Gabriel Munoz

Hélène Budzinski

Marc Babut

Hilaire Drouineau

Mathilde Lauzent

Karyn Le Menach

Jérémy Lobry

Jonathan Selleslagh

Caroline Simonnet-Laprade

Pierre Labadie
email: pierre.labadie@u-bordeaux.fr

Evidence for the Trophic Transfer of Perfluoroalkylated Substances in a Temperate Macrotidal Estuary

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Halogenated organic compounds encompass a broad range of molecules that have the potential to be persistent, bioaccumulative and toxic, the present cornerstones of chemical hazard evaluation. [START_REF] Gobas | Revisiting bioaccumulation criteria for POPs and PBT assessments[END_REF] Organochlorine pesticides and polychlorinated biphenyls fulfill such criteria and have been the focus of intense regulatory action and monitoring since the 1970s. [START_REF] Muir | Are there other persistent organic pollutants? A challenge for environmental chemists[END_REF] Perfluoroalkyl and polyfluoroalkyl substances (PFASs), in contrast, came under scrutiny more recently (late 1990s) when the occurrence of perfluoroalkyl acids (PFAAs) -notably, perfluoroalkyl carboxylates (PFCAs) and perfluoroalkyl sulfonates (PFSAs)-across multiple environmental media was revealed. [START_REF] Moody | Determination of perfluorocarboxylates in groundwater impacted by fire-fighting activity[END_REF][START_REF] Giesy | Global distribution of perfluorooctane sulfonate in wildlife[END_REF] Since then, academic research on PFOS and related compounds has been extensive, and PFASs have been recognized as ubiquitous pollutants with potential for long range transport. 5, [START_REF] Yeung | Vertical Profiles, Sources and Transport of PFASs in the Arctic Ocean[END_REF] The long-chained PFAAs (i.e. PFCAs bearing 8 or more carbon atoms and PFSAs of 6 or more carbon atoms) are of particular concern due to their partitioning properties and toxicity potential. This provided the grounds for the addition of perfluorooctane sulfonate (PFOS) to Annex B of the Stockholm Convention on persistent organic pollutants (POPs) in 2009. 7 In biota, PFASs are found predominantly in protein-rich compartments such as blood and liver, rather than in lipid-rich tissues, a somewhat unique feature amongst POPs. [START_REF] Martin | Bioconcentration and tissue distribution of perfluorinated acids in rainbow trout (Oncorhynchus mykiss)[END_REF][START_REF] Olivero-Verbel | Perfluorooctanesulfonate and related fluorochemicals in biological samples from the north coast of Colombia[END_REF][START_REF] Conder | Are PFCAs bioaccumulative? A critical review and comparison with regulatory criteria and persistent lipophilic compounds[END_REF] In view of these specific characteristics, the bioaccumulation potential of anionic PFASs such as PFSAs and PFCAs cannot be reliably inferred from the standard octanol-water partitioning coefficient (Kow). In laboratory partitioning experiments, Martin et al. determined bioconcentration factors (BCFs) for rainbow trout exposed to a suite of PFCAs and PFSAs, and observed that their bioaccumulation potential was strongly related to perfluoroalkyl chain length and polar end group nature. [START_REF] Martin | Bioconcentration and tissue distribution of perfluorinated acids in rainbow trout (Oncorhynchus mykiss)[END_REF] Thereafter, in-situ measurement of bioaccumulation factors (BAFs = concentration in biota relative to that of the surrounding water) corroborated that BAFs for PFCAs and PFSAs were positively correlated to perfluoroalkyl chain length. [START_REF] Kwadijk | Distribution of perfluorinated compounds in aquatic systems in The Netherlands[END_REF][START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF][START_REF] Ahrens | Stockholm Arlanda Airport as a source of per-and polyfluoroalkyl substances to water, sediment and fish[END_REF] Concentrations in biota > 5000 times those in water (i.e., Log BAF > 3.7) have been reported for PFOS and C10-C14 PFCAs, 11,12,14 indicative of very bioaccumulative pollutants. [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] Biotasediment accumulation factors (BSAFs = biota wet weight concentration relative to the sediment dry weight concentration) have also been documented, and ingestion of sediment is postulated as a major entry route for PFASs into benthic food webs. 12, [START_REF] Nakata | Perfluorinated contaminants in sediments and aquatic organisms collected from shallow water and tidal flat areas of the Ariake Sea, Japan: environmental fate of perfluorooctane sulfonate in aquatic ecosystems[END_REF][START_REF] Loi | Trophic magnification of poly-and perfluorinated compounds in a subtropical food web[END_REF][START_REF] Bertin | Bioaccumulation of perfluoroalkyl compounds in midge (Chironomus riparius) larvae exposed to sediment[END_REF] In addition to direct exposure to dissolved PFASs, the bioaccumulation of PFASs may occur via dietary uptake, which may be evaluated through the calculation of biomagnification factors (BMFs) (predator-prey concentration ratios), sometimes adjusted according to trophic level (BMFTL). [START_REF] Borgå | Trophic magnification factors: considerations of ecology, ecosystems, and study design[END_REF] Because of differences in biomass and contaminant transfer efficiencies, exponential models have been used to describe the increase of contaminant concentrations through entire food webs. [START_REF] Borgå | Trophic magnification factors: considerations of ecology, ecosystems, and study design[END_REF] Therefore, concentrations are usually Log-transformed prior to regression versus δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] N or trophic level (TL), the antilog of the regression slope yielding the trophic magnification factor (TMF). 19, [START_REF] Jardine | Applications, considerations, and sources of uncertainty when using stable isotope analysis in ecotoxicology[END_REF] TMFs > 1 have been reported for long-chain PFAAs and perfluorooctane sulfonamide (FOSA), strongly suggesting biomagnification potential for these chemicals in aquatic ecosystems. 17,21-26 However, given the wide range of TMF values observed across different food webs, the biomagnification of PFASs remains difficult to predict. Houde et al. have urged prudence in study designs, indicating an overt bias in BMF and TMF calculation when muscle tissue or liver or blood concentrations are used for larger species, while smaller biota species are analyzed as whole individuals or pooled homogenates. [START_REF] Houde | Monitoring of perfluorinated compounds in aquatic biota: an updated review[END_REF] Because they increase the risk of selection biases, small sample sizes can greatly affect the conclusions drawn for studies regarding size-or sex-related PFAS levels in wildlife, 27,28 but a similar comment could in fact apply to biomagnification studies. Even within a spatially and temporally integrated ecosystem, inherent biological variability in a species could lead to contaminant concentrations in some individuals to deviate substantially, which could obscure patterns. Another potential source of confusion lies in the varying abilities of organisms to metabolize PFOS-precursors (e.g., FOSA) and PFCA-precursors (e.g., fluorotelomer unsaturated carboxylates). Hence, the apparent biomagnification potential of PFOS and PFCAs may be inflated. 11, [START_REF] Tomy | Fluorinated organic compounds in an eastern arctic marine food web[END_REF] Other common pitfalls that may affect the validity and reliability of TMFs have been extensively reviewed by Borgå et al. [START_REF] Borgå | Trophic magnification factors: considerations of ecology, ecosystems, and study design[END_REF] Albeit there exists no straight answer to such conundrums, the determination of TMFs could possibly be improved via appropriate study design and robust data treatment procedures. Uncertainties due to sampling design, analytical pitfalls, and statistical issues have been articulated in recent reviews, [START_REF] Borgå | Trophic magnification factors: considerations of ecology, ecosystems, and study design[END_REF][START_REF] Houde | Monitoring of perfluorinated compounds in aquatic biota: an updated review[END_REF][START_REF] Franklin | How reliable are field-derived biomagnification factors and trophic magnification factors as indicators of bioaccumulation potential? Conclusions from a case study on per-and polyfluoroalkyl substances[END_REF] but some aspects remain yet to be addressed in practice. This constituted a first important knowledge gap to be explored. In the present work, several measures were initiated in an attempt to tackle various sources of uncertainty associated with the determination of biomagnification factors. A large set of biota samples (N = 147; 18 taxa) were collected in a spatially and temporally integrated aquatic ecosystem. PFAS concentrations were determined on a whole-body wet weight basis for all biota samples, thus avoiding the BMF/TMF uncertainties arising from different tissues/organs collected at different trophic levels. Original strategies were presented to simultaneously take into consideration left-censored data (non-detects) and the interspecific variability of PFAS levels and δ 15 N. Specific regression approaches based on linear mixed models accounting for censored responses were therefore implemented, involving functions from the NADA and LMEC R-packages. [START_REF] Vaida | Fast implementation for normal mixed effects models with censored response[END_REF] Rather than proposing definite answers to the question of PFAS trophic magnification, the overarching aim of the present study was to provide a practical approach for a more robust determination of TMFs, attempting to control sources of bias as much as possible. Another original contribution was the examination of PFAS trophodynamics in a typical temperate macrotidal estuary. Hitherto, PFAS trophodynamics have been essentially documented in marine 22,24,25 or lake 21,26,31 food webs, while dynamic estuarine systems have seldom been investigated. [START_REF] De Vos | Accumulation of perfluorooctane sulfonate (PFOS) in the food chain of the Western Scheldt estuary: Comparing field measurements with kinetic modeling[END_REF] As noted by Borgå et al., the characteristics of ecosystems, including species composition, productivity, and latitude and longitude, may also exert effects in contaminant exposure and TMF. [START_REF] Borgå | Trophic magnification factors: considerations of ecology, ecosystems, and study design[END_REF] Estuaries typically present different biological and physical features from the previously studied ecosystems. The Gironde estuary (South Western France), the ecosystem under survey, presents a rather intricate trophic web structure, with two intertwined benthic and demersal sub-food webs. [START_REF] Pasquaud | Determination of fish trophic levels in an estuarine system[END_REF] Most common predators in this food web are transient fish speciesjuveniles and sub-adult fish that reside within its waters before sexual maturation and migration offshoreand migratory fish species. The Gironde is a highly dynamic hydrosystem, subject to wide seasonal variations in freshwater discharge, salinity and sediment resuspension. It harbors an almost permanent maximum turbidity zone, stretching over several tens of kilometers, which may play a pivotal role in the exposure pathways of biota and in the sequestration of micropollutants. [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF][START_REF] Sottolichio | A synthesis on seasonal dynamics of highly-concentrated structures in the Gironde estuary[END_REF] To our knowledge, this is the first time a PFAS trophic magnification study of such scope and comprehensiveness has been conducted in an estuarine ecosystem.

Experimental

Chemicals and Standards

A full list of chemicals and solvents is provided in the Supporting Information (SI). Certified PFAS native compounds and isotope-labelled internal standards (ISs) were acquired from Wellington Labs, Inc. (BCP Instruments, Irigny, France). The native PFASs targeted included PFCAs and PFSAs of various chain lengths, perfluorooctane sulfonamide (FOSA), N-alkylated sulfonamides (MeFOSA, EtFOSA) and N-alkylated sulfonamide acetic acids (MeFOSAA, EtFOSAA). [START_REF] Ahrens | Stockholm Arlanda Airport as a source of per-and polyfluoroalkyl substances to water, sediment and fish[END_REF] C2-PFHxA, [START_REF] Ahrens | Stockholm Arlanda Airport as a source of per-and polyfluoroalkyl substances to water, sediment and fish[END_REF] C4-PFOA, [START_REF] Ahrens | Stockholm Arlanda Airport as a source of per-and polyfluoroalkyl substances to water, sediment and fish[END_REF] C2-PFDA, 13 C2-PFUnDA, 13 C2-PFDoA, 13 C4-PFOS, D3-N-MeFOSAA, 13 C8-FOSA, D3-N-MeFOSA, and D5-N-MeFOSA were the isotope-labelled ISs used. Note that, in this paper, L-PFOS refers to the linear isomer of perfluorooctane sulfonate and Br-PFOS to the branched isomers (PFOS = L-PFOS + Br-PFOS). In the case of Br-PFOS, the concentrations were calculated from the calibration curve used for the linear isomer (L-PFOS), and using a closely matched isotope-labelled IS ( 13 C4-PFOS). Details on analyte names, acronyms, structures and corresponding ISs are enclosed in the SI (Table S1).

Description of the study site

Located on the French Atlantic coast, the Gironde estuary (SW France) is one of the largest in Europe (SI Fig. S1). This highly turbid environment is poorly conducive to photosynthesis; hence, detritus rather than phytoplankton is the base of the food web. [START_REF] Lobry | Diversity and stability of an estuarine trophic network[END_REF] The Gironde estuary is subject to high seasonal fluctuations of physicochemical factors (flow rate, salinity, temperature, tide, turbidity) and anthropogenic pressures. However, it is associated with high ecological production and a noteworthy and iconic biodiversity. [START_REF] Lobry | Diversity and stability of an estuarine trophic network[END_REF][START_REF] Lobry | Structure of the Gironde estuarine fish assemblages: a comparison of European estuaries perspective[END_REF][START_REF] David | Long-term changes of the zooplankton variability in a turbid environment: the Gironde estuary (France)[END_REF][START_REF] Selleslagh | Seasonal succession of estuarine fish, shrimps, macrozoobenthos and plankton: Physico-chemical and trophic influence. The Gironde estuary as a case study[END_REF] The Gironde is of great ecological value: it is an important nursery ground for numerous marine fish species of the Bay of Biscay, a migratory corridor for several diadromous fish typical of Western Europe, and the last known natural breeding area of European sturgeon (Acipenser sturio). [START_REF] Lobry | Diversity and stability of an estuarine trophic network[END_REF] In the long run, synergistic effects of climatic change (e.g. temperature increase and salinization) and micropollutants may however durably affect biodiversity. 40-44

Sample Collection and Preparation

A total of 147 biota samples were collected between May and November 2012 in the mesohaline zone of the Gironde estuary. Common seabass (Dicentrarchus labrax, n = 9), spotted seabass (Dicentrarchus punctatus, n = 28), grey mullet (Liza ramada, n = 12), meagre (Argyrosomus regius, n = 12), anchovy (Engraulis encrasicolus, n = 6), sprat (Sprattus sprattus, n = 3), common sole (Solea solea, n = 31) and flounder (Platichthys flesus, n = 13) samples were collected by bottom trawling or dragnet fishing. [START_REF] Selleslagh | Seasonal succession of estuarine fish, shrimps, macrozoobenthos and plankton: Physico-chemical and trophic influence. The Gironde estuary as a case study[END_REF] In parallel, Copepods (Copepoda, ind.), mysids (Mysidacea, ind.), white shrimps (Palaemon longirostris), brown shrimps (Crangon crangon), gammarids (Gammarus spp.) and gobies (Pomatoschistus spp.) were collected with a cone-shaped WP-2 net (mesh: 200 μm). Other benthic invertebrates were collected at low tide along intertidal mudflats of the southern (S t Christoly) and northern banks (Talmont-sur-Gironde, Mortagne) of the estuary (SI Fig. S1).

Fish samples were weighed and measured prior to dissection. All biota samples were freeze-dried (72 h) and ground. Note that small fish and invertebrates were prepared as pooled whole-body homogenates, while muscle tissues were processed for larger fish (> 100 mm). Therefore, a correction factor was determined and used to convert PFAS muscle concentrations into whole-body (w-b) concentrations. The conversion factor generally ranged between 2-3, consistent with previous observations (SI Table S2). [START_REF] De Vos | Accumulation of perfluorooctane sulfonate (PFOS) in the food chain of the Western Scheldt estuary: Comparing field measurements with kinetic modeling[END_REF] Further details regarding the collection and handling of water and sediment samples are provided in the SI.

PFAS Chemical Analyses

Analytes were quantified using the isotopic dilution method, ISs being gravimetrically added to the samples, procedural blanks and reference materials at the beginning of the extraction procedure.

Briefly, water samples (0.5 L) were concentrated using solid phase extraction on Strata X-AW cartridges, while sediment samples (1 g) underwent a microwave extraction with MeOH prior to ENVI-Carb graphite clean-up. [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and perfluoroalkyl substances in freshwater ecosystems: a French nationwide survey[END_REF] Biota samples (~ 250 mg dry weight (dw)) were processed using a microwave extraction with ethanol followed by Strata X-AW/graphite clean-up. [START_REF] Munoz | Spatio-temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to periphytic biofilm in an urban river: case-study on the River Seine[END_REF] PFAS chemical analyses were performed with an Agilent 1200 LC system interfaced with an Agilent 6460 triple quadrupole mass spectrometer (Agilent Technologies, Massy, France). Analyte separation was achieved with a Zorbax Eclipse Plus C18 column using chromatographic conditions described in the SI. Further details on mass spectrometry acquisition parameters are provided elsewhere. [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and perfluoroalkyl substances in freshwater ecosystems: a French nationwide survey[END_REF] Limits of detection (LODs) were determined as described elsewhere [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and perfluoroalkyl substances in freshwater ecosystems: a French nationwide survey[END_REF] and were in the range 0.003-0.3 ng L -1 , 0.001-0.1 ng g -1 dw and 0.002-0.05 ng g -1 wet weight (ww) for surface water, sediment and biota samples, respectively (SI Table S3). Due to the low expected concentration of short-chain (C4-C6) PFCAs in sediments or biota and their background presence in corresponding procedural blanks, the latter were measured only in water samples.

Whole-method recovery was controlled through replicate analyses of mineral water samples (fortified at 1 ng L -1 ), reference sand samples (fortified at 1 ng g -1 dw) and brown trout fillets from the Kerguelen archipelago (Southern Ocean) (fortified at 3 ng g -1 ww), and ranged between 53-134 %, 56-86 % and 51-107 % for the water, sediment, and biota matrices, respectively (SI Tables S4-S6). Whole-method accuracy was determined using mineral water, reference sand and brown trout spiked samples (supplemented with both native analytes and ISs at the start of the preparation procedure) and remained generally between 80-120 % (SI Tables S4-S6). Additionally, a non-spiked spotted seabass sample (dorsal muscle) was used as an in-house control matrix; the relative standard deviation of PFAS concentrations determined in this matrix averaged 6 % (range: 1.8-18 %) (SI Table S7). Matrix effects were evaluated by comparing solvent-based analyte to internal standard area ratios to those of brown trout extracts spiked post-preparation, corrected by the non-spiked sample initial contribution. [START_REF] Munoz | Quantitative analysis of poly-and perfluoroalkyl compounds in water matrices using high resolution mass spectrometry: Optimization for a laser diode thermal desorption method[END_REF] Method trueness was controlled through the analysis of NIST SRM 1947 reference samples (n = 4) (Lake Michigan Fish Tissue) (SI Table S7). The concentrations determined for PFOS and PFCAs were in excellent agreement with previous reports. 31,48,49

Stable Isotope Analyses

To determine the isotopic compositions of biota samples (C and N), freeze-dried biota samples were ground into fine and homogeneous powder with a micro ball mill (25 Hz) and lipids subsequently extracted by accelerated solvent extraction. [START_REF] Bodin | ASE extraction method for simultaneous carbon and nitrogen stable isotope analysis in soft tissues of aquatic organisms[END_REF] Samples were weighed (0.2 ± 0.1 mg) in tin capsules and stable isotope ratios determined using a Thermo Finnigan Delta V EA-IRMS (Elemental Analyzer -Isotope Ratio Mass Spectrometry) with a Conflo IV interface. Carbone and nitrogen isotope compositions were expressed as per mil (‰) in the δ notation relative to Vienna PeeDee Belemnite (vPDB) and atmospheric N2, respectively. Isotopic analyses were performed in triplicate for each biota sample and standard deviations remained in the range 0.03-0.23 ‰ for δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] N and δ [START_REF] Ahrens | Stockholm Arlanda Airport as a source of per-and polyfluoroalkyl substances to water, sediment and fish[END_REF] C values of an in-house control mussel matrix averaged 13.57 ± 0.18 ‰ and -14.18 ± 0.17 ‰, respectively (multibatch replicate measurements, n = 9) (quality control chart provided in Fig. S2 of the SI).

Determination of Trophic Levels and TMFs

Trophic levels were calculated according to the formula for two food source: TL = λ + [δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] Nconsumer -{α δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] Nbase1 + (1 -α) δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] Nbase2}] / Δn, where λ is the estimated trophic position of the organism at the base of the food web (for primary consumers, λ = 2), δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] Nbase1 and δ 15 Nbase2 are the mean δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] N of the baseline organisms for the benthic and demersal food webs, respectively, and Δn is the mean trophic fractionation of δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] N across two successive trophic levels (Δn = 3.4 ‰, as per Post). [START_REF] Post | Using stable isotopes to estimate trophic position: models, methods, and assumptions[END_REF] α is a coefficient used to adjust the relative importance of each nitrogen food source for a given consumer, derived in our case from the known feeding ecology of fish from the Gironde estuary food web (see Table S8 of the SI). [START_REF] Pasquaud | Determination of fish trophic levels in an estuarine system[END_REF] For all the fish taxa considered, it was deemed acceptable to consider that the benthic and intermediate pelagic sources were the major food sources, since the contribution of other sources to the diet (i.e., detritic or phytoplanktonic sources) remained below 15 % on average. [START_REF] Pasquaud | Determination of fish trophic levels in an estuarine system[END_REF] In the case of zooplankton, small pelagic fish (anchovy, sprat) and shrimps, α was set at 0, while benthic invertebrates (ragworm, shore crab and gammarids) were assigned the value of α = 1.

The R statistical software (R version 2.15.3, R Core Team, 2013) and Sigmaplot TM 11.0 (Systat Software) were used to conduct data analysis. Statistical significance was set at p < 0.05. In view of the presence of non-detect data, functions from the NADA (Non-detects And Data Analysis) and LMEC (Linear Mixed-Effects Models with Censored Responses) R-packages were used to perform regression analyses. Logarithm-transformed PFAS concentrations were plotted against trophic level, the TMF being subsequently obtained as 10 slope .

Two regression approaches were considered in parallel. The cenken function (NADA) imputes nondetects based on the distribution of observed data prior to determination of the Akritas-Theil-Sen (ATS) line (slope, intercept, and Kendall's τ nonparametric correlation coefficient). In an attempt to consider non-detect data as well as inter-species variability of δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] N and PFAS levels (random effects), we used a linear mixed effect model with censored responses, implemented in R via the function lmec. [START_REF] Vaida | Fast implementation for normal mixed effects models with censored response[END_REF] The latter model was as follows: Log Concentration = ~ TL + (1|Species), i.e. a standard linear regression between log concentration and trophic level, but including a random effect on species. This approach should also account for the TMF distortion due to differences in number of samples between taxa (e.g. Nspotted seabass >> Nsprats) (see also Table S10 of the SI). Scripts for the cenken and lmec procedures are provided in the SI. Statistically significant biomagnification (i.e. TMF <1 or >1) was based on the p-value for the cenken procedure (i.e. p< 0.05), while the criterion examined for the lmec procedure was based on the 95% confidence interval (i.e. the 95% confidence interval associated to the slope of the regression should not include the zero value). Also note that compounds with more than 80 % censored observations were not considered in the determination of TMFs since tenuous statistics may be obtained above this threshold.

Results and discussion

Trophic Levels

The Gironde estuary is characterized by two intertwined sub-food webs, a benthic food web mainly composed of flat fish (sole, flounder), endobenthic invertebrates (polychaetes, clams), and epibenthic crustaceans (shore crab, gammarids), and a bentho-pelagic ('demersal') food web dominated by top predators (seabass, meagre) that may feed on both intermediate pelagic (e.g., zooplankton, shrimps, small pelagic and juvenile fish) and benthic food sources. [START_REF] Pasquaud | Determination of fish trophic levels in an estuarine system[END_REF] Individual δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] [START_REF] Pasquaud | A preliminary investigation of the fish food web in the Gironde estuary, France, using dietary and stable isotope analyses[END_REF] Oysters and scrobicularidae displayed consistently low δ 15 N (7.7 ± 1.1 and 7.3 ± 1.1 ‰, respectively) and were used as baseline organisms (TL = 2) for the determination of TLs of higher-level consumers (see also Section 2.6).

PFAS concentrations in Surface Water and Sediments

Among the 23 PFASs analyzed, 15 were detected in surface water samples (n = 6). ΣPFASs ranged between 4.2-7.9 ng L -1 , individual compounds generally remaining at sub ng L -1 levels (SI Table S9).

PFOS prevailed over other PFASs (23 ± 3 % of ΣPFASs), followed by C5-C8 PFCAs (between 8-15 % each) and PFHxS (8 ± 1 %). In sediment samples (n = 5), 18/20 PFASs were detected. With an average ΣPFASs of 1.2 ± 0.3 ng g -1 dw, levels in sediments remained in the same order of magnitude than those reported at French nationwide scale (mean ΣPFASs = 1.8 ng g -1 dw). [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and perfluoroalkyl substances in freshwater ecosystems: a French nationwide survey[END_REF] The highest level of PFAS in sediments was that of PFOS (0.38 ± 0.11 ng g -1 dw), followed by C8-C12 PFCAs (0.077 ± 0.030 to 0.13 ± 0.037 ng g -1 dw) (SI Table S9).

PFAS Levels and Composition Profiles in Biota

Overall detection frequencies and concentration ranges of PFASs in biota are reported in Table 1, and the mean ΣPFASs across taxa is illustrated in Fig. 1 (see also Table S10 of the SI for concentration ranges of individual PFASs and ΣPFASs for each species). In biota samples (n = 147), L-PFOS and FOSA displayed the highest detection frequencies (DF) (100 %), and C9-C13 PFCAs were almost systematically detected (DF = 86-95 %). Average ΣPFASs in fish were in the range 4.6-20.7 ng g -1 ww w-b, a moderate burden compared to concentrations reported in some Canadian lakes, 21,31 but in the same order of magnitude than total concentrations in fish from Sarasota Bay (Florida, USA) and Mai Po Marshes (Hong Kong, China). 17, [START_REF] Houde | Biomagnification of perfluoroalkyl compounds in the bottlenose dolphin (Tursiops truncatus) food web[END_REF] PFAS concentrations in juveniles of flounder (length = 25-95 mm; ΣPFASs range = 20-44 ng g -1 ww w-b) were significantly higher than those in larger specimens (length = 140-340 mm; median ΣPFASs = 3.7 ww w-b). In addition, for both common sole and spotted seabass, a negative linear relationship was observed between ∑PFASs and length (R 2 : 0.23-0.43, p < 0.01). This is concordant with Lescord et al. who reported mean ΣPFASs between 1.5-4.3 times higher in juvenile Arctic char (Salvelinus alpinus) than in adult char at 4/6 Canadian lake sampling sites. [START_REF] Lescord | Perfluorinated and polyfluorinated compounds in lake food webs from the Canadian high arctic[END_REF] A significant decreasing trend of ΣPFASs with increasing age was also observed in bottlenose dolphins from southeast US estuaries. [START_REF] Fair | Assessment of perfluorinated compounds (PFCs) in plasma of bottlenose dolphins from two southeast US estuarine areas: relationship with age, sex and geographic locations[END_REF] Lower PFAS concentrations in adults compared to juveniles are possibly a consequence of growth dilution and changes in diet or metabolic rates with increasing age. A plausible additional explanation in our specific case might lie in the different life traits displayed by juveniles of fish that remain confined to the estuarine area; they might therefore be subject to enhanced PFAS exposure compared to larger subadult specimens that may occasionally venture into offshore coastal waters. Median ΣPFAS levels in sole (20.4 ng g -1 ww w-b) were nearly two-fold higher than those in pelagic fish (9.3, 9.6 and 10 ng g -1 ww w-b for common seabass, spotted seabass and meagre, respectively). Relatively high PFAS levels were also found in the endobenthic polychaete Nereis diversicolor compared to other invertebrates, ΣPFASs reaching up to 45 ng g -1 ww w-b. This concurs with previous observations by Nakata et al. who also reported elevated ΣPFASs in lugworms Arenicola marina from the Ariake Sea food web (ΣPFASs ~ 80 ng g -1 ww w-b), greatly exceeding those in bivalves or crabs. [START_REF] Nakata | Perfluorinated contaminants in sediments and aquatic organisms collected from shallow water and tidal flat areas of the Ariake Sea, Japan: environmental fate of perfluorooctane sulfonate in aquatic ecosystems[END_REF] PFASs are relatively water soluble, which could promote direct exposure of biota. However, taken together, the above findings further suggest that the ingestion of sediments may play a critical role in PFAS accumulation for sediment-dwelling organisms. Low total PFAS concentrations were observed in oyster and peppery furrow shell, ΣPFASs ranging between 0.66-1.2 and 0.89-1.3 ng g -1 ww w-b, respectively, in excellent agreement with So et al. [START_REF] So | Alkaline digestion and solid phase extraction method for perfluorinated compounds in mussels and oysters from south China and Japan[END_REF] The low bioaccumulation potential of PFASs filter-feeders may be a result of overall low affinity binding (reversible uptake), while elimination of the higher affinity binding PFAS fraction might be mediated via multixenobiotic resistance transporter proteins. [START_REF] Stevenson | New perspective on perfluorochemical ecotoxicology: Inhibition and induction of an efflux transporter in the marine mussel, Mytilus californianus[END_REF] L-PFOS was generally the dominant PFAS in biota, albeit with some species-specific characteristics (SI Fig. S4). In pelagic organisms, L-PFOS represented 49 ± 11 % of ΣPFASs on average, followed by FOSA and PFDA (18 ± 14 % and 6.7 ± 4 % of ΣPFASs, respectively), while long-chain PFCAs (C11-C14) were less prominent (0.5-3.7 % of ΣPFASs each, on average). The congener patterns observed are in excellent agreement with previous reports. for one exceedance (SI Fig. S5). In gammarids, PFOA was the second most abundant congener after L-PFOS (15 ± 15 % Vs 32 ± 8 % of ΣPFASs), akin to patterns reported for Gammarus wilkitzkii from the Barents Sea. [START_REF] Haukas | Bioaccumulation of per-and polyfluorinated alkyl substances (PFAS) in selected species from the Barents Sea food web[END_REF] The relative abundance of FOSA invariably exceeded that of L-PFOS in oysters (74 ± 7 % Vs 12 ± 7% of ΣPFASs). This distinctive pattern is consistent with profiles observed in shellfish from the Seine and Loire estuary (France), [START_REF] Munschy | Levels and Trends of the Emerging Contaminants HBCDs (hexabromocyclododecanes) and PFCs (perfluorinated Compounds) in Marine Shellfish along French Coasts[END_REF] green-lipped mussels Perna viridis from the Chinese coast, [START_REF] So | Alkaline digestion and solid phase extraction method for perfluorinated compounds in mussels and oysters from south China and Japan[END_REF] and mussel standard reference material SRM 2974a, [START_REF] Reiner | Determination of perfluoroalkyl acid concentrations in biological standard reference materials[END_REF] and could be related to the lower metabolic capacity of filter-feeding bivalves as regards the biotransformation of PFOSprecursors such as FOSA.

In order to investigate the influence of life traits (e.g., benthic Vs demersal) on PFAS accumulation profiles, it has been previously suggested to examine PFOA/PFOS concentration ratios. [START_REF] Nakata | Perfluorinated contaminants in sediments and aquatic organisms collected from shallow water and tidal flat areas of the Ariake Sea, Japan: environmental fate of perfluorooctane sulfonate in aquatic ecosystems[END_REF] In our case, this approach could not be implemented as such due to the lower detection frequency of PFOA (63 %) relative to L-PFOS (100 %). Instead, we attempted to consider PFNA and FOSA Vs L-PFOS, compounds of low censoring percentages (0-9 %). Average PFNA/L-PFOS concentration ratios in flatfish were 1-2 orders of magnitude higher than those of pelagic fish. Likewise, benthic invertebrates showed relatively high PFNA/L-PFOS ratios (2.0 ± 1.0 and 0.58 ± 0.28 for ragworm and shore crab, respectively) compared to other invertebrates (Fig. 2). This is consistent with Nakata et al. who observed higher PFOA/PFOS ratios in tidal flat organisms than those from shallow water. [START_REF] Nakata | Perfluorinated contaminants in sediments and aquatic organisms collected from shallow water and tidal flat areas of the Ariake Sea, Japan: environmental fate of perfluorooctane sulfonate in aquatic ecosystems[END_REF] Another similarity between ragworm and shore crab was the prevalence of other PFCAs: these species were the only ones with concentrations of PFHpA above 1 ng g -1 ww w-b, and had the highest PFOA/L-PFOS concentration ratios (1.4 ± 0.6 and 0.94 ± 0.08 for ragworm and shore crab, respectively).

Previous laboratory and field studies have demonstrated that FOSA and related derivatives could biotransform to PFOS, for instance via microbially-mediated transformation in soils or sediments [START_REF] Benskin | Biodegradation of N-ethyl perfluorooctane sulfonamido ethanol (EtFOSE) and EtFOSE-based phosphate diester (SAmPAP diester) in marine sediments[END_REF][START_REF] Mejia-Avendaño | Generation of perfluoroaklyl acids from aerobic biotransformation of quaternary ammonium polyfluoroalkyl surfactants[END_REF] as well as via ingestion and in vivo metabolization in higher order organisms. [START_REF] Martin | PFOS or PreFOS? Are perfluorooctane sulfonate precursors (PreFOS) important determinants of human and environmental perfluorooctane sulfonate (PFOS) exposure?[END_REF] Galatius et al. reported a high degree of variability of FOSA to PFOS ratios across marine mammal species. [START_REF] Galatius | PFAS profiles in three North Sea top predators: metabolic differences among species?[END_REF] Possible explanations include different metabolic capacities 61,62 as well as differences in exposures between distant sampling locations or over time as regulations regarding PFOS and related precursors come into effect. [START_REF] Dassuncao | Temporal Shifts in Poly-and Perfluoroalkyl Substances (PFASs) in North Atlantic Pilot Whales Indicate Large Contribution of Atmospheric Precursors[END_REF] In the present survey, the samples were collected within a relatively short period of time and over a geographically limited area; this could have contributed to limit the interspecific variability of precursors/PFAA ratios. In most organisms from the present survey, FOSA/L-PFOS ratios were < 1 (Fig. 2b), concurring with previous observations by Martin et al. in a Lake Ontario food web. [START_REF] Martin | Perfluoroalkyl contaminants in a food web from Lake Ontario[END_REF] Average FOSA/L-PFOS concentration ratios did not span more than 2 orders of magnitude, with maximum values for oysters (7.4) and sprats (6.9) and minimum values for benthic fish and crabs (0.080-0.15) (Fig. 2b). When examining each food web separately, it was apparent that FOSA/L-PFOS ratios remained within a rather consistent range of values for all taxa (i.e. both invertebrates and fish). For the demersal food web for instance, even when excluding the two outliers (i.e. oysters and sprats), no significant difference in mean FOSA/L-PFOS ratios was detected between invertebrates and fish. In the absence of clear differences between invertebrates and fish for each food web, it was hypothesized that biotransformation of FOSA at different metabolic rates between species would not play a major role in the transfer of PFOS in the Gironde estuary food webs. While the four other FOSA-related compounds were not preponderant in water, sediment, or biota samples, the possible contribution of other PFAA precursors (not targeted in the present survey) could not entirely be ruled out.

Ragworm

Bioaccumulation

Regardless of taxa, average BAFs were consistently high for FOSA (7430-151200), followed by PFUnDA (1030-54400), L-PFOS (122-7490) and PFDA (89-7370), while those of shorter-chain compounds were sensibly lower (e.g., 9.5-697 and 20-1250 for PFHxS and PFOA, respectively) (SI Table S11). This again underscores the importance of perfluoroalkyl chain length and polar end group nature on PFAS bioaccumulation. For C8-C11 PFCAs (i.e. PFCAs bearing 7-10 perfluoroalkyl carbon atoms), Log BAF evolved in a linearly fashion with perfluoroalkyl chain length, each additional -CF2 moiety contributing to an increase of 0.59 ± 0.10 log units (slope range for the different taxa considered: 0.45-0.77), in reasonable agreement with previous reports. 11 -13 With the notable exception of Scrobicularidae, BSAFs did not follow the linear chain-length dependency in the benthic food web. Higher values were actually observed for PFNA and PFDA than for C11-C14 PFCAs, or for PFHxS than for PFOS (SI Table S12). For instance, BSAFs in Nereis diversicolor were consistently high for PFNA (BSAF = 61 ± 15) and increased linearly from PFHpA to PFNA (+ 23 on average for each additional -CF2), while those of long-chain PFCAs (C11-C14) were in the narrow range 1.2-5.5 on average. Similar trends were observed in a bioaccumulation experiment under controlled laboratory conditions, the BSAFs of the oligochaete Lumbriculus variegatus being significantly higher for C8-C10 PFCAs than for C11-C12 PFCAs, verified in organisms exposed to either spiked or non-spiked sediments. [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF] As discussed in Higgins et al., the relatively high bioaccumulation of PFNA in worms might be a consequence of a lower elimination rate constant of this compound. [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF] The distinctive BSAF patterns of Scrobicularidae may be related to different exposition pathways:

Scrobicularidae are deposit-feeders while ragworms can alternate between predation, deposit-feeding and filter-feeding. 65

Food Web Biomagnification

It has been previously hypothesized that biological variables such as different protein content could be an influential factor of BMF and TMF estimation for proteinophilic contaminants such as PFASs, [START_REF] Houde | Monitoring of perfluorinated compounds in aquatic biota: an updated review[END_REF][START_REF] Franklin | How reliable are field-derived biomagnification factors and trophic magnification factors as indicators of bioaccumulation potential? Conclusions from a case study on per-and polyfluoroalkyl substances[END_REF] while other components, such as phospholipids, could also play a role in PFAS uptake. [START_REF] Armitage | Development and evaluation of a mechanistic bioconcentration model for ionogenic organic chemicals in fish[END_REF] Protein normalization of PFAS concentrations, although infrequently applied, 24 may be useful when different tissues/organs are collected at different trophic levels. In the present study, the trophic level span was typically shorter than in previous studies and concentrations were determined on a whole-body wet weight basis for all biota samples. Additionally, the interspecific protein content of crustaceans and a large number of fish species from the adjacent Bay of Biscay has been shown to vary within a rather limited range (~15-20 % ww). [START_REF] Spitz | Proximate composition and energy content of forage species from the Bay of Biscay: high-or low-quality food?[END_REF] In view of the aforestated, we did not attempt at normalizing PFAS concentrations to protein levels for bioaccumulation and biomagnification assessment.

Predator-prey biomagnification factors (BMFs) were calculated by dividing the pollutant concentration in the predator by the mean of that of its prey. Mean BMFs were generally > 1 for L-PFOS (Fig. 3), FOSA, and long-chain PFCAs, suggesting biomagnification (see also Table S13 of the SI). Likewise, BMFs corrected for trophic level (BMFTL) were also often > 1 (SI Table S14).

Trophic magnification factors (TMFs) could be more reliable indicators than BMFs since the concentration of contaminants is examined across food webs through a continuous x-variable such as δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] N or TL, contrary to BMFs that are typically examined for exclusive predator-prey couples (a rather unrealistic assumption). However, inconsistent results may still be obtained for TMFs if study design and data treatment are not appropriately addressed. [START_REF] Borgå | Trophic magnification factors: considerations of ecology, ecosystems, and study design[END_REF] These include, for instance, the choice of the organism for the baseline of the food web, seasonal variations in contaminant levels or δ 15 N (especially for lower TLs), analytical considerations such as matrix effects, and data analysis such as the importance of the statistical treatment of non-detects (data < LOD). In the present study, TLs were determined based on the formula for two food sources, referring to the two dominant food webs in the system. In the case of higher-order consumers, the coefficients for each baseline δ [START_REF]REACh Annex XIII on Criteria for the identification of persistent, bioaccumulative and toxic substances, and very persistent and very bioaccumulative substances[END_REF] N were adjusted according to relative percentage diet compositions (Section 2.6). It was documented that PFAS levels and profiles remained relatively stable at the water-year scale in water, sediment and biota (i.e. maximum/minimum concentration ratio <2.5 in water or zooplankton) (unpublished data). Therefore, the fact that sampling was spread over a five-month period should not have excessively affected TMFs. Differing matrix effects between samples may possibly lead to inaccurate quantitation and hence bias the determination of TMF. The use of adequate isotopelabelled ISs (added prior to extraction) can to some extent compensate for variable recovery and matrix effects between samples. In our case, low to moderate matrix effects were obtained regardless of analyte concentration over the tested range (SI Table S15). This was achieved by combining a relatively small sample size (250 mg), efficient purification, and isotopic dilution using matched or closely-matched isotope-labelled ISs for all target analytes (Section 2).

It has been also suggested that the substitution of non-detects by a single arbitrary value (e.g., 0.5 x LOD or DF x LOD), although a rather common practice, has no theoretical basis and may lead to poor correlation estimates. [START_REF] Helsel | Statistics for Censored Environmental Data Using Minitab and R[END_REF] To circumvent this, more statistically robust methods have been developed, wherein a lognormal distribution is usually fitted to the data set prior to the imputation of unknown observations. [START_REF] Helsel | Statistics for Censored Environmental Data Using Minitab and R[END_REF] In the case of PFUnDA in the intermediate demersal food web, for instance, relatively high TMFs were generated when using a substitution by 0.5 x LOD or DF x LOD (p < 0.0001; R² = 0.23-0.24; TMF = 3.2-3.7) (Fig. 4), while an alternative technique such as the Akritas-Theil-Shen estimator (cenken function) suggested a non-significant relationship (p = 0.08; Kendall's τ = 0.13; slope = 0.15; TMF = 1.4). The conclusions were similar when applying a linear mixed effect model with censored responses, the regression slope returned by the lmec function being non-significantly different from 0 (0.86 ≤ TMF ≤ 1.01) (Fig. 4). This again shows that the use of substitution, even at low censoring percentages (< 12 % non-detects for PFUnDA in the intermediate demersal food web), leads to such a distortion of TMFs that conflicting conclusions can be drawn.

The regressions between TL and the logarithm of PFAS concentrations (wet weight whole-body basis) using lmec yielded TMFs in the range 0.18-1.5 and 0.33-6.0 for the demersal and benthic food webs, respectively (Table 1). Note that analogous results were produced with cenken (SI Table S16). TMFs for all taxa combined (N = 147) are also provided (SI Table S17) and revealed significant biomagnification for C8-C12 PFCAs, PFHxS, PFOS and FOSA. In the demersal food web, TMFs were significantly > 1 for PFDoDA, PFHxS, Br-PFOS and FOSA (TMF range: 1.2-1.5), while those of other PFCAs were in the range 0.88-1.2 and that of L-PFOS significantly < 1 (TMF = 0.94). These findings differ from lacustrine or coastal food webs from Northern America (e.g., TMFPFOS = 5.8-6.3), 21,23 but are not dissimilar to those reported in some freshwater food webs from China. [START_REF] Lescord | Perfluorinated and polyfluorinated compounds in lake food webs from the Canadian high arctic[END_REF] In addition to food web structure, differences in TMFs among studies may be related to differences in study design and calculation methodology. In the benthic food web, TMFs were > 1 for nearly all the compounds considered. Another salient feature of the benthic food web was the particularly high TMFs of PFOA and PFNA (6.0 and 3.1, respectively). In fact, TMFs computed for benthic taxa followed an exponential decrease with increasing perfluoroalkyl chain length for C8-C14 PFCAs (SI Fig. S6). Previous studies reported different trends in pelagic marine Arctic food webs 24,25 or in temperate lakes, [START_REF] Fang | Trophic Magnification and Isomer Fractionation of Perfluoroalkyl Substances in the Food Web of Taihu Lake, China[END_REF] which indicates that PFAS chemical structure might not be necessarily predictive of TMFs in aquatic ecosystems and further suggests that biomagnification is influenced by the ecosystem characteristics. [START_REF] Borgå | Trophic magnification factors: considerations of ecology, ecosystems, and study design[END_REF] TMFs were significantly < 1 in the benthic food web for PFTrDA and PFTeDA, suggesting apparent biodilution (Table 1). Likewise, the linear isomer of PFOS (TMF = 2.5) was less readily biomagnified than PFHxS or Br-PFOS (TMF = 3.9-4.3).

In summary, higher levels of PFASs were generally found in benthic-dwelling biota, with differing bioaccumulation profiles compared to pelagic biota. In the benthic food web, trophic magnification was more pronounced for PFHxS, PFOA or PFNA than for their longer-chain analogs, while no particular trend emerged in the demersal food web. This study stresses once again that the validity of TMFs hinges on appropriate study design and data treatment. In future work studying the influence of environmental and ecological parameters on PFAS bioaccumulation and biomagnification potential, the authors reiterate the need for appropriate sampling design, well-vetted analytical methods, and suitable statistical procedures. To endorse conclusions based on laboratory-or field-derived measurements, contaminant concentrations should be standardized across the species studied (e.g., whole body burden). Particular care should also be given to seasonal variations in levels of contaminants and δ 15 N, analytical artifacts, and statistical processing of left-censored data. In that respect, substitution approaches of non-detects (e.g., 0.

  N. Every 10-15 analyses, IAEA-N2 (δ 15 N = 20.3 ‰) and USG-24 (δ 13 C = -16.1 ± 0.2 ‰) reference materials were run to control for analytical drift, and averaged 20.59 ± 0.07 ‰ (n = 15) and -15.82 ± 0.26 ‰ (n = 28), respectively.

  N values were in the range 5.1-15.4 ‰. Mean δ 15 N values of the ichthyofauna were in the following order: meagre ~ common seabass ~ spotted seabass > sole > flounder > mullet ~ sprat ~ goby > anchovy (SI Fig.S3), in good agreement with Pasquaud et al. 33,

Fig. 1 .

 1 Fig.1. Mean total PFAS concentrations (ΣPFASs) in fish and invertebrates from the Gironde estuary (grey bars: benthic food web; blue bars: demersal food web). Concentrations are expressed in ng g -1 wet weight (ww) whole-body (w-b) (juv. = juveniles). Error bars correspond to standard deviation.

FOSAFig. 2 .

 2 Fig.2. Evolution of the PFNA / L-PFOS (2.a) and FOSA / L-PFOS (2.b) concentration ratios across biota species collected in the Gironde estuary (juv. = juveniles). Grey bars: benthic food web; blue bars: demersal food web.

Fig. 3 .

 3 Fig.3. Illustration of the biomagnification factors (BMFs) (mean ± standard deviation) of L-PFOS (blue font) and FOSA (red font) in a demersal (3.a) (not shown: meagre A. regius, common seabass D. labrax) and benthic (3.b) Gironde estuary food web.

17

 17

  ,

19 , 29 Fig. 4 .

 19294 Fig.4. Illustration of Log (CPFUnDA) (concentrations expressed in ng g -1 ww whole body) Vs trophic level (TL) regression lines and the resulting TMFs in the case of the intermediate demersal food web, using traditional substitution techniques (substitution of non-detects by either 0.5 x LOD or DF x LOD) (DF: detection frequency) and an alternative approach based on linear mixed effect models with censored responses (LMEC).

  5 x LOD) should be avoided. Environmental factors not considered in the present study (e.g. salinity gradient), biological variables (e.g. sex, physical condition), as well as potential exposure to additional co-occurring precursors, could also possibly influence the bioaccumulation and biomagnification potential of perfluoroalkyl acids at land/sea interfaces. 27,49,70-72 Associated content Supporting Information. Chemicals and solvents, collection of water and sediment samples, LC-MS/MS operating details, R scripts for the determination of TMFs via cenken and lmec, analytical method validation, QA/QC, stable isotope signature of biota samples, determination of muscle to whole-body PFAS concentrations, values for the α and (1 -α) coefficients, PFAS concentration ranges in surface water and sediment samples, PFAS mean abundance profiles for each biota species, PFAS concentration ranges in biota samples, bioaccumulation and biomagnification factors, trophic magnification factors via cenken.

Table 1 .

 1 Overall detection frequency (%) and concentration range (min-max) (ng g -1 wet weight whole-body (ww w-b)) of PFASs in biota from the Gironde estuary food web (N = 147) and summary of trophic magnification factors (TMFs). TMFs were determined with a linear mixed effect model with censored responses (lmec function of the LMEC R-package) (TMF estimate, TMF 95 % confidence interval, and Akaike information criterion AIC). TMFs significantly different from 1 are indicated in bold.

		Detection Frequency (%)	Concentration range (min-max) (ng g -1 ww w-b)	TMFBENTHIC (n = 67) Estimate [95%] (AIC)	TMFDEMERSAL (n = 80) Estimate [95%] (AIC)
	PFHpA	18	ND*-1.7	NC**	NC
	PFOA	63	ND-8.2	6.0 [5.0;7.3] (120)	1.0 [0.91;1.1] (101)
	PFNA	91	ND-12	3.1 [2.7;3.5] (116)	0.88 [0.81;0.97] (122)
	PFDA	95	ND-4.1	1.7 [1.6;1.9] (100)	0.96 [0.91;1.0] (74)
	PFUnDA	90	ND-4.0	1.8 [1.6;2.0] (139)	0.93 [0.86;1.0] (110)
	PFDoDA	93	ND-2.8	1.1 [0.94;1.2] (150)	1.3 [1.1;1.4] (154)
	PFTrDA	86	ND-2.4	0.66 [0.49;0.87] (196)	0.96 [0.89;1.0] (120)
	PFTeDA	59	ND-0.35	0.33 [0.20;0.54] (221)	1.2 [1.0;1.5] (246)
	PFHxS	62	ND-1.3	4.3 [3.5;5.1] (116)	1.5 [1.2;1.9] (196)
	PFHpS	31	ND-1.1	NA***	NA
	Br-PFOS	95	ND-6.6	3.9 [3.3;4.6] (156)	1.5 [1.3;1.6] (124)
	L-PFOS	100	0.085-22	2.5 [2.3;2.6] (81)	0.94 [0.92;0.97] (33)
	PFDS	21	ND-0.077	NA	NA
	MeFOSAA	50	ND-0.58	NA	0.18 [0.08;0.42] (287)
	EtFOSAA	30	ND-0.43	NA	NA
	FOSA	100	0.057-5.4	2.3 [2.2;2.4] (237)	1.2 [1.20;1.25] (8)
	MeFOSA	1	ND-0.080	NC	NC
	ΣPFASs	-	0.66-45	-	-

*ND: not detected (< LOD). **NC: not calculated (censoring percentage > 80 %). ***NA: not available.

Acknowledgments

The authors are thankful to Virginie Bocquet, Emmanuel Geneste, and Patrick Pardon for their contribution to this study. Excellent assistance in field work (zooplankton and nekton harvesting) was provided by Mariange Cornet and Nathalie Tapie. This study has been carried out under the framework of the PFC-Gironde CNRS project (EC2CO-Ecodyn INSU) and with financial support from the French National Research Agency (ANR). This study was conducted in the frame of the 'Investments for the future' Program, within the Cluster of Excellence COTE (ANR-10-LABX-45). IdEx Bordeaux (ANR-10-IDEX-03-02) provided the PhD grant allocated to G. Munoz. The authors also acknowledge funding from ORQUE SUDOE (SOE3/P2/F591), as well as the Aquitaine Regional Council and the European Union (CPER A2E project). Europe is moving in Aquitaine with the European Regional Development Fund (FEDER).


P Monneyron

M.-H Manero

J.-N Foussard

F Benoit-Marquiã

M.-T Maurette
email: maurette@chimie.ups-tlse.fr

Heterogeneous photocatalysis of butanol and methyl ethyl ketone-characterization of catalyst and dynamic study

Keywords: Adsorption, Photochemistry, VOC, H igh silica zeolites, TiO 2, Di usion

New titanium dioxide (TiO2) based catalysts were prepared by impregnating commercial zeolites in pellets form using a sol-gel technique. Characterization was done with chemical analysis, X-Ray di raction, scanning electron microscopy, and BET measurements, together with volatile organic compounds (VOC) adsorption equilibrium experiments. TiO2 happened to ÿx on the inert binder leading to a close intimacy of mixing with the zeolites crystallites, without signiÿcant modiÿcation of support properties. A di usion cell was used to produce dilute polluted air streams for dynamic experiments, in which adsorption and photodegradation phases were alternatively carried out. Regeneration of adsorbent was evaluated regarding experimental conditions. Through a comparison with the results obtained on impregnated mesoporous borosilicate beads, it was clariÿed that zeolite supports had no e ect on 1-butanol (BuOH ) photooxidation mechanisms. Yet, evidence for mass transfer limitation was found, and attributed to intracrystalline di usion in zeolites.

Introduction

Volatile organic compounds (VOC) are major air pollutants coming largely from industrial processes. Thus, puriÿcation of e uents is of great interest for chemical engineering, and one of the main techniques available towards dilute polluted airstreams is adsorption onto a porous material. This process is usually conducted in two steps, since the saturated material requires regeneration (Le [START_REF] Cloirec | Les composà es organiques volatils dans l'environnement[END_REF][START_REF] Salden | Multifunctional adsorber/reactor concept for waste-air puriÿcation[END_REF]. Alternatively, photooxidation of air pollutants has been largely developed using the classical UV-sensible catalyst, titanium dioxide (TiO 2 ) [START_REF] Ollis | Photocatalytic puriÿcation and treatment of water and air[END_REF][START_REF] Legrini | [END_REF]. Most of the current wide interest in using TiO 2 in catalytic studies stems from the highly reactive radicals (OH • and O •- 2 ) formed when irradiated together with handling facilities (Al-Ekabi, Serpone, Pelizetti, & Minero, 1989). Nevertheless, since TiO 2 is mainly produced in powder form, which is technologically impracticable in continuous engineering processes, many attempts have been made to prepare supported catalysts, using glass beads (Xu & Chen, 1990), ÿber glass [START_REF] Robert | [END_REF]Mattews, 1987), silica (Sato, 1988), stainless steel (Zhu, Zhang, Wang, Fu, & Cao, 2001), ÿber textile (Ku, Ma, & Shen, 2001), quartz beads (Benoit-Marquià e, 1997), honeycomb (Fernandez, et al., 1995), activated carbon (Nozawa, Tanigawa, Hosomi, Chikusa, & Kawada, 2001;[START_REF] Takeda | In uence of carbon black as an adsorbent used in photocatalyst ÿlms on photodegradation behaviors of propyzamide[END_REF], and zeolites (Green & Rudham, 1993). Besides a large adsorption capacity, high silica zeolites (HSZ) exhibit notably a very low dependence on e uent humidity, contrary to activated carbon (Brosillon, Manero, & Foussard, 2001a, b), and on compound's polarity, which may be of particular interest since non-polar molecules hardly adsorb on pure TiO 2 . In order to develop enhanced photoactivity of titanium dioxide, investigators elaborated very di erent methods to support active titanium on zeolites, from simple amalgam of powders through mechanical mixing [START_REF] Hashimoto | Photocatalytic oxidation of nitrogen oxide over titania-zeolite composite catalyst to remove nitrogen oxides in the atmosphere[END_REF] or with papermaking techniques [START_REF] Ichiura | Photocatalytic decomposition of VOC by Zeolite-TiO 2 composite sheet prepared using papermaking technique[END_REF] to chemical vapor deposition [START_REF] Ding | Synthesis of anatase TiO 2 supported on porous solids by chemical vapor deposition[END_REF], cation exchange [START_REF] Kim | TiO 2 /Y-Zeolite encapsulating intramolecular charge transfer molecules: A new photocatalyst for photoreduction of methyl orange in aqueous medium[END_REF] or direct synthesis [START_REF] Kang | E ect of improved crystallinity of titanium silicalite-2 on photodecomposition of simple aromatic hydrocarbons[END_REF] which tend to create doi:10.1016/S0009-2509(02)00637-1 Ti-O-Si bonds. In this study, a sol-gel method was used to impregnate zeolites in pellets form, of two well-known structures, faujasite Y and ZSM-5, to be used in the degradation of VOC from industrial waste gas streams. Most of impregnation methods are based on acid-catalyzed sol-gel formation [START_REF] Anderson | Titania and aluminia ceramics membranes[END_REF] which may alter framework structure of zeolites (Takeda, Torimoto, Sampath, Kuwabata, & Yoneyama,1995), and studies are to deÿne to what extend the support undergo physical or chemical modiÿcations. Here, characterization of new TiO 2 -zeolite catalysts was carried out using global elemental analysis, X-ray di raction, scanning electron microscopy (SEM) with microprobe elemental analysis and BET measurements. Speciÿc adsorption capacity of the di erent zeolites-based catalysts was appraised toward daily used industrial solvents (1-butanol and 2-butanone). Aiming to close in on industrial e uents conditions, dilute VOC containing gases were generated in a di usion cell, and then oxidized through dynamic photodegradation experiments. This particular process was also directed towards assessing the e ciency of photocatalysis in terms of adsorbent regeneration.

Experimental section

Chemicals and zeolites supports

Titanium (IV) butoxide (99%), 2,4-pentanedione (99%), 1-butanol (99.5%), and 2-butanone (99.5%) were all purchased from Aldrich, and used without further puriÿcation. Absolute ethanol came from ACS for Analysis, RPE, Carlo Erba. The commercial zeolites used in this study were cylindrical pellets (diameter 2 mm, length 5 mm) supplied by Degussa. The granular solids were made of microcrystals of zeolites arranged together with a clay binder (20% weight). Table 1 summarizes the main physical properties of the HSZ used in this study.

Preparation of supported titanium dioxide catalysts (Bailleux & Benoit-Marquià e, 2001)

The catalysts were prepared by impregnation of supports with a TiO 2 sol-gel. The synthesis method is summarized here. 0.1 mole of titanium (IV) butoxide was dissolved in 1 mol of absolute ethanol in an argon atmosphere and reuxed for 12 h. 0:05 mol of 2,4-pentanedione and 0:01 mol of double distilled water were added dropwise under vigorous stirring. After re uxing for several hours, the clear solution was concentrated by solvent distillation. An amorphous and translucid gel was obtained. It contains enough alcohol to avoid aging and could therefore be stored unchanged for several weeks. The TiO 2 coating was made by completely immersing the di erent supports in the gel. The wet materials could then undergo a two-step hot air treatment. In the ÿrst stage the catalyst system was dried at 100 • C, whereas in the second part the desired crystalline anatase phase was obtained at 450 • C. From now on, the DAY (resp. DAZ) based catalysts are referred as DAY* (resp. DAZ*).

Physical and chemical characterization of catalysts

Elemental analysis was performed by the analysis central center of the Centre National de la Recherche Scientiÿque (CNRS) using ame emission spectrometry. The titanium crystallized phase obtained after the thermal treatment was identiÿed by X-ray di raction, with an automatic di ractometer (Seifert XRD3003TT). Di raction of the K radiations emitted by Copper ( 1 = 1:5406 A and 2 = 1:5444 A) was analyzed for 2Â varying between 20 • and 50 • with a scan time of 4 s=0:02 • . The speciÿc surface area and porous distribution of adsorbents were determined using argon adsorption-desorption experiments at 77 K, using a conventional BET adsorption apparatus (ASAP 2010, Micrometrics). Degassing of samples was performed at 120 • C overnight. This equipment allowed the description of both microporosity (pore size smaller than 2 nm) and mesoporosity (between 2 and 50 nm). A scanning electron microscopy (JSM-840 A, JEOL) was operated at 20 keV, providing information on local properties together with chemical composition of material activated by electronic bombardment (EDS facility). Prior to analysis, the granulates were coated with gold to ensure conductivity. Both external and cross-section surfaces of samples were analyzed. In order to characterize the in uence of impregnation on adsorption capacities of zeolites, batch adsorption isotherms were performed using a volumetric method (Brosillon, Manero, & Foussard, 2001a, b). The adsorbent was introduced into an atmosphere polluted by liquid VOC injection, followed by evaporation; adsorption occurred at a ÿxed temperature (20 • C). Once equilibrium time was reached (2 h), analysis of the gas phase was carried out with a Hewlett-Packard gas chromatograph (HP 5890 II). The calculated value of surface area was done considering that the surface area of adsorbent came only from zeolites crystals, and consequently, by normalizing the surface areas with the zeolite mass content. Expression of calculation is then [S Calc = (S Ads =0:80) × 0:69 + S SGP × 0:15]:

SEM-EDS analysis

Characterization of intimacy and homogeneity of TiO 2 loading is of primary importance for further investigations and understanding of catalysts photoactivity. Results of external and cross-section surfaces where very similar in terms of mixing and titanium content, determined through Si/Ti ratio calculations. Fig. 3 shows SEM pictures of cross-section surfaces for the two catalysts.

On the DAZ* sample, the zeolites crystallites can be easily isolated via their rectangular shape. Using the microprobe elemental analysis (EDS), no titanium was detected on the zeolites crystals whereas a high content of titanium was found in the clearer irregular parts, mixing TiO 2 microcrystals and binder, strengthening the XRD analysis conclusions. The DAY* structure is quite di erent from DAZ*. The zeolites crystals are much smaller and they could not be distinguished from binder or TiO 2 , showing a greater intimacy of loading during sol-gel method. Homogeneity of catalysts was found to be fairly satisfactory, and strongly determined by the initial material, and zeolite crystals size.

BET analysis

BET adsorption isotherms on the di erent samples were all of type Ia of IUPAC classiÿcation (IUPAC Physical Chemistry Division, 1985), corresponding to a microporous adsorbent with a small hysteresis coming from multilayer adsorption/desorption in mesopores. Microporous distribution was checked using Horvath-Kawazoe model extended by Sa to and Foley for a cylindrical pore geometry. Structures of zeolites were conÿrmed, with a monomodal porous distribution for faujasite Y, at 13:8 A and bimodal for ZSM-5, at 10.0 and 12:6 A. The modiÿcation of support's surface due to TiO 2 loading was investigated by two means. First, the surface area of catalysts where determined with Langmuir approach as shown in Table 2. This model was preferred to BET or Dubinin-Radushkevich equation considering the monomolecular adsorption taking place in microporous adsorbent.

The very good agreement between experimental and calculated surface areas conÿrms that TiO 2 loading does not change greatly the support physical properties. Aiming to supplement this conclusion, BJH model was used to study adsorption isotherms desorption parts. To understand coating's in uence on mesoporous distribution of supports, the di erential volumes given in Fig. 4 have been normalized according to zeolite mass content, representative of the unchanged number of pellets.

The global mesoporous volume of DAY is much larger than DAZ one. On both adsorbents, the TiO 2 coating developed a noticeable porous volume. Since the gel (2000a). The greater a nity of TiO 2 toward alcohols due to their hydroxyl group interactions is to explain why aldehydes outlet concentration was greater than the corresponding alcohol one. The adsorption isotherms on SGP presented in Fig. 5a support this interpretation. These ÿndings tend to indicate that the zeolite used in this study does not interfere with the oxidative mechanisms that occur on the active TiO 2 UV-sensible sites; the unloaded zeolites had no catalytic properties when irradiated in identical conditions. Supporting TiO 2 on zeolites may have two di erent impacts on photocatalysis reactions: ÿrstly, it is clear that by creating a high concentration of compounds around TiO 2 sites, kinetic rates are to increase signiÿcantly. This phenomenon was observed in batch experiments by many researchers [START_REF] Sampath | Photocatalytic degradation of gaseous pyridine over zeolite-supported titanium dioxide[END_REF][START_REF] Chen | Preparation and characterization of TiO 2 incorporated Y-zeolite[END_REF]. Secondly, the zeolites, being acid material, may in uence selectivity of reactions through chemisorption on Lewis or Br onsted strong acid sites, induced by aluminum atoms [START_REF] Brueva | Distribution of acid-site strengths in hydrogen zeolites and relationship between acidity and catalytic activity[END_REF][START_REF] Beaune | Selective photocatalytic oxidation of hydrocarbon compounds over zeolites[END_REF]. Here, the impact of acidity on oxidation rate remains unclear but may tend to reduce mass transfer between external adsorption sites, and TiO 2 sites. The same study was performed with a BuOH inlet concentration of 2000 mg m -3 , leading to similar sub-products curves, but to a di erent degradation steady state of 75%, which can be easily explained by the competitive adsorption and photodegradation mechanisms. Finally, the DAZ* catalyst was studied with a 2000 mg m -3 inlet concentration: irradiation lead very rapidly to a steady state of 40% of degradation, but only a very small adsorbent regeneration was obtained (about 5%). The outlet gas content obtained during the ÿrst irradiation phase is presented in Fig. 9. When beginning the irradiation phase, a smaller thermodesorption was observed compared with the DAY* experiments, conÿrming that faujasite structure is more favorable to desorption than ZSM-5. Moreover, it should be noticed that the initial slope of BuAL curve is signiÿcantly di erent, the concentration being initially very di erent from 0. This phenomenon can be explained by the di erent a nity of zeolites towards alcohol and aldehyde, and may be clariÿed by further competitive adsorption investigations. These ÿndings clearly illustrate that a mass transfer limitation occurs in zeolite crystals. In this study, two main parameters are distinguishing DAY* and DAZ* catalysts that can explain the di erences observed in photocatalysis experiments. Firstly, it is obvious that the zeolite framework structure has a decisive impact, intracrystalline di usion being faster in faujasite Y than in ZSM-5. Secondly, SEM measurements showed that DAY crystals were smaller than DAZ ones, creating a greater intimacy of mixing and a larger mesoporous volume. Therefore, zeolite crystals size is likely to limit mass transfer in the catalyst. It was not possible to determine here their respective in uence, but in both cases, intracrystalline di usion is the microscopic decisive parameter. By investigating the correlation between adsorption energy and the rate of photodegradation of mixed TiO 2 /adsorbent towards propionaldehyde, [START_REF] Yoneyama | Titanium dioxide/adsorbent hybrid photocatalysts for photodestruction of organic substances of dilute concentrations[END_REF] also pointed at the major in uence of di usion in adsorbent on heterogeneous photocatalysis e ciency.

Conclusions

The zeolites in pellets form used in this study were original supports for a titanium sol-gel impregnation, and physical characterization of materials showed that a great intimacy of mixing was obtained without signiÿcant modiÿcation of adsorbent. Interestingly, these promising ÿndings unabled us to discuss dynamic experiments, explaining that the zeolites did not interfere with oxidation mechanism of BuOH, and clarifying the decisive role of intracrystalline di usion in heterogeneous catalysis. These conclusions were essential prior to any investigations on a more light-e cient reactor design adapted to industrial requirements.

Fig. 3 .

 3 Fig. 3. SEM pictures (G = 1200) of internal surface. DAZ* (left), DAY* (right).

Fig. 9 .

 9 Fig. 9. Outlet content during the irradiation phase of saturated DAZ* (C inlet = 2000 mg m -3 ).

Table 2

 2 Speciÿc surface area of catalysts

	Adsorbent	Speciÿc surface area of adsorbent a (m 2 g -1 )	Speciÿc surface area of TiO 2 -loaded adsorbent b (m 2 g -1 )	Calculated surface area of mixture c (m 2 g -1 )
	SGP	65
	DAY	645	568	566
	DAZ	379	337	336

a Zeolites adsorbent have a binder mass content of 20%. b The composition of catalysts is zeolite-binder-TiO 2 (69:16:15). c

Acknowledgements

We would like to thank Degussa for supply of zeolites, Gustave Tayebi for glass work, l'Ecole Nationale Supà erieure d'Aeronautique (Toulouse) for SEM experiments, and Midi-Pyrà enà ees Region for ÿnancial support.


L A Blas

M Bonilla
email: mbonilla@cinvestav.mx

S Salazar

M Malabre
email: michel.malabre@ls2n.fr

V Azhmyakov
email: vazhmyako@eafit.edu.co

Luis Angel

Blas Sanchez

Synthesis of a robust linear structural feedback linearization scheme for an experimental quadrotor

. This control scheme has the advantage of combining the classical linear control techniques with the sophisticated robust control techniques. This control scheme is specially ad hoc for unmanned aircraft vehicles, where it is important not only to reject the actual nonlinearities and the unexpected changes of the structure, but also to look for the simplicity and effectiveness of the control scheme.

I. INTRODUCTION

Recently, there has been a great interest in finding simple and effective control schemes for unmanned aircraft vehicles, able to reject the actual nonlinearities and the unexpected changes of structure. In [START_REF] Lee | Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter[END_REF], the authors present two types of nonlinear controllers for an autonomous quadrotor helicopter. However, to program this control scheme in the embedded autopilot of the quadrotor is rather difficult due to the needed derivative estimations. In [START_REF] Zhou | Design of Feedback Linearization Control and Reconfigurable Control Allocation with Application to a Quadrotor UAV[END_REF], the authors present attitude and trajectory tracking control designs based on an inner/outer-loop control structure for normal flight conditions. Once again, to program this control scheme in the embedded autopilot of the quadrotor is rather difficult due to the needed derivative estimations. In [START_REF] Liu | Robust Tracking Control of a Quadrotor Helicopter[END_REF], the authors propose a robust controller based on the time-scale separation approach to achieve the automatic take-off, hovering, trajectory tracking, and landing missions for a quadrotor helicopter. The authors only show experimental results in indoor environments.

In this paper, we present a synthesis procedure of the recently robust linear control scheme proposed in [START_REF] Bonilla | Robust Structural Feedback Linearization Based on the Nonlinearities Rejection[END_REF], which is based on failure detection techniques. Such a linear control approach is intended to reject linearly structured uncertainties, which are treated as failure signals affecting the systems dynamics. The implementability and efficiency of the proposed robust control methodology is illustrated with a quadrotor laboratory prototype in hover flying. We present simulation results and experimental results in open field (outdoor environments).

In Section II, we describe the quadrotor laboratory prototype. In Section III, we give the necessary preliminaries to synthesize the control scheme recently proposed in [START_REF] Bonilla | Robust Structural Feedback Linearization Based on the Nonlinearities Rejection[END_REF]. In Section IV, we synthesize the exact structural feedback linearization and the robust asymptotic feedback linearization for the dynamics of the longitudinal trajectory x together with the rotational pitch trajectory θ of the quadrotor. In Section V, we do some simulation for tuning our control scheme. In Section VI, we test our proposition in open field. In Section VII, we conclude.

II. QUADROTOR DESCRIPTION

Let us consider a quadrotor where the total mass is M q , the moments of inertia about axis ox, oy and oz are: 1 I xx , I yy and I zz , and the distance of each rotor with respect to the centre of gravity of the quadrotor is L m (see Fig. 4). The motion is referred to a fixed orthogonal axis set (earth axes) (oxyz), where oz points vertically down along the gravity vector 0 0 g

= φ θ ψ T .
The quadrotor is represented by the following state space representations (see [START_REF] Blas | IFAC-World Congress[END_REF] for details): a) State representation of the xθ dynamics:

d dt x x = A x x x + B x u x + S x q ox , x = C x x x , (2.1)
where x x = x dx/dt θ dθ/dt T , q ox = q x q θ T , and

the matrices A x , B x , S x and C T x are, respectively,    0 1 0 0 0 0 -g 0 0 0 0 1 0 0 0 0    ,    0 0 0 1/Iyy    ,    0 0 1 0 0 0 0 1    and    1 0 0 0    (2.2)
b) State representation of the yφ dynamics:

d dt x y = A y x y + B y u y + S y q oy , y = C y x y , (2.3)
where x y = y dy/dt φ dφ/dt T , q oy = q y q φ T , and the matrices A y , B y , S y and C T y are, respectively,   

0 1 0 0 0 0 g 0 0 0 0 1 0 0 0 0    ,    0 0 0 1/Ixx    ,    0 0 1 0 0 0 0 1    and    1 0 0 0    (2.4)
1 Since the quadrotor is mechanically symmetric its cross inertia are zero.

c) State representation of the ψ dynamics:

d dt x ψ = A ψ x ψ + B ψ u ψ + S ψ q ψ , ψ = C ψ x ψ ,
where x ψ = ψ dψ/dt

d dt x z = A z x z + B z ∆u z + S z q z , z = C z x z , (2.5)
where x z = z dz/dt T , and the matrices A z , B z , S z and C T z are, respectively,

0 1 0 0 , 0 1/M q , 0 1 and 1 0
In the fifth Section of [START_REF] Blas | IFAC-World Congress[END_REF], we show how the incremental control actions, u x , u y , u z = ∆u z -M q g and u ψ , are related with the thrusters of the four rotors, f 1 , f 2 , f 3 and f 4 . The nonlinear signals, q x , q y , q z , q φ , q θ and q ψ , are:

  q x q y q z   =   θ -q xx -φ -q yy -q zz   g + 1 M q   q xx q yy q zz   ∆u z , (2.6)
  q φ q θ q ψ   = J -1 (η) -J -1 (0) τ -J -1 (η)C(η, dη/dt) dη dt , (2.7
) where J and C(η, dη/dt) are the inertial and the Coriolis matrices, defined in the Appendix of [START_REF] Blas | IFAC-World Congress[END_REF], and: 2

q xx = c φ s θ c φ + s φ s ψ , q yy = c φ s θ s ψ -φ c ψ , q zz = c φ c θ -1 .
(2.8)

III. PRELIMINAIRES

Let us consider a nonlinear system described by the following nonlinear state space representation:

d dt x(t) = Ax(t) + Bu(t) + Sq(x(t), u(t)), y(t) = Cx(t), (3.1
) where u ∈ R m and y ∈ R p are the input and the output, respectively, x ∈ R n is the state and q ∈ R µ is a nonlinear perturbation signal, here called an uncertainty vector. We do the following assumption:

H1: Structural hypothesis: 1) ker B = 0.

2) The pair (A, B) is controllable, namely (see for example [START_REF] Wonham | Linear Multivariable Control: A Geometric Approach[END_REF]):

R n = A | Im B = Im B + A Im B + • • • + A n-1 Im B.
3) The pair (C, A) is observable.

We need two results stated in [START_REF] Bonilla | Robust Structural Feedback Linearization Based on the Nonlinearities Rejection[END_REF].

Lemma 1 ([3]

): Under assumptions H1.1 and H1.2, there exist two linear transformations, M : R n → R n and X : R n → R m , solving the matrix equality:

AM + BX = I , (3.2)
2 We use the abbreviated notations: (c φ , c θ , c ψ ) for (cos φ, cos θ, cos ψ) and (s φ , s θ , s ψ ) for (sin φ, sin θ, sin ψ).

satisfying: X = B (I -AM ) and M n = 0, where B : R n → R m is a left inverse of B : R m → R n , B B = I, and M : R n → R n has a nilpotent index not greater than n.

Equality (3.2) directly follows from H1.2: R n = A | Im B ⊂ Im B + Im A ⊂ R n ;
for the other ones see the proof in [START_REF] Bonilla | Robust Structural Feedback Linearization Based on the Nonlinearities Rejection[END_REF].

Defining:

C (M, S) = S M S • • • M (n-1) S , (3.3)
Ψ n (d/dt) = I I d/dt • • • I d n-1 /dt n-1 T , (3.4)
and assuming:

H2: The subspace M Im S is contained in the unobserv- able subspace ker C | M = ker C ∩ M -1 ker C ∩ • • • ∩ M -(n-1) ker C, namely: CM C (M, S) = 0, (3.5
) the following Theorem is obtained: Theorem 1 ( [START_REF] Bonilla | Robust Structural Feedback Linearization Based on the Nonlinearities Rejection[END_REF]): Given the linear transformations M and X from Lemma 1, consider the following change of variable:

ζ(t) = x(t) + M C (M, S) Ψ n (d/dt) q(x(t), u(t)) . (3.6)
Under Assumptions H1.1, H1.2 and H2, the state representation (3.1) is externally equivalent to the following3 :

d dt ζ(t) = Aζ(t)+B (u(t) + q * (x(t), u(t))) , y(t) = Cζ(t), (3.7
) where the nonlinear uncertainty signal, q * , is given by:

q * (x(t), u(t)) = XC (M, S) Ψ n (d/dt) q(x(t), u(t)). (3.8)
Theorem 1 is important because it provides us the change of basis (3.6), which aim is to map the uncertainty vector (nonlinear perturbation signal), q, to the nonlinear uncertainty signal (3.8), q * , contained in Im B. Thus,

u(t) = -q * (x(t), u(t)), (3.9)
exactly linearizes (3.7).

In the case when it is not possible to reconstruct analytically the nonlinear uncertainty signal q * , or it is a heavy and tedious task to do it, one can still estimate it. For this, we need to add the following assumption:

H3: The state space description Σ(A, B, C) (3.1) has no finite invariant zeros at the origin, namely:

Im B ∩ A ker C = 0 .
(3.10) Assumptions H1.3 and H3 make it possible to apply results of [START_REF] Bonilla | A Robust Linear Control Methodology based on Fictitious Failure Rejection[END_REF] and to design a robust disturbance rejection (based on the Beard-Jones filter, see [START_REF] Massoumnia | A geometric approach to the synthesis of failure detection filters[END_REF] and the reference there included):

d dt w(t) = A K w(t) -Ky(t) + Bu(t), q * (t) = -G (Cw(t) -y(t)), u(t) = -q * (t).
(3.11)

where A K . = (A + KC) with K : R p → R m an output injection such that: σ{(A + KC)} ⊂ C -, and G is a left inverse of the static gain -C(A + KC) -1 B. The remainder generator is expressed as:

d dt e(t) = A K e(t)-Bq * (x, u), q * (t) = -G Ce(t), (3.12)
where e(t) = w(t)ζ(t). In the case when the classic Laplace transform of q * (x, u) is well-defined, we have the following transfer function:

F e (s) = G C (sI -A K ) -1 B . (3.13)
Under the natural boundedness assumption for q * (x, u) with a bandwidth ω q , we have to synthesize a Hurwitz low-pass filter F e (s) with a corner frequency ω c , which aim is to reconstruct q * (x, u). Indeed, the nonlinear uncertainty signal q * is affecting the closed loop behavior throw the high-pass filter 1 -F e (s), so the corner frequency ω c of the low-pass filter F e (s) should be sufficiently greater than the bandwidth ω q , in order to reject q * . This is with the aim to achieve a robust disturbance in a neighborhood around the equilibrium point (x, u) = (0, 0), namely:

q * (ω)-q * (ω) ≤ (I -F e (ω)) XC (M, S) Ψ n (ω) q(ω) .

IV. LINEAR ROBUST CONTROL SYNTHESIS

In this Section, we synthesize the exact structural feedback linearization (3.8) and (3.9), and the robust asymptotic feedback linearization (3.11), for the xθ dynamics (2.1) and (2.2); the other ones are done in a very similar way.

A. Locally Stabilizing Feedback

Applying the feedback [START_REF] Brunovsky | A classification of linear controllable systems[END_REF] I yy /g a x,3 I yy /g -a x,2 I yy -a x,1 I yy , (4.1) to (2.1), one gets:

u x = F x x x + ūx , F x = a x,
d dt x x = A Fx x x + B x ūx + S x q ox , x = C x x x , (4.2)
where:

A Fx = A x + B x F x =     0 1 0 0 0 0 -g 0 0 0 0 1 a x,4 /g a x,3 /g -a x,2 -a x,1     , (4.3)
with the following Hurwitz characteristic polynomial:

π xx (s) = det (sI -A Fx ) = s 4 +a x,1 s 3 +a x,2 s 2 +a x,3 s+a x,4 . (4.4)

B. Exact Structural Feedback Linearization

The matrices M x and X x solving the algebraic equation (cf. (3.2)): A Fx M x +B x X x = I 4 , and the operators (3.3) and (3.4) are:

M x =     0 0 0 0 1 0 0 0 0 -1/g 0 0 0 0 1 0     , X x = -a x,3 I yy /g -a x,2 I yy /g a x,1 I yy I yy , C (Mx, Sx) =     0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1/g 0 0 0 0 0 0 1 0 0 -1/g 0 0 0     , Ψ 4 (d/dt) = I 2 I 2 d/dt I 2 d 2 /dt 2 I 2 d 3 /dt 3 T . ( 4
ζ x = x x - 1 g     0 0 0 0 1 0 d/dt 0     q x q θ . (4.6)
The nonlinear uncertainty signal (3.8) is (cf. (4.5)):

q x, * = - I yy g a x,2 + a x,1 d/dt + d 2 /dt 2 q x + I yy q θ . (4.7)
The state space representation in the new variable ζ x is (cf. (4.6) and (4.2)):

d dt ζ x = A Fx ζ x + B x (ū x + q x, * ) , x = C x ζ x . (4.8)
and its transfer function is:

F ζx (s) = C x sI -A Fx -1 B x = - g I yy π xx (s)
. (4.9)

Thus, the exact structural feedback linearization is: ūx = -q x, * (x(t), u(t)).

C. Robust Asymptotic Feedback Linearization

The observer for rejecting the nonlinear uncertainty signal q x, * is (cf. (3.11)):

d dt w x = A Kx + B x G x C x w x -K x + B x G x x, ūx = G x C x w x -G x x, (4.10)
where:

A Kx = A Fx + K x C x , G x = -C x A -1 Kx B x = - I yy a xo,4 g , K x =     a x,3 a x,2 -a x,1 g -g a x,2 a x,1 -g 0 a x,1 1 0 0 1 0 0 0     -1     a x,4 -a xo,4 a x,3 -a xo,3 a x,2 -a xo,2 a x,1 -a xo,1     .
(4.11) The characteristic polynomial of the remainder generator (3.12) is:

π ex (s) = det (sI -A Kx ) = s 4 + a xo,1 s 3 + a xo,2 s 2 + a xo,3 s + a xo,4 . (4.12)
The transfer function of (4.10) is: So, following a root locus procedure, both polynomials, π ex (s) and πwx (s), can be made Hurwitz.

F wx (s) = I yy a xo,

D. Closed Loop System

Defining the error signal, e x = w xζ x , we get the closed loop state space representation (cf. (4.8) and (4.10)):

d dt

e x ζ x = A CL e x ζ x + B CL q x, * , x = C CL e x ζ x , (4.16
)

A CL = A Kx 0 B x G x C x A Fx , B CL = -B x B x , C CL = 0 C x .
(4.17)

The transfer functions are (recall (4.12), (4.9) and (4.15)):

F ex (s) = G x C x (sI -A Kx ) -1 B x = a xo,4 π ex (s) (4.18) F CL (s) = C CL (sI -A CL ) -1 B CL = 0 | C x • (sI -A Kx ) -1 0 (sI -A Fx ) -1 B x G x C x (sI -A Kx ) -1 (sI -A Fx ) -1 • -B x B x F CL (s) = F ζx (s) 1 -F ex (s) = - g I yy π xx (s) 1 - a xo,4 π ex (s) = - g I yy π xx (s) s πwx (s) π ex (s) , ( 4
G HPFx (s) = 1 -F ex (s) = 1 -a xo,4 π ex (s) = s πwx (s) π ex (s).
(4.20) Hence, if the nonlinear uncertainty signal q x, * has a finite bandwidth, it is then sufficient to synthesize the high-pass filter with a cutoff frequency sufficiently higher than the bandwidth of q x, * .

V. NUMERICAL SIMULATIONS

The numerical values of our laboratory prototype are:

M q = 1.

A. Locally Stabilizing Feedbacks

The state feedbacks were computed by LQR techniques, namely by solving the algebraic Riccati equation,

A T P + P A -P B(ρ I) -1 B T P + Q = 0,
with the following matrices choices:

Q x = Q y = 900     1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2.25     , Q z = 1 0 0 0.23 , Q ψ = 1 0 0 0.6 , (ρ x , ρ y , ρ z , ρ ψ ) = 1, 1, 1 19600 , 1 12100 .
The optimal state feedbacks are: (5.

F x =
2) The spectrums of A Fx , A Fy , A Fz and A F ψ are:

Λ x (s) = {-3214, -1.911, -0.9536 ± 1.585}, Λ y (s) = {-3358, -1.911, -0.9536 ± 1.585}, Λ z (s) = {-2.087, -49.32}, Λ ψ (s) = {-1.291, -3328}.
(5.

3) The spectrum sets Λ x and Λ y are lower bounded by: = √ 0.9536 2 + 1.

B. Nonlinear Uncertainty Signals Observation

Since the quadrotor is planned to move on a (x, y)-plan over a fixed altitude, z = z, we only synthesize nonlinear uncertainty signals observers for q x, * and q y, * .

1) Observation's dynamics:

The dynamics of the remainder generator (3.12) and the nonlinear uncertainty signal observer (4.10) are given by the polynomials (4.12) and (4.14), respectively; these two polynomials are related by (4.15). Following a root locus procedure, we get:4 (5.7) 2) Beard-Jones filter: For simplicity, the Beard-Jones filter (4.10) is synthesized in its observer canonical form [START_REF] Kailath | Linear systems[END_REF]:

d dt w x = A Kx + B x G x C x w x -K x + B x G x x , ūx = G x C x w x -G x x , (5.8)
where: A Kx = A x + K x C x , and (recall (5.1), (4.4), (5.4), (4.12) and (5.6)): 6

A x =     0 0 0 -a x,4 1 0 0 -a x,3 0 1 0 -a x,2 0 0 1 -a x,1     , B x , C x , K x =         -g/Iyy 0 0 0     ,     0 0 0 1     T ,     a x,4 -a xo,4 a x,3 -a xo,3 a x,2 -a xo,2 a x,1 -a xo,1         , G x = -C x A -1 Kx B x = -(a xo,4 I yy )/g, K x = -843351429 -26924674 -259467 2311.6 T . (5.9)

C. Simulation Results

In Fig. 2, we show some simulation results obtained in a e MATLAB R platform. We have considered that the earth axes 5

Doing: |GHPF x ( ω)| = 1, one gets: 2ax o , 4 ω 4 -2ax o , 2 ax o,4 ω 2 + a 2
xo, 4 = 0. (oxyz) is located at height z = 2 [m], above the ground level, and with the initial conditions:

6 wx = T -1 ox wx, Tox =    ax, 3 ax, 2 -ax, 1 g -g ax, 2 ax, 1 -g 0 ax, 1 1 0 0 1 0 0 0    -1 , (Ax, Bx, Cx, Kx) = (T -1 ox A Fx Tox, T -1 ox Bx, CxTox, T -1 ox Kx), G x = -Cx A Fx + KxCx -1 Bx = -Cx A -1 Kx Bx .
x(0) = y(0) = z(0) = 0 [m], dx(0)/dt = dy(0)/dt = dz(0)/dt = 0 [m s -1 ], φ(0) = θ(0) = ψ(0) = α 0 , α 0 = π/6 [rad], dφ(0)/dt = dθ(0)/dt = dψ(0)/dt = 0 [rad s -1 ].
The initial conditions of the Beard-Jones filter (5.8) and (5.9) were set up as (cf. [START_REF] Blas | IFAC-World Congress[END_REF]):

w x (0) = -a x,1 g g 0 0
T tan α 0 (cos α 0 + tan α 0 ) , w y (0) = a y,1 g g 0 0 T tan α 0 (1sin α 0 ) , w ψ (0) = α 0 a ψ,1 α 0 T .

(5.10) From Fig. 2, we can verify that the nonlinear uncertainty signal estimation ū, x , obtained via the Beard-Jones filter (5.8) and (5.9), closely follows the nonlinear uncertainty signal q x, * , computed via (4.7), (2.6)-(2.8).

VI. EXPERIMENTAL RESULTS

In Fig. 3, we show some experimental results obtained in open field; we compare the horizontal position trajectories x: (i) when both control laws are applied, the locally stabilizing feedback F x x x (4.1) and (5.2) plus the estimation of the nonlinear uncertainty signal ūx (5.8) and (5.9) (solid line), and (ii) when only the locally stabilizing feedback F x x x (4.1) and (5.2) is applied. From this figure, we can point out the correct rejection of the nonlinear uncertainty signal q x, * , via the Beard-Jones filter (5.8) and (5.9).

VII. CONCLUSION

In [START_REF] Bonilla | A Robust Linear Control Methodology based on Fictitious Failure Rejection[END_REF], we have shown that for a system modeled by the state space representation (3.1), where q is an uncertainty signal, and the map S is contained in the image of B, namely there exists a Q such that: S = BQ, then the uncertainty signal q can be rejected by means of the Beard-Jones filter (3.11). Such proposition was tested via the altitude control of a planar vertical takeoff and landing (PVTOL) aircraft a laboratory setting.

In [START_REF] Blas | IFAC-World Congress[END_REF], we have shown that the linear control scheme, based on failure detection techniques, introduced in [START_REF] Bonilla | A Robust Linear Control Methodology based on Fictitious Failure Rejection[END_REF] is in fact a structural feedback linearization technique, where the nonlinearities, affecting the systems dynamics, are treated as failure signals. Based on the Brunovsky canonical form [START_REF] Brunovsky | A classification of linear controllable systems[END_REF], we have proposed the change of variable (3.6), for changing from the state space representation in its Brunovsky canonical form to a nice state space representation, where the uncertainty signal q * is inside of the image of the input map, and thus, with a Beard-Jones filter type, q * is rejected. This control scheme was illustrated with a e MATLAB R numerical simulation of a quadrotor in hover flying.

In [START_REF] Bonilla | Robust Structural Feedback Linearization Based on the Nonlinearities Rejection[END_REF], the two previous results were formalized to the more general nonlinear state space representation (3.1), and we generalized the change of variable (3.6), based on the algebraic equation (3.2), issued from the assumption that the pair (A, B) is controllable. Under such a change of variable, we have obtained once again the state representation (3.7), where the nonlinear uncertainty signal (3.8) is contained in the image of B. We have also generalized the previous Beard-Jones filters to the control scheme (3.11).

In this paper, we have shown in detail the synthesis procedure of the control scheme recently proposed in [START_REF] Bonilla | Robust Structural Feedback Linearization Based on the Nonlinearities Rejection[END_REF]. This control scheme has the advantage of combining the classical linear control techniques with the sophisticated robust control techniques. This control scheme is specially ad hoc for unmanned aircraft vehicles, where it is important not only to have the capability of rejecting the actual nonlinearities and the unexpected changes of structure, but also to obtain simplicity and effectiveness of the control scheme.

We have tested the effectiveness and simplicity of our proposition with the quadrotor laboratory prototype, in hover flying, having the numerical values (5.1). In order to tune our control scheme, we have first done some simulation proofs, shown in Section V, and then we have tested our proposition in open field, as shown in Section VI. Because of lack of place, comparison with alternative approaches will be done in an extended version of the present contribution.

. 5 )

 5 Note that: M 4 x = 0 and C x M x C (Mx, Sx) = 0. The change of variable (3.6) is (cf. (4.5)):

  36 [kg], g = 9.81 [m s -2 ], I xx = 0.0134 [kg m 2 ], I yy = 0.0140 [kg m 2 ], I zz = 0.0256 [kg m 2 ], (5.1) and: L m = 0.245 [m], k τ = 4.31 × 10 -9 [N m/rpm 2 ], k f = 1.98 × 10 -7 [N/rpm 2 ] and γ = k τ /k f = 0.0218 [m].

  30 32.4264 -171.9158 -45.0535 , F y = -30 -32.4260 -171.9116 -45.0512 , F z = -140 -69.92 , F ψ = -110 -85.2387 .

  585 2 = 1.85. The characteristic polynomial (4.4) is: π xx (s) = s 4 + 3218 s 3 + 12279 s 2 + 22722 s + 21022 . (5.4)

2 xo, 2 = 0 .

 220 s (s + 4.75)(s + 4)(s + 3.5) + 28.125 = (s + 1) 2 (s 2 + 10.25 s + 28.125) . (5.5) Scaling the polynomials (5.5) by a factor c , 40 times the lower bounded , we get (s = c s, c = 40 = 74): s πwx (s) = s (s + 4.75 c )(s + 4 c )(s + 3.5 c ) π ex (s) = (s + c ) 2 (s 2 + 10.25 c s + 28.125 2 c ) . (5.6) In Fig 1, we show the Bode plot of the high-pass filter G HPFx ( ω), (4.20) and (5.6). The cutoff frequency ω c of the Bode plot, of the high-pass filter G HPFx ( ω), (4.20) and (5.6), is (recall (4.12), (4.20), (5.5) and (5.6)): 5 ω c = a xo,2 /2 1 -1 -2 a xo,4 /a 5339 c = 39.5 rad/s .

Figura 4 . 3 :Fig. 1 .

 431 Figura 4.3: Gráfica de Bode de magnitud. |p 1 | = 74, |s 2 | = 351.5, |s 3 | = 296, |s 4 | = 259, ωn = 392.44 rad/s y ζ = 0.966.

Fig. 2 .

 2 Fig. 2. (a) Horizontal position, x [m]. (b) Pitch position, θ [ • ]. (c) Estimated nonlinear uncertainty signal (cf. (5.8) and (5.9)), ūx vs computed nonlinear uncertainty signal (cf. (4.7), (2.6)-(2.8)), qx, * . (d) Estimation error, qx, *ūx.

Fig. 3 .

 3 Fig. 3. (a) Horizontal position, x [m]. (b) Pitch position, θ [ • ]. (c) Locally stabilizing feedback Fzxz [N m]. (d) Estimated nonlinear uncertainty signal (cf. (5.8)), ūx. (e) Comparison of the horizontal positions, x [m], obtained with the application of both, the locally stabilizing feedback Fxxx (4.1) and (5.2) plus the estimation of the nonlinear uncertainty signal ūx (5.8) and (5.9) (solid line), against only the application of the locally stabilizing feedback Fxxx (4.1) and (5.2) (dashed line).

2 Figura 1 : 1 Fig. 4 .

 2114 Figura 1: Vista del arreglo experimental

  T , and the matrices A ψ , B ψ , S ψ

	and C T ψ are, respectively,	0 1 0 0	,	0 1/I zz	,	0 1	and	1 0	.
	d) State representation of the z dynamics:

  πwx (s) = s 3 + a xo,1 s 2 + a xo,2 s + a xo,3 ,(4.14)Let us note that (cf. (4.14) and (4.12)):

	g	4	π xx (s) s πwx (s)	,	(4.13)
	π ex (s) = s πwx (s) + a xo,4 .		(4.15)

  + a xo,1 s 2 + a xo,2 s + a xo,3 ) s 4 + a xo,1 s 3 + a xo,2 s 2 + a xo,3 s + a xo,4 + 906.5 s 2 + 271746.5 s + 26947396) s 4 + 906.5 s 3 + 271746.5 s 2 + 26947396 s + 843372455 . En la figura 4.3 se muestra el diagrama de Bode de (4.41).

	4.2. Simulación numérica
	del sistema en lazo cerrado ūx , ver figura 4.1.
	Para los valores obtenidos en la subsección 4.2.2 (cf. (4.19) y (4.18)) se tiene
	G(s) = 1 -s(s 3 = a xo,4 π ex (s) = s(s + 351.5)(s + 296)(s + 259) (s + 74) 2 (s 2 + 758.5 s + 154012.5) = s (s 3 (4.41)

Recall that two representations are called externally equivalent if the corresponding sets of all possible trajectories for the external variables expressed in an input/output partition (u, y) are the same[START_REF] Willems | Input-output and state-space representations of finitedimensional linear time-invariant systems[END_REF],[START_REF] Willems | Introduction to Mathematical Systems Theory: A Behavioral Approach[END_REF].

The natural frequency and the damping ratio of the second order factor are respectively: ωn =

5.3 rad/s and = 0.966.