière (http://professionnels.ign.fr/donnees).Temperature data are from the WorldClim database (http://worldclim.org/version2;Fick 5