Guillaume Carazzo
email: guillaumecarazzo@ipgp.fr

Stephen Tait

Audrey Michaud-Dubuy

Allan Fries

Edouard Kaminski

Transition from stable column to partial collapse during the 79 cal CE P3 Plinian eruption of Mt Pelée volcano (Lesser Antilles)

Keywords: Mt Pelée volcano, Plinian eruption, tephra fallout, partial collapse, tephrostratigraphy, radiocarbon dating

Highlights

-We determine the eruptive sequence of the P3 Plinian eruption of Mt Pelée volcano -New radiocarbon dating measurements provide a refined age of 79 ± 21 cal CE -We estimate key eruptive parameters of this VEI 5 eruption in the transitional regime -Increasing eruption rate and decreasing gas content led to partial column collapse -The transition occurred at conditions well predicted by our 1D theoretical model

Introduction

Plinian eruptions are amongst the most powerful and destructive volcanic events on Earth.

These explosive eruptions generally form a sustained stable column that can rise up to 40 km in the atmosphere (e.g., the 1991 Pinatubo eruption) and spread out laterally as an umbrella cloud carrying pyroclasts at large distances from the volcano [START_REF] Koyaguchi | Origin of the giant eruption cloud of Pinatubo, June 15, 1991[END_REF].

Abrupt or progressive changes in eruptive conditions at the base of a Plinian column can lead to a radically different behavior in which the column collapses as a turbulent fountain producing hazardous pyroclastic density currents (PDC) that may reach and destroy populated areas [START_REF] Wilson | Volcanic hazard impacts to critical infrastructure: a review[END_REF]. One important goal in physical volcanology is to identify the key processes affecting the column stability in order to improve hazard assessment.

Recent real-time observations of volcanic plumes and field-based studies on fallout tephra from past eruptions show that explosive eruptions commonly have a complex behavior where both a stable Plinian column and a collapsing fountain feeding PDC are contemporaneous (Carazzo et al., 2015 and references therein). This transitional regime of partial column collapse occurs for Plinian eruptions ranging in size from small to large (e.g., the 79 CE Vesuvius [START_REF] Shea | Column collapse and generation of pyroclastic density currents during the A.D. 79 eruption of Vesuvius: The role of pyroclast density[END_REF], 186 CE Taupo [START_REF] Wilson | The Taupo eruption, New Zealand. I General aspects[END_REF], 1150 Quilotoa (Di [START_REF] Muro | Transport and sedimentation dynamics of transitional explosive eruption columns: the example of the 800 BP Quilotoa eruption (Ecuador)[END_REF], 1912 Novarupta-Katmai [START_REF] Fierstein | The Plinian eruptions of 1912 at Novarupta, Katmai National Park, Alaska[END_REF], and 1963 Agung [START_REF] Self | The 1963-1964 eruption of Agung volcano (Bali, Indonesia)[END_REF] eruptions). Detailed mapping and analysis of eruptive products emplaced during the transitional regime provide valuable data to better understand the mechanisms controlling the partitioning of a Plinian column, and can be used to robustly test numerical and analog models of explosive volcanic eruptions (Di [START_REF] Muro | Contemporaneous convective and collapsing eruptive dynamics: the transitional regime of explosive eruptions[END_REF][START_REF] Carazzo | The timing and intensity of column collapse during explosive volcanic eruptions[END_REF][START_REF] Suzuki | Inter-comparison of three dimensional models of volcanic plumes[END_REF]. However, the number of natural cases for which the partial collapse of an initially stable column is described in detail (i.e., in terms of time variation in mass eruption rate, gas content, grain-size distribution and exit velocity) remains too small to fully constrain theoretical models of volcanic plumes [START_REF] Michaud-Dubuy | A revisit of the role of gas entrapment on the stability conditions of explosive volcanic columns[END_REF]. With an aim of increasing the inventory of well-constrained past eruptions, we have undertaken a long-term study of the Plinian eruptions of Mt Pelée volcano (Lesser Antilles) as they systematically produced sustained columns that ultimately collapsed [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF]. Because the Mt Pelée eruptions share many characteristics including similar preeruptive magma storage conditions [START_REF] Martel | Magma storage conditions and control of eruption regime in silicic volcanoes: experimental evidence from Mt Pelée[END_REF], they can be used to decipher the mechanisms controlling the behavior of a Plinian plume. In previous studies, we reconstructed the dynamics of the 1300 CE P1 [START_REF] Carazzo | The recent Plinian explosive activity of Mt. Pelée volcano (Lesser Antilles): The P1 AD 1300 eruption[END_REF], and 280 CE P2 Plinian eruptions [START_REF] Carazzo | Marginally stable recent plinian eruptions of Mt. Pelée volcano (Lesser Antilles): The P2 AD 280 eruption[END_REF] focusing on the causes for column collapse. We now extend this work to study the P3 eruption deposits whose structure suggests the entrance into the partial collapse regime at some stage of the eruption [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF][START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF], making it an excellent candidate to improve the volcanological database on transitional eruptions.

The P3 eruption is described in the literature [START_REF] Roobol | Stratigraphic studies of Mount Pelée, Martinique[END_REF][START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF][START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF][START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF] but the exact sequence of events and the eruptive parameters are currently poorly known. Here, we use data from a new comprehensive field study together with physical models to reconstruct the detailed time evolution of this eruption and to discuss the mechanisms responsible for the transition from stable column to partial collapse. We identify the eruptive conditions leading to this transitional regime and compare the results to previous work on P3, and on younger Plinian eruptions in Martinique (P1 and P2). We then compare our estimated eruptive parameters for the column at collapse with theoretical predictions from a model of volcanic plumes.

Overview of the P3 eruption

The P3 deposits were first identified by [START_REF] Roobol | Stratigraphic studies of Mount Pelée, Martinique[END_REF] as a thick pumice fallout unit on the western flank of Mt Pelée volcano standing above the 2406 and 2447 yr BP horizons of their stratigraphic sections. [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF] provided the first age, synthetic stratigraphic section and distribution map of the P3 deposits (Fig. 1a). The P3 Plinian eruption is currently dated at 2010 ± 140 yr BP based on the average of five 14 C ages [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF][START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF]. According to these studies, the eruption began with the formation of a sustained Plinian column that covered the western flank of the volcano with a meter of coarse lapilli, lithic-rich, pumice fallout deposit (phase P31). This initial stage was immediately followed by the production of high-concentration PDC in the Grande Savane, Habitation Depaz and Falaise River paleo-valleys (Fig. 1a). The second eruptive phase identified by [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF] consisted of a sustained Plinian column that spread fine lapilli pumice to the south with a striking elongated axis of dispersion (phase P32). The P3 eruption ended up with the formation of a pumice ash-rich bed (phase P33) interbedded with high-concentration PDC deposits (Fig. 1a). Later, [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF] excluded the second phase (P32) whose distal deposits were found below tephra from an eruption older than P31. Recent work by [START_REF] Michaud-Dubuy | Impact of wind direction variability on hazard assessment in Martinique (Lesser Antilles): the example of the 13.5 ka cal BP Bellefontaine Plinian eruption of Mount Pelée volcano[END_REF] confirmed that the deposits named P32 by [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF] are not interbedded between P31 and P33 but belong to a much older event, the 13.5 ka cal BP Bellefontaine Plinian eruption. [START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF] studied the distal products of a Plinian eruption dated between 1800 and 2200 yr BP (their subunit d), which corresponds to the P3 eruption identified by [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF]. Their synthetic stratigraphic section includes a basal pumice-rich low-concentration PDC (named 'surge') deposit overlain by a pumice fallout deposit interbedded with high-concentration PDC (named 'flow') and low-concentration PDC (named 'ash hurricane') deposits. According to their distribution map of the deposits (Fig. 1b), the high-concentration PDC flowed in the Fond Canonville valley, Grande River, Bijou River, and Falaise River, whereas the low-concentration PDC that elutriated from the top of the current spread on hills at distances up to 20 km from the vent. Isopachs of the pumice fallout deposit exhibit a SSW elongation (Fig. 1b), in good agreement with the one inferred by [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF] (Fig. 1a). [START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF] interpreted their complete stratigraphic succession as resulting from the partial and final collapse of an initially stable Plinian column.

The eruptive parameters of the P3 event are currently poorly constrained. Volume estimates for the fallout tephra of the P3 eruption yield a relatively small value of 0.19 km 3 dense rock equivalent (DRE) [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF]. The direction of tephra dispersal during the initial phase (P31) suggests that the column was affected by low altitude tropospheric winds, and thus was certainly more than 6 km [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF], but no more than 12 km in height [START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF]. Such a large uncertainty on the maximum column height makes it difficult to estimate its mass eruption rate. Overall, these sparse and loosely constrained data cannot be used to understand the conditions leading to column collapse.

Methodology

Fieldwork

We identified the P3 eruption deposits at 102 locations in Martinique (Fig. 2). In most cases, these deposits are easily recognizable by their strong internal layering, the abundance of juvenile and accidental lithic fragments in the pumice fallout units, and the presence of the P1 and/or P2 deposits above them [START_REF] Carazzo | The recent Plinian explosive activity of Mt. Pelée volcano (Lesser Antilles): The P1 AD 1300 eruption[END_REF]2019). The P3 outcrops are distributed all around the volcano except to the northwest where exposure is very limited due to dense tropical forest and difficult conditions of access. The thickness of each layer of P3 was measured at every site in order to construct isopach maps. We also excavated a standard 25 x 20 cm area of each fall layer and measured the major axes of the five largest lithic fragments found in order to produce isopleth maps.

Radiocarbon dating

We dated four charcoals sampled within the P3 deposits at sites 6 (unit A-G), 97 (unit A), 178 (unit A), and 180 (unit A-G), and a paleosol sampled beneath unit A at site 145 (see locations in Fig. 2 and unit descriptions in section 4.1) in order to refine the age of the P3 eruption.

Ages were determined using accelerator mass spectrometry at the LMC14 (Artemis, Laboratoire de Mesure du Carbone 14, CEA Saclay, France), and calibrated using the free software OxCal 4.3 [START_REF] Bronk Ramsey | Bayesian analysis of radiocarbon dates[END_REF] with the atmospheric IntCal13 calibration curve commonly used for the Northern hemisphere [START_REF] Reimer | Selection and treatment of data for radiocarbon calibration: an update to the international calibration (IntCal) criteria[END_REF]. The radiocarbon ages obtained for our stratigraphically-constrained samples were combined with those of [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF] and validated using the R_combine function of Oxcal and χ 2 test prior to calibration [START_REF] Ward | Procedures for comparing and combining radiocarbon age determinations: a critique[END_REF].

Grain-size analysis

We carried out grain-size analyses on twenty samples from ten locations representative of the seven different units (A to G) (see Table 1). The samples were dried for 24 h in an oven and sieved by hand down to 6φ. We separated the lithic fragments from the pumices by hand in the size range -6φ to -4φ, and used a binocular microscope to discard crystals and lithic fragments in the size range -4φ to -2φ. Volume calculations for isomass maps for each φ interval were then used to determine the grain-size distributions of single sub-layers. The total grain-size distribution was estimated from the total mass in sieve class φ, , by the volume integral [START_REF] Kaminski | The size distribution of pyroclasts and the fragmentation sequence in explosive volcanic eruptions[END_REF]

) = ℎ d , ( 1
)
where ℎ is the deposit thickness, is the concentration of class φ at distance l from the vent, d is the area bounded by isopachs at distances l and l+dl, and L is the distance where h or drop to zero. We used linear interpolations for h and between the localities.

The cumulative frequency curves were determined assuming a power-law size distribution of the rock fragments [START_REF] Turcotte | Fractals and fragmentation[END_REF][START_REF] Kaminski | The size distribution of pyroclasts and the fragmentation sequence in explosive volcanic eruptions[END_REF], where the number of particles with a radius larger than r is given by:

≥ = , (2)
with D the power-law exponent that commonly varies between 2.9 and 3.9 for Plinian eruptions [START_REF] Girault | The effects of total grainsize distribution on the dynamics of turbulent volcanic plumes[END_REF]. Because fragmentation is a size-invariant process, the exponent D can be estimated accurately using any sufficiently large range of sizes. Thus, the lack of fine particles lost out at sea does not affect our estimations of D.

Eruptive parameters

The volume of tephra fallout produced during an explosive eruption can be inferred using several methods based on the thinning trend of the deposit with distance from the source.

Here, we used the exponential, power-law and Weibull fits [START_REF] Pyle | The thickness, volume and grainsize of tephra fall deposits[END_REF][START_REF] Bonadonna | Total grain-size distribution and volume of tephra fall deposits[END_REF][START_REF] Bonadonna | Estimating the volume of tephra deposits: a new simple strategy[END_REF]) computed using the AshCalc software [START_REF] Daggit | AshCalc -a new tool for the comparison of the exponential, power-law and Weibull models of tephra deposition[END_REF]. Bearing in mind that only proximal and furthermore incompletely preserved deposits are available in Martinique, the calculated volumes of fall deposits should be taken as minimum estimates. The volume of dilute PDC deposits was calculated using the observed relationship between the volume and area covered by dilute PDC [START_REF] Dade | Long runout rockfalls[END_REF][START_REF] Calder | Mobility of pyroclastic flows and surges at the Soufriere Hills Volcano, Montserrat[END_REF], as in [START_REF] Carazzo | The recent Plinian explosive activity of Mt. Pelée volcano (Lesser Antilles): The P1 AD 1300 eruption[END_REF][START_REF] Carazzo | Marginally stable recent plinian eruptions of Mt. Pelée volcano (Lesser Antilles): The P2 AD 280 eruption[END_REF] for the P1 and P2 eruptions. The volume of dense PDC was calculated using the product of the average thickness and area covered by the dense PDC. This method is bound to provide minimum estimates since only proximal and furthermore incompletely preserved deposits are available in Martinique.

The maximum column heights associated with the fall deposits were estimated from the distribution of lithic fragments on our isopleth maps using the method of [START_REF] Carey | The 1982 eruptions of El Chichon volcano, Mexico (2): Observations and numerical modelling of tephra-fall distribution[END_REF]. Error bars were calculated using the three values of maximum height inferred from the 8, 16, and 32-mm isopleths (see Fig. 17 in [START_REF] Carey | The 1982 eruptions of El Chichon volcano, Mexico (2): Observations and numerical modelling of tephra-fall distribution[END_REF].

The alternative method of [START_REF] Bonadonna | Plume height, volume, and classification of explosive volcanic eruptions based on the Weibull function[END_REF] based on variations of grain size with the distance from the source was also used to confirm the robustness of the estimates.

The mass discharge rate feeding the eruption during phases of stable column was inferred from a given column height by using the empirical relationship from [START_REF] Mastin | A multidisciplinary effort to assign realistic source parameters to models of volcanic ash-cloud transport and dispersion during eruptions[END_REF] and the predictions of the model of [START_REF] Girault | Combined effects of total grain-size distribution and crosswind on the rise of explosive volcanic columns[END_REF], which explicitly includes the effect of total grain-size distribution on the plume dynamics. Calculations were made for tropical atmospheric conditions and for a crystal-bearing rhyolitic magma (andesitic bulk composition) with an initial temperature of 1,150 K [START_REF] Martel | Diversity of eruptive styles inferred from the microlites of Mt. Pelée andesite (Martinique, Lesser Antilles)[END_REF] and a dense rock density of 2,400 kg m -3 [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF]. The mass discharge rates for the collapsing phases were calculated using the model of [START_REF] Bursik | The dynamics and thermodynamics of large ash flows[END_REF], which treats pyroclastic density currents as supercritical dilute suspensions entraining air as they propagate. [START_REF] Doyle | A two-layer model for the evolution and propagation of dense and dilute regions of pyroclastic currents[END_REF] showed that this assumption is valid for tall, fine-grained column collapses, for which the flow slowly transfers its mass to the dense basal flow. The model of [START_REF] Bursik | The dynamics and thermodynamics of large ash flows[END_REF] is thus relevant for collapsing phases characterized by the formation of dilute PDC deposits, and was used here.

The P3 eruptive succession

Stratigraphy

Fig. 3a shows a composite stratigraphic section of the P3 deposits, divided into seven major phases based on diagnostic stratigraphic and lithofacies associations, which we describe in more detail below.

Unit A

The stratigraphic succession begins with a layer of clast-supported, coarse white pumice lapilli (Fig. 4a-d). Unit A contains juvenile and accidental lithic fragments in a total amount that typically increases from ≈20 wt.% at base to ≈25 wt.% at top (Fig. 3c). At most sites, median pumice size remains relatively constant, whereas both the maximum lithic size and the sorting increase from base to top (Fig. 3b-c).

In the downwind direction (to the southwest), unit A has a maximum thickness of 180 cm at 4.5 km from the crater (Fig. 4c). In the crosswind direction, unit A is 130 cm thick at 4.6 km, and steadily thins to 50 cm within 6.1 km of the crater (Fig. 4d). The relatively widespread nature of this deposit, its uniformly decreasing thickness with distance from the source, its clast-supported framework, and its pumice and juvenile lithic fragments characteristics identify unit A as a fall deposit.

Unit B

Unit B consists of light brown fine ash material in which pumice, lithic fragments and crystals are dispersed in a matrix of dense, angular, glass fragments (Fig. 4b,c,e). Most clasts range in size from fine to coarse ash but a few large pumices are present (Fig. 3b). The total amount of lithic fragments in unit B commonly reaches ≈28 wt.%. Where unit B is present, the contact with the underlying layer is sharp, which suggests that there was no time break between deposition of the two units.

Unit B varies irregularly in thickness with distance from the source, and ranges from 18 to 35 cm at 3.8 km from the eruptive center (Fig. 4), but is absent beyond 7 km from the vent. Where thick, unit B contains a few lenses of coarse lapilli, angular to sub-rounded pumices. At some sites in valleys, pumice lapilli and blocks are rounded and account for a large proportion in the matrix of white fine ash. The relatively limited dispersal of this unit, its irregular thickness, matrix-supported framework and grain types (juvenile and accidental lithic fragments), as well as the nature of the lower contact, indicate that unit B is a lowconcentration pyroclastic density current deposit [START_REF] Branney | Pyroclastic density currents and the sedimentation of ignimbrites[END_REF].

Unit C

Unit C is a relatively thin blanket of clast-supported, white pumice lapilli (Fig. 4b,c,e) containing juvenile and accidental lithic fragments in a total amount that reaches ≈25 wt.% in most studied outcrops (Fig. 3c). At most field sites, unit C is easily distinguishable from unit A, the former being distinctly richer in lithic fragments and coarse lapilli pumice. The maximum lithic size in unit C is, however, always lower than the maximum lithic size at the top of unit A (Fig. 3c).

Unit C was dispersed in approximately the same direction as unit A, and is the thickest ≈3.7 km southwest of the volcano in the downwind direction, where it reaches 22 cm. This layer steadily thins with distance from the vent, and is still 10 cm thick at 6.2 km in the crosswind direction. At most sites, the upper part of unit C was eroded by the pyroclastic density current that overrode it and deposited unit D (see below). The relatively widespread nature of unit C, its uniformly decreasing thickness with distance from the source, its clastsupported framework, and its pumice and juvenile lithic fragments characteristics identify it as a fall deposit.

Unit D

Unit D is a relatively thin layer of fine ash and small rounded pumice lapilli dispersed in a matrix of dense, angular, glass fragments (Fig. 4a,c,f). At distal sites, this layer is thin, stratified and unconsolidated. The total amount of lithic fragments in unit D commonly reaches ≈20 wt.% (Fig. 3c). Where unit D is present, the contact with the underlying layer is sharp and exhibits some erosion of unit C.

Unit D varies irregularly in thickness with distance from the vent, and ranges from 5 to 17 cm at 3.8 km from the volcano (Fig. 4). This layer is, however, absent beyond 7 km from the vent. These irregular thicknesses, the relatively limited dispersal of this deposit, the clast and matrix types, and the nature of the lower contact indicate that unit D is a lowconcentration pyroclastic density current deposit.

4.1.5. Unit E Unit E is a layer of clast-supported, white pumice lapilli (Fig. 4b,c,e) containing juvenile and accidental lithic fragments in a total amount that typically reaches ≈18 wt.% (Fig. 3c). At most sites, both the median grain-size and the maximum lithic size are lower than those measured in unit C (Fig. 3c).

Material was dispersed in approximately the same direction as units A and C to the southwest of the volcano. The maximum thickness is 13 cm at 3.7 km, and steadily thins to 9 cm within 4.8 km from the vent in the downwind direction. The full thickness of unit E is however poorly preserved due to significant erosion by the overlying pyroclastic density current that overrode it and deposited unit F (see below). The relatively widespread nature of this deposit, its uniformly decreasing thickness with distance from the source, its clastsupported framework, and its pumice and juvenile lithic fragments characteristics identify unit E as a fall deposit.

4.1.6. Unit F Unit F is a matrix-supported layer of fine to coarse ash containing rounded pumice lapilli and lithic fragments (Fig. 4b, f), the latter of which typically reaches ≈15 wt.% (Fig. 3c). Where unit F is present, the contact with the underlying layer is sharp and exhibits some erosion of unit E.

Unit F varies irregularly in thickness with distance from the vent depending on the topography, ranges from 6 to 75 cm at 3.8 km from the volcano, and is absent 7 km from the vent (Fig. 4). The relatively limited dispersal of this unit, its irregular thickness, matrix-supported framework and grain types (juvenile and accidental lithic fragments), as well as the nature of the lower contact, indicate that unit F is a low-concentration pyroclastic density current deposit.

Unit G

Unit G is the uppermost layer in the P3 sequence and consists of a blanket of fine to coarse white pumice lapilli (Fig. 4a,b,f). This unit contains juvenile and accidental lithic fragments in a total amount that reaches ≈20 wt.% at most studied outcrops (Fig. 3c) with a maximum lithic size similar to that of unit C (Fig. 3c).

In the downwind direction (to the southwest), unit G has a maximum thickness of 80 cm at 1.4 km from the crater, and steadily thins to 20 cm within 4.8 km of the vent. In the crosswind direction, unit G is 30 cm thick at 5 km, and 15 cm at 6.4 km from the vent. The relatively widespread nature of this deposit, its uniformly decreasing thickness with distance from the source, its clast-supported framework, and its pumice and juvenile lithic fragment characteristics identify unit G as a fall deposit.

Age of the P3 eruption

Radiocarbon dates and calibrated ages are reported in Supplementary material Table S1 (Walker, 1973;[START_REF] Roobol | Stratigraphic studies of Mount Pelée, Martinique[END_REF][START_REF] Traineau | Contribution à l'étude géologique de la Montagne Pelée, Martinique[END_REF][START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF] ranging from 1,800 to 2,150 yr BP (Supplementary material

Grain-size distribution of selected samples

Twenty samples from the P3 units were analyzed (Table 1) in order to discuss the evolution of the grain-size distribution during the entire P3 eruption at a single outcrop (Fig. 3), and to determine the total grain-size distribution for the lapilli fraction of unit A deposits (see section 4.6). The objective is twofold: to confirm the fall or flow nature of the P3 units, and to estimate the amount of gas trapped in pumice fragments at the beginning of the eruption (see section 6.3). A detailed analysis of the pumice textures is beyond the scope of this paper and can be found in [START_REF] Martel | Diversity of eruptive styles inferred from the microlites of Mt. Pelée andesite (Martinique, Lesser Antilles)[END_REF].

The fourteen samples from unit A display the typical fallout characteristics with median diameter ranging from 0.7φ to -3.3φ, and sorting ranging from 1.4 to 2.7. These values are relatively close to those obtained by [START_REF] Bardintzeff | The recent pumice eruptions of Mt Pelée, Martinique. Part II: Grain-size studies and modelling the last Plinian phase P1[END_REF] who measured median diameter and sorting ranging from -0.3φ to -3φ, and 1.7 to 2.8, respectively. Most of the samples collected on land belong to proximal deposits since the medial and distal deposits were lost at sea. The grain-size distribution of individual samples is systematically bimodal (Fig. 3b) and the amount of ash particles (< 2 mm) always increases from base (≈9 wt.%) to top (≈36 wt.%). The top of unit A is thus always more poorly sorted than the base, but the median grain-size remains approximately constant throughout the unit (Fig. 3c).

The six samples from units B to G collected at outcrop 163 show that units C, E, and G have typical fallout characteristics similar to unit A. The median diameter for these units ranges between -0.1φ and -3φ, and they have moderate sorting values from 2.5 to 2.7 (Fig. 3c). The amount of ash-sized particles is similar to or larger than in unit A, ranging from ≈28

wt.% to ≈55 wt.%. Units B, D, and F have flow features with median diameter ranging from 1.7φ and 0.4φ, and moderate sorting ranging from 2.2 to 2.6 (Fig. 3c). The amount of ashsized particles is larger than in the fall deposits, ranging from ≈62 wt.% to ≈85 wt.%.

Isopach maps

Fig. 5 shows a stratigraphic correlation of P3 outcrops along three different dispersal axes (i.e., north to south, northwest to southeast, and northeast to southwest, see Fig. 2 for localization). The complete sequence can be found up to 5 km from the vent (sites 13, 163, 101, 78 in Fig. 5). Thickness measurements at each location are reported on isopach maps for the cumulative pumice fallout phases A+C+E+G (Fig. 6a), the pumice fallout phase A (Fig. 6b), the cumulative pyroclastic density current phases B+D+F (Fig. 6c), and the cumulative pumice fallout phases C+E+G (Fig. 6d). These maps are later used to calculate the total grainsize distribution of unit A (see section 4.6), and the volume of deposits (see section 5.1).

The cumulative isopach map of the pumice fallout phases A+C+E+G shows ellipsoidal contour patterns indicating fallout dispersion towards the southwest (Fig. 6a). We find a similar direction of dispersion for the pumice fallout phase A, and the cumulative pumice fallout phases C+E+G (Fig. 6b,d). This direction of dispersion is in relatively good agreement with the results of [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF] and [START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF] (Fig. 1), and is characteristic of the wind profiles in the Lesser Antilles during the wet season [START_REF] Michaud-Dubuy | Impact of wind direction variability on hazard assessment in Martinique (Lesser Antilles): the example of the 13.5 ka cal BP Bellefontaine Plinian eruption of Mount Pelée volcano[END_REF]. In the upwind direction to the northeast and in the crosswind direction to the southeast, the entire P3 succession is reduced to a single layer of clast-supported, white, angular, fine pumice lapilli containing abundant juvenile and accidental lithic fragments, making it difficult to distinguish the pumice fallout units A, C, E, and G. At locations near the vent, unit A is however clearly visible under the cumulative pumice fallout of units C+E+G (Fig. 4d), which allows to build an individual isopach map for the pumice fallout phase A (Fig. 6b). We note that the northwestern arms of our isopach maps are not well constrained due to a lack of outcrops (in our study as in previous ones) in a region extremely difficult to access due to the presence of dense tropical forest on steep hills.

Units B, D, and F are widespread on the southwest flank of Mt Pelée volcano and the low-concentration PDC deposits almost reached the sea there (Fig. 6c). The highconcentration PDC deposits are channelized in paleo-valleys and now form large plateaux in the Grande Savane, Habitation Depaz and Ajoupa Bouillon areas (see locations in Fig. 1a), an observation consistent with the results of [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF] and [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF]. However, contrary to [START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF], we found no evidence of highconcentration PDC deposits in the Bijou River, Grande River, and Fond Canonville areas (see locations in Fig. 1b).

Isopleth maps of air fall deposits

Fig. 7 shows the isopleth maps built from the measurements of the major axes of the five largest fragments found at the base and top of unit A, and at the base of unit C. The isopleth map of the base of unit A is well constrained thanks to the good preservation of the deposit (Fig. 7a). However, isopleth contours for the top of unit A and the base of unit C are constrained by only a few points from localities where the two units are separated by the presence of unit B and/or by clear variation in grain-size characteristics (Fig. 7b,c). Isopleth maps for units E and G could not be constructed due to the poor preservation of these deposits. However, in both cases, we were able to draw a single isopleth curve (i.e., the 15 mm-isopleth for unit E and 25 mm-isopleth for unit G) that is not reported in Fig. 7. The main direction of dispersion to the southwest (Fig. 7) is consistent with the one inferred from our isopach maps (Fig. 6). Isopleth contours of the top of unit A are clearly more extended in the crosswind direction than those of the base of units A and C.

Total grain-size distribution (Unit A)

We calculated the total grain-size distribution (TGSD) of unit A using the method of Kaminski and Jaupart (1998) (see section 3.3 for calculation details). The interbedded nature and important erosion of the subsequent units made the reconstruction of the TGSD for units B to G impossible. The TGSD of unit A is bimodal with a primary fine mode at 2φ and a secondary coarse mode at -2φ (Supplementary material Figure S1). The median diameter and sorting for the TGSD of unit A are -0.2φ and 2.3, respectively. The amounts of ash (< 2 )

and fine ash particles (< 63 µm) reach 59 wt.% and less than 1 wt.%, respectively. The latter value should be taken with caution because most of the fine ash particles settled at sea and cannot be taken into account in our grain-size analyses. From these results, we infer that the power law coefficient D that fully characterizes the TGSD at the beginning of the P3 eruption (i.e., unit A) is D = 3.3 ± 0.1 (Supplementary material Figure S1). The time evolution of the value of D after the phase A remains unknown, but this lack of information will not affect our calculations of the stable plume / collapsing fountain transition that occurred at the end of phase A (see section 6.3).

Eruptive dynamics

Erupted volumes

The estimates of volume of tephra fall from phase A using the three integration techniques introduced in section 3 give 0.282 km 3 with the exponential method, 0.316 km 3 with the power law, and 0.306 km 3 with the Weibull function (Fig. 8a). Integration of the exponential, power-law, and Weibull fits for the cumulative pumice fallout C+E+G yields volumes of 0.334, 0.317, and 0.355 km 3 , respectively (Fig. 8b). Because the latter estimates are based on three proximal isopach contours only they remain relatively poorly constrained (Fig. 6d). We thus calculated the volume of the cumulative pumice fallout A+C+E+G in order to achieve a better estimate of the total volume of tephra fall. Integrating the exponential, power-law, and Weibull fits yields 0.735, 0.692, and 0.712 km 3 , respectively (Fig. 8c). We thus retain a minimum volume of 0.30 ± 0.01 km 3 for unit A, and 0.41 ± 0.02 km 3 for the cumulative pumice fall units C+E+G, and 0.71 ± 0.02 km 3 for the total volume of tephra fall.

Based on fallout deposit and magma densities of 1,000 and 2,400 kg m -3 , respectively [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF], we infer the cumulative DRE volume of fall units to be 0.3 km 3 .

The volume of PDC deposits is calculated using the area covered by the dense and dilute PDC deposits. The deposits corresponding to the dilute PDC of phases B, D, and F cover 42, 20, and 36 km 2 , respectively (Fig. 6c), which yield bulk volumes of 0.025 km 3 for unit B, 0.010 km 3 for unit D, and 0.016 km 3 for unit G [START_REF] Calder | Mobility of pyroclastic flows and surges at the Soufriere Hills Volcano, Montserrat[END_REF]. The cumulative dense PDC deposits of the phases B, D, and F cover 7 km 2 in Grande Savane, 9.5 km 2 in Habitation Depaz, and 18 km 2 in Ajoupa Bouillon (see locations in Fig. 1a), with an average thickness of 15, 30, and 2 m, respectively [START_REF] Traineau | Contribution à l'étude géologique de la Montagne Pelée, Martinique[END_REF]. This yields a minimum volume of 0.67 ± 0.02 km 3 DRE for the dense PDC deposits, and gives a total volume of (dense + dilute)

PDC deposits of 0.72 ± 0.02 km 3 DRE.

The final estimate of the total volume of the P3 eruption (units A+B+C+D+E+F+G) is thus 1.02 ± 0.06 km 3 DRE, and the total mass of tephra emitted is estimated to be 2.4 ± 0.1 x 10 12 kg. The P3 eruption thus stands as a VEI 5 event (Newhall and Self, 1984) with a magnitude of 5.4 [START_REF] Pyle | Sizes of volcanic eruptions[END_REF].

Column heights and exit velocities (airfall units)

The estimates of maximum height using our isopleth maps (Fig. 7) with the model of [START_REF] Carey | The 1982 eruptions of El Chichon volcano, Mexico (2): Observations and numerical modelling of tephra-fall distribution[END_REF] give 28.3 ± 3.3 km for the base of unit A, 29.7 ± 1.9 km for the top of unit A, and 16.9 ± 0.4 km for the base of unit C. Following the approach of [START_REF] Bonadonna | Plume height, volume, and classification of explosive volcanic eruptions based on the Weibull function[END_REF], a Weibull fit gives a maximum height of 28.1 ± 1 km for the base of unit A, 30.0 ± 0.5 km for the top of unit A, and 17.2 ± 0.5 km for the base of unit C (Supplementary material Figure S2). The lack of information about the distribution of lithic sizes in unit E and G prevents us from providing a robust estimate for the maximum height. Based on a single isopleth curve in each case, we calculate maximum column heights of 12 ± 4 km for unit E and 13 ± 4 km for unit G using the model of [START_REF] Carey | The 1982 eruptions of El Chichon volcano, Mexico (2): Observations and numerical modelling of tephra-fall distribution[END_REF].

We also use data on the decrease of lithic sizes with distance from the vent in Supplementary material Figure S2 to estimate the minimum exit velocity of the volcanic plume at the vent. Extrapolating the Weibull fits down to A 1/2 = 0.01 km to find the maximum lithic size at the vent, we infer minimum exit velocities of 210 ± 10 m s -1 for the base of unit A, 220 ± 10 m s -1 for the top of unit A, and 220 ± 10 m s -1 for the base of unit C.

Mass eruption rates and duration

We use our new estimates of maximum column height to calculate the mass eruption rate (MER) feeding the plume during the P3 eruption. The model of [START_REF] Girault | Combined effects of total grain-size distribution and crosswind on the rise of explosive volcanic columns[END_REF] used with their complex wind profile, which is close to the average wind profiles in the Lesser Antilles, yields maximum MERs of 10 8 kg s -1 for the beginning of phase A, 1.5 x 10 8 kg s -1 for the end of phase A, 3 x 10 7 kg s -1 for phase C, 1.4 x 10 7 kg s -1 for phase E, and 1.7 x 10 7 kg s -1 for phase G. The empirical formula of [START_REF] Mastin | A multidisciplinary effort to assign realistic source parameters to models of volcanic ash-cloud transport and dispersion during eruptions[END_REF] built on observations of 28 Plinian eruptions yields maximum MERs of 1.4 x 10 8 kg s -1 for the beginning of phase A, 1.9 x 10 8 kg s -1 for the end of phase A, 1.8 x 10 7 kg s -1 for phase C, 4.2 x 10 6 kg s -1 for phase E, and 5.9

x 10 6 kg s -1 for phase G. Based on these two series of estimates, we retain peak MERs of 1.2 ± 0.2 x 10 8 kg s -1 for the beginning of phase A, 1.7 ± 0.2 x 10 8 kg s -1 for the end of phase A, 2.4 ± 0.6 x 10 7 kg s -1 for phase C, 9.1 ± 4.9 x 10 6 kg s -1 for phase E, and 1.2 ± 0.5 x 10 7 kg s -1 for phase G. Combined with masses of fallout deposits (section 5.1), these MER provide minimum durations of ~45 min for phase A, ~1h45 for phase C, ~3h for phase E, and ~2h45

for phase G.

The MER during the collapsing phases B, D, and F is more difficult to assess. The model of [START_REF] Bursik | The dynamics and thermodynamics of large ash flows[END_REF] yields a mass eruption rate of ~ 2.3 ± 0.8 x 10 8 kg s -1 for the three phases B, D, and F. We note that this value does not take into account topographic slopes but [START_REF] Doyle | A two-layer model for the evolution and propagation of dense and dilute regions of pyroclastic currents[END_REF] showed that the runout distance of such a flow mostly depends on the initial collapse height, which is imposed by the MER rather than by ground slopes.

Combined with masses of PDC deposits (section 5.1), this MER provides minimum durations of ~50 min for phase B, ~25 min for phase D, and ~50 min for phase F.

Discussion

Our revisit of the P3 deposits shows that the eruption started with the formation of a stable column that spread pyroclasts to the southwest of the volcano (phase A). This initial phase was immediately followed by a partial collapse of the column producing alternating tephra fallout (phases C, E, G) and pyroclastic density currents (phases B, D, E). We now compare our results to previous work on the P3 eruption, and on the younger P1 and P2 eruptions of Mt Pelée volcano. We then focus our discussion on the causes of partial column collapse during the P3 eruption by using a physical model of volcanic plumes.

Comparison with previous studies of P3 eruption

Our new stratigraphic data regarding the P3 succession largely differs from those of previous studies [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF][START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF][START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF]. The P31 phase identified by [START_REF] Westercamp | The past 5,000 years of volcanic activity at Mt. Pelée Martinique (F.W.I.): implications for assessment of volcanic hazards[END_REF] corresponds to our eruptive unit A, and their P33 phase most likely corresponds to our entire sequence from unit B to unit G. The distal products identified by [START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF] were attributed to the P3 eruption based on a single radiocarbon age determined from a charcoal sampled at the top of their stratigraphic section (see their figure 6). We revisited their outcrop locations 2 and 3 along a main road, and found that their stratigraphic section lies beneath the 13.5 ka cal BP Bellefontaine Plinian eruption [START_REF] Michaud-Dubuy | Impact of wind direction variability on hazard assessment in Martinique (Lesser Antilles): the example of the 13.5 ka cal BP Bellefontaine Plinian eruption of Mount Pelée volcano[END_REF]. To further reinforce our observation, we sampled a paleosol at the base of their stratigraphic section and obtained a radiocarbon age of 17,750 ± 100 yr BP, which indicates that the distal deposits studied by [START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF] are much older than the P3 eruption.

The total volume of the P3 eruption (units A+B+C+D+E+F+G) is calculated to be 1.02 ± 0.06 km 3 DRE, which is one order of magnitude larger than the 0.19 km 3 DRE previously estimated [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF]. We attribute this important discrepancy to the large volume of PDC deposits that were not taken into account in [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF], and to the improvement of the reconstruction techniques used here to calculate the total volume of a pumice fall deposit [START_REF] Bonadonna | Plume height, volume, and classification of explosive volcanic eruptions based on the Weibull function[END_REF]. The maximum column height is estimated to be ~ 30 km at the end of phase A, which is much higher than the previous estimates (> 6 km by [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF]< 12 km by Wright et al., 2016). Again we attribute this important difference to the better quality of our isopleth maps and to the improvement of the reconstruction techniques used to estimate the maximum height from the distribution of lithic fragments in the field.

6.2 Comparison with younger Plinian eruptions in Martinique (P1 and P2)

The three latest Plinian eruptions at Mt Pelée volcano (P1, P2 and P3) have similar depositional successions that can be interpreted to result from the partial collapse of an initially stable Plinian column [START_REF] Traineau | The recent pumice eruptions of Mt. Pelée volcano, Martinique. Part I: Depositional sequences, description of pumiceous deposits[END_REF][START_REF] Carazzo | The recent Plinian explosive activity of Mt. Pelée volcano (Lesser Antilles): The P1 AD 1300 eruption[END_REF][START_REF] Carazzo | Marginally stable recent plinian eruptions of Mt. Pelée volcano (Lesser Antilles): The P2 AD 280 eruption[END_REF][START_REF] Wright | Distal ash hurricane (pyroclastic density current) deposits from a ca. 2000 yr B.P. Plinian-style eruption of Mount Pelée, Martinique: Distribution, grain-size characteristics, and implications for future hazards[END_REF]. The total DRE volume estimated for P3 (~1 km 3 ) is larger than those of the P1 (~0.2

km 3 ) and P2 (~0.8 km 3 ) eruptions. The maximum column height during the phase of sustained Plinian column is also larger for P3 (28-30 km) than for the P1 (19-22 km) and P2 (22-26 km) eruptions. Consequently, the mass eruption rate is estimated to be larger for P3 (1.4 x 10 8 kg s -1 ) than for P1 (3.6 x 10 7 kg s -1 ) and P2 (1.1 x 10 8 kg s -1 ). The minimum eruption durations are 11h for P3, 7h for P2, and 5h for P1. The total grain-size distribution is however relatively similar for the three events, with power law exponent D of 3.3, 3.4-3.5, and 3.2-3.3 for P3, P2, and P1, respectively. Our estimates of exsolved gas contents for P3 (2-2.9 wt.% -see section 6.3 for calculations details) are larger than those of P1 (1.6-2.1 wt.%) and P2 (1.7-2.1 wt.%). The minimum exit velocities inferred from the distribution of lithic fragments for P3

(210-220 m s -1 ) are also larger than those of P1 (150-165 m s -1 ) and P2 (180-200 m s -1 ), a result consistent with our estimates of free gas contents. Table 2 summarizes the eruptive parameters retrieved for the last three Plinian eruptions at Mt Pelée volcano. P3 stands as a large Plinian eruption more powerful and voluminous (VEI 5, M 5.4) than the P1 (VEI 4, M 4.6) and P2 (VEI 4, M 5.2) eruptions. However, because these three eruptions have much in common, in particular similar pre-eruptive conditions [START_REF] Martel | Magma storage conditions and control of eruption regime in silicic volcanoes: experimental evidence from Mt Pelée[END_REF][START_REF] Martel | Diversity of eruptive styles inferred from the microlites of Mt. Pelée andesite (Martinique, Lesser Antilles)[END_REF], they can be used to test the performance of theoretical models in predicting the conditions for column collapse.

The stable plume / pyroclastic fountain transition during a sustained Plinian eruption

The P3 eruption underwent partial column collapse after an initial phase of stable Plinian plume. [START_REF] Wilson | Explosive volcanic eruptions-IV. The control of magma properties and conduit geometry on eruption column behavior[END_REF] showed that the mass eruption rate and the amount of free gas in the volcanic mixture at the vent both strongly control the transition between the stable Plinian plume and the collapsing fountain regimes. Our estimates of the MER show a progressive increase over time from ~1.2 x 10 8 kg s -1 (base of unit A) to ~2.5 x 10 8 kg s -1 (unit B+C) (Fig. 9), an evolution consistent with the increase in maximum lithic sizes throughout unit A (Fig. 3c). Other powerful eruptions underwent a similar evolution leading to column collapse, such as the 79 CE Vesuvius [START_REF] Shea | Column collapse and generation of pyroclastic density currents during the A.D. 79 eruption of Vesuvius: The role of pyroclast density[END_REF], and the 186 CE Taupo [START_REF] Walker | The Taupo pumice: product of the most powerful known (ultraplinian) eruption?[END_REF] eruptions.

The time evolution of total gas content feeding the column at the vent is more difficult to assess. Petro-geochemical measurements provide quantitative estimates of pre-eruptive magma storage conditions, including temperature (875-900°C), pressure (~200 ± 50 MPa), and water content (~5.8 ± 0.5 wt.%) [START_REF] Martel | Magma storage conditions and control of eruption regime in silicic volcanoes: experimental evidence from Mt Pelée[END_REF][START_REF] Martel | Diversity of eruptive styles inferred from the microlites of Mt. Pelée andesite (Martinique, Lesser Antilles)[END_REF]. Here, we use the magmatic water content measured in glass inclusions available in the literature as a total volatile content in the melt (n0). Correcting this value from the presence of crystals and lithic fragments (Table 3), we find that the initial gas content (x0) in the magma decreased from 4.1 to 2.9 wt.% during the eruption (Table 3). As in [START_REF] Kaminski | The size distribution of pyroclasts and the fragmentation sequence in explosive volcanic eruptions[END_REF] and [START_REF] Carazzo | The recent Plinian explosive activity of Mt. Pelée volcano (Lesser Antilles): The P1 AD 1300 eruption[END_REF]2019), we calculate the mass fraction of exsolved gas in the mixture at fragmentation level (xf) for a threshold vesicularity of 70 %, which assumes closed-system conditions consistent with degassing models built on U-series measurements in the P3 eruption products [START_REF] Villemant | U-series disequilibrium in arc magmas induced by water-magma interaction[END_REF]. We find that xf decreases from 2.9 to 2.1 wt.% during the eruption (Fig. 9). To strengthen these estimates, we calculate the theoretical exit velocities at the vent assuming that the volcanic mixture decompresses freely into the atmosphere [START_REF] Woods | The decompression of volcanic jets in a crater during explosive volcanic eruptions[END_REF]. For this, we infer the effective amount of free gas in the volcanic mixture at the base of the column that is modulated by gas entrapment by pumices as a function of their size distribution [START_REF] Kaminski | The size distribution of pyroclasts and the fragmentation sequence in explosive volcanic eruptions[END_REF]. We use the power law exponent D = 3.3 (for unit A) estimated in section 4.6, and a typical open porosity of 60-70 % [START_REF] Michaud-Dubuy | A revisit of the role of gas entrapment on the stability conditions of explosive volcanic columns[END_REF] to calculate an amount of free gas of 2.4-2.7 wt.% for phase A. These estimates provide exit velocities after decompression in the range 215-230 m s -1 (Table 3) that are consistent with those estimated from the distribution of the lithic fragments collected at the base and top of unit A (see section 5.2). This relatively good agreement at least for phase A reinforces the confidence that our estimates of xf provide reasonable values of free gas content during the P3 eruption.

Fig. 10 compares the estimated values of MER and exsolved gas content in the column at collapse with the theoretical 1D predictions for tropical conditions [START_REF] Michaud-Dubuy | A revisit of the role of gas entrapment on the stability conditions of explosive volcanic columns[END_REF]. The conditions at the beginning of the P3 eruption formed a stable plume as predicted by the model. During phase A, the combined effect of a slightly increasing MER and a decreasing gas content led the eruption to conditions close to the plume/fountain transition.

The eruption reached a peak in MER during the concomitant phases B and C, which most likely induced the partial column collapse. During the partial column collapse stage of the eruption (units B to G), the MER did not change significantly but the gas content slowly decreased until the end of the eruption. The fairly good agreement between our field data and the theoretical model can be taken as an indirect confirmation of the proposed evolution of the total gas content feeding the column, even if a direct confirmation is not possible.

Furthermore, our results suggest that the stable column underwent partial collapse soon after the beginning of the eruption (i.e., within less than a hour), an evolution that was also inferred from the analysis of the P1 and P2 Plinian eruption deposits [START_REF] Carazzo | The recent Plinian explosive activity of Mt. Pelée volcano (Lesser Antilles): The P1 AD 1300 eruption[END_REF]2019). In these three eruptions, the transition occurred at conditions well predicted by our theoretical model of volcanic plumes (Fig. 10).

Comparing these results with other historical eruptions requires gathering wellconstrained values of exsolved gas contents, mass eruption rates and power-law exponent D of the TGSD [START_REF] Michaud-Dubuy | A revisit of the role of gas entrapment on the stability conditions of explosive volcanic columns[END_REF]. There are however only a few examples of such well-documented events, and we choose here to compare our results to the 186 CE Taupo (VEI 7) and 79 CE Vesuvius (VEI 5) eruptions. Fig. 10 shows that the model successfully predicts the transition for the Taupo eruption but fails to explain the transition for the Vesuvius eruption. Furthermore, one can note that the collapsing phase of the 79 CE Vesuvius eruption is characterized by the same amount of gas and MER at the source as the stable phase (end of phase A) of the P3 eruption. The only difference between the two cases is the total grain-size distribution. Indeed, as discussed in [START_REF] Michaud-Dubuy | A revisit of the role of gas entrapment on the stability conditions of explosive volcanic columns[END_REF], the 79 CE Vesuvius eruption is characterized by a specific total grain-size distribution (D = 3.0) where pyroclasts are in average not large enough to be lost by sedimentation but not small enough to be in thermal equilibrium with the gas. The hypothesis of thermal equilibrium between the gas and pyroclasts that is used in our 1D model of volcanic plumes, valid for the fine grainsize distribution of the beginning of the P3 eruption (D = 3.3), may therefore not hold anymore for this eruption and may explain the peculiar collapse conditions.

Conclusion

We have presented a new comprehensive field study of the P3 eruption, and a detailed reconstruction of the mechanisms controlling the eruptive dynamics. New radiocarbon measurements, averaged with those previously available, provide a refined age of 79 ± 21 cal CE for this event. The eruption started with the formation of a 28 to 30 km-high stable column (phase A), which partially collapsed due to the combined effect of increasing MER and decreasing gas content (phase B). In the partial collapse regime, the eruptive mixture formed a 12 to 17 km-high marginally stable column (phases C, E, and G) punctuated with the production of PDC fed by the partially collapsing column (phases B, D, and F). Our calculations show that P3 was a large Plinian eruption (VEI 5, M = 5.4) evolving close to the plume/fountain transition. The total volume of tephra reached 1 km 3 DRE, and the mass eruption rate was of the order of 10 8 kg s -1 during a period of at least 11h.

The P3 eruption is more powerful than the last two Plinian eruptions in Martinique but the three eruptions underwent similar evolution towards a marginally stable volcanic column.

This recurrent phenomenon provides a great opportunity to look carefully at the parameters affecting column stability, to constrain theoretical models of volcanic plumes, and thus improve volcanic disaster forecasting. Petrological and geochemical measurements on the P3 eruptive products may help to further investigate the complexity of magma degassing, crystallization and fragmentation in the volcanic conduit [START_REF] Gurioli | Complex changes in eruption dynamics during the 79 AD eruption of Vesuvius[END_REF][START_REF] Martel | Diversity of eruptive styles inferred from the microlites of Mt. Pelée andesite (Martinique, Lesser Antilles)[END_REF][START_REF] Shea | Transitions between fall phases and pyroclastic density currents during the AD 79 eruption at Vesuvius: Building a transient conduit model from the textural and volatile record[END_REF]2014), and thus refine the estimated values of exsolved gas content at the vent. The global consistency between our theoretical predictions and field observations of column collapse for a number of Plinian eruptions confirms that current theoretical 1D models of volcanic plumes predict correctly the conditions of collapse when the total grain-size distribution is dominated by fine fragments (i.e., obeys a power law distribution with an exponent strictly larger than 3). Our results can thus be used to assess the dominant hazard during a Plinian scale event, which may pass from pumice fall to PDC as eruptive conditions vary.

Mt Pelée volcano is currently quiescent but the reconstruction of its eruptive history over the past 5,000 years shows that a Plinian eruption is a major potential scenario in the future. Such an event with the magnitude of the P3 eruption would disrupt the lives of more than 376,000 people living in Martinique and possibly impact other volcanic islands depending on the wind speed and direction. 3: Gas contents and deduced exit velocities. n0 is the total volatile content of the melt [START_REF] Martel | Magma storage conditions and control of eruption regime in silicic volcanoes: experimental evidence from Mt Pelée[END_REF], αc is the percentage of crystals in the melt plus lithics in the flow, x0 is the mass fraction of gas in the magma assuming complete degassing, xf is the mass fraction of exsolved gas in the gas+pyroclasts mixture at fragmentation for a threshold vesicularity of 70%, Ufree is the supersonic velocity after decompression calculated using x0, D = 3.

Sample

  3 and an open porosity of 60-70%[START_REF] Michaud-Dubuy | A revisit of the role of gas entrapment on the stability conditions of explosive volcanic columns[END_REF], and Umin is the eruptive velocity deduced from the distribution of the lithic fragments (section 5.2).

Figure captions Fig. 1 :

 captions1 Figure captions

Fig. 2 :

 2 Fig. 2: Overview of our field area in Martinique (inset). White circles and numbers refer to

Fig. 3 :

 3 Fig. 3: a Composite stratigraphic section showing typical unit thickness and grain-size

Fig. 4 :

 4 Fig. 4: Representative photographs of outcrops of the P3 deposits in Martinique at sites a 57,

Fig. 5 :

 5 Fig. 5: Stratigraphic logs of representative sections of deposits of the P3 eruption. See Fig. 2

Fig. 6 :

 6 Fig. 6: Isopach maps (in centimeters) for a the cumulative pumice fallout (units A+C+E+G),

Fig. 7 :

 7 Fig. 7: Isopleth maps (in millimeters) for the lithic fragments sampled a at the base of unit A,

Fig. 8 :

 8 Fig. 8: Deposit thinning profiles generated from the isopach maps for a unit A, b the

Fig. 9 :

 9 Fig. 9: Summary of the time evolution of the P3 eruptive parameters. a Cumulative erupted mass (in kg). b Maximum column height (in km). c Mass eruption rate (in kg s -1 ). d Total

Fig. 10 :

 10 Fig. 10: Transition diagram depicting the P3 eruptive events and depositional units

Table S1 )

 S1 . Combining these seventeen values using the R_combine function of OxCal[START_REF] Bronk Ramsey | Bayesian analysis of radiocarbon dates[END_REF] provides an age of 1,926 ± 11 yr BP for the P3 eruption. We note that the χ 2 test fails here most likely due to the large number of individual measurements. However, a reasonable correction on the error bar of each dating by a factor of 2 is enough to successfully pass the χ 2 test, reinforcing the confidence that all these otherwise stratigraphicallyconstrained samples belong to the same eruption. Our new refined radiocarbon age for the P3 eruption stands in the lower error bars of the 2,010 ± 140 yr BP proposed byTraineau et al.

(1989)

. Correcting our new estimate with the IntCal13 calibration curve

[START_REF] Reimer | Selection and treatment of data for radiocarbon calibration: an update to the international calibration (IntCal) criteria[END_REF]

available in OxCal gives a mean calendar age of 79 ± 21 cal CE (i.e., 31-37 cal CE at 1.7% probability and 51-125 cal CE at 93.7% probability).

Table 1 :

 1 Sampling of the P3 deposits for grain-size analysis.

		Site	Unit	Subunit	Altitude	Distance	Thickness
					(m)	from the	(cm)
						vent (km)
	1	163	A	(0-40 cm)	269	3.7	160
	2	163	A	(40-60 cm)	269	3.7	160
	3	163	A	(60-100 cm)	269	3.7	160
	4	163	A	(100-140 cm)	269	3.7	160
	5	163	A	(140-160 cm)	269	3.7	160
	6	163	B	Bulk	269	3.7	18
	7	163	C	Bulk	269	3.7	20
	8	163	D	Bulk	269	3.7	15
	9	163	E	Bulk	269	3.7	13
	10	163	F	Bulk	269	3.7	6
	11	163	G	Bulk	269	3.7	37
	12	88	A-G	Bulk	466	4.3	45
	13	66b	A-G	Bulk	371	4.9	65
	14	142	A-G	Bulk	234	5.8	60
	15	194	A-G	Bulk	280	5.8	55
	16	114	A-G	Bulk	195	6.3	105
	17	137	A-G	Bulk	19	6.5	100
	18	191	A-G	Bulk	35	6.5	46
	19	144	A-G	Bulk	47	6.6	80
	20	145	A-G	Bulk	540	11.9	25
	853
	854
	855
	856
	857
	858
	859
	860
	861
	862
	863

Table 2 :

 2 Summary of the estimated eruptive parameters for the P3 eruption, and comparison with P1 and P2[START_REF] Carazzo | The recent Plinian explosive activity of Mt. Pelée volcano (Lesser Antilles): The P1 AD 1300 eruption[END_REF] 2019).

	Phase	n0	αc	x0	xf	Ufree	Umin
		(wt.%)		(wt.%)	(wt.%)	(m s -1 )	(m s -1 )
	Early A	5.8	29	4.1	2.9	230	210
	Late A	5.8	38	3.6	2.5	215	220
	B-C	5.8	42	3.4	2.3	-	220
	D-E	5.8	45	3.2	2.2	-	-
	F-G	5.8	49	2.9	2.1	-	-

Table

Acknowledgements

We warmly thank the staff of the Mt Pelée volcanological observatory (OVSM) for field and administrative assistance, J.-P. Dumoulin, L. Beck, E. Delque-Kolic and C. Moreau (LMC14, CNRS UMS2572) who performed the 14 C dating, G. Delaviel-Anger and T. Crouzal for their help in the field, and A. Jegouzo for enthusiastic discussions about the P3 eruption. This work was partially funded by the Institut National des Sciences de l'Univers -Centre National de la Recherche Scientifique progamme CT3-ALEA, INSU-CNRS Artemis 2016 and 2017 for 14 C dating, and CASAVA (ANR contract ANR-09-ANR-RISK-002) and RAVEX (ANR contract ANR-16-CE03-0002). This study contributes to the IdEx project "Université de Paris" (ANR-18-IDEX-0001).