Lars-Eric Heimbürger
email: lars.heimbuerger@obs-vlfr.fr

Christophe Migon

Aurélie Dufour

Jean-Francois Chiffoleau

Daniel Cossa

Trace metal concentrations in the North-western Mediterranean atmospheric aerosol between 1986 and 2008: Seasonal patterns and decadal trends

Keywords: Trace metals, Aerosols, Anthropic impact, Mediterranean, Anti-pollution policy

Climatic and anthropogenic changes are able to engender modifications in the aerosol composition at different geographical and temporal scales. The present study addresses this question for the trace metal concentrations (TM = Al, Fe, Mn, Co, Ni, Cu, Pb, Cd and Zn) of aerosol from the North-western Mediterranean coast of France (Cap Ferrat, nearby Nice) between 1986 and 2008. From seasonal variations (2006-08) and decadal trends of TM concentrations, three groups of elements can be distinguished. They consist of different aerosol sources: crustal-derived elements (Al, Fe, Mn and Co), trace metals of anthropogenic origin (Pb, Cd and Zn) and a third, intermediate, group of trace metals that presented both anthropogenic and natural/crustal influences (Ni and Cu). Reproducible seasonal patterns were observed for crustal and intermediate elements with highest concentrations between May and November, while anthropogenic trace metals did not show a pronounced seasonal cycle. Nevertheless, highest concentrations of anthropogenic trace metals occurred mostly in autumn/winter. Aerosol concentrations of anthropogenic TMs decreased remarkably over the last two decades, while crustal trace metals did not show any evolution. Nickel and copper aerosol concentrations remained constant, as well. Lead concentrations decreased from 1986 (29.34 ng m -3 ) to 2008 (3.33 ng m -3 ), overall by 90%. Cadmium and zinc aerosol concentrations decreased by 66 and 54%, respectively, between 1998 and 2006-08, from 0.27 to 0.09 ng m -3 and from 23.9 to 10.9 ng m -3 , respectively. These findings demonstrate the response of the atmospheric environment to the implementation of antipollution policies. Possible changes of trace metal emissions sources and local influences are discussed.

Introduction

Atmospheric transport is an efficient (and often the main) transport route by which both natural and anthropogenic compounds are carried from land-based emission sources to coastal and offshore marine waters [START_REF] Jickells | Atmospheric inputs of metals and nutrients to the oceans: their magnitude ad effects[END_REF][START_REF] Guerzoni | The role of atmospheric deposition in the biogeochemistry of the Mediterranean Sea[END_REF]. This is particularly true for the Mediterranean Sea, due to its relatively reduced dimensions (2.5 10 6 km², i.e. only 1% of the world oceanic surface), and because its open waters are never further than 300 km off the coasts. In addition, this semienclosed basin is subjected to ever growing anthropogenic pressure and natural pulsed Saharan dust events [START_REF] Béthoux | Temporal trends in nutrient ratios: chemical evidence of Mediterranean ecosystem changes driven by human activity[END_REF]. Owing to these peculiarities, the interactions between land-based emissions sources and offshore waters are particularly strong, and they significantly affect the biogeochemistry of the Mediterranean Sea. As a result, the Mediterranean Sea is particularly sensitive and reactive to climatic and environmental changes, and can be used as an ocean model for climatic and environmental studies [START_REF] Béthoux | The Mediterranean Sea: a miniature ocean for climatic and environmental studies and a key for the climatic functioning of the North Atlantic[END_REF]. Specifically, the Western basin may be regarded as having specific air mass back trajectories with little variation in the frequency of airflow patterns (World Meteorological Organization, 1985). Meteorological situations are contrasted, with a succession of dry (winter and summer) and wet (spring and autumn) seasons, which significantly determine the seasonal variability and the bioavailability of atmospheric deposition, and, thus, its further involvement in marine biogeochemical cycles [START_REF] Nicolas | Seasonality of dry and wet deposition of trace metals in the Ligurian Sea[END_REF]. The study of temporal trends of natural and anthropogenic compounds, especially trace metals (TM), in the Mediterranean atmosphere is therefore crucial to understand the causal relationships between changes in land-based emission sources and perturbations or evolutions in the biogeochemistry of oceanic areas. On the one hand, the further on-going industrialisation of Europe, in particular that of developing countries of the Eastern part, and of Southern Mediterranean countries, is likely to yield increasing atmospheric anthropogenic pressure on the Mediterranean Sea. On the second hand, the implementation of stricter environmental policies has already shown that the Mediterranean environment is very sensitive to changes in emissions of anthropogenic TMs. For example, the implementation of the antipollution policy on automotive lead in the second half of the 1980s has resulted in the rapid removal of lead in the North-western Mediterranean atmosphere (Migon et al., 1993a[START_REF] Migon | Decrease of lead concentrations in the Western Mediterranean atmosphere during the last 20 years[END_REF]. On the basis of time-series data of atmospheric aerosol acquired at a Ligurian coastal sampling station over a period of more than twenty years, the present work attempts to study the seasonal behaviour and decadal trends of a series of TMs representative of the North-western Mediterranean Sea.

Methods

Study site and sampling protocol

Atmospheric aerosols were collected at the naval signal station of Cap Ferrat, situated on the southeastern coast of France (43°41'N, 7°19'30''E, altitude 130 m; Fig. 1) between 1986 and 2009. The sampling site, situated on top of the peninsula of Cap Ferrat, is sheltered from local sea-spray and direct continental sources, although it exhibits a marked marine influence (Sandroni and Migon, 1997). The average rainfall is approximately 10% lower than that observed at the neighbouring weather station at the airport of Nice, situated on the shoreline (C.S. M., 1988). The Cap Ferrat site is overall affected by a homogeneous European urban-dominated background material, upon which episodic Saharan dust inputs are superimposed [START_REF] Chester | Rain water aerosol trace metal relationships at Cap Ferrat: A coastal site in the western Mediterranean[END_REF]. More detailed discussion on the site (meteorological characteristics, surrounding anthropogenic influences, occurrence of Saharan events, etc.) can be found elsewhere [START_REF] Migon | Separation of anthropogenic and natural emissions of particulate heavy metals in the western Mediterranean atmosphere[END_REF][START_REF] Chester | Rain water aerosol trace metal relationships at Cap Ferrat: A coastal site in the western Mediterranean[END_REF]Sandroni and Migon, 1997). Long-term continuous sampling of atmospheric material is very difficult and even impossible at sea on research vessels. At present day, data are acquired from coastal or island sampling sites therefore (e.g., [START_REF] Chester | The trace metal chemistry of atmospheric dry deposition samples collected at Cap Ferrat: a coastal site in the Western Mediterranean[END_REF][START_REF] Güllü | Temporal variability of atmospheric trace element concentrations over the eastern Mediterranean Sea[END_REF][START_REF] Zhang | Chemical composition of atmospheric wet deposition from the Yellow Sea and East China Sea[END_REF]. Background aerosols in the Ligurian Sea exhibit a relatively low variability, typically within a factor of 1.4 (e.g., Ni) to 3.2 (e.g., Al) from a coastal sampling site to another (Sandroni and Migon, 1997). Atmospheric fluxes of TMs measured at coastal sites may therefore be extrapolated to the sub-basin scale, as shown by comparison with ship-board aerosol sample collection [START_REF] Jickells | Atmospheric inputs of metals and nutrients to the oceans: their magnitude ad effects[END_REF]. Aerosol samples were collected by pumping surrounding air through a Sartorius membrane (SM 11106, cellulose acetate, porosity 0.45 µm, diameter 47 mm), placed on a filter holder connected to a low-volume pump (KNF IP 44) and a flow meter. This sampling apparatus was raised to the top of a 6 m-high mast to avoid contamination with local soil dust. The average pumped volume was 175 m 3 , with a flow rate of ~ 25 ± 1 m 3 d -1 over the duration of one week. Atmospheric aerosol was monitored in 1986-87, 1992-93, 1994, 1995[START_REF] Marticorena | Two-year simulations of seasonal and interannual changes of the Saharan dust emissions[END_REF], 1997-98 and 2002-08. Data-sets for 1995, 1997and 2006-08 are complete. The years 2004and 2005 have also been sampled continuously for lead. Samples have been collected intermittently in 1986, 1987[START_REF] Migon | Effects of reduced leaded fuel consumption on atmospheric lead behaviour[END_REF][START_REF] Marticorena | Two-year simulations of seasonal and interannual changes of the Saharan dust emissions[END_REF], 1998[START_REF] Mahowald | A less dusty future?[END_REF][START_REF] Andral | Monitoring chemical contamination levels in the Mediterranean based on the use of mussel caging[END_REF], although Co, Ni, Cu, Zn, and Cd were not analysed in 2003[START_REF] Andral | Monitoring chemical contamination levels in the Mediterranean based on the use of mussel caging[END_REF] samples.

Sample mineralisation and analysis

All reagents were provided by Merck (Darmstadt, Germany), quality Suprapur. All analyses were carried out under laminar airflow benches in a class 100 clean room. Samples were dissolved by acid treatment by sets of twelve samples, including two blank filters and two certified reference materials (CRM). Each filter was folded into 4 and introduced into an acid cleaned Teflon bottle (7 mL) in which 1 mL HNO 3 (65%) was added. The bottle was closed and put into a larger Teflon bottle (60 mL) and left at room temperature until complete dissolution of the membrane. Then, the apparatus was kept tightly closed for 12h in an oven at 150°C. Bottles were then cooled in a laminar airflow hood and left open until the red smoke had evolved (which indicates that all HNO 3 has evaporated). The remainder was dissolved again with 500 µL HNO 3 (14M) and 300 µL HF (23M) and left for 24 h (without evaporation) prior to being stored again in a drying oven for 12h. A white residue was obtained and dissolved in 1 mL HNO 3 (1M), ultrasonically agitated for two hours and made up to 9 mL with Milli-Q water. The solution was finally stored in an acid cleaned polypropylene bottle (10 mL) until analysis. All reagents were Suprapur® grade, provided by Merck. Due to the relatively long duration of the monitoring (1986 -2008), analyses were carried out by four different detection techniques: graphite furnace atomic absorption spectrophotometry (GFAAS), differential pulse anodic stripping voltammetry (DPASV), inductively coupled plasma atomic emission spectroscopy (ICP-AES) and inductively coupled plasma mass spectrometer (ICP-MS). Table 1 gives an overview of the various techniques applied, and gives references for their analytical characteristics and performances.

Quality assurance and quality control

The analytical procedures (mineralisation + analysis) were regularly checked using CRMs (MESS-2 or MESS-3 from the National Research Council, Ottawa, Canada, and NIST-2783 Air particulate on filter media from the National Institute of Standards & Technology). The results were always within the quoted confidence intervals, given for the CRMs. In addition, taking into account the variety of analytical techniques used over the years, we compared those techniques for the case of Pb, Cd and Zn (TMs for which a temporal decrease was actually observed). Aerosol samples from the 2006-08 series were selected randomly and analysed by GFAAS (Pb; n = 90) and DPASV (Cd and Zn; n = 12) using the same protocol and apparatus as in earlier series, and compared with the more recent ICP-MS results. The variations observed between two values of the same sample never exceeded 10% (Pb 7%, Cd 9% and Zn 10%). Therefore, TM concentration variations higher than 10% must be interpreted as temporal environmental variations independent of any possible analytical bias due to change in the detection procedures.

Results

Raw data is accessible online: www.obs-vlfr.fr/~heimbuerger/Files/AEROSOL online.pdf. Table 3 gives the summary statistics (geometric mean, arithmetic mean, standard deviation, extreme values, number of samples) of aerosol TM concentrations from 1986 to 2008. Geometric means are given, because the distributions of elemental concentrations in the atmospheric aerosol are generally close to log-normality [START_REF] Georgopoulos | Statistical distributions of air pollutant concentrations[END_REF][START_REF] Blackwood | The quality of mean and variance estimates for normal and lognormal data when the underlying distribution is misspecified[END_REF]. In order to circumvent the bias due to incomplete time series, the variation of aerosol TM concentrations in time is presented by sorting the data into six groups, according to sampling dates : 1986-87, 1992-93, 1994-95, 1996-98, 2003-05 and 2006-08; TM concentration distributions of different groups were compared using a twosided t-test for unpaired samples. The 95% confidence interval of the differences between group means and the corresponding p-values are accessible online: www.obsvlfr.fr/~heimbuerger/Files/stats2.pdf. Results indicate that Al, Fe, Mn, Ni and Cu mean concentrations remained constant over the observed time period (1986 -2008), since t-tests revealed no significant differences between the groups. Aluminium and Fe overall mean concentrations were 106±165 and 138±132 ng m -3 , respectively, representing by far the major mass fraction (>34 and >45%, respectively) of total measured TMs in the aerosol. High standard deviations confirm that Saharan dust inputs occur by pulses. However, maximum values, representing those strong Saharan dust inputs, are in the same order of magnitude, whatever the year. Similarly, Mn, Co, Ni and Cu mean concentrations remained constant all over the sampling period with values of 3.3±3.0, 0.07±0.08, 2.2±1.6 and 3.9±3.3 ng m -3 , respectively. Even though mean concentrations did not evolve over time, maximum values decreased continuously for Cu, and minimum values decreased for Ni. Contrastingly, Pb, Cd and Zn mean concentrations decreased over time. The most striking decrease occurred for Pb. Lead aerosol concentrations remained constant from 1986 to 1993, with a geometric mean of roughly 30 ng m -3 (Table 3). A sharp decrease of 31% was observed in 1994-95, down to 21.6 ng m -3 . This trend continued in the following periods of 1996-98 and 2003-05, with decreases of 34% and 59%, respectively, to levels of 14.4 and 5.8 ng m -3 , respectively. In the most recent period, Pb aerosol concentrations continued to decrease, by 43% between 2003-05 and 2006-08, down to concentrations of 3.33 ng m -3 . In summary, Pb concentrations have decreased by 90% from 1986 to 2008. The amplitude of the variation of Pb mean concentrations (SD, min and max, Table 3) has also decreased in the same time. More details on the Pb data set from 1986 to 2005 can be found elsewhere [START_REF] Migon | Decrease of lead concentrations in the Western Mediterranean atmosphere during the last 20 years[END_REF]. Cadmium concentrations did not change from the beginning of the observation period until 1998, with a mean value of 0.27 ng m -3 . In 2006-08, after a 8 year-long period without measurements, Cd mean concentrations have decreased by 66%, from 0.27 to 0.09 ng m -3 , and standard deviations and maximum values cut by two thirds as well (Table 3). Zinc exhibited a comparable trend as Cd. Zinc mean concentrations remained constant at approximately 23.9 ng m -3 , from 1986 to 1998. A steep decrease of 54% was observed between 1998 and 2006-08, down to concentrations of 10.9 ng m -3 . In addition to these long-term observations, short-term variations of TM in the aerosols have been studied during the 2006-08 period on a weekly basis (Fig. 2). It clearly appears that crustal elements (Al, Fe, Mn, and Co) were more concentrated in the atmosphere during summer periods and less concentrated in winter, with a quite regular seasonal cycle. Anthropogenic elements (Pb, Cd and Zn) also displayed significant short-term variations but no marked seasonal cycle appeared. Higher concentrations have occurred in the autumn 2007 and 2008 and in winter 2007-08. Nickel and Cu presented a mixed behaviour, with both crustal and anthropogenic patterns as described previously (Fig. 2).

Discussion

Trace metals can be ordered according to the nature of their emission sources. Table 3 gives the intercorrelation matrix for the analysed TMs. Three different groups can be distinguished. Alumium, Fe, Mn and Co, hereinafter referred to as crustal TMs, present a first group of highly intercorrelated elements. Lead, Cd and Zn form a second group of anthropogenic TMs, highly intercorrelated as well. Nickel and Cu seem to be intermediate between the two groups, since they are highly correlated, on the one hand with some crustal TMs and on the other hand with some anthropogenic TMs. We refer Ni and Cu hereinafter to as intermediate TMs and discuss their particular behaviour.

Seasonal patterns

Crustal TMs presented pronounced seasonal patterns with highest concentrations in summer and lowest in winter. On the contrary, anthropogenic TMs did not show a clear seasonal pattern. This has already been observed in the Eastern Mediterranean basin at sampling sites in proximity to crustal emission sources [START_REF] Koçak | Spatio-temporal aerosol trace metal concentrations and sources in the Levantine Basin of the Eastern Mediterranean[END_REF]. Soil-derived and/or Saharan emissions are characterised by high Al content, this TM being usually taken as the crustal reference (e.g., [START_REF] Wedepohl | The composition of the continental crust[END_REF]. To various extents, Fe, Mn, Co, Ni and Cu also derive from crustal material, and they exhibit roughly similar seasonal patterns (Fig. 2). Saharan episodes generally occur in spring and summer [START_REF] Moulin | Control of atmospheric export of dust from North Africa by the North Atlantic oscillation[END_REF], as observed in our study. However, the occurrence of significant episodes at other periods of the year is not exceptional [START_REF] Bonnet | Atmospheric forcing on the annual iron cycle in the western Mediterranean Sea: A 1-year survey[END_REF]. Therefore, it is not surprising to observe the most significant peaks of crustal TMs not only in July 2006 and June 2008, but also in autumn (October 2007 and 2008, Fig. 2). In addition to this general pattern, common to all the crustal elements studied here (Al, Fe, Mn and Co), intermediate TMs (Ni and Cu) presented high concentrations in aerosols collected in winter 2007-08. This "bump" was also present in the Pb, Cd and Zn time-series (Fig. 2), suggesting anthropogenic sources for these events. The anthropogenic component of Ni concentrations in marine environments is known substantial. In particular, oil combustion is responsible for spreading of significant amounts of Ni [START_REF] Anwari | Lead and nickel levels in Black Sea aerosols by ETA-AAS[END_REF][START_REF] Chiffoleau | Nickel and vanadium contamination of benthic invertebrates following the "Erika" wreck[END_REF]. Major emissions of anthropogenic Ni sources, influencing the whole Mediterranean region, originate from Lebanon, Tunisia, Bulgaria and Cyprus [START_REF] Pirrone | Past, current and projected atmospheric emissions of trace elements in the Mediterranean region[END_REF]. Saharan material also contains significant amounts of Ni, as evidenced by relatively low enrichment factors normalised to Al in the North-western Mediterranean aerosol [START_REF] Chester | Saharan dust incursion over the Tyrrhenian Sea[END_REF]. Aeolian dust samples might also be enriched in North-western Mediterranean areas by the erosion (including anthropogenic landscaping) of serpentine, which is fairly abundant in regional soils, in particular North Corsica, which is approximately 175 km from our sampling station. To a lesser extent, this can be observed for Cu. The relative importance of the crustal component in atmospheric Cu concentrations (up to 20% of total airborne Cu) might be a peculiarity of the North-western Mediterranean region, as already observed in previous works based on Cap Ferrat atmospheric monitoring [START_REF] Migon | Separation of anthropogenic and natural emissions of particulate heavy metals in the western Mediterranean atmosphere[END_REF][START_REF] Migon | Effects of reduced leaded fuel consumption on atmospheric lead behaviour[END_REF]. The Ligurian region might also be influenced by a point source of Ni. In North-east Corsica (see Fig. 1), a chrysotile asbestos mine was operating until 1965 near the village of Canari and several zones with surface deposit of asbestos still remain. High Ni and chromium levels observed in mussels have been linked to waste from the disused mine [START_REF] Andral | Monitoring chemical contamination levels in the Mediterranean based on the use of mussel caging[END_REF]. Lastly, the northern coast of the Ligurian Sea is strongly affected by seasonal cruising ships. However, the seasonal pattern exhibited by Ni concentrations in the aerosol (Fig. 2), with highest concentrations observed between May and November, suggests that the combination of Saharan crustal inputs and regional anthropogenic emissions such as cruise ships is the prevailing source of Ni to the coastal Ligurian atmospheric aerosol. Nevertheless, Saharan inputs are also likely to bring relatively high amounts of anthropogenic material to North-western Mediterranean surface waters (Guieu et al., in press). This may partly explain that, in the present data set, relatively high concentrations of TMs of recognised anthropogenic character such as Cd or Zn are sometimes associated with Saharan dust events, concomitantly with high concentrations of crustal TMs such as Al, Fe, Mn and Co. (e.g. October 20 th 2008). There is a need, therefore, to tentatively allocate the so-called anthropogenic TMs to natural and anthropogenic emission sources. On the one hand, TMs classified as "anthropogenic" have also a natural component since they are present in trace amounts in lithogenic material. Such low concentrations may be counterbalanced by very high loads of material supplied by Saharan dust events. On the other hand, when Saharan air masses pass over polluted North-African cities, they may be significantly enriched by anthropogenic TM emissions.

The anthropogenic component of aerosol samples can be assessed, using enrichment factors (EFs) standardised to Al, which is the most commonly used soil dust reference. These ratios are usually defined for a given element X as (e.g., [START_REF] Artaxo | Aerosol characteristics and sources for the Amazon basin during the wet season[END_REF][START_REF] Herut | Dry atmospheric inputs of trace metals at the Mediterranean coast of Israel (SE Mediterranean): sources and fluxes[END_REF]:

EF x = [(X)/(Al)] aerosol /[(X)/(Al)] soil dust (1)
where (X) is the concentration of the element X in the aerosol or the reference soil dust. Elemental mean concentrations in soil dust or in erodible rocks are very difficult to define accurately, due to inhomogeneous elemental composition of worldwide soils. Moreover, the ratio [(X)/(Al)] soil dust may be dependent on grain size fractionation and chemical alteration during atmospheric transport. Such chemical modifications might involve solubilisation of certain TMs from particles, photo-chemically induced redox-reactions and aggregation processes [START_REF] Desboeufs | Factors influencing aerosol solubility during cloud processes[END_REF]. One may infer that the use of EFs is questionable, therefore. However, their use is permissible if they are used for the comparison of different enrichments standardised to the same (Al) soil dust value [START_REF] Herut | Dry atmospheric inputs of trace metals at the Mediterranean coast of Israel (SE Mediterranean): sources and fluxes[END_REF]. Fig. 3 shows the seasonal variability of EFs during the 2006-08 period. Basically, high EFs for anthropogenic TMs correspond to low Al concentrations. Low EF values are generally observed during the period between May and November, which suggests that the enrichment of natural material by anthropogenic emissions during the transport of Saharan air masses is not significant. The very low EF values (Fig. 3) observed for the three most intense Saharan episodes during the period 2006-08, i.e., in decreasing order, October 20 th 2008, October 3 rd 2007 and July 4 th 2006 (Fig. 2), may partly result from a "dilution effect" caused by the very high loads of Al. Keeping in mind that the three highest Al concentrations were found in samples that exhibited medium to high anthropogenic (e.g., Cu, Cd, Zn) TM concentrations (Fig. 2), it is possible that EF values are distorted for the case of very intense Saharan events. However, the seasonal pattern of EFs for the case of anthropogenic TMs such as Pb, Cd and Zn (Fig. 3) stresses the importance of anthropogenic sources on Pb, Cd and Zn concentrations in the North-western Mediterranean atmospheric aerosol. Anthropogenic inputs, originating generally from the North and the North-East, presumably prevail in winter, in agreement with advective transport of polluted air masses from Europe [START_REF] Duncan | A modelling study of the export pathways of pollution from Europe: seasonal and interannual variations (1987-1997)[END_REF]. This can be observed, e.g., for Pb in January and February 2008, for Cd from December 2007 to March 2008, or for Zn in March 2008 (Fig. 2). This pattern is neither reproducible every year, nor for other TMs, however. Significant anthropogenic inputs are also observed in autumn. Much more reproducible are the peaks observed in October (Fig. 2): all TMs that have a significant anthropogenic component (Ni, Cu, Pb, Cd, and Zn) exhibit significant peaks in this period, every year. These high anthropogenic TM concentrations are presumably associated with a change in the prevailing airflow rate, when the autumnal equinox points to the moving of the polar front to the southward and, thus, the arrival of air masses originating from northern and north-eastern industrialised regions of Europe to the Western Mediterranean. Satellite data show that the Ligurian Sea may be more strongly affected by anthropogenic land-based particulate emissions in the autumn than in the winter [START_REF] Barnaba | Aerosol seasonal variability over the Mediterranean region and relative impact of maritime, continental and Saharan dust particles over the basin from MODIS data in the year 2001[END_REF]. In 2007 and 2008, high concentrations were observed for anthropogenic and crustal TMs as well. The reproducibility of this situation suggests that autumnal meteorological conditions might favour the mixing of Northern/North-eastern and Southern air masses. This may strengthen the statement that, apart from episodic Saharan episodes, the North-western Mediterranean background aerosol is dominated by anthropogenic emission sources.

The case of Zn is believed more specific: On the one hand, high concentrations are sometimes observed in summer, although they are not concomitant with the occurrence of high peaks of crustal TMs. On the second hand, a very high value was observed on December 4 th 2008. Urban emission sources presumably give off amounts of Zn, among which a great part comes from motor vehicle use, owing to tyre wear [START_REF] Wiesner | Metals and colloids in urban runoff[END_REF]. The Ligurian Sea is subject to significant emission sources from the large urbanised area between Toulon and Genoa. In addition, Zn is believed significantly emitted by waste incinerations [START_REF] Nriagu | Quantitative assessment of worldwide contamination of air, water and soils by trace metals[END_REF], which are probably a noticeable source of Zn, particularly when waste plant residual muds are incinerated. Two waste incineration facilities are in the vicinity of Cap Ferrat, one mud incinerator at l'Ariane, roughly 10 km from the shoreline and an another urban incinerator at Antibes 38 km from the sampling site [START_REF] Migon | Phosphorus in rainwater: Partitioning inputs and impact on the surface coastal ocean[END_REF]. Therefore, significant regional emission sources may be responsible for the peculiar pattern of Zn seasonal concentrations in the atmospheric aerosol. The exceptional event observed on 4 December 2008 is believed the signature of an accidental regional-scale contamination, but mere contamination cannot be discarded.

Decadal trends

Crustal TMs (Al, Fe, Mn and Co) The main emission source of crustal TMs (Al, Fe, Mn and Co) in the Western Mediterranean is Saharan dust. Consistently, all these elements are characterized by high intercorrelation factors in our data set from r = 0.85 (Al-Co) to r = 0.96 (Al-Fe) (Table 3). Besides some interannual variation, Al aerosol concentrations remained overall stable (Fig. 4) with a geometric mean of 106±165 ng m -3 . Such variability (>150%) is probably inherent to the pulsed character of Saharan dust emissions, of which interannual variations are mainly due to changes in the occurrence of the most intense dust events, i.e. the frequency of dust events rather than their intensity [START_REF] Marticorena | Two-year simulations of seasonal and interannual changes of the Saharan dust emissions[END_REF].

There is a strong similarity between Al and Fe for the groups 1994-95, 1997-98 and 2006-08. As well, the observed variability from a year to another should be attributed to the pulsed character of Saharan events. For example, [START_REF] Bonnet | Atmospheric forcing on the annual iron cycle in the western Mediterranean Sea: A 1-year survey[END_REF] attributed up to 99% of the total 2004 flux of total atmospheric Fe at Cap Ferrat to these few strong pulses of Saharan dust events. Since the high 2004 loads of Fe were not followed in 2006-08 by any noticeable increase of Al and Fe inputs, it is very likely that the strong events observed in 2004 should be ascribed to the natural variability of such pulsed inputs, as already pointed out by other studies (e.g., [START_REF] Marticorena | Two-year simulations of seasonal and interannual changes of the Saharan dust emissions[END_REF].

Cobalt and Mn exhibit the same temporal trend, which is essentially due to interannual variability. Such decadal patterns suggest that no significant trend arises. Some papers suggest an increase of the frequency of Saharan events in Mediterranean regions (e.g., [START_REF] Avila | Increasing frequency of Saharan rains over northeastern Spain and its ecological consequences[END_REF][START_REF] Rogora | Long-term trends in the chemistry of atmospheric deposition in Northwestern Italy: the role of increasing Saharan dust deposition[END_REF], while others predict worldwide decrease of dust events (e.g., [START_REF] Mahowald | A less dusty future?[END_REF]. This is not observed here (Fig. 4), however.

Intermediate TMs (Ni and Cu)

Nickel and Cu aerosol concentration at Cap Ferrat remained stable over the past two decades. [START_REF] Pirrone | Past, current and projected atmospheric emissions of trace elements in the Mediterranean region[END_REF] predicted an increasing trend for Ni (+44%) and a slight increase of Cu aerosol concentrations (+4.5%) in the Mediterranean region from 1985 until 2010. We did not observe any change in Ni aerosol concentrations, while Cu aerosol concentrations are roughly consistent with those predictions. Oil combustion is still the major source (1998 estimate) of Ni released in the atmosphere [START_REF] Pirrone | Past, current and projected atmospheric emissions of trace elements in the Mediterranean region[END_REF].

Copper emissions in France are almost entirely owed to brake wear of road vehicles and the wear of trolley wires from railways, with increasing trend in both sectors. However, the overall Cu emissions in France remain stable (CITEPA, 2009). Copper aerosol concentrations in the 1980s in the Western Mediterranean area were in the range of 2.5-3.2 ng m -3 (UNEP, 1991). Our measurements of Cu aerosol concentrations at Cap Ferrat were in the same order of magnitude, with most recent values of 3.81 ng m -3 in the period of 2006-08. The case of Cu might be a peculiarity of North-western Mediterranean region, e.g. at Cap Ferrat, the anthropogenic contribution of atmospheric particulate Cu is rather weak. There are apparently very few close sources and the most significant contribution is probably due to long-range transport [START_REF] Migon | Separation of anthropogenic and natural emissions of particulate heavy metals in the western Mediterranean atmosphere[END_REF]. Libya is the major emitter of Cu in the Mediterranean region [START_REF] Pirrone | Past, current and projected atmospheric emissions of trace elements in the Mediterranean region[END_REF] and Cu emissions might thus be associated to southerly crustal inputs, such as Saharan dust events.

Anthropogenic TMs (Pb, Cd and Zn)

Atmospheric inputs of TMs released to the Mediterranean basin by atmospheric deposition and wet scavenging by precipitation are primarily due to industrial and urban emissions and Saharan dust loads (EEA, 1997). The combustion of fossil fuels, non-ferrous metal smelters and waste incineration represent important sources of Pb, Ni, Cu and Cd in the Mediterranean region as a whole. Anthropogenic emissions for those TMs are considered several orders of magnitude higher than the contributions from natural sources [START_REF] Pirrone | Past, current and projected atmospheric emissions of trace elements in the Mediterranean region[END_REF].

Emissions of TMs can be characterised by the use of TM emission factors for specific sources and direct measurements of TM concentrations in the atmosphere. Trace metal emissions estimated by the use of TM emission factors might be afflicted with a considerable uncertainty, above all those of waste incinerators, but often represent the only approach to access TM emissions on a global scale. [START_REF] Pirrone | Past, current and projected atmospheric emissions of trace elements in the Mediterranean region[END_REF] predicted trends for the Mediterranean region from 1985 until 2010 based on emission factors: Pb (-67%) and Cd (-6%). Our aerosol measurements are in agreement with those predictions: Pb, Cd (and Zn) aerosol concentrations decreased remarkably over the last 23 years.

The case of Pb at the Cap Ferrat sampling site over the period 1986-2005 was already described by [START_REF] Migon | Decrease of lead concentrations in the Western Mediterranean atmosphere during the last 20 years[END_REF], readers may find detailed information therein. Briefly, tetra-ethyl Pb was used until the 1990s as an additive in gasoline to increase its octane rating [START_REF] Kummer | Assessment of heavy metal releases from the use phase of road transport[END_REF]. In the 1970s, the German government was the first in Europe to regulate lead additives in gasoline [START_REF] Pacyna | Changes of emissions and atmospheric deposition of mercury, lead, and cadmium[END_REF]. Various EU directives have limited the Pb content of gasoline since. Gasoline and diesel combustion were still considerable Pb emission sources, because antipollution policies concerned primarily organic Pb additives, which were restricted in the EU, but not the natural Pb content, inherent to the crude oil [START_REF] Pirrone | Past, current and projected atmospheric emissions of trace elements in the Mediterranean region[END_REF]. Since 2002, the main source of Pb emission was the manufacturing industry, mainly from iron and steel industry and the processing of non-metallic minerals and construction materials. The broadening of the implementation of these antipollution policies on leaded petrol over Europe yielded a significant decrease of Pb aerosol concentrations in the Western Mediterranean troposphere (Migon et al., 1993[START_REF] Migon | Decrease of lead concentrations in the Western Mediterranean atmosphere during the last 20 years[END_REF][START_REF] Pirrone | Past, current and projected atmospheric emissions of trace elements in the Mediterranean region[END_REF][START_REF] Miralles | Atmospheric lead fallout over the last century recorded in Gulf of Lions sediments (Mediterranean Sea)[END_REF]. Our most recent measurements reveal a further decrease since the measurements of 2005 from 5.87 to 3.33 ng m -3 (Table 2). Cadmium aerosol concentrations in the Western Mediterranean in the 1980s were in the range of 0.8-2.0 ng m -3 (UNEP, 1991). Our measurements during this time at the Cap Ferrat sampling site were significantly lower, with a geometric mean of 0.27 ng m -3 . Based on present observations, Cd aerosol concentrations at Cap Ferrat remained constant until 1998. Cadmium mean concentrations have steeply decreased by 66% to levels of 0.09 ng m -3 in 2006-08. This is in agreement with studies of [START_REF] Pacyna | Changes of emissions and atmospheric deposition of mercury, lead, and cadmium[END_REF], who stated that total atmospheric Cd emissions in Europe decreased by 80% over the last 40 years. Cadmium emissions in France were reduced by 82% since 1990, explained mainly by improvements in industrial sectors such as iron and steel industry, non-ferrous smelters and removal of pollutants from the flue gases generated by household waste incineration plants (CITEPA, 2009).

Zinc aerosol concentrations at Cap Ferrat decreased by 54% over the last decade. In addition to the above-mentioned urban Zn emission sources [START_REF] Wiesner | Metals and colloids in urban runoff[END_REF] and waste incineration [START_REF] Migon | Phosphorus in rainwater: Partitioning inputs and impact on the surface coastal ocean[END_REF][START_REF] Nriagu | Quantitative assessment of worldwide contamination of air, water and soils by trace metals[END_REF][START_REF] Pacyna | Estimation of the atmospheric emissions of trace-elements from anthropogenic sources in Europe[END_REF]

Conclusion

The present work demonstrates that, despite increasing anthropogenic pressure in Europe, the implementation of antipollution policies yielded an actual decrease of anthropogenic TMs in the atmosphere. We observed a rapid response of anthropogenic TM aerosol concentrations to the restriction of emissions. On the contrary, crustal TMs did not show any trend during the last two decades despite global climate change, which has a strong impact on the meteorological settings of the Mediterranean region [START_REF] Béthoux | Warming and freshwater budget change in the Mediterranean since the 1940s, their possible relation to the greenhouse effect[END_REF].

Our findings underline the importance of environmental monitoring during this transition from national to intergovernmental environmental management leading to manifold antipollution policies and directives. Long-term environmental monitoring leads, on the one hand, through the understanding of the impact of certain contaminants, to new directives and, on the other hand, is the tool to evaluate the response of the environment to those directives. Further research should address the impact of the change in aerosol quality on the environment, e.g. cycling of those TMs in the Mediterranean, and a conclusive understanding of the respective natural and anthropogenic fractions of various TMs. : 1986-87, 1992-93, 1994-95, 1997-98, 2003-05 and 2006-08.

Figures

Figure 1 :

 1 Figure 1: Location of the Cap Ferrat sampling station.

Figure 2 Figure 2 :Figure 3 Figure 3 :Figure 4 :

 22334 Figure 2 Figure 2: Seasonal variability of TM aerosol concentrations [ng m -3 ] from January 2006 to December 2008

  , other major Zn emissions sources are the manufacturing industry and wood consumption. Zinc emissions in France decreased by 89% since 1990, mainly caused by technical improvements in electric furnace steel plants, i.e. the installation of dust extractors(CITEPA, 2009) and the implementation of the European directive on waste incineration(Directive 2000/76/CE, 2000), limiting Zn emissions from that particular source.

Table 1 :

 1 Summary of the different analytical techniques used between 1986 and 2008 for the determination of trace metal concentrations in the atmospheric aerosol, with the associated detection limits. 1.1986-87 measurements were performed with a Varian Techtron AA 1275 equipped with a CRA 90 atomiser and Ultra Carbon pyrolytic crucibles. From 1995 analysis were performed with Varian SpectroAA 800 with ZEEMAN correction and autosampler 2. Measurements were performed with a Jobin-Yvon JY 138 S Ultrace analyser, equipped with a Scott nebuliser. 3. Thermo Electron, X series, analytical details are given inIdardare et al. 2008. 4. EG&G Princeton Applied Research 264 A polarographic analysed coupled to a 303 A static Hg drop electrode (1.6 mm 2 area). The auxiliary electrode was a Pt wire, and the Ag/AgCl reference electrode was filled with a saturated solution of ultrapure KCl. For Cd and Pb, a glassy carbon rotating electrode (Tokay, 6 mm in diameter) was used as the working electrode. The measurements were performed with a Tacussel polarographic equipment (PRG-5 polarograph, fitted with two rotating EDI-type electrodes, with automatic Polaromate).The supporting electrolyte was seawater carried over a Chelex 100 resin (cation exchanger). Standard electrolysis times ranged between 3 min (Zn) and 10 min (Cd and Pb). In every case, the detection limit was the smallest readable signal, arbitrarily evaluated to 1 mm. *GFAAS measurements were carried out on sections of the membrane filter (3 mm in diameter) punched out and directly introduced into the carbon-rod atomiser, without any mineralisation. Detection limits are therefore expressed in mass instead of concentration units.

			1986-87 1992-93 1994-95 1996-98 2003-05 2006-08
		Geometric mean	114		113	143	74	86
		Arithmetic mean	144		154	192	135	140
	Al	sd	109		158	151	216	191
		min	33		17	10	13	12
		max	541		1125	746	1298	1327
		n	32		67	69	44	119
		Geometric mean			142	181	116	114
		Arithmetic mean			168	215	158	147
	Fe	sd			109	135	155	131
		min			27	60	31	25
		max			647	816	865	954
		n			67	67	44	119
		Geometric mean				4.42	2.96	2.47
		Arithmetic mean				5.25	3.94	3.14
	Mn	sd				3.07	3.45	2.47
		min				1.02	0.84	0.46
		max				15.7	17.2	17.2
		n				68	37	119
		Geometric mean			0.05			0.09
		Arithmetic mean			0.08			0.11
	Co	sd			0.07			0.08
		min			0.01			0.02
		max			0.28			0.67
		n			67			119
		Geometric mean		1.98	2.20	2.69		1.74
		Arithmetic mean		2.27	2.57	3.23		2.25
	Ni	sd		1.16	1.46	2.39		1.58
		min		0.49	0.50	0.74		0.16
		max		5.53	7.3	15.9		9.52
		n		48	67	69		119
	Cu	Geometric mean	4.69	3.94	3.54	3.39		3.81
		Arithmetic mean	5.91	4.94	4.22	3.94		4.45

Table 2 :

 2 Summary of aerosol TM concentrations. Geometric mean, standard deviation (computed from arithmetic mean), minimum and maximum concentrations are given in ng m -3 .Data are presented in groups over the observed time

Table 3 :

 3 Intercorrelation matrix of the 9 TMs (119 observations per variable, data set 2006-08). Crustal and anthropogenic TMs show highest intercorrelation values (r). All intercorrelations are significant, except those for Zn, which are only significant for Cu, Pb and Cd, highlighting its anthropogenic character.

	r	Al	Fe	Mn	Co	Ni	Cu	Pb	Cd	Zn
	Al	1	0.96	0.87	0.85	0.59	0.43	0.31	0.33	0.07
	Fe	0.96	1	0.95	0.92	0.68	0.64	0.50	0.50	0.19
	Mn	0.87	0.95	1	0.92	0.70	0.71	0.57	0.59	0.16
	Co	0.85	0.92	0.92	1	0.80	0.71	0.50	0.52	0.16
	Ni	0.59	0.68	0.70	0.80	1	0.67	0.36	0.37	0.08
	Cu	0.43	0.64	0.71	0.71	0.67	1	0.72	0.66	0.37
	Pb	0.31	0.50	0.57	0.50	0.36	0.72	1	0.81	0.62
	Cd	0.33	0.50	0.59	0.52	0.37	0.66	0.81	1	0.30
	Zn	0.07	0.19	0.16	0.16	0.08	0.37	0.62	0.30	1

Acknowledgements

This work was partly supported by the Conseil Général des Alpes-Maritimes (project AIRMED 06) and with the partnership of the Agence de l'Eau Rhône Méditerranee Corse (Rhône-Mediterranean-Corsica Water Agency). We wish to thank Dominique Auger and Emmanuelle Rozuel for their valuable assistance with sample preparation and logistics, and Bernard Gentili for technical assistance. We are also indebted to the Université de Nice-Sophia Antipolis. We also wish to thank the French Marine team of the Cap Ferrat naval signal station. Lastly, we are grateful for the constructive review comments which greatly improved this manuscript.


Francis Mairet
email: francis.mairet@usm.cl

Olivier Bernard

Elliot Cameron

Monique Ras

Laurent Lardon

Jean-Philippe Steyer

Benoît Chachuat

Three-reaction model for the anaerobic digestion of microalgae

Keywords: Anaerobic digestion, microalgae, dynamic model, Chlorella vulgaris, hydrolysis, Contois kinetics, ammonia inhibition

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

Introduction

Microalgae are currently considered one of the most promising feedstock for biofuels [START_REF] Rittmann | Opportunities for renewable bioenergy using microorganisms[END_REF][START_REF] Wijffels | An Outlook on Microalgal Biofuels[END_REF]. But on the path to making large-scale microalgae culture sustainable, one needs to consider the management of large quantities of residual algal biomass along with the supply of large amounts of fertilizers. Not only does anaerobic digestion appear to be in an ideal position for addressing these two challenges, but it also presents encouraging economic and energetic performances [START_REF] Sialve | Anaerobic digestion of microalgae as a necessary step to make microalgal biodiesel sustainable[END_REF][START_REF] Mussgnug | Microalgae as substrates for fermentative biogas production in a combined biorefinery concept[END_REF][START_REF] Zamalloa | The techno-economic potential of renewable energy through the anaerobic digestion of microalgae[END_REF]. Coupling microalgae culture and anaerobic digestion is therefore a promising alternative for producing methane from solar energy [START_REF] Sialve | Anaerobic digestion of microalgae as a necessary step to make microalgal biodiesel sustainable[END_REF][START_REF] De Schamphelaire | Revival of the biological sunlight-to-biogas energy conversion system[END_REF][START_REF] Ehimen | Energy recovery from lipid extracted, transesterified and glycerol codigested microalgae biomass[END_REF]. However, due to their inherent complexity, the design and operation of such coupled systems presents many challenges. Mathematical models are particularly helpful for their analysis and design as well as for devising robust control strategies. The emphasis in this paper is on the development of a dynamic model for anaerobic digestion of microalgae, as a first step towards developing a full model of the coupled process.

The anaerobic digestion ecosystem is known to be complex, involving hundreds of bacterial species. While many anaerobic digestion models have been developed since the 1970s, including the well-accepted IWA anaerobic digestion model 1 (ADM1) [START_REF] Batstone | Anaerobic Digestion Model No[END_REF], only one study has been devoted specifically to the modeling of the anaerobic digestion of algal biomass to our knowledge (Mairet et al., 2011b). It was shown that a modified version of ADM1 that employs Contois kinetics for the hydrolysis steps is able to adequately describe the anaerobic digestion of microalgae. But with more than 30 state variables, this model is hardly amenable to mathematical analysis [START_REF] Bernard | Dynamic models of biochemical processes: properties of models[END_REF].

Our goal is to develop a reduced model based on experimental data obtained from anaerobic digestion of the freshwater microalgae Chlorella vulgaris over a period of 140 days. We aim to accurately represent the key variables of the process, yet with the lowest possible level of complexity. In particular, we pay special attention to the low biodegradability of common microalgae along with their large nitrogen content which, when converted into ammonia, can inhibit the bacterial activity [START_REF] Chen | Inhibition of anaerobic digestion process: A review[END_REF].

A two-reaction model, referred to as AM2 subsequently, was developed by [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF] for anaerobic digestion of highly concentrated wastewater, whereby a population of acidogenic bacteria first degrade the organic substrate to produce CO 2 and volatile fatty acids (VFAs) and a second population of methanogenic bacteria then consume the VFAs and produce CO 2 and methane. This model, which features a good trade-off between accuracy and simplicity, has been widely used for analysis, monitoring and control [START_REF] Steyer | Lessons learnt from 15 years of ICA in anaerobic digesters[END_REF][START_REF] Hess | Advanced dynamical risk analysis for monitoring anaerobic digestion process[END_REF][START_REF] Rincon | Control of an anaerobic digester through normal form of fold bifurcation[END_REF]. However, extensive numerical simulation has revealed that AM2 cannot accurately describe the anaerobic digestion of microalgae, especially regarding the fate of nitrogenous compounds. This clearly calls for further developments.

The following procedure is used in this paper to develop a reduced dynamic model. In section 2, we describe the experimental set-up and the methodology used to determine the minimum number of reactions needed to match the variability in the available experimental data set. Then, a reaction scheme is proposed in section 3, based on a simplification of ADM1.

In section 4, the resulting model-called MAD (Microalgae Anaerobic Digestion model) hereinis calibrated from the available experimental data and the fit quality is compared to that of the modified ADM1. Important features of the MAD model are also discussed in this section.

Materials and Methods

Experimental Methodology

Experimental Setup Experiments were carried out using the freshwater microalgae Chlorella vulgaris, strain CCAP 211/11B (grown under non-limiting conditions) in a 1 L continuousstirred-tank anaerobic digester, with 0.1 L headspace, maintained at 35 • C, and without pH control.

Feed Stream Characterization A detailed characterization of the feed stream can be found in [START_REF] Ras | Experimental study on a coupled process of production and anaerobic digestion of Chlorella vulgaris[END_REF] and Mairet et al. (2011b). Such feed was introduced as slugs, with an average organic load of 1 g COD.L -1 .d -1 , while equal volumes of reactor medium were removed to maintain a constant liquid volume. This feed policy was chosen in order for the process to operate under a wide range of conditions, both close to steady state for three different dilution rates and in transient mode by applying large substrate pulses. The dilution rate profile (daily average) along with the substrate additions are shown in Fig. 1. The average concentrations of other relevant inlet components are reported in Tab. I.

Measurement Techniques

The following quantities were measured on a daily basis: total COD (by colorimetric method); ion concentrations (by ion chromatography); biogas volume (by water displacement); biogas composition (by gas chromatography); and pH. Random samples were also selected on a less frequent basis for VFA determination. See [START_REF] Ras | Experimental study on a coupled process of production and anaerobic digestion of Chlorella vulgaris[END_REF] for details on the applied protocols.

Determining Model Complexity

The first step in the modeling methodology applied in section 3 consists in identifying the least number of reactions required to explain the variability in the experimental data set. This analysis can be performed based on principal component analysis (PCA), following the approach described by [START_REF] Bernard | On the estimation of the pseudo-stoichiometric matrix for mass balance modeling of biotechnological processes[END_REF] and [START_REF] Bernard | Can we assess the model complexity for a bioprocess? theory and example of the anaerobic digestion process[END_REF], which is summarized hereafter.

A general mass-balance model of the following form is considered for the system:

ξ(t) = Kr (•) + D(t) ξ in (t) -ξ(t) -q (•) , (1)
where ξ, ξ in ∈ IR n ξ are the state variables in the reactor liquid phase and in the feed stream, respectively; D, the dilution rate; K ∈ IR n ξ ×nr , the stoichiometric matrix; r ∈ IR nr , the reaction rate vector; and q ∈ IR n ξ , the gaseous rate vector.

The number of state variables that can be directly measured is quite limited in most biotechnological processes, and the available measurements often correspond to combinations of the state variables, such as total COD. Sometimes, measurements can also be related to the reaction rates, for example for gaseous outflows of low soluble species such as methane. The analysis throughout this subsection is thus conducted for an output vector of the form:

y =    y y    =    C ξ C r (•)    , (2)
where n y = n y + n y is the total number of measurements, such that n y ≥ n r . The matrices C ∈ R n y ×n ξ and C ∈ R n y ×nr represent the combinations for the state variables and the reaction rates.

For any time instants t i < t j , let u(•, •), v(•, •) and w(•, •) be defined as:

u(t i , t j ) =    y (t j ) -y (t i ) - t j t i D(t)[y in (t) -y (t)]dt t j t i y (t)dt    v(t i , t j ) = t j t i r(•)dt, and w(t i , t j ) = t j t i q(•)dt.
Suppose that N records of u(•, •), v(•, •) and w(•, •) with N > n r are available, and define the matrices U = (u(t 0 , t 1 ), . . . , u(t N -1 , t N )) and V, W alike. From (1) and ( 2), it is not hard to see that the following linear relationship holds:

U =    C K C    =: Γ V +    C 0    W. (3)
Under the additional assumptions that the matrix Γ is full rank-which requires that the measurements y are non redundant-and that the measured liquid species y are not involved in (significant) liquid-gas transfer-which enforces W ≈ 0-the number of reactions required to describe the data can directly be assessed from the PCA of the matrix U = ΓV. Specifically, each principal axis is representative of a given reaction, and the corresponding principal component represents the relative proportion of the overall variability in the data set that can be accounted for by that reaction. Dividing by the largest eigenvalue makes it easy to determine the cumulative variability for a set of principal components, and thus the minimum number of reactions required to account for a variability in the data greater than a given threshold; e.g., 95% of the variability.

In making this PCA analysis, care must be taken to normalize and center the data in each row of U in order to give the same weighting to all the variables:

U i = U i -µ(U i ) √ N σ(U i ) , i = 1, . . . , n y ,
where µ(U i ) and σ(U i ) are, respectively, the mean and the standard deviation of U i .

3 Microalgae Anaerobic Digestion Model

Model Development

Minimum Number of Reactions We start by determining the minimum number of reactions need to explain the variability in the available data by applying the PCA methodology outlined in subsection 2.2. The matrix U is calculated using the available liquid-phase measurements in total COD, inorganic nitrogen and VFA concentrations, along with the methane flow rate measurements that are representative of the methanogenic bacteria activity. The time instants t 1 , t 2 , . . . , t N +1 are directly taken as the measurement times, and cubic spline interpolants are used to compute the integral terms. Note that none of the measured liquid-phase species are involved in liquid-gas transfer, and therefore the PCA results can be interpreted in terms of biological reactions; that is, U = ΓV. PCA is applied to the centered and normalized data, and the cumulative variability for the principal components is presented in Fig. 2. These results show that 2 or 3 reactions are a minimum for explaining, respectively, 95% and 99% of the variability in the data set.

Biological Reaction Pathway Having settled on the number of reactions required to describe the available data, the next step in our modeling methodology is to determine the reaction scheme. This step was carried out on the basis of a simplification of ADM1. In order to preserve a strong biological interpretation, a three-reaction scheme was selected.

The algal biomass substrate is first divided in two parts, denoted as S 1 and S 2 . S 1 is mainly composed of sugars and lipids and does not contain nitrogen, while S 2 mainly consists of proteins and thus contains nitrogen. Both substrates degrade to VFAs, denoted as S 3 , through the action of specific bacterial populations denoted by X 1 and X 2 , respectively. Finally, as in the AM2 model, a methanogenic population X 3 converts the VFAs into methane. Unlike ADM1, a separation between lipids and sugars is not considered in order to keep a low model complexity.

Finally, a fraction of the microalgae is considered to yield inert substrate, denoted as S I , in agreement with batch experiment observations (data not shown).

A summary of the three-biological reactions in the MAD model is as follows (see Fig. 3):

• VFA production from hydrolysis-acetogenesis of sugars-lipids:

α 1 S 1 + α 2 NH + 4 µ 1 (•) X 1 -----→ X 1 + α 3 S 3 + α 4 CO 2 (R 1 )
• VFA and ammonia production from hydrolysis-acetogenesis of proteins:

α 5 S 2 µ 2 (•) X 2 -----→ X 2 + α 6 S 3 + α 7 NH + 4 + α 8 CO 2 (R 2 )
• Methane production via methanogenesis of the VFAs:

α 9 S 3 + α 10 NH + 4 µ 3 (•) X 3 -----→ X 3 + α 11 CH + 4 + α 12 CO 2 . (R 3 )
In the following, S i and X i are expressed in gCOD.L -1 , while NH + 4 , CO 2 and CH 4 are in mol.L -1 (M).

Biological Reaction Kinetics The specific growth rates for the hydrolysis-acidogenesis reactions (R 1 ) and (R 2 ) are modeled as Contois functions of the corresponding substrates:

µ i (S i , X i ) = μi S i S i + K Si X i , for i = 1, 2. (4)
A Haldane function is used to model the methanogenesis specific growth rate in (R 3 ), and it is multiplied by an ammonia inhibition term:

µ 3 (S 3 , NH 3 ) = μ3 S 3 S 3 + K S3 + S 2 3 /K I3 K I NH 3 K I NH 3 + NH 3 . ( 5
)
Charge Balance and pH In order to determine the pH in the digester, all the acid-base pairs are supposed to be in equilibrium. Assuming a pH no higher than 8, the concentration of carbonate ions CO 2- 3 can be neglected and the total inorganic carbon concentration, denoted by C, reduces to the sum of the dissolved carbon dioxide concentration CO 2 and the bicarbonate concentration HCO - 3 . Considering the dissociation constant

K C = h[HCO - 3 ] [CO 2 ]
for the pair HCO - 3 /CO 2 , the bicarbonate concentration reads:

[HCO - 3 ] = K C h + K C C. (6)
where h = [H + ], expressed in M.

Similarly, dissociation of the total inorganic nitrogen between free ammonia and ammonium

ions (N = [NH 3 ] + [NH + 4 ]
) and of the VFA between non-ionized HVFA and ionized VFA -

(S 3 = [HVFA] + [VFA -]) leads to: [NH + 4 ] = h K N +h N VFA -= K VFA K VFA +h S 3 , (7)
with

K N = h[NH 3 ] [NH + 4 ] and K VFA = h[VFA -]
[HVFA] the dissociation constants for the pairs NH 3 /NH + 4 and VFA -/HVFA. Assuming that the VFAs are mainly composed of acetate, the dissociation constant of acetate can be used for VFA; note that the dissociation constants of the different VFA as propionate and butyrate are very close anyway.

We define the inert charge imbalance z as follows:

z = [Cat I ] - [An I ], (8)
where Cat I and An I are those cations and anions not affected by the anaerobic digestion (Na + , K + , Cl -, etc.), multiplied by their valence. Then, charge balance leads to the following equation:

z + [NH + 4 ] + h = [OH -] + [HCO - 3 ] + [VFA -]/ MVFA , (9)
where MVFA stands for the COD content of VFAs (64 gCOD.mol -1 assuming pure acetate),

and

[OH -] = K H 2 O /h.
Combining equations ( 6), ( 7) and ( 9) yields:

K H 2 O h + K C h + K C C + K VFA K VFA + h S 3 MVFA -z - h K N + h N -h = 0, ( 10
)
which relates the pH (= -log 10 h) in the digester to the other state variables z, N , C and S 3 .

Liquid-Gas Transfer

The liquid-gas transfer rate of CO 2 (in mol.L -1 .d -1 ) is modeled as follows:

ρ CO 2 = k L a([CO 2 ] -K H,CO 2 P CO 2 ) = k L a( h K C +h C -K H,CO 2 P CO 2 ), (11)
where P CO 2 is the partial pressure of CO 2 in the headspace, K H,CO 2 Henry's constant for CO 2 and k L a the liquid-gas transfer coefficient. On the other hand, we consider that all of the produced methane is transfered to the headspace, due to its very low solubility:

ρ CH 4 = α 11 µ 3 X 3 . ( 12
)
The biogas flow rate can be computed by assuming an overpressure in the headspace as:

q gas = max (0; k p (P CH 4 + P CO 2 -P atm )) , (13)
with k p the pipe resistance coefficient [START_REF] Batstone | Anaerobic Digestion Model No[END_REF]. Finally, the methane content (% CH 4 ) of the biogas flow can be obtained as:

% CH 4 = P CH 4 P CH 4 + P CO 2 . ( 14
)
Mass Balance in the Headspace The dynamics of the partial pressures in CO 2 and methane are given by:

ṖCO 2 = -P CO 2 q gas V gas + ρ CO 2 V liq RT op V gas (15) ṖCH 4 = -P CH 4 q gas V gas + ρ CH 4 V liq RT op V gas (16) (17)
where V liq and V gas are the volumes of the liquid and gas phases, T op is the operating temperature, and R is the gas law constant.

Mass Balance in the Liquid Phase Considering a perfectly mixed reactor fed with microalgae characterized by their fraction in sugars-lipids β 1 , proteins β 2 , and inerts β I , the dynamics of the species concentrations in the liquid phase read:

Ṡ1 = D(β 1 S in -S 1 ) -α 1 µ 1 X 1 (18) Ṡ2 = D(β 2 S in -S 2 ) -α 5 µ 2 X 2 (19) Ṡ3 = -DS 3 + α 3 µ 1 X 1 + α 6 µ 2 X 2 -α 9 µ 3 X 3 (20) Ẋ1 = (µ 1 -D) X 1 (21) Ẋ2 = (µ 2 -D) X 2 (22) Ẋ3 = (µ 3 -D) X 3 (23) Ṅ = D(N in -N ) -α 2 µ 1 X 1 + α 7 µ 2 X 2 -α 10 µ 3 X 3 (24) Ċ = D(C in -C) + α 4 µ 1 X 1 + α 8 µ 2 X 2 + α 12 µ 3 X 3 -ρ CO 2 (25) ż = D(z in -z) (26) ṠI = D(β I S in -S I ) ( 27
)
where D is the dilution rate, S in , N in , C in and z in are, respectively, the concentrations of COD, inorganic nitrogen, inorganic carbon, and inert charge imbalance in the feed.

Numerical Simulation of the MAD Model Overall, the MAD model consists of the mass balance equations in the headspace ( 15)-( 16) and in the liquid phase ( 18)-( 27), together with the charge balance equation ( 10). The specific growth rates µ i in these equations are defined by ( 4) and ( 5), with NH 3 = K N K N +h N . Moreover, the liquid-gas transfer rates ρ CO 2 and ρ CH 4 are defined in ( 11) and ( 12).

The fact that feed was introduced as sludges during the experiment requires special treatment in the numerical simulations. The effect of each addition (at time t i ) on the liquid-phase concentrations (as represented by the vector ξ) are computed based on mass-balance considerations as follows:

ξ(t + i ) = ξ(t - i ) + V in (t i ) V liq ξ in (t i ) -ξ(t - i ) ( 28
)
where V in and ξ in are the volume and the concentrations of the feed additions. The MAD model is then solved with D = 0 until the next feed (from t + i to t - i+1 ), and so on.

Model Calibration

Feed Substrate Characterization Using an average biochemical composition of Chlorella vulgaris [START_REF] Becker | Micro-algae as a source of protein[END_REF][START_REF] Pruvost | Systematic investigation of biomass and lipid productivity by microalgae in photobioreactors for biodiesel application[END_REF], Mairet et al. (2011b) have determined COD fractions corresponding to proteins (40%), lipids (22%), carbohydrates (8%) and inerts (30%). From this characterization, the feed composition parameters β 1 , β 2 and β I in the MAD model could be easily deduced, as reported in Tab. II.

Stoichiometric Parameters

The values of the stoichiometric coefficients α i in Tab. II were deduced from [START_REF] Batstone | Anaerobic Digestion Model No[END_REF] and from conservation laws based on the substrate, product and biomass compositions given in Tab. III.

Kinetic Parameters

The kinetic parameters were identified with a minimization algorithm (function fminsearch in Matlab R implementing the Nelder-Mead simplex algorithm [START_REF] Nelder | A simplex method for function minimization[END_REF]) using the whole experimental data set, composed of the following measurements:

COD (= S + X), gas flow rate, methane content, VFA and inorganic nitrogen. This algorithm was used to find the set of parameters that minimizes an error criterion J summing the relative errors between the model and the measurements as:

J = p j=1 ω j n j n j i=1 y e j (t i ) -y m j (t i ) ȳm j 2 , ( 29
)
where, for each measured variable j, y m j (t i ), y e j (t i ) and ȳm j are respectively the measurement and the model estimation at time t i and the average value of the measurement, and ω j is the weight attributed to the variable j.

Moreover, in order to assess the quality of the fit for the various measurements, a fitting index was defined as

I j = 1 n j n j i=1 y e j (t i ) -y m j (t i ) ȳm j 2 , ( 30
)
for each measured variable j.

Results and Discussions

Comparisons with Experimental Data The simulation results are plotted in Fig. 4 (red lines), and parameter values are given in Tab. II. The MAD model describes fairly accurately the experimental data, in particular the COD, VFA and inorganic nitrogen concentrations (Fig. 4 A, C, and E). The gas flow rate is well predicted too (Fig. 4 B), along with the methane content (Fig. 4 D) except at the end of the experiment (after day 100) when larger slugs are fed to the reactor. The liquid-gas transfer model is a possible source of error as large feed slugs can create transients during which ρ CO 2 ≤ 0 and q gas = 0. Modeling such large disturbances using a constant mass transfer coefficient k L a may not be suitable. Indeed, the specific interfacial area per unit volume of liquid in the reactor, a, is largely dependent on the gas production rate [START_REF] Pauss | Liquid-to-gas mass transfer in anaerobic processes: inevitable transfer limitations of methane and hydrogen in the biomethanation process[END_REF][START_REF] Merkel | Mass transfer of carbon dioxide in anaerobic reactors under dynamic substrate loading conditions[END_REF]. Nevertheless, this phenomenon should not occur for a continuous feed policy, therefore the model was not modified. Finally, the discrepancy in the pH (Fig. 4 F) can be attributed to a poor characterization of the feed composition, which was not regularly monitored and probably varied during the 140-day experiment.

The good agreement between the model predictions and the experimental data confirms that a three-reaction system is sufficient to explain the majority of the variability in the data set (see subsection 2.2). Since both inorganic nitrogen and VFA accumulations can lead to inhibition and process instability, the good representation of these species is a first hint that the model shall be suitable for on-line control and monitoring purposes.

In the model simulation, almost all the biodegradable part of the microalgae is digested when low dilution rate are applied (first 70 days in the available data set). On the other hand, a high dilution rate can produce a decrease of the protein degrader population X 2 and therefore an accumulation of protein S 2 (see Fig. 5 after day 70), while sugars and lipids are almost completely degraded because of a higher maximal growth rate of X 1 . This leads to a nitrogen release (due to protein degradation) not correlated to the methane production, as it was already observed experimentally [START_REF] Ras | Experimental study on a coupled process of production and anaerobic digestion of Chlorella vulgaris[END_REF] and with the modified ADM1 (Mairet et al., 2011b). Although it is rarely pointed out, this phenomenon can also be observed, for example, in the anaerobic digestion of primary sludge [START_REF] Miron | The role of sludge retention time in the hydrolysis and acidification of lipids, carbohydrates and proteins during digestion of primary sludge in cstr systems[END_REF]. Using two parallel steps for acidogenesis, as it is proposed in the MAD model, is therefore necessary to catch the complex dynamics of microalgae anaerobic digestion. This also explains why a two-reaction model such as AM2 could not describe these experiments well.

Recall that it was assumed during model development (see subsection 3.1) that the VFAs are mainly composed of acetate, meaning that acetogenesis is included in the two hydrolysisacidogenesis reactions (R 1 ) and (R 2 ). This assumption is necessary in calculating the stoichiometric coefficients and writing the ion balance. Numerical simulations under various operating conditions using the modified ADM1 show that acetate represents over 80% of VFA (in COD) at steady state. However, this assumption may no longer be verified during long transients, thereby leading to an underestimation of the pH.

Comparisons with ADM1

The predictions of the MAD model are compared with those of the modified ADM1 in Fig. 4. It should be noted that the late was calibrated from the same experimental data set in previous work (Mairet et al., 2011b).

While the MAD model complexity is much lower than that of ADM1, the fit quality of these two models, in terms of the fit indices (30), appear to be almost the same (for total COD, inorganic nitrogen and gas flow rate) or even better (for methane content and VFA)see Tab. IV. Note that for both model calibrations, six parameters were identified using a minimization procedure. Regarding the modified ADM1, only the kinetic parameters involved in the three parallel hydrolysis reactions were estimated, which could explain why the MAD model yields better results. Clearly, the fitting performance of ADM1 could be improved by estimating additional kinetic parameters. However, due to the relatively few measured outputs and the high model complexity, trying to estimate too many parameters inevitably results in structural and practical identifiability issues [START_REF] Dochain | Dynamical Modelling and Estimation in Wastewater Treatment Processes[END_REF].

Considerations on Experimental Measurement Techniques

Assessing the evolution of the various biomass populations would provide a better insight in the process complexity. It would also be of great help for monitoring the process, and maintain optimal working conditions. However, despite some promising recent studies [START_REF] Rivière | Towards the definition of a core of microorganisms involved in anaerobic digestion of sludge[END_REF][START_REF] Carballa | Correlations between molecular and operational parameters in continuous lab-scale anaerobic reactors[END_REF], analytical techniques are currently lacking to study the anaerobic microbial diversity.

Monitoring microbial population dynamics remains a real challenge. Molecular techniques, such as polymerase chain reaction (PCR), denaturing gradient gel electrophoresis (DGGE) and terminal restriction fragment length polymorphism (T-RFLP), have recently emerged but most of these tools remain qualitative, or specific to a bacterial community [START_REF] Lee | Quantitative analysis of methanogenic community dynamics in three anaerobic batch digesters treating different wastewaters[END_REF]. New improvements in analytical techniques are required to quantify and to determine the metabolic functions of all the microorganisms involved in the process. Similarly, the measurements of all the intermediate products at industrial scale would require substantial efforts and costs. Model simulations can thus provide useful estimations of population and substrate dynamics and help to detect sub optimal working modes.

Considerations on Species Conservation Based on the substrate, product and biomass compositions given in Tab. III, the stoichiometric coefficients in Tab. II guarantee that COD and nitrogen are conserved in each reaction. This analysis is shown in Tab. V. On the other hand, the carbon balance is not closed because S 3 is assumed to be only VFA, while it should also include H 2 . Nevertheless, the dynamics of H 2 and VFA are very different due to the liquid-gas transfer of H 2 and a very low half saturation constant for the hydrogenotrophic methanogenesis.

In order to keep model complexity as low as possible, H 2 was not included in the MAD model.

It follows that the model overestimates VFA production in reactions (R 1 ) and (R 2 ).

Considerations on Biological Kinetics Hydrolysis is known to be the limiting step in microalgae anaerobic digestion (Mairet et al., 2011b). The Contois model, which includes the saturation of both substrate and biomass, is a reliable way of describing hydrolysis [START_REF] Vavilin | Hydrolysis kinetics in anaerobic degradation of particulate organic material: An overview[END_REF], in particular for microalgae (Mairet et al., 2011b). On the other hand, a Haldane function is suitable to model the methanogenesis specific growth rate as it accounts for VFA inhibition [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF]. Since methanogens are the least tolerant to ammonia among all the populations involved in anaerobic digestion [START_REF] Chen | Inhibition of anaerobic digestion process: A review[END_REF], an ammonia inhibition function is used only for this population. Nevertheless, as the experiments were carried out at a low loading rate, no significant inhibitory accumulation of ammonia or VFA could be observed. It follows that the inhibition parameters could not be estimated from these data and their values had to be taken from other studies: [START_REF] Batstone | Anaerobic Digestion Model No[END_REF] for ammonia (K I NH 3 )

and [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF] for VFA (K I3 ). These inhibition terms were however retained in the kinetic expressions since they are expected to play an important role in the future use of the model (control and monitoring).

Applications to Other Microalgae Species Although it was developed and calibrated for the anaerobic digestion of Chlorella vulgaris, we expect that the MAD model can also be used with other microalgae species, provided that some of its parameter values are adjusted.

First, the biochemical composition typically varies for each microalgal species and also depends on the culture conditions (nutrients, light, temperature, etc..) [START_REF] Harrison | Effects of nutrient and light limitation on the biochemical composition of phytoplankton[END_REF]Mairet et al., 2011a). Therefore, the feed composition parameters β 1 , β 2 and β I must be adjusted for other microalgae species and/or culture conditions. On the other hand, assuming that the main composition of protein, lipid and carbohydrate is constant, the stoichiometric coefficients should not vary too much. Finally, the kinetic parameters should be adjusted for different microalgae species as the digestibility kinetics have shown to be species dependent [START_REF] Mussgnug | Microalgae as substrates for fermentative biogas production in a combined biorefinery concept[END_REF]. In particular, significant changes are expected for marine species in connection to sodium toxicity [START_REF] Sialve | Anaerobic digestion of microalgae as a necessary step to make microalgal biodiesel sustainable[END_REF].

Conclusions

In this paper, we have proposed a three-reaction model for the anaerobic digestion of microalgae, the so-called MAD model. As the methane and inorganic nitrogen productions are not correlated, the distinction between sugar-lipid and protein degradations is necessary to obtain a good representation of the available experimental data. The fit quality with the MAD model is comparable to that of the modified ADM1 (Mairet et al., 2011b), yet its complexity is much lower, which makes it better suited for mathematical analysis and for derivation of control and monitoring algorithms. As part of future work, we expect to validate the model under higher load conditions; that is, leading to larger ammonia and VFA accumulations and inhibitions.

This model will then serve as the basis for optimizing the design and operation of anaerobic digesters when coupled to microalgae culture.

Tables

Figure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Total variance explained with respect to the number of reactions for the anaerobic digestion of Chlorella vulgaris.

Figure 5 :

 5 Figure 5: Prediction of substrate and bacteria population dynamics with the MAD model. A substrate and its associated bacteria population are represented with the same line type.

Table I

 I

			: Feed characterisation
	Parameter	Value	Meaning
	z in	0.017 M Inert charge imbalance concentration
	pH in	9.6
	C in	0.019 M Inorganic carbon concentration
	N in	0.011 M Inorganic nitrogen concentration

Table IV :

 IV Comparison of the fit qualities with the MAD and modified ADM1 models; a smaller value means a better fit.

	Measurement Table V: Biological reactions: COD, nitrogen and carbon balances Fitting Index I j α 1 S 1 + α 2 NH + 4 X 1 + α 3 S 3 + α 4 CO 2 -→ g COD R 1 12.5 + 0 = 1 + 11.5 + 0
	mmol N	0	+	6.2	MAD model Modified ADM1 = 6.2 + 0	+	0
	mmol C	Total COD 309 +	0	0.059 =	31	+	0.053 359	+	30
	Inorganic nitrogen Gas flow rate % CH 4 X 2 α 5 S 2 -→ 9.1 = 1 VFA mmol N 60.3 R 2 g COD = 6.2 Mean mmol C 230 = 31 R 3 α 9 S 3 + α 10 NH + 4 g COD 20 + 0	0.011 0.36 0.0063 + α 6 S 3 + α 7 NH + 0.016 0.41 4 + 8.1 + 0 0.020 1.0 + 0 + 54.1 2.5 0.3 + 253 + 0 0.6 X 3 + α 11 CH 4 + α 12 CO 2 + α 8 CO 2 + 0 + 0 + 30 -→ = 1 + 19 + 0
	mmol N	0	+	6.2	=	6.2	+	0	+	0
	mmol C	626	+	0	=	31	+	300	+	200

Acknowledgements

This work benefited from the support of the Symbiose research project founded by the French National Research Agency (ANR). Francis Mairet thanks the support of Fondo Basal, Centro de Modelamiento Matematico -U. de Chile. Elliot Cameron is grateful to NSERC and OGS

for graduate scholarships. 8))

For the parameters, refer to Tab. II.