Hélène Balcone-Boissard
email: boissardhelene.balcone_boissard@upmc.fr

G Boudon

J D Blundy

Caroline Martel

R A Brooker

E Deloule

C Solaro

V Matjuschkin

• G Boudon

• C Martel

• V Matjuschkin

Deep pre-eruptive

Keywords: Melt inclusion, Volatiles, Arc magma, Dominica, Lesser Antilles arc

come

Introduction

Subduction zone volcanic rocks reflect diverse contributions to arc magma generation in terms of chemical modification of the mantle by recycled oceanic lithosphere (e.g.

Communicated by Othmar Müntener.

Electronic supplementary material

The online version of this article (https ://doi.org/10.1007/s0041 0-018-1528-4) contains supplementary material, which is available to authorized users. [START_REF] Macdonald | The Lesser Antilles volcanic chain: a study in arc magmatism[END_REF]. The chemical diversity of arc magmas provides insights into crustal differentiation processes [START_REF] Yanagida | Differentiation of a hydrous arc magma recorded in melt inclusions in deep crustal cumulate xenoliths from Ichinomegata Maar, NE Japan[END_REF], whereas their magmatic volatiles afford clues to eruption dynamics and pre-eruptive magma storage conditions [START_REF] Gurenko | A melt inclusion record of volatiles, trace elements and Li-B isotope variations in a single magma system from the Plat Pays Volcanic Complex, Dominica, Lesser Antilles[END_REF][START_REF] Balcone-Boissard | Behavior of halogens during the degassing of felsic magmas[END_REF]), a key parameter in developing a better evaluation of volcanic hazard, and in hydrothermal mineralization [START_REF] Wilkinson | Triggers for the formation of porphyry ore deposits in magmatic arcs[END_REF]. The primary geochemical signature of erupted magmas is inherited ultimately from the mantle source region with subsequent modification and evolution during differentiation and pre-eruptive ascent and storage in the crust. The role of different components in generating the diversity of arc magma composition (e.g. fluids derived from subducted oceanic crust and sediments, crustal contamination) remains a matter of debate [START_REF] Thirlwall | Resolution of the effects of crustal assimilation, sediment subduction, and fluid transport in island arc magmas: Pb-Sr-Nd-O isotope geochemistry of Grenada, Lesser Antilles[END_REF]Blundy et al. 2008;[START_REF] Labanieh | Martinique: a clear case for sediment melting and slab dehydration as a function of distance to the trench[END_REF].

Volatiles play a major role in determining the eruptive style of magma, through the interplay of degassing with magma rheology and phase relations [START_REF] Esposito | An assessment of the reliability of melt inclusions as recorders of the pre-eruptive volatile content of magmas[END_REF]. Characterization of volatile contents is essential in predicting the potential explosivity of magma, especially in a subduction context. Much of our understanding of magmatic volatile contents comes from melt inclusions (MI), small glassy pockets of magma trapped by phenocrysts during their growth, that preserve the pre-eruptive volatile content prior to eruption and degassing of the matrix. Carefully interpreted, MI data can help us to constrain the pre-eruptive conditions in terms of magma composition in major, trace and volatile elements [START_REF] Moore | Interpreting H 2 O and CO 2 contents in melt inclusions: constraints from solubility experiments and modeling[END_REF].

The aim of this work is to characterize the geochemical fingerprint of magmas responsible for the large pumiceous eruptions in the central part of Dominica (Lesser Antilles volcanic arc) as well as for those from the Morne aux Diables volcanic center in the northern part, by analysing MIs trapped in the major phenocrysts of the different eruptions, for the full spectrum of major, trace and volatile elements, including H 2 O, CO 2 , F, Cl, Br and S. In addition, magma storage conditions at the scale of the Lesser Antilles arc are discussed.

Geological context

The Lesser Antilles arc results from the oblique subduction of the Atlantic sea floor (North and South American plates) beneath the Caribbean Plate at a mean convergence rate of 2 cm/year [START_REF] Wadge | Comparison of volcanic production rates and subduction rates in the Lesser Antilles and Central America[END_REF]. The volcanic arc is 850 km long, extending from the island of Saba in the north to Grenada in the south, with an eastwards convexity. Dominica lies in the central part of the arc (Fig. 1a). North of Dominica the arc splits into two branches: the Outer or Older arc (Eocene to mid-Oligocene) and an Inner or Recent arc (Miocene to Recent). This jump in the northern sector has been ascribed to ancient subduction of an aseismic ridge in the center of the arc causing a rupture in the subduction plate and a displacement of volcanic activity to the West in the early-Miocene (~ 20 Ma; [START_REF] Bouysse | Subduction of Atlantic aseismic ridges and Late Cenozoic evolution of the Lesser Antilles island arc[END_REF]. South of Dominica the two branches merge, creating a single volcanic arc active since the Miocene. The active part of the arc (Saba to Dominica in the north, and Dominica to Grenada in the south) has 12 currently active volcanic centers, the most well-known being Soufrière (Guadeloupe), Montagne Pelée (Martinique), Soufrière Hills (Montserrat) and Soufrière (Saint-Vincent). In the last 300 years, these centers have produced several historic effusive and explosive eruptions spanning a broad range of styles and chemistries. Recent activity of the arc (< 2.0 My) shows an important segmentation [START_REF] Macdonald | The Lesser Antilles volcanic chain: a study in arc magmatism[END_REF]. Three segments can be defined: Saba-Montserrat, Guadeloupe-Martinique and St Lucia-Grenada [START_REF] Sigurdsson | Marine tephrochronology and quaternary explosive volcanism in the lesser antilles arc[END_REF][START_REF] Wadge | Segmentation of the Lesser Antilles subduction zone[END_REF]. The segmentation is also manifested in terms of magma production rate. Over the last 0.1 Ma, the central segment is characterized by the largest magma production rate, with Dominica reaching a peak at ~ 40 km 3 and Martinique and Guadeloupe at ~ 8 km 3 [START_REF] Wadge | Comparison of volcanic production rates and subduction rates in the Lesser Antilles and Central America[END_REF]. The north and south segments of the arc have produced significant smaller volumes of about 0-5 km 3 over the same time period [START_REF] Macdonald | The Lesser Antilles volcanic chain: a study in arc magmatism[END_REF][START_REF] Wadge | Comparison of volcanic production rates and subduction rates in the Lesser Antilles and Central America[END_REF].

Dominica is the only island in the Lesser Antilles arc that exhibits multiple active volcanic centers. From North to South these are: Morne aux Diables (MAD), Morne Diablotins (MD), Morne Trois-Pitons-Micotrin (MTPM), and Morne Plat Pays (also referred to as Plat Pays Volcanic Complex, PPVC). South of Morne Trois-Pitons-Micotrin numerous satellite volcanic centers exist, including Grand Soufrière Hills, Morne Anglais and Foundland. Dominica has produced several km 3 of volcanic products since the Pleistocene [START_REF] Sigurdsson | Partly-welded pyroclast flow deposits in Dominica, Lesser Antilles[END_REF][START_REF] Lindsay | Dominica[END_REF][START_REF] Smith | The volcanic geology of the mid-arc Island of Dominica, Lesser Antilles; the surface expression of an island-arc batholith[END_REF][START_REF] Howe | Reevaluation of the Roseau Tuff eruptive sequence and other Ignimbrites in Dominica, Lesser Antilles[END_REF][START_REF] Howe | Evolution of young andesiticdacitic magmatic systems beneath Dominica, Lesser Antilles[END_REF][START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF].

Recent studies have identified several voluminous pumiceous eruptions, including three large eruptions, expelled from the two central active centers: Layou (51 ka) from Morne Diablotins (MD), and Roseau (33 ka) and Grand Fond (24 ka) from Morne Trois Pitons-Micotrin (MTPM), each involving 3-5 km 3 of magma [START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF]. Studies of eruptive deposits [START_REF] Wadge | Comparison of volcanic production rates and subduction rates in the Lesser Antilles and Central America[END_REF][START_REF] Lindsay | Dominica[END_REF][START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF] have demonstrated that eruption volumes of the central part of Dominica are one order of magnitude larger than those from the volcanoes on neighbouring islands (Montagne Pelée, Martinique or Soufrière of Guadeloupe). In the most recent period (< 20 ka), at least six Plinian eruptions have been described originating from Morne Diablotins and Morne Trois Pitons-Micotrin [START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF].

Morne aux Diables volcano (MAD) forms the northern tip of Dominica. Morne aux Diables is composed of one central and several parasitic andesitic lava domes from which block-and-ash pyroclastic density current and a few pumiceous and/or andesitic pyroclastic density current deposits radiate out in all directions [START_REF] Smith | The volcanic geology of the mid-arc Island of Dominica, Lesser Antilles; the surface expression of an island-arc batholith[END_REF]. Age dating indicates that the main dome-building activity occurred between 1.5 and 1.0 million years ago, but valley-fill block-and-ash pyroclastic density current deposits suggest more recent activity. One such deposit on the north-east flank of the volcano has been recently dated at 43,710 year BP [START_REF] Smith | The volcanic geology of the mid-arc Island of Dominica, Lesser Antilles; the surface expression of an island-arc batholith[END_REF]. Although there have been no historical eruptions at Morne aux Diables, there is some evidence of restlessness. This includes the presence of warm, acidic, sulfate-rich springs on the summit of the volcano, hot springs on the coast and the occurrence of shallow earthquake swarms partially located beneath the volcano, the most recent being in 2003 and 2009. Other periods of such increased seismic activity occurred in 2000, 1893 and 1841.

Morne Plat Pays or Plat Pays Volcanic Complex (PPVC) is located in the southwestern corner of Dominica. The stratigraphic framework of Plat Pays Volcanic Complex shows a wide range eruptive styles but, as for Morne aux Diables, dome-forming activity dominates. Published work on Plat Pays Volcanic Complex has focussed on volcanic history and chronostratigraphy [START_REF] Lindsay | Geological history and potential hazards of the late-Pleistocene to Recent Plat Pays volcanic complex, Dominica, Lesser Antilles[END_REF][START_REF] Lindsay | Dominica[END_REF][START_REF] Friant | L'île de la Dominique: zone d'émission des avalanches de débris les plus volumineuses de l'arc des Petites Antilles[END_REF][START_REF] Samper | Radiometric dating of three large volume flank collapses in the Lesser Antilles Arc[END_REF]) and on petrology and geochemistry [START_REF] Halama | Pre-eruptive crystallization conditions of mafic and silicic magmas at the Plat Pays volcanic Complex, Dominica (Lesser Antilles)[END_REF][START_REF] Gurenko | A melt inclusion record of volatiles, trace elements and Li-B isotope variations in a single magma system from the Plat Pays Volcanic Complex, Dominica, Lesser Antilles[END_REF][START_REF] Lindsay | Dominica[END_REF]. A number of lava domes generated abundant block-and-ash pyroclastic density currents. The last of these, Morne Patate lava dome, is dated at 450 ± 90 year BP [START_REF] Roobol | Calderas or gravityslide structures in the Lesser Antilles island arc?[END_REF]. Several flank collapses have occurred, generating voluminous debris avalanche deposits that flowed into the Caribbean Sea [START_REF] Friant | L'île de la Dominique: zone d'émission des avalanches de débris les plus volumineuses de l'arc des Petites Antilles[END_REF][START_REF] Boudon | Volcano flank instability in the Lesser Antilles Arc: diversity of scale, processes, and temporal recurrence[END_REF].

Material

Deposit characteristics and magma composition

Morne Diablotins and Morne Trois Pitons-Micotrin

The MI-bearing phenocrysts studied here were selected through detailed sampling of the fallout deposit of the three major pumiceous eruptions (Fig. 2): Layou, Roseau and Grand Fond. All three eruptions involved a plinian phase that generated pumice fallout deposits followed by voluminous ash-and-pumice pyroclastic density currents that filled the valleys and flowed into the sea generating turbidite currents. In the upper parts of the valleys, where the deposits are thickest (up to 100 m), they are welded. For each ignimbritic eruption, a volume of 3-5 km 3 DRE has been estimated based on stratigraphical investigations. These eruptions involved magmas that follow the andesite-dacite domain for whole rocks (Fig. 3a; [START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF]. The magmas at the start of the Morne Diablotins (Layou) and Morne Trois Pitons-Micotrin (Roseau and Grand Fond) pumiceous eruptions are at the limit between acid andesite and dacite and the residual glasses are rhyolitic. Only MI-Opx pairs were used to constrain temperatures for Roseau and Layou at 887 ± 25 °C and 852 ± 25 °C, respectively. Further details of the revised stratigraphy, sampling and eruption characteristics (ages, deposit volumes, compositions etc) are given in [START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF].

Morne aux Diables

The Morne aux Diables complex at the north end of Dominica comprises several Upper Pleistocene to Holocene andesitic lava domes emplaced into a sequence of pyroclastic deposits associated with the deeply eroded, 2.0-1.7 Ma proto-Morne aux Diables stratovolcano [START_REF] Smith | The volcanic geology of the mid-arc Island of Dominica, Lesser Antilles; the surface expression of an island-arc batholith[END_REF][START_REF] Howe | Evolution of young andesiticdacitic magmatic systems beneath Dominica, Lesser Antilles[END_REF]. Block-and-ash pyroclastic density currents are associated with some lava domes. MI-bearing phenocrysts were studied from four selected pumices, whose compositions are representative of this volcanic center (andesite-dacite; Fig. 3a), and one mafic enclave. Two of the five samples (DC 25 and DC 06) are pumice clasts from cross-bedded pyroclastic surge deposits collected in river valleys near Guillet (15°36′28.7″N 61°27′50.1″W) and on the road to Carib Point (15°37′57.6″N 61°25′27.5″W), respectively. The deposits at Guillet are those shown in Fig. 31 of [START_REF] Smith | The volcanic geology of the mid-arc Island of Dominica, Lesser Antilles; the surface expression of an island-arc batholith[END_REF] who ascribe them to the proto-Morne aux Diables stratovolcano. The characteristics of the deposits at both locations suggest that they represent the same eruptive event. In contrast, DC08 and DC139 are vesiculated pyroclasts from block-and-ash pyroclastic density currents at Guillet (15°36′19.8″N 61°27′43.4″W) and Penneville (15°37′16.9″N 61°24′59.3″W), respectively, associated with collapse of Morne aux Diable domes. The block-and-ash pyroclastic density current at Guillet has been radiocarbon dates at 43.7 ± 1.6 kyr by [START_REF] Smith | The volcanic geology of the mid-arc Island of Dominica, Lesser Antilles; the surface expression of an island-arc batholith[END_REF]. Finally, DC02 is a quenched microgranular enclave from a block-and-ash pyroclastic density current near East Cabrits (15°35′03.2″N 61°28′09.8″W), a dome associated with the western flanks of the proto-Morne aux Diables stratovolcano. Samples DC06, 08, 25 and 139 are silicic andesites (see SI1) containing phenocrysts of orthopyroxene, clinopyroxene and zoned plagioclase. DC08 also contains sparse amphibole phenocrysts with very thin reaction rims. DC06 and DC08 contain rare quartz. Andesite enclave DC02 consists of phenocrysts and glomerocrysts of orthopyroxene, clinopyroxene, plagioclase and Fe-Ti oxides set in a finegrained matrix. Thermometry [START_REF] Ghiorso | Thermodynamics of rhombohedral oxide solid solutions and a revision of the Fe-Ti twooxide geothermometer and oxygen-barometer[END_REF] of touching ilmenite-magnetite phenocrysts rims from DC02 yields 843-851 °C and NNO + 0.45 log units. Touching oxide pairs in glomerocrysts yield consistently higher temperatures (882-963 °C) at similar fO 2 (NNO + 0.30 to 0.35). These higher temperatures may reflect magmatic conditions in the andesite magma prior to mixing with the host magma.

Plat Pays Volcanic Complex

A selection of mafic samples from Dominica was collected (see SI2). We focus on scoriaceous deposits, possibly originating from Plat Pays Volcanic Complex, that represent the potential basic endmember composition of Dominica's magmas (hereafter referred as the mafic samples). We studied two decimetre-thick scoria fallout deposits at Fond Baron Estate (15°16′26″N, 61°21′31″W) and La Sorcière-Soufrière (15°14′01″N, 61°21′46″W). Both sites display similar characteristics. Scoria clasts, up to a few cm in diameter, are basaltic with low phenocryst content (mainly plagioclase). Only whole rock chemistry of these samples is reported here.

Samples: melt inclusion host and preparation

Morne Diablotins and Morne Trois Pitons-Micotrin

For each eruption from Morne Diablotins and Morne Trois Pitons-Micotrin, the density distribution of the first eruptive unit for each Plinian fallout deposit was obtained from a population of at least 100 pumice clasts identified and sieved at 16-32 mm. Depending on the density distribution, six to ten pumice clasts were collected from the density mode (Gaussian distribution) to ensure that the pumice clasts are representative. Clasts were gently crushed to powder, then sieved in different size fractions, the largest of which (0.315-0.500 mm, 0.500-0.750 mm and 0.750-1 mm) were recovered for crystal handpicking under a binocular microscope. Orthopyroxene (Opx) and plagioclase (Pl) crystals from each eruption of Morne Diablotins and Morne Trois Pitons-Micotrin were then mounted in epoxy resin and polished to 0.3 µm.

Morne aux Diables

Clasts were lightly crushed and handpicked for phenocrysts. Separated orthopyroxene (Opx), clinopyroxene (Cpx), plagioclase (Pl) crystals were mounted in epoxy resin and polished to 0.3 µm.

Results

Melt inclusion host minerals

A total of 113 melt inclusions were analysed across all three volcanic centers Morne Diablotins and Morne Trois Pitons-Micotrin (43) and Morne aux Diables (70) (Table 1). Details of host mineral compositions are provided in SI4.

Morne Diablotins and Morne Trois Pitons-Micotrin

Opx and Pl phenocrysts from Layou, Roseau and Grand Fond were mounted separately. As Pl-hosted melt inclusions were consistently scarcer and smaller, we obtained more numerous data for Opx than Pl. Opx and Pl composition ranges between En 49-56 (n = 7) and An 52-53 (n = 3) (Layou), En 50-53 (n = 13) and An 46-60 (n = 6) (Roseau), and En 52-55 (n = 6) and An 49-59 (n = 6) (Grand Fond). In Opx, MI are ubiquitous from core to rim with sizes from a few µm up to more than 50 µm (Fig. 2a,b). Analyzed MI were glassy with no evidence of rim crystallization in SEM images. In plagioclase, scarce MI are smaller than 40 µm. In strongly zoned plagioclase MIs form a sieve-texture ring of numerous small inclusions parallel to the zoning (Fig. 2c), whereas in unzoned plagioclase they have a random distribution (Fig. 2d). These textural characteristics are similar in all three eruptions.

Morne aux Diables

Opx, Pl and Cpx were mounted separately (Fig. 2e,f

Melt inclusion glass compositions

Major elements

Melt inclusions from the three studied Morne Diablotins and Morne Trois Pitons-Micotrin eruptions are rhyolitic in composition regardless of their host crystal (TAS classification, Fig. 3a,b), with variations in Na 2 O + K 2 O from 4.9 to 6.5 wt% (anhydrous) and SiO 2 content of 75.6-79 wt% for Opx, and variations in Na 2 O + K 2 O of 5.0-5.6 wt% for a SiO 2 range of 76.1 to 78.2 wt% for Pl. MIs plot in the calc-alkaline field, as defined by the SiO 2 vs. K 2 O content (Fig. 4a), with Al 2 O 3 contents between 11 and 15 wt% (Fig. 4b) and low CaO content, between 1 and 2.5 wt% (Fig. 4c). There is no textural evidence for post-entrapment crystallization of the host mineral (Fig. 2). Pl-and Opxhosted MI evidence some differences in composition for certain elements, i.e. Opx-hosted MI tend to be richer in Fe and Mg than those hosted in Pl (Fig. 4d). Melt inclusions from Morne aux Diables are almost all rhyolitic, although some lie at the border with dacite (Fig. 3a). They describe a differentiation trend spanning a large SiO 2 range between 70 and 79.5 wt% (Figs. 3b,4). The trend is clear for CaO, FeO, K 2 O or Al 2 O 3 (Fig. 4). The Morne Diablotins and Morne Trois Pitons-Micotrin MIs described above lie at the most differentiated end of this trend (Fig. 4).

Trace elements

Trace elements analyses of MIs from the Morne Diablotins and Morne Trois Pitons-Micotrin volcanic centers are discussed by element groups for each eruption (Fig. 5) and compared to whole rock compositions for Morne Diablotins, Morne Trois Pitons-Micotrin and Morne aux Diables.

1. High Field Strength Elements (HFSE: U, Th): There is a strong positive correlation between the HFSE for MIs, whole rock, matrix glass, mafic samples and crystals as shown by U-Th (Fig. 5a). All eruptions describe the same linear correlation passing through the origin, independent of the MI host. However Grand Fond tends to sit at the lower end of this correlation (Th = 8.3-10.6 ppm) with respect to Roseau and Layou, which display the most differentiated melt (Th = 8-12.7 and 9.9-11.7 ppm, respectively). Compared to whole rock compositions of Morne Diablotins, Morne Trois Pitons-Micotrin and Morne aux Diables, MIs lie at the silica-rich end of this differentiation trend, which is common to all three eruptive centers. A striking feature of this plot is the tendency of MIs to be more differentiated in terms of trace elements (higher U, Th) than the matrix glasses, although the major element chemistry is quite similar (Fig. 4). The same feature has been observed previously at a number of volcanoes, e.g. Ruapehu, New Zealand [START_REF] Kilgour | Small volume andesite magmas and melt-mush interactions at Ruapehu, New Zealand: evidence from melt inclusions[END_REF] or Uturuncu, Bolivia [START_REF] Muir | Experimental constraints in dacite pre-eruptive magma storage conditions beneath Uturuncu volcano[END_REF], where it is attributed to protracted crystallization within a crystal mush prior to eruption. 2. Large Ion Lithophile Elements (LILE) Rb, K, Sr and Ba: The Sr-K 2 O plot (Fig. 5b) illustrates the compatible behavior of Sr, consistent with Pl-dominated fractionation. Conversely, Ba-Th (Fig. 5c) shows a good correlation, albeit with slight differences between Opx and Pl MI composition, reflecting a lack of biotite and alkali feldspars in the crystallizing assemblage in any significant proportion. Once again, all eruptions, including Morne aux Diables, describe on the same relationship and MIs are more evolved than matrix glasses. 3. LILE and REE vs. HFSE systematics: The Rb vs. Zr diagram (Fig. 5d) illustrates first the three correlations identified for each Morne Diablotins and Morne Trois Pitons-Micotrin eruption using whole rock and matrix glass composition [START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF]. MIs from Grand Fond plot in the same domain as the matrix glass. The compositional domain covered by Grand Fond MIs is less scattered than that of Layou and Roseau. These two eruptions have MI compositions that depart from the matrix glass, being Rb-rich and Zr-poor. The tendency for MIs to plot at lower Zr and at elevated Rb is indicative of zircon saturation at advanced stages of crystallization that are recorded by MIs, but not matrix glass. That zircon saturation is confined to evolved MIs, but not matrix glasses is consistent with derivation of phenocrysts from a cool magmatic mush prior to entrainment in hotter magma during eruption. The calculated zircon saturation temperatures are 743-795 °C [START_REF] Watson | Zircon saturation revisited: temperature and composition effects in a variety of crustal magma types[END_REF]. These temperatures are consistent with low melt-fraction, evolved melts, but are almost 100 °C lower than the calculated Opx-MI and Fe-Ti oxide temperatures presented above (852-877 °C). This temperature difference can be ascribed to heating during magma ascent and crystallization via latent heat release [START_REF] Blundy | Magma heating by decompression-driven crystallization beneath andesite volcanoes[END_REF] or entrainment of crystals from mush by a hotter carrier melt [START_REF] Kilgour | Timescales of magmatic processes at Ruapehu volcano from diffusion chronometry and their comparison to monitoring data[END_REF]. 4. Li and B trace elements: The B-K 2 O diagram (Fig. 6a) illustrates a common signature for Opx-hosted MIs from all eruptions, with Grand Fond MIs describing the lower end of this relationship and Roseau the upper end. Plhosted MIs show roughly the same relationship, slightly extended towards higher values of B. Boron and Li show some relationship with each other for MIs in Opx (Fig. 6b); for Pl the data are displaced to slightly higher Li over a greater range in B, but with little evidence for any relationship. The signature in Li is roughly the same for the three eruptions (43 ± 5 ppm) whatever the H 2 O content (between 4.5 and 7.5 wt%; Fig. 6c), with a slight enrichment for Roseau. For some Pl-hosted MIs, the Li content decreases from 43 ± 5 ppm down to zero, without any accompanying H 2 O loss. This may reflect rapid diffusive migration of Li through the host crystal. 5. Volatile components (H 2 O, CO 2 , F, Cl, Br, S).

Volatile contents for Morne Diablotins, Morne Trois Pitons-Micotrin and Morne aux Diables, are presented as histograms in Fig. 7 for H 2 O and CO 2 content and Fig. 8 for halogen (F, Cl, Br) and SO 2 content. Histograms distinguish between MIs hosted in different minerals.

Water H 2 O contents of Morne Diablotins and Morne

Trois Pitons-Micotrin MI range from 4.5 to 7.6 wt% (Fig. 7). This entire range is captured in the Opx-hosted MI. The maximum H 2 O is 7.6 wt% for Layou (range 6.5-7.6 wt%), 7.5 wt% for Roseau (5.5-7.5 wt%), and 6.3 wt% for Grand Fond (4.5-6.3 wt%). The maximum H 2 O of Pl-hosted MIs (Fig. 7) is slightly lower than for Px, i.e. 6. Some MIs from Morne Diablotins and Morne Trois Pitons-Micotrin and from Morne aux Diables show high CO 2 content (≤ 4000 ppm). Such high values could result from contamination, although the 12 C+ signal was stable during SIMS analysis, which is consistent with high intrinsic CO 2 contents rather than any surficial carbon-rich contamination. Similarly CO 2 -rich melt inclusions have been described from other silicic arc volcanoes (e.g. [START_REF] Blundy | A case for CO 2 -rich arc magmas[END_REF] and have been attributed to fluxing of melts with magmatic CO 2 -rich fluids by [START_REF] Bouysse | Subduction of Atlantic aseismic ridges and Late Cenozoic evolution of the Lesser Antilles island arc[END_REF]. For these reasons, we include the high-CO 2 Dominica MIs in our discussion.

Halogens: Fluorine in Morne Diablotins and Morne

Trois Pitons-Micotrin MIs ranges between 100 and 600 ppm (Fig. 8). Roseau shows a maximum distribution between 150 and 600 ppm. Grand Fond MIs show roughly the same range, whereas those from Layou are shifted towards the F-poor endmember. Like CO 2 F shows a negative variation with Th (Fig. 10a), suggestive of partitioning into the fluid phase during crystallisation. Morne aux Diables MIs display the highest F content endmember, with Opx-hosted MI reaching 677 ppm and Pl-hosted MI 798 ppm.

Chlorine contents in Morne Diablotins and Morne Trois Pitons-Micotrin range from 1800 to 3140 ppm. The Cl range within Opx-hosted MI is generally greater than in Pl (Fig. 8). For Opx-MI from each eruption, Cl values fall within a restricted range over a significant range in Th content, with 2303 ± 78 ppm for Layou, 2355 ± 340 ppm for Roseau and 2446 ± 96 ppm for Grand Fond (Fig. 10b).

P l

Cpx Opx

Diables MIs describes the same trend, although some Pl-hosted MIs depart from this trend being Cl-rich and H 2 O-poor. Bromine data were acquired only for Opx-hosted MIs from Layou, Roseau and Grand Fond (Fig. 8). They display contrasted Br contents with a clearly distinct domain for Roseau (13-16 ppm) compared to lower values for Layou (7-13 ppm) and intermediate values for Grand Fond (10-15 ppm). There is no clear relationship between Br and Th (Fig. 10c). There is a wide range in Br at almost constant Cl (Fig. 10f). Like Cl, the Br concentrations lie at the high end of the global range in silicic magmas reported by [START_REF] Webster | Halogens in mafic and intermediate-silica content magmas[END_REF].

4. Sulfur Sulfur content of 160 ± 20 ppm has been measured in a few Opx-hosted MI from Morne Diablotins and Morne Trois Pitons-Micotrin (Fig. 8) Sulfur in Morne aux Diables MIs has been more extensively investigated. MIs exhibit higher values, up to 569 ppm in Opx-hosted MIs (with one value at 1015 ppm; off-scale in Fig. 9), 360 ppm for Cpx-hosted MIs and 300 ppm in Pl-hosted MIs (Fig. 9). Sulfur is inversely correlated with Th (Fig. 10d). The low S contents of the melts are consistent with sulfide saturation in silicic melts at pressures of 1-2 kbar and temperatures of 850-900 °C [START_REF] Carroll | Sulfur speciation in hydrous experimental glasses of varying oxidation state: results from measured wavelength shifts of sulfur X-rays[END_REF]. However, daughter sulfide minerals were not identified in any of the MI studied.

Bulk scoria fallout composition

The studied mafic samples collected from the southwestern coast of Dominica are basaltic in bulk composition (TAS classification, Fig. 3a), with SiO 2 between 49 and 51 wt% and Na 2 O + K 2 O between 2.5 and 4.5 wt%. Their bulk trace element signature describes the same linear trend in U-Th space as the more differentiated products (U = 0.3-0.4 ppm, Th = 1-1.4 ppm) (Fig. 5a). The mafic samples are homogeneous composition in Rb, Zr, and even Ba (Fig. 5b-d).

Discussion

We first discuss the major and trace element MI compositions, then the volatile contents. Plat Pays Volcanic Complex MIs, using data from [START_REF] Gurenko | A melt inclusion record of volatiles, trace elements and Li-B isotope variations in a single magma system from the Plat Pays Volcanic Complex, Dominica, Lesser Antilles[END_REF] are included in the discussion at the scale of Dominica, in terms of a comparison of pre-eruptive conditions of magma storage and ascent.

MI composition in equilibrium: test through Kd determination

Although MIs provide valuable information concerning the pre-eruptive melt volatile contents, they are prone to post-entrapment modification such as post-entrapment crystallization (PEC), involving growth of the host crystal or daughter crystals, or leakage and decrepitation, diffusion of volatile species through the host crystals (or exchange between host and melt) or partitioning of volatile species into shrinkage bubbles. These potential problems need to be evaluated where possible [START_REF] Wallace | Volatiles in subduction zone magmas: concentrations and fluxes based on melt inclusion and volcanic gas data[END_REF][START_REF] Esposito | An assessment of the reliability of melt inclusions as recorders of the pre-eruptive volatile content of magmas[END_REF]).

As we have avoided MIs with bubbles, that may contain significant exsolved CO 2 , we will confine our discussion of post-entrapment modification to tests of equilibrium between MI (Table 1) and their host crystal (SI4 and SI5). For this exercise we use the exchange coefficient K D (Fe-Mg)Opxliq = 0.23 ± 0.02 for Opx and K D (An-Ab)pl-liq = 2.46 ± 0.09 for Pl (Solaro-Müller 2017). These exchange coefficients are taken from Opx-melt and Pl-melt compositions of phase equilibria experiments conducted on Layou and Roseau dacites, between 1.5 and 4 kbars and 800-900 °C [START_REF] Solaro-Müller | Storage conditions and dynamics of magma reservoirs feeding the major pumiceous eruptions of Dominica (Lesser Antilles Arc)[END_REF]Solaro et al. in revision). The experimental K D ((Fe-Mg)Opx-liq from these experiments (0.23 ± 0.02) is slightly lower than that proposed by [START_REF] Putirka | Thermometers and barometers for volcanic systems[END_REF] at 0.29 ± 0.06. Considering that his value decreases slightly with increased silica content we calculate, following [START_REF] Putirka | Thermometers and barometers for volcanic systems[END_REF] proposed influence of SiO 2 , a K D ((Fe-Mg)Opxliq value for Dominica magmas of 0.19-0.20, slightly closer to our experimental value. As the value of 0.23 is based on experiments performed on the actual magma compositions studied here, it is preferred to test equilibrium of MI. Using KD(Fe-Mg)Opx-liq = 0.23 we calculate that Opx-MI show only minor evidence of PEC at 1-2%. The experimentallydetermined K D (An-Ab)pl-liq of 2.46 ± 0.09 for Pl in the T, P and composition range studied experimentally by [START_REF] Solaro-Müller | Storage conditions and dynamics of magma reservoirs feeding the major pumiceous eruptions of Dominica (Lesser Antilles Arc)[END_REF], was used to constrain post-entrapment evolution of MIs. Contrary to Opx, Pl-hosted MIs exhibit PEC between 0 and 19%. Only Pl-hosted MIs showing PEC below 8% have been selected for plotting and discussion. Note that the amounts of calculated PEC for both Opx-and Pl-hosted inclusions has little bearing on the measured volatile contents, being limited to major elements in both Opx and Pl.

Volatile content and behavior: implications for pre-eruptive magma storage

Melt inclusions reveal high volatile contents, in particular H 2 O, for the pre-eruptive magma storage reservoir in central and northern Dominica. Frequency histograms highlight that some MI in Opx have H 2 O content up to 7.6 and 7.5 wt% for Layou and Roseau, respectively, similar to Morne aux Diables with 7.6 wt%, whereas Grand Fond show lower maximum H 2 O content (6.3 wt%). Layou consistently exhibits higher H 2 O content MIs than Roseau, with 70% of the MIs containing more than 7 wt%. As MIs with H 2 O content higher than 7 wt% are rarely reported, our data place the central Dominica magmas amongst the wettest in the world, comparable, for example, to dacites from Pinatubo, Philippines [START_REF] Wallace | Volatiles in subduction zone magmas: concentrations and fluxes based on melt inclusion and volcanic gas data[END_REF]. [START_REF] Edmonds | Extensive, water-rich magma reservoir beneath southern Montserrat[END_REF] have proposed similarly H 2 O-rich andesite magmas (≤ 9.4 wt%) for Soufriere Hills Volcano, Montserrat, on the indirect basis of the H content of orthopyroxene phenocryst cores. On this basis, they invoke magma storage at depths of 5-16 km beneath Montserrat. For comparison, [START_REF] Laumonier | Giant magmatic water reservoirs at mid-crustal depth inferred from electrical conductivity and the growth of the continental crust[END_REF] suggest, on the basis of electrical conductivity and experimental phase relations, that andesitic partial melt in the Altiplano-Puna Magma Body ~ 15 km beneath the Bolivian Altiplano contains 8-10 wt% H 2 O.

Melt inclusion pressure of entrapment

MI volatile contents may be converted into minimum pressures of entrapment using joint H 2 O-CO 2 solubility models (Fig. 9b), providing that melts are volatile-saturated at the time of entrapment as demonstrated for Morne Diablotins and Morne Trois Pitons-Micotrin MIs by a negative correlation between CO 2 and Th (Fig. 9a; Blundy and Cashman 2008).

H 2 O-CO 2 content

Various solubility models using mixed H 2 O-CO 2 fluids have been developed, including [START_REF] Tamic | The solubility of H 2 O and CO 2 in rhyolitic melts in equilibrium with a mixed CO 2 -H 2 O fluid phase[END_REF], [START_REF] Newman | VolatileCalc: a silicate melt-H 2 O-CO 2 solution model written in Visual Basic for excel[END_REF], [START_REF] Papale | The compositional dependence of the saturation surface of H 2 O + CO 2 fluids in silicate melts[END_REF] and [START_REF] Ghiorso | An H 2 O-CO 2 mixed fluid saturation model compatible with rhyolite-MELTS[END_REF]. The two latest models are calibrated on published experimental data on H 2 O and CO 2 solubility as well as mixed fluids. "Magmasat" [START_REF] Ghiorso | An H 2 O-CO 2 mixed fluid saturation model compatible with rhyolite-MELTS[END_REF] is used here to calculate saturation pressure and volatile compositions for all volcanic centers. As Magmasat is a compositionally-sensitive solubility model, it is not straightforward to calculate isobars in CO 2 -H 2 O space for MIs that span a range of compositions. For this purpose we have used the generic "VolatileCalc" rhyolite solubility model of [START_REF] Newman | VolatileCalc: a silicate melt-H 2 O-CO 2 solution model written in Visual Basic for excel[END_REF] to show representative isobars in Fig. 9b. For individual MIs we performed Magmasat calculations using the measured major element composition, an assumed fO 2 of NNO to determine ferric-ferrous ratios and at temperatures calculated from mineral-melt thermometry.

Where this was not possible we used an estimated temperature of 890 °C.

Considering the entire MI dataset, magmas erupted during Dominica's large pumiceous eruptions (Morne Diablotins and Morne Trois Pitons-Micotrin) equilibrated at pressures of 1.5 to 7.5 kbar. This corresponds to a depth range of 5-27 km, supposing lithostatic pressure and a crustal density of 2800 kg/m 3 (Fig. 9c). Similarly, for Morne aux Diables, with the exception of a single ruptured inclusion (0.09 kbar), magmas originated from 0.8 to 5.8 kbar (3-21 km depth). The maximum depths lie close to the crustal thickness (28 km) beneath northern Dominica as determined by the seismic experiment of [START_REF] Kopp | Deep structure of the central Lesser Antilles Island Arc: relevance for the formation of continental crust[END_REF]. This deep origin for silicic magmas is compatible with the transcrustal magmatic system proposed by Blundy and Cashman (2008) and [START_REF] Cashman | Vertically extensive and unstable magmatic systems: a unified view of igneous processes[END_REF] and the mush model inferred for sub-volcanic magma storage (Solaro-Müller 2017; Bachmann and Huber 2016). Cumulate troctolite and gabbronorite xenoliths from Dominica, described by [START_REF] Ziberna | Multiple-reaction geobarometry for olivine-bearing igneous rocks[END_REF], record equilibration conditions of 1.9 ± 0.9 to 3.6 ± 0.8 kbar (7 ± 4 to 13 ± 3 km depth), again consistent with magma storage and differentiation over a wide range of crustal depths.

Fluid compositions, expressed as XH 2 O = molar H 2 O/ (H 2 O + CO 2 ), calculated using Magmasat are in the range 0.7-1.0 for the majority of MIs with trapping pressures of 1-3 kbar (Fig. 9c). However, the highest pressure MIs show a trend to lower XH 2 O, consistent with decompression-driven degassing, accompanied by crystallization, that serves to increase XH 2 O as degassing proceeds (Blundy and Cashman 2008). [START_REF] Kilgour | Small volume andesite magmas and melt-mush interactions at Ruapehu, New Zealand: evidence from melt inclusions[END_REF] observed a similar XH 2 O-P variation for melt inclusions from Ruapehu. There are also some lower pressure Dominica MIs with XH 2 O < 0.7 (Fig. 9c). This behavior is reminiscent of fluxing of shallower-stored magmas with deep-derived CO 2 -rich fluids, as proposed for a number of arc volcanoes (e.g. [START_REF] Blundy | A case for CO 2 -rich arc magmas[END_REF][START_REF] Bouysse | Subduction of Atlantic aseismic ridges and Late Cenozoic evolution of the Lesser Antilles island arc[END_REF]. Fluxing of shallow magmas with deep-derived fluids is consistent with a vertically extensive system of fluid-rich magmas in which melt and fluid movement can become decoupled (e.g. [START_REF] Christopher | Crustal-scale degassing due to magma system destabilisation and magma-gas decoupling at Soufrière Hills Volcano, Montserrat[END_REF].

Systematic variations between different volcanic centers can be used to evaluate spatial and temporal variations in magma storage conditions. For Layou, magma storage pressures are the greatest of the three large pumiceous eruptions from central Dominica, with a range of values between 2.5 and 3.5 kbar (9-13 km), with most Opx values between 3.0 and 3.5 kbar. Roseau Opx MIs span a large, rather continuous, domain of pressure between 2.0 and 3.0 kbar (7-11 km), with a single value at 1.5 kbar. Grand Fond Opx MIs describe a narrower domain of pressure, the shallowest of the three eruptions, between 1.6 and 2.7 kbar (6-10 km). However, a single Grand Fond MI records the highest pressure (7.5 kbar), suggestive of some entrainment of host Fig. 8 Frequency histograms of halogen (F, Cl, Br) and SO 2 contents of melt inclusions. Morne Diablotins-Morne Trois Pitons-Micotrin is separated from Morne aux Diables for clarity. Host-mineral is specified. Morne aux Diables: opx: grey domain; cpx: dark grey vertical line ◂ crystals from the Dominica lower crust. For the three eruptions, MIs in Pl from Roseau and Layou correspond to lower calculated pressures compared to MIs in Opx. We may thus infer that the likely depth range for the magma feeding to the Roseau and Grand Fond eruptions from the Morne Trois Pitons-Micotrin center is 6-11 km, and slightly deeper for the Morne Diablotins -derived Layou eruption (9-13 km). This general pressure range agrees with phase equilibria experiments conducted on the same sample set that suggests equilibration at 3.0-3.5 kbar (Solaro-Müller 2017, in revision). For Morne aux Diables, the bulk of the MI correspond to the same pressure and depth domain (0.8-4 kbar, 3-15 km) as for Morne Diablotins and Morne Trois Pitons-Micotrin, but with a few Pl-hosted MI recording pressures up to 5.7 kbar (Fig. 8c), again suggestive of some deeper silicic melt generation and extraction.

Halogen signature

The entrapment pressure recorded by MI may be also extracted from H 2 O-Cl solubility relations [START_REF] Webster | Chloride and water solubility in basalt and andesite melts and implications for magmatic degassing[END_REF]Fig. 11). Experimental determinations of Cl solubility show that H 2 O and Cl content may be used together as a geobarometer for magmas of rhyolitic composition [START_REF] Webster | Chloride and water solubility in basalt and andesite melts and implications for magmatic degassing[END_REF]. Chlorine contents of Dominica MIs show a wide range of values (Figs. 8,11) [START_REF] Webster | Chloride solubility in felsic melts and the role of chloride in magmatic degassing[END_REF], these MIs are consistent with pressures above 2 kbars; however, Cl contents of melts afford significantly lower precision pressure estimates than those obtained by H 2 O-CO 2 solubility models.

For Morne Diablotins and Morne Trois Pitons-Micotrin the matrix glass composition has a mean Cl content of 2380 ± 200 ppm [START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF]) similar to MI values (Fig. 11). Chlorine behavior is generally related to H 2 O through the partition coefficient of Cl into the H 2 O-rich vapor phase [START_REF] Kilinc | Partitioning of chloride between a silicate melt and coexisting aqueous phase from 2 to 8 kbars[END_REF][START_REF] Webster | Experimental constraints on the partitioning of Cl between topaz rhyolite melt and H 2 O and H 2 O + CO 2 fluids: new implications for granitic differentiation and ore deposition[END_REF]. But here, given the similar values between MI and the matrix glass, degassing processes at shallow depth ▸ during magma ascent do not appear to be the dominant processes controlling the Cl content of magmas (Fig. 11). The different Cl signature between the different volcanic centers is likely to be inherited from magma source at depth without significant modification by degassing processes at depth is similar (Fig. 10e). The Cl-Br diagram shows large variations in Br content with respect to Cl that remains roughly constant (Fig. 10f). The large range of Br/Cl ratio may be linked to variable assimilation rate of seawaterderived brines.

Comparison with other volcanic system from Dominica and the Lesser Antilles arc

Here, we review the information on magma plumbing system architecture and dynamics within Dominica and the wider Lesser Antilles arc, looking at the volatile content of melts as well as insights from experimental petrology. Dominica:

Plat Pays Volcanic Complex (PPVC)

Magma storage pressures can only be discussed using Cl-H 2 O data for the dacites of Plat Pays Volcanic Complex in the last 40 kyrs [START_REF] Gurenko | A melt inclusion record of volatiles, trace elements and Li-B isotope variations in a single magma system from the Plat Pays Volcanic Complex, Dominica, Lesser Antilles[END_REF]; Fig. 8) as no CO 2 data were obtained by these authors. For Plat Pays Volcanic Complex, the total range of H 2 O contents in pumice (airfall deposits) is 2-6 wt % and, generally, MIs in Opx have higher water concentrations than those in Pl. The highest pre-eruptive H 2 O content is thus consistent with other MIs investigations that provide 5.2-6.5 wt% for pre-eruptive melt [START_REF] Halama | Pre-eruptive crystallization conditions of mafic and silicic magmas at the Plat Pays volcanic Complex, Dominica (Lesser Antilles)[END_REF]. The MI Cl contents in Plat Pays Volcanic Complex describe a wide range of values, between 1500 and 3500 ppm [START_REF] Gurenko | A melt inclusion record of volatiles, trace elements and Li-B isotope variations in a single magma system from the Plat Pays Volcanic Complex, Dominica, Lesser Antilles[END_REF][START_REF] Halama | Pre-eruptive crystallization conditions of mafic and silicic magmas at the Plat Pays volcanic Complex, Dominica (Lesser Antilles)[END_REF]. Based on H 2 O-Cl solublity, the dacitic magma feeding the recent volcanic activity of Plat Pays Volcanic Complex was stored at ~ 2 kbars (Fig. 11). This pressure is similar with those based on melt H 2 O solubility [START_REF] Ghiorso | An H 2 O-CO 2 mixed fluid saturation model compatible with rhyolite-MELTS[END_REF] suggestive of relatively low CO 2 contents.

Lesser Antilles arc

Montagne Pelée (Martinique)

The pre-eruptive conditions, either for Plinian or lava domeforming eruption, at Montagne Pelée (Martinique) were determined experimentally by [START_REF] Martel | Magma storage conditions and control of eruption regime in silicic volcanoes: experimental evidence from Mt[END_REF]. For pumice clasts from recent Plinian eruptions, a pressure of 2 ± 0.5 kbars (depth 6-9 km) and a H 2 O melt content of 5.3-6.3 wt% (slightly below the saturation value of ∼ 6.9 wt.% H 2 O) were determined. MIs have a Cl concentration of 2100 ± 100 ppm [START_REF] Villemant | Transition between dome-forming and Plinian eruptive style: H 2 O and Cl degassing behavior[END_REF][START_REF] Balcone-Boissard | Behavior of halogens during the degassing of felsic magmas[END_REF], which corresponds, when combined with H 2 O, to the lower In addition, the last 40,000 years of activity of the volcano highlights the presence of mafic magmas beneath Montagne Pelée, even though the most recently erupted products have andesite bulk compositions. Therefore, the magma storage zone is best viewed as a compositionally zoned igneous system, with a mafic part and an andesitic part [START_REF] Pichavant | Physical conditions, structure, and dynamics of a zoned magma chamber: Mount Pelée (Martinique, Lesser Antilles Arc)[END_REF]. The crystallization of mafic magma occurs through a substantial pressure range of 4-10 kbars consistent with the upper end of the pressures recorded by Dominica MIs. Evolution toward more silicic composition is related to amphibole crystallization at low T (< 1000 °C). Plutonic xenoliths from Martinique have mineral assemblages consistent with pressures ≤ 4 kbar [START_REF] Cooper | Plutonic xenoliths from Martinique, Lesser Antilles: evidence for open system processes and reactive melt flow in island arc crust[END_REF].

Soufrière (Guadeloupe)

Magma storage conditions have also been determined by experimental petrology, specifically for the last subplinian magmatic eruption that occurred in 1530 AD [START_REF] Poussineau | Dynamique des magmas andésitiques: approche expérimentale et pétrostructurale; application à la Soufrière de Guadeloupe et à la Montagne Pelée[END_REF]. The most likely pressure domain of the reservoir is between 1.35 and 1.7 kbars, with a maximum at 2 kbars.

Recently, new data on MI in the eruptive products of the 1530 AD eruption provide a large range of H 2 O content but a maximum H 2 O of 5.5 wt% [START_REF] Pichavant | Experimental parameterization of magma mixing: application to the 1530 AD eruption of La Soufrière, Guadeloupe (Lesser Antilles)[END_REF]. A key factor in explaining the overall behaviour of La Soufrière volcano, seems to be an exceptionally high flux of mafic magma from depth, consistent with continuous chemical zonation and the predominance of the mafic component in eruption products. This observation suggests that magma accumulation at shallow depth primarily depends on processes taking place in the middle to lower part of the arc crust beneath Guadeloupe [START_REF] Pichavant | Experimental parameterization of magma mixing: application to the 1530 AD eruption of La Soufrière, Guadeloupe (Lesser Antilles)[END_REF].

Soufriere Hills Volcano (Montserrat)

Based on H content of orthopyroxene phenocryst cores [START_REF] Edmonds | Extensive, water-rich magma reservoir beneath southern Montserrat[END_REF] have proposed H 2 O-rich andesite magmas (≤ 9.4 wt%), interpreted as due to a magma storage at depths of 5-16 km beneath Montserrat. The magma plumbing system beneath this volcano has also been described through the prism of the mush based on the excess of SO 2 flux interpreted as resulting from a decoupled sulfur degassing through transcrustal magmatic system. Thus, it is envisaged that Soufriere Hills Volcano is underlain by a vertically extensive large igneous mush system formed over tens of thousands of years and perhaps extending from the shallow crust (> 4 km) to the Moho [START_REF] Christopher | Crustal-scale degassing due to magma system destabilisation and magma-gas decoupling at Soufrière Hills Volcano, Montserrat[END_REF]. Geophysical images of the crust beneath Montserrat identify a region of partial depth that extends from 5 km to at least 9 km [START_REF] Paulatto | Magma chamber properties from integrated seismic tomography and thermal modeling at Montserrat[END_REF].

St. Kitts

St. Kitts lies in the northern Lesser Antilles. A series of dacitic to rhyolitic MIs with H 2 O content between 2 and 6 wt%, trapped in Opx and Pl from plutonic xenoliths yields calculated saturation pressures from 0.5 to 3.8 kbars [START_REF] Melekhova | Petrological and experimental evidence for differentiation of waterrich magmas beneath St. Kitts, Lesser Antilles[END_REF]. These conditions are corroborated by experiments that show the observed amphibole-bearing assemblages of cumulate xenoliths from St. Kitts require crystallization pressures of 1.5 to 6 kbar from parental hydrous basaltic andesite magmas [START_REF] Melekhova | Petrological and experimental evidence for differentiation of waterrich magmas beneath St. Kitts, Lesser Antilles[END_REF]). These findings were interpreted as corresponding to silicic magmas that ascended and equilibrated at shallow depths following generation from basaltic andesite parents at pressures up to 6 kbars. Thus St. Kitts magmas also testify to mid-crustal differentiation of low-MgO basalt and basaltic andesite magmas within a trans-crustal, magmatic mush system.

Magmatic processes within the reservoir

The emerging concept of a crustal magmatic reservoir is moving away from a single volume of melt (magma chamber) towards the idea of a crystal mush, comprising partial melt within a crystalline framework that can extend more or less continuously throughout a crustal column. Within this dynamic zone, magma accumulates, differentiates, and can become destabilized, leading to eruption [START_REF] Christopher | Crustal-scale degassing due to magma system destabilisation and magma-gas decoupling at Soufrière Hills Volcano, Montserrat[END_REF][START_REF] Cashman | Vertically extensive and unstable magmatic systems: a unified view of igneous processes[END_REF]. Matrix glass records the final, degassed melt that is quenched throughout the fragmentation process during eruption. Conversely, MIs represent the pre-eruptive melt at different stages of the differentiation process. Thus, comparing matrix glass and MI composition can be helpful to constrain pre-eruptive dynamics. The analyzed MIs of this study have suffered little post-entrapment crystallization, especially for Opx, and so may be used as a proxy for magma generation and ascent processes.

Comparison of matrix glass and MI from all three large pumiceous eruptions from Morne Diablotins and Morne Trois Pitons-Micotrin shows, somewhat surprisingly, that MI trapped in Opx (and Pl) are more differentiated than the matrix glass (Fig. 5a-c). This difference in composition is more clearly preserved through trace elements than major elements. Because the melts have major element compositions close to the granitic minimum (eutectic) the effects of different melt fraction are much more pronounced for incompatible trace elements than for major elements. Trace element variations, in particular in Ba-Th or Rb-Zr (Fig. 5 c,d), do not support the evolution of the matrix glass through simple decompression crystallization of the trapped melt as recorded by MIs. The behavior of Zr is consistent with zircon saturation in the MI, but not in the matrix glasses. Consequently, the MI appear to be trapped aliquots of evolved melt formed at lower temperatures. In contrast, the higher temperatures recorded by MI-Opx and Fe-Ti oxide thermometry suggest that prior to eruption phenocrysts experienced temperatures some 100 °C higher. This temperature increase could be related to the release of latent heat of crystallization, which is of the order 2.5 °C for each percent crystallised [START_REF] Blundy | Magma heating by decompression-driven crystallization beneath andesite volcanoes[END_REF]. Conversely, eruption could have been preceded by a recharge event followed by efficient mixing that produces a less differentiated matrix melt or by mixing between different parts of the same mush displaying different degrees of melt differentiation. Melt-bearing mush accumulations are highly susceptible to segregation of melt-rich layers by compaction and shear (e.g. [START_REF] Solano | Melt segregation in deep crustal hot zones: a mechanism for chemical differentiation, crustal assimilation and the formation of evolved magmas[END_REF]. Thus mixing in the mush need not necessarily involve a mafic magma, since a recharge with a hotter, slightly less evolved silicic magma may also occur and will leave little vestige of the mixed-in composition. Migrating evolved melts may entrain crystals from portions of the mush that are both cooler and more crystallized. In that case, melt inclusions in entrained crystals may record lower temperatures and melt fractions than the carrier magma. We speculate that this process may have operated on Dominica.

Supposing the extreme case of a recharge event by a basic magma (such as that represented by the Dominica scoria clasts), we can calculate mixing proportions between the scoria clasts and the MI composition (Supplementary material SI1). In this way, we estimate a mixing proportion of 25% for Layou, 5% for Roseau and 40% for Grand Fond. Based on this analysis, we may infer that the mixing event is heterogeneous at depth and varies from eruption to eruption. For Layou, the Th contents encompass a large range, from 4 to 7.5 ppm (Fig. 5a). The Grand Fond eruption displays the lowest mixing proportion. Mineralogical evidence for mixing includes An-rich layers in plagioclase and En-rich rims on orthopyroxene. However, hand specimens do not show obvious evidence for mixing such as mafic inclusions or banded pumice that have been reported elsewhere [START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF]. Some mafic enclaves within Micotrin, Trois Pitons, Plat Pays and Grand Soufrière Hills [START_REF] Howe | Evolution of young andesiticdacitic magmatic systems beneath Dominica, Lesser Antilles[END_REF]) lava dome products have similar Th content to the basic scoria, suggesting mixing heterogeneity. Thus, the mixing event may have been efficient enough for explosive eruptions to erase any evidence of the two components on the hand-sample scale. On the other hand, considering the mush model, we may also infer that mixing event occurs between various rhyolitic or dacitic melts that differ slightly in composition and temperature or that the main impact of the mafic magma is heat transfer, since the small changes in overall magma chemistry and the small percentage of relatively intact enclaves do not support extensive mingling.

Our findings contrast with what is observed on Guadeloupe within the 1530 AD eruption deposits that clearly preserve a mixing event prior to eruption through banded pumice and a wide range of composition of the eruptive products attesting to a chemically and physically heterogeneous reservoir at depth [START_REF] Pichavant | Experimental parameterization of magma mixing: application to the 1530 AD eruption of La Soufrière, Guadeloupe (Lesser Antilles)[END_REF]. At Montagne Pelée, there is evidence for magma mixing on a macroscopic scale via the presence of mafic enclaves (51-59 wt% SiO 2 ) and banded rocks in the 1902-1929 lava dome products [START_REF] Fichaut | Magmatology of Mt Pelée (Martinique FWI). III: fractional crystallisation versus magma mixing[END_REF][START_REF] Gourgaud | Magmatology of Mt. Pelée (Martinique FWI). I: Magma mixing and triggering of 1902 and 1929 nuées ardentes[END_REF]). On a microscopic scale, magma mixing is also evidenced by the presence of ubiquitous high-Ca plagioclase microlites, interpreted as crystallizing from a mafic melt intruding the andesitic reservoir [START_REF] Martel | Basalt-inherited microlites in silicic magmas: evidence from Mount Pelée (Martinique, French West Indies)[END_REF].

Conclusion

This study highlights the geochemical fingerprint of magmas involved in the three large pumiceous eruptions in the central part of Dominica (Layou, Roseau and Grand Fond) and the dome-forming eruptions of Morne aux Diables in the north. Phenocryst-hosted, silicic melt inclusions, analysed for major, trace and volatile elements, reveal that: (1) these magmas are among the most water-rich yet recorded (≤ 8 wt% H 2 O); (2) magmas are stored pre-eruptively over a wide pressure within the crust (up to ~ 750 MPa); (3) deeper magmas are associated with more CO 2 -rich fluids with evidence for the interaction of such fluids with shallow-stored magmas; and (4) magmatic evolution involved fractional crystallization and magma mixing or melt percolation processes within a vertically extensive magma mush that may extend to the Moho beneath Dominica. This magmatic architecture is consistent with that proposed by [START_REF] Smith | The volcanic geology of the mid-arc Island of Dominica, Lesser Antilles; the surface expression of an island-arc batholith[END_REF]. Mixing processes occurred between melts with relatively low contrast in viscosity and/or with sufficient time prior to eruption to homogenize melts, rendering mixing cryptic on Dominica, in contrast to Martinique or Guadeloupe where macroscopic evidence of mixing is preserved. The high water contents of the magmas together with the high proportion of exsolved fluids have implications for the rheology of the mush and timescales for mush reorganization. High water contents can also account for the unusually explosive nature of silicic magmatism on Dominica compared to other Lesser Antilles islands. Vertically-extensive magmatic mushes are consistent with melt inclusion and plutonic xenolith data for other silicic and intermediate eruptions in the northern Lesser Antilles and may be an important aspect of arc magmatism more widely.

Fig. 1

 1 Fig. 1 Geological context of Dominica (Lesser Antilles). a The Lesser Antilles arc. b Main volcanic centers from North (Morne aux Diables) to South (Morne Plat Pays), through the central part with

Fig. 2

 2 Fig. 2 SEM/optical images of MIs in Opx, Cpx and Fd. a Orthopyroxene from Layou (SEM); b Orthopyroxene from Roseau (SEM); c Plagioclase from Grand Fond (SEM); d Plagioclase from Layou

  ). Host mineral composition are as follows: DC25 Opx-En 49-54 (n = 10), Pl-An 55-74 (n = 5) and Cpx-Wo 41-42 (n = 11); DC06 En 58-62 (n = 6) and An 60-87 (n = 4); DC08 En 53-57 (n = 4) and An 55-73 (n = 7); DC139 En 54-62 (n = 12), An 66-79 (n = 3) and Wo 41-43 (n = 3); DC02 An 55-89 (n = 4) and Wo 43 (n = 2).

Fig. 4 Fig. 5 Fig. 6

 456 Fig. 4 Selected major element composition of melt inclusions. All data are plotted volatile-free, summed to 100%. a K 2 O, b Al 2 O 3 , c CaO, and d FeO. Whole rocks (WR) and matrix glasses (MG) from[START_REF] Boudon | A revised chronostratigraphy of recurrent large pumiceous eruptions in Dominica (Lesser Antilles Arc): implications on the behavior of the magma plumbing sytem[END_REF]. Symbols as in Fig.3

Fig. 7

 7 Fig. 7 Frequency histograms of CO 2 and H 2 O contents of the melt inclusions. Morne Diablotins-Morne Trois Pitons-Micotrin is separated from Morne aux Diables for clarity. Host-mineral is specified. Morne aux Diables: opx: grey domain; cpx: dark grey vertical line ◂

Fig. 9

 9 Fig. 9 H 2 O-CO 2 behaviour. a CO 2 vs. H 2 O variations with generic 850 °C rhyolite isobars from VolatileCalc for reference. b CO 2 vs. Th relationship. c Calculated XH 2 O of coexisting fluid vs. trapping pressure (kbar) as calculated for individual melt inclusions. Symbols as in Fig. 3

(Fig. 10

 10 Fig. 10 Halogen and sulfur behaviour. a F vs. Th; b Cl vs. Th; c Br vs. Th; d S vs. Th; e Cl vs. F; f Cl vs. Br

Fig

  Fig. 11 H 2 O vs. Cl variation. Purple dashed lines denotes Plat Pays Volcanic Complex MI composition for Opx and Pl from[START_REF] Gurenko | A melt inclusion record of volatiles, trace elements and Li-B isotope variations in a single magma system from the Plat Pays Volcanic Complex, Dominica, Lesser Antilles[END_REF]. The 2 kbar isobar is from[START_REF] Webster | Chloride solubility in felsic melts and the role of chloride in magmatic degassing[END_REF]. Symbols as in Fig.3. Dashed brown lines give the weight percentage of NaCl in aqueous fluids required to produce the observed Cl/H 2 O ratios

Table 1

 1 Melt inclusion compositions of major and selected trace elements and volatiles Sample Comment SiO

	SO 2 (ppm)	90	86	106	59	93	bdl	bdl	57		77	86	77	108	6	bdl	bdl	138		60	68	109	80	102	105	90	112	77	93	82	128	126	bdl	bdl	bdl
	Cl Br	(ppm) (ppm)	2197 11	2232 11	2299 11	2426 6	2269 10	2344 11	2353 12	2504 12		2432 15	2187 13	2535 15	2217 13	2549 14	1804 15	1779 n.d.	2268 n.d.		1997 n.d.	2363 n.d.	2506 n.d.	2422 n.d.	2755 n.d.	2220 n.d.	3137 n.d.	2408 n.d.	2412 n.d.	2307 11	2483 9	2595 15	2475 12	2242 n.d.	2238 n.d.	1619 n.d.
	F	(ppm)	158	322	137	bdl	243	bdl	bdl	302		212	312	325	bdl	bdl	247	bdl	200		bdl	317	338	423	557	294	135	329	173	373	301	373	238	219	215	380
	sd (%) CO 2 (ppm) sd (ppm)	0.31 392 27	0.35 840 26	0.27 356 26	0.29 217 28	0.21 121 7	0.27 121 42	0.18 43 9	0.16 61 8		0.38 89 10	0.38 300 21	0.13 147 8	0.10 118 18	0.24 146 10	0.17 123 15	0.45 65 9	0.12 168 8		0.13 68 9	0.13 178 16	0.35 254 9	0.33 92 10	0.38 198 12	0.39 149 9	0.37	0.38 253 17	0.38 387 15	0.37 209 18	0.39 296 11	0.33 252 40	0.50 4012 487	82	3334	217
	Total H 2 O (wt%)	91.05 7.11	92.17 6.71	90.05 6.57	89.74 7.43	90.71 7.63	90.26 7.07	90.65 7.46	92.28 6.41		92.21 6.18	91.21 5.49	90.81 6.10	91.76 7.53	92.42 6.15	93.26 6.03	92.77 6.11	90.52 5.91		92.25 5.09	91.28 7.30	90.55 6.38	90.28 5.89	90.88 6.92	90.03 6.72	89.65 6.52	90.67 5.64	90.03 6.29	90.82 4.66	90.88 4.47	90.93 5.76	88.14 6.17	90.46 6.5	91.28 6.3	92.36 6.2
	P 2 O 5	0.07	0.02	0.01	0.02	0.05	0.00	0.04	0.04		0.03	0.00	0.03	0.02	0.03	0.08	0.05	0.04		0.02	0.04	0.01	0.03	0.06	0.00	0.00	0.02	0.03	0.07	0.02	0.02	0.04	0.02	0.10	0.06
	2 TiO 2 Al 2 O 3 FeO MnO MgO CaO Na 2 O K 2 O	P17 L1c4-MI1 71.87 0.17 11.70 1.70 0.04 0.19 1.87 1.04 2.40	L1c4-MI2 72.53 0.18 12.27 2.06 0.05 0.19 1.88 0.71 2.29	L1c4-MI3 72.50 0.15 12.16 1.93 0.02 0.18 1.88 0.16 1.07	L5c5-MI1 70.42 0.29 12.37 1.74 0.13 0.23 1.87 0.55 2.12	L5c5-MI2 71.23 0.11 11.73 1.81 0.06 0.17 1.62 1.58 2.34	L5c11-MI1 70.78 0.06 11.67 2.00 0.09 0.14 1.54 1.52 2.44	L5c11-MI2 71.70 0.09 11.42 2.23 0.03 0.13 1.48 0.88 2.65	RP1 L1c3-72.10 0.07 11.57 1.91 0.08 0.20 1.39 2.07 2.86	MI1(1)	L1c3-MI2 72.39 0.06 11.49 2.23 0.14 0.19 1.43 1.69 2.54	L2c6-MI1 72.13 0.07 11.02 1.80 0.12 0.17 1.46 1.86 2.57	L3c3-MI1 70.90 0.19 11.67 2.05 0.15 0.15 1.44 1.39 2.84	L3c3-MI2 72.55 0.10 11.97 1.57 0.03 0.19 1.51 1.35 2.47	L4c4-MI1 71.71 0.21 12.13 2.51 0.13 0.22 1.70 0.97 2.81	L4c6-MI1 72.23 0.11 11.81 2.22 0.12 0.19 1.70 2.36 2.44	L4c6-MI2 71.64 0.14 12.04 2.09 0.06 0.22 1.68 2.31 2.56	L4c7-71.60 0.06 11.90 1.63 0.05 0.16 1.55 1.20 2.35	MI1(1)	L4c7-MI2 73.91 0.20 10.84 1.83 0.09 0.16 1.26 1.05 2.89	L4c9-MI1 72.87 0.10 11.55 2.17 0.06 0.20 1.45 0.59 2.25	SAN3 L2c5-MI1 70.88 0.14 11.93 2.10 0.05 0.20 1.58 1.20 2.45	L2c5-MI2 71.84 0.12 11.22 1.92 0.03 0.23 1.58 0.94 2.37	L1c7-MI1 71.94 0.16 11.41 1.91 0.11 0.23 1.58 0.96 2.52	L1c7-MI2 70.99 0.09 11.90 2.31 0.07 0.16 1.75 0.60 2.16	L1c7-MI3 70.52 0.20 11.60 2.26 0.12 0.15 1.70 0.68 2.42	SAN3 L3c2-RL1 71.88 0.13 11.84 2.14 0.00 0.27 1.72 0.60 2.08	L3c2-RL2 71.19 0.24 11.86 1.90 0.11 0.23 1.65 0.61 2.21	L2c1-RL1 71.14 0.20 11.60 2.32 0.12 0.23 1.79 1.14 2.23	L2c1-RL2 70.32 0.15 11.45 2.53 0.12 0.24 1.67 1.90 2.48	L1c8-RL1 69.52 0.21 12.16 2.34 0.04 0.26 1.85 1.75 2.78	L1c8-RL2 68.89 0.24 11.84 2.26 0.03 0.28 1.69 0.72 2.13	P8 L5C1 70.78 0.14 11.76 1.42 0.08 0.23 1.46 1.81 2.76	L6C4 70.90 0.24 11.70 1.32 0.04 0.19 1.57 2.22 2.99	L7C1 72.73 0.20 11.38 1.18 0.03 0.19 1.49 2.27 2.83
			Layou-	Opx						Roseau-	Opx																	Grand	Fond-	Opx				Layou-	Pl

Table 1

 1

  5, 5.8 and 5.7 wt% for Layou, Roseau and Grand Fond, respectively. This may reflect diffusive H 2 O-loss through the host crystal or MI-trapping in Px under slightly less H 2 O-rich conditions. MIs from Morne aux Diables show the same high H 2 O content of 7.6 wt%, in a Cpx-hosted MI, although the H 2 O spread is larger for Cpx (1.2-7.6 wt%) than Opx. Opx display a Gaussian distribution of H 2 O content but with a slightly lower maximum value (3.2-6.7 wt%). Contrary to Morne Diablotins and Morne Trois Pitons-Micotrin, Pl-hosted MIs from Morne aux Diables exhibit comparably high H 2 O content to pyroxene, with the highest value (7 wt%) lying between the maximum H 2 O content in Cpx and Opx. 2. Carbon dioxide The majority of Morne Diablotins andMorne Trois Pitons-Micotrin CO 2 contents lie in the range 50-834 ppm. The range in Pl-hosted MI is lower than that in Opx-hosted MI, with the highest CO 2 content being 439 ppm for Grand Fond (Fig.7). In contrast to H 2 O, Grand Fond sits at the higher end of the CO 2 range. Two very high CO 2 values were measured (off-

	scale in Fig. 7): 3998 ppm in an Opx MI from Grand
	Fond, 3334 ppm in a Pl MI from Layou. Morne aux
	Diables MIs in both Px and Pl show a larger range of
	values than for Morne Diablotins and Morne Trois
	Pitons-Micotrin. Two Opx-hosted MIs have 1117 and
	1239 ppm, and five Cpx-hosted MIs describe a restric-
	tive domain between 1134 and 1149 ppm. In Pl-hosted
	MIs, high CO 2 values are also present: 2455 ppm and 2613 ppm. CO 2 shows a broad overall inverse variation with the incompatible element Th (Fig. 9a) consist-
	ent with volatile-saturated crystallization conditions
	(Blundy and Cashman 2008).

  , regardless of the eruption, but with the highest content for Morne aux Diables and the lowest content Morne Diablotins and Morne Trois Pitons-Micotrin. For Morne Diablotins and Morne Trois Pitons-Micotrin the values of MI in Pl correspond to lower pressure, close to 2 kbar, whereas Opx-hosted MI indicate higher pressure. For Morne aux Diables most of the MIs in Opx indicate a roughly equivalent to that obtained for the MIs in Opx for Morne Diablotins and Morne Trois Pitons-Micotrin. Based on the experimental data of

Acknowledgements We thank R. Arculus, R. Watts and S. Skora for help with sampling at Morne aux Diables, S. Hidalgo for help with sample preparation, M. Fialin, N. Rividi, S. Kearns and B. Buse for EPMA analyses and O. Boudouma for SEM investigations. This work was supported by the TelluS-ALEAS (2013) funding from INSU-CNRS, ERC Advanced Grant CRITMAG and EC FP7 Grant VUELCO.


Olivier Cortier
email: olivier.cortier@esitc-caen.fr

O Maquaire

M Boutouil

Keywords: Hydrological behaviour, FlexPDE, Modeling, Permeable pavement, Pervious concrete

HAL is

Modeling of the hydrological behaviour of pervious pavements, a physically based approach with FlexPDE

Introduction

Rainwater management is one of the key concerns to address to enable the development of sustainable cities. When a city expands itself onto green areas, a large number of Sustainable Urban Drainage Systems (SUDS) already exist and can be used, such as swales and ponds. However, to be fully sustainable, urban planning must avoid as much as possible to use these green areas but instead try to re-build the city itself. When an urban project is in a dense urban area, permeable pavements offer an alternative drainage system which presents both the advantage of being sustainable and the advantage of saving construction space. They do not require a specific space; they can be integrated to roads, car parks and public realm.

Permeable pavements are well studied all over the world by the scientific community [START_REF] Tennis | Pervious concrete pavements[END_REF], [START_REF] Illgen | Runoff and Infiltration characteristics of permeable pavements -Review of an intensive monitoring program[END_REF]. However, these techniques are still not yet frequently used in urban projects. Research is still needed on issues such as clogging and evaporation, etc. This work focused on the analysis of the hydrological processes within the pervious structures. The infiltration and retention of water inside permeable structures have already been well studied but only a few studies focus on the evaporation process. Inspired by various German studies (Göbel et al., 2013;[START_REF] Hollenbeck | Water-permeable pavements as the sole storm water management strategy -problems and possibilities[END_REF] which have experimentally demonstrated the performance of permeable pavements for evaporation, this research aims to take evaporation into account.

Methods

Modelling approach

In order to quantify the impact of each parameter, a physics based modelling approach was chosen. A model was built using FlexPDE, which is a multi-physics finite element solution environment for partial differential equations. The model is based on the Richard equation (Equation 1) (Marsily (de), 1981), [START_REF] Dakhlaoui | Fonctionnement hydraulique des structures réservoirs pour l'assainissement pluvial : étude des dispositifs de diffusion d'eau et modélisation[END_REF]. The soil-water characteristic curve and the relation between the permeability and the water content are described for each material using the Van Genuchten laws (Equation 2 and 3).

𝜃(ℎ) = 𝜃 𝑟 + (𝜃 𝑠 -𝜃 𝑟 ) • ( 1 1+(𝛼•ℎ) 𝑛 ) 𝑚 (2) 𝐾(𝜃) = 𝐾 𝑠 • ( 𝜃-𝜃 𝑟 𝜃 𝑠 -𝜃 𝑟 ) 1 2 ⁄ • [1 -(1 -( 𝜃-𝜃 𝑟 𝜃 𝑠 -𝜃 𝑟 ) 1 𝑚 ⁄ ) 𝑚 ] 2 (3) With:
 ϴs, the saturated volumetric water content  ϴr, the critical volumetric water content  K s , the saturated coefficient of permeability  α, n and m, the Van Genuchten coefficients Boundary conditions are applied to simulate rainfall, evaporation, outflow and infiltration. Newman boundary conditions are used for each boundary. The drain outflow is modeled using the orifice equation (Equation 4) with a maximum value corresponding to the chosen limited outflow.

𝑄 = 𝐶 𝑑 × √2 • 𝑔 • ℎ (4) With: C d , the orifice coefficient
The evaporation values used were recorded by the weather station Caen Carpiquet, distant to seven km form the site. The infiltration used to build the model corresponds to the infiltration rate measured on field at the ESITC Caen.

The model was built using proprieties of materials used for the construction of a field study of twelve parking lots made with pervious concrete blocks. Particular focus was made on parameter estimation. All parameters used in the model have been physically defined. For the Van Genuchten parameters the Modified Kovacs Model [START_REF] Aubertin | A model to predict the water retention curve from basic geotechnical properties[END_REF] has been used in order to estimate the value of "a" and "n" for each material.

Field study and laboratory experiment

A research project named VECOPEXP is being conducted at ESITC laboratory. This project is following two pervious parking lot sites, in Epron and Caen, in Normandy. The pervious pavement structures were designed and built following different permeable pavement guides [START_REF] Faleyeux | Elements modulaires en beton pour revetement des ouvrages d'infiltration des eaux pluviales : référentiel technique[END_REF], [START_REF] Abdo | Voiries et aménagements urbains en béton -Revêtements et structures réservoirs (Road and urban equipment in concrete -permeable pavement)[END_REF]. The originality of the structure is that their top layer is composed of pervious Sand 2/6 mm concrete pavers made with crushed seashell as a substitute for natural aggregates, [START_REF] Nguyen | Valorization of seashell by-products in pervious concrete pavers[END_REF] .

The first site, at Epron, was used to build the model. This site is composed of twelve pervious parking spaces. Four of them are studied; they have impermeable lining on the sides and the bottom. The catchment is composed of 147m² of impervious parking area that discharges into the 50m² pervious pavements.

Weather condition, outflow and water pressure inside the structure are monitored in the field. Data collected from these sensors are used in order to build and validate the model.

Fig 2. Parking spaces made with pervious concrete pavers -ESITC Caen, Epron, France

In addition to the field study, a laboratory experiment was designed to reproduce the permeable pavement. This structure will allow for experimentation with different materials or designs as well as measuring the effects of clogging and pollutants filtration. Results from these tests will be used to improve the numerical model.

Results and Discussion

The model is still under sensitivity analysis stage. This sensitivity analysis is conducting with several parameters including structure and material parameters (permeability, clogging, structure dimensions, drain position, etc.) and site and weather parameters (soil permeability, permeable/impermeable ratio, potential evaporation, storm intensity, etc.).

The first parameters used are presented in the table 2, the rain event used for the simulation are presented in the figure 3. Runoff from impermeable catchment is coming from the left.

Tab 2. First parameters used for the sensitivity analysis

Fig 3. Storm event used for the sensitivity analysis

This event corresponds to a real storm that occurs in Caen (France) in July 2013 with a total of 83.5 mm of rain in 2.5 hours. After the storm, the simulation runs for twelve hours with a potential evaporation that corresponds to 4 mm per day.

First results are presented in figure 4; they show in percentage the water balance twelve hour after the end of the rainfall event. Simulations are classed according to the % of infiltration. The last simulation corresponds to a different rainfall event; 5.8 mm in 1.5 hour.

Fig 4. First results of the sensitivity analysis -work still in progress

These first results showed the importance of structural and environmental parameters for the hydrological performances of permeable pavements. As expected, evaporation is negligible for an extreme storm event but raise up to 17% for non-extreme event. Regarding the structural parameters, vertical and horizontal drain position have an important influence. Knowing this could be interesting to reduce drain outflow and maximise infiltration with a better design.

In the future different scenarios will be built, based on the most influent parameters, in order to quantify the different hydrological processes within the pervious structure. A better comprehension of hydrological processes is expected. The results will be used as input for the modelling of pervious pavement impacts at the urban catchment scale.

Conclusions

Pervious pavers are one of the solutions that contribute to finding an innovative and sustainable answer to effective rain water management in urban area. A better understanding of hydrological processes within the pervious structure is needed as a first step to quantify their benefits. In order to achieve this, a numerical model of the different hydrological processes inside a permeable structure was built using FlexPDE software, including evaporation. Results will give understanding for the use of this technique in different environmental situation to help maximise their benefits.

O

  . Cortier 1,2,* , O. Maquaire 2 , M. Boutouil 1 1 COMUE NU -ESITC, ESITC Caen, 1, rue Pierre et Marie Curie, F-14610, EPRON-FRANCE 1 rue Pierre et Marie Curie 2 Normandie Univ, UNICAEN, CNRS, LETG -Campus 1, Bâtiment A, Esplanade de la Paix, 14032 Caen Cedex 5, France

  the hydraulic water head  z, the altitude  ϴ, the volumetric water content

Tab 1 .Fig 1 .

 11 Fig 1. View of the structure built on site and modelling in FlexPDE

Acknowledgement

The work presented in this article is a part of the PhD of Olivier Cortier, financed by Regions of Normandie (France). The authors wish to thank the Regions of Normandie and all VECOPEXP project partners and financers for their support.


L Krähenbühl

R Scorretti

A Bréard

C Vollaire

Senior Member, IEEE J.-M Guichon

O Chadebec

G Meunier

A Urdaneta-Calzadilla

V C Silva

C A F Sartori

Large Surface LC-resonant Metamaterials: from Circuit Model to Modal Theory and Efficient Numerical Methods

We study the harmonic magnetodynamic behavior (without wave propagation) of a resonant surface metamaterial, made up of many identical and regularly arranged LC cells. The circuit model gives the exact solution, but is not numerically efficient for the simulation of very large structures (e.g. 1000×1000 cells). For the first time, we highlight the modal character of the solutions, which makes it possible to explain their frequency and spatial related properties. From these results, we show under what assumptions it is possible to homogenize the metamaterial, which opens the way for using this approach together with efficient numerical methods.

Index Terms-LC metamaterials, resonance, circuit analysis, modal analysis, homogenization, matrix reduction, integral equations I. INTRODUCTION: TYPICAL DEVICE HE typical device that we consider was first proposed in with 8×8 resonant LC cells arranged on a plane surface (Fig. 1). The goal of the present work is to explain the frequency behavior of these devices and to propose efficient numerical methods to simulate them even for arrangements with a far greater number N cells (e.g. 1000×1000, N=10 6 ). Fig. 1. Experimental setup applied to wireless power coupling studies [START_REF] Nishimura | Enhancing the inductive coupling and efficiency of wireless power transmission system by using metamaterials[END_REF] Natural frequency of the isolated cell:

1/ 2 .

II. CIRCUIT ANALYSIS TECHNIQUE (REFERENCE SOLUTION)

For quite small systems, the reference solution is easy to obtain using the circuit analysis technique. We get a complex full N×N matrix with main terms around the diagonal:

1 (1)
We suppose that the excitation current I s is known and that there is no current in the receiver (I r =0); the method may be applied for other choices by considering the corresponding equations. The mutual inductors (matrix and vectors and ) may be analytically [START_REF] Mohan | Simple accurate expressions for planar spiral inductances[END_REF][START_REF] Bilotti | Equivalent-circuit models for the design of metamaterials based on artificial magnetic inclusions[END_REF] or numerically computed; it is then possible to obtain the cell currents and the flux in the receiver as a function of the angular frequency.

global values are particularly significant for the CAD approach; first, the square norm of the cell currents:

| | ∑ " " (2)
which expresses the intrinsic reaction of the metamaterial; second, the ratio # $ , between the flux through the receiver in the $ position, respectively with and without presence of the metamaterial, or its norm # ℓ on a length ℓ, which express the frequency effect of the metamaterial for an energy transmission between the source and the receiver:

# $ , 1 ' (3)
# ℓ 1 ℓ ( )#) $, *$ + ,-.ℓ + ,- (4)
For small structures, the circuit analysis gives the exact reference solutions, but it is not practicable for large ones and it does not give the key to understand how the device works.

III. MODAL APPROACH

To simplify the explanations, we establish here the modal character of the solutions only for 2D field problems with 1D metamaterials (Fig. 2); the extension to the real 3D situation with 2D metamaterial, will be presented in the extended paper.

Assuming that the length of the metamaterial is infinite, i.e. the excited area is small compared to this length, we can rewrite the circuit equations as independent modal equations:

T 1 A 4 ? 4 3 4 9 0 … / D /2 (7)
where the mutual inductance A 4 of the mode k corresponding to the spatial frequency 9/ /′E , is defined by: A 4 A 567 2 9 $ $ :

.F GF (8) (the result does not depend on i because of the infinite limits).

Even if the number of equations (1+N'/2) is of the same order of magnitude as for the circuit method, the modal method is much more efficient because these equations are independent. Moreover, we can evaluate and use only the predominant modes (e.g. 10%), without perceptible loss of accuracy.

Data (see Fig. 2) for the numerical results of Fig. 3 and Fig. 4: The modal equation ( 8) highlights an electric resonance frequency 1/ 2 A 4

Metamaterial
for each spatial mode k, fastest spatial variations corresponding to lowest electric resonance frequencies. The two characteristic quantities ( 2) and ( 4) typically have the aspects given in Fig. 4: Note that in the real situation of §I, we would obtain a modal mutual A with two indices, and bidirectional modes (Fig. 5).

IV. HOMOGENIZATION

If the elementary cells are small with respect to the excitation and reception coils dimensions, the amplitude of the higher modes is small and their effect will be negligible on the solution I i and on the flux in the receiver (| | (2), # (3) or # ℓ (4)). It is then possible to reduce the number of degrees of freedom of the solution without substantially reducing its accuracy. By way of example, the solution presented in Fig. 4 (left) was calculated in the following 3 ways:

complete reference circuit solution, using N=361 cell currents (361×361 full matrix); -reduced modal solution, using only the 10% main modes (= low-pass spatial filtering, 37 unconnected equations); the global behavior is correctly described, but the resonances are not precisely obtained (peak values and frequencies), because the metamaterial is considered as infinite (the source field is also repeated at infinity); -reduced circuit solution, obtained by projection of the unknowns I i and of the circuit equations on a mesh 10 times rougher than the cell dimension (37×37 full matrix). Like the reduced modal method, this method results in low-pass filtering of the reference solution, but this time it is possible to take into account the finite dimension of the metamaterial. Accuracy is excellent for the frequency band of interest (see "detail" on Fig. 4,left). This result implies that a way to achieve an homogenization should be found. We will show in the extended paper that for surface metamaterials, the reduced matrix can be efficiently constructed directly using a 2D surface mesh much rougher than the size of the elementary cells. The currents in the cells are represented by a surface density of normal dipoles whose effect, calculated by an integral method, replaces the calculation of mutual inductances. It is thus possible to take into account metamaterial of complex, non-planar shapes.

The homogenization step consists in modifying the classical integral method to introduce (i) the close interactions (known analytically) that the integral method with coarse mesh cannot describe precisely, and (ii) the 1 ⁄ terms of (1).

Fig. 2 .

 2 Fig. 2. 2D problem with a linear metamaterial Let's develop in spatial Fourier series, over a length L=N'D (typically /′ 1 /), the source flux 2 and the current solution I i . For the cell located at the abscissa x i we get: 2 3 4 567 82 9 $ : ; 4 < = /

Fig. 3

 3 Fig. 3 Typical behavior of the modal mutual inductance A 4 (8) in function of spatial frequency

Fig. 4 :

 4 Fig. 4 : Typical intrinsic (left) and transfer (right) behaviors (2) and (4). Detail window ( §IV): reference solution in blue; the reduced modal solution (yellow) is roughly correct; the reduced circuit solution (red) is more accurate.