M Crozatier
email: mathilde.crozatier@ensam.eu

S Terekhina

F Dau

L Guillaumat

MECHANICAL CHARACTERIZATION OF COMPOSITE MATERIALS FROM CURVED STRUCTURES

Keywords: curved structures, mechanical characterization, inverse approach, filament winding

Mechanical behavior of composite laminates depends strongly on the manufacturing process. It is necessary to use representative samples of the material, and therefore of the process. In the case of filament winding, specimens are necessarily cylindrical or barrel extracted. In our case, a full-scale fiberglass composite structure is used for radial compression and axial cuts experimental performances. This work aims to estimate the elastic properties of composite laminate from a curved structure taking into account the manufacturing process. An inverse approach using an optimization process is adopted. By coupling a radial compression experiment with a 3D model obtained by Finite Element Method (FEM), a mechanical characterization becomes possible. Furthermore, these identifications combined with experiments of axial cuts enable the estimation of residual manufacturing stresses.

Introduction

Among many manufacturing processes for composite materials, filament winding is a highperformance method for the development of laminate circular cylinders. It is used for the manufacturing of large capacity tanks for agriculture or chemical industry, foodstuff or liquid storage. The transportation industry also contributes to this development by manufacturing aircraft fuselage or rocket, missile envelope, tank truck, etc.

With flat plates, elastic properties are generally determined by standardized experiments. When the sample is curved, their identification is more complex. Nowadays, there is a lack of representative samples capable both of predicting the mechanical behavior of a composite material from curved structures and taking into account the manufacturing process. Regarding filament winding, specimens extracted from the cylinder present two curved faces and two straight ones (respectively along the curvature and the generatrix of the cylinder). Moreover, it is well known that such a process induces residual manufacturing stresses [START_REF] Hahn | The stress development during filament winding of thick cylinders[END_REF][START_REF] Lazuardi | Une approche du rôle des contraintes internes liées à l'élaboration sur le comportement des composites stratifiés[END_REF] which can be released during the cutting of the coupons. Some authors [START_REF] Ballère | Tolérance aux dommages par impacts de structures courbes composites -Effet d'échelles[END_REF][START_REF] Casari | Characterization of residual stresses in wound composite tubes[END_REF] have found resulting strains after cutting a structure manufactured by filament winding. The cut sections exhibit a smaller radius of curvature than that of the cylinder before cutting and a significant warping of the assembly. The specimens extracted in this way are therefore not exactly representative of the initial material.

The work presented in this article aims at raising and solving the issues associated with the mechanical characterization of composite materials manufactured by filament winding process. The objectives are dual:

 Identification of the elastic properties;  Estimation of the residual manufacturing stresses.

For the first step, given the curved shape of the structure, material properties are estimated with an inverse approach using an optimization process. For the second one, experiments of axial cuts are led on a real scale composite ring. They reveal the presence of compressive stresses, as the curvature radius decreases after the first cutting.

When a direct method is not available to characterize a material, another way must be found. Pierron et al. [START_REF] Pierron | Identification of the through-thickness properties of thick laminated tubes using the virtual fields method[END_REF][START_REF] Moulart | Identification of the through-thickness rigidities of a thick laminated composite tube[END_REF] identify the orthotropic rigidities with a virtual fields method, on thick glass/epoxy tubes. Calme et al. [START_REF] Calme | 3D braided composite rings under lateral compression[END_REF] estimate the properties by micromechanical analysis. Nemat-Alla [START_REF] Nemat-Alla | Reproducing hoop stress-stain behavior for tubular material using lateral compression test[END_REF] evaluates material properties in the hoop direction with an optimization algorithm, and identifies the stress-strain curve by inverse method, via radial compression test on brass tubes. The same kind of approach is used in the present study.

Mechanical characterization by inverse approach

To characterize the wound composite, experiments of radial compression are adopted. Firstly, the structure and the experiment are presented. Next, the numerical model and the optimization process are detailed.

Curved structure and experiment

The glass/vinylester ring is manufactured by filament winding. A glass mat layer of 2.5 mm thick, positioned inside, is the first layer of the ring. Next, a stacking sequence recovers the mat. It is made of forty-two layers and contains twice more circumferential layers than axial ones. Every layer has a thickness of approximately 0.43 mm. The dimensions of the ring are summarized in Table 1, where d i is the internal diameter, l the length and h the thickness. Figure 1 shows the experimental sample. The experiment consists in a radial compression of the ring, applied with compression plates diametrically opposed (Fig. 2). The ring is clamped on the lower part. The upper plate carries out the compression through the testing machine, a Zwick 10kN. Measurement instrumentation is used to enrich the experiment. Four rosettes are glued to the ring to follow local strains during the experiment. Rosettes 1 and 3 are glued to the inside surface of the ring, whereas rosettes 2 and 4 are located outside. In order to obtain more experimental information, two configurations in the rosettes positions relative to the loading direction are adopted (Fig. 3). Furthermore, a speckle is performed on a transverse ring edge to follow the thickness strain by an image correlation method [START_REF] Hild | CORRELI Q4 : A software for[END_REF]. The ring is also instrumented by two comparators which are placed at 90° relative to the loading direction (blue rectangle), to measure the horizontal displacement of the ring.

a) b)

Figure 3. Schematic drawings of measurement instrumentation.

Inverse approach

An inverse problem uses the results to get the causes. In our case, the results come from experiment and the causes are material properties. To build the inverse approach, not only a numerical model is necessary to test various causes but also an optimization process to select the best ones and to converge on a solution.

Numerical model

Numerical simulations by Finite Element Method (FEM) are carried out using Abaqus CAE. The sample is modeled with shell elements (S4R). In order to reproduce the experiment, the loading is applied on the upper part of the ring via a surface pressure load, and the line diametrically opposed is clamped except the axial displacement which is not restrained. Figure 4 illustrates the boundaries conditions. After a convergence study, the structure is meshed with a mesh size of 10 mm. There are thus thirty elements in the ring length, and four hundred seventy eight along the circumference. The stacking sequence is reproduced by Section Shell Composite tool.

Particle Swarm Optimization

The aim of an optimization is to obtain a parameter set which minimizes an objective function under some constraints. Particle Swarm Optimization (PSO) is adopted [START_REF] Kennedy | Particle swarm optimization[END_REF]. It includes the initialization, the particles movement and the process stop criterion.

Firstly, PSO initializes the optimization domain with a defined swarmsize. The swarm includes all the particles. Each is associated to a parameter set.

Next, the particles move to a definite velocity. This movement is governed by Eq. 1:

v i = ω v i + 𝝋 p r p (p i -x i ) + 𝝋 g r g (g -x i ). (1)
where:

v i velocity of the particle i; x i position of the particle i; ω particle velocity scaling factor; p i best known position of the particle i; g best swarm position;

𝝋 p and 𝝋 g scaling factors;

r p and r g random numbers between 0 and 1.

The scaling factors ω, 𝝋 p and 𝝋 g are constants to define. After a sensitivity study of this parameters, the triplet (ω; 𝝋 p ; 𝝋 g ) = (0.4; 0.6; 0.6) is retained. Indeed, a 20% gain is visible compared to the default values (0.5).

Results and discussions

Elastic properties

Above all, in order to determine the elastic properties, the experiment must be carried out on the elastic material domain. The loading-displacement curve obtained from a compression test is linear (Fig. 5). Furthermore, the rosettes strains return to zero at the end of the unloading. These phenomena prove that the work is led on the elastic domain. The objective function is a quadratic one, as defined in Eq. 2:

f = Σ (1 -u i n / u i e ) ² + Σ (1 -ɛ i n / ɛ i e ) ². i i (2)
where: The aim is to minimize this function. The quantities are standardized by the experimental quantities to permit a comparison. The objective function includes a sum on ten terms, four on displacement and six on strain.

u i n numerical displacement; u i e experimental displacement;
A typical parameter set contains eight parameters (six characterizing a unidirectional ply of the stacking sequence and only two for the mat layer, which is supposed to be isotropic):

 E 1 and E 2 : Young modulus;  ν 12 : Poisson coefficient;  G 12 , G 13 and G 23 : shear modulus;  E mat and ν mat .

Orientation 1 corresponds to the circumferential direction. Direction 2 is the axial one, and direction 3 is radial. During the optimization process, values of each parameter are taken in a physically acceptable interval to restrict the research domain.

The optimization process enables to get material properties by an inverse approach. Indeed, experiment is not enough. The digital model serves as a tool for the optimization. Many parameter sets are tested through numerical simulation. The optimization method chooses the best sets and by successive iterations, enables to reach a solution set. Table 2 presents a solution parameter set. The circumferential modulus of the composite is governed by Eq. 3:

E c = h s /h (2/3 E 1 +1/3 E 2 ) + h m /h E mat . (3)
and is equal to 28187.2 MPa. h s is the thickness of the stacking sequence and h m is the mat thickness.

Residual manufacturing stresses

To get residual manufacturing stresses, experiments of axial cuts are led on the ring. Indeed, during this experiment, the rosettes give residual manufacturing strains. In the previous paragraph, a set of material elastic properties have been obtained. By using Hooke's law, the evaluation of stresses becomes possible.

The experiment consists in progressive axial cuts of the ring. Indeed, during the first cut, the ring closes due to the pressure of internal compressive stresses. That is why it is decided to cut the ring step by step (each 2 mm), by extracting small sections until the ring does fold on itself anymore. Five cuts are needed. The experiment shows finally that 68.4 mm of material must be removed from the ring, in order to fully remove internal stresses. The end state of the ring is exposed on Figure 6. The final values given by the gauges glued in the circumferential direction are summarized in Table 3.

Only circumferential measurements are given since they are the most significant. It is consistent that the gauges glued in the axial directions measure low strains. The gauge r1_0 and r3_0 values are respectively 15 and 27 µdef in the final state. These measurements enable the estimation of residual manufacturing stresses. By considering a relaxation of 250 µdef and a circumferential modulus around 28 GPa (E c ), Hooke's law (σ = E ɛ) gives a circumferential compression stress of 7 MPa.

Conclusions

Mechanical characterization of composite laminates is essential to complete simulation in order to dimension real structures. Including the filament winding process in the elastic properties identification requires the use of curved samples during experiments. During the manufacturing process, internal stresses appear. They are due to the tension applied to the fibers during the winding. Therefore, it is necessary to involve the whole tubular structure, which is the case in this work.

An experimental protocol of radial compression is set up to realize measurements. They serve as a benchmark to carry out the optimization process using a digital model. The inverse approach, based on PSO, enables to obtain elastic properties of the unidirectional ply and the mat layer. These properties are determined via an experiment performed on a curved structure presenting residual manufacturing stresses. The characterization is thus done on the final structure, with the same stresses state that in real operating conditions.

7 Figure 1 .

 71 Figure 1. Composite ring: experimental sample.

Figure 2 .

 2 Figure 2. Radial compression set-up.

Figure 4 .

 4 Figure 4. Numerical model: boundaries conditions.

Figure 5 .

 5 Figure 5. Load-displacement curve from a radial compression test.

Figure 6 .

 6 Figure 6. Experimental sample after axial cuts: end state.

Figure 7

 7 Figure7presents the rosettes strains versus time. For example, the curve r4_90 gives the circumferential strain measured by the circumferential gauge in the rosette 4. On this curve, each level, marked by a horizontal black line, corresponds to an axial cut.

Figure 7 .

 7 Figure 7. Rosettes strains versus time.

Table 1 .

 1 Experimental sample dimensions.

  ECCM17 -17 th European Conference on Composite Materials Munich, Germany, 26-30 th June 2016 6

M. Crozatier, S. Terekhina, F. Dau and L. Guillaumat

Table 2 .

 2 A solution set at the end of the optimization process.

	E 1	E 2	ν 12	G 12	G 13	G 23	E mat	ν mat
	(MPa)	(MPa)		(MPa)	(MPa)	(MPa)	(MPa)
	40690.5 8310.7	0.34	2507.8	2280.8	2450.7 16011.9	0.34

Table 3 .

 3 Circumferential strains at the end state.

	Gauge number	r1_90	r2_90	r3_90	r4_90
	ɛ (µdef)	-170.16	130.64	-251.76	207.06


Gabriel Reygondeau

Cécile Guieu

Fabio Benedetti

Jean-Olivier Irisson

Sakina-Dorothée Ayata

Stéphane Gasparini

Philippe Koubbi

Biogeochemical regions of the Mediterranean Sea: an objective multidimensional and multivariate environmental approach

Keywords: biogeography, Longhurst approach, 3D partition, ocean, vertical divisions, environmental conditions, semi-enclosed sea

When dividing the ocean, the aim is generally to summarise a complex system into a representative number of units, each representing a specific environment, a biological community or a socio-economical specificity. Recently, several geographical partitions of the global ocean have been proposed using statistical approaches applied to remote sensing or observations gathered during oceanographic cruises. Such geographical frameworks defined at a macroscale appear hardly applicable to characterise the biogeochemical features of semi-enclosed seas that are driven by smaller-scale chemical and physical processes. Following the Longhurst's biogeochemical partitioning of the pelagic realm, this study investigates the environmental divisions of the Mediterranean Sea using a large set of environmental parameters. These parameters were informed in the horizontal and the vertical dimensions to provide a 3D spatial framework for environmental management (12 regions found for the epipelagic, 12 for the mesopelagic, 13 for the bathypelagic and 26 for the seafloor). We show that: (1) the contribution of the longitudinal environmental gradient to the biogeochemical partitions decreases with depth; (2) the partition of the surface layer cannot be extrapolated to other vertical layers as the partition is driven by a different set of environmental variables. This new partitioning of the Mediterranean Sea has strong implications for conservation as it highlights that management must account for the differences in zoning with depth at a regional scale.

Introduction

In recent decades, several divisions of the global ocean have been proposed. Each division aims at summarising environmental and/or biological global complexity into comprehensive atlases: the Large Marine Ecosystems (LME, [START_REF] Sherman | The Large Marine Ecosystem Approach for Assessment and Management of Ocean Coastal Waters[END_REF] , the Marine Ecoregions Of the World (MEOW, [START_REF] Spalding | Marine Ecoregions of the World: A Bioregionalization of Coastal and Shelf Areas[END_REF] or the BioGeoChemical Provinces (BGCP, [START_REF] Longhurst | Ecological geography of the Sea[END_REF]. Yet, such macro-ecological partitions are hardly applicable for regional seas since they do not intend to capture the full biogeochemical and physical complexity inherent to such scale [START_REF] Reygondeau | Dynamic biogeochemical provinces in the global Ocean[END_REF]. However, marine ecosystem management policies are developed and implemented at Oceanic basin or semi-enclosed sea scales (e.g., OSPAR, CCAMLR, HELCOM, GFCM, etc.), thereby requiring regionally specific ecosystem information and spatial delineation. In order to provide optimal conservation management, appropriate downscaling approaches must be performed.

The Mediterranean Sea (MS) is a semi-enclosed regional sea surrounded by heavily populated areas of 23 different countries, and where the number of endemic species is considered one of the highest in the world ocean [START_REF] Cuttelod | The Mediterranean: a biodiversity hotspot under threat. Wildlife in a Changing World-An Analysis of the[END_REF].

Historically, the MS has been divided into 8 zones by the International Hydrographic Organisation: Adriatic Sea, Aegean Sea, Alboran Sea, Levantine Sea, Ionian Sea, Tyrrhenian Sea, Algerian-Provencal basin and Tunisian-Syrian Gulf (see supplementary Fig. 1). However, these divisions relied on the basin's topography and coastline morphology as well as sea governance delineation (e.g. Exclusive Economic Zone). Nevertheless, these partitions have been widely used for the European Marine Strategy, for fishing quotas quantification, and for other economic and political management strategies.

Recent ecological studies promoting ecosystems-based management have stressed the need for a more objective division based on environmental/ ecological parameters, in order to provide an accurate representation of the ecological complexity. So far, only coarse partitions of the MS have been proposed in macro-ecological studies: 1 biogeochemical province according to Longhurst (2006) and 6 MEOWs mostly relying on the EEZ (i.e. Exclusive Economic Zone) definition according to [START_REF] Spalding | Marine Ecoregions of the World: A Bioregionalization of Coastal and Shelf Areas[END_REF]. More recently, some studies have attempted to partition the MS either by using classical abiotic parameters (temperature, salinity or chlorophyll-a; [START_REF] Gabrié | Statut des Aires Marines Protégées en mer Méditerranée[END_REF], hydrodynamics [START_REF] Rossi | Hydrodynamic provinces and Oceanic connectivity from a transport network help designing marine reserves[END_REF][START_REF] Berline | A Connectivity-Based Eco-Regionalization Method of the Mediterranean Sea[END_REF], satellite-derived estimates of chlorophyll-a seasonality (D'Ortenzio and D'Alcala, 2009), or meso-scale environmental parameters [START_REF] Nieblas | Defining Mediterranean and Black Sea biogeochemical subprovinces and synthetic Ocean indicators using mesoscale Oceanographic features[END_REF]. Such approaches rely solely on surface and a few selected parameters, therefore failing to fully capture the environmental complexity of the MS.

In this study, we aim to identify all the various environmental / pelagic habitat conditions that could be encountered at the scale of the MS. We investigate whether the considerations of a larger number of environmental parameters and the vertical dimension would better capture the full hydrodynamic and biogeochemical complexity of the basin. Following the macroecological approach promoted by Longhurst, we provide a new regional delineation here named biogeochemical regions (BGCR) based on annual mean biogeochemical and hydrodynamic conditions. First, the depth of each vertical boundary of the water column (epipelagic, mesopelagic and bathypelagic) and seafloor is numerically quantified. Second, based on a comprehensive annual environmental climatology (16 physical, chemical and biophysical variables), the biogeochemical regions within each pelagic layer and seafloor are characterised by using several multivariate analyses (validated by independent measures for the shallow waters). For each vertical layer, the strength of the boundaries between each BGCR is quantified and the contribution of each environmental parameter to the partitioning is provided. Finally, after a validation process involving recent independent in situ observations, the first 3D biogeochemical partition of the MS is proposed.

Materials and Methods

Environmental data

To identify the different types of environmental conditions and hence the marine habitats that could be encountered in the MS, the annual climatologies of 16 environmental parameters were gathered. The set of environmental parameters used for this study (Table 1.), was established according to the literature on macroecological partitioning [START_REF] Longhurst | Ecological geography of the Sea[END_REF][START_REF] Sherman | The Large Marine Ecosystem Approach for Assessment and Management of Ocean Coastal Waters[END_REF]Spalding et al., 2008;[START_REF] Reygondeau | Dynamic biogeochemical provinces in the global Ocean[END_REF]. It has been gathered to depict and/or characterise specific oceanographic features according to geography (shelf break, river runoff, …), hydrodynamics (gyral system, frontal structure, coastal upwelling) or Low Nutrient Low Chlorophyll (LNLC) areas. All the information about the dataset are summarised in Table 1.

Most of the environmental parameters were collected from a single source (MEDAR/MEDATLAS datasets; MEDAR Group, 2002): temperature, salinity, nitrates, nitrites, orthophosphates, silicates, pH, chlorophyll-a concentration, and dissolved oxygen concentration (see Table 1.). These datasets were obtained from oceanographic campaigns and remote sensing observations. Each environmental variable is spatially resolved over the whole basin at a 0.2° resolution from 9.3° W to 36.5° E of longitude, and from 30° N to 46° N of latitude, and vertically informed for 26 depths layer (see MEDAR Group, 2002) on a non-linear scale between 0 and the seafloor (maximum depth of 5,267m). Each annual climatology used in the present study was calculated using the same methodologies (MEDAR Group, 2002).

Additional environmental parameters were also added to the dataset from the literature [START_REF] D'ortenzio | Seasonal variability of the mixed layer depth in the Mediterranean Sea as derived from in situ profiles[END_REF][START_REF] Henson | Global patterns in efficiency of particulate organic carbon export and transfer to the deep Ocean[END_REF][START_REF] Morel | Examining the consistency of products derived from various Ocean color sensors in open Ocean (Case 1) waters in the perspective of a multi-sensor approach[END_REF][START_REF] Reygondeau | Water column stability and Calanus finmarchicus[END_REF]. This addition of environmental parameters aimed at describing the vertical physical composition of the water column using: Mixed Layer Depth, thermocline, euphotic depth or transport of organic matter. Each environmental parameter represented an annual average and was spatially resolved on the same horizontal and vertical resolution as the MEDAR/MEDATLAS parameters (see Table 1).

In addition, raw values were standardized to reduce the effects of environmental parameters amplitude of variation (i.e. variance) on the clustering methodologies [START_REF] Legendre | Numerical Ecology[END_REF]. Nonetheless, it is important to keep in mind that there are under-sampled areas in the MS, especially in the southern parts of the basin. Therefore, the results could be biased by the low quality of the observation in these regions. Also, since the temporal fluctuations of each environmental parameter gathered was not available, no time series analysis was performed.

Statistical Methodologies

We aimed at identifying biogeochemical regions in the MS (sensu [START_REF] Longhurst | Ecological geography of the Sea[END_REF], relying on an exhaustive set of environmental parameters resolved in both horizontal and vertical dimensions, using a procedure based on the methodology developed by [START_REF] Oliver | Bioinformatic approaches for objective detection of water masses on continental shelves[END_REF]. Each step of the methodology is summarised in supplementary Fig. 2.

Vertical partition of the MS.

The vertical dimension of the basin was subdivided into 4 layers, 3 representing the pelagic environment (epipelagic, mesopelagic and bathypelagic) and 1 the seafloor. The boundaries separating each pelagic layer were adapted from the original definition retrieved in the literature [START_REF] Hardy | The open sea. Its natural history: the world of plankton[END_REF][START_REF] Pérès | La vie benthique[END_REF][START_REF] Pérès | la vie pélagique[END_REF]. Contrary to the original boundaries' definitions that suggested constant vertical divisions at 200 m, 1000 m and the depth of the seafloor, we used the approach that accommodates the spatial heterogeneity of the water column. Depth of the seafloor layer was here defined on the bathymetry values for each grid cell.

To summarise the approach (step. 1, Supplementary. Fig. 2), the boundary between the epipelagic and the mesopelagic layers was defined as the depth where the environmental conditions do not allow any primary production [START_REF] Behrenfeld | Abandoning Sverdrup's Critical Depth Hypothesis on phytoplankton blooms[END_REF][START_REF] Sverdrup | On Conditions for the Vernal Blooming of Phytoplankton[END_REF]. Since vertical profiles of net primary production were not available for the whole basin, this depth was approximated at the shallowest depth between the euphotic zone and the mixed layer depth, for each geographical cell of the basin. The annual climatology of the epipelagic/mesopelagic boundary is mapped on Fig. 1a.

As there is presently no common definition for the mesopelagic/bathypelagic boundary in the literature across oceanographic disciplines, we here considered the gradient of the Flux of Particulate Organic Carbon (FPOC). Indeed, since the calculation of FPOC uses temperature and salinity profiles, surface chlorophyll-a concentrations and are calibrated using POC values from sediment trap [START_REF] Henson | Global patterns in efficiency of particulate organic carbon export and transfer to the deep Ocean[END_REF], the FPOC product represents a biogeochemical merge of the main vertical gradients in the water column. Therefore, depth of the boundary between the mesopelagic and the bathypelagic environment was defined as the depth where 5 consecutive FPOC concentrations show no significant change. First, each profile was interpolated every 5 metres between 0 and 5000 m (spline interpolation; [START_REF] Legendre | Numerical Ecology[END_REF]. Second, the derivative function of FPOC against depth was computed and the depth of the boundary was set at the depth where the decrease of FPOC between 5 consecutive points was not significantly different from the previous iteration (t-test, p-value>0.05). The resulting depth of the boundary is mapped in Fig. 1b. Also, a test in each MEOWS has been performed to test if the interpolation of the FPOC did not alter the value of the depth boundary. Finally, the boundary between the bathypelagic and the seafloor was set using the bathymetry of the basin mapped on Fig. 1c.

Characterisation of the environmental conditions of the pelagic and seafloor layers

Based on the gathered environmental dataset (described in 2.1 and Table 1, and here named X all ), a vertical average was computed within each pelagic vertical range to depict the mean environmental conditions in the pelagic and seafloor layers (step 2.1, Supp. Fig. 2).

Four distinct environmental matrices were thus calculated: (1) between 0 m and the depth of the epipelagic/mesopelagic boundary (Fig. 1a) for the epipelagic layer (i.e. X epipeligagic ); (2) between the epipelagic/mesopelagic and the mesopelagic/bathypelagic boundaries (Fig. 1b) for the mesopelagic layer (X mesopelagic ); (3) between mesopelagic/bathypelagic and the seafloor (Fig. 1c) for the bathypelagic layer (X bathypelagic ); ( 4) at the seafloor level (X seafloor ). In addition, the annual climatology of the non-vertically discretised environmental variables indicating the water column stability (euphotic depth, mixed layer depth, wind speed, intensity and depth of the thermocline) were added to the X epipelagic and X mesopelagic matrices. The bathymetry was added to X seafloor to account for the basin's topography and better depict the different types of benthic habitats. Spatial distributions of each parameter for each layer can be retrieved on Supplementary Fig. 4, 5, 6 and7.

To characterise the main environmental parameters driving the spatial variance of each layer (step 2.2, Supp. Fig. 2), a Principal Component Analysis (PCA; [START_REF] Jolliffe | Principal Component Analysis[END_REF] was performed on the environmental matrix of each layer. The first and second components (i.e. coordinates values of each geographical cells in each PCA dimension) of each PCA are mapped on Fig. 2 as well as the result of the PCA.

Identification of the spatial distribution of the BGCR

To identify an objective environmental spatial division, the methodology proposed by [START_REF] Oliver | Bioinformatic approaches for objective detection of water masses on continental shelves[END_REF] was applied (step 2.3, Supp. Fig. 2). This numerical procedure uses 4 types of clustering methodologies, here applied on each of the normalised matrices X: (1) Kmeans [START_REF] Hartigan | A k-means clustering algorithm[END_REF], (2) C-means [START_REF] Quackenbush | Computational analysis of microarray data[END_REF], (3) agglomerative with Ward linkage [START_REF] Ward | Hierarchical grouping to optimize an objective function[END_REF], and (4) with complete linkage [START_REF] Legendre | Numerical Ecology[END_REF]) (step 2.2; Fig. 1). The 4 types of clustering algorithms were selected from [START_REF] Oliver | Bioinformatic approaches for objective detection of water masses on continental shelves[END_REF] according to their ability to synoptically group similar environmental variables. Each method was combined owing to their different but complementary ways to handle low dissimilarity clusters (i.e. sensible cluster). Each clustering algorithm was run to retrieve between 2 and 50 clusters, based on the Euclidian distance. The C-means and K-means were repeated 999 times per iteration and the most frequently retrieved division was selected.

The next step of this methodology was dedicated to the identification of the optimal number of clusters (step 2.4, Supp. Fig. 2). The 'Figure Of Merit' (FOM) analysis [START_REF] Yeung | Validating clustering for gene expression data[END_REF] is used, as recommended by [START_REF] Oliver | Bioinformatic approaches for objective detection of water masses on continental shelves[END_REF]. It quantifies the variation of the total environmental variance explained between 2 successive numbers of clusters (i.e. here 2 to 50) for each agglomerative clustering method. A small FOM value indicates that the cluster centroid predicts better the other members of its cluster and that the variance within the cluster is comparatively small. A normalised Average Slope Function (ASF) is calculated using the FOM of each clustering methodology to summarise the information. The ASF exhibits a negative exponential decrease with a rapid decrease for the low number of clusters and a slower decrease after a point k of inflexion (represented by dashed black line on Fig. 2).

The point k was considered as the optimal number of clusters because the deviation between cluster means and the individual observations in each cluster becomes very small [START_REF] Oliver | Bioinformatic approaches for objective detection of water masses on continental shelves[END_REF]. The point k is the threshold of acceptable flatness (TAF), which is defined as the first number of clusters where the decrease is inferior to 1% of the maximum ASF for 3 consecutive clusters. The FOM, ASF and TAF analyses were represented on Supp. Fig. 3. The step 2.5 of the numerical procedure aimed to identify an objective distribution of the BGCR. The strength of the boundaries (named effectiveness; [START_REF] Oliver | Bioinformatic approaches for objective detection of water masses on continental shelves[END_REF], as identified by each clustering methodology, was first computed by taking into account all delineation from 2 to k clusters. Indeed, for every iteration, K-means and C-means procedures modify the spatial distribution (i.e. number of clusters imposed by the operator), as these methodologies divide objectively the space in accordance to the centres of inertia detected.

The map of the effectiveness (Fig. 3b, 4b, 5b and 6b) represents the percentage of a boundary retrieved in a given geographic cell for each methodology and from 2 to k clusters.

The last step of the procedure identified a compromise distribution of the clusters determined by the 4 methods. Contrary to the procedure of [START_REF] Oliver | Bioinformatic approaches for objective detection of water masses on continental shelves[END_REF] that sums the clusters number retrieved with all clustering methodologies used, we here attempted to find a trade-off between all the obtained spatial partitions. To do so, we used a methodology called "watershed" [START_REF] Meyer | Topographic distance and watershed lines[END_REF], implemented from imagery analysis. The watershed function uses the environmental variance within each cluster computed with all methodologies at k (optimal number of clusters defined with FOM) and tests the environmental difference between clusters (Kruskall-Wallis, see [START_REF] Legendre | Numerical Ecology[END_REF]. All clusters showing non-significant differences in their environmental variance were spatially merged by taking into account the spatial distribution of the boundary effectiveness. The procedure stops once k clusters are retrieved. The resulting objective distribution of the BGCRs for each layer is shown in Fig. 3a, 4a, 5a and 6a. Values of the parameters contributing the most to the PC1 and PC2 (see 2.2.3) were computed using the vertical range and spatial distribution of each BGCR identified. These environmental profiles are represented as violin plots on Fig. 3c,4c, 5c and 6c.

Comparison of the environmental profiles of all pelagic BGCRs

To examine the differences in the environmental profile (multivariate environmental variation) of each BGCR of each pelagic layer, the mean and standard deviation of each parameter of X epipelagic , X mesopelagic and X bathypelagic were calculated. Only the parameters common to all environmental matrices were considered here: temperature, salinity, nitrates, nitrites, orthophosphate, silicates, pH, Chlorophyll-a concentration, and dissolved oxygen concentration. A PCA was performed on the computed data, and the position of each BGCR was plotted in the dimension of the PC1 and PC2 (Fig. 7). BGCRs located on the seafloor, in the Marmara Sea or in the Atlantic Ocean were not considered in this analysis as they represent non-Mediterranean areas, and thus could bias the PCA analysis and the comparison between MS BGCRs.

Results

Vertical division of the Mediterranean pelagic realm

Using the shallowest depth between the mixed layer depth and the euphotic depth, the annual climatology of the epipelagic/mesopelagic boundary is found to vary between 10 m and 75 m (Fig. 1a). The deepest boundaries are found in open sea areas, covering most of the oriental basin and the Tyrrhenian Sea. These areas are oligotrophic with low detritus concentration allowing deeper light penetration. In contrast, the more productive areas located in the occidental basin and continental shelf areas exhibit shallower depth of the epipelagic/mesopelagic boundary. In those regions, the waters above 200 m are more 'turbid' resulting in shallower epipelagic layer than in tropical areas (Fig. 1a).

The annual climatology of the lower boundary separating the mesopelagic and the bathypelagic layers (Fig. 1b) varies between 140 m and 1500 m. The areas with the deepest mesopelagic boundary are located in open sea areas of low biological activity. The vertical distribution of this boundary appears to be strongly influenced by the basin's bathymetry (i.e. that defines the seafloor depth) with the deepest boundaries following the shape of the deep-sea basins (Fig. 1c).

Environmental

The Epipelagic layer

The epipelagic layer is partitioned into 12 BGCRs (Fig. 3). 4 BGCRs (1, 2, 7 and 11) subdivide the Western-Eastern environmental gradient depicted on Fig. BGCR 3) are also well characterised by high concentration of NO 2 .

The mesopelagic layer

The mesopelagic layer is partitioned into 10 strictly Mediterranean BGCRs (plus one in the adjacent North Atlantic Ocean, and one in the Marmara Sea). The mesopelagic BGCRs differ environmentally and spatially from those found in the epipelagic layer, especially in the Western Basin. Additionally, their mapping (Fig. 4) reveals a patchier distribution pattern. This pattern can be attributed to the strength of the water-column stratification index (i.e. thermocline depth variable, see Fig. 2). For instance, the NW part of the MS is subdivided into 5 regions (i.e. 1, 2, 4, 6 and 8) while the epipelagic layer is subdivided into 3 BGCRs. The patchiest areas exhibit the highest values of boundary effectiveness (Fig. 4b). The 6 th BGCR represents the region where the bathymetry is too shallow for the existence of a bathypelagic area. In the oriental basin, the mesopelagic layer shows a general partition similar to the one encountered in the epipelagic layer, with Ionian Sea, Levantine Basin and Aegean Sea being distinguished by low values of effectiveness.

The bathypelagic layer

The bathypelagic layer is divided into 12 BGCRs within the MS (Fig. 5). Large BGCRs are found for all the MS characterising the longitudinal environmental gradient (see Fig. 2 and Supplementary Figs. 4 to 7). The latitudinal divisions marked by low values of effectiveness of the boundaries are depicted in the large regions of the western basin (BGCRs 9 and 10) and of the eastern basin (BGCRs 12 and 13) due to slight differences in SiO 2 concentrations.

The seafloor layer

Along the topography of the MS, several distinct environmental conditions within this layer can be identified such as the coastal system, i.e. the slope or the deepsea environment resulting in the most important range of variation in all the parameters considered in the study. For example, nitrate concentrations exhibit huge variations ranging from undetected concentrations up to 9 mmol.l -1 (Fig. 6c). Regional environmental features for similar depths ranges show important differences (nitrates ultimately influence the partitioning of the BGCRs; for example, BGCRs 2 and 4 that have about the same depth, present a twofold difference in NO 3 concentrations).

Consequently, high variations in environmental conditions, which are linked to the bathymetric gradient, combined with basin-wide environmental patterns, and local specificities, results in a very patchy distribution of a higher number of BGCRs in the seafloor layer.

Comparison of Mediterranean pelagic BGCRs environmental conditions

In order to compare the environmental conditions of all the Mediterranean pelagic BGCRs together, a PCA was performed (Fig. 7). Most of the total environmental variance was supported by the vertical position of the BGCRs along the water column (PC1= 40.9%). BGCRs are well sorted from the bathypelagic layer to the epipelagic layer along the PC1. This sorting shows that environmental conditions are more structured along the vertical than along the horizontal dimension. For instance, geographically adjacent BGCRs in different layers (for example BGRs 4E, 10M and 6B in the Levantine area) exhibit highly different environmental conditions and hence, projected in distinct locations in the PCA dimensions.

The second component depicts the environmental longitudinal gradient over the basin. For instance, the BGCRs located in the western basin are found in the negative part of the PC2 axis, while the BGCRs in the eastern basin are in the positive part. Also, on the PCA representation, the maximal distance between representative BGCR points within the bathypelagic layer appears smaller compared to the BGCRs of the pelagic layers. This implies that the BGCRs of the bathypelagic layer are more environmentally homogeneous compared to the BGCRs of the upper layers, because of a decreasing environmental gradient with depth (as depicted in Fig. 2 a-b-c). This analysis reveals that vertically adjacent BGCRs do display highly similar environmental conditions such as the epipelagic Ligurian regions (BGCR 9E) and the mesopelagic Adriatic region (BGCR 6M).

Discussion

Ecological divisions of the Oceanic realm generally aim at providing an objective geographical framework that delineates the environmental and biotic characteristics of a given area. Presently, most of the regional or global divisions proposed in the literature (i.e. for the MS: [START_REF] Sherman | The Large Marine Ecosystem Approach for Assessment and Management of Ocean Coastal Waters[END_REF][START_REF] Spalding | Marine Ecoregions of the World: A Bioregionalization of Coastal and Shelf Areas[END_REF][START_REF] Longhurst | Ecological geography of the Sea[END_REF][START_REF] D'ortenzio | On the trophic regimes of the Mediterranean Sea: a satellite analysis[END_REF][START_REF] Berline | A Connectivity-Based Eco-Regionalization Method of the Mediterranean Sea[END_REF][START_REF] Rossi | Hydrodynamic provinces and Oceanic connectivity from a transport network help designing marine reserves[END_REF] are based on a limited number of environmental parameters that are often representative of the surface waters [START_REF] Reygondeau | Dynamic biogeochemical provinces in the global Ocean[END_REF]. Such environmental selection is attributed to the difficulty in gathering large multivariable datasets resolved in both the horizontal and vertical dimensions. As the epipelagic layer only represents less than 10% of the global ocean, one could argue that former partitions might provide a limited picture of the complexity of the whole system [START_REF] Robinson | Mesopelagic zone ecology and biogeochemistry-a synthesis[END_REF][START_REF] Webb | Biodiversity's Big Wet Secret: The Global Distribution of Marine Biological Records Reveals Chronic Under-Exploration of the Deep Pelagic Ocean[END_REF].

The spatial partitioning of the epipelagic layer (Fig. 3) identified 12 BGCRs.

This study used a larger number of environmental parameters than previous ones (hydrodynamic constraints [START_REF] Rossi | Hydrodynamic provinces and Oceanic connectivity from a transport network help designing marine reserves[END_REF]Berline et al., 2014), chlorophyll phenology (D'Ortenzio andD'Alcala, 2009), biophysical parameters including mesoscale processes [START_REF] Nieblas | Defining Mediterranean and Black Sea biogeochemical subprovinces and synthetic Ocean indicators using mesoscale Oceanographic features[END_REF]. All studies found surface partitions of similar spatial distributions. Such similarities are not surprising since the division of the shallowest waters (between 0 and 70 m, see Fig. 1) is indeed driven by the strong longitudinal gradient in temperature, salinity and chlorophyll-a concentration (Figure 2), parameters that were used in the previous studies. The finding of a common trend in the distribution of all proposed environmental partitions of the epipelagic zone, while using different sets of parameters and methodologies, strongly supports (i) the robustness of previous partitions, and (ii) the need for only a classic and simple set of environmental parameters in order to partition that layer.

The longitudinal environmental gradient driving the epipelagic division is also found in other pelagic layers (Figure 2). However, the interval of variation and the contribution of all the considered parameters changes with depth (Figure . 2). Indeed, the PCA (Fig. 7) reveals that environmental dissimilarity between the BGCRs within a pelagic layer decreases with depth. The BGCRs' delineation provided for the mesopelagic or the bathypelagic layers appears less influenced by the longitudinal gradient of classical parameters (temperature, salinity and chlorophyll), and more impacted by other variables such as vertical mixing, nutrient concentrations or bathymetry (Figure 2.). For instance, the mesopelagic layer shows a patchier pattern than the epipelagic layer, especially in the western basin where most of the water convection areas occur (The MerMex Group, 2011). The bathypelagic layer, being relatively isolated from winter convection, and thus from the influence of atmospheric interactions, is mostly partitioned according to deep-water circulation and morphological features. Partitioning of the seafloor layer is mostly driven by the bathymetric gradient with a strong environmental opposition between coastal, slope and deep-sea regions but also by the longitudinal environmental gradient, to a lesser extent.

These results reveal that the use of parameters such as temperature, salinity and chlorophyll in biogeographical studies are sufficient to capture most of the environmental variance of the MS, hence providing a realistic delineation of the surface waters. Nonetheless, since the environmental variance is not supported by the same set of parameters with the depth (Figure . 2), environmental partitioning of a given layer cannot be projected to another one due to the non-congruence of the BGCRs delineation between vertical layers.

The MS is composed of a large number of biotopes that can be represented as a 3D jigsaw puzzle of biotopes each driven by a specific set of environmental parameters. The 3D partition can thereby be interpreted as an annual average of the different environmental biotopes that can be encountered in the whole basin. Each of those environmental envelopes delineates a BGCR defined by a given interval of variation for each of the biogeochemical and physical parameters considered. [START_REF] Odum | Fundamentals of ecology[END_REF] defined such ecological units, or ecosystems, as intervals of variation among all the environmental possibilities where an assemblage of adapted species can develop and maintain their population.

BGCRs are separated by boundaries where effectiveness reflects the intensity of exchanges in between two adjacent regions. Therefore, exchanges of energy and/or matter characterise the interactions in between BGCRs [START_REF] Odum | Fundamentals of ecology[END_REF]. The strength of those exchanges could here be approximated by the map of boundary effectiveness provided for each layer on an annual basis. The lower the yearly averaged index is, the more the adjacent provinces present an overlap of environmental envelopes, which suggests exchange of matter or energy [START_REF] Reygondeau | Dynamic biogeochemical provinces in the global Ocean[END_REF].

The Mediterranean is known to exhibit strong interactions of physical processes that act on a large spectrum of spatial and temporal scales and that directly impact the ecosystem dynamics [START_REF] Mermex | Marine ecosystems' responses to climatic and anthropogenic forcings in the Mediterranean[END_REF]. Maps of the boundary effectiveness (Fig. 5b, 6b and 6c) for the pelagic layers coincide with the complex dynamic features of the thermohaline circulation over the MS such as currents, fronts and sub-mesoscale structures [START_REF] Millot | Circulation in the Mediterranean Sea. The Mediterranean Sea[END_REF][START_REF] Rossi | Hydrodynamic provinces and Oceanic connectivity from a transport network help designing marine reserves[END_REF][START_REF] Berline | A Connectivity-Based Eco-Regionalization Method of the Mediterranean Sea[END_REF]. High values of boundary effectiveness correspond to regions of low interactions such as gyre cores, closed coastal systems or fronts. High mesoscale features characterise surface waters in the MS, in particular along the African shelf [START_REF] Millot | Circulation in the Mediterranean Sea. The Mediterranean Sea[END_REF]. There, BGCRs boundaries (for example along the Tunisian and Libyan coasts) follow the anticyclonic eddies that characterise the whole area: in this way, the shape of the BGCR 5 in the epipelagic layer reflects the 50-150 km chlorophyll-poor circular structures. It is thus not surprising that our analysis finds that effectiveness of boundaries are closely related to well recognized dynamic features [START_REF] Rossi | Hydrodynamic provinces and Oceanic connectivity from a transport network help designing marine reserves[END_REF][START_REF] Berline | A Connectivity-Based Eco-Regionalization Method of the Mediterranean Sea[END_REF].

The statistical approach to partitioning should not prevent biogeochemical interpretation. A closer look at the regions that show high environmental similarities could be interpreted together as a 'nested environmental system". For instance, in the epipelagic layer, BGCR 2 and 4 show a short distance in the PCA dimensions indicating that a single region could actually be enough to characterise half of the eastern basin well. A similar possible reduction in the number of BGCR, using results from PCA (Fig. 7), can also be made for the mesopelagic. Merging short distance BGCR in this layer would result in a large region covering most of the eastern basin (BGCR 5 and BGCR 10). Similarly, the very close similarity between BGCR 1 and 8 also leads to a simplification of the regions in the most western MS. In the bathypelagic layer, BGCR 12 and 13 are also very similar and a single region could rather be retained, corresponding to the whole Ionian Sea. This fine analysis of the environmental variance indicates thus that a slightly lower number of BGCRs could be sufficient to capture the full 3D environment of the MS in a more global analysis.

Conclusion and perspective

Past divisions of ocean have never fully the full of physical, chemical and biotic complexity of this realm. This bias is historically driven by data availability at the spatial scale of the study (global, Oceanic basin, regional) together with the topic of interest of the authors (ecology, biogeochemistry, economics or politics). So far, studies attempting to investigate the benefits of a multivariate and multidimensional approach are scarce. Here we considered the multivariate approach over the whole water column to propose a 3D partition of the MS environmental conditions.

The present study show that the distribution of the boundaries is closely related to well recognized oceanographic dynamic features of the basin. This confirms the importance of considering a highly resolved environmental dataset to account for meso-scale processes that drive most of the MS spatial and vertical biogeochemical variability. We also confirmed that a classical set of environmental parameters (temperature, salinity and chlorophyll), used in most of the previous studies, is sufficient to partition the epipelagic layer since it is mostly driven by the westerneastern gradient in the MS but their influence decreases with depth. Thus, other environmental parameters are needed to characterise specific deep water conditions that are driven by different biogeochemical processes compared to the epipelagic layer. This study clearly revealed the crucial need for a multidimensional and multivariate approach to model spatial distribution of deep or vertical migrating species. This is of major importance for conservation management as we show that one cannot rely only on surface or bottom parameters to delineate an optimal zone for marine conservation.

These multivariate and multidimensional approaches represent the first step towards a partition that copes with the full complexity of the MS. Indeed, the approach proposed in the present study only coped with 1 of the 2 components of an ecosystem: the biotope (sensu Odum, 1974). The next step towards an optimal ecosystem division is thereby an extension of the present study to species community distribution and trophic linkage to provide a useful geographic framework for ecosystem management planning (fisheries quotas, biodiversity conservation planning or implementation of marine protected areas).

Tables captions

Table 1. Spatial resolution, units and reference of the environmental variables used in the study. variations of at least one of the parameters sampled. However, changes of the in situ data are also detected within some BGCR.

Figures captions

  and spatial characterisation of the BGCRs 60 biogeochemical regions are identified within the MS. Pelagic layers exhibit a similar number of clusters: 12 for the epipelagic, 12 for the mesopelagic, 13 for the bathypelagic while the seafloor is partitioned by 26 biogeochemical regions. Each vertical layer is here divided into a specific number of BGCRs, each one characterised by a spatial distribution with a given strength of boundaries and a specific environmental range (Figures 3 to 6). BGCRs represent either significant multivariate shifts along the environmental gradient, or local features driven by changes in only one variable. To simplify the description of each BGCR, only key environmental parameters are represented on Figures 3 to 6(right panels) according to the analysis described in Figure 2.

  2. The strength of the boundary is highly marked in the occidental basin and decreases towards the eastern basin, suggesting a less marked environmental spatial change across the longitudinal environmental gradient. The Adriatic, Aegean or Ligurian Seas are well captured as they exhibit a particular environmental range compared to the longitudinal gradient (i.e. change in the chlorophyll-a concentration) underlined by high boundary effectiveness. The Gulf of Trieste and the Algerian Coast (i.e.

Figure 1 .

 1 Figure 1. Map of the depth of the vertical boundaries of the water column and

Figure 2 .

 2 Figure 2. Left Panel: results of the PCA performed on the environmental matrices of

Figure 3 .

 3 Figure 3. (a) Map of the spatial distribution of the epipelagic BGCRs and (b)

Figure 4 .

 4 Figure 4. (a) Map of the spatial distribution of the mesopelagic BGCRs and (b)

Figure 5 .

 5 Figure 5. (a) Map of the spatial distribution of the bathypelagic BGCRs and (b)

Figure 6 .

 6 Figure 6. (a) Map of the spatial distribution of the Seafloor BGCRs and (b) associated

Figure 7 .

 7 Figure 7. Scatter plot of the pelagic BGCRs position according to the principal

Figure 1

 1 Figure 1 Upper panel: Map of the BOUM cruise superimposed on the map of the epipelagic biogeochemical regions of the MS. Lower panel: Plot of the boundary effectiveness, SST (Sea Surface Temperature), SSS (Sea Surface Salinity), fluorimetry (named here chlorophyll-a) and dissolved oxygen concentration gathered along the cruise. Colours superimposed on the plot of the boundary effectiveness stand for the BGCR crossed. Black vertical dashed lines represent region of changing BGCR. All plots have been smoothed by a running average of 5.

Acknowledgments

This work is a contribution to the EC FP7 PERSEUS Project (Policy-oriented marine Environmental Research in the Southern EUropean Seas; Grant. Agr. 287600). A post-doctoral research grant provided by the PERSEUS Project supported GR. The authors wish to also thank the MISTRALS-MERMEX program (Institut des Sciences de l'Univers, INSU), as a contribution to the Surface Ocean -Lower Atmosphere Study (SOLAS), the Integrated Marine Biogeochemistry and Ecosystem Research (IMBER) and the LOICZ (Land-Ocean Interactions in the Coastal Zone) projects. G.R would also aknowledge the support from the Nippon Foundation-the University of British Columbia (UBC) Nereus Program. The authors would like to thank Lindsay

Lafreniere for her help in the editing of the manuscript. We also thank the 3 anonymous reviewers who helped to improve this manuscript. This work is dedicated to the memory of our colleague and friend Frederic Ibañez.

Validation of the spatial distribution of the epipelagic BGCRs

To test the robustness of detected boundaries, the resulting environmental partition was confronted to an independent set of in situ data (collected during an cruise).

Owing to the difficulty to retrieve deep environmental sampling originating from the same cruise, and covering both occidental and oriental basins, only the epipelagic layer division (Fig. 1a; main manuscript) could be tested. We here used the surface data collected during the BOUM (Biogeochemistry from the Oligotrophic to the Ultraoligotrophic Mediterranean) cruise [START_REF] Moutin | Introduction to the Biogeochemistry from the Oligotrophic to the Ultraoligotrophic Mediterranean (BOUM) experiment[END_REF].

First, the mean value of each parameter gathered along the cruise (Sea Surface Temperature, Sea Surface Salinity, Dissolved oxygen concentration and fluorimetry) was computed for each epipelagic BGCR encountered. Then, a Kruskall Wallis test was performed to test if the mean environmental values were significantly different among BGCR. Second, shift in the values of effectiveness between each BGCR encountered across the cruise were compared to surface parameters gathered along the cruise (Fig. 5 and Fig. 10). An examination of the change in BGCR (marked by an important effectiveness value) was empirically compared to the variation of each nearest parameter values collected during the BOUM campaign (Annexe 1, Fig. 1).

The Kruskall-Wallis test shows significant differences (p-value < 0.05) over the mean environmental conditions of all the BGCRs crossed during the cruise. Second, the

Highlights

 This study provides the first 3D atlas of Biogeochemical Regions in the Mediterranean Sea (12 for the epipelagic, 12 for the mesopelagic, 13 for the bathypelagic and 26 for the seafloor)  The Eastern-Western environmental gradient has a decreasing contribution to the biogeochemical partitions with depth  The partition of the surface layer cannot not be extrapolated to underneath layers as the partition is driven by different environmental variables  The study highlights the need of a third level of macro-ecological division at a regional scale to quantify the influence of meso-scale environmental variability that mostly drive semi-enclose seas biogeochemical processes and thus marine habitats.