Jens Rassmann
email: jens.rassmann@lsce.ipsl.fr

Bruno Lansard

Lara Pozzato

Christophe Rabouille

Carbonate chemistry in sediment porewaters of the Rhône River delta driven by early diagenesis (northwestern Mediterranean)

The Rhône River is the largest source of terrestrial organic and inorganic carbon for the Mediterranean Sea. A large fraction of this terrestrial carbon is either buried or mineralized in the sediments close to the river mouth. This mineralization follows aerobic and anaerobic pathways, with a range of impacts on calcium carbonate precipitation and dissolution in the sediment near the sediment-water interface. This study focuses on the production of dissolved inorganic carbon (DIC) and total alkalinity (TA) by early diagenesis, consequential pH variations and the effect on calcium carbonate precipitation or dissolution. The sediment porewater chemistry was investigated along a transect from the Rhône River outlet to the continental shelf. TA and concentrations of DIC, SO 2- 4 and Ca 2+ were analyzed on bottom waters and extracted sediment porewaters, whereas pH and oxygen concentrations were measured in situ using microelectrodes. The average oxygen penetration depth into the sediment was 1.7 ± 0.4 mm close to the river mouth and 8.2 ± 2.6 mm in the continental shelf sediments, indicating intense respiration rates. Diffusive oxygen fluxes through the sediment-water interface ranged between 3 and 13 mmol O 2 m -2 d -1 . In the first 30 cm of the sediment, TA and DIC porewater concentrations increased with depth up to 48 mmol L -1 near the river outlet and up to 7 mmol L -1 on the shelf as a result of aerobic and anaerobic mineralization processes. Due to aerobic processes, at all stations pH decreased by 0.6 pH units in the oxic layer of the sediment accompanied by a decrease of the saturation state regarding calcium carbonate. In the anoxic layer of the sediments, sulfate reduction was the dominant mineralization process and was associated with an increase of porewater saturation state regarding calcium carbonate.

Ultimately anoxic mineralization of organic matter caused calcium carbonate precipitation demonstrated by a large decrease in Ca 2+ concentration with depth in the sediment. Carbonate precipitation decreased in the offshore direction, together with the carbon turnover and sulfate consumption in the sediments. The large production of porewater alkalinity characterizes these sediments as an alkalinity source to the water column, which may increase the CO 2 buffering capacity of these coastal waters. Estuarine sediments should therefore receive more attention in future estimations of global carbon fluxes.

Introduction

The coastal ocean is a net sink of atmospheric CO 2 and plays an important role in the global carbon cycle [START_REF] Hedges | Sedimentary organic matter preservation: an assessment and speculative synthesis[END_REF]Chen and Borgès, 2009;[START_REF] Bauer | The changing carbon cycle of the coastal ocean[END_REF][START_REF] Laruelle | Global multi-scale segmentation of continental and coastal waters from the watersheds to the continental margins[END_REF]. This dynamic region is not only a sink for atmospheric CO 2 , but also a location where terrestrial organic and inorganic carbon is buried or recycled [START_REF] Hedges | Sedimentary organic matter preservation: an assessment and speculative synthesis[END_REF][START_REF] Cai | Estuarine and Coastal Ocean Carbon Paradox: CO 2 Sinks or Sites of Terrestrial Carbon Incineration?[END_REF]. Due to strong pelagic-benthic coupling, a large fraction of organic matter (OM) is mineralized in continental shelf sediments [START_REF] Mckee | Transport and transformation of dissolved and particulate materials on continental margins influenced by major rivers: benthic boundary layer and seabed processes[END_REF][START_REF] Burdige | Estuarine and Coastal Sediments -Coupled Biogeochemical Cycling, Treatise[END_REF][START_REF] Bauer | The changing carbon cycle of the coastal ocean[END_REF]. Estuaries and deltas are a very dynamic part of coastal ocean regions, characterized by high carbon turnover [START_REF] Hedges | Sedimentary organic matter preservation: an assessment and speculative synthesis[END_REF][START_REF] Cai | Estuarine and Coastal Ocean Carbon Paradox: CO 2 Sinks or Sites of Terrestrial Carbon Incineration?[END_REF]. They are the principal link between continents and oceans, and receive inputs of terrestrial organic and inorganic carbon, in both particulate and dissolved phases [START_REF] Mckee | Transport and transformation of dissolved and particulate materials on continental margins influenced by major rivers: benthic boundary layer and seabed processes[END_REF][START_REF] Cai | Estuarine and Coastal Ocean Carbon Paradox: CO 2 Sinks or Sites of Terrestrial Carbon Incineration?[END_REF][START_REF] Dai | Spatial distribution of riverine DOC inputs to the ocean: an updated global synthesis[END_REF][START_REF] Bauer | The changing carbon cycle of the coastal ocean[END_REF]. An important Published by Copernicus Publications on behalf of the European Geosciences Union.

fraction of these inputs remains on-site and undergoes oxic and anoxic mineralization [START_REF] Andersson | Coastal ocean and carbonate system in the high CO 2 world of the anthropocene[END_REF][START_REF] Aller | Carbon remineralization in the Amazon-Guianas tropical mobile mudbelt: A sedimentary incinerator[END_REF][START_REF] Chen | Strong sources of CO 2 in upper estuaries become sinks of CO 2 in large river plumes[END_REF]. Despite their importance for the coastal carbon cycle, there is a lack of knowledge about the links between early diagenesis and the carbonate system in river-dominated sediments [START_REF] Mckee | Transport and transformation of dissolved and particulate materials on continental margins influenced by major rivers: benthic boundary layer and seabed processes[END_REF].

Aerobic and anaerobic reaction pathways contribute to the production of dissolved inorganic carbon (DIC), resulting in the acidification of the bottom waters. Anaerobic reactions also lead to production of total alkalinity (TA) that increases the CO 2 buffer capacity of seawater [START_REF] Thomas | Enhanced ocean carbon storage from anaerobic alkalinity generation in coastal sediments[END_REF]. Variations in DIC and TA affect the partial pressure of CO 2 (pCO 2 ) in seawater and ultimately the CO 2 exchange with the atmosphere [START_REF] Emerson | Chemical Oceanography and the Marine Carbon Cycle[END_REF]. By increasing the CO 2 buffer capacity of seawater, the release of TA from anaerobic sediments into the water column could account for a majority of the CO 2 uptake in shelf regions and deliver as much TA to the oceans as is derived from rivers [START_REF] Thomas | Enhanced ocean carbon storage from anaerobic alkalinity generation in coastal sediments[END_REF]. Due to high dynamics, spatial heterogeneity and complex biogeochemical mechanisms, estimations of TA fluxes from the sediments are affected by high uncertainties (Krummins et al., 2013). The processes by which TA is produced in the sediments are still not well understood. Anaerobic respiration (e.g., denitrification, sulfate reduction, iron and manganese reduction) may play a major role, although dissolution/precipitation of calcium carbonate may also have a large impact on TA concentrations [START_REF] Jahnke | CaCO 3 dissolution in California continental margin sediments: the influence of organic matter remineralization[END_REF][START_REF] Thomas | Enhanced ocean carbon storage from anaerobic alkalinity generation in coastal sediments[END_REF][START_REF] Krumins | Dissolved inorganic carbon and alkalinity fluxes from coastal marine sediments: model estimates for different shelf environments and sensitivity to global change[END_REF]. Indeed, the changes in sediment porewater composition and pH can lead to over-or undersaturation of the calcium carbonate saturation state ( ), and therefore influence carbonate dissolution and burial in sediments. Furthermore, carbonate dissolution was correlated to alkalinity fluxes across the sediment-water interface (SWI; [START_REF] Mucci | The fate of carbon in continental shelf sediments of eastern Canada: a case study[END_REF].

Using in situ microelectrode measurements, [START_REF] Komada | Dissolved inorganic carbon profiles and fluxes determined using pH and pCO 2 microelectrodes[END_REF] and [START_REF] Cai | pH and pCO 2 microelectrode measurements and the diffusive behaviour of carbon dioxide species in coastal marine sediments[END_REF] investigated small-scale changes in pCO 2 , pH and DIC in deep marine sediments and the associated exchange fluxes. In continental shelf sediments, [START_REF] Mucci | The fate of carbon in continental shelf sediments of eastern Canada: a case study[END_REF] found that oxic mineralization can induce carbonate dissolution below the sediment-water interface, extending the observations of [START_REF] Jahnke | CaCO 3 dissolution in California continental margin sediments: the influence of organic matter remineralization[END_REF] and [START_REF] Jahnke | Calcium carbonate dissolution in deep sea sediments: reconciling microelectrode, pore water and benthic flux chamber results[END_REF] to coastal sediments. [START_REF] Burdige | Rates of carbonate dissolution in permeable sediments estimated from pore-water profiles: The role of sea grasses[END_REF][START_REF] Burdige | The widespread occurence of coupled carbonate dissolution/reprecipitation in surface sediments on the Bahamas Bank[END_REF] pointed out that carbonate dissolution is also driven by oxic respiration in the shallow carbonated sediments of the Bahamas Banks. Concerning anoxic processes, Van Capellen and Wang (1996) demonstrated that high manganese and iron contents in the sediments of the Skagerrak (eastern North Sea) and associated OM mineralization can increase porewater pH by proton-consuming reduction processes of oxidized iron and manganese. These authors, with [START_REF] Froelich | Early oxidation of organic matter in pelagic sediments of the eastern equatorial Atlantic: suboxic diagenesis[END_REF] and [START_REF] Berner | Early diagenesis: A theoretical approach[END_REF] as precursors, highlighted the complexity of the multiple competing reaction pathways in anoxic sediment.

In regions with a high carbon turnover, sulfate reduction is a large contributor to anoxic early diagenesis and can even be the dominant mineralization process for OM [START_REF] Mucci | The fate of carbon in continental shelf sediments of eastern Canada: a case study[END_REF][START_REF] Burdige | Anaerobic oxidation of methane and the stoichiometry of remineralization processes in continental margin sediments[END_REF]Pastor et al., 2011a). Sulfate reduction slightly decreases pH [START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF][START_REF] Soetaert | The effect of biogeochemical processes on pH[END_REF], but nevertheless, it tends to enhance carbonate precipitation because of its coupling with precipitation of sulfide minerals from iron oxides [START_REF] Gaillard | Chemical diagenesis in coastal marine sediments[END_REF][START_REF] Mucci | The fate of carbon in continental shelf sediments of eastern Canada: a case study[END_REF][START_REF] Burdige | Estuarine and Coastal Sediments -Coupled Biogeochemical Cycling, Treatise[END_REF]. As an example, in sapropelic sediments from Mangrove Lake, [START_REF] Mackenzie | Comparative Geochemistry of Marine Saline Lakes[END_REF] reported a stable pH throughout the sulfatereduction zone and a buildup of supersaturation with respect to carbonate with depth. These results contrast with the theoretical perspective that sulfate reduction was supposed to lead to carbonate dissolution because of the pH decrease [START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF]. Even today, the reproduction of measured porewater profiles in the sediments and the estimation of TA and DIC fluxes across the SWI by modeling are very challenging [START_REF] Arndt | Quantifiying the degradation of organic matter in marine sediments: A review and synthesis[END_REF][START_REF] Krumins | Dissolved inorganic carbon and alkalinity fluxes from coastal marine sediments: model estimates for different shelf environments and sensitivity to global change[END_REF][START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF]. In addition, the magnitudes of DIC and TA fluxes across the SWI are not well constrained and can vary significantly between different study sites [START_REF] Mucci | The fate of carbon in continental shelf sediments of eastern Canada: a case study[END_REF].

The objective of this study is to improve our understanding of the influence of early diagenesis of organic matter on carbonate dissolution and precipitation, and the production of DIC and TA. Therefore, we collected seawater and sediment samples along a transect from the Rhône River delta to the Mediterranean Sea continental shelf, covering a broad range of biogeochemical characteristics [START_REF] Lansard | In situ oxygen uptake rates by coastal sediments under the influence of the Rhône River (NW Mediterranean Sea)[END_REF][START_REF] Cathalot | Temporal variability of carbon recycling in coastal sediments influenced by rivers: assessing the impact of flood inputs in the Rhône River prodelta[END_REF][START_REF] Cathalot | The fate of river organic carbon in coastal areas: A study in the Rhône River delta using multiple isotopic (δ 13 C, 14 C) and organic tracers[END_REF]. The Rhône River delta receives inputs of terrestrial organic and inorganic carbon, in both particulate and dissolved phases which decrease with the distance to the river mouth. The majority of these inputs remains on-site and undergoes mineralization in the sediments (Pastor et al., 2011a). Therefore sediments display strong spatial gradients in biogeochemical parameters such as nutrients, organic and inorganic carbon, affecting the diagenetic transport-reaction network [START_REF] Bourgeois | Distribution and lability of land-derived organic matter in the surface sediments of the Rhône prodelta and the adjacent shelf (Mediterranean Sea, France): a multi proxy study[END_REF][START_REF] Lansard | Benthic remineralization at the land-ocean interface: A case study of the Rhône River (NW Mediterranean Sea)[END_REF]. High sedimentation rates and resuspension events make this environment very dynamic and heterogeneous [START_REF] Cathalot | Temporal variability of carbon recycling in coastal sediments influenced by rivers: assessing the impact of flood inputs in the Rhône River prodelta[END_REF]. The predominance of sediment accumulation over other dynamic processes and the absence of tidal mixing and dominant marine currents differentiate the prodelta of the Rhône from other deltaic environments like the Amazon, where the surface sediments are constantly reworked [START_REF] Aller | Mobile deltaic and continental shelf muds as suboxic, fluidized bed reactors[END_REF]. Previous studies in this region often focused on organic matter mineralization pathways measurements in the oxic sediment layers and analysis of particulate carbon [START_REF] Lansard | In situ oxygen uptake rates by coastal sediments under the influence of the Rhône River (NW Mediterranean Sea)[END_REF][START_REF] Cathalot | Temporal variability of carbon recycling in coastal sediments influenced by rivers: assessing the impact of flood inputs in the Rhône River prodelta[END_REF] or could not provide simultaneous DIC and TA porewater measurements (Pastor et al., 2011a). These studies did not provide information on TA production and fluxes at the SWI. Accordingly, we designed a study to investigate the interaction of mineralization processes on porewater pH and the fate of solid calcium carbonates. For that purpose, we used a combination of in situ oxygen and pH microelectrode measurements and porewater analysis of DIC, TA, SO 2- 4 and Ca 2+ concentrations to examine various diagenetic pathways on different vertical scales. We investigated a transect of stations characterized by various biogeochemical conditions (from oxic-dominated to sulfate-reduction-dominated sediments). Furthermore, we calculated and discussed the calcium carbonate saturation state in regards to the different intensity of biogeochemical processes in these river-dominated sediments, and estimated how early diagenesis impacts the bottom water carbonate chemistry (DIC, TA and pCO 2 ).

2 Study site and methods

The Rhône River delta

With a drainage basin of 97 800 km 2 and a mean waterdischarge of 1700 m 3 s -1 , the Rhône River is the largest river of the Mediterranean Sea in terms of freshwater discharge, inputs of sediment and terrestrial organic and inorganic matter [START_REF] Pont | Les débits solides du Rhône à proximité de son embouchure : données récentes (1994-1995)/The discharge of suspended sediments near to the mouth of the Rhône recent statistics (1994-1995[END_REF][START_REF] Durrieu De Madron | Particulate matter and organic carbon budgets for the Gulf of Lions (NW Mediterranean)[END_REF][START_REF] Sempéré | Carbon inputs of the Rhone River to the Mediterranean Sea: Biogeochemical implications[END_REF]. The Rhône River mouth is a wavedominated delta located in the microtidal Mediterranean environment of the Gulf of Lions [START_REF] Sempéré | Carbon inputs of the Rhone River to the Mediterranean Sea: Biogeochemical implications[END_REF]. Its river plume is mostly oriented southwestward, due to the Coriolis effect and the wind forcing [START_REF] Estournel | The plume of the Rhone: numerical simulation and remote sensing[END_REF]. The annual discharge of particulate inorganic carbon (PIC) is estimated to be 0.68 ± 0.45 × 10 9 gC yr -1 (Sempéré et al., 2009). The total particulate organic carbon (POC) deposition in the Rhône delta system (265 km 2 ) is approximately 100 ± 31 × 10 9 gC yr -1 , with the deltaic front accounting for nearly 60 % of the total POC deposition [START_REF] Lansard | Benthic remineralization at the land-ocean interface: A case study of the Rhône River (NW Mediterranean Sea)[END_REF]. In front of the river mouth, the deposited sediments are of a cohesive nature and composed of fine-grained sediments (e.g., > 90 % silt and clay; [START_REF] Roussiez | Early muddy deposits along the Gulf of Lions shoreline: A key for a better understanding of land-to-sea transfer of sediments and associated pollutant fluxes[END_REF]Lansard et al., 2007). Previous studies demonstrated that the carbonate content in the surface sediments varies between 28 and 38 % [START_REF] Roussiez | Sources and sinks of sedimentbound contaminants in the Gulf of Lions (NW Mediterranean Sea): A multi-tracer approach[END_REF], and the content of organic carbon (OC) varies between 1 and 2 % [START_REF] Roussiez | Early muddy deposits along the Gulf of Lions shoreline: A key for a better understanding of land-to-sea transfer of sediments and associated pollutant fluxes[END_REF][START_REF] Roussiez | Sources and sinks of sedimentbound contaminants in the Gulf of Lions (NW Mediterranean Sea): A multi-tracer approach[END_REF][START_REF] Lansard | In situ oxygen uptake rates by coastal sediments under the influence of the Rhône River (NW Mediterranean Sea)[END_REF][START_REF] Lansard | Benthic remineralization at the land-ocean interface: A case study of the Rhône River (NW Mediterranean Sea)[END_REF]. The PIC in the sediments is composed of autochthonous and allochthonous carbonates, with the most abundant calcifying organisms in this area being foraminifera [START_REF] Mojtahid | Microhabitat selection of benthic foraminifera in sediments off the Rhône River mouth (NW Mediterranean)[END_REF].

The seafloor bathymetry shows that the delta is divided into three zones, characterized by different water depth, sedimentation rate and strength of bathymetric slope. [START_REF] Got | The Holocene sedimentation on the Gulf of Lions margin: a quantitative approach[END_REF] defined three major domains: the proximal domain, in a radius of 2 km from the river outlet with water depth ranging from 10 to 30 m; the prodelta domain, between 2 and 5 km from the river mouth with depth ranging from 30 to 70 m; and the distal domain, with depth between 70 and 80 m, which passed 5 km from the river mouth. Annual sedimentation rates reach up to 30-48 cm yr -1 close to the river mouth [START_REF] Charmasson | Long-core profiles of 137 Cs, 134 Cs, 60 Co and 210 Pb in sediment near the Rhône River (Northwestern Mediterranean Sea)[END_REF] and rapidly decrease below 0.1 cm yr -1 on the continental shelf [START_REF] Miralles | 210Pb sedimentation rates from the NorthwesternMediterranean margin[END_REF]. The seafloor in this region is a dynamic environment based on sediment deposition and accumulation and with important heterogeneity regarding diagenetic activities, sediment porewater profiles and exchange fluxes at the sediment-water interface [START_REF] Lansard | Benthic remineralization at the land-ocean interface: A case study of the Rhône River (NW Mediterranean Sea)[END_REF][START_REF] Cathalot | Temporal variability of carbon recycling in coastal sediments influenced by rivers: assessing the impact of flood inputs in the Rhône River prodelta[END_REF]. Diffusive oxygen fluxes into the sediment show spatial variability, both with the distance from the river mouth (decreasing in offshore direction) and on the horizontal scale of a few squared centimeters [START_REF] Lansard | Benthic remineralization at the land-ocean interface: A case study of the Rhône River (NW Mediterranean Sea)[END_REF]Pastor et al., 2011b). Anoxic mineralization processes play a major role in the prodelta sediments and are dominated by iron and sulfur cycling (Pastor et al., 2011a).

Sampling stations

Ten stations were sampled along the main direction of the Rhône River plume during the DICASE oceanographic cruise that took place in the Gulf of Lions between 2-11 June 2014 on board the RV Tethys II (http://dx.doi.org/10. 17600/14007100). The positions and main characteristics of the sampling stations are shown in Fig. 1 and in Table 1. The stations were between 2 and 25 km distance from the Rhône River mouth, covering a bathymetric gradient ranging from 20 to 80 m of water depth and representing the three different domains (A, Z: proximal domain; AK, B, K, L: prodelta domain; and C, D, E, F: distal domain). The stations in the proximal domain A and Z have been sampled twice, in order to investigate spatial variability at these two stations. During this cruise, a benthic lander was used to measure in situ oxygen and pH micro profiles, and sediment cores were taken for porewater extraction and solid-phase analysis. The cruise took place during a period of low water discharge (957 m 3 s -1 ) and air temperatures between 20 and 30 • C.

( • E) ( • N) (km) (m) ( • C) (µmol L -1 ) (µmol L -1 ) (µmol L -1 ) (mmol L -1 ) (calculated) (µatm) Z,

In situ measurements

To measure in situ oxygen and pH micro profiles at the sediment-water interface, an autonomous lander (Unisense ® ) was used. This lander is equipped with a high precision motor capable of simultaneously moving five oxygen microelectrodes [START_REF] Revsbech | An oxygen microsensor with a guard cathode[END_REF], two pH microelectrodes and a resistivity probe [START_REF] Andrews | Measurements of diffusivity near the sediment-water interface with a fine-scale resistivity probe[END_REF] with a vertical resolution of 100 µm. The recorded oxygen profiles were calibrated using oxygen concentrations measured in bottom waters by Winkler titration [START_REF] Grasshoff | Methods of Seawater Analysis[END_REF] and the zero oxygen measured in the anoxic zone [START_REF] Cai | The development of pH and pCO 2 , microelectrodes for studying the carbonate chemistry of pore waters near the se Cai[END_REF]. The SWI was positioned where the strongest vertical oxygen gradient was measured [START_REF] Rabouille | Oxygen demand in coastal marine sediments: comparing in situ microelectrodes and laboratory core incubations[END_REF]. The calibration of the pH electrodes was carried out using NBS buffers, thus allowing the estimation of the slope of the electrode signal as a function of pH variation at onboard temperature. The slope was then recalculated at in situ temperature, and the electrode signal variation was transformed into pH changes. The pH of bottom waters was determined using the spectrophotometric method with m-cresol purple following [START_REF] Clayton | Spectrophotometric seawater pH measurements: total hydrogen ion concentration scale calibration of m-cresol purple and at-sea results[END_REF] and [START_REF] Dickson | Guide to best practices for ocean CO 2 measurements[END_REF]. Porewater pH on the total proton scale (pH t ) was recalculated using the signal of the microelectrode adjusted to this pH-bottom water value. At each depth, the profiler waited for 20 s to stabilize the electrode before measurements were recorded. Each data point is an average of five measurements carried out at every depth. For all in situ profiles, the signal drift of each microelectrode was examined to ensure it was < 5 % from the beginning to the end of the measurements. The slope of the pH electrodes was double-checked to make sure it was at least 95 % of the theoretical slope from the Nernst equation of -59 mV per pH-unit at 25 • C. At each station, five oxygen profiles and two pH profiles were measured simultaneously on a sediment surface of 109 cm 2 .

Calculation of oxygen fluxes across the sediment-water interface

Sediment oxygen uptake rate has been widely used to assess benthic OC mineralization during early diagenesis. The total oxygen uptake (TOU) rate can be split into two parts: (i) the diffusive oxygen uptake rate (DOU) and (ii) the advective oxygen uptake. The DOU rates were calculated using Fick's first law [START_REF] Berner | Early diagenesis: A theoretical approach[END_REF]:

DOU = -D s • ϕ d [O 2 ] dz z=0 , (1) with:
-D s : apparent diffusion coefficient adjusted for diffusion in porous environment calculated following

D s = D o 1+3(1-ϕ)
, where D 0 is the diffusion coefficient in free water according to [START_REF] Broecker | Gas exchange rates between air and sea[END_REF] φ: sediment porosity

-d[O 2 ]
dz z=0 : oxygen gradient at the sediment-water interface.

Sampling and ex situ measurements

Bottom water samples were collected with a 12 L Niskin bottle as close as possible to the seafloor at each station. For these samples, temperature was measured using a digital thermometer with a precision of 0.1 • C, and salinity was measured using a salinometer with a precision of 0.1. The pH and concentrations of DIC, TA and dissolved O 2 were measured on board within 1 h for pH and within 6 h for DIC and TA. The pH of seawater was measured using a spectrophotometer and m-cresol purple as dye [START_REF] Clayton | Spectrophotometric seawater pH measurements: total hydrogen ion concentration scale calibration of m-cresol purple and at-sea results[END_REF][START_REF] Dickson | Guide to best practices for ocean CO 2 measurements[END_REF], with uncertainties smaller than 0.01 pH units. Oxygen concentrations were determined using Winkler titration with an average uncertainty of 0.4 µmol L -1 . All DIC concentrations (bottom waters and porewaters) were measured on a DIC analyzer (Apollo SciTech ® ) using 1 mL sample volume with 4 to 6 replicates. The principle of the method is to acidify the sample with 10 % phosphoric acid to transform all forms of DIC into CO 2 . The sample is then outgassed using ultra-pure nitrogen as a vector gas. The degassed CO 2 is quantified by a LICOR ® gas analyzer, containing a non-dispersive infrared detector. To calibrate the method, a certified reference material (CRM batch no. 122, provided by A. Dickson, Scripps Institution of Oceanography) was used at least twice a day to confirm the accuracy of the DIC and TA measurements. TA concentrations were measured in a potentiometric open cell titration on 3 mL sample volume [START_REF] Dickson | Guide to best practices for ocean CO 2 measurements[END_REF]. In our study, TA refers to total alkalinity, including silicates, phosphates, sulfides, organic alkalinity, etc. The DIC and TA uncertainties in the sediment porewaters were below 0.5 %.

Sediment cores were sampled using an UWITEC ® single corer (60 cm length, 9.5 cm inner diameter). After sampling, the cores were rapidly introduced in a glove bag with a N 2 atmosphere, to avoid oxidation, and porewaters were extracted using Rhizons, with pore size of 0.1-0.2 µm [START_REF] Seeberg-Elverfeldt | Rhizon sampling of porewaters near the sediment-water interface of aquatic systems[END_REF]. The Rhizons had been degassed and stored in a N 2 -filled gas tight box before use. Porewaters were extracted with a 2 cm vertical resolution and split into subsamples for DIC, TA, SO 2- 4 and Ca 2+ analysis. Sulfate concentrations were measured in the laboratory using a turbidimetric method [START_REF] Tabatai | A rapid method for determination of sulfate in water samples[END_REF]. Concentrations of calcium ions were measured using ICP-AES (Ultima 2, Horiba ® ) by the "Pôle Spectométrie Océan" in Brest (France) with a relative uncertainty of 0.75 %. The calcium concentrations were salinity-corrected by assuming constant Na + concentrations with depth in the porewater to avoid any evaporation effects due to sample storage. All bottom water concentrations were measured as triplicates. Small sample volumes in porewaters only allowed for replicates for the DIC, SO 2- 4 and Ca 2+ analysis but not for TA. At each station, additional cores were taken for solidphase analysis. To establish porosity profiles, fresh sediment samples were weighed, dried for 1 week at 60 • C and weighed again. Knowing the salinity and density of seawater and sediment, porosity was calculated from the weight loss after drying. Total carbonate content of the solid phase was analyzed using a manocalcimeter with uncertainties of 2.5 % of CaCO 3 . A manocalcimeter is a small, gas-tight container where the sediment can be acidified with HCl to dissolve calcium carbonates. The resulting increase of pressure is measured with a manometer and is directly proportional to the carbonate content of the sediment sample. Sediment samples have also been analyzed to quantify the calcite/aragonite proportion via X-Ray diffraction (XRD) on a X-Pert Pro diffractometer, using the θ -θ technique with the K-α-line of copper. The uncertainties of the XRD measurements were below 5 % of the aragonite proportion [START_REF] Nouet | Dissolution effects on the crystallography and Mg/Ca content of planktonic foraminifera Gloorotalia tumida (Rotaliina) revealed by X-ray diffractometry[END_REF].

Calculation of carbonate speciation, CaCO 3 saturation states and pH in porewaters

According to [START_REF] Orr | Comparison of ten packages that compute ocean carbonate chemistry[END_REF], the best way to compute the nine parameters of the carbonate system at in situ conditions is to start with DIC and TA concentrations. The thermodynamic constants proposed by [START_REF] Lueker | Ocean pCO 2 calculated from dissolved inorganic carbon, alkalinity, and equations for K 1 and K 2 : validation based on laboratory measurements of CO 2 in gas and seawater at equilibrium[END_REF] were used to calculate DIC speciation and porewater pH with the program CO2SYS [START_REF] Lewis | Program developed for CO 2 system calculations[END_REF]. The calcium carbonate saturation state, for both calcite and aragonite, is expressed as the solubility product of calcium and carbonate ions concentrations divided by their solubility constant k sp :

Ca = Ca 2+ CO 2- 3 k sp . ( 2
)
The solubility constant k sp was calculated for in situ temperature, salinity and pressure following [START_REF] Millero | Thermodynamics of the carbon dioxide system in seawater[END_REF], [START_REF] Mucci | The solubility of calcite and aragonite in seawater at various salinities, temperatures and one atmosphere total pressure[END_REF] and [START_REF] Millero | Thermodynamics of the carbon dioxide system in the oceans[END_REF].

3 Results

Bottom waters

In June 2014, the Rhône River water discharge had been low and close to 1000 m 3 s -1 for the previous 2 months. Accordingly, the extent and thickness of the Rhône River plume were limited and bottom waters were not influenced by the river outflow, even close to the river mouth. Bottom water temperature, salinity, O 2 , DIC, TA, pH, SO 2- 4 and pCO 2 are reported in Table 1. Salinity remained very constant close to the seafloor, whereas temperature decreased with water depth from 16.8 to 14.3 • C. Bottom waters were well oxygenated and oxygen concentrations also decreased with increasing water depth. DIC and TA concentrations varied slightly, and the TA / DIC ratio in the bottom waters of all stations was 1.1 ± 0.02. The pH of bottom water was locally variable with a general decrease in offshore direction. SO 2- 4 concentrations were constant between the stations with typical values for seawater around 30 mmol L -1 . During the sampling period, the Integrated Carbon Observation System (ICOS) station at Manosque (l'Observatoire de Haute Provence, https://icos-atc.lsce.ipsl.fr/?q=OHP) measured a pCO 2 of 410 ppm. At most stations, the bottom water pCO 2 was oversaturated compared to the atmosphere, with the lowest values calculated close to the river mouth (stations A and Z) and the highest values calculated at the shelf stations.

The oxic layer

Figure 2 shows all oxygen profiles measured in situ during the DICASE cruise. The oxygen penetration depth (OPD) into the sediment was 1.7 ± 0.4 mm in the proximal domain, 3.3 ± 1.3 mm in the prodelta domain and 8.2 ± 2.6 mm in the distal domain. Some profiles had burrows, creating small oxygen peaks below the OPD. The diffusive oxygen uptake rate (DOU) calculated from the measured oxygen profiles is plotted in Fig. 3 as a function of the distance to the river mouth in the direction of the river plume. The positive value signifies an uptake of O 2 into the sediment. The DOU decreases exponentially with distance from 12.3 ± 1.1 mmol m -2 d -1 at station A towards the minimum flux of 3.8 ± 0.9 mmol m -2 d -1 at station F.

In situ pH micro profiles were measured in the top 4 cm of the sediment at all stations (Fig. 4). Immediately below the SWI, the pH decreases by 0.6 to 0.7 pH units in the oxic layer. Similarly to the oxygen micro profiles, the pH gradient in the OPD is stronger close to the river mouth and weaker in the distal domain. Just below the first drop, pH increases by 0.1-0.2 pH units and tends towards an asymptotic value between 7.4 and 7.6. The pH inflexion point, i.e., where the pH decrease stops and pH starts increasing, is located deeper in the distal zone than in the proximal zone, just below the OPD. Note that pH profiles show high spatial heterogeneity, even at one station.

DIC and TA porewater concentrations and calculated pH

Figure 5 shows the DIC and TA porewater profiles measured during the DICASE cruise. All porewater gradients across the sediment-water interface were strongest close to the river mouth and decreased in offshore direction. At the SWI, the DIC gradients were stronger than the TA gradients for all stations. Despite the spatial heterogeneity in the sediments, the three major areas defined by [START_REF] Got | The Holocene sedimentation on the Gulf of Lions margin: a quantitative approach[END_REF] in this region display different biogeochemical gradients. Accordingly, stations from each group will be reported and discussed separately. In the proximal domain (stations A and Z), DIC concentrations and TA increase immediately below the SWI and reach a maximum value of 48 mmol L -1 at 20 cm depth in the sediments, where the concentrations stabilize. In the prodelta domain (stations AK, B, K and L), DIC concentrations and TA increase to values of 5 mmol L -1 in the first 10 to 15 cm depth. Below this depth, the gradients become stronger and DIC concentrations increase with TA up to 12 to 15 mmol L -1 at the bottom of the cores (i.e., around 25 cm). This succession of two different gradient shapes in the TA and DIC profile is also observed in the distal domain (stations C, D, E and F), but the absolute values of the gradients are weaker. In the first 10 to 15 cm, the concentrations reach values of 3.5 mmol L -1 and increase up to 5 to 7.5 mmol L -1 at the bottom of the core. These very high DIC concentrations in the sediment are related to large DIC and TA gradients, which are 4 to 10 times stronger in the proximal domain than at the other sites. The DIC and TA porewater profiles are well correlated in each core and the concentrations show a linear correlation with a slope of 1.01 and an r 2 of 0.998 (130 data points). The sediment pH profiles were calculated from TA and DIC concentrations using CO2SYS. The pH is reported on the total proton scale (pH t ). In the first millimeter, the pH drops at all stations due to aerobic respiration (Fig. 6). Below the oxygen penetration depth, the pH varies between 7.2 and 7.8 and converges towards the range of 7.4 to 7.6.

Existing numerical tools have been developed for the oxic water column. Nevertheless, we used them in the sediments knowing that porewater concentrations (e.g., DIC, TA) are much larger than those in the water column and that reduced metabolites are unfortunately neglected. Despite this potential artifact, the calculated outputs (e.g., pH) agree with our measurements. A linear relationship of the pH data measured with microelectrodes against pH calculated by CO2SYS shows a correlation with a slope of 1.01 ± 0.02 and an r 2 of 0.7483 (graph not shown).

Calcium and sulfate concentrations

At all stations, bottom water Ca 2+ concentration varies between 10 and 11 mmol L -1 (Fig. 7). In the proximal domain, the Ca 2+ concentration decreases just below the SWI to reach a minimum of 2 mmol L -1 at 15-20 cm depth, where DIC and TA concentrations reach a maximum and sulfate concentration a minimum. In the prodelta domain, the Ca 2+ concentration remains stable with depth until 10-15 cm in relation to the weaker TA and DIC gradients (Fig. 7). Below this depth, where the TA and DIC gradients increase, Ca 2+ decreases to values around 7 mmol L -1 at the bottom of the cores. The distal domain is characterized by constant Ca 2+ concentrations that remain above 10 mmol L -1 , and the sulfate concentrations stay close to bottom water concentration.

In extracted sediment porewater, sulfate concentrations range from 5 to 32 mmol L -1 from the surface down to 30 cm depth. Our measurements indicate strong sulfate consumption rates in the proximal domain (Fig. 8) where DIC and TA gradients are strong as well. In the proximal domain, sulfate concentration decreases in the first centimeter below the SWI compared to the bottom water. In the prodelta domain, sulfate reduction starts to occur between 10 and 15 cm depth, the same depth where TA and DIC gradients increase. In the distal domain, no significant sulfate reduction occurs in the first 30 cm, as sulfate concentration remains constant and TA and DIC gradients are low compared to the other domains.

Solid carbonates and calcium carbonate saturation state

The carbonate content of the solid phase was scattered around 35 % at all stations, from the surface down to 30 cm. Table 2. Diagenetic reactions and their effect on the carbonate system (TA, DIC, pH and ).

Reaction TA / DIC pH Carbonate chemistry R1 CO 2 dissolution CO 2 + H 2 O ←→ H 2 CO 3 ←→ HCO - 3 + H + ←→ CO 2- 3 + 2H + - - R2a Carbonate dissolution CaCO 3 + H 2 O + CO 2 → Ca 2+ + 2HCO - 3 +2/1 + + R2b Carbonate precipitation Ca 2+ + 2 HCO - 3 → CaCO 3 + H 2 O + CO 2 -2/-1 - - Aerobic reactions R3 Aerobic mineralization CH 2 O + O 2 → HCO - 3 + H + 0/1 - - R4 Nitrification + 4 + 2O 2 → NO - 3 + H 2 O + 2H + -2/0 - - R5 Iron oxidation 4Fe 2+ + O 2 + 10H 2 O → 4Fe(OH) 3 + 8H + -8/0 - - R6 Manganese oxidation 2Mn 2+ + O 2 + 4HCO - 3 → 2MnO 2 + 4CO 2 + 2H 2 O -4/0 - -
+ 9HS - + 7H + → 8FeS + SO 2- 4 + 20H 2 O -2/0 + + R14 Pyrite precipitation 8Fe(OH) 3 + 15HS - + SO 2- 4 + 17H + → 8FeS 2 + 28H 2 O 2/0 + + R15 Anaerobic methane oxidation CH 4 + SO 2- 4 → HS - + HCO - 3 + H 2 O 2/1 + (if pH < 7.9) + R16 Methanogenesis CH 2 O → 1 2 CH 4 + 1 2 CO 2 0/0.5 - -
The composition of sedimentary CaCO 3 was dominated by calcite (≈ 95 %), with a small fraction of magnesian calcite (< 5 %), and only traces of aragonite (data not shown).

Accordingly, only calcite is reported since calcite is dominant and aragonite is insignificant in the sedimentary CaCO 3 . The CaCO 3 saturation state, calculated with CO2SYS from our TA / DIC and Ca 2+ data, is presented in Fig. 9 for the three domains. At all stations, the calcite saturation state in porewaters drops in the oxic layer. In the proximal domain (Fig. 9), the saturation state increases immediately below this first drop to reach very high values of around 5 to 10. In the prodelta domain, the saturation state remains very close to 1 at a depth between 5 and 10 cm, before increasing to super saturation (3 to 4) below 10 to 15 cm depth. In the distal domain, the saturation state shows no variation below the first drop into the sediment.

Discussion

Principal diagenetic reactions and their influence on the carbonate system

As the diagenetic transport-reaction network is complex, so are the interactions of these reactions with carbonate chemistry [START_REF] Krumins | Dissolved inorganic carbon and alkalinity fluxes from coastal marine sediments: model estimates for different shelf environments and sensitivity to global change[END_REF]. Table 2 summarizes the main diagenetic reactions (simplified) and their impact on DIC and TA porewater concentrations. DIC is always produced by OM mineralization and decreases pH, whereas the TA budget of these reactions and the resulting pH variation can be positive or negative [START_REF] Soetaert | The effect of biogeochemical processes on pH[END_REF]. The dissolution and dissociation of metabolic (or atmospheric) CO 2 in seawater results in the formation of carbonic acid (R1) and the consumption of CO 2- 3 , and ultimately leads to carbonate dissolution (R2a; [START_REF] Soetaert | The effect of biogeochemical processes on pH[END_REF][START_REF] Emerson | Chemical Oceanography and the Marine Carbon Cycle[END_REF] 2008). Aerobic mineralization consumes O 2 and produces CO 2 , decreasing pH without TA production (R3), and finally decreases . In the sediments, oxygen is also used to reoxidize reduced species, a process that decreases pH even more strongly than aerobic respiration (R4-6), and thus reoxidation decreases as well [START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF][START_REF] Glud | Oxygen dynamics of marine sediments[END_REF]. In contrast, anaerobic mineralization causes much weaker pH reductions compared to the oxic processes and can even increase pH (R7-10; [START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF][START_REF] Soetaert | The effect of biogeochemical processes on pH[END_REF]. OM mineralization by nitrate reduction produces DIC and TA, has been related to TA release from the sediments and is even estimated to be a major TA source to the oceans [START_REF] Thomas | Enhanced ocean carbon storage from anaerobic alkalinity generation in coastal sediments[END_REF]. Sulfate reduction is usually associated with a weak decrease in pH, although with significant DIC and TA production [START_REF] Mucci | The fate of carbon in continental shelf sediments of eastern Canada: a case study[END_REF][START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF]. The resulting sulfide ions can either diffuse towards the surface to be oxidized within the oxic layer or precipitate with iron. The precipitation of sulfur minerals does not affect the amount of porewater DIC, but can have a major influence on pH and TA (R11-13; [START_REF] Soetaert | The effect of biogeochemical processes on pH[END_REF]. The two reactions R14 and R15 deal with the coupling of sulfate reduction and methanogenesis and its impact on DIC.

In the Rhône River delta sediments, OM mineralization leads to DIC production, and under anoxic conditions, also to TA production. Our results demonstrate strong DIC and TA porewater gradients in the anoxic layer of the sediments, indicating high anaerobic respiration rates. As a result, DIC and TA diffuse towards the SWI. No reaction in the oxic zone consumes DIC except potential carbonate precipitation.

Our results indicate that more DIC is produced in the sediments than consumed by precipitation of CaCO 3 . This means that OM mineralization in the sediments leads to strong DIC fluxes from the sediments into the water column. For TA, the situation is more complicated, as oxidation of reduced species can consume as much TA as has been produced to reduce these species (Table 2). In a 1-D system, where no precipitation occurs and no reduced species can be exported, an important fraction of the anaerobic TA would be consumed in the oxic layer. Denitrification forms an exception to this, as the reduced end product N 2 of this reaction can escape the sediments. Thus the TA produced by denitrification is not consumed in the oxic sediment layer. [START_REF] Krumins | Dissolved inorganic carbon and alkalinity fluxes from coastal marine sediments: model estimates for different shelf environments and sensitivity to global change[END_REF] reported that the effective TA flux from the sediments into the water column is far less important than the anaerobic TA production due to the TA loss in the oxic layer. Unfortunately, the resolution of the DIC and TA porewater profiles in this current study does not give precise information about the gradients in the oxic layer. Thus, we can only speculate about the oxic TA consumption in this region and related TA fluxes across the SWI. According to Pastor et al. (2011a), 97 % of the reduced species precipitate in the anoxic sediments in the Rhône prodelta. Therefore, the majority of the produced TA is likely released into the water column, which can counterbalance the effects of the DIC fluxes and increase the CO 2 buffer capacity of the overlaying waters.

The impact of oxic and suboxic processes on the carbonate system

The upper part of the sediment is defined as the oxic zone, supporting aerobic respiration (R3 -Table 2). Generally, the oxygen penetration depth (OPD) is related to respiration rates [START_REF] Cai | The development of pH and pCO 2 , microelectrodes for studying the carbonate chemistry of pore waters near the se Cai[END_REF]. Aerobic respiration consumes O 2 to mineralize organic matter, produces metabolic CO 2 in the sediment porewater, increases the DIC concentration, lowers pH and possibly decreases the CaCO 3 saturation state [START_REF] Cai | The development of pH and pCO 2 , microelectrodes for studying the carbonate chemistry of pore waters near the se Cai[END_REF][START_REF] Cai | Microelectrode studies of organic carbon degradation and calcite dissolution at a California Continental rise site[END_REF]. The OPD and oxygen fluxes are therefore key parameters to assess the effect of aerobic respiration on calcium carbonate in the sediment [START_REF] Jahnke | CaCO 3 dissolution in California continental margin sediments: the influence of organic matter remineralization[END_REF][START_REF] Jahnke | Calcium carbonate dissolution in deep sea sediments: reconciling microelectrode, pore water and benthic flux chamber results[END_REF]).

In the Rhône River delta, the OPD increases with water depth and distance from the Rhône River mouth as reported in previous studies [START_REF] Lansard | In situ oxygen uptake rates by coastal sediments under the influence of the Rhône River (NW Mediterranean Sea)[END_REF][START_REF] Lansard | Benthic remineralization at the land-ocean interface: A case study of the Rhône River (NW Mediterranean Sea)[END_REF][START_REF] Cathalot | Temporal variability of carbon recycling in coastal sediments influenced by rivers: assessing the impact of flood inputs in the Rhône River prodelta[END_REF]. These low values of O 2 penetration depths are typical of river-dominated ocean margins and they depend mainly on the sedimentation rate, the OM flux, the age and the oxidation state of OM [START_REF] Lansard | Benthic remineralization at the land-ocean interface: A case study of the Rhône River (NW Mediterranean Sea)[END_REF][START_REF] Cathalot | The fate of river organic carbon in coastal areas: A study in the Rhône River delta using multiple isotopic (δ 13 C, 14 C) and organic tracers[END_REF]. Few in situ O 2 profiles show oxygen peaks at depth below the OPD. These are likely the effect of sediment bioturbation by the benthic macrofauna. As reported by Bonifácio et al. (2014), the macrofauna community is dominated by polychaetes and the highest activity is found in the prodelta domain. Nevertheless, comparisons between TOU and DOU rates have demonstrated that the DOU accounts for about 80 % of total oxygen uptake rate into the sediments [START_REF] Lansard | In situ oxygen uptake rates by coastal sediments under the influence of the Rhône River (NW Mediterranean Sea)[END_REF]. As a consequence, diffusive transport is dominant compared to advective transport and bioturbation (i.e., bioirrigation and bioventilation). Diffusive O 2 fluxes calculated from in situ 1-D micro profiles (Fig. 2) are therefore representative of total oxygen uptake rates. As shown in Fig. 3, the diffusive oxygen fluxes into the sediment decrease exponentially with the distance from the river mouth, from 12.3 ± 1.1 mmol O 2 m -2 d -1 , close to the Rhône River mouth, to 3.8 ± 0.9 mmol O 2 m -2 d -1 offshore. According to Pastor et al. (2011a), the POC flux in the proximal domain is 1 order of magnitude higher than in the offshore regions of the Rhône prodelta. This OM flux, especially its labile fraction, supports oxygen consumption and is completely mineralized in the oxic layer (Pastor et al., 2011a).

During aerobic respiration, the ratio of oxygen to DIC during OM mineralization is close to 1, according to the stoichiometry of reaction R3 (Table 2). As a result, DIC concentrations increase just below the SWI at all stations (Fig. 5). The balance between O 2 flux and carbon oxidation in the sediment is affected by O 2 consumption linked to the oxidation of inorganic species produced via anoxic OC degradation (NH + 4 , Fe 2+ , Mn 2+ and HS -). The oxidation of reduced diagenetic products has a profound effect on porewater O 2 and pH profiles in O 2 limited sediments [START_REF] Cai | The development of pH and pCO 2 , microelectrodes for studying the carbonate chemistry of pore waters near the se Cai[END_REF]. These reactions (R4 to R6), in addition to aerobic bacterial respiration, consume TA and decrease porewater pH and therefore decrease the calcium carbonate saturation state as well.

There is a large contribution of anoxic processes to total OM mineralization in sediments near the Rhône River mouth, certainly due to large inputs of fresh organic material combined with high sedimentation rates (Pastor et al., 2011a). The diagenetic byproducts originally produced during anoxic mineralization are almost entirely precipitated and buried in the sediment, which leads to a relatively low contribution of the re-oxidation of reduced products to total oxygen consumption. Still, between 10 and 40 % of the oxygen flux is used to oxidize reduced species of iron and manganese, contributing to lower pH (Pastor et al., 2011a). Again, the upward flux of reduced species in the sediments is higher in the proximal domain than in the others. Offshore, less OM is available and the diagenetic activity is weaker, providing less reduced species from deeper sediment layers. The pH drops below the SWI, caused by all oxic processes, are visible on the in situ pH micro profiles and decrease until the OPD is reached (Figs. 2 and4). As the OPD is smaller and the oxygen fluxes are higher in the proximal domain, the pH minima are reached at shallower depth in the sediment than in the other domains. The pH drop is lowering by consuming carbonate ions [START_REF] Emerson | Chemical Oceanography and the Marine Carbon Cycle[END_REF]Jourabchi et al., 2005). The decrease of , due to both aerobic respiration and the oxidation of reduced species, is clearly visible between the first two points located above and below the SWI interface (Fig. 9). In agreement with the current understanding of anoxic diagenesis, the observed pH increase of 0.1 to 0.2 units below the OPD can be attributed to OM mineralization via reduction of iron and manganese (R8 and R9 -Table 2). These anoxic reactions release TA and increase pH in the oxicanoxic transition zone [START_REF] Aguilera | A knowledge-based reactive transport approach for the simulation of biogeochemical dynamics in Earth systems: earth system dynamics[END_REF][START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF]. This pH increase and the release of TA create a strong increase in the porewater saturation state ( ). Previous research indicated that the turnover of Fe and Mn is high in the sediments close to the river mouth (Pastor et al., 2011a). The first porewater data point sampled in the sediments represents a mixture of oxic and anoxic porewater. Therefore, we potentially overestimate in the oxic layer based on calculations from porewater concentrations [START_REF] Cai | Carbon Cycling and the Coupling Between Proton and Electron[END_REF]. Different measurements in the deep sea revealed that shows a minimum in the oxic layer [START_REF] Cai | The development of pH and pCO 2 , microelectrodes for studying the carbonate chemistry of pore waters near the se Cai[END_REF][START_REF] Cai | Microelectrode studies of organic carbon degradation and calcite dissolution at a California Continental rise site[END_REF][START_REF] Cai | The development of pH and pCO 2 , microelectrodes for studying the carbonate chemistry of pore waters near the se Cai[END_REF][START_REF] Hales | Calcite dissolution in sediments of the Cera Rise: In situ measurements of porewater O 2 , pH and CO 2(aq)[END_REF]. As pH decreased at all stations to the same value, but the TA and DIC gradients at the interface are the strongest in the proximal domain, should show the highest values in the oxic sediments of the proximal domain and decrease in offshore direction. High TA concentrations in the oxic layer, resulting from anoxic OM mineralization below, prevent the carbonate saturation state from getting below 1. Thus, potential dissolution in the oxic layer would most likely occur in the distal domain, but could be inhibited in the proximal domain.

In contrast to other nearshore environments, nitrate reduction has been shown to only account for 2-5 % of OM mineralization in the sediments of the prodelta of the Rhône, whereas other anaerobic mineralization processes account for 30-40 % in the distal domain and up to 90 % in the proximal domain (Pastor et al., 2011a). Nitrate reduction produces less TA than DIC (TA / DIC ratio = 0.8/1), and thus lowers in the porewaters. Nevertheless, denitrification is a net TA source from the sediments to the bottom water as the end product N 2 undergoes no further oxidation.

Finding this clear succession of reactions is interesting, particularly the pH profiles that look typical in the aerobic sediment layers sampled from this complex and dynamic system. As OPDs only measure a couple of millimeters, molecular diffusion is by far the dominant transport process (Peclet number 1 on a scale of the OPD). The microstructure of these sediments is restored very fast after disturbances like resuspension events (Toussaint et al., 2014). Furthermore, the comparison with previous studies shows that despite the high sediment dynamics in this region, the general biogeochemical tendencies are maintained throughout time.

Sulfate reduction and its impact on carbonate chemistry

With sulfate concentration in seawater around 30 mmol L -1 , SO 2- 4 reduction can generate large amounts of DIC and TA during organic matter mineralization through sulfate reduction. Indeed, in organic rich sediments, sulfate reduction can account for the majority of OM mineralization [START_REF] Gaillard | Chemical diagenesis in coastal marine sediments[END_REF][START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF][START_REF] Burdige | Estuarine and Coastal Sediments -Coupled Biogeochemical Cycling, Treatise[END_REF][START_REF] Fenschel | Bacterial Biogeochemistry: The Ecophysiology of Mineral Cycling, 3rd Edn[END_REF]. Following reaction R9, two units of DIC and TA are produced for one unit of sulfate consumed [START_REF] Mucci | The fate of carbon in continental shelf sediments of eastern Canada: a case study[END_REF][START_REF] Krumins | Dissolved inorganic carbon and alkalinity fluxes from coastal marine sediments: model estimates for different shelf environments and sensitivity to global change[END_REF].

To estimate the actual DIC / SO 2- 4 ratio due to diagenetic processes, the slope of the correlation between produced DIC ( DIC) and consumed sulfates ( SO 2- 4 ) in the porewaters (Fig. 10) has to be corrected for molecular diffusion following the equation proposed by [START_REF] Berner | Early diagenesis: A theoretical approach[END_REF]. Accordingly, we used the diffusion coefficients determined by Li and Gregory (1973). Below 10 cm depth, the observed diffusion-corrected DIC / SO 2- 4 ratio equals 1.8 ± 0.02. The deviation of this measured value, from the theoretical value of 2, can be linked to higher oxidation states of organic matter, which increases the SO 2- 4 requirement for DIC production (in an extreme case, if methane undergoes oxidation, the DIC/ SO 2- 4 ratio equals 1), carbonate precipitation lowering DIC concentrations or methanogenesis that increases DIC without consuming SO 2- 4 [START_REF] Burdige | Anaerobic oxidation of methane and the stoichiometry of remineralization processes in continental margin sediments[END_REF][START_REF] Antler | Sulfur and oxygen isotope tracing of sulfate driven anaerobic methane oxidation in estuarine sediments[END_REF]. All three factors may interact in the proximal zone. A large OM fraction in this zone is of terrestrial origin, aged and partly oxidized before being deposited [START_REF] Cathalot | The fate of river organic carbon in coastal areas: A study in the Rhône River delta using multiple isotopic (δ 13 C, 14 C) and organic tracers[END_REF]. Calcium carbonates precipitate in the porewaters of these sediments (Fig. 7) and lower DIC concentrations. In addition, the presence of methane has been reported by Garcia-Garcia et al. (2006).

As demonstrated by [START_REF] Burdige | Estuarine and Coastal Sediments -Coupled Biogeochemical Cycling, Treatise[END_REF] and Burdige and Komada (2011), the interactions of all diagenetic pathways are hard to disentangle and do not provide clear evidence of changes in the DIC / SO 2- 4 ratio. Nonetheless, the value of the observed DIC / SO 2- 4 ratio (1.8 ± 0.1) points towards the dominance of sulfate reduction in the deeper layers of the sediment (below 10 cm depth). Despite all these diverse reactions that affect the DIC / SO 2- 4 ratio, they are balanced in a way that DIC and SO 2- 4 correlate well and do not show a deviation in the slope throughout the whole sediment depth investigated (Fig. 10). Sulfate reduction is also attested by the co-production of alkalinity and DIC (Fig. 5), which is by far the most important alkalinity producer in marine sediments [START_REF] Krumins | Dissolved inorganic carbon and alkalinity fluxes from coastal marine sediments: model estimates for different shelf environments and sensitivity to global change[END_REF]. Sulfate reduction creates a TA / DIC ratio very close to 1 in the porewaters. This situation is very similar to Mangrove Lake sediments [START_REF] Mackenzie | Comparative Geochemistry of Marine Saline Lakes[END_REF] where depletion of sulfate is almost complete and DIC and TA concentrations build up to 40 mmol L -1 in the sediment porewaters, or to other coastal environments [START_REF] Burdige | Estuarine and Coastal Sediments -Coupled Biogeochemical Cycling, Treatise[END_REF][START_REF] Antler | Sulfur and oxygen isotope tracing of sulfate driven anaerobic methane oxidation in estuarine sediments[END_REF]. No other reaction in the anoxic zone has a TA / DIC production ratio near 1. As pH is buffered, probably by precipitation of FeS and FeS 2 (R12), this large increase of alkalinity is accompanied, in the proximal zone, by a large increase of the saturation state of porewaters with respect to calcite (Fig. 9) up to values of oversaturation ( ) from 5 to 10.

The effect of sulfate reduction and the carbonate saturation state has been a matter of debate since the early work of [START_REF] Ben-Yaakov | pH buffering of pore water of recent anoxic marine sediments[END_REF]. Indeed, sulfate reduction produces large quantities of both alkalinity, which increases , and protons, which decrease . This has been summarized in a model by [START_REF] Jourabchi | Quantitative interpretation of pH distributions in aquatic sediments: A reactiontransport modeling approach[END_REF] by estimating that sulfate reduction would lead to a decrease of if it were the only ongoing reaction. The sediments from the proximal area of the Rhône River delta show, on the contrary, that pH stabilizes between 7.2 and 7.6. In these sediments, mineralization is driven by sulfate reduction that generates an increase of saturation state with respect to calcite (Fig. 9). This situation is very similar to [START_REF] Mackenzie | Comparative Geochemistry of Marine Saline Lakes[END_REF] and [START_REF] Mucci | The fate of carbon in continental shelf sediments of eastern Canada: a case study[END_REF], who also showed an increase of when sulfate reduction is significant. Using a closed system model, Ben [START_REF] Ben-Yaakov | pH buffering of pore water of recent anoxic marine sediments[END_REF] estimated that oxidation of HS -coupled to iron hydroxide reduction with FeS precipitation (as in R11 or R12) would buffer or even increase pH.

The Rhône River is known to be the most important riverine input of iron into the Mediterranean Sea [START_REF] Guieu | Atmospheric Versus River Inputs of Metals to the Gulf of Lions, Total Concentrations, Partitioning and Fluxes[END_REF] with an iron content varying between 2 and 4 % in the solid-phase discharge. In the proximal zone of the Rhone Delta, dissolved sulfide is absent from the first tens of centimeters in the sediment (Pastor et al., 2011a), indicating that re-oxidation and/or precipitation of sulfide is occurring in these sediments. Pastor et al. (2011a) estimated that sulfides are the limiting factor for pyrite precipitation in this environment. Therefore, [START_REF] Charles | Ecogeochemical fate of coarse organic particles in sediments of the Rhône River prodelta[END_REF] suggested that OM mineralization in the prodelta of the Rhône could be coupled to pyritization. With this important FeS coupling, pH is stabilized or tends to increase, and a large oversaturation with respect to calcium carbonate is created due to produced carbonate ions.

In the proximal domain, the large super saturation, with respect to calcite, induces calcite precipitation as evidenced by a large decrease of dissolved calcium in the porewaters [START_REF] Gaillard | Chemical diagenesis in coastal marine sediments[END_REF][START_REF] Boudreau | Early diagenesis in a marine sapropel, Mangrove Lake, Bermuda[END_REF]. Indeed, Ca 2+ concentration decreases by 9 mmol L -1 between the bottom water and 25 cm depth in proximal sediments. This precipitation consumes about 10 to 15 % of anaerobically produced DIC and TA. Following R2b, this should affect the TA / DIC ratio, but the observations do not show any deviations of the TA / DIC ratio from 1. The missing TA is likely provided by pyrite formation (R12).

In the prodelta domain (Fig. 8), a similar set of reactions involving sulfate reduction and sulfide re-oxidation and precipitation is also visible with lower amplitude as sulfate depletion is only 5 mmol L -1 . Oversaturation with respect to calcite reaches values ranging from 3 to 4 only below 15 cm, and the Ca 2+ decrease is limited and arises deeper. In the distal zone where is around 2 down to 25 cm, no calcium decrease is visible, indicating that precipitation does not occur.

As the alkalinity fluxes produced by anaerobic processes are high and likely not much reduced by reoxidation of reduced species in the oxic layer due to iron sulfide precipitation, net TA fluxes of the same order of magnitude as DIC fluxes are likely to occur. Therefore, the alkalinity buildup in the anoxic zone could diffuse across the oxic sediment layer and contribute to buffer bottom waters and increase CO 2 storage capacity of these waters. The large precipitation of calcium carbonate in the proximal zone may have implications for the CO 2 source potential from the sediment. Indeed, calcium carbonate precipitation generates CO 2 (R2b), which can then be exported to the water column. In addition, calcium carbonate precipitation consumes TA. However, the order of magnitude of the TA consumption by carbonate precipitation in these sediments is below the quantity of TA produced by sulfate reduction. Without this TA flux, the pCO 2 of the bottom waters in the prodelta of the Rhône would likely be much higher than observed.

Conclusions

This study demonstrated that the three major domains of the Rhône River prodelta are characterized by different organic and inorganic particulate carbon interactions. Close to the river mouth, where the carbon turnover is highest, the biogeochemical gradients are the strongest, resulting in high chemical fluxes across the SWI. This confirms that the biogeochemistry in the prodelta region is driven by the import and processing of material from the Rhône River.

The oxic reactions produce CO 2 and create a pH drop of 0.6 to 0.8 pH units and reduce . As a consequence, calcium carbonate might dissolve in the oxic layer, but the saturation state of bottom waters and porewaters just below the OPD suggests that this is unlikely to happen. The majority of oxygen is used for OM mineralization as most reduced species precipitate in anoxic sediments and do not contribute to oxygen consumption. The mineralization of OM, presumably by Fe and Mn oxides, increases pH and below the oxic layer to several millimeters in depth.

The strong TA and DIC gradients observed in the sediments of the Rhône River prodelta suggest that OM mineralization is dominated by anaerobic processes. Close to the river mouth, where the OC content in the sediments is highest, sulfate reduction is the dominant mineralization process for OM degradation, creating a strong coupling between TA and DIC in porewater profiles. Despite its theoretical lowering effect on pH, sulfate reduction is related to an increase of by important alkalinity production and via the simultaneous pH increase by precipitation of iron-sulfate minerals. As a result, porewaters are oversaturated at all sampled stations. Calcium carbonate precipitation occurs in the proximal and in the prodelta domain, depleting the majority of dissolved calcium ions in the proximal domain. This carbonate precipitation could represent an additional CO 2 source from the sediments to the water column, but is outbalanced by TA production by sulfate reduction. Due to this important anoxic TA production, the pCO 2 of bottom waters remains relatively low compared to the high release of DIC due to OM mineralization.

Data availability

The dataset will soon be made available in the French repository Mistrals/SEDOO/Mermex (during October 2016). Metadata are already available at http://mistrals.sedoo.fr/?editDatsId=1373&datsId= 1373&project_name=MERMeX.

Figure 1 .

 1 Figure 1. Map of the Rhône River mouth (northwestern Mediterranean Sea) with the stations investigated during the DICASE cruise in June 2014. The ocean bathymetry (in m) is indicated by the continuous lines.

Figure 2 .

 2 Figure 2. All in situ oxygen micro profiles measured during the DICASE cruise, in the proximal, prodelta and distal domains. The sedimentwater interface is marked by a horizontal line (depth = 0).

Figure 3 .

 3 Figure 3. Diffusive oxygen uptake (DOU) across the sedimentwater interface as a function of the distance from the Rhône River mouth. The fluxes decrease exponentially following DOU = F min + Ae (-x/t) , with F min being the flux in the offshore region, x the distance to the river mouth in km and A and t being the numerical constants. Error bars are standard deviations between the diffusive fluxes calculated from the five single oxygen profiles measured at each station.

Figure 4 .

 4 Figure 4. All pH t micro profiles measured during the DICASE cruise in the proximal, prodelta and distal domains. The sediment-water interface is marked by a horizontal line.

Figure 5 .

 5 Figure 5. DIC (black) and TA (red) porewater profiles in the first 40 cm of sediment in the proximal, the prodelta and the distal domains. For a better visibility of the profiles in each domain, the scale of the concentrations has been individually adjusted for each domain.

Figure 6 .

 6 Figure 6. Calculated pH t porewater profiles of the proximal, the prodelta and the distal domains. The error bars are estimations of the error propagation from the measured data in the calculation.

Figure 7 .

 7 Figure 7. Porewater concentrations of Ca 2+ (mmol L -1 ); proximal domain in red, prodelta domain in blue and distal domain in black. The error bars represent the uncertainties of the ICP-AES measurements.

Figure 8 .

 8 Figure 8. Sulfate profiles measured in the porewaters (mmol L -1 ) of the proximal, the prodelta and in the distal domains.

Figure 9 .

 9 Figure 9. Porewater calcium carbonate saturation state ( ) of the proximal, prodelta and distal domains. The saturation limit for calcium carbonates dissolution/precipitation ( = 1) is marked by a vertical line.

Figure 10 .

 10 Figure 10. Scatter plot of DIC vs SO 2- 4 with linear regression. designates the difference between the corresponding porewater and bottom water concentration. The slope of the correlation is -1.65 ± 0.017 with a correlation coefficient of r 2 = 0.992.

Table 1 .

 1 Stations investigated during the DICASE cruise in June 2014 with the main properties of bottom waters; dist denotes the distance from the Rhône River mouth.

	Station Long.	Lat.	Dist. Depth	T	Salinity	O 2	DIC	TA	pH t	SO 2-4	pCO 2

Biogeosciences, 13, 5379-5394, 2016 www.biogeosciences.net/13/5379/2016/

www.biogeosciences.net/13/5379/2016/ Biogeosciences, 13, 5379-5394, 2016

Acknowledgements. We thank David J. Burdige, an anonymous referee and J. Patrick Laceby for their constructive comments that helped increase the quality of the paper. Furthermore, we would like to thank Bruno Bombed and Jean-Pascal Dumoulin for their technical help during the DICASE cruise and in the laboratory. We also thank the captain and crew of the RV Tethys II (INSU) for their excellent work at sea. A lot of our gratitude is for the SNAPO-CO2 for the intercomparison of DIC and TA concentrations in our seawater samples. We are grateful to Celine Liorzou for the ICP-AES measurements and to Serge Miska for the help with the X-Ray diffraction analysis, and we want to thank Stephanie Duchamp-Alphonse for putting a manocalcimeter at our disposal. This research was financed by the Mistrals/MERMEX project (http://mermex.pytheas.univ-amu.fr/?page_id=62) and through the MERMEX Rivers action. This paper is LSCE contribution 5887.

Edited by: J. Middelburg Reviewed by: D. Burdige and one anonymous referee


Marie Semaan

Pierric Mora

Simon Bernard

Franck Launay

Cédric Payan

Philippe Lasaygues

Martine Pithioux
email: author.martine.pithioux@univ-amu.fr

Cécile Baron

Assessment of elastic coefficients of child cortical bone using resonant ultrasound spectroscopy

Keywords: Resonant ultrasound spectroscopy, pediatrics, cortical bone, anisotropic elasticity coefficients

The assessment of the anisotropic elastic properties of non-pathological child cortical bone remains a challenge for the biomechanical engineering community and an important clinical issue. Resonant ultrasound spectroscopy (RUS) can be used to determine bone stiffness coefficients from the mechanical resonances of bone specimens. Here, a RUS protocol was used on 7 fibula specimens from children (mean age 14±3 years) to estimate the whole elastic stiffness tensor of non-pathological child cortical bone considered as orthotropic. Despite a small number of sample, results are consistent with this hypothesis, even if a trend towards transverse isotropy is discussed. Indeed, the average values of the 9 independent stiffness coefficients obtained in this study for child bone are: C11 = 16.730.19 GPa, C22 = 16.190.12 GPa, C33 = 24.470.30 GPa, C44 = 4.140.08 GPa, C55 = 4.160.07 GPa, C66 = 3.130.05 GPa, C12 = 10.140.20 GPa, C13 = 10.670.27 GPa, C23 = 10.250.14 GPa.

Introduction

Bone is a hierarchical and organized structure with properties varying by successive stages from juvenile to mature stage. Currently, Dual Energy X-ray Absorptiometry (DEXA) scanning is the most commonly used bone densitometry method to assess skeletal status in adults and children with bone diseases. Recently, some advances in clinical research assess geometrical and microstructural parameters derived from Computerized Tomography (CT) images. Nevertheless, they not provide measurements of the mechanical characteristics of bone although they have been widely demonstrated to be major determinants of bone quality and fracture risk. Nowadays, using ultrasounds is recognized as a relevant way to provide additional data on the mechanical behavior of bone [START_REF] Laugier | Bone quantitative ultrasound[END_REF]. In the context of mechanical characterization of bone tissue, one of the challenges is to take into account the elastic anisotropy of the material. Indeed, the elastic anisotropy is one of the expressions of physiological adaptation of the bone as a living tissue, and can be a key parameter in the estimation of bone quality. A smart protocol using resonant ultrasound spectroscopy (RUS) has recently been developed to assess the whole stiffness tensor of cortical bone at millimeter scale. The relevant protocol and method are well presented and discussed in the articles by [START_REF] Bernard | Elasticity-density and viscoelasticity-density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements[END_REF], 2015, 2013), and recently supplemented by works of Cai et al. [START_REF] Cai | Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone[END_REF]. This work, as most of the work conducted on bone, has been carried out on adult bone and more precisely on ageing human bone, which is nowadays a well-documented material. In contrast, cortical bone of children and juveniles remains poorly studied, although it is known to exhibit specific behavior compared with adult bone [START_REF] Currey | The mechanical properties of bone tissue in children[END_REF]. Contrary to what has been admitted for years, the mechanical characteristics of child bone cannot be directly deduced from adult bone measurements and require dedicated studies. Nevertheless, child bone pieces are very difficult to collect. The few studies on child bone were conducted on pathological tissue (osteogenesis imperfecta [START_REF] Albert | Bone properties by nanoindentation in mild and severe osteogenesis imperfecta[END_REF][START_REF] Imbert | Mechanical and mineral properties of osteogenesis imperfecta human bones at the tissue level[END_REF], traumatic brain injury [START_REF] Davis | The mechanical and morphological properties of 6 year-old cranial bone[END_REF]).

During the last years, pioneer studies have been published on non-pathological child cortical bone (NPCCB) [START_REF] Bala | Pore network microarchitecture influences human cortical bone elasticity during growth and aging[END_REF]Berteau et al., 2012aBerteau et al., , 2012b;;[START_REF] Lefèvre | Analyzing the anisotropic Hooke׳s law for children׳s cortical bone[END_REF]. [START_REF] Lefèvre | Analyzing the anisotropic Hooke׳s law for children׳s cortical bone[END_REF] measured the diagonal stiffness coefficients of NPCCB (fibula) specimens, which were collected under the same conditions as in the present study (same anatomical site). They provided the values of the six diagonal stiffness coefficients, and their statistical sample shows a trend toward transverse isotropy for this kind of material. Unfortunately, the small dimensions of the specimens extracted from the collected pieces prevented the assessment of the off-diagonal coefficients, and the elasticity tensor remained incomplete. This is where the RUS turns out to be a valuable tool.

RUS characterization is fully applicable on low damping materials such as single crystals [START_REF] Isaak | Elastic constants of chrome-diopside: application of resonant ultrasound spectroscopy to monoclinic single-crystals[END_REF], quasi crystals [START_REF] Spoor | Elastic Isotropy and Anisotropy in Quasicrystalline and Cubic AlCuLi[END_REF], and metallic composites [START_REF] Ledbetter | Orthotropic elastic constants of a boron-aluminum fiber-reinforced composite: An acoustic-resonance-spectroscopy study[END_REF]. The method has been proved capable of characterizing complex materials such as wood [START_REF] Longo | Elastic characterization of wood by Resonant Ultrasound Spectroscopy (RUS): a comprehensive study[END_REF], rock and concrete [START_REF] Payan | Applying nonlinear resonant ultrasound spectroscopy to improving thermal damage assessment in concrete[END_REF][START_REF] Remillieux | Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry: RUS for arbitrary shape and high damping[END_REF]. Also, when combined with a probabilistic approach, it has been able to provide, in a single measurement, the elastic coefficients of specimens of millimetric size of a low-quality factor (Q  20-25) material such as bone [START_REF] Bernard | Elasticity-density and viscoelasticity-density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements[END_REF][START_REF] Bernard | Bayesian normal modes identification and estimation of elastic coefficients in resonant ultrasound spectroscopy[END_REF]. This case study based on research by [START_REF] Bernard | Elasticity-density and viscoelasticity-density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements[END_REF][START_REF] Bernard | Bayesian normal modes identification and estimation of elastic coefficients in resonant ultrasound spectroscopy[END_REF], is providing the first estimation of the full set of stiffness coefficients of NPCCB initially assumed to be an orthotropic material.

Based on our results, we will discuss this hypothesis.

Materials and methods 5

Specimen preparation

Experiments were conducted on 7 NPCCB specimens extracted from 7 fibulae of children (mean age 14±3 years). The specimens, collected in the distal 1/3 of the fibula, were surgical waste recovered from corrective surgery at the Timone Children's Hospital (Marseille, France) after a fracture at the growth plate or equinovarus of the foot with no impact on the bone mechanical properties [START_REF] Rauch | Intracortical remodeling during human bone development-A histomorphometric study[END_REF]. Children were ambulatory prior to surgery and none were under medication known to affect bone modeling or remodeling. Thus, these specimens could be considered as NPCCB specimens. Our experimental protocol respected the legal clauses stated in the French code of Public Health and by the National Commission for Data Protection and Liberties (CNIL-France). Informed consents were obtained from the children legal representatives.

The specimens were cut into rectangular parallelepipeds using a water-cooled low-speed diamond saw (Buehler Isomet 4000, Buehler, Lake Bluff, IL, USA). Fig. 1 shows the dimensions along the three directions, radial, circumferential and axial. The geometry of the extracted bone specimens has to be as close as possible to a perfect rectangular parallelepiped in order to conduct the experimental protocol of RUS. Consequently, a specimen holder was specially developed to ensure the parallelism of opposite faces and the perpendicularity of adjacent faces of the bone specimens in the three directions. The proper surface condition of the specimens used in this study was controlled by high-resolution imaging (Phoenix Nanotom 180 S, General Electric, Germany). The specimen dimensions were measured using a digital caliper (Absolute digimatik solar, Mitutoyo, Kanagawa, Japan, measurement error of 0.03 mm). The area in contact with the sample at the level of the caliper jaws was of the same order of magnitude. The specimen dimensions presented in table 1 can therefore be considered as average values, whose uncertainty is the one of the caliper. The mass density ρ (in g/𝑐𝑚 3 ) was determined using a micrometric balance with a density kit (Voyager 610, Ohaus Corporation, Florham Park, NJ, USA, measurement uncertainty of 0.001g/cm3). The fresh specimens were frozen and stored at -20°C [START_REF] Crandall | Considering evolutionary processes in conservation biology[END_REF]. They were thawed at room temperature, so that during the RUS experiments, measurements were made on fully-hydrated specimens. Freeze-thaw cycles could have a influence on the mechanical properties of bone [START_REF] Kang | Effects of multiple freezing-thawing cycles on ultimate indentation load and stiffness of bovine cancellous bone[END_REF]. In this work, the number of cycles was limited to only two cycles per sample.

Resonant ultrasound spectroscopy (RUS) set-up & protocol

The RUS experiment was conducted in transmission mode using two shear transducers (V151, Panametrics, Olympus Corporation, Waltham, MA, USA) facing each other with their axes aligned (Fig. 2), one being used as a transmitter and the other as a receiver [START_REF] Wang | Resonant ultrasound spectroscopy in shear mode[END_REF]. The bone specimen was placed in between. The center frequency was 500 kHz, with a frequency bandwidth from 60 to 800 kHz. The RUS method is a method for measuring the stiffness coefficients Cij following Hooke's law [START_REF] Migliori | Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids[END_REF]. The method is based on the excitation of the natural vibrational modes of a specimen and the measurement of the spectrum resonance peaks. The general protocol is divided into 3 steps. The first step is to estimate theoretical resonant frequencies from the measurement of the dimensions and mass of the bone specimen and an initial guessed value of the elasticity tensor.

In this work, we considered NPCCB as orthotropic and we then had to evaluate 9 stiffness coefficients. As a result, the frequency range to be considered was defined so as to enclose 30 resonant frequencies for each specimen. The initial values of the coefficients of the presumed elasticity tensor were the six diagonal coefficients values published in [START_REF] Lefèvre | Analyzing the anisotropic Hooke׳s law for children׳s cortical bone[END_REF] (Table 1). The three off-diagonal coefficients were supposed to be equal and deduced from 𝐶 12 = 𝐶 13 = 𝐶 23 = 𝐶 11 -2𝐶 66 = 10.24𝐺𝑃𝑎.

The second step is the excitation of the specimen over the theoretical frequency range obtained in the first step. The measurement RUS protocol requires free surface boundary conditions [START_REF] Migliori | Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens[END_REF]. Our specimens were rectangular parallelepipeds. The contact surface with the transducers was reduced to its corners (Fig. 2) whose symmetry was low so that there would be no vibration node there. This position allows all natural modes to be excited and a maximum number of frequencies to be measured.

Both generated and stored signals were managed using RITA (Resonance Inspection Techniques and Analyses) software, designed and implemented by the LANL Wave Physics group [START_REF] Payan | Quantitative linear and nonlinear resonance inspection techniques and analysis for material characterization: Application to concrete thermal damage[END_REF][START_REF] Remillieux | Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry: RUS for arbitrary shape and high damping[END_REF]. Measurements were repeated and the specimen removed and repositioned 6 times, so as to detect the maximum number of resonant frequencies (Fig. 3). This repositioning can lead to slight variations in coupling between the transducers and the specimen, and increases the possibility of obtaining weakly excited modes. Repeated measurements reduce the number of missed modes and are a way of estimating the uncertainty on resonant modes.

Total bone specimen testing time was roughly 30 minutes.

The third step is the detection of the actual resonant frequencies, and the resolution of the inverse problem on identifying the stiffness coefficients. The positions of the peaks in the modulus spectra were detected using the "peak-finder" option of the RITA software. Once the local maxima are identified, a parabolic fit is performed over the few points close to the max to increase the frequency resolution. Among these peaks, the user selected those which correspond to a phase shift. Details can be found in [START_REF] Payan | Quantitative linear and nonlinear resonance inspection techniques and analysis for material characterization: Application to concrete thermal damage[END_REF]. However, due to the low-quality factor of cortical bone material, the resonant peaks obtained experimentally were often overlapped and were difficult to detect, leading to missed resonant modes. Moreover, it is tricky to obtain the right pairing between experimental and theoretical modes. To tackle these issues, we implemented the Bayesian approach described in [START_REF] Bernard | Bayesian normal modes identification and estimation of elastic coefficients in resonant ultrasound spectroscopy[END_REF]. The Bayesian inference is a subjective probabilistic model which integrates prior information on the parameters. Then it estimates the likelihood of a set of parameters to obtain the data. In our case, however, existing knowledge of the parameters could not easily be translated into probability distributions, so we used Gibbs sampling to randomly explore the posterior probability density function following a Markov Chain Monte Carlo method. Details can be found in [START_REF] Bernard | Bayesian normal modes identification and estimation of elastic coefficients in resonant ultrasound spectroscopy[END_REF].

Results and discussion

The stiffness coefficients Cij were calculated after 300 iterations, related to the convergence of the Markov chains from the values obtained over 1000 random statistical samples (Gibbs sampling). These elastic constants are also translated in terms of elastic moduli Ei, shear moduli Gij and Poisson's ratios ij (i, j = 1, 2, 3 for radial, circumferential and axial directions). The experimental protocol (holding of the sample, transducers location, etc.) was carefully validated on comparable size aluminum samples. Following this protocol, all of the spectra were used to enhance the detection of resonant frequencies over the 6 independent measurements performed for each sample. No prior judgment was assumed related to the quality of the measurement.

Results for bones are presented in Table 1 andTable 2. Table 2 presents the stiffness coefficients of adult and child cortical bones obtained by [START_REF] Bernard | Elasticity-density and viscoelasticity-density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements[END_REF], [START_REF] Lefèvre | Analyzing the anisotropic Hooke׳s law for children׳s cortical bone[END_REF], and in this case study. [START_REF] Lefèvre | Analyzing the anisotropic Hooke׳s law for children׳s cortical bone[END_REF] evaluated only the diagonal stiffness coefficients for the NPCCB while [START_REF] Bernard | Elasticity-density and viscoelasticity-density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements[END_REF] evaluated the whole stiffness matrix for adult cortical tibia specimens with millimetric dimensions comparable to the dimensions of the present NPCCB specimens (from 5 to 37 mm 3 ).

The diagonal stiffness coefficients for child bone are consistent with those obtained by Lefèvre et al., with differences ( 𝛿𝑥 𝑥 ) ranging from 0.6% (C44 and C66) to 2.71% (C55). The measured coefficients for child bone are lower than for adult bone. The relative differences range from 8.1% (C33) to 35% (C12). For the adult bone values presented in Table 2, the hypothesis chosen by [START_REF] Bernard | Elasticity-density and viscoelasticity-density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements[END_REF] is transverse isotropy; commonly assumed for the adult long bone cortex. The stiffness coefficients C11 and C22 (respectively C55 and C44) are then identical.

In the analysis of our results, coefficients C11 and C22 are on average close to each other; equal to 16.73 GPa and 16.19 GPa, with a relative difference of 3.22%. The coefficients C44 and C55 can be considered as identical, equal to 4.14 GPa and 4.16 GPa, with a relative difference of 0.5%.

Due to the scarcity and the small dimensions of specimens, working on NPCCB is challenging.

The preparation (cutting and cleaning) of the samples remains a delicate step in the experimental protocol to provide satisfying geometry and surface quality (roughness and flatness) of the sample. Moreover, an important criterion in the RUS protocol is the parallelism of the specimen [START_REF] Migliori | Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens[END_REF]. It is important to have a rectangular parallelepiped specimen as perfect as possible without pores on faces, edges and corners. Even using a specially-designed specimen holder, some of our specimens showed open pores at the boundaries, thus compromising the flatness of the faces and the correspondence between the theoretical and experimental resonant frequencies. Such specimens were removed after high-resolution imaging control using an X-ray scanner, which further reduced the number of specimens available. The low number of specimens was thus an important limitation in this work. It prevented any statistical analysis of the relationship between age and stiffness coefficients or of the degree of anisotropy of NPCCB specimens (orthotropic versus transversely isotropic material).

Following the orthotropy hypothesis, the inverse problem should provide 9 independent elastic coefficients. According to Lebedev's work [START_REF] Lebedev | Method of linear prediction in the ultrasonic spectroscopy of rock[END_REF], the number of modes to measure should be equal to 5 times the number of coefficients to calculate. That is 45 modes in our case.

Given our assumptions introduced in the first step, the theoretical frequency range encloses the 30 first modes. But due to the low-quality factor of bone material, the detection of each of the 30 modes was not always possible. The minimum number of frequencies identified for a specimen was 21. However, following the work of [START_REF] Bernard | Elasticity-density and viscoelasticity-density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements[END_REF][START_REF] Bernard | Bayesian normal modes identification and estimation of elastic coefficients in resonant ultrasound spectroscopy[END_REF], we used the Bayesian approach to circumvent this problem and to solve the inverse problem of calculating stiffness coefficients from a number of resonant frequencies lower than 5 times the number of coefficients to calculate and with a minimal error [START_REF] Cai | Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone[END_REF].

Despite a small number of samples and statistical values, results are consistent with the orthotropic hypothesis for NPCCB specimens studied in this work. But the results also show a trend towards transverse isotropy for this kind of material, which should be confirmed using a representative statistical sample. However, the low number of specimens precludes making statistical analysis on the significance of the differences between C11 and C22, C44 and C55, and C13 and C23. This hypothesis warrants further investigation, by considering NPCCB as a transversely isotropic material in the forward problem (step 1). Regarding the operational conditions (low sample count, possible number of thawing cycles, limited number of tests), and with no certainty on the degree of anisotropy, the most general case of orthotropy was retained in this study.

Conclusions

The assessment of the complete elastic stiffness tensor of non-pathological child cortical bone (NPCCB) remains challenging and critical needs for the biomechanics community. Although relevant studies exist, bibliographic references are relatively rare, and few studies focus on NPCCB. In this work, we present values for NPCCB elastic coefficients at millimeter scale, obtained from Resonant ultrasound spectroscopy (RUS) measurements. RUS has been demonstrated to be suitable for the evaluation of bone elasticity, in particular by the work of Bernard et al., from which this study is strongly inspired. This work is a case study of the use of RUS for NPCCB characterization. Although it has been conducted on a small number of specimens, this study is the first, to our knowledge, to provide a complete elastic stiffness tensor for NPCCB. These values obtained at millimeter scale can be crucial to implement homogenization methods to assess macroscopic properties and develop realistic numerical child bone models.

A

  waveform generator (PXI-5406, National Instrument, Austin, Texas, USA) was used to produce a constant amplitude stepped sine wave. The transmitted signal was amplified by a high voltage amplifier (WMA-30NN, Falco Systems BV Remisestraat 1 2225 TH Katwijkaan Zee, The Netherlands). The resulting vibrating signal was recorded using an A/D converter (PXI-5122 A/D, National Instrument, Austin, Texas, USA). The signal processing algorithms were implemented on an ordinary personal computer, using Matlab (The MathWorks, Inc., Natick, Massachusetts, United States) and Python (2001-2018 Python Software Foundation).

FiguresFig. 1 .

 1 Figures

Fig. 2 .

 2 Fig. 2. Photograph of the bone specimen inserted between the two transducers. Scheme of the

Fig. 3 .

 3 Fig. 3. Typical set of spectra measured for a NPCCB specimen (13 y. o.). Each curve

Acknowledgments

We are grateful to the donors or their legal representatives. This work benefited from the help of Eric Debieu, Vincent Long, Clémentine Boullai, Magali Gaiani and Angela D'Arienzo in setting up experiments. We thank Claude-Hélène Mignard for English language revision.

Funding sources

This work was funded by Aix-Marseille University, Erasmus Mundus HERMES program, and the STAR Carnot Institute.

Declarations of interest

None.

Tables Table 1 Values, mean and standard deviation (SD) of sizes, densities and measured stiffness coefficients, elastic moduli, shear moduli and Poisson's ratios for seven child fibula samples. All coefficients except Poisson's ratios are in GPa.

Table 2 Mean stiffness coefficients of adult and child cortical bones (all values in GPa).