Vincent Mouchi
email: vmouchi@gmail.com

Justine Briard

Stéphane Gaillot

Thierry Argant

Vianney Forest

Laurent Emmanuel

Reconstructing environments of collection sites from archaeological bivalve shells: case study from oysters (Lyon, France)

The flat oyster, Ostrea edulis, was consumed as a luxury dish by the Romans in antiquity.

Numerous shells are found in archaeological sites in the Lyon region, Central France. This area is located over 250 kilometres away from the nearest coastline (the Mediterranean Sea) and little is known about the origin of these oysters prior to transport for consumption. The chemistry of biogenic carbonates reflects that of the fluid they precipitate from at the time of formation. Stable isotopes and Mg/Ca ratios in oyster shells have previously been used as palaeoenvironmental proxies. As Mg/Ca ratio amplitude in bivalve shells has been reported to differ according to local hydrologic settings, we suggest that geochemical differences observed in each shell can be used to identify the type of environment (e.g. estuary, lagoon or marine) from which the specimens originated.

In this study, we analyzed the elemental composition of six archaeological O. edulis shells of unknown provenance, collected in the Lyon region dated from the 3 rd century AD to the 5 th century AD. In addition, stable carbon and oxygen analyses from three of these specimens were performed to reconstruct intra-annual fluctuations of seawater chemistry. Overall results show a strong heterogeneity in values. One shell exhibits large fluctuations in δ 13 C (from -2 to 1 ‰) and δ 18 O (from -2 to 3 ‰), interpreted as evidence for an estuarine origin.

The Mg/Ca amplitude (from 5 to 35 mmol.mol -1 ) also indicates proximity to a river outlet, as such values were previously reported from modern estuarine oyster shells. Two other specimens present a restricted amplitude in Mg/Ca values (from ~0 to 5 mmol.mol -1 ), similar to values measured in modern open marine locations. Four other specimens exhibited intermediate Mg/Ca ratios and more restricted stable isotope composition ranges which indicate that these specimens lived in waters with limited freshwater input.

The geochemical data from these shells support the hypothesis that fishermen of Antiquity collected oysters from a variety of environments/locations. A clear identification of the living localities of these specimens is still to be defined, as the present data cannot discriminate whether these shells originated from the Mediterranean Sea or the Atlantic Ocean coastline.

Introduction

The flat oyster, Ostrea edulis, was consumed as a luxury dish by the Romans during Antiquity. As a result, numerous shells are commonly found in archaeological sites of rich dwelling places in the Lyon region, Central France. As this city is 250 km away from the nearest coastline (Mediterranean Sea), these specimens were transported for consumption and little is known on their locality of origin during the Roman Empire. [START_REF] Bardot-Cambot | Consommer dans les campagnes de la Gaule Romaine[END_REF] reconstructed a map of commercial routes from this period, and suggested that most molluscs in Lyon originated from the Mediterranean Sea. Though still debated, oyster farming on the French Mediterranean coastline is thought to have started during the 19 th century AD (Bardot-Combot and Forest, 2013;[START_REF] Faget | Cultiver la mer : biodiversité marine et développement de l'ostréiculture dans le Midi méditerranéen français au XIXe siècle[END_REF]. Using an archaeozoological approach applied to Roman shells supplemented by written sources analysis, Bardot-Combot and Forest (2013) suggested that Romans did not perform aquaculture per se and probably collected wild oysters. Hence, the exact localities and living environments of fished oysters remain unknown.

The environmental record of geochemical fluctuations in oyster shells represents a promising proxy for palaeoenvironment reconstructions. Oysters appeared over 200 million years ago and their thick calcite shells are generally preserved with regards to diagenesis [START_REF] Stenzel | Oysters[END_REF]. Moreover, they offer sufficiently large structures for high-resolution sampling to study intra-annual (e.g. seasonal) fluctuations for several consecutive years of growth [START_REF] Kirby | Stable isotope sclerochronology of Pleistocene and Recent oyster shells (Crassostrea virginica)[END_REF]Lartaud et al., 2010a;[START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF].

The chemistry of biogenic carbonates reflects that of the fluid it precipitates from at the time of formation [START_REF] Epstein | Carbonate-water isotopic temperature scale[END_REF](Epstein et al., , 1953;;[START_REF] Mccrea | On the isotopic chemistry of carbonates and a paleotemperature scale[END_REF]. Bivalve shells present incremental growth that preserve older parts, which allows for a continuous record of the evolution of seawater composition during the organism's lifespan. Such mollusc shells have been used in Earth Sciences since the middle of the 20 th century [START_REF] Urey | Measurement of paleotemperatures and temperatures of the Upper Cretaceous of England, Denmark, and the Southeastern United States[END_REF] for reconstructing physicochemical parameters of seawater. In particular, seasonal temperature reconstructions of seawater have been proposed for geological timescales (i.e., several hundred million years ago) using fossils [START_REF] Anderson | Stable isotopes of oxygen and carbon and their application to sedimentologic and paleoenvironmental problems[END_REF][START_REF] Craig | Measurements of oxygen isotope paleotemperatures[END_REF]Epstein et al., 1951Epstein et al., , 1953)). These estimates from shell analysis are based on modern breeding in natural sites or laboratory experiments under controlled conditions that lead to the formulation of mathematical equations linking shell geochemistry and physicochemical parameters of seawater (i.e., temperature, salinity, pH). These models can subsequently be utilized to determine past environmental settings.

Stable carbon isotopes (δ 13 C) in mollusc shells have been reported to depend on the combination of the influence of both dissolved inorganic carbon (DIC) and organic carbon sources from food consumption (Lartaud et al., 2010b;[START_REF] Mcconnaughey | Carbon isotopes in mollusk shell carbonates[END_REF]. It has been demonstrated that δ 13 C signals from oyster soft tissues [START_REF] Gaudron | The comparison of δ 13 C values of a depositand a suspension-feeder bio-indicates benthic vs. pelagic couplings and trophic status in contrasted coastal ecosystems[END_REF] and shells [START_REF] Walther | Drought and flood signals in subtropical estuaries recorded by stable isotope ratios in bivalve shells[END_REF] differ from purely marine to estuarine environments due to distinct food sources. In particular, shell δ 13 C can be used jointly with stable oxygen isotope measurements to indicate flooding events [START_REF] Walther | Drought and flood signals in subtropical estuaries recorded by stable isotope ratios in bivalve shells[END_REF].

Several temperature proxies are commonly used on mollusc shells such as stable oxygen isotope 18 O/ 16 O ratios (δ 18 O; [START_REF] Bougeois | A high resolution study of trace elements and stable isotopes in oyster shells to estimate Central Asian Middle Eocene seasonality[END_REF][START_REF] Bougeois | Mg/Ca in fossil oyster shells as palaeotemperature proxy, an example from the Palaeogene of Central Asia[END_REF][START_REF] Duprey | Calibration of seawater temperature and δ 18 Oseawater signals in Tridacna maxima's δ 18 Oshell record based on in situ data[END_REF][START_REF] Epstein | Carbonate-water isotopic temperature scale[END_REF]Epstein et al., , 1953;;[START_REF] Klein | Bivalve skeletons record seas-surface temperature and δ 18 O via Mg/Ca and 18 O/ 16 O ratios[END_REF]Lartaud et al., 2010c;[START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF][START_REF] Surge | Controls on isotopic chemistry of the American oyster, Crassostrea virginica: Implications for growth patterns[END_REF][START_REF] Vander Putten | High resolution distribution of trace elements in the calcite shell layer of modern Mytilus edulis: environmental and biological controls[END_REF]. Some uncertainties exist since calcium carbonate of the shells δ 18 O (δ 18 O c ) is a function of temperature and seawater δ 18 O (δ 18 O w ). This last parameter co-varies with salinity, which is often not properly constrained in the past [START_REF] Rohling | Paleosalinity: confidence limits and future applications[END_REF]. A variety of calibrations of δ 18 O w from salinity have been published based on different modern marine settings (e.g., [START_REF] Epstein | Variation of O 18 content of waters from natural sources[END_REF][START_REF] Pierre | The oxygen and carbon isotope distribution in the Mediterranean water masses[END_REF][START_REF] Voelker | Oxygen and hydrogen isotope signatures of Northeast Atlantic water masses[END_REF], and a specific model is chosen according to the studied locality. Classically, palaeosalinities are estimated by studying the ecology of the fauna associated with the studied material or by taking modern values in similar settings. Temperatures are reconstructed from these estimations of δ 18 O w and the measured δ 18 O c [START_REF] Mccrea | On the isotopic chemistry of carbonates and a paleotemperature scale[END_REF].

Multiple models also exist for this relationship according to the mineralogy and the taxon.

For calcitic mollusc shells, such as oyster shells, the calibration provided by [START_REF] Anderson | Stable isotopes of oxygen and carbon and their application to sedimentologic and paleoenvironmental problems[END_REF] is relevant and widely utilized (Equation 1).

Equation 1: T = 16 -4.14 (δ 18 O c -δ 18 O w ) + 0.13 (δ 18 O c -δ 18 O w )² [START_REF] Anderson | Stable isotopes of oxygen and carbon and their application to sedimentologic and paleoenvironmental problems[END_REF] Strontium to calcium and magnesium to calcium ratios have also been exploited as temperature proxies in biogenic carbonates [START_REF] Bougeois | A high resolution study of trace elements and stable isotopes in oyster shells to estimate Central Asian Middle Eocene seasonality[END_REF][START_REF] Bougeois | Mg/Ca in fossil oyster shells as palaeotemperature proxy, an example from the Palaeogene of Central Asia[END_REF][START_REF] Freitas | Inter-and intra-specimen variability masks reliable temperature control on shell Mg/Ca ratios in laboratory and field cultured Mytilus edulis and Pecten maximus (Bivalvia)[END_REF][START_REF] Freitas | The potential of combined Mg/Ca and δ 18 O measurements within the shell of the bivalve Pecten maximus to estimate seawater δ 18 O composition[END_REF][START_REF] Klein | Bivalve skeletons record seas-surface temperature and δ 18 O via Mg/Ca and 18 O/ 16 O ratios[END_REF][START_REF] Lazareth | High-resolution trace element profiles in shells of the mangrove bivalve Isognomon ephippium: a record of environmental spatio-temporal variations? Estuarine[END_REF][START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF][START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF][START_REF] Ullmann | The Giant Pacific Oyster (Crassostrea gigas) as a modern analog for fossil ostreoids: Isotopic (Ca, O, C) and elemental (Mg/Ca, Sr/Ca, Mn/Ca) proxies[END_REF][START_REF] Vander Putten | High resolution distribution of trace elements in the calcite shell layer of modern Mytilus edulis: environmental and biological controls[END_REF][START_REF] Wanamaker | Experimentally determined Mg/Ca and Sr/Ca ratios in juvenile bivalve calcite for Mytilus edulis: implications for paleotemperature reconstructions[END_REF]. These Me/Ca ratios in carbonates are also commonly considered to fluctuate according to several factors.

Mineralogy has an influence and each locality used for model definition has different environmental settings which are reflected in the shell geochemistry.

Although these proxies were proven useless in some bivalve species such as clams [START_REF] Carré | Calcification rate influence on trace element concentrations in aragonitic bivalve shells: evidences and mechanisms[END_REF][START_REF] Gillikin | Strong biological controls on Sr /Ca ratios in aragonitic marine bivalve shells[END_REF]Poulain et al., 2005;[START_REF] Surge | Geochemical variation in microstructural shell layers of the southern quahog (Mercenaria campechiensis): Implications for reconstructing seasonality[END_REF] or scallops [START_REF] Lorrain | Strong kinetic effects on Sr/Ca ratios in the calcitic bivalve Pecten maximus[END_REF], temperature seems to be the main factor causing fluctuations within a specimen for mussels and oysters [START_REF] Freitas | Inter-and intra-specimen variability masks reliable temperature control on shell Mg/Ca ratios in laboratory and field cultured Mytilus edulis and Pecten maximus (Bivalvia)[END_REF][START_REF] Klein | Bivalve skeletons record seas-surface temperature and δ 18 O via Mg/Ca and 18 O/ 16 O ratios[END_REF][START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF][START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF]Tynan et al., in press;[START_REF] Vander Putten | High resolution distribution of trace elements in the calcite shell layer of modern Mytilus edulis: environmental and biological controls[END_REF]. Still, some vital effects (compositional shifts from seawater composition and physicochemical parameter response) may induce at least a certain amount of geochemical variability [START_REF] Bougeois | A high resolution study of trace elements and stable isotopes in oyster shells to estimate Central Asian Middle Eocene seasonality[END_REF][START_REF] Bougeois | Mg/Ca in fossil oyster shells as palaeotemperature proxy, an example from the Palaeogene of Central Asia[END_REF][START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF][START_REF] Saenger | Magnesium isotope fractionation in biogenic and abiogenic carbonates: implications for paleoenvironemental proxies[END_REF][START_REF] Schöne | Unraveling environmental histories from skeletal diaries -Advances in sclerochronology[END_REF].

Magnesium incorporation in single oyster shells presents different calculated thermodependance equations when considering calcification that occurred from autumn to winter (decreasing temperatures) compared to the period from spring to summer (increasing temperatures), probably due to different metabolic response (see Fig. 6 in [START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF]. This metabolic impact prevents the effective use of Mg/Ca for temperature reconstructions for spring and autumn, restricting estimations from this proxy to thermal amplitude between winter and summer. [START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF] also reported that high-frequency and large amplitude fluctuations in shell Mg/Ca correspond to successive lunar cycles not related to temperature variations.

Finally, for the marine and brackish mussel genus Mytilus, a clear locality-specificity was noted in Mg incorporation [START_REF] Freitas | Inter-and intra-specimen variability masks reliable temperature control on shell Mg/Ca ratios in laboratory and field cultured Mytilus edulis and Pecten maximus (Bivalvia)[END_REF][START_REF] Klein | Bivalve skeletons record seas-surface temperature and δ 18 O via Mg/Ca and 18 O/ 16 O ratios[END_REF][START_REF] Vander Putten | High resolution distribution of trace elements in the calcite shell layer of modern Mytilus edulis: environmental and biological controls[END_REF][START_REF] Wanamaker | Experimentally determined Mg/Ca and Sr/Ca ratios in juvenile bivalve calcite for Mytilus edulis: implications for paleotemperature reconstructions[END_REF]. The same observation was made for the Saccostrea glomerata oyster species (Tynan et al., in press). A model must therefore be carefully chosen to avoid incorrect interpretations.

In this study, using isotopic and elemental analyses of the shells, we gather physicochemical evidence to characterize the historically important fishing areas. As geomorphology of the Mediterranean coastline presented strong heterogeneity in Antiquity [START_REF] Carozza | La plaine du Roussillon au cours de l'Holocène : apport d'une démarche géoarchéologique et géomorphologique à la connaissance des interactions homme-milieu[END_REF][START_REF] Dubar | The Holocene deltas of Eastern Provence and the French Riviera: geomorphological inheritance, genesis and vulnerability[END_REF][START_REF] Raynal | Holocene evolution of languedocian lagoonal environment controlled by inherited coastal morphology (northern Gulf of Lions, France)[END_REF][START_REF] Rescanières | Essai sur le cadre géographique antique du Narbonnais[END_REF][START_REF] Rey | Deltaic plain development and environmental changes in the Petite Camargue, Rhône Delta, France, in the past 2000 years[END_REF], these various settings should be reflected in the geochemistry of oyster shell specimens. In particular, using the locality-specificity of Mg/Ca in oyster shells, we attempt to define whether fishermen had clustered sources of oysters or if they collected from a broader variety of environments.

Materials and Methods

Archaeological sites

The oyster specimens (Ostrea edulis) used in this study were collected from archaeological sites in Lyon, France. The first site, referred to as Antiquaille (Hofmann, in prep), corresponds to an abandoned residential area located on the Fourvière hill, at the heart of the Lugdunum primitive colony. Eleven oyster specimens were selected from the community found on this site. The stratigraphic unit from which those shells were collected was dated to the 2 nd or 3 rd century AD by ceramics.

A second collection site corresponds to a filling pit dated to the 5 th century AD on the 16 rue Bourgelat site (Bertand, 2011). This large pit (3.70 by 5.5 m) included small items (fauna remains, ceramics) and large quantities of broken parts from furnaces and dwelling places.

The quality of these broken parts indicates the demolition of wealthy residences. The top of this pit is in direct contact with the modern age levels. A total of 51 oyster shells were recovered from this site as well as some Bourgogne snails (Helix pomatia) shells. Twelve oyster specimens were selected from this site.

Finally, three shells were selected from the 8-14 rue Gadagne site, in the Old Lyon district. This site is located on the east side of the Saône River at the base of the Fourvière hill. It was built from 50-70 BC, prior to Lugdunum foundation. During the Gallo-Roman age, a large building was occupied between the 3 rd and the 4 th centuries AD.

All specimens are considered to have been consumed by a high social level community and must have travelled some considerable distance from a coastline. Although most specimens probably originated from the Mediterranean Sea, bivalve shells from species endemic to the Atlantic coastline have been discovered on site [START_REF] Bardot-Cambot | Consommer dans les campagnes de la Gaule Romaine[END_REF]. The exact origin of the oysters consumed in Lyon during Antiquity is therefore still unknown.

Oyster shells

Specimens presenting no visible perforation in the umbo region by lithophagous fauna were manually cleaned from potential epibionts attached on the shell surface using deionized water. Ultrasonic baths were not utilized due to the fragile aspect of our specimens. The umbo region of the left valve was mounted in resin and cut from the rest of the shell using a Buehler Isomet Low Speed Saw (Huntsman Araldite 2020) in order to prevent the fine lamellae inside the umbo from breaking during preparation. Polished thick sections (200-500 µm thick) were cut along the maximum growth axis to expose the inner part of the umbo (Fig. 1). This process allows access to a complete and continuous accretionary growth record on a spatially-restricted area [START_REF] Bougeois | A high resolution study of trace elements and stable isotopes in oyster shells to estimate Central Asian Middle Eocene seasonality[END_REF][START_REF] Bougeois | Mg/Ca in fossil oyster shells as palaeotemperature proxy, an example from the Palaeogene of Central Asia[END_REF][START_REF] Kirby | Stable isotope sclerochronology of Pleistocene and Recent oyster shells (Crassostrea virginica)[END_REF][START_REF] Langlet | Experimental and natural cathodoluminescence in the shell of Crassostrea gigas from Thau lagoon (France): ecological and environmental implications[END_REF]Lartaud et al., 2010a;[START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF][START_REF] Richardson | The age determination and growth rate of the European flat oyster, Ostrea edulis, in British waters determined from acetate peels of umbo growth lines[END_REF].

Seasonal calibration using cathodoluminescence

The umbo region of each oyster shell was observed under cathodoluminescence (CL) using the principles described in [START_REF] Langlet | Experimental and natural cathodoluminescence in the shell of Crassostrea gigas from Thau lagoon (France): ecological and environmental implications[END_REF] and Lartaud et al. (2010c). Natural luminescence is emitted in response to electronic bombardment due to the presence of activators (mainly Mn) within the crystal lattice. The intensity of luminescence (IL) is mainly related to the proportion of Mn 2+ (de Rafélis et al., 2000). It has been observed that Mn 2+ incorporation in the shell is increased during summer months compared to the winter [START_REF] Langlet | Experimental and natural cathodoluminescence in the shell of Crassostrea gigas from Thau lagoon (France): ecological and environmental implications[END_REF]Lartaud et al., 2010c). This is due to enhanced phytoplankton consumption in summer (with more frequent blooms), as phytoplankton species can incorporate up to 4 orders of magnitude of Mn compared to surrounding waters [START_REF] Sunda | Regulation of cellular manganese and manganese transport rates in the unicellular alga Chlamydomonas[END_REF]. This cyclic annual Mn concentration pattern has been used as a temporal calibration of mineral accretion in the umbo of fossil oyster shells [START_REF] Bougeois | A high resolution study of trace elements and stable isotopes in oyster shells to estimate Central Asian Middle Eocene seasonality[END_REF][START_REF] Bougeois | Mg/Ca in fossil oyster shells as palaeotemperature proxy, an example from the Palaeogene of Central Asia[END_REF][START_REF] Lartaud | Description of seasonal rythmicity in fossil oyster shells Crassostrea aginensis Tournouer, 1917 (Aquitanian) and Ostrea bellovacina Lamarck, 1806 (Thanetian). Cathodoluminescence and sclerochronological approaches[END_REF]. CL also allows to attest the pristine state of calcium carbonate structures.

CL observations were undertaken with a Cathodyne-OPEA cold cathode at 15-20 kV and 200-400 µA.mm -2 , with a pressure of 0.05 Torr. No diagenetic overprint was noted on any of the 26 specimens. Assembly of colour pictures of the observation of each specimen was converted to grey-scale and line transects following shell growth in the foliated area were chosen for analysis with the NIH-ImageJ software (v. 1.50i). These transects of grey intensity variations were then used to locate areas of bright luminescence (i.e. are synchronous to summer periods) and dull luminescence (associated to winter periods). Six specimens from the initial 26 were selected for further analyses according to the quality of this temporal calibration: four specimens from stratigraphical units dated to the 2 nd or 3 rd century AD in Site 1 (US547-1, US654-1, US654-3 and US915-1), one specimen from a stratigraphical unit dated to the 5 th century AD in Site 2 (US46-2) and a final specimen from a stratigraphical unit dated to the 4 th century AD in site 3 (US118-3).

Geochemical analyses

Mg/Ca ratios

The six selected shells were carbon coated and analyzed by electron probe microanalysis (EPMA) at the Camparis service of ISTeP, UPMC, Paris. A CAMECA SX Five was used, operating at 25 kV potential with a 130 nA current and 25 µm defocused beam diameter, as used by [START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF]. Detection limits for the measured elements were 100 ppm for Ca and 60 ppm for Mg. A diopside crystal was used as an internal standard for both elements. According to the size of the specimens, successive interconnected transects (to accommodate for the curvature of the umbo; Fig. 1b) were performed along the foliated area of the umbo presenting no obvious physical alteration to obtain several continuous millimeters of elemental measurements per specimen. With the chosen sampling resolution, we obtained between 244 and 497 regularly spaced (25 µm) measurements per shell.

High-frequency fluctuations (which do not reflect physicochemical parameters of seawater; [START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF] were removed by performing a moving average on 15 points on all data series.

Stable oxygen and carbon isotope ratios

Stable carbon and oxygen isotopic analyses were performed on three of the specimens following umbo growth. For each sample, 40 µg of powder were collected from thick sections using a micromill at the Muséum National d'Histoire Naturelle, Paris. Drilling was operated to extract carbonate powder from separated curved transects over 1-2 mm long (depending on the available space of foliated calcite) and 250 µm depth for each sample.

Seasonal calibration from CL was used to define a resolution allowing multiple samples per season when possible for consistency over several successive years of accumulation. We collected 12 samples for isotope analysis from specimen US547-1 (2 samples were rejected due to lack of material), 23 samples from specimen US46-2 (no rejection) and 17 samples from specimen US654-1 (1 sample rejected due to lack of material). Carbon dioxide was extracted on carbonate powder using a Kiel IV carbonate device after dissolution in anhydric orthophosphoric acid at 70°C [START_REF] Mccrea | On the isotopic chemistry of carbonates and a paleotemperature scale[END_REF] and analyses were performed on a DELTA V isotope ratio mass spectrometer at the Université Pierre et Marie Curie (Paris, France).

Isotope values are reported in delta notation relative to Vienna Peedee Belemnite. Repeated analyses of a marble working standard (calibrated against the international standard NBS-19) indicate an accuracy and precision of 0.1‰ (1 σ).

For temperature estimations, the model of [START_REF] Anderson | Stable isotopes of oxygen and carbon and their application to sedimentologic and paleoenvironmental problems[END_REF]; Equation 1) was used for thermodependance of shell δ 18 O. The model of [START_REF] Pierre | The oxygen and carbon isotope distribution in the Mediterranean water masses[END_REF], defined from current values of the Mediterranean Sea, was used for estimating δ 18 O w (Equation 2). As a comparative model for δ 18 O w , we used the model of [START_REF] Lartaud | Les fluctuations haute fréquence de l'environnement au cours des temps géologiques. Mise au point d'un modèle de référence actuel sur l'enregistrement des contrastes saisonniers dans l'Atlantique nord[END_REF] which was established from different locations from the French Atlantic and the English Channel coastline (Equation 3).

Equation 2: δ 18 O w = 0.27 * S -8.9 [START_REF] Pierre | The oxygen and carbon isotope distribution in the Mediterranean water masses[END_REF] Equation 3: δ 18 O w = 0.22 * S -7.3 [START_REF] Lartaud | Les fluctuations haute fréquence de l'environnement au cours des temps géologiques. Mise au point d'un modèle de référence actuel sur l'enregistrement des contrastes saisonniers dans l'Atlantique nord[END_REF]

Results

Growth rates

According to the studied specimens, different behaviors are observed concerning the growth rates (Fig. 2) when using cathodoluminescence as temporal calibration (high luminescence corresponds to summer periods; low luminescence to winter periods). The specimens US46-2, US654-1, US654-3, US547-1 and US915-1 present a decreasing growth rate over time in accordance to the classic growth model of von Bertalanffy. US915-1 presents very high growth rates during the juvenile stage (> 4 mm.yr -1 ), whereas shell growth rates from all other specimens range between 1.8 and 3 mm.yr -1 . The specimen US118-3 displays a particular behavior with a relatively low juvenile growth rate (1.5 mm.yr -1 ) and an increase of calcification rate during its fourth and seventh year (based on cathodoluminescence temporal calibration).

Figure 2: Reconstructed growth rates from all specimens based on cathodoluminescence temporal calibration [START_REF] Langlet | Experimental and natural cathodoluminescence in the shell of Crassostrea gigas from Thau lagoon (France): ecological and environmental implications[END_REF]Lartaud et al., 2010c).

Mg/Ca variations

All specimens exhibit Mg/Ca fluctuations (Fig. 3). Several groups of specimens can be differentiated from ranges of values of low frequency fluctuations (see smoothed data on Fig. 3). Specimens US547-1 (Fig. 3a) and US654-3 (Fig. 3d) present a range of values from approximately 3 to approximately 10 mmol.mol -1 , with mean values of 6.67 ± 2.23 and 5.21 ± 3.37 mmol.mol -1 for US547-1 and US654-3, respectively. A second group is defined by specimens US118-3 (Fig. 3b) and US915-1 (Fig. 3f) with lower values, generally ranging from approximately 1 to 5 mmol.mol -1 , although specimen US118-3 presents increased amplitude with ontogeny. Mean values are 4.90 ± 5.58 and 3.32 ± 2.82 mmol.mol -1 for US118-3 and US915-1, respectively. Specimen US654-1 (Fig. 3c) exhibits values ranging from 7 to 12 mmol.mol -1 approximately (9.99 ± 3.20 mmol.mol -1 ). Finally, specimen US46-2 (Fig. 3e) has the highest values of the dataset, ranging from 5 to 35 mmol.mol -1 with a mean value of 19.74 ± 10.70 mmol.mol -1 . A positive ontogenic trend is visible for specimen US547-1 (Fig. 3a) and a negative trend is visible for specimen U46-2 (Fig. 3e).

When compared to luminescence intensity (IL), specimens US118-3 (Fig. 3b), US654-3 (Fig. 3d) and US915-1 (Fig. 3f) present a fair graphic correlation between cathodoluminescence signal and Mg/Ca for the entire studied transects. Graphic correlation for specimen US547-1 (Fig. 3a) can be validated until 8 mm from the start of the hinge (Fig. 3a). Specimens US547-1 and US46-2 exhibit partial graphic correlation only. Specimen US46-2 presents a positive graphic correlation at first from 6 to 8.5 mm on the transect, while the rest of the measured line presents Mg/Ca values that do not reflect any resemblance to the IL signal (Fig. 3e).

Relation between these two signals is more complex for specimen US654-1 which seem to present a partial anti-correlation from 1 to 4 mm and from 5.5 to 8.5 mm (Fig. 3b).

Isotope ratios

The δ 18 O values range from -0.50 to 1.68 ‰ (mean: 0.21 ± 0.73 ‰) for specimen US547-1, from -1.32 to 1.01 ‰ (mean: -0.36 ± 0.67 ‰) for US654-1 and from -1.91 to 2.95 ‰ (mean: 0.54 ± 1.34 ‰) for US46-2 (Fig. 4). The δ 13 C values range from 0.53 to 1.48 ‰ (mean: 1.11 ± 0.34 ‰), from 0.18 to 0.96 ‰ (mean: 0.56 ± 0.28 ‰) and from -1.66 to 0.80 ‰ (mean: -0.54 ± 0.69 ‰) for US547-1, US654-1 and US46-2, respectively.

Discussion

Reconstructing seasonal evolution of seawater chemistry from stable isotope analyses When evaluating the results for δ 13 C and δ 18 O, additional information can be inferred about the temporal dynamic change of the surrounding waters along the organism's lifespan.

Figure 5 presents the seasonal record of isotopic composition of the studied shells. Upon initial observation there is no obvious seasonal difference between δ 13 C and δ 18 O for each specimen (Fig. 5). Secondly, specimens US547-1 and US654-1 are relatively restricted in amplitude for δ 13 C, with US547-1 values more enriched than those of US654-1. Finally, US46-2 presents larger amplitudes in both δ 13 C and δ 18 O and δ 13 C values are generally depleted compared to the other specimens. In oyster shells, δ 13 C values generally reflect fluctuations in dissolved inorganic carbon (DIC) and/or organic carbon from diet (phytoplankton) whose interactions, challenging to constrain, complicate the interpretation as an environmental proxy [START_REF] Emery | Resource use of an aquacultured oyster (Crassostrea gigas) in the reverse estuary Bahia San Quintin, Baja California, Mexico[END_REF][START_REF] Klein | Bivalve skeletons record seas-surface temperature and δ 18 O via Mg/Ca and 18 O/ 16 O ratios[END_REF]Lartaud et al., 2010b;[START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF][START_REF] Surge | Reconstructing estuarine conditions: Oyster shells as recorders of environmental change, southwest Florida[END_REF]. Still, this large amplitude indicates that specimen US46-2 was living in a less stable environment than both other specimens in terms of food supply and salinity.

The initial part of the US46-2 shell presents relatively enriched values for both isotope ratios (Fig. 4c). Two features are noted for this part of the sequence involving a sudden decrease in both δ 13 C and δ 18 O. A drop in δ 18 O can be interpreted as both an increase in temperature and a drop in salinity. If we consider that this specimen originates from the French Mediterranean coastline, the main river reaching this area is the Rhone River, whose flow is controlled by the melting of the Alps glaciers. Thus, an increase in temperatures recorded in the Mediterranean Sea can also be synchronously happening in the Alps and cause stronger melting, inducing a more pronounced flow of the Rhone River. This larger amount of freshwater, when reaching the shore, would subsequently be responsible for a decrease of salinity, as observed in the present data. However, other possibilities to provide freshwater exist, such as important floods during high-intensity rainfall events. Indeed, it has been reported that strong variations in δ 13 C and δ 18 O in oyster shells can be linked to flooding events [START_REF] Walther | Drought and flood signals in subtropical estuaries recorded by stable isotope ratios in bivalve shells[END_REF]. Such events can also be proposed as a cause for a nonseasonal Mn incorporation (and hence CL signal) as nutrient input would vary and induce episodic Mn-rich phytoplankton blooms. Such an interpretation would explain the complexity of the CL signal from this specimen (Fig. 4c) compared to the others.

The synchronous decrease in δ 13 C can also be explained by the same type of event, as cold freshwater reaching the shore from melting glaciers would contain substantial concentrations of nutrients. These nutrients would induce phytoplankton development, reducing the DIC δ 13 C as organic matter incorporates more 12 C, but would provide a substantial food source for the oysters, which would in turn enrich their shells in light carbon.

For the rest of the shell, when following growth, several clusters of δ 13 C and δ 18 O are recorded. It seems that local seawater conditions lingered at a certain steady-state before being strongly and suddenly changed to a new equilibrium for another few years. Contrary to the other specimens that demonstrate more stable conditions, it seems here that US46-2 is native to a dynamic location. Temperature reconstruction using estimated δ 18 O w Oxygen isotope ratios were converted to temperatures using the equation of [START_REF] Anderson | Stable isotopes of oxygen and carbon and their application to sedimentologic and paleoenvironmental problems[END_REF] based on calcitic molluscs (Equation 1). As an estimation of δ 18 O w -required for the temperature calculations -we used the equations of Pierre (1999; Equation 2) and Lartaud (2007; Equation 3), defined from the Mediterranean Sea and the French Atlantic coastline, respectively. To do this, we used a constant modern mean salinity value of 35.5 ‰ for the Atlantic area model and 39.0 ‰ for the Mediterranean area model. The corresponding calculated δ 18 O w values from Equations 2 and 3 are 1.63 ‰ and 0.51 ‰ for the Mediterranean Sea and the North-East Atlantic, respectively. Resulting calculations are shown on Figure 6. As growth rates of oyster shells are known to be reduced in winter months (Lartaud et al., 2010c) and since our sampling resolution is spatially constant between consecutive samples, winter values are likely to be overestimated (i.e., samples from winter periods will probably contain parts from previous autumn and/or subsequent spring, inducing an elevated mean value).

Figure 6: Temperature reconstruction from δ 18 O for two hypothetical origins of the oyster shells: Mediterranean Sea (solid line) and French Atlantic coast (dashed line). Values of δ 18 O w used for calculations using the model of [START_REF] Anderson | Stable isotopes of oxygen and carbon and their application to sedimentologic and paleoenvironmental problems[END_REF] are 1.63 ‰ (considering a constant salinity of 39 ‰ and using the model of Pierre, 1999; Equation 2) and 0.51 ‰ (considering a constant salinity of 35.5 ‰ and using the model of [START_REF] Lartaud | Les fluctuations haute fréquence de l'environnement au cours des temps géologiques. Mise au point d'un modèle de référence actuel sur l'enregistrement des contrastes saisonniers dans l'Atlantique nord[END_REF] Equation 3) for the Mediterranean Sea and the North-East Atlantic, respectively. Limits of winter (W) and summer (S) seasons, based on CL model [START_REF] Langlet | Experimental and natural cathodoluminescence in the shell of Crassostrea gigas from Thau lagoon (France): ecological and environmental implications[END_REF], are located by dashed vertical grey lines. a: US547-1. b: US654-1. The missing transect (underlined by '?' signs) corresponds to a damaged part of the shell that was not sampled. c: US46-2.

Temperatures reconstructed using this estimated constant δ 18 O w show generally synchronous fluctuations for specimen US547-1 compared to the seasons interpreted from CL signal (Fig. 6a). Temperature values range from 11.3 to 20.3 °C for the Atlantic hypothesis and from 15.8 to 25.4 °C for the Mediterranean Sea hypothesis, though most variations occur over a modelled 6 to 7 °C interval for the entire section, which is lower than the values currently measured on the French coasts (generally 16 °C amplitude for the Mediterranean Sea, from 11 to 27 °C, and approximately 12 °C amplitude for the Atlantic, from 8 to 20 °C; http://www.meteociel.fr/accueil/sst.php). The calculated summer temperature values for the Mediterranean Sea origin hypothesis are in accordance with [START_REF] Luterbacher | European summer temperatures since Roman Times[END_REF], who indicated for this period that mean summer temperatures for the studied time period were approximately 2.5°C lower than those from present day.

For specimen US654-1, reconstructed temperatures range from 14 to 24 °C for the Atlantic hypothesis, corresponding to a modelled temperature amplitude of 10 °C (Fig. 6b). For the Mediterranean origin hypothesis, reconstructed temperatures range from 18.6 to 29.3 °C.

The age model from CL appears here to be contrary to the calculated temperatures. The second winter and third summer indicated by the CL fluctuations has however no corresponding isotope samples to check for this discrepancy. Still, subsequent samples, which would correspond to a winter period, present high temperatures and slowly decreasing at the end of this winter period, which is consistent with previous parts of this shell.

Specimen US46-2 presents temperatures ranging from 6.7 to 26.7 °C for the Atlantic hypothesis and from 10.8 to 32.3 °C considering a Mediterranean origin, corresponding to a thermal contrast on the extrema of over 20 °C (Fig. 6c). However, a positive trend is visible from the start to 7.5 mm before a strong drop in values. When comparing to local minima and maxima, the contrast rarely exceeds 10 °C. High and low temperature values do not reflect CL seasons, which tends to indicate that this specimen lived in a less stable environment than specimens US547-1 and US654-1. In this specimen, salinity must have varied throughout the organism's lifespan, and probably from one season to the next (see Fig. 4), suggesting some freshwater influence in substantial proportions to significantly change the δ 18 O w . Indeed, seasonal or monthly fluctuations in δ 18 O w have been reported to induce errors of ± 3°C in estimations of sea surface temperatures compared to a mean annual value, even without important freshwater influence (e.g. [START_REF] Prendergast | Oxygen isotopes from Phorcus (Osilinus) turbinatus shells as a proxy for sea surface temperature in the central Mediterranean: A case study from Malta[END_REF].

For all specimens, none of the hypotheses (Atlantic Ocean or a Mediterranean Sea origin for the oyster shells) can be ruled out from the reconstructed temperatures. As stable isotope values cannot efficiently discriminate the living environment, other methods need to be investigated.

Environmental interpretation and collection sites in ancient times

In view of the stable isotope data discussed above, we note an influence of the level of freshwater input from rivers on Mg/Ca in addition to temperature. However, salinity was reported to have no influence in Mg/Ca in mussel [START_REF] Vander Putten | High resolution distribution of trace elements in the calcite shell layer of modern Mytilus edulis: environmental and biological controls[END_REF] and oyster shells [START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF][START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF]Tynan et al., in press) and Mg concentrations in seawater is not linked to Mg incorporation in the shell (Tynan et al., in press;[START_REF] Vander Putten | High resolution distribution of trace elements in the calcite shell layer of modern Mytilus edulis: environmental and biological controls[END_REF]. Given that alternative explanations for Mg/Ca variations are not currently viable, the mean Mg/Ca content in oyster shells can be used to characterize the living sites of specimens of unknown origin. Indeed, [START_REF] Bougeois | A high resolution study of trace elements and stable isotopes in oyster shells to estimate Central Asian Middle Eocene seasonality[END_REF][START_REF] Bougeois | Mg/Ca in fossil oyster shells as palaeotemperature proxy, an example from the Palaeogene of Central Asia[END_REF] tested a variety of models on Eocene oyster shells from the Proto-Paratethys epicontinental sea and the best fitting model for their shells corresponded to a model defined with no direct influence of freshwater. We propose to use such an empirical relationship to identify the environment of collection sites visited by fishermen during Antiquity. The specific use for these models is practical here as the shells used in this study were unearthed from a locality different to that of the (unknown) living environment of the oysters.

A variety of shell Mg/Ca range values have been reported in the literature for normal seawater temperature settings (Fig. 7). The differences transcribed in these relationships probably represent several forcing factors of Mg incorporation.

Firstly, contrary to δ 18 O that is in equilibrium with seawater for most molluscs and foraminifera (Epstein et al., 1953;[START_REF] Erez | Experimental paleotemperature equation for planktonic foraminifera[END_REF], taxonomy has been suggested to have an impact on Mg incorporation [START_REF] Elderfield | A biomineralization model for the incorporation of trace elements into foraminiferal calcium carbonate[END_REF]) but it appears not to be the case for mussels and oysters, as indicated by the similar relationships (Fig. 7) found by Vander Putten et al. (2000; M. edulis), [START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF]C. virginica) and Tynan et al. (in press; Saccostrea glomerata). Moreover, similar Mg/Ca ranges were measured from specimens of two oyster species (O. edulis and C. gigas) bred simultaneously on the same site [START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF]. Shell Mg/Ca range is similar in the specimens bred in the same location [START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF][START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF]Vander Putter et al., 2000;Tynan et al., in press), indicating that the range of incorporation of Mg in bivalve shells depends much more on the locality and the type of hydrologic settings than on potential vital effects. Indeed, shells from all estuarine locations exhibit a strong Mg incorporation [START_REF] Klein | Bivalve skeletons record seas-surface temperature and δ 18 O via Mg/Ca and 18 O/ 16 O ratios[END_REF][START_REF] Surge | Evaluating Mg/Ca ratios as a temperature proxy in the estuarine oyster, Crassostrea virginica[END_REF]Tynan et al., in press;Vander Putter et al., 2000), while all but one marine location from those studied correspond to a weak Mg incorporation in bivalve shells. The location that do not fit this observed relationship, Moreton Bay (Tynan et al., in press), presents a typical marine salinity (35.1-36.7 ‰) but corresponds to a sheltered area with a relatively long residence time of seawater (up to 100 days). This may be responsible for the differences observed in Mg incorporation in bivalve shells compared to other sites with more open marine influence.

The equation derived by [START_REF] Wanamaker | Experimentally determined Mg/Ca and Sr/Ca ratios in juvenile bivalve calcite for Mytilus edulis: implications for paleotemperature reconstructions[END_REF] for M. edulis indicates high values of shell Mg/Ca compared to other studies for similar temperatures. This model was established from a laboratory experiment using water derived from seawater collected in the Damariscotta River, Maine, far from the open sea. At this location, salinity is known to fluctuate from season to season between 5 to 28 ‰ [START_REF] Thompson | Phytoplankton in the Damariscotta River Estuary[END_REF], suggesting strong freshwater input from rivers. The M. edulis models providing equivalent temperature values were defined from locations presenting both open marine influence and freshwater input [START_REF] Klein | Bivalve skeletons record seas-surface temperature and δ 18 O via Mg/Ca and 18 O/ 16 O ratios[END_REF][START_REF] Freitas | Inter-and intra-specimen variability masks reliable temperature control on shell Mg/Ca ratios in laboratory and field cultured Mytilus edulis and Pecten maximus (Bivalvia)[END_REF]. The six specimens from our study can be associated with the environmental relationships of these models and by extension to the type of settings according to their Mg/Ca range values.

In particular, specimens US547-1, US654-1 and US654-3 probably lived at locations subject to both marine and freshwater influence (Mg/Ca range: approx. 3-12 mmol.mol -1 ).

Interestingly, the age model from CL fluctuations indicates that the higher Mg/Ca values in specimen US654-1 occur during the winter months and the lower values during the summer months, as confirmed by temperatures calculated from δ 18 O from this specimen. Such an relationship between seasonal growth / temperature and Mn incorporation indicates that Mn (as a CL activator) in this specimen is seasonally opposed to that of the other specimens from this study and all modern specimens studied by Lartaud et al. (2010c) and [START_REF] Mouchi | Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations[END_REF]. Such a difference may be caused by differences in seawater chemistry between the living locality of US654-1 when compared to localities with no important freshwater input.

Additional examination under CL of other modern oyster shells from confirmed estuarine areas would be required to check this assumption. Therefore, the locations of origin of specimens US547-1, US654-1 and US654-3 may correspond to lagoons with partial freshwater input from small rivers or groundwater. Specimens US118-3 and US915-1, with low Mg/Ca values (approx. 0-5 mmol.mol -1 ), are generally compatible with an open marine environment. Specimen US118-3 presents the particularity to change the amplitude of Mg/Ca values from simple to double around 5 mm from the start of the umbo (after the second year of growth, according to the CL seasonal calibration). This can be interpreted as a change in local hydrologic regime during the organism lifespan, corresponding to an increased freshwater input. Growth rates (based on CL seasonal calibration; Fig. 2) are indeed different for this specimen compared to the others, as the shell appears to have grown faster during its fourth and seventh year and slower the other years, suggesting an instable site in terms of food supply and favourable environmental factors.

Finally, the Mg/Ca range in specimen US46-2 (approx. 10-30 mmol.mol -1 ) indicates a strong freshwater influence. As δ 18 O values also reflect strong impact of freshwater input, the living locality of this specimen must have been close to a river outlet.

The French Mediterranean coastline comprises numerous lagoons [START_REF] Derolez | Suivi estival des lagunes méditerranéennes françaises -Bilan des résultats[END_REF] that are partly supplied by freshwater from rivers and karstic groundwaters [START_REF] Fleury | Submarine springs and coastal karst aquifers: A review[END_REF].

Groundwater can have a strong influence on the water composition of lagoons and substantially change water chemistry compared to adjacent areas [START_REF] Stieglitz | Karstic groundwater discharge and seawater recirculation through sediments in shallow coastal Mediterranean lagoons, determined from water, salt and radon budgets[END_REF].

Therefore, the heterogeneity of geochemical signals in the oyster shells presented here reflects a diversity of locality settings, most likely on the Mediterranean coastline.

The precise identification of the localities from which originated the oysters is impossible with the present data and would require substantial analyses of the geochemistry of multiple oyster shells from a variety of areas on the French Mediterranean coastline to be compared with that of these specimens (although it cannot currently be excluded that these specimens originated from other regions than the Mediterranean coastline). However, it appears clear that specimen US46-2 originated from a different type of environment than the other specimens. The locality for this specimen was subjected to an alternating and strong freshwater influence, as suggested by the δ 13 C and δ 18 O data (Fig. 5). The largest freshwater source in this region of the Mediterranean is the Rhone River. The Rhone River forms a delta, hence providing an important flow of freshwater and large floods which could possibly correspond to the results of δ 18 O and mean Mg/Ca from this specimen.

However, the Rhone River may not have been the origin of specimen US46-2 as this outlet (whose limits strongly varied over the ages) is too dynamic and unstable to grant survival of long term oyster communities. Specimen US46-2 may have been collected from a large estuary, close to the river outlet. An exact location for oyster harvest is however impossible to determine at this time, partly due to the current complex coastline with multiple lagoons, and partly because the position of the shoreline has changed since Antiquity [START_REF] Bardot-Cambot | Du conchylioreste à l'environnement : de la nature à l'homme, de l'homme à la nature[END_REF][START_REF] Rey | Données nouvelles sur les lobes deltaïques du paléogolf d'Aigues-Mortes à l'Holocène [Petite Camargue, France[END_REF] and most lagoons are nowadays entirely emerged.

Conclusion

This study used two geochemical proxies for environmental reconstruction and cathodoluminescence from six oyster shells on archaeological specimens dated from the 3 rd century AD to the 5 th century AD and found in archaeological sites in Lyon, Central France.

Though the original living locality of these specimens is not known, the geochemical heterogeneity among the shells indicates that these specimens did not live in the same area and were under the influence of different mixing waters. Stable isotope analyses from three shells indicate various regimes in freshwater input, with one specimen probably originating from a locality in direct proximity to a river outlet while the two others present more stable marine conditions.

As Mg/Ca ratio amplitude in bivalve shells has been reported to be different according to the locality and the hydrologic setting in equivalent temperature ranges, we suggest that the geochemical differences observed in each shell can be used to identify the environment (estuary, lagoon, marine) from which the specimens originated. Our results indicate that fishermen were probably not restricted to a single locality for oyster collection during Antiquity but harvested oysters from a variety of areas. This study also highlights the importance of careful choice of a Mg/Ca model to estimate palaeotemperatures in coastal areas where freshwater input may have been a factor.

Figure 1 :

 1 Figure 1: Oyster sample preparation. a: Left valve of oyster shell showing location and

Figure 3 :

 3 Figure 3: CL intensity of luminescence (IL; in arbitrary units) and Mg/Ca ratio along the

  Variations of IL generally present opposed fluctuations with δ 18 O for specimen US547-1. On the contrary, specimen US654-1 shows synchronous fluctuations of IL and δ 18 O. Specimen US46-2 presents strong fluctuations with little relation to IL variations.

Figure 4 :

 4 Figure 4: Isotopic ratios (axis on the left-hand side) from all three shells in relation to CL

Figure 5 :

 5 Figure 5: Isotopic composition of oyster shells. Samples from winter and summer periods of

Figure 7 :

 7 Figure 7: Bivalve shell Mg/Ca range values for common seawater temperature settings from

Acknowledgements

The authors would like to thank Nathalie Labourdette from UPMC for analyzing the isotope samples. We are grateful to Elise Dufour for giving us access to the micromill at the MNHN.

We also thank Quentin Crowley for the editing he provided to this manuscript. Finally, we would like to thank Michel Fialin and Nicolas Rividi from the Camparis service for their help and time during the EPMA experiments.

SUPPLEMENTARY INFORMATION

Pecten maximus

Mg/Ca = 0.17*T + 2.56 [START_REF] Freitas | The potential of combined Mg/Ca and δ 18 O measurements within the shell of the bivalve Pecten maximus to estimate seawater δ 18 O composition[END_REF]


Ignacio Rubio
email: ignacio.rubioscola@gipsa-lab.fr

Scola Gildas Besançon
email: gildas.besancon@gipsa-lab.fr

Didier Georges
email: didier.georges@gipsa-lab.fr

Marcos L Guillén
email: marcosg@ula.vegrupotermofluidodinámica.dpto.de

Jean-F Dulhoste

Rafael Santos
email: rsantos@ula.vegrupotermofluidodinámica.dpto.de

SENSITIVITY ANALYSIS OF END PRESSURES AND FLOWS WITH RESPECT TO A BLOCKAGE INSIDE A PIPELINE

Keywords: Pipeline, Sensitivity analysis, Blockage, Modeling

The present paper is based on the sensitivity analysis of input and output pressures and flows of a pipeline for the detection and location of a blockage in a pipeline. To that end, three ways of modeling a blockage in a pipe have been designed . The first model assumes that the blockage is punctual like an orifice plate placed online in the pipeline. For the second and third model, a longitudinal blockage is assumed along the pipeline. In the second model, it is only considered a reduction of the pipeline cross-section in a particular stretch of the pipeline. In the third model, the blocked segment is modeled by considering two orifice plates and between the plates there is a blocked pipe stretch. These models have four different outputs, pressure and flow rate at the input and pressure and flow rate at the output. The aim of this work is to determine which pair of outputs have the highest sensitivity to the change of blockage position in order to improve the detection and location of the blockage. In this study, the energy for each output and for each position is calculated and the magnitude of the energy variation with respect to blockage position is then obtained. Numerical simulations are presented for the different models.

Fluid transportation by pipeline is really cheap and efficient, but faults, such as leaks or blockages, can generate a loss in money and repairing time if there are not detected in short time. A lot of work has been done on leaks detection and location but not so much on blockages detection and location (Wang et al. [START_REF] Wang | Detection and location of a partial blockage in a pipeline using damping of fluid transients[END_REF] and Guillén et al. [START_REF] Guillén | Study of A Flow Model for Detection and Location Of Leaks and Obstructions In Pipes[END_REF]). Particularly, in this work, a sensitivity analysis is done to show how detectable is the position of a blockage when the input and output flows and pressures are measured.

The paper is organized as follows: section 2 presents the different models considered and section 3 explains the sensibility analysis done. Section 4 then shows the results in simulation, and section 5 concludes the paper.

DIFFERENT PIPELINE MODELS WITH LUMPED BLOCKAGE

As mentioned in Chaudry [START_REF] Chaudry | Applied Hydraulic Transients[END_REF], if convective changes in velocity and constant liquid density could be considered, then the dynamics of the fluid in a pipeline can be described by the Water Hammer partial differential equations:

∂H ∂t + c 2 gA ∂Q ∂z = 0 ∂Q ∂t + Ag ∂H ∂z + f Q|Q| 2DA = 0 (1)
where H means the pressure head (m) and Q the flow rate in the pipeline (m 3 /s), both varying in time t (s) and space z (m). In addition, the wave speed in the fluid (m/s), the gravitational acceleration (m/s 2 ), the cross-sectional area of the pipe (m 2 ), the diameter of the pipe (m), the friction coefficient, and the pipe length (m) are represented by the constant parameters c, g, A, D, f and L respectively. The boundary conditions on Q, H, for z ∈ {0, L} and the initial conditions for the fluid dynamics must be fixed at Q(z, 0), H(z, 0) for z ∈ [0, L]. The partial differential equations Eq.( 1) must be discretized in space in order to solve them numerically by using a finite-difference approximation of the spatial differential operators. If the boundary conditions on Q(0, t) and H(L, t) are imposed, then the equations for each section (i) are:

Ḣi = - c 2 gA Q i+1 -Q i z i+1 -z i Qi = -Ag H i -H i-1 z i -z i-1 - f i Q i |Q i | 2DA (2)
where the H i 's and Q i 's refer to the approximate values of H, Q at z i 's and Fig. 1 illustrates the discretization.

H 1 H 2 H n Q 1 Q 2 H i Q i Q n H i-1 Q i+1 z1 z2 zi-1 zi zi+1 zn Figure 1: Pipeline dicretized in n sections. Bomba H in H out H 1 H n Q 1 R in H b R out Q n P Pipeline Figure 2: Pump-Restriction-Pipeline-Restriction configuration.
The boundary conditions will be given by a pump and a restriction that are connected at the beginning of the pipeline and at a restriction the end of it, as shown by Fig. 2. As the dynamics of the pump and the restrictions are much faster than the pipeline the static equations could be used, for the pump and the first restriction the equation are:

H b -H in = A P Q 2 1 + B P Q 1 + C H b -H 1 = R in Q 2 1 (3)
and for the second restriction:

H N -H out = R out Q 2 N (4)
where H in and H b are the pressure in the input and output of the pump, H out is the output pressure of the second restriction and the constants parameters A P , B P , C P are the pump parameters and R in and R out are the input and output restriction values respectively. The first model is based on the hypothesis that the blockage is punctual at position z o (see Besançon et al. [START_REF] Besanc ¸on | Observer-based detection and location of partial blockages in pipelines[END_REF]), as shown by Fig. 3, the relation between the pressure before the blockage (H o ) and after (H * o ) could be described as an orifice plate, so by using Bernoulli's equation the flows on the blockage is modified as follows:

Blockage considered as punctual

Qo = -Ag H o+1 -H * o z o+1 -z o - f o Q o |Q o | 2DA o H * o = H o - Q 2 o 2gA 2 A A o 2 -1 -h L (5)
In the second equation of ( 5) h L represents the pressure losses due to the blockage, if the worst case of h L = 0 is considered (its geometry is unknown), then the blockage modeled is bigger than the real one. Equations 2 describes the dynamics of the other pressures and flows.

For the second model the blockage is modeled as a piece of pipeline (with length l o ) which its cross section area is reduced (from A to A o ), Fig. 4 illustrates the blockage. The equations describing the pressure (H o ) at the beginning and the flow (Q o+1 ) at the end of reduced part of the pipeline are modified (with respect to Eq. 2):

H 1 Q 1 H o+1 H o H N Q N Q o Q o+1 z1 zo zo+1 zN l o A A o
Ḣo = - c 2 gA o Q o+1 -Q o l o Qo+1 = -A o g H o+1 -H o l o - f o+1 Q o+1 |Q o+1 | 2DA o (6)

Blockage considered as a reduced section with both sides geometry

The last model is based on the second one, but it also takes into account the phenomena that occurs in the borders of the longitudinal blockage where first exists a contraction in the cross section of the pipe (from A to A o ) and then occurs an expansion of it (from A o to A), shown in Fig. 5. Equation (7) describes the dynamics of the pressures and the flows before (H o and Q o+1 ) and after the blockage (H o+1 and Q o+2 ).

H 1 Q 1 H o+1 H o H N Q N Q o Q o+1 z1 zo zo+1 zN H o H o+1 * * Q o+2 zo+2 H o+2 l o A A o
Ḣo = - c 2 gA o Q o+1 -Q o l o Qo+1 = -A o g H o+1 -H * o l o - f o+1 Q o+1 |Q o+1 | 2DA o Ḣo+1 = - c 2 gA Q o+2 -Q o+1 z o+2 -z o+1 Qo+2 = -Ag H o+2 -H * o+1 z o+2 -z o+1 - f o+2 Q o+2 |Q o+2 | 2DA (7)
The pressures just after the beginning and the end of the blockage are H * o and H * o+1 , are modified using Bernoulli's in order to represent the change in the cross section area of the pipe.

H * o = H o - Q 2 o 2gA 2 A A o 2 -1 and H * o+1 = H o+1 - Q 2 o+1 2gA 2 o A o A 2 -1 (8)
Three different ways of modeling a blockage are shown in this section, next section gives a methodology for comparing the sensibility of the different outputs respect to the blockage's position.

SENSITIVITY ANALISYS

In order to quantify the effects of different blockage's positions in the measured variables, the sensibility (S) of one output (y) respect to the position (z) is introduced as the variation of the energy (E) of that output respect to the position (z):

S y z = ∂E y ∂z = ∂ ∂z T 0 y(z) 2 dt (9)
The sensibility increases with the change of the energy of an output when the position moves, what implies that, the bigger this function is, the easier is to distinguish two different locations from that output. Sensibility analysis is also useful for parameter identifiability analysis (see Dötsch et al. [START_REF] Dötsch | Test local structural identifiability of high-order non-linearly parametrized state space models[END_REF]). In the next section, the three models will be simulated with the same inputs conditions and the sensibility analysis will be done for each measured variable.

NUMERICAL RESULTS

Using a simulation software (Simulink from MathWorks c ) the three models are simulated with the same inputs, H in = 1 + 0.5sin(2πt) (m) and H out = 1 (m). Then defining the measured variables as H 1 , H N Q 1 and Q N the eq. ( 9) is calculated for each model and each output. The time windows used is T = 2s and 83 different positions are simulated taking 85 sections for the discretization of the pipeline. Table 1 shows the numerical values of the average of the absolute values of the sensibility. In order to understand this table, the values of the pressures H 1 and H N are around 6.5 (m) and 3.5 (m) and the flows are near 4.3 • 10 -3

CONCLUSIONS

In this work a sensibility analysis respect to the position of a blockage in a pipeline has been done for three different way of modeling a blockage. The numerical results shows that there are two model which are more sensible and in all the models there is a pair of outputs that show a bigger sensibility over the other two. In all the cases the values of sensibility founded are very low and to distinguish between two different positions is very difficult. In the future this sensitivity analysis will be done to more complex models to increase the value of this sensibility and guarantee a strong distinguishability between two different blockage positions.

Figure 3 :

 3 Figure 3: Pipeline with a punctual blockage at z o .

Figure 4 :

 4 Figure 4: Pipeline with a cross section reduction between z o and z o+1 .

Figure 5 :

 5 Figure 5: Pipeline with a cross section reduction between z o and z o+1 and the sides effects.

Table 1 :

 1 Energy variation average for each output and each model. 10 -05 1.42 • 10 -04 1.43 • 10 -04 H out 8.27 • 10 -07 1.31 • 10 -05 1.35 • 10 -05 Q in 8.52 • 10 -12 9.35 • 10 -12 9.46 • 10 -12 Q out 1.31 • 10 -12 2.27 • 10 -11 2.33 • 10 -11 (m 3 /s) The second and third model have a similar sensibility but the first model has a minor sensibility than last two. The best pair of measures with bigger sensibility are H in and Q out , but it is still very low and if noise around 1% is injected in the outputs then two different positions will be indistinguishable.

	Output	Model 1	Model 2	Model 3
	H in	2.31 •

Acknowledgements

This work was supported in part by a French-Venezuelan collaboration program ECOS-Nord V11M02/ PI-2010000303 Fonacit, Fundayacucho Venezuela.


Ignacio Rubio
email: ignacio.rubioscola@gipsa-lab.fr

Scola Gildas Besançon
email: gildas.besancon@gipsa-lab.fr

Didier Georges
email: didier.georges@gipsa-lab.fr

Marcos L Guillén
email: marcosg@ula.vegrupotermofluidodinámica.dpto.de

Jean-F Dulhoste

Rafael Santos
email: rsantos@ula.vegrupotermofluidodinámica.dpto.de

ON THE DESIGN OF A NONLINEAR STATE OBSERVER FOR THE LOCATION OF A BLOCKAGE IN A PIPELINE

Keywords: Modeling, Pipeline, Blockage, Nonlinear Observer

This paper presents a design of a nonlinear state observer in order to locate a blockage in a pipeline. First, a mathematical model of the pipeline is designed using the water hammer equations and applying the finite difference method for the solution with n sections. Then, based on the experience obtained from the leak location with nonlinear observers, a second mathematical model is obtained from a discretization in only two sections and a nonlinear state observer is build. In this new model, the blockage is at the beginning of the second section of pipeline. By analytical analysis, it is found that to achieve satisfactory the location of the blockage, the observer requires certain specific inputs, called persistent inputs.These persistent inputs are found empirically.

Then, numerical simulations are performed with the state observer and the mathematical model with two sections and applying both entries obtained above. A satisfactory location of the blockage is obtained. Also simulations where measurements are subject to white Gaussian noise are done.

INTRODUCTION

Nowadays, pipelines are a cheap way to transport liquids. But faults, as leaks or blockages, can cause big and expensive problems to solve, generating a loss in money and time repairing it. A lot of work have being done on leaks detection and location but not so much on blockages detection and location ( [START_REF] Wang | Detection and location of a partial blockage in a pipeline using damping of fluid transients[END_REF] and [START_REF] Besanc ¸on | Observer-based detection and location of partial blockages in pipelines[END_REF]). Particularly, in this work, the problem is solve using model based techniques.

PIPELINE MODEL WITH PUNTUAL BLOCKAGE

The dynamics of the fluid in a pipeline could be described by the Water Hammer partial differential equations considering convective changes in velocity and constant liquid density [START_REF] Chaudry | Applied Hydraulic Transients[END_REF]:

∂H ∂t + c 2 gA ∂Q ∂z = 0, ∂Q ∂t + Ag ∂H ∂z + f Q|Q| 2DA = 0 (1)
where H means the pressure head (m) and Q the flow rate in the pipeline (m 3 /s), varying in space z (m) and time t (s). Then, the constants parameters c, g, A, D, f and L represent the wave speed in the fluid (m/s), the gravitational acceleration (m/s 2 ), the cross-sectional area of the pipe (m 2 ), the diameter of the pipe (m), the friction coefficient, and the pipe length (m) respectively. The initial conditions for the fluid dynamics must be fixed at Q(z, 0), H(z, 0) for z ∈ [0, L] and also the boundary conditions on Q, H, for z ∈ {0, L}. As showed in the previous figure, the pipeline input

Bomba H in H out H 1 H 2 H n Q 1 Q 2 R in H 3 H b R out Q n P Figure 1: Schema of system Pump-Restriction-Pipeline-Restriction, the pipeline is dicretized in n sections.
is connected to a pump (P ) with a restriction (R in ) and the pipeline output is only connected to a restriction (R out ). The dynamics of the pump and both restrictions are hundred time faster than the pipeline dynamics, so the static equations could be used to describe the behavior of these elements. The follows equations described the static relations between the pressures of the pump and both restrictions:

H in -H b = A P Q 2 1 + B P Q 1 + C P ; H b -H 1 = R in Q 2 1 ; H n -H out = R out Q 2 n (2)
where H in is the pump input pressure, H b is the pressure between the pump and the first restriction, H 1 and H n , Q 1 and Q n are the input and output pipeline pressures and flows of the pipeline respectively, H out is the output pressure of the second restriction and finally the constants A P , B P , C P are the pump constants and R in and R out are the restrictions constants.

In order to solve numerically the partial differential equations Eq.( 1) a dicretization in space must be done. Imposing as boundary conditions H(0, t) and H(L, t) the discretized equations for each section (i) are:

Ḣi = - c 2 gA Q i+1 -Q i z i+1 -z i ; Qi = -Ag H i -H i-1 z i -z i-1 - f i Q i |Q i | 2DA (3)
where the H i 's and Q i 's refers to the approximate values of H, Q at z i 's.

The model accuracy will depend on the number of points taken for such discretization, but for a purpose of observer design based on this model, so in order to reduce the observer computational burden, the minimum number of sections are would be chosen. If a punctual blockage occurs at

H 3 z 1 z 2 z 3 A A b H 1 H 2 H 2 - Q 1 Q 2 Figure 2:
Pipeline discretized in 2 sections with a blockage at position z 2 (begin of the second section).

some position z 2 , the pipe cross-sectional area A would be reduced into some A b . Three sections are enough to include the blockage position z b , as in Fig. 2 (z 1 = 0, z 2 = z b , and z 3 = L). Finitedifference model [START_REF] Besanc ¸on | Observer-based detection and location of partial blockages in pipelines[END_REF] in that case reduces to:

Q1 = -Ag H 2 -H 1 z 2 -z 1 - f 2 Q 1 |Q 1 | 2DA Ḣ2 = - c 2 gA Q 2 -Q 1 z 3 -z 2 Q2 = -Ag H 3 -H - 2 z 3 -z 2 - f 3 Q 2 |Q 2 | 2DA (4)
As the blockage is considered punctual, the relation between the pressure before the blockage (H 2 ) and after (H - 2 ) could be described as an orifice plate using Bernoulli's equation:

H - 2 = H 2 - Q 2 2 2gA 2 A A b 2 -1 -h L (5)
In this equation h L represents the pressure losses due to the blockage, as its geometry is unknown the worst case should be considerate, that is h L equal to zero. In practice the blockage will be smaller than the represented by this equation.

Finally the connection between the pipeline model and the pump and both restriction is done by these two following equations:

H 1 = -(R in + C P )Q 2 1 -B P Q 1 -A P + H in = F P (H in , Q 1 ) H 3 = R out Q 2 2 + H out = F R (H out , Q 2 ) (6)
In the next section the equations of the state space model and the equations of the observer will be discussed.

Considering the following state vector:

Obs = A A b 2 -1 2gA 2 ; x T = [Q 1 , H 2 , Q 3 , z 2 , Obs] T (7)
and the equations from the previous section (Eq.4, Eq.5 and Eq.6) the state space model is build:

ẋ1 = -Ag x 2 -F P (u 1 , x 1 ) x 4 - f 2 x 1 |x 1 | 2DA ẋ2 = - c 2 gA x 3 -x 1 x 4 ẋ3 = -Ag F R (u 2 , x 3 ) -x 2 + x 2 3 x 5 L -x 4 - f 3 x 3 |x 3 | 2DA y = [x 1 , x 3 ] T (8)
Before trying to localize the blockage, first the blockage should be detected. The detection of the blockage could be solved if the pipeline is in steady state [START_REF] Besanc ¸on | Observer-based detection and location of partial blockages in pipelines[END_REF]. So, considering u 1 and u 2 in constant value for a long time enough, the dynamics of the pipeline model are zero ( ẋ = 0) and also the friction losses are equal among the pipeline (f 2 = f 3 = f ). The information of the blockage is found solving the following equations:

x 5 = F R (u 2 , y 2 ) -F P (u 1 , y 1 ) y 2 2 + f L 2DA 2 g |y 2 | y 2 ẋ5F = α(x 5 -x 5F ); A b A = 1 1 + 2gA 2 x 5F (9)
The first part of the second equation is just a first order low-pass filter to make the detection algorithm robust respect to the output variables noise where α -1 is the time constant and x 5F is x 5 filtered. Now that the blockage is detected in steady state, an observer for the location is build. The followed change of coordinates:

ζ 1 = x 1 Ag , ζ 2 = 1 x 4 , ζ 3 = -x 2
x 4 with the new inputs u ζ1 = y 1 , u ζ2 = y 2 produced the follow system:

ζ1 = F P (u 1 , u ζ1 )ζ 2 + ζ 3 - f 2 u ζ1 |u ζ1 | 2DA 2 g ; ζ2 = 0; ζ3 = c 2 Ag (u ζ2 -u ζ1 )ζ 2 2 (10)
which is a system of type:

ζ = A ζ (u)ζ + Φ ζ (ζ, u); y ζ = C ζ ζ (11)
with the matrices:

A ζ (u) =   0 F P (u 1 , u ζ1 ) 1 0 0 0 0 0 0   , Φ ζ (u, ζ) =    -f 2 2DA 2 g u ζ1 |u ζ1 | 0 c 2 Ag (u ζ2 -u ζ1 )ζ 2 2    , C ζ = 1 0 0 (12)
and under a persistent input u 1 and γ large enough ,an exponential observer for such system is:

ζ = A ζ (u) ζ + Φ(u, ζ) -K(C ζ ζ -ζ 1 ) K = P C T ζ R -1 ; P (0) > 0 Ṗ = γP + A ζ P + P A T ζ -P C T ζ R -1 C ζ P + Q (13)
where Q, R and γ are positive tuning parameters, for more details see [START_REF] Besanc ¸on | Nonlinear Observers and applications[END_REF]. Φ needs to be Lipschitz, assuming that the blockage position z 2 is to be found within some interval [ε, L -ε] for some small > 0, Φ can be extended to be Lipschitz over IR 3 for the observer design. The position of the blockage is

x 4 = 1 ζ 2 .
With the persistent input applied the system is no more in steady state so a new way to measure the blockage is build. The change of coordinates ξ 1 = x 3 (L-x 4 ) Ag , ξ 2 = x 5 and the inputs

u ξ1 = y 1 , u ξ2 = y 2 , u ξ3 = -ζ3 ζ2 , u ξ4 = 1 ζ2 result in the system: ξ1 = -F R (u 2 , u ξ2 ) + u ξ3 -u 2 ξ2 ξ 2 - f 3 (L -u ξ4 ) 2DA 2 g u ξ2 |u ξ2 |; ξ2 = 0 (14)
which is a system of type:

ξ = A ξ (u)ξ + B ξ (u); y ξ = C ξ ξ (15)
and the matrices of such system are:

A ξ (u) = 0 -u 2 ξ2 0 0 , B ξ (u) = u ξ3 -F R (u 2 , u ξ2 ) - f 3 (L-u ξ4 ) 2DA 2 g u ξ2 |u ξ2 | 0 , C ξ = 1 0 (16)
Using Eq.13 an exponential observer is build with parameters γ O , R O and Q O . The relation A b A is found in the same way as Eq.9 replacing x 5F by ξ 2

SIMULATIONS

In this section, the prototype described in [START_REF] Begovich | Online implementation of a leak isolation algorithm in a plastic pipeline prototype[END_REF] is presented as practical example where its parameters are listed in Table .1. The simulation consist on first on a steady state operation mode, with u 1 = 6.5m and u 2 = 1. Suddenly, at time t = 10s, a blockage, A b = 0.9A appears at z 2 = 25m. When the blockage is detected, the persistent input is injected, u 1 = 6.5+0.5sin(2πt)+ 1.5sin(2.06πt), and the position is estimated. To show the second part of the observer, the blockage, at time t = 500, is moved to z 2 = 80m and is augmented to A b = 0.5A. There is a noise of some percent of the output value in the outputs of the system. The parameters of the algorithms are: [START_REF] Chaudry | Applied Hydraulic Transients[END_REF] shows the simulation results, the observer recovers well the position and the blockage size. Also the simulation shows that the noise robustness augments as the obstruction augments.

α = 1, R = 1, Q = I D , γ = 4, R O = 1, Q O = I D and γ O = 1. Figure.
g (m/s 2 ) c (m/s) A (m 2 ) f (s -2 ) L (m)
9.81 373 0.003 0.0189 85

CONCLUSIONS AND FURTHER WORK

In this paper, a technique to detect and locate blockage in a pipeline has being proposed. Based on a mathematical model an observer was build and the performance and accuracy were shown on some figures of numerical simulations.

In the future, the noise robustness will be improved and also the observer will be improved to be applied to real data.

Figure 3 :

 3 Figure 3: Simulation of one blockage in two different positions and different sizes.

Table 1 :

 1 Pipeline parameters.

Acknowledgements

This work was supported in part by a French-Venezuelan collaboration program ECOS-Nord V11M02/ PI-2010000303 Fonacit, Fundayacucho Venezuela.