ALICE (Assessment of Landslides Induced by Climatic Events): a single tool to integrate shallow and deep landslides for susceptibility and hazard assessment

Keywords: landslides, slope stability, hazard, mapping

The increasing evolution of urban areas in landslide-prone regions and the modification of precipitation due to global climate change have led to a growing need for landslide hazard assessment (LHA) for local land management and security services. LHA is based on the definition of the spatial and temporal probability of landslide occurrences and is split into three steps: (i) a phenomenon inventory, (ii) a landslide susceptibility analysis, and (iii) a landslide hazard analysis. Nevertheless, in practice, essential information is often missing, and LHA corresponds most of the time to landslide susceptibility assessment acquired by expert knowledge. This article presents a physical-based model (ALICE -Assessment of Landslides Induced by Climatic Events) that can integrate different types of landslides (shallow and deep) with different sizes. This tool can be used at the meso or broader scale (1:25 000 to 1:10 000) of work according to expert knowledge. However, a calibration must be carried out to fit observations and to take uncertainties into account. Thus, a specific strategy is applied to the model on a study site located in the French South Alps where numerous different landslide types were observed and analyzed. After calibration on a small representative area, the best-fitted parameters are applied to a larger area for different types of landslides. Three landslide susceptibility maps (shallow translational landslides, rotational landslides and complex landslides) are produced, and the different susceptibility classes are compared with a landslide susceptibility map produced by a geomorphological approach. The different susceptibility envelopes computed by the model are well integrated into the high-susceptibility envelopes defined by the socalled expert geomorphological approach. Thus, the tool makes it possible to improve the mapping of potentially unstable areas by taking into account parameters, such as the groundwater level in different surficial formations or the geotechnical values of landslide-prone formations, that experts are not always able to integrate. ALICE is therefore proven to be a useful tool for mapping potential landslide-prone areas if the tool is well calibrated, taking into account the expert vision of the field, different landslide types, and different triggering factors, including rainfall and seismic acceleration.

Introduction

With increasing urbanization and climate change modifying precipitation patterns, landslide hazard assessment (LHA) has become a challenge in recent years for the prevention and prediction of territory for local land management and security services. LHA is based on the definition of the spatial and temporal probability of landslide occurrences in a territory within a reference period for a given intensity [START_REF] Varnes | Slope Movement Types and Processes[END_REF][START_REF] Soeters | Slope instability recognition, analysis, and zonation[END_REF][START_REF] Van Westen | Landslide hazard and risk zonation -Why is it still so difficult?[END_REF][START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF]. It takes into account the failure probability, the runout and the magnitude of the phenomena. To assess landslide hazards, three steps are generally followed: (i) a phenomenon inventory, (ii) a landslide susceptibility analysis, and (iii) a landslide hazard analysis [START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF][START_REF] Thiery | Improvement of landslide hazard assessments for regulatory zoning in France: STATE-OF-THE-ART perspectives and considerations[END_REF].

i.

The landslide inventory is considered to be the essential basis for any LHA. Different methods and techniques (i.e., aerial photograph interpretation, field survey, high-resolution imagery, and LiDAR interpretation; [START_REF] Guzzetti | Landslide inventory maps: New tools for an old problem[END_REF] can be used to build a landslide database with adequate information about landslide locations, activity, occurrence frequency, failure mechanisms, causal factors, and volumes (Wieczorek 1984;Guzetti et al., 2012;[START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF].

ii.

Landslide susceptibility represents the potential occurrence of phenomena based on predisposing factors (topographical, geological, geotechnical, soil, and land-cover conditions) and triggering factors (rainfall and earthquakes) for different slope failure surfaces. Four types of approaches exist, depending on the scale of the work and on the data accuracy [START_REF] Fell | Guidelines for landslide susceptibility, hazard and risk zoning for land-use planning[END_REF][START_REF] Van Westen | Spatial data for landslide susceptibility, hazard, and vulnerability assessment: An overview[END_REF][START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF]: inventory-based methods (IBMs: event-based landslide inventory maps), knowledge-driven methods (KDMs: geomorphologic hazard maps or spatial multicriteria evaluation), data-driven methods (DDMs: like bivariate or multivariate statistics), and physical-based methods (PBMs: infinite slope-based static methods or dynamic methods taking into account rainfall).

iii.

Landslide hazard analysis relies on the two previous steps. It takes into account the runout, magnitude, and return period for a given intensity [START_REF] Varnes | Slope Movement Types and Processes[END_REF]. Runout and magnitude integrate the propagation mode, velocity, and volume, depending on the mechanics laws governing the runout area [START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF].

An exhaustive review of the different techniques for LHA can be found in [START_REF] Van Westen | Landslide hazard and risk zonation -Why is it still so difficult?[END_REF] and [START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF]. In practice, several scientific and technical obstacles can prevent each step from achieving LHA [START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF]. For instance, when no trigger or activity date are available or when the run-out of landslides cannot be assessed, the LHA cannot be fully complete. Additionally, it appears difficult to jointly analyze both shallow and deep-seated landslides over large and complex areas because (i) the predisposing and triggering factors are different, and (ii) there is large uncertainty and variability in geotechnical parameters [START_REF] Zêzere | Probabilistic landslide risk analysis considering direct costs in the area north of Lisbon ( Portugal )[END_REF]Thiery et al., 2017a). Therefore, depending on the quality of available data, the size of the study area, the complexity of the context, and the means, the scientist or the expert must choose which steps they can complete totally. Finally, in many cases, the third step is rarely completed, and the landslide susceptibility assessment is converted by expert knowledge into the LHA [START_REF] Van Westen | Landslide hazard and risk zonation -Why is it still so difficult?[END_REF][START_REF] Simoni | Modelling the probability of occurrence of shallow landslides and channelized debris flows using GEOtop-FS[END_REF][START_REF] Fell | Guidelines for landslide susceptibility, hazard and risk zoning for land-use planning[END_REF].

In recent years, to improve a qualitative landslide assessment, spatial PBMs that simulate landslide failure for large areas have become considerably democratized. If these models do not allow an analysis of the hazard specifically, they make it possible to obtain quantitative analysis by the production of failure probability maps, taking into account geotechnical parameters and triggering factors. Moreover, it is possible to test some scenarios (e.g., failure evolution) and to analyze the model sensitivity to different triggering factors. The results of such models are more concrete and consistent than those of other approaches (IBMs, KDMs, and DDMs; [START_REF] Thiery | Improvement of landslide hazard assessments for regulatory zoning in France: STATE-OF-THE-ART perspectives and considerations[END_REF].

PBMs often rely on the limit equilibrium method (LEM). Table 1 overviews some of the existing tools and the characteristics of each tool in terms of landslide geometry, slope stability methods, temporal components, hydrological comportment, triggering, and probabilistic approaches. These tools generally combine hydrogeological models and slope stability models (e.g., [START_REF] Hammond | Level I Stability Analysis (LISA) documentation for version 2[END_REF][START_REF] Dietrich | A process-based model for colluvial soil depth and shallow landsliding using digital elevation data[END_REF][START_REF] Wu | A Distributed Slope Stability Model for Steep Forested Basins[END_REF][START_REF] Dietrich | Hillslopes. channels and landscape scale[END_REF][START_REF] Dhakal | Long-term modelling of landslides for different forest management practices[END_REF][START_REF] Tarolli | A new method for determination of most likely landslide initiation points and the evaluation of digital terrain model scale in terrain stability mapping[END_REF][START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF][START_REF] Haneberg | A Rational Probabilistic Method for Spatially Distributed Landslide Hazard Assessment[END_REF]Mergili et al., 2014aMergili et al., , 2014b)). Hydrological models can be complex and time dependent for local-scale areas or simplified and static over large areas. Some distributed slope stability models are not directly combined with a hydrological model; the user has to impose, for instance, an empirical groundwater table derived from hypothesis, observation, field data interpolation, and complex hydrogeological models.

LEM assumes that the slope is made of rigid materials and that possible failure occurs along a single failure plane (the slip surface) under the influence of gravity. The shear stress acting on the slip surface is compared to the shear strength of the resisting materials along the slip surface. The ratio of these contrasting forces acting on the failure plane is expressed by the factor of safety FoS [START_REF] Carson | Hillslope Form and Process[END_REF][START_REF] Crozier | Landslides: Causes, Consequences and Environment[END_REF][START_REF] Duncan | Soil Strength and Slope Stability[END_REF]. Hence, FoS is the ratio between the sum of the resisting (stabilizing) forces and the sum of the driving (destabilizing) forces [START_REF] Duncan | State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes[END_REF]. The methods used to calculate FoS differ according to the complexity of the considered landslide geometry (shape of the potential sliding surface) in two dimensions [START_REF] Fellenius | Erdstatische Berechnungen[END_REF][START_REF] Janbu | A pplication of com posite slip surfaces for stability analysis[END_REF][START_REF] Bishop | The use of the Slip Circle in the Stability Analysis of Slopes[END_REF][START_REF] Morgenstern | A numerical method for solving the equations of stability of general slip surfaces[END_REF] and in three dimensions [START_REF] Hovland | Three-dimensional slope stability analysis method[END_REF][START_REF] Hungr | An extension of Bishop's simplified method of slope stability analysis to three dimensions[END_REF][START_REF] Lam | A general limit equilibrium-model for 3-dimensional slope stability analysis[END_REF]Mergili et al., 2014a). Stability classes proposed by [START_REF] Kirsten | Significance of the probability of failure in slope engineering[END_REF][START_REF] Pack | Assessing Terrain Stability in a GIS using SINMAP[END_REF] are used to characterize slope stability: when FoS ≥ 1.5, the slope is considered stable; when 1.5 > FoS ≥ 1.2, the slope is considered potentially stable; and when 1.2 > FoS ≥ 1, the slope is considered potentially unstable. A FoS value equal to 1 indicates a meta-stable condition. When this occurs, the slope is considered to be at the failure point. Finally, when FoS < 1, it is an indication of the slope instability following the considered scenario.

The simplest method is to evaluate FoS on each individual raster cell without taking into account the neighboring cells (i.e., assumption of infinite slope). The 1D infinite slope method is adapted to regional analysis with the assumptions of a planar slope of infinite length and of a failure plane parallel to the topographic surface. The infinite slope analysis is used for shallow landslides with a plane failure surface parallel to the topography. Several models use this method (cf. Table 1); they are reserved for relatively homogeneous environments composed of a shallow surface layer and a substratum not impacted by landslides. Two-dimensional slope analysis can be used to take into account shallow or deep-seated landsides and can be useful to evaluate any failure surface. Twodimensional and three-dimensional analyses are more adapted to more or less complex environments with several lithological layers. Generally, it is more difficult, in terms of calculation, to perform 3D analyses than 2D analyses.

Because 2D analyses provide conservative results compared to those of 3D analyses, 2D analyses provide a reasonable and sufficiently accurate approach to most practical problems of the stability of soil slopes [START_REF] Wu | Landslide Hazard and Risk Assessment in Landslides Investigation and Mitigation[END_REF].

By taking into account physical laws coupled with probabilistic approaches in the calculation process, with assigning statistical distributions to soil parameters instead of a single deterministic value, some models such as GEOtop-FS and HIRESS attempt to reduce environmental uncertainties and improve the location of landslideprone areas [START_REF] Simoni | Modelling the probability of occurrence of shallow landslides and channelized debris flows using GEOtop-FS[END_REF][START_REF] Rossi | HIRESSS: A physically based slope stability simulator for HPC applications[END_REF]. However, these approaches are only dedicated to shallow translational landslides. [START_REF] Darcy | Les Fontaines publiques de la Ville de Dijon[END_REF]) unsaturated flow [START_REF] Richards | Capillary condition of liquids through porous medium[END_REF] Use of an empirical method [START_REF] Charalambus | Methodology development for the stability evaluation of natural and man-made slopes against static and seismic loads in a GIS environment[END_REF] These software tools have been calibrated and tested for different areas. Nevertheless, the majority were designed for shallow landslides with no integration of environmental uncertainties. Hence, the implementation of a landslide susceptibility analysis for a complex and heterogeneous environment over large areas faces two major challenges:

(i) taking into account different slope failures (in terms of shape and depth) and (ii) taking into account the uncertainty of the geotechnical parameters due to inherent spatial variability and the lack of representative data, which affect the final computed FoS values (i.e., overestimation or underestimation of the results; Mergili et al. (2014aMergili et al. ( , 2014b)).

This article presents a landslide susceptibility analysis tool, ALICE (Assessment of Landslides Induced by Climatic Events), which can be used in different environmental contexts (e.g., tropical, mountainous, and plateau; Sedan et al., 2013c;[START_REF] Vandromme | A novel approach to integrate effects of vegetation changes on slope stability[END_REF]Thiery et al., 2017aThiery et al., , 2017b) ) and takes into account different landslide geometries and environmental uncertainties. It has been developed to optimize the automated execution of failure calculation by a probabilistic approach on input parameters with the Monte Carlo method. In so far as the border between shallow and deep landslides is not a clear definition or a fixed value [START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF], ALICE software allows varying several geometric parameters that can range from shallow to deep failures by imposing minimum and maximum depths or a geometrical interface between two lithologies. Hence, the tool allows for a sensitivity analysis on different geometrical and geotechnical parameters, permitting an increase in the predictive power of the simulated maps for different types of instabilities, as an expert should do for a qualitative map but in a quantitative way.

However, to obtain satisfactory results, a specific strategy must be undertaken, taking into account field observations and measurements and uncertainties linked to information about the surficial formations information.

Hence, the aim of this work is to ascertain a reproducible procedure for ALICE and any PBMs, taking into account different types of failures and some environmental uncertainties in surficial formations. The procedure adopted for this research includes three steps:

(i)

Identification of more representative landslide parameters (geometry and size) to be introduced in the model (i.e., type, depth, and length of failure);

(ii) Sensitivity analysis on landslide probability calculations (a minimal number of Monte Carlo simulations and identification of the distribution probabilities for each geotechnical parameter); and

(iii) Evaluation of the best-simulated maps in comparison with the landslide inventory and a direct landslide susceptibility map obtained by the geomorphological approach and expert knowledge.

The model and the specific strategy are applied on the north-facing slope of the Barcelonnette basin (French South Alps), where numerous different landslide types were observed and analyzed [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF][START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF][START_REF] Schlögel | Analysis of a landslide multi-date inventory in a complex mountain landscape: The Ubaye valley case study[END_REF].

Geomorphological setting

The Barcelonnette basin

Located in the middle section of the Ubaye Valley (Fig. 1), the Barcelonnette basin extends from 1100 to 3000 m a.s.l. and is representative of climatic, lithological, and geomorphological conditions observed in the South French

Alps. The climate is controlled by mountain and Mediterranean influences with (i) high interannual rainfall variability (734±400 mm over the period 1928-2013) and intense and violent summer rainstorms (>50 mm h -1 ),

(ii) a significant daily temperature range (>20°C) and (iii) between 120 and 130 days of freezing per year. An authentic geological window developed in the autochthonous Callovo-Oxfordian black marls, the basin, over an area of approximately 300 km 2 , is surrounded by the two allochthonous Eocene crystalline sheet thrusts of the Parpaillon and Autapie [START_REF] Maquaire | Instability conditions of marly hillslopes: Towards landsliding or gullying? The case of the Barcelonnette Basin, South East France[END_REF]. This particular geomorphological context is the consequence of the action of glaciers completed by torrential erosion, which has carved out a large basin of 13 000 ha in the soft rocks (i.e., black marls; [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF]. Comprising limestones, sandstones, flysch and gypsum, the sheet thrusts shape the high crests and the steepest slopes ranging from 2200 to 3100 m in elevation. Below them, the upper slopes (from 1800 to 2200 m) are covered by scree deposits with a thickness from 2 to 10 m. The lower slopes present irregular topography with (i) steep slopes (>35°) carved in black marl outcrops and commonly gullied in badlands and (ii) gentle slopes (5-35°) with planar or hummocky topography. The majority of these deposits are composed of moraine deposits (thickness from 2 to 20 m) overlying black marls. These slopes, covered by forests and/or natural grasslands, are affected by large relict, latent and active landslides (deep complex and rotational landslides; shallow translational and rotational landslides) and/or surficial soil creep. Most of the active landslides are nonstabilized landslides and are located along streams or on gentle slopes where the moraine deposits or the contact moraine deposits/black marls create a hydrological discontinuity favorable to failure [START_REF] Flageollet | Landslides and climatic conditions in the Barcelonnette and Vars basins (Southern French Alps, France)[END_REF]Malet et al., 2007b;[START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF]. With more than 80% of the different landslide types of the Barcelonnette basin, the north-facing slopes are the most affected by different types of landslides [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF], which is why our study focuses on this area.

Landslide characteristics

The landslide inventory used is based on field investigations and aerial photograph interpretation [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF] and an update completed by [START_REF] Schlögel | Analysis of a landslide multi-date inventory in a complex mountain landscape: The Ubaye valley case study[END_REF] by remote sensing. Table 3 gives some morphometric indications about the landslide initiation zones retained for this study (Fig. 4) for (i) shallow translational slides (20-30 m length and up to 3 m depth), (ii) moderately deep rotational slides (50-60 m length and up to 6 m depth) and (iii) complex slides with rotational initiation (100-120 m length and up to 10 m depth). These characteristics set the modeling hypotheses, which are considered representative of field reality. An expert landslide susceptibility map (Fig. 4e), produced initially by [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF] and [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF], is used to assess the different numerical simulations. The map, requiring a geomorphological overview of the area and the environmental characteristics for each landslide type, is elaborated following the French legal procedure at a 1:10 000 scale (MATE/MATL, 1999; [START_REF] Leroi | Global rockfalls risk management process in "La Désirade" Island (French West Indies)[END_REF]. Each polygon represents a homogenous physiogeographical area favorable to one or more types of landslides and integrates expert rule information described in [START_REF] Thiery | Application of expert rules in indirect approaches for landslide susceptibility assessment[END_REF]. The polygons take into account (i) the landslide types and state of activity (active continuously or intermittently, dormant, stabilized)), (ii) the main environmental factors considered prone to one or several types of instabilities (slope gradient, slope aspect, land use, land degradation), and (iii) the considered susceptibility class with four classes (null, low, moderate and high). The possibilities of landslide developments for the forthcoming one hundred years are integrated by aerial photograph interpretation from 1948 [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF][START_REF] Thiery | Application of expert rules in indirect approaches for landslide susceptibility assessment[END_REF][START_REF] Schlögel | Analysis of a landslide multi-date inventory in a complex mountain landscape: The Ubaye valley case study[END_REF].

Materials and methods

ALICE model

ALICE was developed by the French Geological Survey (BRGM) to support landslide susceptibility assessment and mapping for areas ranging from elementary watersheds to large areas (Sedan et al., 2013a;Thiery et al., 2017a,b;[START_REF] Vandromme | A novel approach to integrate effects of vegetation changes on slope stability[END_REF]. Developed in a GIS environment, ALICE is a PBM based on an LEM that computes the FoS along 2D profiles derived from a digital terrain model (DTM) of the entire area. It can integrate the different geometries of the landslides, the spatial and inherent heterogeneity of the surficial deposits and geology as well as their geotechnical parameters, triggering factors (i.e., water and seismicity), and land use change (Fig. 2). The shear strength of the soil along the potential failure plane is given by the Mohr-Coulomb failure criterion. The Morgenstern andPrice (1965, 1967) method is used to calculate FoS. It is based on a 'slice approach' that subdivides the potential sliding mass into slices for instability calculation; a detailed review of the calculation processes can be found in [START_REF] Duncan | State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes[END_REF] and [START_REF] Duncan | Soil Strength and Slope Stability[END_REF]. This method was chosen because (i) it satisfies the equilibrium conditions and involves the least numerical difficulty; (ii) any slip surface geometry can be calculated; and (iii) it takes into account interslice forces across the sliding mass [START_REF] Duncan | State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes[END_REF][START_REF] Duncan | Soil Strength and Slope Stability[END_REF]. The iteration process relies on Zhu et al.'s (2005) concept, which reduces the number of iterations about the resolution of the interslice function. In the model, the slice size can be adjusted to obtain a better compromise between precision and calculation duration.

Landslide geometries

Based on an LEM, the slope stability calculation is used to solve the forces applied on sliding bodies along a potential slip surface that can be circular or along an interface (Fig. 2c). Depending on the study site and based on field observations, the user must elaborate a typology of the landslides to identify the representative landslide geometries. Rotational slip surfaces are characterized by a length, a minimal depth and a maximal depth (Fig. 2c).

Shallow translational slip surfaces are defined by an interface (contact between two formations), a length, and a scarp angle (Fig. 3). The model evaluates FoS maps for each landslide geometry.

Shallow transition landslides are specific with depth not exceeding 2 or 3 m [START_REF] Cruden | Landslides: investigation and mitigation. Chapter 3-Landslide types and processes[END_REF]. Spatial evaluation of shallow translational landslide stability is often performed using the infinite slope method, taking into account the interface between two formations as the slip surface, usually on each individual raster cell (Table 1). However, shallow translational landslides can occur in deep formations, but their depth remains no more than 2 or 3 m [START_REF] Cruden | Landslides: investigation and mitigation. Chapter 3-Landslide types and processes[END_REF][START_REF] Hungr | The Varnes classification of landslide types, an update[END_REF]. Thus, to take into account this parameter, the concept of the "scarp angle" has been introduced to characterize the geometry of shallow translational failure. This "scarp angle" is the angle between the average slope of the landslide top surface and the sliding surface at each end (Fig. 3). It can be parameterized if the slip surface is an interface between two lithologies below the ground surface and if the phenomena occur in deep formations (Fig. 3a). It is possible to vary this angle to fit the observations. If the scarp angle is too high, the slip surface would have a rectangular shape that is not realistic.

Usually, this angle ranges between 30° and 45° depending on the slope values (Sedan et al., 2013c): the upstream sliding surface makes an angle between 20° to 30° with vertical, which is approximately the order of magnitude of the friction angle (limit stability angle for surficial material). This value needs to be adapted to each case study depending on the soil depth, slope, and landslide length.

2D profile extraction

The 2D profiles are automatically generated from a DTM using a local drain direction (LDD) network, which indicates the direction of the steepest downhill slope (Fig. 2b). The LDD is computed with an eight-direction (D8) flow model and follows an approach presented by [START_REF] Jenson | Extracting topographic structure from digital elevation data for geographic information system analysis[END_REF]. Each profile starts on a ridge (i.e., pixel with no upstream elements) and stops when it intersects a thalweg (deepest portion) or another profile (Fig. 2b). Thalweg pixels are defined as cells having more than N contributing upstream elements. The N value varies depending on the type of topography of the study area and the DTM resolution and reflects the scale at which the channel network is extracted from the DTM [START_REF] Tarboton | On the extraction of channel networks from digital elevation data[END_REF]. The greater N is, the longer the profiles. This N value must be evaluated by the user to identify slope toes. Hence, profiles are a succession of slices oriented on the grid according to a 45° azimuthal scheme.

The slope stability assessment is performed on each 2D profile (Fig. 2b), which covers the whole studied area. The number of profiles varies with DTM resolution and the size of the study area. 2 provides more detailed information on the input data necessary for performing the landslide analysis.

Geotechnical model and uncertainties

The geometry of the studied area is introduced in the tool as a dataset in raster format. The tool needs the elevation represented by a DTM and its derivative to calculate the 2D profiles ("Topography and derivatives" in Table 2).

The surficial formation and geological layers are represented by other DTMs representing the basal surface of each layer ("Geology" in Table 2). Geotechnical characteristics (i.e., cohesionc', friction angle -ϕ' and volumetric weightγ') are associated with each geological and surficial deposit layer ("Geotechnical parameters" in Table 2). ("Triggering factors" in Table 2). Similar to the other geometrical inputs of the model, the GWL is implemented in raster format (as a piezometric map) with minimum and maximum levels. When no information about rainfall and piezometric levels is available, it is possible to define the GWL empirically as a saturation level from 0 (dry conditions, minimum level) to 1 (saturated conditions, maximum groundwater level) (Sedan et al., 2013a).

Conversely, when rainfall and piezometric data are available, ALICE can be linked to the global hydrological model, GARDENIA (Global Reservoir Model for Simulation of Discharge and Groundwater Levels; [START_REF] Thiéry | Logiciel GARDÉNIA version 6.0. Guide d'utilisation[END_REF], to consider the variations in the GWL depending on the time series of effective rainfall events at the scale of the site studied (Fig. 2, blue modulus). The GARDENIA module, however, is outside the scope of this paper, and only the empirical hydrogeological module included in ALICE is used.

ALICE is able to use the PGA as a parameter of the seismic triggering factor. The values can come from the literature or a PGA map obtained using other software (e.g., Armagedom software, Sedan et al. 2013b).

3.1.6. Calculations and map production ALICE is able to produce (i) FoS maps and (ii) failure probability maps (i.e., the probability that FoS ≤1):

• (i) FoS maps are output when the user enters constant geotechnical parameter values (c', ϕ' and γ'); the FoS is evaluated for all possible sliding surfaces along each profile, and the smallest FoS value is attributed to the concerned cells

• (ii) Geotechnical parameters (c', ϕ' and γ') can be implemented with probabilistic distributions to take into account their spatial variability and their uncertainties. Probability distributions have to be defined by the expert and with the help of the literature if no survey or geotechnical test can be made. Different shapes of distributions can be used within ALICE, such as constant, uniform, triangular, trapezoidal, or Gaussian distributions [START_REF] Rohmer | Importance ranking of parameter uncertainties in geo-hazard assessments[END_REF]. Hence, ALICE conducts a random selection of each geotechnical value using the Monte Carlo method. For each geotechnical parameter drawn, an FoS map is calculated as in (i). Once all maps are calculated, the probability that the FoS is below 1 (i.e., of failure) is attributed to each concerned cell. slopes [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF](Thiery et al., , 2017b) ) Layer 2: Defined by expert knowledge [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF](Thiery et al., , 2017b) ) Geotechnical parameters

Cohesion

Depending on the material ( The elevation (DTM) is obtained by the interpolation of a network of triangle triplets issued from the digitization of elevation lines from 1:25 000 scale topographic maps enlarged by the French Geographical Institute at 1:10 000 scale [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF]. The elevation accuracy is validated by several statistical tests with DGPS point control, elevation lines and first derivatives (slope and aspect). The strategy to validate the DTM is described in [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF]. The 10 m DTM, produced in 2007, has been locally corrected to obtain a prelandslide relief [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF][START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF]. To obtain the 2D profiles needed for the stability analysis, the slope map, the flow direction map and the flow accumulation map are computed following classical derivative equations of ArcGIS. A detailed review of the calculation principles for flow direction and flow accumulation can be found in [START_REF] Burrough | Natural Objects With Indeterrminate Bondaries[END_REF].

Two elevation rasters provide different base thicknesses of the materials: (i) layer 1, representing the base of the surficial formations, and (ii) layer 2, representing the base weathering materials under the surficial formations.

Layer 1 is initially obtained by subtracting the thickness class of the surficial formations from the DTM [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF]. Layer 2, representing the weathered materials under the surficial deposits, is obtained by considering a 3 m weathered thickness, which is generally observed in the field area [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF]. Below the weathered materials, the substratum is considered continuous and infinite.

The type of surficial formation (SF) is obtained by the segmentation of the landscape in homogeneous geomorphological macro areas closely associating facies and shape [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF]. The lithological map (LM) is based on the main lithological units observed on a geological map produced by the French Geological Survey (BRGM, 1974) at a 1:50 000 scale and completed by fieldwork and the analysis of aerial photographs.

Other variables

During the last thirty years, several geotechnical investigations have been performed all over the Barcelonnette basin [START_REF] Caris | Geophysical, geotecnical and hydrological investigations of a small landslide in the French Alps[END_REF][START_REF] Phan | Propriétés physiques et Caractéristiques des Terres Noires du Sud-Est de la France[END_REF][START_REF] Bibliography Antoine | Geological and geotechnical properties of the "Terres Noires" in southeastern France: Weathering, erosion, solid transport and instability[END_REF][START_REF] Buma | Finding the most suitable slope stability model for the assesment of the impact of climate change on a landslide in South East France[END_REF][START_REF] Maquaire | Une approche multidisciplinaire pour la connaissance d'un glissement-coulée dans les marnes noires du Callovien-Oxfordien -(Super-Sauze, Alpes-de-Haute-Provence, France)[END_REF][START_REF] Maquaire | Instability conditions of marly hillslopes: Towards landsliding or gullying? The case of the Barcelonnette Basin, South East France[END_REF][START_REF] Malet | Les 'glissements de type écoulement' dans les marnes noires des Alpes du Sud. Morphologie , fonctionnement et modélisation hydro-mécanique[END_REF][START_REF] Remaître | Flow behaviour and runout modelling of a complex debris flow in a clay-shale basin[END_REF][START_REF] Thiery | Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment To cite this version : HAL Id : hal-00276818 Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment[END_REF][START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF][START_REF] Remaitre | Morphologie et dynamique des laves torrentielles : Applications aux torrents des Terres Noires du bassin de Barcelonnette ( Alpes du Sud )[END_REF][START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF]Malet et al., 2007b).

They were carried out on weathered black marls, substratum and surficial formations (moraine deposits, colluviums). Table 5 shows the different values of geotechnical parameters collected and the retained values for this study. For the first calculation of the FoS, the simplest method is to use average values for the geotechnical parameters.

The order of magnitude of the density of a material is quite easy to determine according to its nature and bibliography. On the other hand, the friction angle and the cohesion are not always obvious to estimate because of the spatial heterogeneity. In the Monte Carlo calculations, these uncertainties can be taken into account using different types of distribution laws. Hence, a triangular law with a low amplitude will be used to describe the cohesion of a homogeneous marly formation, whereas a trapezoidal law with a large amplitude will be more adapted to estimate the cohesion of a moraine formation, which can be highly heterogeneous (mixture of fine and coarse materials) (Fig. 5).

Fig. 5. Example of geotechnical parameter distributions for moraines and weathered marls.

Triggering factors

In the last thirty years, several studies have attempted to correlate rainfall (volume and intensity) with landslide occurrences [START_REF] Flageollet | Landslides and climatic conditions in the Barcelonnette and Vars basins (Southern French Alps, France)[END_REF][START_REF] Thiery | Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment To cite this version : HAL Id : hal-00276818 Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment[END_REF]Malet et al., 2007b;[START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF][START_REF] Remaître | Regional Rainfall Thresholds for Shallow and Deep-Seated Mass Movements Triggering in the South Eastern French Alps[END_REF], but no specific thresholds have been found for each landslide type. Therefore, local analyses were carried out by back-analyses coupling field observations and hydrogeological and slope stability models [START_REF] Caris | Geophysical, geotecnical and hydrological investigations of a small landslide in the French Alps[END_REF][START_REF] Thiery | Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment To cite this version : HAL Id : hal-00276818 Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment[END_REF]Malet et al., 2007b;[START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF]. The results established the GWL as the main triggering factor for landslides up to 10 m deep occurring in surficial formations (morainic deposits and/or weathered black marls). The identified critical level was approximately 0.9 (ratio between the thickness of the surficial formations and the height of the GWL), meaning a GWL value corresponding to near the surface [START_REF] Caris | Geophysical, geotecnical and hydrological investigations of a small landslide in the French Alps[END_REF][START_REF] Malet | Triggering conditions and mobility of debris flows associated to complex earthflows[END_REF]Malet et al., , 2007b;;[START_REF] Thiery | Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment To cite this version : HAL Id : hal-00276818 Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment[END_REF]. Therefore, the groundwater level is fixed to 0.9 for each simulation (Table 4), corresponding to a water table level between 0.4 and 1.5 m under the topography following the thickness of the surficial formations.

Methodology

During the last decade, ALICE was used by the BRGM in French mountain areas [START_REF] Baills | Changing patterns in climate-driven landslide hazard: An alpine test site[END_REF][START_REF] Vandromme | A novel approach to integrate effects of vegetation changes on slope stability[END_REF][START_REF] Bernardie | Estimation of Landslides Activities Evolution Due to Land-Use and Climate Change in a Pyrenean Valley[END_REF]Thiery et al., 2017a) and West French Indies (Sedan et al., 2013c;Thiery et al., 2017b). Nevertheless, for each case study, large discrepancies were observed depending on the local context and expert knowledge. Here, a calibration methodology based on different steps is presented. The method should be applicable for different environments but also for other PBMs similar to ALICE.

The strategy is made: (i) to obtain representative failure slope types taking into account shallow and deep-seated landslides, (ii) to reduce the uncertainty linked to the environment, and (iii) to obtain reliable results representative of field observations. To achieve these objectives, three main steps are defined: (i) a calibration step focusing on landslide characteristics, (ii) a calibration step focusing on the probability calculations, and (iii) an evaluation step (Fig. 6). Steps (i) and (ii) are applied on a calibration area, approximately 11.5 km², representative of the different environmental conditions of the north-facing slope [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF], whereas the evaluation step is applied on a larger area of approximately 110 km².

At each substep and step, a series of reliability tests (Table 6), based on the methods proposed by [START_REF] Brenning | Spatial prediction models for landslide hazards: review, comparison and evaluation[END_REF], [START_REF] Beguería | Validation and evaluation of predictive models in hazard assessment and risk management[END_REF], [START_REF] Guzzetti | Estimating the quality of landslide susceptibility models[END_REF] and [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF], are computed between the landslide susceptibility simulated maps, the landslide inventory (i.e., landslide triggering area) and the expert landslide susceptibility map (ELSM). Once the reliability tests are accepted (Table 6), the best parameters are retained to be introduced into the following step or substep (Fig. 6). The susceptibility classes used for the various reliability tests are set according to thresholds conventionally used for stability analyses (Table 7; [START_REF] Kirsten | Significance of the probability of failure in slope engineering[END_REF]Kirsten, pack et al., 2001;;[START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF] Table 6.

Tests Description Equation

Computed with landslide inventory (triggering area) Relative error (ξ)

L L L O P Ο - = ξ

ROC-AUC

Receiver Operating Characteristic Curve [START_REF] Hanley | The Meaning and Use of the Area under a Receiver Operating Characteristic (ROC) Curve[END_REF] Step 1 is devoted to identifying the best landslide parameters to introduce into the model: the optimal slice size for all landslide types (which affect the precision and calculation time of the results) and the best representative scarp angle for shallow translational slides (Section 2.2).

Step 2 focused on the minimal number of Monte Carlo simulations and the probability distributions adapted for this alpine environment. In step 3, the best parameters for each landslide type, defined in steps 1 and 2, are integrated into the whole study area to calculate one susceptibility map for each landslide type for a fixed groundwater level of 0.9 (which is most likely to trigger landslides according to [START_REF] Caris | Geophysical, geotecnical and hydrological investigations of a small landslide in the French Alps[END_REF], [START_REF] Thiery | Strategy to Reduce Subjectivity in Landslide Susceptibility Zonation by GIS in Complex Mountainous Environments[END_REF][START_REF] Thiery | Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment To cite this version : HAL Id : hal-00276818 Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment[END_REF] and [START_REF] Malet | Triggering conditions and mobility of debris flows associated to complex earthflows[END_REF]Malet et al. ( , 2007b))).

Results

Landslide calibration step

For each calibration step, several landslide susceptibility maps were computed and assessed according to the strategy (Fig. 6). Fig. 7 presents the results of the reliability tests computed for each substep, which shows the most significant analyses of the achieved accuracy. More details are explained within the next subsections. The first substep aims to identify the best size of slices for stability calculation. Three landslide types with different lengths and geometries are retained for this step: translational landslides with lengths of 30 m and rotational landslides with lengths of 60 m and 120 m. Five and six slices were chosen from 0.5 to 20 m (Fig. 8). Fig. 7a shows that, for the three landslide types, for slices from 20 to 5 m, the accuracy of the computed maps is improving and no longer evolves from 1 m to 0.5 m slices. Therefore, to optimize the calculation time and to be the more precise, the 1 m value is retained for other simulations. The second substep should assess and diagnose the best-adapted scarp angle to approximate the geometry of shallow translational failure. Following this angle value, the internal forces computed for each slice are not the same, and the simulated unstable area could be modified. Several series of simulations are carried out with different scarp angles (i.e., 10°, 30°, 45°, 60° and 90°). The results are shown in Figs. 7B and9. For simulations calculated with low scarp angles (<10°), the relative error is very high, and small areas are computed as unstable. For simulations computed with very high scarp angles (>60°), the relative error is very low (Table 8). The user could consider this result to be satisfactory, but the simulated maps (Fig. 9) show large areas computed as unstable (72% of the surface), but it is not realistic from a physical and geomorphological point of view. Regarding the ROC-AUC value results, the optimal result is obtained with angles between 30° and 45°, with values of 0.73 and 0.75, respectively. The simulated maps are very similar, with 16.5% and 20.7% of the areas computed as unstable for angles of 30° and 45°, respectively (Table 8). Finally, an angle of 45° is retained to approximate the more representative geometry of shallow translational failure. This value is the best compromise between expert knowledge, statistical tests and simulated maps. The third substep consists of robustness in reducing the uncertainty linked to the geotechnical characteristics of an environment. The accuracy of the Monte Carlo simulations depends on the number of simulations [START_REF] Kalos | Monte Carlo Methods[END_REF]. In other words, the higher the number of simulations run, the more accurate the probabilities and estimations will be. This step defines the minimum number of random samplings to obtain stable results about landslide failure probabilities (i.e., FoS ≤ 1). Indeed, a small number of random samplings with the same probability distribution give different results, with probability differences of more than 50% for the same cell. To overcome this point, several series of simulations of the geotechnical parameters with a range from 10 to 20,000 random samples by Monte Carlo simulation are conducted. The distribution defined for each simulation was based on triangular distributions for each geotechnical value of each surficial formation and the associated thicknesses.

Twenty-one maps are produced for each landslide type. The different accuracy tests (Table 9 and Figs. 7d and10)

show a first step at approximately 1,000 random samples and a second step at approximately 10,000 random samples. In general, from 10,000 random samples, the discrepancies between the results are below 1%, except for the shallow translational landslides for which the largest differences are observed, especially in areas where slope angles change abruptly. Therefore, 10,000 random samples are considered a minimum to obtain robust results for rotational landslides and complex landslides and 20,000 samples for shallow translational landslides. between maps obtained with 10 000 simulations and 1000 simulations, c) difference between maps obtained with 10 000 simulations and 5 000 simulations, and d) difference between maps obtained with 10 000 simulations and 501 9 000 simulations.

502

Table 9 503

Reliability test comparison for different Monte Carlo simulations for different landslide types in the calibration 504 area.

because of the ease of investigation/sampling at shallow depths and the visual observations that experts can make on the ground. Hence, the triangular distribution adjusted by the expert relates well with reality. Overall, the differences between the indexes are very small between the 2 types of distribution. After calibration, the best-fitted parameters are applied to all of the north-facing slopes of the Barcelonnette basin, and three landslide susceptibility maps (shallow translational landslides, rotational landslides and complex landslides) representing the landslide probability occurrences for a GWL of approximately 0.9 are computed (Fig. 12). The evaluation of the ALICE map is performed by the same index calculations used previously. Fig. 12 shows the map and index values for each landslide type. The detection rate of the landslide-simulated susceptibility map by comparison with the existing landslide inventory is very satisfying, with relative errors of 0.25, 0.29 and 0.40 for shallow translational, moderately deep rotational and complex landslides, respectively. The shallow translational numerical simulation shows a better approximation of the real observational data (ROC-AUC and CCR approximately 0.8 and ξ approximately 0.25). For the two other landslide types, we can notice that the index stays in the ideal good fit area (Fig. 12). Even if some errors remain, the majority of the landslides are well detected, which is an interesting result for a large and complex study area. By comparing Figs. 11 and12D, we notice that the modeling performance is still correct for all area applications. Indeed, the statistical indexes are in the same range of magnitude. , 1999). Thus, a unified landslide occurrence probability was produced by combining each landslide occurrence probability map computed for each phenomenon. The different classes of the landslide occurrence probability maps were merged by giving priority to the highest probability class for each cell independent of the type of landslide (Fig. 13). In parallel, for each cell, the information about the different probability of failure of each phenomenon is stored in a database, allowing a certain traceability.

The evaluation was performed by comparing the different surfaces of the very high and high probability of failure with the different ELSM classes and the highest ELSM class with the different probability of failure classes (Fig. 14). This map shows that the same high-susceptibility sectors are identified by both approaches with correct classification rates of 0.8, 0.79 and 0.77 for shallow translational, moderately deep rotational and complex landslides, respectively. Nevertheless, some areas are more extensive on the ELSM; this is why the Kappa index, computed taking into account all the susceptibility classes, is between 0.55 and 0.4. Thus, the ALICE approach provides a finer mapping of potentially unstable areas by taking into account parameters that are not always possible to integrate into an expert map, such as the groundwater level in different surficial formations or the geotechnical values of landslide-prone formations.

Fig. 14. Representation of areas detected by the ALICE approach and the expert map (ELSM, [START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF]

Discussion

Producing landslide susceptibility numerical maps by failure modeling probabilities with a spatialized physicalbased model has become, in the last 15 years, one of the most widely used means to ascertain landslide susceptibility in a quantitative way [START_REF] Reichenbach | A review of statistically-based landslide susceptibility models[END_REF] for small and large catchments [START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF][START_REF] Thiery | Improvement of landslide hazard assessments for regulatory zoning in France: STATE-OF-THE-ART perspectives and considerations[END_REF] Recent studies have highlighted (i) the interest in producing one map by type of phenomenon because each landslide type has its own predisposing and triggering factors [START_REF] Van Westen | Landslide hazard and risk zonation -Why is it still so difficult?[END_REF] and (ii) the integration of the environmental uncertainties by a probabilistic approach integrated in the physicalbased model (Sedan et al., 2013a;Mergili et al., 2014a).

The goal of this study was to present ALICE, taking into account these two components through a well-known open-air laboratory for landslide research. The tool allows the selection of all the parameters depending on the study site and influences the different landslide types (shallow or deep; rotational or translational). If the tool is complete, it is necessary to set the models to obtain reliable results. The adopted methodology has benefited from the experience (geomorphological, geotechnical, mapping, inventory) previously acquired in the catchment to test all the parameters one by one and to orient the results according to field observations. Thus, if the results show a good adequacy between the landslide inventory and the landslide susceptibility map produced by the expert approach, it appears necessary to discuss (i) the reliability of the results and (ii) the comparison of the results with previous works obtained with methods taking into account physical processes.

Consideration of the reliability of the results

The methodology adopted consists of (i) calibrating the model on a small area by iteratively selecting the best parameters adapted to the site to reduce the number of characteristics and some uncertainties linked to the complex environmental context and (ii) to applying the best-fitted parameters on the whole area. While the methodology is not new in itself and has already been used for other studies on landslide susceptibility mapping methodologies [START_REF] Chung | Validation of spatial prediction models for landslide hazard mapping[END_REF][START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF], it is rarely used for PBMs.

With a relative error of 0.21, 18 and 0.15, an ROC-AUC of 0.75, 0.69 and 0.75 and a correct classification rate of 0.63, 0.70 and 0.62, for shallow translational, moderately deep rotational and complex landslides, respectively, the results obtained on the calibration area can be considered good. These parameters, applied for the entire site, allow equally correct reliability tests to be obtained. For instance, by comparison with the landslide inventory, the relative error is 0.25, 0.29 and 0.40 for shallow translational, moderately deep rotational and complex landslides, respectively. The comparison between the final ALICE results and the ELSM also demonstrates that the same high-susceptibility sectors are identified by both approaches with correct classification rates of 0.8, 0.79 and 0.77 for shallow translational, moderately deep rotational and complex landslides, respectively. To obtain such results, it was necessary to multiply the random sampling by Monte Carlo draws because between a small number of draws and a large number, it is possible to have more than 50% difference in the same calculation cell. The Monte Carlo theory is based on the law of large numbers [START_REF] Rohmer | Importance ranking of parameter uncertainties in geo-hazard assessments[END_REF], and because a wide range of geotechnical values was used, it is essential to proceed to a large number of random samplings to minimize uncertainties. Thus, the minimum number of random samplings is fixed at 10,000.

However, despite the good results, some areas are subject to questioning because they are not well recognized in very high or high susceptibility classes by the final simulated map, especially some covered by complex landslides. Indeed, this type of phenomenon may have a roto-translational initiation difficult to integrate in ALICE, and because this type of phenomenon is deep, it is possible that the simplification of the regolith (Layers 1 and 2) and the GWL has an influence on our models and final results. Three main reasons were identified:

(i)

The thickness of the surficial formations was spatialized according to outcrop observations in the field and the DTM slopes. The methodology used to compute the thickness assumes a strong relationship between the thicknesses observed and the associated slope angles. Therefore, a great simplification was made, which is the reason why some areas are not well simulated as susceptible to slope instabilities, while on the ELSM, these areas are identified as highly susceptible. Finally, the identified errors for the surficial formation thickness are localized, especially on steep slopes. This has very few impacts on the different simulations because the modeled thicknesses on these slopes are very thin and the different parameters introduced into ALICE by the expert do not take into account the type of training on these slopes.

(ii) As the surficial formation data, a great simplification was performed for the weathered materials (i.e., thickness of 3 m). Mapping this type of formation over large areas is very complex, especially when very extensive morainic deposits cover slopes. It is obvious that the weathered material thickness varies and may be thicker or thinner. This information is confirmed locally by previous drilling [START_REF] Caris | Geophysical, geotecnical and hydrological investigations of a small landslide in the French Alps[END_REF][START_REF] Remaitre | Morphologie et dynamique des laves torrentielles : Applications aux torrents des Terres Noires du bassin de Barcelonnette ( Alpes du Sud )[END_REF] but integrating and extrapolating this local information remains difficult for a large area of approximately 100 km². One way to obtain spatial information on the type and thickness of the regolith would be to use airborne geophysics. The results can be satisfactory in complex environments [START_REF] Baron | Airborne geophysical survey of the catastrophic landslide at Stoẑe, Log pod Mangrtom, as a test of an innovative approach for landslide mapping in steep alpine terrains[END_REF][START_REF] Supper | Airborne geophysical mapping as an innovative methodology for landslide investigation: Evaluation of results from the Gschliefgraben landslide, Austria[END_REF]Thiery et al., 2017a).

(iii) Concerning the hydrogeological aspect, ALICE is based on a homogeneous approach with only one water table level extrapolated over the entire study area. However, the hydrogeological impacts are complex between morainic deposits and weathered marls (Van Asch and [START_REF] Van Asch | Modelling groundwater fluctuations and the frequency of movement of a landslide in the Terres Noires region of Barcelonnette (France)[END_REF][START_REF] Van Asch | A view on some hydrological triggering systems in landslides[END_REF]Malet et al., 2007b). Therefore, it is difficult to simulate the local effects of subsurface water due to preferential flow paths for large catchments. In this way, thanks to other studies on this site (i.e., [START_REF] Caris | Geophysical, geotecnical and hydrological investigations of a small landslide in the French Alps[END_REF][START_REF] Thiery | Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment To cite this version : HAL Id : hal-00276818 Test of Fuzzy Logic Rules for Landslide Susceptibility Assessment[END_REF]Malet et al., 2007b;[START_REF] Gance | Permanent electrical resistivity measurements for monitoring water circulation in clayey landslides[END_REF] about the role and behavior of water in those clayey and morainic environments, it has been possible to simplify the GWL and to fix it at 0.9 (water table level between 0.4 and 1.5 m under the topography following the thickness of the surficial formations).

However, if these values are valuable for shallow translational and moderately rotational landslides, they remain more complex for complex landslides (Malet et al., 2007b;[START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF].

Despite the simplifications, we note that the results, acquired with the different data used for previous studies in this area or specifically used for this study and the specific methodology, are able to detect the majority of slope instabilities. Compared with the expert landslide susceptibility map, the results are more precise and integrate a triggering component. obtained with ALICE without sensitivity analysis [START_REF] Baills | Changing patterns in climate-driven landslide hazard: An alpine test site[END_REF], and c) landslide occurrence probability for all types of landslides simulated with ALICE for this study.

Several landslide susceptibility maps produced by different methods for the Barcelonnette Basin were proposed during the last 15 years (Fig. 15). Few have used physical-based models with the integration of geotechnical information and the GWL to compute numerical maps. Malet et al. (2007a) and [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF] attempted to introduce geotechnical information and triggering factors (i.e., GWL) to produce such a map by a procedure coupling the data-driven method with the physical-based method. [START_REF] Baills | Changing patterns in climate-driven landslide hazard: An alpine test site[END_REF] proposed a first try using ALICE. These works were exploratory, but they deserve a comparison with this study.

For the first case (Malet et al., 2007a;[START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF], the method used was split into two steps with a susceptibility map produced by a data-driven method (bivariate method) to locate the main susceptible source areas on the hill slopes [START_REF] Thiery | Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment[END_REF]. The model simulates the relationship between factors controlling landslide location and the past and present landslide distribution. Second, their triggering probabilities are simulated with a coupled hydrology-slope stability model based on critical rainfall thresholds identified through Monte Carlo simulations (Malet et al., 2007a). Two types of landslides were taken into account with rotational and complex landslides, and a landslide hazard map was proposed following a focus on the highest landslide susceptibility class (Fig. 15a). For the second case, [START_REF] Baills | Changing patterns in climate-driven landslide hazard: An alpine test site[END_REF] used ALICE for rotational landslides with a length of 50 m. They used ALICE in a very simple way by only calculating the FoS (Fig. 15b). Thus, they did not perform a sensitivity analysis on different parameters to take into account environmental uncertainties.

Obviously, the results of these two previous studies differ from those acquired here. This is particularly true for the areas located in moraines covering flyschs for the first case or for areas located on badlands carved in weathered black marls, marls covered by moraines and denudated flyschs for the second case (Fig. 15). For the first, the differences are due to the initial susceptibility computation method taking into account the past and present event density per class of spatial data. Because, there are few complex landslides located on flyschs covered by moraines, the susceptibility map computed with the data-driven method shows a very low susceptibility for these slopes.

Thus, as the method integrates the results obtained with the hydrology-slope stability model in the highest susceptible areas, the slopes located on the flyschs covered by the moraines are not identified (Fig. 15a). For the second case, the differences are due to the parametrization of ALICE with (i) an oversimplification of the geotechnical model (e.g., especially the thickness of the regolith with wrong thicknesses of colluviums and weathered materials, mismatch with the type of surficial formations, erroneous geotechnical values), (ii) the use of one type of landslide with different characteristics (length and deepness), and (iii) the minimum number of random samplings, which was not tested (Fig. 15b).

Thus, by paying attention to the types of phenomena to take into account, their morphometric characteristics, by integrating appropriate geotechnical characteristics (i.e., geotechnical values and thicknesses) and the right Monte Carlo simulations, it has been possible to improve the results and to focus on the truly potentially unstable sectors (Fig. 15c). Beyond the fact that the methodology used in this study has optimized the results for each type of landslide and the number of simulations for this basin, this type of step-by-step methodology based on calibration area should be implemented for each site with a complex geomorphology and a large environmental heterogeneity.

Conclusion

The implementation of a landslide susceptibility analysis in a complex and heterogeneous environment over large areas faces two major challenges: (i) taking into account different slope failures (in terms of shape and depth) and

(ii) taking into account the uncertainty of the geotechnical parameters due to inherent spatial variability. The aim of this article was to present the landslide susceptibility analysis tool ALICE (Assessment of Landslides Induced by Climatic Events). The specific performances of ALICE notably concern (i) the GIS structure, (ii) the possibility of simulating different types of landslides (shallow translational, moderately deep rotational and complex), (iii) the processing uncertainties, and (iv) the possibility of working from mesoscale to large scale (1:25 000 -1:5 000) depending on data resolution. Thanks to a specific parameter calibration strategy, it provides the uniformity of a standardized approach.

The model and its calibration were applied on a study site located in the French South Alps. After calibration on a small area (11.5 km²), the best-fitted parameters were applied to all the north-facing slopes of the Barcelonnette basin (110 km²). Finally, three landslide susceptibility maps (shallow translational landslides, rotational landslides and complex landslides) represent the landslide probability occurrences for one conservative scenario with high GWL corresponding to antecedent local studies (Fig. 13). The detection rate of the landslide-simulated susceptibility map with the existing landslide inventory is very satisfying. Moreover, the comparison with the ELSM shows that the procedure used here with ALICE provides a finer mapping of potentially unstable areas by taking into account parameters that are not always possible to integrate into an expert map, such as the groundwater level in different surficial formations or the geotechnical values of landslide-prone formations.

Thus, in any case, to establish realistic modeling with ALICE, several minimum observational and geomorphological data are needed, such as an exhaustive landslide inventory over a long time and a threedimensional lithological model (with good knowledge of the spatial variation in the surficial material depth). If more data are available (expert susceptibility maps, water level maps, etc.) the simulations would be better and more precise. Recently, ALICE was used in different mountainous, plateau and tropical environments at different scales with success using empirical scenarios of the GWL and the strategy described in this research [START_REF] Vandromme | A novel approach to integrate effects of vegetation changes on slope stability[END_REF][START_REF] Bernardie | Estimation of Landslides Activities Evolution Due to Land-Use and Climate Change in a Pyrenean Valley[END_REF]Thiery et al., 2017a). It is now necessary to go further in the hazard analysis by (i) analyzing triggered precipitation, (ii) introducing climate change scenarios [START_REF] Bernardie | Modelling landslide hazard under global change : the case of a Pyrenean valley[END_REF] or (iii)

coupling ALICE with a simple propagation model to produce detailed landslide hazard maps.

Fig. 1 .

 1 Fig. 1. Presentation of the study site: a) Barcelonnette location; b) location of the active landslides, the calibration and the validation areas in the Barcelonnette basin; c) shallow translational landslide; d) moderately deep rotational landslide; and e) complex landslide.

Fig. 2 .

 2 Fig. 2. ALICE concepts and principles: a) modular structure of ALICE coupled with the hydrogeological module GARENIA, b) example of 2D profiles computed with ALICE and extraction of the lithological layer for one

Fig. 3 .

 3 Fig. 3. Characterization of the translational landslide geometry in ALICE. The scarp angle, α, represents the angle defined by the expert to represent the limit of the translational failure.

Fig. 2

 2 Fig. 2 presents an overview of the modular design of the model and different operating principles. Table2 provides

Fig. 4 .

 4 Fig. 4. Input data maps: a) slope, b) surficial formations, c) thickness materials, d) lithology, e) flow direction, f)flow accumulation, g) weathered marl thickness, and h) expert landslide susceptibility[START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF].3.2. Materials3.2.1. Spatial variablesEight classes of spatial variables are used (Fig.4). Four are derived from the initial topography with (i) the elevation data (DTM), (ii) the slope degrees, (iii) the flow direction, and (iv) the flow accumulation. Two classes represent the depth of different materials above the substratum with (v) the surficial formation thickness (Layer 1) and (vi) the weathered lithology thickness (Layer 2). Finally, two classes depict the type of lithology and surficial formations with (vii) the surficial formation type (SFT) and (viii) the lithological type (LT) (Table4, Theme

Fig. 6 .

 6 Fig. 6. Strategy for the calibration and validation of landslide susceptibility maps computed with ALICE

  Reliability tests used to assess the different computed landslide susceptibility maps: OL is the observed landslide cells (number of cells representing the landslide triggering area); PL is the predicted landslide cells (number of cells predicted in the high and very high susceptibility class -FoS ≤1); N is the number of cells in the study area; a = True positives (number of cells with FoS<1 and contained in observed landslide cells); b = False positives (number of cells with FoS<1 and not contained in observed landslide cells) ; c = False negatives (number of cells with FoS>1 and contained in observed landslide cells); and d = True negatives (number of cells with FoS>1 and not contained in observed landslides cells).

  between the landslide occurrence probability and landslide triggering areas. The Area Under the Curve (AUC) equals 1 for a perfect model and 0.5 for a purely random model. The area under the curve (ROC-AUC) is used to assess the success accuracy; the closer the ROC-AUC is to 1, the better the degree of fit of the model Computed with landslide expert susceptibility map

Fig. 7 .

 7 Fig. 7. Results of different accuracy and statistical tests on the calibration area: a) slice size influence for each landslide type, b) ROC curve example for shallow translational simulation with different scarp angles, c) influence of the Monte Carlo random simulations on relative error, and d) difference of the very high and high probability of failure (p > 0.05) surface according to the number of Monte Carlo simulations for shallow translational landslides.

Fig. 8 .

 8 Fig. 8. Simulated maps with different slice sizes for shallow translational landslides (4 m max depth; 30 m length): a) landslide susceptibility map computed with a slice size of 1 m and b) landslide susceptibility map computed with a slice size of 10 m.

Fig. 9 .

 9 Fig. 9. Influence of scarp angle value for shallow translational landslides (4 m max depth; 30 m length): a) simulated map computed with a scarp value of 10°, b) simulated map computed with a scarp value of 30°, c) simulated map computed with a scarp value of 45, and d) simulated map computed with a scarp value of 60°.

Fig. 10 .

 10 Fig. 10. Difference in probability values between maps obtained with different random sampling (Monte Carlo simulations): a) differences between maps obtained with 10 000 simulations and 10 simulations, b) difference

Fig. 11 .

 11 Fig. 11. Reliability tests and landslide susceptibility maps computed on the calibration area for each landslide type. The different landslide susceptibility maps are computed with 10 000 Monte Carlo simulations and triangular distribution. The reliability tests are carried out for different Monte Carlo simulations: a) results for shallow translational landslides, b) results for moderately deep rotational landslides, and c) results for complex landslides.

Fig. 12 .

 12 Fig. 12. Reliability tests and landslide susceptibility maps computed on the validation area for each landslide type. The different landslide susceptibility maps and reliability tests are computed with 10 000 Monte Carlo simulations and triangular distribution: a) results for shallow translational landslides, b) results for moderately deep rotational landslides, c) results for complex landslides, and d) reliability tests for each landslide susceptibility map.

Fig. 13 .

 13 Fig. 13. Landslide occurrence probability for all types of landslides simulated with ALICE

5. 2

 2 Comparison with previous landslide susceptibility maps taking into account physical parameters.

Fig. 15 .

 15 Fig. 15. Comparison with previous landslide susceptibility maps: a) landslide susceptibility map obtained by combination of the data-driven method and physical-based model (Thiery, 2007), b) landslide susceptibility map

Table

  Overview of existing hazard software for the implementation of spatial PBMs for slope stability evaluations

	122
	123
	Models/Code	Authors	Landslide	Slope	Temporal	Hydrological	Seismic	Probabilistic
					type	stability	component	component		approach
					modeled	method
	Acronym		Name
	SHALSTAB		SHAllow	(Montgomery	Shallow	Infinite	Static	Wetness Index	Not taken into	No
			Landslide	and Dietrich,	translational	slope		(Beven and	account
			STABility	1994;		(1D)		Kirkby, 1979)
			model	Dietrich and
				Montgomery,
				1998;
				Dietrich et
				al., 2001))
	SINMAP		Stability	Pack (1998);	Shallow	Infinite	Static	Topographically	Not taken into	Allows
			INdex	Pack et al.	translational	slope		based model	account	uniform
			MAPping	(2001);		(1D)		(Pack, 1998;		probability
				Thiebes et al.				Pack et al.,		distribution
				(2016)				2001)		of the
										variables
	TRIGRS	and	Transient	Baum et al.	Shallow	Infinite	Time	Transient pore	Not taken into	Yes (for
	TRIGRS-P		Rainfall	(2008); Raia	translational	slope	dependent	pressure	account	TRIGRS-P)
			Infiltration	et al. (2014)		(1D)		distribution
			and Grid					(Iverson, 2000)
			based
			Regional
			Slope
			stability
			model
	STARWARS +	STorage And	Van Beek	Shallow	Infinite	Time	Water level,	Not taken into	No
	PROBSTAB		Redistribution	(2002); Malet	translational	slope	dependent	effective degree	account
			of Water on	(2003); Malet	but adapted	(1D) +		of saturation,
			Agricultural	et al. (2005,	to particular	finite		bedrock storage
			and	2007a)	deep	slope(2D)
			Revegetated		contexts
			Slopes		(Malet,
					2003;
					Thiery,
					2007)
	CHASM (web-	Combined	Thiebes et al.	Circular and	Finite	Time	Water level,
	based GIS)		Hydrology	(2013)	complex	slope	dependent	infiltration
			And Stability			(2D)
			Model, Web-
			based GIS

Table 3 .

 3 Characteristics of the landslide initiation zone used for this study (from[START_REF] Thiery | Susceptibilité du Bassin de Barcelonnette (Alpes du sud, France) aux 'mouvements de versant' : cartographie morphodynamique, analyse spatiale et modélisation probabiliste[END_REF]

	Landslide	Main environmental characteristics of	Length	Max depth	Slope range (°)
	type	landslides initiation zones	range (m)	(m)
	Shallow	Relatively small and mainly located on steep	20-30	3	15-55
	translational	slopes or along streams. They occur on the
		weathered bedrock or at the contact of
		moraine deposits/bedrock
	Moderately	Located along streams but more on gentle	50-60	6	10-40
	deep	slopes than the shallow translational slides.
	rotational	They occur principally in moraine deposits,
	slides	sometimes at the contact between surficial
		deposits and bedrock
	Complex	Combination of rotational landslide	100-120	10	15-30
	slides with	(triggering area) and translational landslide
	rotational	(accumulation area). They occur mostly in
	initiation	thick moraine deposits and sometimes in the
		weathered marls which cover it
	3.3. Existing expert landslide susceptibility map

Table 2 .

 2 Data needed for ALICE

	Themes	Subthemes	Type of data and format
	Landslides	Type	To be integrated into the parameter
			interface -based on field experiences
		Morphometry (Length, L, Depth, D)
		Slice size
		Scarp angle
	Topography &	Elevation	Spatial data in raster format
	derivatives	Slope
		Flow direction
		Flow accumulation
	Geology	Lithology	Raster
		Surficial formations	Raster
		Thickness of different surficial	Raster
		formations
	Geotechnical	Cohesion
	parameters	Angle of friction
		Bulk unit weight
	Triggering factors	GWL (groundwater level)	To be integrated into the parameter
			interface
		PGA (peak ground acceleration)	Constant
	3.1.5. Triggering factors

The triggering factors are (i) the groundwater level (GWL) or (ii) the seismic peak ground acceleration (PGA)

Table 4

 4

	, Theme

Table 4 .

 4 Data used for landslide analysis with ALICE

	Themes	Subthemes	Unit	Type of	Values or classes	Source of information and
				data and	used for this	approach used to obtain
				format	study	them for this study
	Landslides	Type	--	To be	Translational or	Expert knowledge and field
				integrated	Rotational	observations (Thiery, 2007;
		Morphometry (Length, L, Depth, D)		into the parameter interface -based on		Schlögel et al., 2015)
				field
				experiences

Table 5

 5

		Defined according to the
	)	literature based on field
		investigations

Table 5 .

 5 Geotechnical data collected and retained for the study

	Formation Type of	Values based on the literature * and	Value introduced in ALICE
		formations	slope stability analyses by LEM **		(*** values voluntarily increased to fix
									the bedrock limit conditions)
			Cohesion -c' (kPa)	Friction angle -ϕ' (°)	Specific bulk unit weight -γd (kn.m -3 )	Cohesion -c' (kPa)	Friction angle -ϕ' (°)	Specific bulk unit weight -γd (kn.m -3 )
			Min Max Min Max Min Max Min Max Min Max Min Max
	Surficial	Moraine	5** 21* 17	32	13	21	5	21	17	32	13	21
	formations	deposits
		Reworked	8** 21* 17	28	14	21	8	21	17	28	14	21
		morainic
		deposits
		Moraine	2	21	22	32	12	16	2	21	22	32	12	16
		colluvium
		deposits
		Marly	10	22	31	36	12	16	10	22	31	36	12	16
		colluvium
		deposits
		Other	10	18	23	25	13	17	10	18	23	25	13	17
		colluvium
		deposits
		Highly	6	16	27	33	13	15	6	16	27	33	13	15
		weathered
		marls
	Weathered	Weathered	12	16	27	34	14	16	12	16	27	34	14	16
	materials	marls type
		01
		Weathered	6	17	34	39	11	14	6	17	34	39	11	14
		marls type
		02
	Substratum Flysch	25	120 34	42	30	31	200***	50***		30***
		Black	30	100 30	45	19	20	200***	50***		30***
		marls

Table 8

 8 Influence of the scarp angle on results

		Scarp angle value (°)
		10	30	45	60	90
	Relative error	0.64 0.35	0.2	0.08	0.035
	ROC-AUC	0.69 0.73	0.75	0.70	0.63
	Surface computed with FoS ≤ 1	3.8	16.5	20.7	72.0	89.2
	(in % of area)
	4.2. Calibration probabilities step
	4.2.1. Influence of Monte Carlo simulations

in only one material (the surficial formation layer). Moderately deep rotational and complex landslides are longer

and deeper and cross several layers. Being on the surface, the surficial formations can be well characterized


A Leurent

M Sanglier

M Rouez

R Moscoviz

R Escudie

F Guilayn

BIOCHAR FOR ENCHANING ANAROBIC DIGESTION OF FOOD WASTE

Keywords: Biogas, biomethane, biowaste, propionate, pyrolysis 2. Highlights

• Preliminary results from a meta-analysis on AD enhancement by biochar addition • Biochar seems effective even at lowest dosages • Performance amelioration seems more significant with high substrate loading rates

• Lack of biochar characterization jeopardizes the evaluation of process mechanisms

Purpose

Anaerobic digestion (AD) is recognized as one of the most energy-efficient and environmentally beneficial technologies for treating and transforming organic residues into biomethane (energy) and digestate (fertilizer) [START_REF] Capson-Tojo | Addition of biochar and trace elements in the form of industrial FeCl 3 to stabilize anaerobic digestion of food waste: dosage optimization and long-term study: Biochar and trace elements (industrial FeCl 3 ) to stabilize anaerobic digestion of food waste[END_REF][START_REF] Guilayn | Valorization of digestates from urban or centralized biogas plants: a critical review[END_REF]. However, AD of highly concentrated and biodegradable substrates such as FW is prone to failure if not properly managed. The main issue is the accumulation of biological inhibitors such as free ammonia and volatile fatty acids [START_REF] Capson-Tojo | Addition of biochar and trace elements in the form of industrial FeCl 3 to stabilize anaerobic digestion of food waste: dosage optimization and long-term study: Biochar and trace elements (industrial FeCl 3 ) to stabilize anaerobic digestion of food waste[END_REF]. Recently, conductive material addition as biochar in AD reactor has been proven to trigger microbial enhancement, electron transfer among syntrophic consortia, ammonia/organic acid tolerance, providing buffering capacity and globally improving biogas production kinetics [START_REF] Qiu | A review on biochar-mediated anaerobic digestion with enhanced methane recovery[END_REF]. Addressing a major scientific gap, the objectives of this meta-analysis are to clarify such mechanisms and identify optimal biochar characteristics and doses as an additive for the enhancement of food waste AD.

Materials and methods

This review is based on a literature exploration using the query ("anaerobic digestion" AND ("food waste" OR "biowaste") AND "biochar") in title and abstract and performed in ScienceDirect for peer-reviewed articles since 2000. The resulting articles were then manually screened by title and abstract. Experiments dealing with organic substrate other than sourceseparated biowaste were excluded (notably agricultural residues and sewage sludge, except for some co-digestion cases). For each article, the information summarized in Table 1 was extracted or calculated from the available information if possible, and then organized as a database where each line represents a single experimental condition from each study. This ongoing work has resulted so far in a library of 11 peer-reviewed articles (list available under request) representing a database of 72 experimental conditions (including control tests without biochar).

Results and discussion

As can be observed in Figure 1, left: improvement of CH4 rate max range from 0 to 150%; right: reduction of time to reach plateau range from 0 to 50%. Biochar doses inferior to 10 g.L - 1 always improved maximum methane rate. Increasing the biochar dosage tended to attenuate this advantage, although kinetics remained at least equal to control conditions for all biochar doses (Figure 1, left).

Another glaring observation is that the reduction of time to reach CH4 plateau 1 increases with S/X (substrate over inoculum ratio). It is possible that this observation would be explained by the improvement of volatile fatty acids syntrophic oxidation and microbial activities [START_REF] Wang | Redox-active biochar facilitates potential electron tranfer between syntrophic partners to enhance anaerobic digestion under high organic loading rate[END_REF]. Several biochar quality parameters could clarify mechanisms for AD enhancement, such as atomic O/C ratio, cation exchange capacity, electrical conductivity, electron donating/accepting capacity (redox capacity) [START_REF] Chiappero | Review of biochar role as additive in anaerobic digestion processes[END_REF][START_REF] Masebinu | A review of biochar properties and their roles in mitigating challenges with anaerobic digestion[END_REF][START_REF] Viggi | Enhancing methane production from food waste fermentate using biochar: the added value of electrochemical testing in pre-selecting the most effective type of biochar[END_REF][START_REF] Wang | Redox-active biochar facilitates potential electron tranfer between syntrophic partners to enhance anaerobic digestion under high organic loading rate[END_REF][8][9]. The identified articles so far provided poor biochar characterization. Thus, the underlying mechanism of FW AD improvement by biochar are still unclear.

Conclusions and perspectives

Biochar can be an expensive material (up to 500 -2000 €/t). The preliminary results from this study suggest that biochar is mostly effective at low doses (<10 g.L -1 ). Biochar addition can thus be an attractive opportunity to enhance food waste AD while promoting carbon sequestration. The results will be confirmed by extending the database and performing further statistical analysis. In the future, an economic and environmental assessment is recommended. Additionally, it is expected that this work could set best practices in terms of biochar characterization for future experiments on AD enhancement by conductive material. 1 time for methane production curve to approach asymptote.

Table 1 -

 1 Overview of parameters selected for the meta-analytical study *the analysis included the variation of these parameters in the conditions with biochar compared to the control from the same study. a. Number of observations -b. Hydrogen to carbon ratio -c. Substrate to inoculum ratio in AD. OLR: Organic loading rate in AD.-VFA: Volatile fatty acids. COD: chemical oxygen demand. VS: volatile solids.

Figure 1 :

 1 Figure 1: Effect of biochar on AD performance. *Calculated as: 1 -(result by adding biochar to AD / results of control).