Keywords: Laves torrentielles, Analyse de susceptibilité, Contrôles morphométriques, Analyse discriminante linéaire, Régression logistique Debris-flows, Susceptibility analysis, Morphometric controls, Linear discriminant analysis, Logistic regression Hillslope erosion, mapping, multi-sources, multi-scales, infrared orthophotos

Ce premier chapitre expose le cadre géographique, conceptuel et méthodologique dans lesquel s'inscrit ce travail. Les caractéristiques physiographiques, géologiques et climatiques des Alpes du Sud, où sont appliquées les différentes méthodologies développées, sont décrites dans les trois premières sections. Le réseau hydrographique étudié est ensuite brièvement présenté en lien avec ces différents éléments contextuels. Les vulnérabilités et les enjeux de ce territoire sont ensuite introduites.

Le cadre conceptuel est détaillé en quatre sections afin de présenter les caractéristiques générales des laves torrentielles, de rappeler les conditions nécessaires au déclenchement, à la propagation et au dépôt de ce type de processus.

Enfin, les deux dernières sections de ce chapitre introductif décrivent les données utilisées, ainsi que les différentes méthodologies géomatiques et statistiques qu'il est possible de mettre en oeuvre.

Mes remerciements vont d'abord à Hervé Piégay, mon directeur de thèse, pour son soutien, ses conseils et son enthousiasme. Merci à Frédéric Liébault, mon encadrant, très enthousiaste également, qui a su m'entraîner dans sa passion pour les processus torrentiels. Je remercie mon école doctorale, l'ED483 et mon établissement d'inscription, l'ENS de Lyon. J'adresse des remerciements tout particulier pour les deux structures sur lesquelles j'ai été à cheval pendant ces trois ans (et demi) : l'Unité Mixte de Recherche 5600 (Environnement Ville Société) et l'IRSTEA de Grenoble (ETNA).

Je remercie l'Office National des Forêts, en particulier le service de Restauration des Terrains de Montagne, qui a fourni un travail très important dans le cadre du projet PARAmount.

Un grand merci à toutes les personnes avec qui j'ai pu avoir des échanges techniques intéressants : Lise Vaudor et Nicolas Eckert pour leurs conseils de statisticiens, Guillermo Castilla pour les discussions sur les procédures de segmentation des orthophotos, Bastiaan Notebaert et Loïc Grosprêtre, pour les échanges sur la délimitation des bassins versants.

Merci également à Jean-Marc Tacnet, grâce à qui mes travaux ont trouvé une application directe (merci à ses stagiaires) dans le domaine des transports (projet PARAmount). Je tiens à remercier également toutes les personnes rencontrées en colloques et avec qui j'ai été ravie d'échanger durant les sessions de posters.

Merci également à toutes les personnes ayant participé aux comités de thèse : Dominique Laigle (IRSTEA -ETNA), Pierre Javelle et Patrice Mériaux (IRSTEA -OHAX), Kenji Ose (UMR TETIS) dont les avis précieux ont guidé mon travail durant ces trois années.

Un grand merci à Karen Johnstone pour sa relecture de l'article sur la Drôme, qui en a grandement facilité la publication. Je tiens à remercier également S. Gregory, S. Hulse et O.

Oetter qui m'ont sollicitée pour écrire leur chapitre dans l'ouvrage [START_REF] Carbonneau | River Management and Remote Sensing[END_REF]. Enfin je remercie les relecteurs anonymes pour leurs commentaires très pertinents qui ont aidé à améliorer les articles soumis au cours de cette thèse.

Enfin, j'ai une pensée pour les personnes qui m'ont encouragée tout au long de ce travail, ma famille, mes amis, mes collègues. Merci à tous !

Sommaire -Contents

Remerciements

Introduction générale

Les territoires de montagne sont très souvent soumis aux aléas naturels, agissant parfois de manière combinée. La prise en compte des risques associés à ces aléas dans l'aménagement du territoire fait depuis longtemps l'objet de réglementations dans les Plans de Prévention des Risques, et de campagnes de communication à l'échelle nationale visant le grand public (http://www.prim.net). Ainsi, la problématique d'évaluation des aléas, particulièrement en montagne, a suscité de nombreuses études afin d'accroître la connaissance de ces phénomènes et de mieux savoir les prédire. De nombreux projets à l'échelle des régions vont dans ce sens. Des projets européens et inter-alpins (PARAMOUNT, RISKNAT, SEDALP, parmi tant d'autres) ont également été engagés pour la caractérisation et la prévention de ces aléas. Depuis quelques années, les études conduites visent aussi à caractériser les effets du changement climatique sur les aléas naturels afin de prédire leurs tendances et mieux étudier l'aggravation ou non des situations à risques [START_REF] Prudent-Richard | Changements climatiques dans les Alpes : Impacts et risques naturels[END_REF]. L'intégration de ces connaissances dans les analyses de risques est cruciale pour l'amélioration de leur gestion, aussi bien à long terme (aménagement durable du territoire, gestion préventive) qu'à très court terme (gestion de crise).

Les « laves torrentielles » se classent parmi les phénomènes les plus destructeurs, produisant le plus de dégâts et de victimes par rapport à leur emprise, à leur fréquence et à leur magnitude [START_REF] Jakob | Debris-flow Hazards and Related Phenomena[END_REF]. Des efforts importants ont été engagés depuis plusieurs années pour délimiter à l'échelle locale les terrains susceptibles d'être affectés par ces écoulements, et pour identifier leurs conséquences [START_REF] Lenzi | Long-term monitoring of bed-load and debris flows in two small alpine basins of different morphological settings[END_REF].

Néanmoins, ces approches ne sont pas transposables aux échelles régionales. Appliquées aux phénomènes torrentiels, le développement de telles approches est aujourd'hui nécessaire.

Une connaissance régionalisée de la susceptibilité à cet aléa est, en effet, indispensable pour mieux planifier l'organisation des secours en cas d'événements intenses, ainsi que pour réaliser des infrastructures efficaces (ouvrages de correction torrentielle, digues) pour lutter contre ce type d'événement.

Les apports sédimentaires provenant des laves torrentielles entrainent des modifications de la morphologie des lits des cours d'eau en aval [START_REF] Miller | Effects of punctuated sediment supply on valley-floor landforms and sediment transport[END_REF]. A l'échelle régionale, la mosaïque des styles fluviaux en est donc modifiée [START_REF] Liébault | Approches géomorphologiques de la production sédimentaire des torrents[END_REF], entrainant également des changements dans la distribution des différents habitats aquatiques et terrestres [START_REF] Bigelow | On Debris Flows, River Networks, and the Spatial Structure of Channel Morphology[END_REF][START_REF] Miller | A probabilistic model of debris-flow delivery to stream channels, demonstrated for the Coast Range of Oregon, USA[END_REF]. La gestion des milieux aquatiques nécessite là encore de se placer à une échelle plus large [START_REF] Piégay | System Approaches in Fluvial Geomorphology[END_REF] afin de prévoir leur durabilité. La production de jeux de données à l'échelle régionale, et le développement des méthodologies associées est donc encore un enjeu important.

Dans les Alpes du Sud, l'aléa « laves torrentielles » est encore mal connu malgré les travaux des services de Restauration des Terrains en Montagne (RTM, http://www.onf.fr) dans ce domaine et notamment le référencement des événements et des dispositifs de protection dans une base de données, régulièrement mise à jour par les services et archivant tous les évènements passés depuis plusieurs siècles. Les torrents susceptibles de déclencher CHAPITRE 1. INTRODUCTION des laves torrentielles sont pour la plupart connus de ces services, dans les secteurs à forte vulnérabilité. Cependant, l'identification des processus et la prédiction de leur intensité ne sont pas envisageables à l'échelle régionale à partir du recollement de ces données partielles.

Afin de limiter la vulnérabilité des territoires affectés par ces phénomènes, il est impératif de mieux identifier les sites les plus exposés aux écoulements torrentiels qu'il s'agisse de crues rapides ou de laves torrentielles.

Problématique et plan du manuscrit de thèse

L'objet de cette thèse, au coeur de tous les développements méthodologiques qui vont suivre, est la susceptibilité torrentielle, c'est-à-dire non pas l'étude physique du phénomène de lave torrentielle en tant que tel, mais plutôt l'étude de sa probabilité d'occurrence spatiale à l'échelle régionale. Cette étude s'inscrit dans une branche de la géographie (physique) appelée géomorphologie fluviale, voire torrentielle, et n'a pas pour objet l'étude de la vulnérabilité des territoires des Alpes du Sud.

Cette thèse comporte également un volet opérationnel important (elle s'inscrit dans le cadre du projet RHYTMME, http://rhytmme.irstea.fr/), puisque ce travail a conduit à une restitution spatiale de la susceptibilité torrentielle, qui une fois croisée avec les forçages hydro-climatiques ou les enjeux, permettra de produire des cartes d'aide à la décision en matière de gestion du risque torrentiel (mise en pré-alerte, cartographie des infrastructures exposées aux phénomènes torrentiels). Ce projet RHYTMME repose sur l'implantation de radars de nouvelle génération dans les Alpes du Sud dans le but de mieux couvrir les zones de montagne ; ceci a pour but de constituer, à terme, une plateforme d'avertissement des aléas naturels liés aux précipitations, afin de permettre aux acteurs locaux d'anticiper les événements dangereux et de mieux prendre en compte les risques montagnards.

Les apports scientifiques de cette thèse portent ainsi sur le développement d'une méthodologie géomatique qui vise notamment à identifier, au sein du réseau hydrographique régional, les types d'écoulements torrentiels dominants (laves torrentielles et charriage) et à définir et hiérarchiser l'activité géomorphologique du réseau à partir d'indicateurs propres à chaque type d'écoulement.

Les méthodes utilisées pour répondre à cette question systémique et régionale sont à la fois statistiques et géomatiques. A ces échelles, il est en effet impossible d'extraire à moindre coût les variables d'entrée nécessaires aux approches mécanistes. La caractérisation de l'érosion torrentielle à large échelle (> 50 km ) privilégie donc l'utilisation de modèles statistiques qui explorent la variabilité régionale des réponses torrentielles à partir du croisement d'inventaires phénoménologiques et de données à références spatiales (relief, géologie, occupation du sol). En géomorphologie, les méthodes géomatiques ont souvent montré leur pertinence pour la caractérisation physique des milieux [START_REF] Carbonneau | River Management and Remote Sensing[END_REF]. Ces méthodes présentent l'avantage de pouvoir être appliquées à des jeux de données spatialisées de grande taille, largement disponibles à l'heure actuelle.

Le travail de thèse s'intéresse plus particulièrement aux points suivants : [START_REF] Meyzenq | A propos de la limite Alpes du Nord -Alpes du Sud. Limites, pays de marge et organisation spatiale en montagne, évolution des concepts[END_REF]. Les Alpes du Sud en tant qu'ensemble régional présentent une certaine homogénéité, tant au niveau du climat, que des caractéristiques hydrographiques [START_REF] Blanchard | Régimes hydrauliques et climatiques. Alpes du Sud et ensemble des Alpes françaises[END_REF]. En

Conglomérats

Roches calcaires

Dolomite

Roches sédimentaires carbonatées Calcaires

Roches granitiques

Monzogranite Granitoïdes

Roches métamorphiques

Roches volcaniques

Volcanisme basique Volcanisme acide Roches ignées

Unités morphostructurales

Sources : BD ALTI®, GeoFLA®, © IGN Paris ; © BRGM

Influences climatiques

Les caractéristiques climatiques décrites ci-après sont issues de l'analyse des bases de données COMEPHORE et SAFRAN ré-analysées au pas de temps horaire [START_REF] Defrance | Adaptation et évaluation d'un système d'anticipation de crues éclair sur des bassins de montagne non-jaugés -Valorisation de relevés de dégâts[END_REF][START_REF] Defrance | Adaptation et évaluation d'un système d'anticipation de crues éclair sur des bassins de montagne non-jaugés -Valorisation de relevés de dégâts[END_REF]. Celles-ci recensent les lames d'eau radar et les données de neige, de température et de ratio pluie/neige.

Les climats que l'on peut observer sur le secteur d'étude (Figure 1 sont reconnus [START_REF] Defrance | Adaptation et évaluation d'un système d'anticipation de crues éclair sur des bassins de montagne non-jaugés -Valorisation de relevés de dégâts[END_REF][START_REF] Benda | Stochastic forcing of sediment supply to channel networks from landsliding and debris flow[END_REF][START_REF] Miller | Effects of punctuated sediment supply on valley-floor landforms and sediment transport[END_REF][START_REF] Stock | Erosion of steepland valleys by de-RÉFÉRENCES BIBLIOGRAPHIQUES bris flows[END_REF] [START_REF] Arnaud-Fassetta | La part respective des facteurs hydroclimatiques et anthropiques dans l'évolution récente (1956-2000) de la bande active du Haut Guil, Queyras, Alpes françaises du Sud[END_REF]. Un déficit sédimentaire important peut être à l'origine d'un enfoncement du lit de la rivière, comme sur la Drôme [START_REF] Liébault | Tributaries and the Management of Main-Stem Geomorphology[END_REF], et peut également causer la destruction d'infrastructures proches. L'identification des tronçons sensibles est donc un enjeu important pour améliorer la gestion des risques d'inondations.

Enjeux socio-économiques du territoire

Le territoire des Alpes du Sud est soumis à de nombreux dangers naturels, notamment aux instabilités de versants (éboulements, glissements, coulées) et aux crues torrentielles [START_REF] Remaître | Morphologie et dynamique des laves torrentielles : Applications aux torrents des Terres Noires du bassin de Barcelonnette (Alpes du Sud)[END_REF] [START_REF] Meyzenq | A propos de la limite Alpes du Nord -Alpes du Sud. Limites, pays de marge et organisation spatiale en montagne, évolution des concepts[END_REF].

Le patron géographique des infrastructures de transport correspond à celui de la densité de population (Figure 1.12). La répartition géographique des différents axes de transport est ainsi très inégale. De fortes densités s'observent dans les différentes vallées, notamment celle de la Durance, qui est l'axe privilégié de cette région, en raison du relief. D'autres facteurs expliquent cette disparité : sur le littoral comme au niveau des stations de ski des Hautes-Alpes, la forte densité des infrastructures est liée à l'activité touristique. Les laves torrentielles se produisent dans le lit des torrents. Ce sont « des cours d'eau de montagne à forte pente, s'inscrivant à l'amont d'un système fluvial dont ils assurent l'essentiel de la recharge sédimentaire. » [START_REF] Thénard | Torrents et torrentialité dans la vallée de la Guisane. Contribution d'une étude géographique à la gestion durable du risque torrentiel à Serrechevalier[END_REF]. La définition hydraulique retient un seuil de pente du talweg supérieur à 6% pour caractériser les torrents (Figure 1.13). Les laves torrentielles se définissent comme un mouvement de terrain, très fréquent dans les régions à fort relief, dont l'écoulement rapide s'effectue dans des chenaux torrentiels à fortes pentes [START_REF] Slaymaker | The distinctive attributes of debris torrents[END_REF]. Le terme « laves torrentielles » désigne un mélange fluide d'eau et de particules solides, montrant une hétérogénéité granulométrique très forte (les particules ont des tailles allant du micron jusqu'au mètre) et fortement concentré. En effet, la concentration peut excéder 0,5 en volume et 0,7 en masse [START_REF] Costa | Developments and Applications of Geomorphology[END_REF][START_REF] Coussot | Rhéologie des laves torrentielles[END_REF], ce qui leur confère des propriétés d'écoulement particulières (comportement fluide des matériaux). La matière organique, notamment les débris ligneux sont un composant important des dépôts de laves torrentielles (jusqu'à 6 % d'après [START_REF] Jakob | Debris-flow Hazards and Related Phenomena[END_REF]).

Gap

Nice

Cannes

Veynes

Manosque

Briançon

Barcelonnette

Digne-les-Bains

!

Villes principales

Départements

Mises en évidence et étudiées par de nombreux chercheurs depuis plusieurs dizaines d'années [START_REF] Tricart | Une lave torrentielle dans les Alpes Autrichiennes[END_REF][START_REF] Takahashi | Estimation of potential debris flows and their hazardous zones : Soft countermeasures for a disaster[END_REF][START_REF] Johnson | Debris flow[END_REF][START_REF] Vandine | Debris flows and debris torrents in the Southern Canadian Cordillera[END_REF][START_REF] Van Steijn | Morphological and mechanical aspects of debris flows in parts of the French Alps[END_REF] les laves torrentielles montrent des caractéristiques très spécifiques par rapport aux autres processus d'écoulements gravitaires en termes de déclenchement, de propagation et de dépôts, qui en font un type particulier de mouvement de terrain. Elles se différencient par :

1) le comportement rhéologique de l'écoulement [START_REF] Coussot | Rhéologie des laves torrentielles[END_REF], 2) le volume sédimentaire,

3) la teneur en eau , 4) la granulométrie des sédiments, 5) la chenalisation ou non et 6) la vitesse de déplacement [START_REF] Iverson | The physics of debris flow[END_REF][START_REF] Rickenmann | Empirical Relationships for Debris Flows[END_REF] (Figure 1.15). ni la probabilité d'occurrence temporelle [START_REF] Horton | Debris flow susceptibility mapping at a regional scale[END_REF]. L'analyse de susceptibilité met en lumière les facteurs de prédisposition d'un terrain. Elle est souvent utilisée aux échelles régionales comme une première étape de la caractérisation des aléas naturels en montagne, comme les glissements de terrain [START_REF] Conoscenti | GIS analysis to assess landslide susceptibility in a fluvial basin of NW Sicily (Italy)[END_REF] ou dans le cas de cette thèse les laves torrentielles [START_REF] Carrara | Comparing models of debris-flow susceptibility in the alpine environment[END_REF], pour dans un premier temps caractériser la sensibilité des variables physiques et climatiques, parfois appelées les facteurs de prédisposition [START_REF] Bovis | The role of debris supply conditions in predicting debris flow activity[END_REF] et facteurs de déclenchement [START_REF] Caine | The rainfall intensity -Duration control of shallow landslides and debris flows[END_REF]Fannin et Rollerson, 1993 ;[START_REF] Bonnet-Staub | Mécanismes d'initiation des laves torrentielles dans les Alpes françaises -Contribution à la maitrise du risque[END_REF][START_REF] Bardou | Méthodologie de diagnostic des laves torrentielles sur un bassin versant alpin[END_REF].

Lors des événements de laves torrentielles on peut distinguer trois phases : le déclenchement, la propagation et l'étalement qui correspondent à des conditions d'énergie différentes.

Quelques éléments conceptuels sont détaillés pour chaque phase dans les sections suivantes. [START_REF] Cannon | Wildfire-related debris-flow initiation processes[END_REF][START_REF] Larsen | Geologic versus wildfire controls on hillslope processes and debris flow initiation in the Green River canyons of Dinosaur National Monument[END_REF], les éruptions volcaniques [START_REF] Pareschi | Volcaniclastic debris flows in the Clanio Valley (Campania, Italy) : insights for the assessment of hazard potential[END_REF], les tremblements de terre [START_REF] Chen | The Critical Rainfall Characteristics for Torrents and Debris Flows in the Wenchuan Earthquake Stricken Area[END_REF] ou autres aléas naturels, en générant de grandes quantités de matériaux, peuvent aussi favoriser le déclenchement de laves torrentielles.

Déclenchement des laves torrentielles

Les aléas climatiques sont un facteur déclenchant des laves torrentielles. De nombreux articles dans la littérature mettent en relation leur déclenchement avec des événements météorologiques extrêmes tels des orages [START_REF] Berti | Field observations of a debris flow event in the Dolomites[END_REF]Fuchu et al., 1999 ;[START_REF] Godt | Alpine debris flows triggered by a 28 July 1999 thunderstorm in the central Front Range[END_REF] ou des cyclones [START_REF] Chen | Recent rainfallinduced landslides and debris flow in northern Taiwan[END_REF][START_REF] Chang | Analysing the relationship between typhoontriggered landslides and critical rainfall conditions[END_REF]. Ces forçages climatiques contrôlent la fréquence et la magnitude des événements. De nombreuses publications ont tenté de démontrer qu'il existe des seuils intensité / durée d'événement de fortes précipitations qui permettent le déclenchement de laves torrentielles [START_REF] Bacchini | Relations between rainfall and triggering of debrisflow : case study of Cancia (Dolomites, Northeastern Italy)[END_REF][START_REF] Chen | Rainfall duration and debris-flow initiated studies for realtime monitoring[END_REF][START_REF] Coe | Initiation conditions for debris flows generated by runoff at Chalk Cliffs, central Colorado[END_REF][START_REF] Guzzetti | The rainfall intensity-duration control of shallow landslides and debris flows : an update[END_REF][START_REF] Badoux | A debrisflow alarm system for the Alpine Illgraben catchment : design and performance[END_REF]Floris et al., 2010). Cependant, il reste un certain nombre de questions, en particulier concernant les conditions de saturation des matériaux précédant les événements (phase de préparation).

Les conditions météorologiques et hydrogéologiques précédant un événement à l'origine du transport de matériaux au sein d'un torrent semblent jouer un rôle prépondérant dans le déclenchement des laves, quand les facteurs morphométriques et géologiques prédisposent déjà à ce type d'événement.

Propagation

La vitesse d'écoulement des laves torrentielles est comprise entre 1 et 20 m/s [START_REF] Iverson | The physics of debris flow[END_REF] selon leur viscosité et leur composition. La propagation s'effectue par émission de bouffées intermittentes de composition variable et se manifeste sur une distance de quelques centaines de mètres à plusieurs kilomètres [START_REF] Meunier | Eléments d'hydraulique torrentielle[END_REF].

La quantification de la propagation a fait l'objet de nombreuses études tant le sujet est complexe. Les laves torrentielles entrainent avec elles des matériaux dans des sections raides et confinées, et les déposent dans des sections à plus faible pente et non confinées (Fannin et Rollerson, 1993). Le volume déposé est directement corrélé à la distance parcourue par les laves torrentielles [START_REF] Miller | A probabilistic model of debris-flow delivery to stream channels, demonstrated for the Coast Range of Oregon, USA[END_REF]. La quantité de sédiments entrainés par une coulée dépend également de l'occupation du sol : une lave torrentielle s'arrête plus facilement si elle traverse une forêt dont les arbres sont plus anciens et plus grands (ibid.).

Pendant cette phase de propagation, on observe un tri granulométrique longitudinal avec développement d'un front de propagation à particules grossières à l'aval [START_REF] Iverson | The physics of debris flow[END_REF].

Le front subit de fortes contraintes qui sont susceptibles de le stopper ; les changements de rugosité dans le fond du chenal, ou des variations de pente et de géométrie font que le front peut perdre de l'énergie. Les matériaux alors immobilisés peuvent être repris lors de la propagation d'une nouvelle bouffée. Ce sont là encore des facteurs morphométriques, [START_REF] Defrance | Adaptation et évaluation d'un système d'anticipation de crues éclair sur des bassins de montagne non-jaugés -Valorisation de relevés de dégâts[END_REF][START_REF] Dietrich | Construction of sediment budgets for drainage basins[END_REF][START_REF] Benda | Stochastic forcing of sediment supply to channel networks from landsliding and debris flow[END_REF][START_REF] Stock | Erosion of steepland valleys by de-RÉFÉRENCES BIBLIOGRAPHIQUES bris flows[END_REF][START_REF] May | Sediment and Wood Routing in Steep Headwater Streams : An Overview of Geomorphic Processes and their Topographic Signatures[END_REF] (Harvey, 2001 ;[START_REF] Heckmann | Geomorphic coupling and sediment connectivity in an alpine catchment -Exploring sediment cascades using graph theory[END_REF]. Cela peut donc être un facteur limitant de la propagation de lave torrentielle.

Dépôts

Les dépôts de laves torrentielles façonnent progressivement les cônes de déjection des torrents qui acquièrent une pente caractéristique. L'analyse de la littérature montre que les caractéristiques morphométriques des cours d'eau à laves torrentielles (leur bassin versant et leur cône de déjection) sont différentes de celles des cours d'eau où le transport solide se fait uniquement par charriage [START_REF] Kostaschuk | Depositional process and alluvial fan-drainage basin morphometric relationships near Banff, Alberta, Canada[END_REF][START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF][START_REF] Marchi | Flow processes on alluvial fans in the Eastern Italian Alps[END_REF]. Les dépôts de laves torrentielles présentent des traits qui permettent de les reconnaître facilement sur le terrain : les matériaux sont grossiers et non triés, ils forment des bourrelets latéraux orientés parallèlement à l'écoulement, enfin le volume de blocs dans le bourrelet frontal est très important. La propagation est souvent stoppée au niveau des cônes de déjection, où les dépôts (Figure 1.16) prennent des formes lobées caractéristiques [START_REF] Tricart | Une lave torrentielle dans les Alpes Autrichiennes[END_REF][START_REF] Vandine | Debris flows and debris torrents in the Southern Canadian Cordillera[END_REF]. Les laves torrentielles s'immobilisent car elles perdent de l'énergie. Cela peut correspondre à une diminution de la pente [START_REF] Laigle | A Two-Dimensional Model for the Study of Debris-Flow Spreading on a Torrent Debris Fan[END_REF], à un élargissement de la bande active, permettant l'étalement des dépôts, ou à un changement brutal de la direction de l'écoulement qui peut dans certains cas complètement stopper la propagation et dans d'autres uniquement la ralentir. Les dépôts de laves torrentielles se situent souvent à des confluences [START_REF] Miller | A probabilistic model of debris-flow delivery to stream channels, demonstrated for the Coast Range of Oregon, USA[END_REF].

Il existe dans la littérature divers seuils de pente au-delà desquels les laves ne se propagent plus. Bonnet-Staub (1998) reporte un seuil autour de 8°-12°, [START_REF] Rickenmann | Empirical Relationships for Debris Flows[END_REF] signale une pente de l'ordre de 3-4°. [START_REF] Guthrie | An examination of controls on debris flow mobility : Evidence from coastal British Columbia[END_REF] montrent qu'il existe un seuil de dépôt plus élevé pour les laves torrentielles issues des versants (18°-24°), que pour les laves torrentielles canalisées (12°-15°). Ces seuils sont plus élevés que ceux reportés dans [START_REF] Hungr | A review of the classification of landslides of the flow type[END_REF] ou VanDine (1996) (8°-10°). La variabilité des pentes de dépôts montre l'importance du contexte géographique dans lequel s'inscrivent les torrents à laves torrentielles. Les données de la base RTM ont permis de vérifier dans une moindre mesure la validité de la susceptibilité torrentielle que nous avions prédite.

Contexte méthodologique

Données issues de la bibliographie

La BD Morphométrie est constituée de données morphométriques issues de la littérature qui nous ont permis de construire un modèle robuste de prédiction des réponses torrentielles.

Nous avons analysé un grand nombre de publications abordant l'évaluation de l'aléa

Introduction

Small torrents are prone to extreme run-off events that may have dramatic consequences for exposed people and infrastructures. These events are generally triggered by intense convective rainfalls that occur on steep and eroded terrains. At the catchment outlet, these run-off events can take different forms depending on the sediment concentration of the flowing mixture. As this concentration increases, clear water run-off progressively transforms into a sediment-laden flood and finally into a debris-flow at a threshold around 50 % of sediment concentration. Although extreme floods in small torrents may induce catastrophic damages and loss of lives, it is generally recognized that the most dangerous torrents are those that are prone to debris-flows. A recent study in the Eastern Italian

Alps showed that for a same return period, debris-flow volumes are two to three orders of magnitude higher than bedload volumes transported by floods [START_REF] Mao | Sediment transfer processes in two Alpine catchments of contrasting morphological settings[END_REF]. It is also recognized that for a same drainage area, debris-flow peak discharges are much higher than those of floods [START_REF] Hungr | A review of the classification of landslides of the flow type[END_REF]. Therefore, in flood hazard assessment in mountains, there is a great concern to determine debris-flow susceptibility. It refers to the spatial probability of occurrence of debris-flow, that is, the likelihood that an event occurs in an area under particular physical conditions, not including the temporal dimension. This kind of analysis is often used as a first step in hazard assessment [START_REF] Jakob | Debris-flow hazard analysis[END_REF].

Several literature studies focus on morphometric indicators to roughly assess the dominant flow type on alluvial fans and classify them into two categories: alluvial fans dominated by sediment gravity flows named debris-flow fans, and alluvial fans dominated by fluid gravity flows named fluvial fans [START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF]. The pioneer works were initiated in the 1980s by [START_REF] Kostaschuk | Depositional process and alluvial fan-drainage basin morphometric relationships near Banff, Alberta, Canada[END_REF], [START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF] and [START_REF] Wells | Sedimentologic and geomorphic variations in storm-generated alluvial fans, Howgill Fells, northwest England[END_REF] who tried to identify the debris-flow hazard on alluvial fans using catchment and fan metrics. Studies conducted in the Canadian Rockies [START_REF] Kostaschuk | Depositional process and alluvial fan-drainage basin morphometric relationships near Banff, Alberta, Canada[END_REF][START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF] showed that the Melton index and the fan slope were the most powerful indicators to predict the dominant process occurring in the few small upland catchments they studied. The Melton index (or Melton's ruggedness number) is an index of the ruggedness of the catchment [START_REF] Melton | The geomorphic and paleoclimatic significance of alluvial deposits in southern Arizona[END_REF] and is calculated as the ratio of the catchment relief (difference between the maximal elevation of the catchment and the elevation of the fan apex) by the square root of the catchment area measured at the fan apex. It is a normalized index of the gravitational energy of the catchment. Fan slope is conventionally measured as the drop rate between the fan apex and the lowest point along the fan perimeter [START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF]. These early works have been followed up by an increasing number of studies in different upland environments over the last 20 years (e.g. [START_REF] Marchi | Flow processes on alluvial fans in the Eastern Italian Alps[END_REF][START_REF] Calvache | Controls on fan development -evidence from fan morphometry and sedimentology ; Sierra Nevada, SE Spain[END_REF][START_REF] Sorriso-Valvo | Controls on modern fan morphology in Calabria, Southern Italy[END_REF][START_REF] Marchi | Les cônes de déjection torrentiels dans les Alpes franà §aises, morphométrie et processus de transport solide torrentiel[END_REF][START_REF] De Scally | Morphometric controls and geomorphic responses on fans in the southern Alps, New Zealand[END_REF][START_REF] Rowbotham | The identification of debris torrent basins using morphometric measures derived within a GIS[END_REF]; Santos Alonso 2011; amongst others).

The prediction of the dominant sediment transport process at a catchment outlet from morphometric properties of both fans and catchments is based on several assumptions.

CHAPTER 2. DEBRIS-FLOW SUSCEPTIBILITY OF UPLAND CATCHMENTS Alluvial fans are sedimentary deposits resulting from a long and complex history of aggradation and degradation cycles related to the changing nature of environmental controls affecting the sediment and water regimes of the catchment [START_REF] Harvey | Debris Flows and Fluvial Deposits in Spanish Quaternary Alluvial Fans : Implications for Fan Morphology[END_REF][START_REF] Blair | Alluvial fans and their natural distinction from rivers based on morphology, hydraulic processes, sedimentary processes, and facies assemblages[END_REF]. During the long-lasting period of fan formation, it is likely that the dominant sediment transport process shifted from one type to another, as a response to land-use or climate change. Therefore, some of the present features visible at the surface or in the stratigraphic record of the fan may result from processes which are no more active today. The prediction of the dominant sediment transport process acting on the fan from morphometric indicators is based on two basic assumptions that may or may not be always valid. It must be assumed that (i) no change in the dominant transport process has occurred at the timescale considered in the study and that (ii) this dominant process can be inferred from the present morphological signature of the fan. Here, the timescale we considered as valid for the identification of the processes occurring on the fans is multi-decadal or secular.

Recent regional-scale studies compared debris-flows inventories with potential driving factors (topography, geology, land-use). Some of them proposed multivariate models integrating geological controls (D'Agostino and [START_REF] D'agostino | Debris flow magnitude in the Eastern Italian Alps : data collection and analysis[END_REF][START_REF] Crosta | Controls on modern alluvial fan processes in the central Alps, northern Italy[END_REF].

These studies suggest that multivariate analyses are efficient methods to discriminate the processes occurring on the fans, but they are more difficult to implement considering the greater number of indicators needed, and their results are not significantly improved compared to more sparing bivariate models. Moreover, most of them are based on a reduced number of catchments (always below 130, and generally few tenths); thus, the discriminant thresholds proposed are not very robust. To build a broader-scale statistical model for flow type identification in upland catchments, we revisited these studies and compiled data from various alpine environments. Our objective was to test whether a robust statistical model, adapted to different regional conditions, could be obtained to discriminate debris-flow catchments from fluvial catchments by using only the two most widely used morphometric indicators for debris-flow susceptibility (Melton index and fan or channel slope). These two basic indicators present the advantage of being easily automatically extracted from DEM or contour-level maps. We tested two multivariate statistical models: a linear discriminant analysis (LDA) and a logistic regression (LR). The results and the performance of these two models were compared. Here, we present (i) the database compiled from the literature and (ii) the results from the two implemented statistical models.

Material and methods

Database compilation

A database of 620 small upland catchments was compiled from the alpine literature of the last three decades. We selected scientific papers and technical or academic reports in which relevant information can be obtained on catchment morphometry and geomorphic

MATERIAL AND METHODS

responses. For each catchment, we collected the Melton index (R) calculated at the fan apex, the slope of the alluvial fan (S), and the dominant sediment transport process at the catchment outlet (debris-flow vs. fluvial processes) (Table 2.1). For half of the studies, the data were digitized from graphs. For the others, the Melton index was calculated from the raw data given in the papers. In one of the compiled studies, the fan slope was not reported but channel slope was available [START_REF] Liébault | Les rivières torrentielles des montagnes drômoises : évolution contemporaine et fonctionnement géomorphologique actuel (massifs du Diois et des Baronnies)[END_REF]. This concerns 51 fluvial-dominated catchments in the Southern

French Prealps where the channel slope was measured in the field along a reach near the catchment outlet with a length equal to between 10 and 20 active channel widths.

We considered that fan slope can be substituted by channel slope to characterize local (at-a-point) topographic conditions. In alluvial constructions, both are controlled by the sediment transport regime of the reach and both provide local gravitational conditions allowing conveying a debris-flow downstream.

Most of the studies we used identified the dominant flow processes thanks to field expertise of the fan/channel morphology or air-photographs interpretation, and a very few are purely based on historical archives (maps, past inventories or technical reports) about past activity. In those cases, the authors used the recognition of the actual flow process on the field to validate the historical data. Given the unavailability of the raw data used to classify each catchment, it was not possible to evaluate the classification and to propose our own interpretation of the dominant sediment transport process. Therefore, we supposed that the identification of debris-flow process in the case studies as robust and chose to consider only two groups of catchments: (i) those that are known to produce CHAPTER 2. DEBRIS-FLOW SUSCEPTIBILITY OF UPLAND CATCHMENTS debris-flows as attested by field surveys and/or historical documents, and (ii) those that never produce debris-flow. The fans presenting any of the evidences of debris-flow activity (lobes, boulder levees, isolated boulders on the fan surface with diameters exceeding about 1 m, amongst others [START_REF] Kostaschuk | Depositional process and alluvial fan-drainage basin morphometric relationships near Banff, Alberta, Canada[END_REF][START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF][START_REF] Wilford | Recognition of debris flow, debris flood and flood hazard through watershed morphometrics[END_REF] were identified as debris-flow fans. Fans are classified as fluvial if any sign of debris-flow activity was recorded in historical archives and/or field surveys.

In the literature, other groups may be proposed, such as debris flood [START_REF] Scheidl | Empirical prediction of debrisflow mobility and deposition on fans[END_REF] or mixed fans [START_REF] Marchi | Flow processes on alluvial fans in the Eastern Italian Alps[END_REF][START_REF] Marchi | Les cônes de déjection torrentiels dans les Alpes franà §aises, morphométrie et processus de transport solide torrentiel[END_REF]. We considered that these distinctions may be ambiguous and difficult to determine in the field or by using historical archives, so we decided to adopt a more objective binary classification.

Mixed fans were classified as debris-flow fans, since it is recognized that they are susceptible to be affected by debris-flows. Debris flood fans were classified as fluvial fans, in agreement with the commonly used definition of debris flood, a term which refers to a rapid surging flow of water, heavily charged with debris [START_REF] Hungr | A review of the classification of landslides of the flow type[END_REF]. The presence of a free water surface in debris floods clearly shows that this type of flow is closer to water floods than debris-flows. From the 620 catchments in the database, 72% are classified as debris-flow and 28% as fluvial. We referred as fluvial processes when no evidences of debris-flow are reported for the site; in this case, we assume the channel is only shaped by bedload transport. The database presents a great prevalence of positive cases (a positive case being defined as an observation of the most dangerous phenomenon, i.e. the debris-flow in our case). This is not very common in natural hazards studies, where negative cases are generally much more prevalent than positive ones since dangerous phenomena are by nature infrequent [START_REF] Beguería | Validation and Evaluation of Predictive Models in Hazard Assessment and Risk Management[END_REF]. The prevalence of debris-flow catchments in the compiled database is due to the integration of studies exclusively addressing debris-flow fans and to Pyrenees and to a lesser extent Alps and French Prealps). On the over hand, they cover a very wide spectrum of geological conditions (sedimentary, metamorphic and volcanic rocks), palaeoclimatic heritages (glacial and periglacial conditions during the last glacial period), present-day tectonic activity, and hydrological regimes (from rainfall to melt-water dominated runoff).

Statistical analysis

An ANOVA analysis was first performed to validate that there are some significant morphometric differences between debris-flow and fluvial responses. Then two statistical procedures were tested to calculate discriminant thresholds of morphometric variables: (i) linear discriminant analysis (LDA) and (ii) logistic regression (LR). LDA, also known as the Fisher's discriminant analysis, is a statistical process searching for the projection axis which maximises the ratio of interclass to intraclass variability. Here, the response is a categorical dependent variable with two modalities (debris-flow vs. fluvial groups). The interclass and intraclass variances are calculated and kept constant. The calculated linear function of the log-transformed variables is the one that maximizes group separability and is defined as:

log(S) = a log(R) + b ⇐⇒ S = e b R a (2.1)
Log-transformed values of R and S were used to satisfy the normality condition of the LDA, but the standardization of the variables did not appeared necessary in our case. The logistic regression calculates the probability of belonging to a group and is often used to predict the occurrence of a binary variable by quantifying the effect of potential controlling variables. The response binary variable either takes a value of 0 for fluvial response or a value of 1 for debris-flow response. The probability that the response variable takes a value of 1 or 0 is noted as p. The logistic regression is based on the hypothesis that the logarithm of the odds ratio ( log p 1-p or logit function) is a linear function of the two control variables:

log p 1 -p = β 0 + i=n i=1 β i Xi = β 0 + β 1 log R + β 2 log S (2.2)
Here n = 2, β 0 is the constant term, β i are the coefficients applied to the two predictive variables X i which in our case, X 1 and X 2 , are the log-transformed R and S, respectively.

The probability of belonging to the debris-flow response group is given by:

p = e β 0 R β 1 S β 2 1 + e β 0 R β 1 S β 2 (2.3)
These two kinds of multivariate statistical models were implemented in R software (Venables et al. 2012) with the functions lda and glm.

The compiled database of 620 catchments presents much more objects in the debris-flow group than the fluvial group (Table 2.1). The sample prevalence may have a negative effect on both LDA and LR. This is still under debate in the statistician community [START_REF] Xue | Do unbalanced data have a negative effect on LDA ?[END_REF][START_REF] Jiménez-Valverde | The effect of prevalence and its interaction with sample size on the reliability of species distribution models[END_REF]; and there is no clear theoretical argument to conclude about a significant negative effect. We therefore performed the Results of the two models were compared for balanced and unbalanced response groups with two performance indicators not influenced by prevalence [START_REF] Beguería | Validation and Evaluation of Predictive Models in Hazard Assessment and Risk Management[END_REF]. The first is the sensitivity score, which was calculated as the ratio of correctly predicted debris-flow catchments (true positives) in the validation set. The second one is the specificity score, which gives the ratio of correctly predicted fluvial catchments in the validation set (true negatives). As the logistic regression models give a probability of debris-flow response, we use probability threshold of 0.5 to establish in which category the response is predicted. It means that catchments with a probability of debris-flow response higher than 0.5 have a predicted debris-flow response and catchments with a probability to debris-flow response lower than 0.5 have a predicted fluvial response.

After comparing the results of the two designs with the two statistical models, we built the two final models taking into account the entire dataset. We compared both final models with receiver operating characteristic (ROC) curves (i.e., a graphical plot of the performance where the x-axis is the false positive rate (1 -specificity) and the y-axis is the true positive rate (sensitivity) both calculated for different thresholds).

We also evaluated the models by performing a Leave-One-Out Cross Validation (LOOCV) and calculated the 95% confidence intervals for the LDA and LR coefficients.

This validation method consists in n repetition of model building (n is the number of observed catchments) taking n -1 catchments as training data and the remaining catchment as the validation data (i.e., each catchment is used once as validation data).

Results

ANOVA tests

A preliminary analysis for the entire dataset reveals significant differences between

Prevalence effect on statistical model performances

The sensitivity and specificity scores of LDA models built with balanced and unbalanced response groups show significant differences (Figure 2.3a). The 95% confidence intervals for the sensitivity scores obtained with balanced and unbalanced groups are 0.89-0.94 and 2.3. RESULTS 0.91-1.00, respectively. Median values are also slightly higher for the unbalanced designs (0.96 for unbalanced designs vs. 0.91 for balanced designs). It means that prevalence does not have a negative effect on the sensitivity of LDA models. The 95% confidence interval of specificity scores is higher with balanced designs (0.61-0.93) compared to unbalanced designs (0.56-0.89) and the median values are also slightly higher for balanced designs (0.77 for balanced design and 0.73 for unbalanced design). Prevalence has a negative effect on specificity scores of LDA models. Since the objective of the study is to predict occurrence of debris-flow catchments, an unbalanced design for LDA is more appropriate as it allows a better prediction of debris-flow catchments even if a few fluvial catchments will be predicted as debris-flow catchments.

When we compare the sensitivity and specificity scores of the LR by taking balanced and unbalanced response groups, the results are similar to those found with LDA models (Figure 2.3b). The 95% confidence interval of sensitivity scores is much higher with unbalanced designs (0.89-1.00) compared to balanced designs (0.84-0.92). The median values show the same trend (0.88 for balanced design and 0.96 for unbalanced design). For the specificity scores, the 95% confidence interval is higher for the balanced designs (0.61-1.00) than for the unbalanced designs (0.56-0.95). Results are equivalent for the median values (0.83 and 0.72 for balanced and unbalanced designs, respectively). Prevalent datasets were also used for the final LR model since unbalanced designs tend to better predict occurrence of debris-flow catchments. The LR model was also built with the entire dataset (Figure 2.5). From the logit function, we calculated the probability for a catchment to belong to the debris-flows group following equation (2.3). Here the coefficients of the logit function are:

log p 1 -p = -0.65 + 1.66 • log R + 2.00 • log S (2.5)
Hence:

p = e -0.65 R 1.66 S 2.00 1 + e -0.65 R 1.66 S 2.00

(2.6) 2.3. RESULTS

Figure 2.5 -Prediction of catchments response with the LR model

We focused on the effect of collinearity of the predictors, to know if we could apply both model without inducing a statistical bias. Indeed, the two predictive variables show a 0.59 coefficient of determination. We measured the Variance inflation factor (VIF) (O'brien, 2007) in order to characterize the degree of collinearity. In our case, the VIF is only 2.44, which is much less than 4, 5 or 10, the thresholds proposed in the literature above which collinearity is expected to have a strong effect on parameters variance. This shows that some collinearity exists between the predictors but is not excessive. This means that the standard error for the coefficient of Melton is 1.56 times greater than if the collinearity between Melton and the fan slope was almost null.

Collinearity of predictors impacts the precision of the estimated coefficients of the regression but not their significance (p-value lower in both cases) and does not induce a statistical bias for the LDA model. We have considered a relation of the inverse form (the response depends primarily on fan slope and then on Melton), and the signs of the coefficients were unchanged (positive). In our case, this collinearity does not change the sign of the coefficients, so it does not change the sign of the estimated effect and plays a very negligible role in the statistical analysis.

Performances of the two statistical models were first compared with the sensitivity

Discussion and conclusion

Data compilation from 620 upland catchments in various mountain ranges of the world under temperate climate provided the opportunity to test the performance of morphometric indicators for the identification of catchments prone to debris-flow. This study confirms that the Melton index and the fan or channel slope are very good predictors of the dominant sediment transport process of small upland catchments. Debris-flow prone catchments are characterized by steeper catchments and steeper channel slopes than those which only produce bedload transport, as already observed in many regional studies [START_REF] Kostaschuk | Depositional process and alluvial fan-drainage basin morphometric relationships near Banff, Alberta, Canada[END_REF][START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF][START_REF] Marchi | Flow processes on alluvial fans in the Eastern Italian Alps[END_REF][START_REF] Marchi | Les cônes de déjection torrentiels dans les Alpes franà §aises, morphométrie et processus de transport solide torrentiel[END_REF][START_REF] De Scally | Morphometric controls and geomorphic responses on fans in the southern Alps, New Zealand[END_REF][START_REF] De Scally | Controls on fan depositional processes in the schist ranges of the Southern Alps, New Zealand, and implications for debris-flow hazard assessment[END_REF].

Most of the previous studies [START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF] shows that the fan/channel slope threshold above which debris-flow occurs decreases when the Melton index increases. This is in good agreement with experiments of granular collapses over sloping bed [START_REF] Références Bibliographiques Hungr | Simplified models of spreading flow of dry granular material[END_REF][START_REF] Mangeney | Erosion and mobility in granular collapse over sloping beds[END_REF] which shows that the slope of the deposit (an analogue to the fan slope) decreases with the increase of the slope of the plane along which the granular flow is routed (an analogue to the catchment gravitational energy). This suggests that the minimum slope at which debris-flows can propagate is controlled by the mean slope of the catchment.

We used LDA and LR to discriminate fluvial and debris-flow processes. These two models show almost identical sensitivity and specificity scores. LDA specificity is a little lower compared to LR model. Thus false alarms will be more frequent with the LDA. Both statistical models perform well, but better predictions are obtained with LR. The morphometric approach of debris-flow susceptibility assessment presents some limits. As we previously said, the distribution of both morphometric indicators for debrisflow and fluvial response overlaps which is critical for the discrimination of the catchment's response (Figure 2.1). The local slope we took into account is not always the fan slope, especially for fluvial fans in the Southern French Prealps. We considered that the channel slope is a good surrogate for fan slope when the channel is not constrained by bedrock.

The morphometric approach is restricted to the characterization of the minimum gravitational energy required for debris-flows to propagate along the stream network (steep catchments are expected to produce debris-flows susceptible to stop at lower slopes and then to travel longer distances). But debris-flow occurrence is only partly explained by gravitational energy. The spatial variability of debris-flow occurrence along a stream network is also controlled by the magnitude and properties of the sediment supply (Theule et al., 2012). These sediment controls are very difficult to constrain at the regional scale, because they are closely linked with the geomorphic and geological variability of the landscape. We can argue that the morphometric approach provides a conservative assessment of debrisflow catchments, since the discriminant thresholds allow identifying all the catchments presenting enough gravitational energy to produce a debris-flow. Some of them will not produce debris-flow because sediment supply is insufficient or because the grain-size distribution of the sediment supply (which has an influence on the rheological properties of debris-flow) induces a lower than expected runout distance. Another limitation is that the morphometric approach ignores the conditions of sediment transfer in the catchment, which could be interrupted by sediment trap (i.e. glacial lakes) or a reduction of the gravitational energy along the streams from upstream to downstream [START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF][START_REF] Marchi | Flow processes on alluvial fans in the Eastern Italian Alps[END_REF].

DISCUSSION AND CONCLUSION

This gravitational energy can be quantified by morphometric parameters that can be easily constrained at regional scales from low resolution (≈ 10-50 m) Digital Elevation Models. The statistical models derived from this study are very useful for regional scale mapping of debris-flow susceptibility along a stream network. Each segment of the stream network can be classified according to its probability to be travelled through by a debris-flow.

Chapter 3

Hillslope erosion mapping from multi-resolution and multi-sources remote sensing data: application in the Southern French Alps

Mots-clés

Erosion de versant

• cartographie • multi-sources • multi-échelle (multiscalaire) • orthopho- tographies infrarouges

Abstract

The demand for accurate land-cover maps, especially for erosion features is very needed in cases such as debris-flow susceptibility assessment because of the predisposing role of sediment supply on the debris-flow triggering and run-out. Such specific feature mapping required the development of an adapted methodological framework as only one land-cover class was identified. In this study, we proposed a new methodology to map erosion availability in the Southern French Alps, in order to prepare an input which will improve the debris-flow susceptibility assessment. At such a wide scale and in this context of mountainous area, erosion mapping is a critical issue, as the only available and accurate data source is the infrared orthophotos (0.5m). Helped with the Landsat 7 ETM+ images, we defined a new complex combination of classification models to take advantages of the spatial resolution of the orthophotos and of the wide spectral resolution of Landsat 7 ETM+ images. Results

showed that this combination of multi-source and multi-resolution data significantly improved the erosion patches detection as the global overall accuracy of the classification of orthophotos of the validation dataset is 90%.

3.1. INTRODUCTION

Introduction

In alpine environments, it is common to find patches on hillslopes where the surface is almost continuously eroded by geomorphic agents. The persistence of instability on these terrains prevents a sustained vegetation establishment, and maintains exposure of bedrock or colluvium. When these active surfaces are coupled with the stream network, they can have a dramatic impact on the sediment supply to stream channels. The most active debris-flow torrents in the European Alps are always associated with large active erosion cells in their catchment. This is for example the case of the Illgraben in the Swiss Alps, an emblematic debris-flow torrent which delivers much of the Upper Rhône River sediment load [START_REF] Bennett | Patterns and controls of sediment production, transfer and yield in the Illgraben[END_REF]. Another reported case is the Réal Torrent in the Southern French Alps, where the recurrent debris flow occurrence (several each year) has been associated with large active gullies cut in deep fluvio glacial deposits [START_REF] Navratil | Highfrequency monitoring of debris-flow propagation along the Réal Torrent, Southern French Prealps[END_REF]. It has been also long recognized that sediment yields of upland streams can be controlled by punctual sediment sources, typically representing less than 10% of drainage area [START_REF] Mosley | Mapping sediment sources in a New Zealand Mountain Watershed[END_REF][START_REF] Benda | Stochastic forcing of sediment supply to channel networks from landsliding and debris flow[END_REF][START_REF] Gomez | Gully erosion and sediment production : Te Weraroa Stream, New Zealand[END_REF]. In this context, extracting the spatial distribution of active erosion patches is critical for the anticipation of natural hazards related to sediment disasters (debris flows and torrential floods), but also for the catchment-scale management of sediment transport in environmental studies.

In the Southern French Alps, the recent deployment of X-band meteorological radars dedicated to the real-time forecasting of extreme rainfall events has increased the demand for regional-scale debris-flow susceptibility maps [START_REF] Westrelin | Hydrometeorological risks in Mediterranean mountainous areas, RHYTMME Project : risk management based on a radar network[END_REF]. These maps are expected to deliver spatially explicit information about small catchments prone to debris flows from the extraction of relevant geomorphic properties that can be constrained at the regional scale. One key element for the identification of these torrents is the presence of active erosion patches in their catchment, which concentrate in relatively small areas large quantities of renewable loose debris where debris flows can initiate. These potential triggering areas can be easily recognized on high-resolution orthophotos and manually digitized using classic GIS toolkits.

In early studies [START_REF] Ray | Aerial photographs in geologic interpretation and mapping[END_REF][START_REF] Trustrum | Selection of hill-country pasture measurement sites by interpretation of sequential aerial photographs[END_REF][START_REF] Morgan | Application of aerial photographic and computer analysis to the USLE for areawide erosion studies[END_REF], experts interpreted erosion patches for small to medium-sized catchments, typically less than 1000 km [START_REF] Marden | Pre-and postreforestation gully development in Mangatu Forest, East Coast, North Island, New Zealand[END_REF]. This operation is too much time consuming for larger areas. The development of automatic mapping procedures was therefore necessary, not only for the production of regional-scale decision-support tools, but also for improving reproducibility in erosion mapping.

Studies that can help us to assess sediment availability can be classified in two main categories: those which are specifically designed for quantifying erosion rates at large scales (using remote sensing methods to characterize soil coverage and imperviousness, [START_REF] King | Spatial assessment of erosion : Contribution of remote sensing, a review[END_REF]) and those which are developed for land use / land cover mapping purpose. In the first category, the use of statistical and physical modelling is dominating;

the modelling process integrates the use of remote sensing for soil coverage evaluation [START_REF] Benzer | Using the Geographical Information System and Remote Sensing Techniques for Soil Erosion Assessment[END_REF][START_REF] Jain | Estimation of Sediment Yield and Areas of Soil Erosion and Deposition for Watershed Prioritization using GIS and Remote Sensing[END_REF][START_REF] Krasa | Predicting spatial patterns of sediment delivery and impacts of land-use scenarios on sediment transport in Czech catchments[END_REF]. The second category experienced a growth in term of number of papers since about twenty years, as remote sensing and image analysis considerably spread to respond to large scale geo-localized databases demand.

Example of erosion features mapping are rare in the literature but some papers [START_REF] Metternicht | Estimating Erosion Surface Features by Linear Mixture Modeling[END_REF][START_REF] Vrieling | Automatic identification of erosion gullies with ASTER imagery in the Brazilian Cerrados[END_REF][START_REF] Torkashvand | The possibility in providing soil surface erosion map by the supervised classification of ETM+ satellite images in a mountainous basin (Roodbar sub-basin, Guilan, Iran)[END_REF] show methods especially designed using Landsat 7 ETM+ images or orthophotos analysis.

A second generation of remote sensing studies appeared to automatically map the landscape. They mainly focused at first on the vegetation coverage mapping, explaining the invariable use band ratios thresholds [START_REF] Pickup | Use of landsat radiance parameters to distinguish soil erosion, stability, and deposition in arid Central Australia[END_REF] and vegetation indices [START_REF] Cyr | Vegetation indices derived from remote sensing for an estimation of soil protection against water erosion[END_REF]. Several vegetation indices followed, to exploit the spectral response of green chlorophyllian leaves (PVI, TSAVI, amongst others). Even if the strength of this kind of approach has widely been demonstrated, allowing to isolate vegetation patches, it suffered of misclassification issues between non vegetation features, for example between erosion patches and roads. A unique threshold is in that case insufficient to discriminate the features. Following this observation, many more sophisticated methods were developed and can be classified in two categories: i) supervised and ii) unsupervised designs. Some of these developments were specifically designed for erosion mapping, but most come from the land-cover mapping broader topic. Examples of supervised methods used for erosion features mapping are the Maximum Likelihood Classification [START_REF] Hochschild | Delineation of erosion classes in semi-arid southern African grasslands using vegetation indices from optical remote sensing data[END_REF]El Tahir et al., 2010), the Gaussian Mixture Models (Floras and Sgouras, 1999), the Minimum Distance Classification as the Discriminant Function [START_REF] Coulibaly | Evaluation of the potential of various spectral indices and textural features derived from satellite images for surficial deposits mapping[END_REF] for surficial deposits mapping, Parallelepiped Classification as the Non-Parametric rules (Yüksel et al., 2008a;Eroglu et al., 2010), Nearest Neighbour [START_REF] Schneevoigt | Detecting Alpine landforms from remotely sensed imagery. A pilot study in the Bavarian Alps[END_REF] and Spectral Angle Mapper [START_REF] Chikhaoui | A spectral index for land degradation mapping using ASTER data : Application to a semi-arid Mediterranean catchment[END_REF]. Other examples of supervised methods families were not specifically used for erosion mapping but involved other land covers, as the Parallelepiped Classification, e.g. Mahalanobis distance [START_REF] Carrão | Contribution of multispectral and multitemporal information from MODIS images to land cover classification[END_REF], the Support Vector Machine [START_REF] Huang | An assessment of support vector machines for land cover classification[END_REF][START_REF] Zhu | Classification using ASTER data and SVM algorithms ; : The case study of Beer Sheva, Israel[END_REF][START_REF] Dixon | Multispectral landuse classification using neural networks and support vector machines : one or the other, or both ? International[END_REF] and finally the Neural Network [START_REF] Berberoglu | The integration of spectral and textural information using neural networks for land cover mapping in the Mediterranean[END_REF][START_REF] Ashish | Land-use classification of multispectral aerial images using artificial neural networks[END_REF][START_REF] Aitkenhead | Automating land cover mapping of Scotland using expert system and knowledge integration methods[END_REF]. Some models can either be used within supervised or unsupervised designs: the end-members and unmixing models. Examples of erosion assessment using unmixing can be found in [START_REF] Haboudane | Land degradation and erosion risk mapping by fusion of spectrally-based information and digital geomorphometric attributes[END_REF] and [START_REF] Metternicht | Estimating Erosion Surface Features by Linear Mixture Modeling[END_REF].

The Decision tree models, compatible with integration of expert knowledge, appeared thirty years ago but were only used for land cover classification problems since the late 90's (Friedl and Brodley, 1997;[START_REF] Pal | An assessment of the effectiveness of decision tree methods for land cover classification[END_REF][START_REF] Schneevoigt | Detecting Alpine landforms from remotely sensed imagery. A pilot study in the Bavarian Alps[END_REF]. Other kinds of designs which do not need a training dataset are call clustering or unsupervised methods (based on similarity metrics and clustering criteria). The algorithm ISO-DATA was used by [START_REF] Bannari | Intégration des variables spectrales et géomorphométriques dans un SIG pour la cartographie des aires exposées à l'érosion[END_REF] for erosion assessment. Other algorithms as K-means [START_REF] Han | A land cover classification product over France at 1 km resolution using SPOT4/VEGETATION data[END_REF] or Hierarchical Clustering [START_REF] Gonçalves | An unsupervised method of classifying remotely sensed images using Kohonen self-organizing maps and agglomerative hierarchical clustering methods[END_REF] are the most often found in the literature for classical problem of land use classification. Between those two approaches, hybrid methods have more recently appeared [START_REF] Kuemmerle | Crossborder comparison of land cover and landscape pattern in Eastern Europe using a hybrid classification technique[END_REF].

All those methods supervised or not, have shown their great potential to predict land 3.1. INTRODUCTION cover since the validation step often scores higher than 70% for overall accuracy. However, for the unique land cover classification problem we study, the erosion patches mapping, some progress is still needed. Some of these methods are not suited for unique class identification as they attempted to disseminate all the pixels of an image into classes with identical rates. At a wide scale, the variability of spectral values for a class is very high, and it is reinforced in our case by the number of images to process, in which the conditions of shooting can greatly vary (angle of incidence). The methods introduced previously have to be adapted for our large scale unique feature classification objectives, for example by being integrated at multiple scales.

Beyond recent advances in classification algorithms, erosion mapping also benefitted from progress in image segmentation, which initiates a shift from pixel-based toward objectoriented mapping designs [START_REF] Kettig | Classification of Multispectral Image Data by Extraction and Classification of Homogeneous Objects[END_REF][START_REF] Nazif | Low Level Image Segmentation : An Expert System[END_REF]. Indeed, pixel-oriented approaches showed their limits [START_REF] Drăguţ | Automated classification of landform elements using object-based image analysis[END_REF] as event for a multivariate analysis of pixels, the topological relationships of neighbourhood or shape information are not included. The object-oriented approach allows to reduce the noise, isolated pixels classified in a different class from their neighbourhood, also known as the salt-and-pepper effect of the classification result. Some of these methods present the advantage to be already implemented in public and commercial softwares as eCognition [START_REF] Baatz | Multiresolution Segmentation : an optimization approach for high quality multi-scale image segmentation[END_REF][START_REF] Benz | Multiresolution, object-oriented fuzzy analysis of remote sensing data for GIS-ready information[END_REF], SAGA © [START_REF] Böhner | SAGA -Analysis and Modelling Applications[END_REF] or ENVI ® feature extraction workflow [START_REF] Xiaoying | Segmentation-based image processing system[END_REF].This last one has already been proved efficient when used on orthophotos for riverscape [START_REF] Wiederkehr | Physical characterisation of river corridors from orthophotos : challenging issues and first application to the Rhône hydrographic network[END_REF][START_REF] Bertrand | Sensitivity analysis of environmental changes associated with riverscape evolutions following sediment reintroduction : geomatic approach on the Drôme River network, France[END_REF] and mountainous landscape mapping [START_REF] Gholoobi | Comparing pixel based and object based approaches in land use classification in mountainous areas[END_REF]. Within a regional-scale natural hazard management perspective, it is already possible to identify debris-flow prone catchments using statistical laws based on relief descriptors that can be extracted from Digital Elevation Models (DEMs) (Bertrand et al., 2013a). But to better constrain debris-flow susceptibility, it is crucial to integrate information relative to sediment supply conditions in upland catchments. Thus, this paper presents a new method specifically designed for erosion mapping in the alpine environment, using a multi-scalar approach with multi-source data. Hillslope erosion objects are considered within our image analysis approach as exposed (unvegetated) areas. We hypothesize that using combined supervised classification designs, associated with multiple data sources (with various spatial and spectral resolutions) allows mapping precisely erosion cells. Indeed, we think that combining multiple maps of erosion patches built with various algorithm allows to better identify erosion areas because if the information is redundant, the probability to well map the erosion patches is higher than if we consider only one single algorithm. This kind of approach, sometimes implemented in the 2000s for land-cover mapping [START_REF] Liu | Integration of classification methods for improvement of land-cover map accuracy[END_REF], has never been proposed in the particular case of erosion mapping.

Study area

The On the northern side of the subalpine ranges, a unit of high-elevation mountains is found, with maximum elevations ranging between 3000 and 4000 m asl. We can refer it as the intra-alpine unit, which geology is much more complex than for the subalpine unit. This region is characterized by the outcropping of the crystalline Palaeozoic basement of the Alpine range (granite and schist), and the presence of thrust nappes composed of Cretaceous flysch. Mesozoic sedimentary rocks are also outcropping in the most northeastern part of the unit (limestone, gypsum). Some glaciers are present in the highest ranges (like the Ecrins-Pelvoux Massif) and the glacial imprint of the Würmian period is very important.

The climate is mountainous, with important snow cover during winter. Mean annual precipitations are generally above 1000 mm.

A third unit corresponds to the molassic basin unit, which is only present in the southern parts of the Alpes-de-Haute-Provence and Alpes-Maritimes. This small region is composed of Tertiary molassic rocks (mainly conglomerate), with low relief (maximum elevations around 900 m asl). The climate is Mediterranean, with hot and dry summers, and mean annual precipitation around 750 mm.

Method

The available remote sensing data used (Table 3.1) shows various spectral and spatial resolutions. Landsat 7 ETM+ images have a coarse resolution but a wide spectral range, useful to distinguish erosion from other patches. We used three summer images in different path/row scenes dated from 2001 to 2003. More than 800 orthophotos with 50 cm resolution were used in addition to satellite images. They were acquired in July and August 2009.

Extents of the raw images used are presented in Figure 3.2. scripts were used and developed for other image processing and spatial vector analysis.

As the mapping purpose is focused on the erosion patches, which do not show an equally distributed spatial representation with the other land covers taken together and because of the high degree of misclassification which could exist between numerous land uses as the roads, buildings, arable lands and truly eroded bare soil areas, we think that unsupervised methods would not have been appropriate, so we only tested supervised methods. We chose to use various commonly used supervised classification methods which have been largely

proved to be efficient in the literature. It is hypothesized that their weighted combination provides advantages of the spectral resolution of Landsat 7 ETM+ images and of the fine 3.3. METHOD spatial resolution of the infrared orthophotos. The approach is presented in Figure 3.3a.

We combined both pixel-based and object-oriented approaches, respectively with the two sources of images: Landsat 7 ETM+ data and infrared orthophotos. The training and validation datasets are independent (Figure 3.2) and both constituted from a visual expert interpretation of 30 orthophotos segmentations randomly selected (10 randomly selected per department). In those two datasets, the polygons were separated into erosion / non erosion classes. best one of the outputs showed a small probability to be classified as an erosion patch).

Values between 2 and 12 which represent highest cumulated probabilities were classified as erosion prone areas. This first model of pixel based classification of Landsat 7 ETM+ images is further integrated at a larger scale within the object-oriented approach which is described after.

Processing of the infrared orthophotos

A general overview of the workflow is presented in This combination has been previously tested and validated [START_REF] Shen | Comparaison des méthodes de classification supervisée pour la cartographie des zones en érosion[END_REF] and showed the highest scores compared to different groups of raw variables. (the value is a little higher than the threshold found in the literature to take into account the seasonal low alpine vegetation). This model is less restrictive as it only takes the NDVI threshold into account; whereas the previous one integrated also Rate 2 and Rate 3 (Rate 1 is the NDVI).

Combination of the Landsat 7 ETM+ images and the orthophotos

The pixel-based classification of Landsat 7 ETM+ images was then integrated by overlaying with the polygons informed with the results of the three object-oriented classifications (the Landsat 7 ETM+ classification converted into polygons intersects the object-based approaches over 80%).

Here we propose a model which is a weighted combination of the designs described previously. We preferred the weighted combination instead of a design based on conditional statements and decisions as the consensus builder method developed in [START_REF] Liu | Integration of classification methods for improvement of land-cover map accuracy[END_REF], which is more constraining and which have excluded the redundancies in classification. Each of the Landsat 7 ETM+ and orthophotos classifications outputs were weighted according to Table 3.2 and summed to produce a final classification. We post processed the results of this classification, by erasing the few patches recognized as erosion that matched with the roads, and those which were included within the alluvial and which correspond to gravel bars.

Explanation for chosen the weights

As the NDVI threshold model showed the highest scores in terms of both sensitivity and specificity indicators we gave it the highest weight, then we gave a lower one to the rule-based design. As the classification of Landsat 7 ETM+ images showed a very good specificity, we gave it the same weight as the rule-based model. Finally, the neural network model was given the lowest weight as its specificity was lower than the Landsat 7 ETM+ classification.

The weighted sum gives an index corresponding to the probability for each object being an erosion patch. To have a binary result, only objects with values higher than 0.5 were considered as erosion (binary reclassification into 1 for erosion prone areas, 0 for the other objects). In this way, each object can either be a true positive, false positive, false negative or true negative. Considering this threshold allows identifying the polygons for which the classification designs show redundant results, at least for the NDVI threshold classification.

Another way to combine all classification designs could have been to find the optimal combination with a calculation of the weights according to the validation dataset. This will be further explained in the discussion part of this paper.

Results

We classified the 831 orthophotos tiles and simplified the results to produce a large scale map of erosion patches (Figure 3.5) that cover 21% of the study area. Some zooms are showed in Figure 3.6. We removed from the results the patches classified as erosion areas within terraces, plateaus and large alluvial fans, as they are not erosion patches, but alluvial deposits. As only values above 0.5 of the weighted sum are considered as erosion prone areas, object classified by the rule-based, Landsat 7 ETM+ classification or the neural network models taken independently can never be considered as erosion patch (as their weights are under 0.5). The redundancy of these three classifications designs and each of them individually combined with the NDVI model allow classifying objects as erosion patch.

If we consider an unweighted combination of the supervised designs, the overall accuracy is slightly lower (i.e. 0.88) (Figure 3.7), the sensitivity stays very good (i.e. 0.81), but the specificity is slightly lower (i.e. 0.92, it means that the number of false positive cases increased). At a more local scale if we compare the overall accuracy for each tile with the weighted and unweighted designs, the weighted one always shows higher scores. This shows that the weights chosen according to the efficiency of the supervised models taken independently are relevant to design an efficient model.

Discussion

Quality of the model compared to previous works

The large scale classification model we applied in the Southern French Alps has shown good agreement with expert identification of erosion prone areas at a regional scale (all the performance indicators are above 0.81). Most of the previous studies are not focused only on the erosion characterization but more generally on all kind of land covers. At this scale an erosion map based on orthophotos analysis has rarely been achieved [START_REF] Alatorre | Identification of eroded areas using remote sensing in a badlands landscape on marls in the central Spanish Pyrenees[END_REF], and our method showed a great reproducibility potential for other mountainous regions. As demonstrated in the approach chosen by [START_REF] Liu | Integration of classification methods for improvement of land-cover map accuracy[END_REF], the integration of several classifiers improved the accuracy of our classification. As it integrated the redundancies in erosion classification directly together instead of using conditional structures with Boolean decisions, the results are even more accurate even the misclassification can also be redundant.

A comparison with classification scores found in the literature (Table 3.5) was not so easy. We took the results of classification of bare soils in various papers with very diverse approaches, sources of data and aims. Our results are slightly higher in term of sensitivity (0.81) and specificity (0.94) compared to [START_REF] Alatorre | Identification of eroded areas using remote sensing in a badlands landscape on marls in the central Spanish Pyrenees[END_REF], [START_REF] Begueria | Identifying erosion areas at basin scale using remote sensing data and GIS : a case study in a geologically complex mountain basin in the Spanish Pyrenees[END_REF] and slightly lower compared to [START_REF] Okeke | Methods for fuzzy classification and accuracy assessment of historical aerial photographs for vegetation change analyses. Part II : Practical application[END_REF] Other studies cited in the introduction could not be compared with our method, as they sometimes did not detail the validation step, or sometimes they were focused on very specific objectives as gully or alpine landforms mapping which are not comparable with our erosion patches class.

To conclude, the proposed method show positive advances for erosion mapping, first because it is object-oriented, easily applicable for large scale datasets, and focused only on the erosion feature, and reproducible on any mountainous terrain for erosion mapping purpose. It has still to be improve compared to other case studies, in order to limit misclassification of agricultural parcels on alluvial fans, on terraces or plateaus.

Problems and potential improvements

At a local scale, our model showed very scatter performance (some of the tiles showed lower scores), and could still be improved, maybe by designing individual model for each of the processed tiles. In order to explain those differences we overlaid the validation dataset on our study area map (Figure 3. The first factor that can explain the variability of the efficiency scores is the quality of the orthophotos. Indeed, raw images of the three departments have been post-processed by different ways by the French National Geographic Institute. For the Hautes-Alpes and the Alpes-de-Haute-Provence, the images are tiled, but for the Alpes-Maritimes, the 5 km width tiles were merged into a big image file (Figure 3.9). Even if the spatial resolution was kept to 0.5 m, the spectral values of all the tiles have been stretched to fit to a 256 values palette. For the Hautes-Alpes, it seems that the quality of the tiles has been degraded compared to those of the Alpes-de-Haute-Provence (i.e. the bare soils appear brighter and bluer for similar lithology). A mean to counteract these effects of image degradation could be, as it was proposed for the rule-based method, the use of ratio instead of raw values in the three bands. A second way could have been to pre-process the individual tiles for example by stretching the histograms of the three bands. This should be further experienced by segmenting and classifying the images matching two different departments after their histogram stretching. However, this would not fix the mega tile problem of the Alpes-Maritimes. This leads us to think that progress in image acquisition procedure are still needed, at least for the first steps of the original data processing (i.e. assembling the We consider that this relief effect should further be studied at a lower scale, maybe at the landscape unit scale, with the slope and curvature indicators to adapt classification method to the morphology of the landscape units.

Another factor that could explain the scattering of the performance of our model is the season the images were taken. If orthophotos and Landsat 7 ETM+ images were taken during the spring (they were taken during summer (Table 3 3.6. CONCLUSION

Conclusion

Erosion map has been developed from an analysis of 2009 infrared orthophotos (0.5 m) and Landsat 7 ETM+ images for the Southern French Alps. The overall accuracy of the map is quite high (0.9) compared to other studies, so the combination of multisource and multi-resolution data significantly improved the detection of erosion patches. This map will be very useful as it will be integrated in many future projects aiming at assessing sediments transfers at large scales, in particular within a debris-flow susceptibility assessment approach.

Chapter 4

GIS application of debris-flow susceptibility assessment within the Southern French Alps

Mots-clés

Lave torrentielle • Indicateurs morphométriques • Disponibilité sédimentaire • SIG •

Susceptibilité

Abstract

The main objective of this chapter is to assess the debris-flow susceptibility in the Southern French Alps. It first consists in evaluating in morphometric and sediment availability perspectives (evaluated in Chapters 2 and 3) the predisposition of small upland catchments to debris-flow triggering. The issue is to evaluate whether debris flows can propagate downstream given the morphometry and the probability of debris-flow occurrence for reaches located just upstream. This chapter presents the implementation of these indicators extraction within a Geographic Information System integrating a hydrological analysis of a Digital Elevation Model, and the probability of spatial occurrence of debris flows at a regional scale. The methodology developped will also be used to characterize the susceptibility to debris-flow propagation, taking both morphometry and sediment supply predispositions into account (network approach).

Morphometric indicators used to characterize susceptibility to debris-flow triggering

Introduction

In the Southern French Alps, hazards related to extreme rainfall events, as debrisflow triggering, is frequent. Within a large scale susceptibility assessment approach, the integration of all the facets of debris-flow triggering and propagation are tackled. Scientific developments introduced in the first chapters of this thesis are now used to identify catchments prone to debris-flow triggering based on the indicators previously described.

This large scale approach is needed for debris-flow risk prediction, in particular since the new deployment of X-band meteorological radars for real-time extreme rainfall forecasting [START_REF] Westrelin | Hydrometeorological risks in Mediterranean mountainous areas, RHYTMME Project : risk management based on a radar network[END_REF].

Early studies of debris-flow susceptibility proposed to discriminate debris-flow versus fluvial catchments from the Melton index and the fan slope [START_REF] Melton | The geomorphic and paleoclimatic significance of alluvial deposits in southern Arizona[END_REF][START_REF] Kostaschuk | Depositional process and alluvial fan-drainage basin morphometric relationships near Banff, Alberta, Canada[END_REF][START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF]. These early works have been followed by a large set of studies in different alpine environments over the last 20 years [START_REF] Marchi | Flow processes on alluvial fans in the Eastern Italian Alps[END_REF][START_REF] Calvache | Controls on fan development -evidence from fan morphometry and sedimentology ; Sierra Nevada, SE Spain[END_REF][START_REF] Sorriso-Valvo | Controls on modern fan morphology in Calabria, Southern Italy[END_REF][START_REF] D'agostino | Debris flow magnitude in the Eastern Italian Alps : data collection and analysis[END_REF][START_REF] De Scally | Morphometric controls and geomorphic responses on fans in the southern Alps, New Zealand[END_REF][START_REF] Rowbotham | The identification of debris torrent basins using morphometric measures derived within a GIS[END_REF] which confirmed the predictive power of these two factors. These studies integrated in addition other parameters as fan area [START_REF] Ceriani | Evaluation of hydrogeological hazard on alluvial fans[END_REF], stratigraphic data [START_REF] Coe | Debris Flow Hazards Mitigation : Mechanics, Prediction, and Assessment[END_REF], or geological characteristics (D'Agostino and [START_REF] D'agostino | Debris flow magnitude in the Eastern Italian Alps : data collection and analysis[END_REF] but improvement was negligible. Based on these findings, we build our own robust broad scale statistical model for debris-flow susceptibility assessment (Bertrand et al., 2013a) (in Chapter 2), by using Melton index and channel slope data from various alpine case studies, and applying linear discriminant analysis and logistic regression models.

These two predictive variables present the advantage of being easily extractible from DEM or contour-level maps.

Even if unlimited sediment supply condition is not needed to trigger a debris-flow activity [START_REF] Bovis | The role of debris supply conditions in predicting debris flow activity[END_REF], the sediment availability in the basin is another control of debris-flow occurrence [START_REF] Rickenmann | The 1987 debris flows in Switzerland : documentation and analysis[END_REF] as it can inhibit debris-flow initiation [START_REF] De Scally | Controls on fan depositional processes in the schist ranges of the Southern Alps, New Zealand, and implications for debris-flow hazard assessment[END_REF] and propagation. The lack of sediment in the basin or presence of sediment traps can prevent the debris flow to reach the fan. Case studies aiming at identifying debris-flow source areas took into account sediment availability from land-use mapping [START_REF] Carrara | Comparing models of debris-flow susceptibility in the alpine environment[END_REF], landslides inventory [START_REF] Brayshaw | Debris flow initiation and sediment recharge in gullies[END_REF][START_REF] Dong | The role of the sediment budget in understanding debris flow susceptibility[END_REF][START_REF] Blahut | Debris flow hazard modelling on medium scale : Valtellina di Tirano, Italy[END_REF]amongst others), typology of available sediment storage [START_REF] Wells | Sedimentologic and geomorphic variations in storm-generated alluvial fans, Howgill Fells, northwest England[END_REF][START_REF] Carrara | Comparing models of debris-flow susceptibility in the alpine environment[END_REF][START_REF] Tunusluoglu | Extraction of potential debris source areas by logistic regression technique : a case study from Barla, Besparmak and Kapi mountains (NW Taurids, Turkey)[END_REF] or the presence of glacier [START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF][START_REF] Huggel | Regional-scale GISmodels for assessment of hazards from glacier lake outbursts : evaluation and application in the Swiss Alps[END_REF].

Most of the case studies mentioned previously focused on the source areas in which debris flow can be triggered, but another aspect of debris-flow susceptibility assessment is the spreading of flow, because the stream network slope pattern strongly controls the debris-flow runout pattern. A certain minimum slope is needed to exceed internal flow resistance of debris flows. Debris-flow runout is often treated with physical models which need to fix several parameters and which exploit non-newtonian theoretical laws from fluid mechanics. Acquisition of needed variables is inconceivable at large scales, so we have to

MATERIAL AND METHOD

found an alternative to this kind of approach.

Some GIS case studies focusing on both triggering and propagation of debris flows developed some methods to identify both the source areas and the runout by integrating slope failure conditions [START_REF] Guinau | GIS-based debris flow source and runout susceptibility assessment from DEM data -a case study in NW Nicaragua[END_REF] and by decomposing the problem into source area (integrating morphometry, hydrology, lithology and land use together) and spreading area (integrating only topographic variables) [START_REF] Horton | Debris flow susceptibility mapping at a regional scale[END_REF]. This kind of approach could potentially be applied in the Southern French Alps.

At such a large scale, the characterization of the morphometric indicators identified for our debris-flow susceptibility assessment involve GIS specifically designed methodologies for extracting the raw variables to calculate these indicators. The first main contributions allowing the characterization of raw morphometric properties were concomitant with computer-based GIS. Pioneer works were initiated in the 60-70's by [START_REF] Greysukh | The possibility of studying landforms by means of digital computers[END_REF][START_REF] Johnston | Digital Detection of Pits, Peaks, Ridges, and Ravines[END_REF][START_REF] Peucker | Detection of Surface-Specific Points by Local Parallel Processing of Discrete Terrain Elevation Data[END_REF] and attempted to classify the landforms based on a DEM analysis. The major works of the 80-90's described methods for DEM analysis, particularly for DEM correction, drainage network definition, watershed delineation and landform analysis [START_REF] Haralick | Ridge and Valley Detection on digital images[END_REF][START_REF] Band | Topographic Partition of Watersheds with Digital Elevation Models[END_REF][START_REF] Jenson | Extracting topographic structure from digital elevation data for geographic informa-tion system analysis[END_REF][START_REF] Martz | CATCH : A FORTRAN program for measuring catchment area from digital elevation models[END_REF][START_REF] Martz | The treatment of flat areas and depressions in automated drainage analysis of raster digital elevation models[END_REF]. Many of the algorithms developed in this period were implemented within GIS software. In the late 90's, two fundamental works [START_REF] Wood | The Geomorphological Characterisation of Digital Elevation Models[END_REF][START_REF] Tarboton | A new method for the determination of flow directions and upslope areas in grid digital elevation models[END_REF] focused on the methods for calculation of flow directions from which most of morphometric indicators can be derived. All these algorithms are now implemented in GIS software solutions as SAGA © GIS, GRASS © , LandSerf © or ArcGIS ™ can be used to extract the morphometric indicators needed.

Consequently, a susceptibility assessment methodology -integrating the development detailed in the previous chapters -was developed for practical purposes to i) identify small upland catchments susceptible to trigger debris flows integrating both morphometric and sediment availability predisposition, and ii) a methodology to predict whether propagation of the debris flow is possible considering those two predisposing factors and the susceptibility of upstream reaches as well to convey it. In this chapter we will present the GIS methodology and the network scale approach we developed to integrate predisposing factors to debris-flow triggering and propagation. This chapter also presents the problems encountered with the automatized procedure of morphometric characterization and a validation with expert knowledge.

Material and method

Available data

Following a prospective aim, we listed all the raw data (presented in Table 1.1) available to extract the morphometric indicators. For the specific morphometry characterization described in this chapter we only used the datasets presented in the following The vector data available at this large scale (BD TOPO ® package) were provided by the French National Institute of Geographic and Forest Information (IGN © ). Exhaustiveness of the data is 99% for the permanent stream network provided at the national scale. The artificial and temporary hydrographic reaches, i.e. ditches, are not always digitized. The planimetric accuracy of this thematic layer ranges from 0.5 m to more than 10 m and the altimetric accuracy ranges from less than 1 m to more than 2.5 m.

The scale of the raw data used to produce the 25 m DEM (BD ALTI ® ) is not homogeneous: the method used to compute the raw map or field data can vary (i.e., manual, scan, photogrammetry) so as the contour interval (from 5 m to 40 m) drawn on the topographic map. In a mountainous environment, altimetric accuracy is often lower than in flat area.

Here, accuracy has been measured relatively to each topographic map sheet. For half of them, altimetric accuracy is higher than 6 m, for a third it is close to 2.5 m and for the other maps, it is close to 4 m or 5 m (IGN © , 2011). For 90% of the topographic maps, the contour lines used are quite recent (after 1979), and for 25% they are even more (after 1990). For 60% of the maps, the contour lines were digitized from the 1:60000 scale, and for 35% of them, they were digitized from the 1:30000 scale. It shows that the accuracy of the raw data used to build the DEM was not spatially homogeneous. As the final planimetric resolution of the DEM is 25 m, all the raw data have been resampled and altimetric accuracy kept less than 2.5 m.

General overview of the methodology

We defined an integrated method to assess the spatial susceptibility of debris flow (i.e. the likelihood that an event occurs in an area under particular physical conditions) at a regional scale (Figure 4.1). We first defined the spatial units which correspond to the triggering and the propagation zones based on a hydrological analysis of the DEM.

Within the triggering zones, we identified upland catchments prone to debris-flow triggering considering (i) the morphometric factors controlling debris-flow activity (Chapter 2), and

(ii) the sediment supply conditions, i.e. the amount of erosion patterns feeding the channels (Chapter 3). For downstream reaches, we defined new homogeneous units considering their slopes (called Homogeneous Slope Reaches, or HSR). For each HSR we first assessed the susceptibility to debris-flow propagation by characterizing the morphometric properties and by calculating the associated debris-flow activity probabilities. Then, from sources to main streams (catchment smaller than 40 km ), the susceptibility to debris-flow propagation was

MATERIAL AND METHOD

recursively adjusted considering the debris-flow triggering or propagation of lower order streams.

The morphometric controls are evaluated with indicators calculated from basic topographic variables within a GIS. The sediment availability is evaluated through the cumulated surface of erosion area, with a binary classification of the responses: 1 if there is a patch greater than five hectares, or is the rate of erosion in the catchment exceed 75% and 0 elsewhere.

                                                                                

Potential debris-flow triggering in source units

Pre-processing of raw data

The original hydrographic network we used comes from the BD TOPO ® , but many manual corrections have been done to provide a network which is well-oriented, connected and informed with elevation values. During the correction step, we noticed that the reliability of these raw data could be discussed. Sometimes it did not fit with the topographic map, especially in the upland areas. It is not easy to determine if this is due to a physical reality or to heterogeneous manual editing of the low order stream network. We preferred an upstream simplification of the network: we deleted the streams which correspond to catchments smaller than 0.1 km . We also deleted artificial reaches such as ditches, by-pass or irrigation canals (Figure 4.2).

Source units definition

After we corrected the hydrographic network, we identified the low order streams in order to delineate their catchments which correspond to the potential debris-flow source units. For each low order reach, we identified a downstream terminal segment (to assess the possibibility that a debris flow could reach this segment) which was fixed as 50 m in length (except for a few cases of shorter reaches). This step is realized with the linear referencing tool within ArcGIS ™ . The upstream node of this terminal segment is considered as the outlet from which we delineated the catchment (Figure 4.4).

Each catchment was delineated within ArcGIS ™ with a specific workflow in the Arc Hydro © Tools (Figure 4.5). This catchment delineation processing workflow was chosen after having tested few others:

• r.watershed with r.water.outlet in GRASS © ;

• GIS based watershed delineation in MWD / TAUDEM © tool;

• Watershed delineation in SAGA © GIS. The manually corrected low order catchments constituted the source units within which we characterized the debris-flow triggering potential.

Morphometric characterization of the source units

We developed a specific GIS methodology to extract the morphometric indicators. We Finally, we added a field to extract the geometric value of the planimetric length of the terminal reaches. We calculated the slope with the following equation:

Slope = Degrees(Atan(Abs(Zup -Zdown)/Length)) (4.1)
Where Zup and Zdown are the elevation values at the upstream and downstream nodes of the segment. We took absolute values to avoid negative slopes errors due to wrong matching between the hydrographic network and the DEM.

Debris-flow activity according to morphometric properties

Once we applied the previously described GIS procedures on the 25 m DEM of the Southern French Alps, we calculated the debris-flow susceptibility of sources areas according to the morphometric properties of upland catchments following the equation (Bertrand et al., 2013a):

p = e -0.65 R 1.66 S 2.00 1 + e -0.65 R 1.66 S 2.00 (4.2)

MATERIAL AND METHOD

Where R is the Melton index and S the channel slope (Chapter 2).

We classed the resulting probability into four classes for mapping purpose according to the following rules: P ≤ 0.02 (Null), 0.02 < P ≤ 0.5 (Low), 0.5 < P ≤ 0.75 (Intermediate), 0.75 < P ≤ 1 (High). This classification is an operational deliverable for end-users (regional and local authorities in charge of natural hazard prevention and management) that need to be rapidly understood, even when it is overlaid with other natural hazards as rockfalls or large mass movements. Except for the first one, these thresholds correspond to the percentile values.

Debris-flow susceptibility integrating the sediment availability

Following the Chapter 3, we mapped the sediments available on hillslopes thanks to image processing methods applied on infrared orthophotos. We intersected this erosion map with the low order catchments, and classified them depending on the sediment availability.

If the rate of erosion within the low order catchments is above 75% or if there is any erosion patches larger than five hectares, we classified the low order catchments as having a high sediment supply potential. For other catchments, the sediment availability potential was classified as low. This allowed adjusting the probability class of debris-flow triggering susceptibility according to both predisposing factors: the morphometry and the sediment availability.

The four probability classes (Null, Low, Intermediate and High) of the low order reaches are adjusted with the two classes (Low and High) of their corresponding catchments according to the rules in Table 4.2. The susceptibility to debris-flow triggering within the sources units is qualified with four level classes after integrating both morphometry and sediment availibility.

Potential debris-flow propagation through the network

In order to identify the stream network along which debris-flow runout may be possible, we first defined some homogeneous hydrographic network units for which we calculated the morphometric indicators. This allows characterizing the potential gravitational energy ASSESSMENT WITHIN THE SOUTHERN FRENCH ALPS available for debris-flow propagation, under the limit of 40 km of catchment area, which is the limit in which debris flows have been observed.

Homogeneous network units definition for debris-flow propagation

Each confluence was considered as a potential discontinuity in term of river compartments, so that the reaches upstream and downstream the confluences are considered as physically different: slopes, amount of sediment, drainage areas can greatly vary. Considering this, the channel courses can also show some discontinuities, particularly in term of slope, which is a major control of debris-flow propagation. We identified homogeneous reaches in terms of slope following the methodology presented in Figure 4.9. We disaggregated the initial channel courses (defined between two confluences) into segments of 50 m in length, and calculated for each a mean slope, i.e. altimetric difference between both upstream and downstream nodes of the segment divided by its length. Then we used the statistical test of Hubert which has been proved to be efficient for evaluating discontinuities within hydrological series and geomorphological series following [START_REF] Leviandier | Comparison of statistical algorithms for detecting homogeneous river reaches along a longitudinal continuum[END_REF]. After the discontinuities were identified, we aggregated the segments with homogeneous slopes. This constituted the basic reaches, called Homogeneous Slope Reaches (HSR), on which we characterized the morphometry, by calculating the Melton index and the channel slope on the terminal part.

Morphometric characterization of HSR

For the Melton index assessment, we did as for low order catchments and decomposed the indicator into the three raw variables mentioned previously: the maximum elevation of the HSR catchment, the elevation of the outlet and the drainage area. As we already knew the maximum elevation of low order catchments, we propagated the highest elevation values to the downstream HSR, recursively with a software we developed in Java ™ . The topological relationships between the low order reaches and HSR, and between HSR together are stored thanks to ID field within a MySQL ™ database. We extracted the outlet elevation with the same method than for low order reaches, except that this outlet was not always located 50 m upstream of the channel end: for the HSR between 5 and 50 m in length the outlet was located 5 m upstream of the channel end and for shorter HSR, the channel slope was calculated for the entire HSR. Those latest are very small part of channel course between two confluences. For the drainage areas, we used various methods depending on the data available. We delineated the local catchments of each HSR as we did for low order reaches, but we only partly checked and manually corrected them. For sectors where the delineation of catchments was manually corrected, we calculated the drainage area as the The channel slope was calculated as for low order reaches, by dividing the difference in elevation between the outlet (we calculated for the Melton index) and the downstream node of the terminal segment by the length of the terminal segment (either 50 m, 5 m or the entire length for the shorter HSR).

CHAPTER 4. GIS APPLICATION OF DEBRIS-FLOW SUSCEPTIBILITY ASSESSMENT WITHIN THE SOUTHERN FRENCH ALPS

Debris-flow activity according to morphometric properties

As for the low order reaches, we calculated the probability of debris flow activity of each HSR taking into account the Melton index and the channel slope extracted thanks to the method described previously. We applied the same logistic regression model than in the previous section. We also classified those probabilities in the four classes Null, Low, Intermediate and High for mapping purpose.

Debris-flow susceptibility integrating the sediment availability

In order to identify the HSR which are able to propagate debris flows, we also took into account the debris-flow susceptibility of upstream reaches (low order reaches and HSR). We adopted a set of rules to qualitatively weight the propagation of debris flow, i.e. the class of susceptibility of each HSR, from the second order reaches (downstream of the low order reaches) to the downstream end of the network. This is another functionality we developed with MySQL ™ and Java ™ , which updated recursively the classes of the downstream HSR thanks to the rules described in the Table 4.3. For each HSR, this function takes into account the current class of susceptibility to debris-flow activity (morphometry) and the class of the upstream reaches (either or HSR) which has been already modified: it integrates both the morphometry and the sediment supply for low order reaches and for downstream HSR the modified susceptibility class (modified considering the same rules, recursively from the source units, Figure 4.1).

Whatever the position of the HSR within the network, the class of susceptibility is modified by taking into account the maximum class value of the upstream reaches. This can be considered as a limitation of the methodology as the size of the upstream networks does not influence the potential debris flow downstream propagation.

Validation dataset for debris-flow susceptibility assessment

We established a validation dataset aiming at validating the debris-flow susceptibility approach. After having validated the statistical model (Chapter 2), we need to face our results with field / truth data. We constituted our own validation dataset with our field knowledge composed of 50 sites along the stream network with a drainage area under 40 km , where the presence / absence of debris-flow signs has been determined in the field (half of them producing debris flows) (Figure 4.10). Even if this sample is very small compared to the entire network we processed, this constitutes a dataset very reliable.

_ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ! ! ! ! !
Sources : BD ALTI®, BD Carthage®, GeoFLA®, © IGN Paris We used performance indicators, presented in the chapters 2 and 3 , in order to evaluate the predictive power of our approach.

Results

Susceptibility to debris-flow triggering in source units

Amongst the 32718 km of drainage network covering the study area, 18975 km (58%) are low-order reaches, with a median length around 610 m. The main descriptive statistics 4.3. RESULTS are also given for the drainage area, Melton number, channel slope and probability to debris-flow activity in the Table 4.5. The corresponding distributions of the main characteristics of the low order reaches are illustrated in the Figure 4.11. The Figure 4.13 shows the spatial distribution of the channel slopes of the low order reaches at a regional scale. It fits well the regional pattern of the Melton numbers, with the highest values preferentially found in the subalpine and alpine units. As shown in the Figure 4.16 the number of low order reaches classified as having a High susceptibility to debris flow is much higher than for other classes. According to the spatial pattern of Melton numbers and channel slopes, and to the spatial distribution of erosion patches at a large scale, the susceptibility to debris-flow triggering shows a gradient from the molassic to the alpine units. Some of those low order reaches constitute the expert validation dataset and their predictability will be discussed in the validation and discussion part.

RESULTS

HSR

Even if the predictions seem correct on the main streams, as they are not susceptible to debris flow, our model seems to over predict debris-flow activity in upland areas (low order reaches). This distribution of the probability (Figure 4.16) does not fit with general knowledge about debris flow, i.e. the predicted probability of spatial occurrence is higher than the non-occurrence, even if this phenomenon is considered rare and extreme. This may be related to the problems we encountered to extract the morphometric indicators of the small upland catchments. On the Figure 4.20, we plotted both morphometric indicators with colors associated with the probability of debris-flow response (calculated with the statistical model described in the previous chapter (Bertrand et al., 2013a). The probability under 0.5 is plotted in green, and above in red. Once again the spatial distribution of probability of debris-flow activity seems to follow a gradient between the molassic unit and the alpine unit. As for the slope distribution, the western part of the study area shows lower probability values, almost along the main stream valleys.

RESULTS

Melton

The modifications applied to the HSR classes according to the Table 4.

Validity of the predicted debris-flow susceptibility

We compared a restricted validation dataset composed of 50 sites (half of them producing debris flows) to the predicted susceptibility to debris-flow activity. The overall accuracy of our model is 80% with a greater number of false negative cases (low order reaches or HSR predicted as non-susceptible to debris-flow transport, even they were). We calculated all the descriptive statistics to evaluate the model (Table 4.7). Even if the restricted size of the validation sample can be arguable, the model we proposed showed very good results. This can be linked to the thresholds used to class the probability to debris-flow activity of both low order reaches and HSR. Some geomatic 4.5. METHODOLOGICAL LIMITATIONS AND PERSPECTIVES errors related to the quality of the data and the methodology could explain why the Melton numbers and channel slopes are often higher than they actually are, and why the probability of debris flow activity is often very high as well (Figures 4.14 and 4.21). Using other thresholds, as for example a natural threshold classification of the probability, could have led to different results. Even the number of class can be discussed, we chose four classes for representation purpose to facilitate the map reading, but maybe two would have been enough.

The way we integrated the sediment availability parameter is also arguable. Indeed we chose to consider that only catchments with a rate of erosion above 75% or with any erosion patches bigger than five hectares are susceptible to sediment supply for debris-flow triggering. These thresholds are both based on expert judgement and could have been chosen according to a wider set of observations. The integration of sediment availability to adjust the debris-flow triggering susceptibility is also arguable. It is based on a qualitative expert judgement. The network approach we developed is very simple as it did not take into account the position of the reach, for which the potential debris-flow propagation is evaluated, within the hydrographic network: the same rules are applied if this reach is located downtream of the confluence of two low order reaches, or one low order reach and a HSR, or two HSR, whatever their respective catchment areas are (i.e., whatever their location within the hydrographic network). We positioned our susceptibility assessment in a high hypothesis frame.

Methodological limitations and perspectives

Even if the susceptibility assessment approach has been validated with field expertise, we would like to draw attention on the quality of the geomatic procedure we developed to extract the morphometric indicators. Indeed, we encountered many technical difficuties to delineate the small upland catchments and to characterize their morphometric properties, considering the rough resolution of the DEM we used, and the steps needed to simplify and automatize the procedure. The morphometric indicators extracted with the GIS procedure, especially the slope, seem to fit with a first qualitative visual interpretation when drapped on the DEM or within the Google Earth © software.

The maximum elevation of the catchment and its drainage area strongly depend on the quality of its delineation. When using the raw BD TOPO ® hydrographic network for stream burning, the delineation of catchment failed for at least one third of them, located in the upstream part, because of their very small size compared to the resolution of the DEM used to delineate them. This is also related to the inconsistency between the DEM and the hydrographic network (the linear features did not match exactly with the talweg). As we explained previously, we simplified the network but still errors persist.

After many tests, trying to improve catchment delineation process, by using or not a burnt DEM, by using various flow direction algorithms we did not achieve to reduce the number of incorrectly delineated catchments significantly, and we finally propose a manual The delineation process applied as described previously showed better results with the 5 m DEM, as only 10% were not correctly delineated, but the automated part was 10 times longer than for a 25 m DEM. Such higher resolution requires implementation of greater and faster computing infrastructures and algorithms. This comparison with a lower spatial resolution DEM allows us to consider that even the quality of our raw data is not fully adapted to our objectives, the GIS procedure is efficient: the drainage area of upland catchments can be extracted in a semi-automatized way.

For higher ranks, we hypothesized that the flow accumulation values extracted after the DEM burning step could be used. The automatized snap of the catchment's outlet on the nearest highest flow accumulation value implies to fix a neighborhood threshold within which this value is searched. Even if we empirically chose this threshold, it shows accurate results at a large scale (even for catchments larger than 40km ): flow accumulation raster can be used to extract the catchment area. However, such data may be insufficiently accurate to extract values for very small catchment (smaller than 1 km ) due to the wrong flow path which conduct to important errors of drainage area.

To conclude, the critical part of the morphometry characterization is the delineation of catchments which strongly depend on the resolution of the DEM processed, the quality of this DEM and the algorithms used to delineate them, based first on the flow direction calculation. Here, we finally choose the classical D8 method (Figure 4.24a), but the alternative Dinf (Figure 4.24b) available in SAGA © GIS for example did not significantly improve the delineation. In the last twenty years, large scale datasets had quite rough spatial resolution, so the size of the raster did not exceed the capacity of the computers, and processing of the DEM with algorithms such as D8 was not a problem even if the results did not fit exactly with the field, and it was considered as enough accurate for large scale studies. Now, available datasets are more and more accurate, and the resolution reaches 1 m even for large areas.

Algorithms are no longer efficient enough to process such DEM, and noise is even more 4.6. CONCLUSION present in large floodplain especially with LIDAR Data.

Conclusion

The automatized morphometric characterization step of the proposed procedure has proved to facilitate the extraction of critical variables in a reliable way. Even if it required a manual step (our methodology could be qualified as semi -automatized) for small upland catchments, it is very accurate for larger scales. Some errors persist but on a whole the procedure showed promising results.

The validation of the entire approach of debris-flow susceptibility also showed advances as it has never been applied at the large scale of the Southern French Alps. We integrated two predisposing factors which are the morphometric properties of the network and the sediment availability in lower order catchments. Our approach could still be improved by integrating a quantitative assessment of the effects of the sediment availability.

This first result is very important to give an insight of the debris-flow susceptibility at the scale of the study area. This has been integrated on a web platform (Figure 4.25), amongst other natural hazards assessment (RHYTMME project), to be overlaid with the precipitation hazards at various temporal scales in order to prevent debris-flow event triggering.

Intégration des facteurs de prédisposition

Il est nécessaire de se questionner sur la manière de prendre en compte les critères de prédisposition pour l'analyse de susceptibilité aux laves torrentielles : quelles sont les contributions relatives des différents facteurs de prédisposition ? Dans l'approche développée, la fourniture sédimentaire n'est que secondairement prise en compte pour ajuster qualitativement la susceptibilité au déclenchement et à la propagation de laves torrentielles : les seuils choisis, pour identifier comme contributeurs ou non les bassins versants de rangs inférieurs, sont fondés sur une analyse experte (voir 4.2.3.5). Cela ramène directement à la question de la prise en compte de la variabilité des apports sédimentaires dans la prédisposition aux événements.

A large échelle, il est apparu nécessaire d'utiliser la surface en érosion active comme proxy du stock sédimentaire facilement mobilisable par les agents d'érosion pour évaluer la prédisposition des bassins versants au déclenchement de laves torrentielles. Le choix de la surface en érosion comme indicateur est un premier pas. Il serait possible d'envisager des modèles statistiques plus complexes que celui proposé en Chapitre 2 et qui intègreraient aussi bien les caractéristiques morphométriques, que la fourniture sédimentaire (le second critère de prédisposition), à l'image de ce qui a été fait dans la littérature [START_REF] Guinau | GIS-based debris flow source and runout susceptibility assessment from DEM data -a case study in NW Nicaragua[END_REF][START_REF] Carrara | Comparing models of debris-flow susceptibility in the alpine environment[END_REF]. Cela permettrait une pondération plus objective de ces deux facteurs.

Afin d'améliorer notre approche, il faudrait également revoir, selon la position des différents tronçons dans le réseau hydrographique, le poids de la contribution potentielle à la propagation de laves torrentielles. Cela passe par la prise en compte non pas de leur rang -discutable au vu de la Figure 4.4, puisque deux tronçons de même rang peuvent présenter des tailles de bassin versant variant de un à plusieurs ordres de grandeur -mais de la taille de leur bassin versant. En d'autres termes, l'amélioration envisageable aurait été d'adapter les règles de décision de propagation présentées dans le Tableau 4.3 selon la taille 5.1. PRÉDISPOSITIONS À LA SUSCEPTIBILITÉ TORRENTIELLE des bassins versants des tronçons qui confluent afin que la classification de la susceptibilité torrentielle d'un tronçon dépendent du réseau qui se situe en amont, même si le facteur limitant de la propagation est la pente.

La connectivité sédimentaire est un autre facteur, contrôlant les flux sédimentaires entre les sources et les zones plus à l'aval du réseau hydrographique. Elle peut être considérée à différentes échelles, aussi bien à l'interface versants/chenal qu'au sein du réseau hydrographique (longitudinalement). Elle permet d'apprécier l'impact des zones en érosion active sur la recharge en sédiments du réseau hydrographique. La prise en compte de la connectivité hydro-sédimentaire dans l'étude de la susceptibilité aux laves torrentielles semble ainsi indispensable afin d'estimer le potentiel de disponibilité sédimentaire des zones en érosion situées en amont de torrents prédisposés à l'activité de laves torrentielles.

L'intégration d'un paramètre de connectivité permettrait de disposer d'une surface en érosion connectée qui améliorerait significativement la démarche d'évaluation de la susceptibilité aux laves torrentielles, abordée ici en s'appuyant sur la seule surface en érosion pour évaluer les apports sédimentaires.

La connectivité hydro-sédimentaire : définition d'un facteur clé pour l'évaluation des apports sédimentaires

Le terme de connectivité a souvent été utilisé en géomorphologie, en hydrologie et en écologie pour désigner le transfert d'énergie et de matière entre deux compartiments paysagers ou à l'intérieur d'un même système, comme un bassin versant (Fryirs et al., 2007). Pourtant, à l'heure actuelle, la communauté scientifique ne s'est pas encore accordée sur une définition commune. Ce terme est employé dans de nombreux cas, tels la connectivité paysagère qui s'applique à l'interface de plusieurs compartiments paysagers, ou les connectivités hydrologiques et sédimentaires dans le cadre de l'étude des flux d'eau et de matériaux [START_REF] Bracken | The concept of hydrological connectivity and its contribution to understanding runoff-dominated geomorphic systems[END_REF].

L'évaluation du degré de connectivité entre plusieurs compartiments paysagers a fait l'objet d'un grand nombre de publications afin de répondre à des objectifs variés tels l'évaluation écologique [START_REF] Urban | landscape connectivity : A graph-theoretic perspective[END_REF][START_REF] Spens | Network connectivity and dispersal barriers : using geographical information system (GIS) tools to predict landscape scale distribution of a key predator (Esox lucius) among lakes[END_REF] ou géomorphologique [START_REF] Burnett | A multi-scale segmentation/object relationship modelling methodology for landscape analysis[END_REF][START_REF] Brierley | Landscape connectivity : the geographic basis of geomorphic applications[END_REF]. En lien avec les bilans sédimentaires établis à large échelle, on recense de nombreux exemples intégrant la connectivité hydrologique pour la caractérisation des flux hydriques et sédimentaires au sein de bassins versants où l'érosion se fait essentiellement par ruissellement. Ces études intègrent des indicateurs topographiques rendant compte de la capacité des sédiments à être transférés vers le réseau hydrographique. Ces indicateurs, le plus utilisé étant SL le facteur topographique dépendant de la longueur et de l'inclinaison de la pente [START_REF] Wischmeier | Predicting rainfall erosion losses -a guide to conservation planning[END_REF], sont facilement extractibles par analyse hydrologique d'un MNT et ont largement été utilisés dans la mise en oeuvre de modèles d'érosion empiriques [START_REF] Wischmeier | Predicting rainfall erosion losses -a guide to conservation planning[END_REF][START_REF] Renard | RUSLE : Revised universal soil loss equation[END_REF][START_REF] De | Regional assessment of soil erosion using the distributed model SEMMED and remotely sensed data[END_REF][START_REF] Krasa | Predicting spatial patterns of sediment delivery and impacts of land-use scenarios on sediment transport in Czech catchments[END_REF], distribués et semi-physiques [START_REF] Morgan | A predictive model for the assessment of soil erosion risk[END_REF], et à base physique [START_REF] Kirkby | Modelling water erosion processes[END_REF][START_REF] Jetten | Erosion models : quality of spatial predictions[END_REF]. Ces différentes études se focalisent sur le ruissèlement dans des milieux dominés par l'agriculture, contexte bien différent de celui des Alpes du Sud. Cependant, elles confirment bien l'importance de l'intégration de la connectivité hydrologique pour évaluer la capacité de transport des fines.

L'étude de la connectivité hydrologique est également indispensable pour l'évaluation des flux sédimentaires grossiers transportés par les cours d'eau, et donc pour la caractérisation de la connectivité sédimentaire. Les travaux de Fryirs et Brierley (2000), d 'Harvey (2001'Harvey ( , 2002) ) et d [START_REF] Hooke | Coarse sediment connectivity in river channel systems : a conceptual framework and methodology[END_REF] sont pionniers dans ce domaine. Ils proposent des modèles conceptuels et des méthodologies pour traiter de la connectivité sédimentaire au sein de systèmes fluviaux (landscape linkages, coupling mechanisms). D'autres exemples plus récents sont proposés dans la littérature (Fryirs et al., 2007 ;[START_REF] Schwab | Contrasting sediment flux in Val Lumnezia (Graubünden, Eastern Swiss Alps), and implications for landscape development[END_REF]. Jain et Tandon [START_REF] Schumm | Geomorphic Thresholds : The Concept and Its Applications[END_REF][START_REF] Piégay | System Approaches in Fluvial Geomorphology[END_REF][START_REF] Piégay | Census and typology of braided rivers in the French Alps[END_REF][START_REF] Alber | Etude multi-scalaire de la dynamique latérale des tronçons fluviaux -Application au bassin rhodanien[END_REF][START_REF] Belletti | Analyse régionale de la structure et de la dynamique biogéomorphologiques des rivières en tresses du bassin du Rhône[END_REF] Cette figure montre qu'il existe une corrélation entre la largeur de bande active et la taille de bassin versant, qui s'exprime de manière un peu moins forte qu'à plus large échelle [START_REF] Belletti | Analyse régionale de la structure et de la dynamique biogéomorphologiques des rivières en tresses du bassin du Rhône[END_REF]. Afin de s'affranchir de l'effet de taille du bassin versant, la largeur de bande active est normalisée (adimensionnalisée) par la valeur de la largeur projetée sur l'ajustement selon une loi puissance (entre largeur et taille de bassin) présentée sur la Courbure tangentielle mesurée à l'intersection des plans définis par la normale à la surface et par une tangente à la perpendiculaire à la direction de la pente maximale [START_REF] Wood | The Geomorphological Characterisation of Digital Elevation Models[END_REF] Maximum curvature Courbure maximale mesurée dans n'importe quelle direction [START_REF] Wood | The Geomorphological Characterisation of Digital Elevation Models[END_REF] Minimum curvature Courbure mesurée dans la direction perpendiculaire à la direction de courbure maximale [START_REF] Wood | The Geomorphological Characterisation of Digital Elevation Models[END_REF] Les valeurs de surface connectées en érosion pour les bassins versants de rangs inférieurs (appelés rangs 1) sont ensuite sommées de l'amont vers l'aval. La cartographie des zones en érosion n'ayant été vérifiée que pour ces rangs 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

Influence des facteurs climatiques sur le déclenchement des laves torrentielles

Les laves torrentielles sont déclenchées par des pluies de forte intensité se produisant le plus souvent au printemps et en été et quelquefois par la fonte des neiges. Dans les Alpes du Sud, leur occurrence est fortement corrélée au nombre de jours de gel ou au nombre de jours présentant des précipitations supérieures à 20 -30 mm [START_REF] Jomelli | Geomorphic variations of debris flows and recent climatic change in the french Alps[END_REF][START_REF] Jomelli | Is the response of hill slope debris flows to recent climate change univocal ? A case study in the Massif des Ecrins (French Alps)[END_REF]

Abstract

The main objective of this thesis is to produce a methodology spatially characterizing the debris flow susceptibility at a regional scale. The methods used are based on geomatic and statistic fields and aim at integrating the predisposing factors to debris flow activity, ecpecially the morphometry and the sediment availability potential.

Robust statistical models allowed to predict the debris flow activity based on the morphometry of the reaches and their catchments in order to discriminate the bedload transport from the debris flow processes.

In source areas, the second predisposing factor, i.e. the sediment availability, was first mapped thanks to the analysis of infrared orthophotos (IGN©) and then expertly combined with the morphometric susceptibility within a GIS. The sediment availability potential of upland catchment consequently weights the probability of debris flow activity (firstly established from the morphometric characteristics) in order to predict the susceptibility to debris-flow triggering. More downstream, the predisposition to debris flow propagation depends on morphometric characteristics and is also controlled by the debris flow susceptibility of the upstream reaches. In the Southern French Alps, the entire approach has been validated with 50 expert observations. This work led to the production of new maps of debris flow triggering and propagation, already integrated on a service platform (RHYTMME project, Irstea and Météo-France). They can be superimposed on maps of precipitation hazard during intense events in order to identify the reaches susceptible to debris flow activity.

Keywords

  Vous avez été tous deux très complémentaires et m'avez laissée beaucoup d'autonomie. En cela je vous remercie sincèrement. Je remercie Catherine Méring et Franck Lavigne pour avoir accepté d'être les rapporteurs de ce travail. Merci à Laurence Hubert-Moy, Marco Cavalli et Patrice Mériaux également pour leur participation au jury de thèse. J'ajouterai une mention spéciale à Patrice qui a souvent été disponible pour valoriser mes travaux au sein du projet RHYTMME, lors de séminaire et avec qui nous avons beaucoup échangé lors de l'intégration des résultats de ma thèse sur la plateforme web co-construite avec MétéoFrance ® . Grazie a Marco Cavalli, i cui lavori sono stati per me un'importante fonte d'ispirazione (Merci à la traduction de B. Belletti). Rien n'aurait été possible sans les financements du projet PARAmount -UE Interreg Espace Alpine (« imProvedAccessibility : Reliability and security of Alpine transport infrastructure related to mountainous hazards in a changing climate ») -et du projet Rhytmme -CPER Provence-Alpes-Côte d'Azur (« Risques HYdrométéorologiques en Territoires de Montagnes et MEditerranéens »). Je suis très fière d'avoir apporté ma contribution et d'avoir été associée à des projets de cette ampleur. Le projet SedAlp (Interreg Alpine Space) qui a démarré en septembre 2012, dans le prolongement de mes travaux, m'a également permis de participer à des séminaires et à des conférences de rayonnement international.

1 ) 4 ) 1 .Figure 1 . 1 - 1

 141111 Figure 1.1 -Synthèse des objectifs et de leur organisation dans le manuscrit

Figure 1 . 2 -

 12 Figure 1.2 -Alpes du Sud et limite biogéographique avec les Alpes du Nord

Figure 1 . 3 -Figure 1 . 4 -Figure 1 Figure 1 . 5 -

 1314115 Figure 1.3 et représentées en fonction de leur population au dernier recensement (2010) d'après les données de l'INSEE.

Figure 1 .

 1 Figure 1.7 -Unités du secteur d'étude définies par leurs caractéristiques morphostructurales

Figure 1 1 . 1 . 4 Figure 1 . 4 .

 111414 Figure 1.8 -Caractéristiques climatiques principales ; (a) Précipitations annuelles moyennes et (b) Températures annuelles moyennes

Figure 1 .

 1 Figure 1.9 -Exemples photographiques des différents styles fluviaux

Figure 1 .

 1 Figure 1.11 -Densités de population des communes du secteur étudié

Figure 1 .

 1 Figure 1.12 -Réseaux routiers et ferrés du secteur étudié

Figure 1 .

 1 Figure 1.13 -Classification des types de rivières permettant de distinguer la rivière torrentielle du torrent selon des critères hydrauliques et sédimentaires, d'après Besson(1996)

Figure 1 .

 1 Figure 1.15 -Schéma d'une lave torrentielle ; D'après (a) Bardou (2002) et (b)[START_REF] Jakob | Debris-flow Hazards and Related Phenomena[END_REF]

Figure 1 .

 1 Figure 1.16 -Dépôts de laves torrentielles dans le torrent du Réal (06)

  the propensity of authors to oversample debris-flow fans in their dataset. Another reason is that the revisited case studies mostly consist of catchments sampled along mountain valleys, where small, rugged catchments building debris-flow fans are much more frequent than large, mild-slope catchments dominated by fluvial processes.The catchments are located in nine different alpine regions of the world: Apennines, Austrian Alps, Canadian Rockies,French Alps and Prealps, Italian Alps, North Cascade of USA, Pyrenees, Southern Alps of New Zealand, and Swiss Alps. The common physical features of all of these regions are the ruggedness of the relief and the humid-temperate or Mediterranean climates (arid and semi-arid mountains, as well as tropical mountains are not present in the sample, but Mediterranean conditions are: i.e. Apennines and Catalan

  statistical processing with balanced and unbalanced training sets to test empirically the effect of prevalence on model performance. Balanced training sets containing 90% of fluvial catchments (158) and an equivalent number of debris-flow catchments (each training set CHAPTER 2. DEBRIS-FLOW SUSCEPTIBILITY OF UPLAND CATCHMENTS contains 316 objects) were randomly sampled 1000 times without replacement. Unselected catchments (n = 304) were used to characterize the performance of the statistical models (referred as target sets). Unbalanced training sets were also sampled 1000 times, each containing 90% of catchments in each category (158 fluvial catchments and 400 debris-flow catchments). Target sets containing unsampled catchments were used to characterize the model performance (18 fluvial catchments and 44 debris-flow catchments). Sampling operation of balanced and unbalanced training and target sets was done twice to perform respectively 1000 LDA and 1000 LR models.

Figure 2 . 1 -Figure 2

 212 Figure 2.1 -Comparison of (a) Melton index and (b) fan or channel slope distributions for each response group; (c) values represented by the box plot, Q are quartiles

Figure 2 . 3 -

 23 Figure 2.3 -Comparison of the sensitivity and specificity indicators for (a) the LDA models based on balanced and unbalanced responses; (b) the LR models based on balanced and unbalanced responses

Figure 2 . 4 -

 24 Figure 2.4 -Prediction of the catchments response with the LDA model

  CHAPTER 2. DEBRIS-FLOW SUSCEPTIBILITY OF UPLAND CATCHMENTS and the specificity scores calculated on the training dataset. The LDA model shows a sensitivity of 0.96 and a specificity of 0.73. The LR model shows a sensitivity of 0.96 and a specificity of 0.75. Performances were also characterized using a cross validation with the Leave-One-Out (LOOCV) method. For the LDA model, the 95% confidence interval of the slopes is between -0.87 and -0.83, and for the intercept between 0.21 and 0.25. For the LR models, the 95% confidence interval of β 0 , β 1 (R) and β 2 (S) are -0.60 and 0.70, 1.63 and 1.70, and 1.98 and 2.03, respectively. The global sensitivity and specificity for the 620 LOOCV LDA models are 0.96 and 0.73, respectively, and the percentage of correct classification is 0.89.The global sensitivity and specificity for the 620 LOOCV LR models are 0.95 and 0.75, respectively, and the percentage of correct classification is 0.89.We evaluated the results of the two final models by building ROC curves based on the training dataset (Figure2.6). The two ROC curves of the final models are very closed of each other and shows a high level of performance, as confirmed by the very high area under the curve for both model (i.e., 0.9393 and 0.9394 for LDA and LR respectively).

Figure 2

 2 Figure 2.6 -ROC curve of the logistic regression unbalanced model prediction

  ;Marchi and Brochot 2000; De Scally and Owens 2004) provided a unique threshold value for single morphometric predictors above which debris-flow may occur. However there is no discontinuity between debris-flow and fluvial response in the distribution of both morphometric indicators, and a great proportion of fluvial catchments take values of Melton and fan slope close to the median values of debris-flow catchments (Figure 2.1). Instead of using unique thresholds, the combination of the two indicators into the proposed discriminant function (with a slope > 0)

CHAPTER 3 .

 3 HILLSLOPE EROSION MAPPING FROM MULTI-RESOLUTION AND MULTI-SOURCES REMOTE SENSING DATA: APPLICATION IN THE SOUTHERN FRENCH ALPS

CHAPTER 3 .

 3 HILLSLOPE EROSION MAPPING FROM MULTI-RESOLUTION AND MULTI-SOURCES REMOTE SENSING DATA: APPLICATION IN THE SOUTHERN FRENCH ALPS

  study area covers most of the Southern French Alps and includes the upper Durance and Drac river basins and the entire Var river basin (Figure 3.1). It spreads over about 16 800 km 2 and corresponds to the three administrative units of the Hautes-Alpes, the Alpes-de-Haute-Provence, and the Alpes-Maritimes departments (Easting range: 5°30'E to 7°42'E, Northing range: 43°28'N to 45°08'N). Elevations range from sea level to 4100 m asl, the highest elevations being located in the Ecrins Massif, in the northern Hautes-Alpes. Both physical and land-use features of the study area show a high spatial variability, from the near pristine conditions of the high-elevation mountains located in the national parks of the Ecrins or Mercantour ranges, to the intensive agricultural landscapes of the Durance valley and Valensole plateau. The study area can be subdivided in three regions of relative homogeneity in terms of physical (geology, relief, and climate) and land-cover conditions. ALTI®, BD Carthage®, GeoFLA®, © IGN Paris

Figure 3 . 1 -

 31 Figure 3.1 -Study area and main physiographic units

CHAPTER 3 .

 3 Figure 3.2 -Available remote sensing images and location of the training and validation orthophotos datasets

Figure 3 . 3 - 3 . 3 . 1

 33331 Figure 3.3 -(a) Overview of the general approach; (b) Workflow of the Landsat 7 ETM+ images processing; (c) Workflow of the infrared orthophotos processing

Figure 3 .

 3 3c. Infrared orthophotos were first cropped in quarters with GDAL © to be segmented with ENVI ® procedures[START_REF] Xiaoying | Segmentation-based image processing system[END_REF] within an IDL ® script. After a few tests with visual expert validation, scale parameter was set to 40, and merge parameter to 90 in order to aggregate finer segments. Each segmentation was exported into vector files containing all the geometrical, spectral and textural attributes. Three object-oriented supervised methods of classification were tested: Neural network, Rule-based classification and a NDVI threshold. Those methods were chosen because of their frequent use in the literature, and their good efficiency.The first method implemented is the Neural Network model. As multicollinearity between the raw attributes can be very high and in order to reduce the computational time needed to train a very complex network, we performed a preliminary statistical analysis to choose the most significant variables for the erosion mapping purpose. A Principal Component Analysis (PCA) (Figure3.4a) was performed in R software to determine correlations between each spectral, textural and geometrical parameter. The Neural Network model was then performed on a group of seven variables chosen from a graphical analysis of the PCA (see correlations onFigure 3.4b). The last one used the following variables: Minimum infrared band, Average infrared band, Minimum green band, Average green band, Infrared / red simple band ratio, Hue and Saturation combined within two layers neural network (hidden layer has seven neurons) with log-sigmoid transfer functions.

Figure 3 . 4 -

 34 Figure 3.4 -(a) Preliminary statistical analysis (PCA) of the raw variables extracted by the ENVI ® feature extraction workflow on orthophotos; Geometric indicators were not considered as discriminating and were not included in this PCA; (b) Group of seven variables chosen from an graphical analysis of the preliminary PCA, used for the Neural Network model implementation

3. 3 . 3 . 1 3 -

 3313 Accuracy assessmentPerformances of each model design and of the final model were assessed using conventionally used indicators. These efficiency indicators allowed to choose the weights accorded to each method design, and to evaluate our model when compared with simplest designs (one design without considering the NDVI indicator, and the other an unweighted combination of all the methods).We used sensitivity (true positive rate, Eq.(3.5)), specificity (true negative rate, Eq.(3.6)) and overall accuracy (correctly classified rate, Eq.(3.7)) indicators to compare the validation dataset with the classification models. These indicators are based on the confusion matrix 3(a + d)/(a + c + b + d) Confusion matrix (a, true positives; b, false positives; c, false negatives; duser's and producer's accuracies for the erosion class and derived respectively commission and omission errors in order to compare with literature scores. The user's accuracy (Eq.(3.8)) is the area correctly classified in erosion category divided by the total area classified as erosion. It represents the probability that the area classified into the erosion category actually represents erosion on the ground. The producer's accuracy represents the capacity of the model to well classify each category compared to all the ground observations. It our particular case, it is calculated as the sensitivity indicator (Eq.(3.5)) for the erosion class and as the specificity for the other class. User's accuracy = a/(a + b) ⇐⇒ 1 -Commission (3.8)

CHAPTER 3 .

 3 HILLSLOPE EROSION MAPPING FROM MULTI-RESOLUTION AND MULTI-SOURCES REMOTE SENSING DATA: APPLICATION IN THE SOUTHERN FRENCH ALPS

Figure 3 . 5 -Figure 3

 353 Figure 3.5 -Final map of erosion areas

  the influence of the NDVI model on the efficiency scores. The ultimate tested is a weighted sum of all the supervised classifications except for the NDVI model with weights proportional to the weights of the final model. All the performance indicators of this design are lower than the ones of the final model we proposed (i.e. 0.79, 0.92 and 0.88 respectively for sensitivity, specificity and overall accuracy indicators). This confirmed the useful role of the NDVI model to map erosion.

Figure 3 . 8 -

 38 Figure 3.8 -Local overall accuracy scores on the validation dataset and potential explanatory factors for their spatial distribution

  photos after the flight, rectifying them and cropping them to tile of 5 km) without loss of quality.

Figure 3 .

 3 Figure 3.10 -(a) Overall accuracy of each of the validation dataset tiles with the Landsat 7 ETM+ classification model taking into account the summer images (x) and the spring images (y); (a) Boxplots of sensitivity and specificity indicators calculated each of the validation dataset tiles with the Landsat 7 ETM+ classification model taking into account the summer images, the spring images and the proposed model

Figure 4 . 1 -

 41 Figure 4.1 -General overview of the debris-flow susceptibility assessment approach

Figure 4 . 2 -Figure 4 . 3 -

 4243 Figure 4.2 -Raw and corrected hydrographic networks

Figure 4 . 4 -Figure 4

 444 Figure 4.4 -Example of source units delimitation with location of terminal segments for slope measurement

Figure 4 . 6 -

 46 Figure 4.6 -Low order catchments manually corrected

Figure 4 . 7 -

 47 Figure 4.7 -Catchment delineations based on the 5 m and the 25 m DEMs

Figure 4

 4 decomposed the two morphometric indicators into three raw variables for the Melton index:(i) the maximum elevation of the catchment, (ii) the elevation of the catchment output, (iii) the drainage area; and two other variables for the channel slope: (a) the elevation of the downstream end of the terminal segment of each low order reach, (b) the terminal segment length (most of the time 50 m, except for smaller reaches).Several methods were tested to calculate the compounds of the Melton index (i.e., the catchment relief and the catchment area), depending on the procedures used to delineate the catchments, and their corresponding border accuracy. The catchment relief is the difference between the highest elevation and the outlet elevation of the catchment. Consequently, this relief depends only on the altimetric accuracy of the DEM and on the location of the catchment borders. We used the geometric value of the low order catchments as drainage area. The maximum elevation of the catchment was measured thanks to a zonal statistic performed within the Geospatial Modelling Environment software. In order to extract an interpolated elevation value at the catchment outlet, we interpolated the elevation values along the low order reaches, every 5 m. We reported the values from the catchments and the points to the reaches with an attribute query. ASSESSMENT WITHIN THE SOUTHERN FRENCH ALPS In order to calculate the terminal channel slope, we considered the downstream part of low order reaches and determined the local slope at the outlet of potential debris-flow initiation zones. We calculated a slope between the outlet and the terminal segment end node (

Figure 4 . 8 -

 48 Figure 4.8 -Method for channel slope calculation

Figure 4

 4 Figure 4.9 -Workflow for the definition of homogeneous slope reaches and their morphometric characterization

  sum of the geometrical values of areas of the local catchments (another function of the software we developed). For the other HSR, where catchment delineation has not been corrected, we used the value of flow accumulation at a snap point within 25 m around the outlet which presented the highest flow accumulation value. Another function we developed in our software is the correction of incoherent drainage area values. It compares flow accumulation values with the maximum value of the catchments located upstream and when it is lower, the value attributed to the current reach is set to the sum of the catchments' areas of the upper streams. It allowed correcting automatically some errors due to wrong flow accumulation values (due to the location of the outlet).

Figure 4 .

 4 Figure 4.10 -Location of the 50 sites of the validation dataset, according to their process responses

  ALTI®, BD TOPO®, GeoFLA®, © IGN Paris

Figure 4 .

 4 Figure 4.12 -Melton numbers of the low order reaches

  ALTI®, BD TOPO®, GeoFLA®, © IGN Paris

Figure 4 .

 4 Figure 4.14 -Probability of debris-flow activity of the low order reaches

Figure 4 .

 4 Figure 4.15 -Probability of debris-flow activity of the low order reaches, and susceptibility to debris-flow triggering according to the sediment availability

CHAPTER 4 .

 4 GIS APPLICATION OF DEBRIS-FLOW SUSCEPTIBILITY ASSESSMENT WITHIN THE SOUTHERN FRENCH ALPS

Figure 4 .

 4 Figure 4.17 -Distribution for the HSR of the (a) Length (m); (b) Drainage area (km ); (c) Melton number; (d) Slope (degree); (e) Probability of debris-flow activity; (f) Susceptibility to debris-flow triggering

Figure 4 .

 4 Figure 4.18 -Melton numbers of the HSR

Figure 4 .

 4 Figure 4.19 -Slopes of the HSR

Figure 4 .

 4 Figure 4.20 -Probability of debris-flow activity according to the morphometric indicators

  3, in order to integrate the debris-flow susceptibility of upstream reaches (both low order reaches and HSR) are shown in Figures 4.17f

  ALTI®, BD TOPO®, © IGN Paris

Figure 4 .

 4 Figure 4.23 -Susceptibility to debris-flow propagation according to the upstream susceptibility

CHAPTER 4 .

 4 GIS APPLICATION OF DEBRIS-FLOW SUSCEPTIBILITY ASSESSMENT WITHIN THE SOUTHERN FRENCH ALPS correction. Considering a lower resolution DEM, available in the upper Var and Tinée sectors, we tested effect of DEM resolution on the capacity to delineate the catchments.

Figure 4 .

 4 Figure 4.24 -Flow direction calculation methods both modified from (Tarboton, 1997) (a) D8; (b) Dinf

Figure 4 .Figure 5 . 1 -

 451 Figure 4.25 -Graphical example of susceptibility map on the web interface (a) for 1h cumulative rainfall; (b) for 72h cumulative rainfall

( 2010 )

 2010 proposent un cadre conceptuel pour la classification des degrés de connectivité, en lien avec le transport sédimentaire et la connectivité physique entre compartiments.[START_REF] Reid | Does hydrological connectivity improve modelling of coarse sediment delivery in upland environments ?[END_REF] proposent, quant à eux, d'évaluer les apports sédimentaires grossiers et de mesurer l'amélioration de leur modèle après l'intégration de la connectivité hydrologique (SHALSTAB couplé à TOPMODEL).Ces différents travaux nous montrent que le degré de connectivité hydro-sédimentaire est contrôlé par la topographie, l'intensité et la durée des précipitations, la couverture neigeuse, la présence de glissements de terrain le long des lits des torrents, et l'occupation du sol sur les versants et dans la plaine alluviale[START_REF] Arnaud-Fassetta | Fluvial geomorphology and flood-risk management[END_REF] et donc l'importance et la nature de la couverture végétale[START_REF] Sandercock | Vegetation effects on sediment connectivity and processes in an ephemeral channel in SE Spain[END_REF]. D'après Theler et al. (2010), la connectivité définit un système dans lequel les particules grossières se déplacent facilement et fréquemment dans le système et peuvent être transportées par des événements de crues de récurrence plutôt faible. Les travaux méthodologiques conduits en géomatique pour caractériser la connectivité sédimentaire se concentrent principalement sur l'extraction d'indices morphométriques. Heckmann et Schwanghart (2013) présentent par exemple un protocole où chaque processus est associé à des degrés de connectivité variés et est identifié sur la base d'un seuil de pente pour le déclenchement des chutes de blocs et d'un modèle statistique pour les laves torrentielles et le charriage. L'indicateur FlowLength (qui permet de mesurer la connectivité des eaux de ruissellement des zones sources) montre une très bonne corrélation avec des mesures locales de ruissellement (en mm) et de production sédimentaire (en kg.ha -1 ) sur les versants (Mayor et al., 2008). Borselli et al. (2008) et Cavalli et al. (2013) proposent aussi de définir des indices de connectivité des flux de sédiments et d'eau, basés sur des informations paysagères et sur une évaluation de terrain, prenant tous deux en compte l'occupation des sols, la topographie et l'intensité des événements. Miller et al. (2012) et Miller et al. (2013) exploitent quant à eux des variables morphométriques mesurées sur le terrain pour définir des zones où il existe un processus dominant, puis les caractérisent d'un point de vue morphologique et topographique, en lien avec le degré de connectivité de ces zones (chenalisation ou non / permanente ou non). L'aire de contribution (CAI, Contribution Area Index) développée dans Dalla Fontana et Marchi (1998) et Dalla Fontana et Marchi (2003) qui combine la surface drainée et la pente locale est aussi utilisée pour 5.1. PRÉDISPOSITIONS À LA SUSCEPTIBILITÉ TORRENTIELLE l'identification des têtes de bassin. Cet indicateur a également été repris dans Marchi et Dalla Fontana (2005) afin de classer les sources sédimentaires en fonction de leur activité et de leur capacité de transport. Une approche similaire a été adoptée dans Daya Sagar et al. (2003), Orlandini et al. (2011) et Vigiak et al. (2012). Les indicateurs morphométriques caractérisant la connectivité hydro-sédimentaire semblent ainsi faire l'objet de toutes les attentions à l'heure actuelle dans les travaux scientifiques. bibliographique des différents proxies de l'apport solide fait état de relations entre les caractéristiques géomorphométriques d'un tronçon, principalement sa largeur de bande active et la taille de son bassin versant

Figure 5 Figure 5 . 3 -

 553 Figure 5.2 -Cumul des surfaces en érosion en km

Figure

  Figure 5.3. A l'échelle régionale des Alpes du Sud, la surface en érosion est également fortement corrélée à la largeur de la bande active et à la taille de bassin versant. Afin d'éliminer la corrélation entre la surface en érosion et la surface drainée, la proportion d'érosion dans le bassin versant (Figure 5.4) est utilisée pour explorer les relations statistiques qu'il existe avec la largeur normalisée de la bande active (Figure 5.5).

Figure 5 . 4 -

 54 Figure 5.4 -Proportion des surfaces en érosion dans les bassins versants

Figure 5 . 6 -

 56 Figure 5.6 -Méthodologie géomatique d'extraction des indicateurs topographiques utilisés pour la caractérisation de la connectivité sédimentaire

Figure 5 . 8 -Figure 5 Figure 5

 5855 Figure 5.8 -Distribution de toutes les valeurs I / D pour les événements recensés dans la bibliographie étudiée, quelle que soient leur nature et la région étudiée

  figurer parmi les éléments à intégrer à l'avenir pour la caractérisation des phénomènes torrentiels.

3 . 3

 33 d'après Fig.1.C) Palaeo-glacial zones (Notebaert et Piégay, 2013) 1.7 Unités du secteur d'étude définies par leurs caractéristiques morphostructurales 1.8 Caractéristiques climatiques principales 1.9 Exemples photographiques des différents styles fluviaux 1.10 Distributions des résidus de la relation entre la largeur et la pente normalisées des fonds de vallées. D'après Fig 6. dans Notebaert et Piégay (2013) 1.11 Densités de population des communes du secteur étudié 1.12 Réseaux routiers et ferrés du secteur étudié 1.13 Classification des types de rivières permettant de distinguer la rivière torrentielle du torrent selon des critères hydrauliques et sédimentaires, d'après Besson (1996) 1.14 Schéma conceptuel d'un bassin versant torrentiel (dessin de N. Sardat) 1.15 Schéma d'une lave torrentielle 1.16 Dépôts de laves torrentielles dans le torrent du Réal (06) 2.1 Comparison of Melton index and fan or channel slope distributions for each response group; values represented by the box plot, Q are quartiles 2.2 Scatter plot of the fan/channel slope (S) versus Melton index (R) for the 620 catchments classified according to their geographic origin; Distribution of the residuals of the linear regression by region; Comparison scatterplot of fan and channel slope (S) versus Melton index (R) for the 620 catchments 2.3 Comparison of the sensitivity and specificity indicators for the LDA models based on balanced and unbalanced responses; the LR models based on balanced and unbalanced responses 2.4 Prediction of the catchments response with the LDA model 2.5 Prediction of catchments response with the LR model 2.6 ROC curve of the logistic regression unbalanced model prediction LISTE DES FIGURES / LIST OF FIGURES 3.1 Study area and main physiographic units 3.2 Available remote sensing images and location of the training and validation orthophotos datasets Overview of the general approach 3.4 Principal Component Analysis (PCA) of the raw variables extracted by the ENVI ® feature extraction workflow on orthophotos; Geometric indicators were not considered as discriminating and were not included in this PCA; Group of seven variables chosen from an graphical analysis of the preliminary PCA, used for the Neural Network model implementation 3.5 Final map of erosion areas 3.6 Geographic zooms of the erosion areas map 3.7 Efficiency scores of the individual and combined classification models 3.8 Local overall accuracy scores on the validation dataset and potential explanatory factors for their spatial distribution 3.9 Comparison of quality of the raw infrared orthophotos depending on the department 3.10 Overall accuracy of each of the validation dataset tiles with the Landsat 7 ETM+ classification model taking into account the summer images (x) and the spring images (y); Boxplots of sensitivity and specificity indicators calculated each of the validation dataset tiles with the Landsat 7 ETM+ classification model taking into account the summer images,the spring images and the proposed model 4.1 General overview of the debris-flow susceptibility assessment approach 4.2 Raw and corrected hydrographic networks 4.3 Pre-processing of the DEM: ellipses are data layers and rectangles are the processing steps 4.4 Example of source units delimitation with location of terminal segments for slope measurement 4.5 Workflow for catchments delineation 4.6 Low order catchments manually corrected 4.7 Catchment delineations based on the 5 m and the 25 m DEMs 4.8 Method for channel slope calculation 4.9 Workflow for the definition of homogeneous slope reaches and their morphometric characterization 4.10 Location of the 50 sites of the validation dataset, according to their process responses 4.11 Distribution of the main morphometric indicators for the low order reaches 4.12 Melton numbers of the low order reaches 4.13 Slopes of the low order reaches 4.14 Probability of debris-flow activity of the low order reaches 4.15 Probability of debris-flow activity of the low order reaches, and susceptibility to debris-flow triggering according to the sediment availabilityRésuméL'objectif de cette thèse est de produire une méthodologie de restitution spatiale de la susceptibilité torrentielle à une échelle régionale. Les méthodes géomatiques et statistiques mises en oeuvre visent à intégrer différents facteurs de prédisposition au phénomène de laves torrentielles, en particulier les caractéristiques morphométriques des tronçons et de leur bassin versant et leur potentiel de fourniture sédimentaire.La définition de modèles statistiques robustes a permis de prédire l'activité torrentielle à partir de la morphométrie des tronçons et de leur bassin versant, et permettent la discrimination des processus de laves torrentielles et de charriage.Au niveau des zones sources, le second facteur de prédisposition qu'est la disponibilité sédimentaire, est cartographié à partir de l'analyse des orthophotographies infrarouges de l'IGN©, puis est combiné à la susceptibilité morphométrique dans un SIG de manière experte. Ainsi, le potentiel sédimentaire des bassins versants sources vient pondérer la probabilité d'activité de lave torrentielle établie à partir du potentiel morphométrique dans le but de prédire la susceptibilité au déclenchement. Plus aval, la prédisposition à la propagation de laves torrentielles dépend des caractéristiques morphométriques et est également contrôlée par la susceptibilité torrentielle des biefs situés juste en amont (approche réseau). L'application de la démarche dans les Alpes du Sud a été validée avec 50 observations expertes.Cette thèse a conduit à la production des cartes des zones de déclenchement de laves torrentielles, et à l'identification de leur zone de propagation potentielle, intégrées à une plateforme de services (projet RHYTMME, Irstea et Météo-France). Elles peuvent être superposées avec les aléas de précipitations pour identifier les secteurs susceptibles à l'activité de laves torrentielles lors d'événements de précipitations de forte intensité. Mots clés : Alpes du Sud • Laves torrentielles • Morphométrie • Statistique • Susceptibilité • Système d'Information Géographique • Télédétection • Zones en érosion

:

  Southern French Alps • Debris flows • Morphometry • Statistiques • Susceptibility • Geographical Information System • Remote sensing • Erosion patches

Table des matières -Contents 1.1 Contexte géographique du terrain d'étude

	générales
	1.2.2 Déclenchement des laves torrentielles
	1.2.3 Propagation
	1.2.4 Dépôts
	1.3 Contexte méthodologique
	1.3.1 Les données utilisées
	1.3.1.1 Données spatialisées numériques
	1.3.1.2 Données issues de la bibliographie
	1.3.2 Les outils de traitement de l'information spatialisée
	1.3.2.1 Les SIG comme outils de visualisation, d'intégration, de struc-
	turation, d'analyse et de communication des données géographiques
	1.3.2.2 Le traitement des images

1.1.1 Présentation générale des Alpes du Sud 1.1.2 Contexte morphostructural et géologique 1.1.3 Influences climatiques 1.1.4 Rivières torrentielles et torrents des Alpes du Sud : le réseau hydrographique étudié 1.1.5 Enjeux socio-économiques du territoire 1.2 Cadre conceptuel : la susceptibilité torrentielle 1.2.1 Définition et caractéristiques

  . Les apports des laves torrentielles conditionnent donc pour partie les formes fluviales observées à l'échelle des réseaux hydrographiques. La caractérisation de leur occurrence spatiale est donc un enjeu important. A l'échelle de l'ensemble des Alpes du Sud, certains tronçons à forte charge et à capacité de transport limitée sont instables car susceptibles de réagir plus rapidement aux modifications des forçages hydro-climatiques. Ces tronçons sont assez fréquents dans les rivières de montagne et posent des problèmes de gestion des risques. En effet, les plaines alluviales sont souvent très anthropisées et un risque accru d'inondation existe du fait de leur présence. Outre la sécurité des personnes qui est en jeu, l'aléa inondation peut également entraîner la destruction d'infrastructures. Cela se manifeste par exemple par la déstabilisation de piles de pont et la destruction de chaussées comme sur le Guil

1.2 Cadre conceptuel : la susceptibilité torrentielle 1.2.1 Définition et caractéristiques générales

Les laves torrentielles, ayant d'une part une capacité de transport très importante et d'autre part des vitesses de propagation très élevées, figurent parmi les aléas naturels les plus dévastateurs, causant le plus de dommages matériels et de pertes humaines, 1.2. CADRE CONCEPTUEL : LA SUSCEPTIBILITÉ TORRENTIELLE indépendamment de leur intensité. Cependant, de nombreux événements n'étant jamais signalés en milieu de montagne car ceux-ci ne touchent pas toujours des zones vulnérables (zones inoccupées), leur occurrence spatiale demeure peu connue.

1.3.1 Les données utilisées

		1.3. CONTEXTE MÉTHODOLOGIQUE 1.3. CONTEXTE MÉTHODOLOGIQUE			CHAPITRE 1. INTRODUCTION
	1.	Topographie	Imagerie	Fond de plan Thématique
		Depuis 2010, l'Institut National de l'information Géographique et Forestière (IGN © ) a
		créé une nouvelle licence pour les chercheurs et enseignants permettant le téléchargement gratuit des jeux de données constitués à l'échelle régionale. La liste des données disponibles Format Raster Raster Raster Raster Raster Raster Format Vectoriel Vectoriel Vectoriel Vectoriel Vectoriel Vectoriel Vectoriel Tableau
		s'en est trouvée considérablement accrue. Ces données offrent l'avantage d'être uniformes,
		référencées spatialement et récentes. D'autres sources de données ont été utilisées : il s'agit de la base de données des événements mise à jour par les services de Restauration des Terrains en Montagne de l'Office National des Forêts, des images Landsat 7 ETM+ et enfin Source IGN IRSTEA NASA et USGS IGN IGN IGN Source IGN IGN Union européenne IGN IGN IGN RTM (ONF) Littérature
		des données issues de la littérature. Un tableau récapitulatif rassemble les caractéristiques des différentes données disponibles pour cette thèse (Tableau 1.1). Un descriptif plus détaillé de chacun des jeux de données sera présenté dans les différentes sections qui suivent. Date 2011 2010 Entre 2001 et 2003 2003 et 2004 2009 2010-2012 Date 2011 2012 2006 2008 Entre 2003 et 2006, dépend de la date des orthophotographies sur lesquelles sont digitalisés les polygones 2009 2012 2012
	Tableau 1.1 -Données disponibles	Echelle -Résolution Echelle -Résolution Etendue géographique Etendue géographique 25 m de résolution spatiale Digitalisées au 1 : 10000, précision 3,63 m de résolution spatiale, erreur géométrique entre 0,5 m et 10 m verticale 1m, horizontale 2m selon la méthode utilisée 3 Départements Haut-Var et Tinée 3 Départements	(photogrammétrie, version antérieure	30 m de résolution spatiale pour les ou calculé) Etablie au 1 : 50000 bandes 1-5 et 7 3 Départements 3 Départements	0,5 m de résolution spatiale 3 Départements	0,5 m de résolution spatiale Etablie au 1 : 100000 ; 44 postes 3 Départements 3 Départements	Échelle 1 : 25000 Etablie au 1 : 100000 3 Départements 3 Départements	Digitalisées au 1 : 10000, précision Bassin RM&C	géométrique entre 0,5 m et 10 m ; La	couche de bande active s'arrête en	amont là où la bande active fait	moins de 7,5 m	Digitalisées sur la base de la BD ALTI ® 50 m de résolution spatiale Bassin RM&C	Digitalisées au 1 : 10000 (événements 3 Départements	localisés sur la couche des routes de	la BD TOPO)	Mondiale
	De nombreuses méthodes, couramment utilisées en sciences environnementales, mais aussi empruntées à d'autres disciplines comme l'histoire ou l'informatique, sont aujourd'hui disponibles pour l'analyse quantitative des données. Certaines d'entre elles sont ainsi mises en oeuvre pour caractériser la susceptibilité torrentielle aux échelles régionales. Elles seront exposées après une rapide présentation de toutes les données disponibles. Description Modèle numérique de terrain Modèle Numérique de Terrain obtenu à partir d'acquisitions aéroportées par radar interférométrique à synthèse d'ouverture (IFSAR) Images satellites large échelle, dont le spectre s'étend du visible à l'infrarouge Orthophotos constituées des bandes bleue, verte et rouge Orthophotos constituées des bandes verte, rouge, et proche infrarouge Carte topographique Version 3 Description Couches vectorielles de la végétation arborée, des lacs, du bâti, des infrastructures de transport et des réseaux hydrographiques Délimitation des zones hydrographiques (de la plus large à la plus fine) : bassin, région, secteur, sous-Secteur, zone hydrographique Occupation du sol à large échelle (Europe) Contours administratifs de départements et communes Bande active issue du traitement de la BD TOPO (méthode définie par M. Bertrand en 2010 et présentée dans Wiederkehr 2012) Délimitation des fonds de vallées à partir d'une analyse d'un MNT (Alber 2012) Base des événements de laves torrentielles ayant eu des impacts sur les réseaux de transport Indicateurs morphométriques de bassins versants étudiés dans la littérature
		Couche Couche d'information d'information BD Alti ®	MNT	Intermap-Geosys ® BD Topo ®	Landsat 7 ETM+ ® BD Carthage ®	BD Ortho Couleur ® Corine Land BD Ortho IRC ® Cover ® Geofla ® Scan 25 ®	Bande Active					FDV	BD RTM ®		BD Morpho-	métrie

3.1.1 Données spatialisées numériques

	Les modèles numériques de terrain BD ALTI ® et MNT Intermap-Geosys © ont permis
	de faire une analyse hydrologique et de comparer les performances des algorithmes de
	délimitation de bassins versants à plusieurs résolutions. Le modèle numérique de terrain
	régional (BD ALTI ® ) a servi à l'extraction de variables morphométriques.
	Les images satellites Landsat 7 ETM+ et les orthophotographies infrarouges ont
	été analysées afin de produire une cartographie des zones en érosion à large échelle.
	Les orthophotographies classiques ont surtout servi pour le repérage sur le terrain et la
	vérification de la classification des orthophotographies infrarouges lors de doutes subsistants
	sur l'identification des zones en érosion.
	Les images du Scan 25 ® , représentation numérique des cartes topographiques que l'on
	retrouve au format papier, ont surtout été utilisées pour se repérer. C'est le cas aussi des
	couches vectorielles délimitant les départements, les communes (GEOFLA ® ), les cours
	d'eau, les réseaux de transport (BD TOPO ® ) et les différents découpages hydrographiques
	de la BD Carthage ® (bassins, régions, secteurs, sous-secteurs, et zones), l'occupation des
	sols (Corine Land Cover ® ) et les couches des bandes actives et des fonds de vallées (définies
	pour les bassins versants très larges).

1.3.2 Les outils de traitement de l'information spatialisée 1.3.2.1 Les SIG comme outils de visualisation, d'intégration, de structuration, d'analyse et de communication des données géographiques

		1.3. CONTEXTE MÉTHODOLOGIQUE	CHAPITRE 1. INTRODUCTION
	1	indispensable pour rassembler les données spatialisées, les exploiter et communiquer sur
		les résultats produits.
		Ce déploiement ne correspond pas, comme beaucoup le pensent, à l'installation d'une so-
		lution logicielle commerciale SIG, comme ArcGIS ™ , édité par la société ESRI © . La démarche
		est plus vaste, puisqu'elle n'englobe pas que les aspects techniques et organisationnels,
		mais permet de réellement s'interroger sur des questions thématiques très variées avec un
		point de vue géographique, notamment sur les questions environnementales. Dans notre
		cas, l'objectif est de caractériser l'activité torrentielle : cela suppose que les jeux de données
		soient suffisamment précis et leur emprise spatiale suffisamment étendue car les objets
		auxquels on s'intéresse (les torrents, leur bassin versant et leurs sources sédimentaires) sont
		de petite taille mais sont distribués au sein d'un vaste ensemble régional.
		En s'interrogeant sur les processus torrentiels en eux-mêmes, on peut établir la liste
		des données permettant la capture d'informations géographiques à partir d'une analyse
		spatialisée. Cette phase de collecte et de sélection des données, qu'elles soient géographiques,
		au sens « intégrables directement dans un SIG » ou issues de la littérature sous formes
		textuelles ou de tableaux (ces données constituant également un état de l'art alimentant la
		réflexion sur les processus) fait partie intégrante de la mise en oeuvre d'un SIG et pourrait
		être considérée comme une première étape de cette démarche.
		Pour ce qui est de la structuration des données, une organisation plutôt classique a été
		adoptée : on distingue les données brutes des données produites pendant la phase d'analyse
		spatiale. Cette structuration évolue au cours de la phase de traitement, puisqu'elle doit
		s'adapter à la création de données nouvelles, résultats des traitements. Les données issues de
		l'analyse bibliographique ont permis de construire un modèle statistique pour la prédiction
		des réponses torrentielles fondé sur une analyse morphométrique du modèle numérique
	de terrain. Cette analyse a ensuite été couplée à l'analyse des orthophotographies dans le torrentiel, et plus particulièrement celles centrées sur la discrimination des processus basée but de caractériser la susceptibilité torrentielle et de commencer à explorer le concept de sur des paramètres morphométriques. Nous avons ainsi réalisé un tableau de données connectivité hydro-sédimentaire. répertoriant les indicateurs de Melton et de pente du cône de déjection, pour 620 bassins L'analyse spatiale des données est la phase de traitement de la démarche de mise en versants, en distinguant ceux qui sont à l'origine de laves torrentielles. Quand les données place du SIG. La liste des solutions logicielles utilisées est donnée ci-après. La caractérisation étaient disponibles directement nous les avons simplement recopiées, lorsque les données morphométrique du terrain d'étude fait intervenir le logiciel ArcGIS ™ mais également de étaient présentées sous forme graphique, nous avons utilisé l'outil Get Data Graph Digitizer © nombreux logiciels libres pour le traitement des rasters (surtout pour les tâches d'analyse afin de récupérer les valeurs. hydrologique) dont la liste est la suivante : SAGA © GIS, GRASS © , LandSerf © , et un
		Plug-in ArcGIS ™ appelé Arc Hydro © Tools. Pour l'analyse des données de réseaux, le
		logiciel ArcGIS ™ a été utilisé mais l'intégration dans une base de données MySQL ™ s'est
		avérée nécessaire pour les requêtes et la mise à jour des informations dépendant de plusieurs
		échelles spatiales.
	Les livrables opérationnels prévus dans le cadre du projet financeur ont été intégrés à la Cette thèse reposant exclusivement sur des analyses de données numériques spatialisées, plateforme de services web SIG, intégrant également les données des autres axes du projet nous avons dû d'adopter une stratégie de structuration des données pour faciliter les telles que l'aléa glissement de terrain, l'aléa hydrologique et l'aléa précipitation, intégré à échanges entre les logiciels que nous avons utilisés lors des différentes phases de traitement. Dans ce cadre, la mise en place d'un Système d'Information Géographique est apparue différents pas de temps.

.3.2.2 Le traitement des images Un

  pré-traitement des orthophotographies a été réalisé à partir de la librairie GDAL © .

	Une calibration des images Landsat 7 ETM+ et l'analyse d'images ayant permis d'aboutir
	à la cartographie des zones en érosion ont été réalisées principalement à partir de fonctions
	disponibles dans le logiciel ENVI ® .
	En raison de l'ampleur des possibilités en termes d'approches et d'algorithmes, l'uti-
	lisation de cette solution logicielle qui n'offre pas l'ensemble des fonctionnalités décrites
	dans la bibliographie à l'heure actuelle se justifie de plusieurs manières. Il s'agit en effet
	de l'unique solution logicielle facilement utilisable, disponible au laboratoire, et proposant
	une méthode orientée objet et une automatisation des traitements. Ce type de méthode
	est apparu indispensable pour traiter les orthophotographies en vue de cartographier les
	zones en érosion. Une rapide revue bibliographique sur la question, présentées en Chapitre
	3, montre que dans les approches de classification orientées objets, les algorithmes traitant
	de la segmentation en elle-même sont extrêmement variés, et pourtant d'un point de
	vue des solutions logicielles, seuls quelques algorithmes sont récurrents. Pour l'étape de
	segmentation, on retrouve très fréquemment, dans les logiciels spécialisés, des algorithmes
	assez simples fondés sur la détection des contours (watershed delineation) ou sur l'accrois-
	sement de région (Seeded Region Growing), alors que la revue bibliographique a montré
	des algorithmes multi-scalaires beaucoup plus performants (Chapitre 3) mais qui ne sont
	pas encore intégrés dans ces logiciels.
	La raison qui motive le choix du logiciel ENVI ® est donc sa disponibilité. Il offre
	l'avantage de disposer des méthodes de classification les plus répandues (ISO CLUSTER,
	Maximum Likelihood) permettant d'explorer dans un premier temps les possibilités de
	cartographie automatisée des orthophotographies.

Chapter 2 Debris-flow susceptibility of upland catchments

	Published in Natural Hazards 67, 497-511 (2013)

Table des matières -Contents 2.1 Introduction 2.2 Material and methods

	2.2.1 Database compilation
	2.2.2 Statistical analysis
	2.3 Results
	2.3.1 ANOVA tests
	2.3.2 Fan/channel slope vs. Melton index
	2.3.3 Prevalence effect on statistical model performances
	2.3.4 Statistical models and performances
	2

.4 Discussion and conclusion Résumé

	Une analyse de la bibliographie a montré qu'il était possible de distinguer les processus
	de charriage et de laves torrentielles sur la base d'indicateurs morphométriques des bassins
	versants torrentiels et de leur cône de déjection. Ces indicateurs sont l'indice de Melton, indice
	normalisé de l'énergie gravitationnelle du bassin versant, et de la pente du cône de déjection.
	L'étude de la variabilité de ces indicateurs a conduit à l'élaboration de modèles statistiques
	robustes, car construits sur des données réparties dans différents espaces montagneux du
	monde. Les modèles proposés sont des analyses discriminantes linéaires et des régressions
	logistiques. Ils montrent des scores de sensibilité et de spécificité très élevés. L'analyse de la
	littérature a aussi montré que la pente du chenal au-delà de laquelle le phénomène de lave
	torrentielle est observé diminue avec l'énergie gravitationnelle du bassin versant. Les limites
	de ce type d'approches ont ensuite discutées.

Table 2 .

 2 1 -References used for database compilation of debris-flow and fluvial catchments classified by alpine regions

	Region	n Debris-flow catchments Fluvial catchments	References
	Australian Alps	31	16	15	Scheidl and Rickenmann 2010
					Ceriani et al. 2000
					D'Agostino and Marchi 2001
					Mambretti 2009
	Italian Alps	198	175	23	Marchi et al. 1993
					Marchi and Cavalli 2007
					Scheidl and Rickenmann 2010
					Lenzi 2000
	Apennines	31	26	5	Sorriso-Valvo et al. 1998
					Malet et al. 2004
					Marchi and Brochot 2000
	French Alpts	134	64	70	Remaître 2006
					Thénard 2009
					Liébault 2003
	Swiss Alpts	40	40	0	Scheidl and Rickenmann 2010
	Pyrenees	5	3	2	Gomez-Villar and Garcia-Ruiz 2000 Hürlimann et al. 2006
					Jackson et al. 1987
	Canadian Rockies	51	35	16	Jordan 2007
					Kostaschuk et al. 1986
	North Cascade USA	12	12	0	Kovanen and Slaymaker 2008
	Southern Alps NZ	118	73	45	De Scally and Owens 2004 De Scally et al. 2010
	Total	620	444	176

Table 2 .

 2 2 -Scores of the local models when used to predict the response of the 620 catchments; Tp: True positive case, Fp: False positive case, Fn: False negative case, Tn: True negative case, (a) and (b) are formulas for lower and upper thresholds of R DEBRIS-FLOW SUSCEPTIBILITY OF UPLAND CATCHMENTS located in other countries or other alpine regions, even if the thresholds proposed by[START_REF] Marchi | Flow processes on alluvial fans in the Eastern Italian Alps[END_REF] Marchi and[START_REF] Marchi | Les cônes de déjection torrentiels dans les Alpes franà §aises, morphométrie et processus de transport solide torrentiel[END_REF] are better than the others. The results of the LDA and the LR models are also quite good locally, compared to the performance of the local models proposed in the previous studies (Table2.3). The sensitivity and specificity scores of these two models are better or very close to those of the model proposed by[START_REF] Jackson | Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountains[END_REF][START_REF] Marchi | Flow processes on alluvial fans in the Eastern Italian Alps[END_REF][START_REF] Marchi | Les cônes de déjection torrentiels dans les Alpes franà §aises, morphométrie et processus de transport solide torrentiel[END_REF], even if the specificity of our models for the catchments studied by De Scally and Owens 2004 is low.Table2.3 -Scores of the local models and of the two regional models proposed in this study when used to predict the response of the local databases; n: the number of catchments of the local databases used; (a) and (b) are formulas for lower and upper thresholds of R

	Models	Models Formulas	Tp Fp Fn Tn Sensitivity Specificity
	LDA (this study)	Equation (2.4)	427	48	17 128	0.96	0.73
	LR (this study)	Equation (2.6)	421	45	21 131	0.96	0.75
	Jackson et al. 1987 (a)		385 101	59	75	0.87	0.43
	Jackson et al. 1987 (b)		383	76	61 100	0.87	0.57
	Marchi et al. 1993	S = -13.67 • R + 7.29 433	61	11 115	0.97	0.65
	Marchi and Brochot 2000 (a)		377	68	67 108	0.85	0.61
	Marchi and Brochot 2000 (b)		370	59	74 117	0.83	0.66
	De Scally and Owens 2004		173	14 271 162	0.39	0.92

The various thresholds or discriminating functions proposed in the previous studies (Table

2

.2) always show lower efficiency to predict the debris-flow response of catchment CHAPTER 2.

Table des matières -Contents

  La caractérisation aux échelles régionales des zones en érosion est un enjeu important pour la mise en oeuvre de l'approche d'évaluation de la susceptibilité torrentielle. Ces zones en érosion représentent en effet un apport sédimentaire potentiel au réseau hydrographique ; il s'agit donc d'un facteur de prédisposition très important pour le déclenchement de laves torrentielles, dont les impacts se répercutent bien en aval de leur introduction aux réseaux hydrographiques.Aux échelles régionales, une évaluation des volumes de sédiments impliqués n'est cependant pas envisageable avec les méthodes de terrain utilisées dans de petits bassins versants. Nous avons donc choisi d'utiliser des méthodes de télédétection avec des jeux de données disponibles à large échelle, en particulier des orthophotographies infrarouges (0,5m) et des images Landsat 7 ETM+. Après une brève revue bibliographique des méthodes couramment utilisées dans la littérature, la méthodologie développée spécifiquement dans le but de cartographier les zones en érosion sera présentée, avec sa mise en oeuvre dans le secteur dans les Alpes du sud. Nous discuterons ensuite des apports scientifiques de cette méthodologie.

	CHAPTER 3. HILLSLOPE EROSION MAPPING FROM MULTI-RESOLUTION AND
	MULTI-SOURCES REMOTE SENSING DATA: APPLICATION IN THE SOUTHERN
	FRENCH ALPS
	Résumé
	3.1 Introduction
	3.2 Study area
	3.3 Method
	3.3.1 Processing of the Landsat 7 ETM+ images
	3.3.2 Processing of the infrared orthophotos
	3.3.3 Combination of the Landsat 7 ETM+ images and the orthophotos
	3.3.3.1 Accuracy assessment
	3.3.3.2 Explanation for chosen the weights
	3.4 Results
	3.5 Discussion
	3.5.1 Quality of the model compared to previous works
	3.5.2 Problems and potential improvements
	3.6 Conclusion

Table 3 .

 3 1 -Available data

	Dataset BD Topo ®	Description Scrubland, lake, build-up, road and	Accuracy -Resolution -Scale Digitized at 1:10000, accuracy be-	Date 2011
		railway features	tween 0.5m and 10m depending on
	Landsat 7 ETM+ ®	Large scale images within visible	the method used 30 m resolution	2001 -2003
	BD Ortho IRC ®	and infrared spectral regions Infrared orthophotos	0.5m resolution	2009

Table 3 .

 3 2 -Weighting of each classification outputs

	Approach Method	Data source	Weights Reasons for this choice of weighting
	Pixel	End-members	Landsat 7 ETM+	0.2 Rough spatial resolution of Landsat 7 ETM+
		classification		images; areas of erosion under 30 • 30m 2 are
				not detected, but showed a high specificity
	Object	Neural network	Infrared	0.1 Based on expert judgements for validation but
			orthophotos	does not take the new indicators into account
				(previous work) and showed lower specificity
				scores.
	Object	Rule-based	Infrared	0.2 Based on new indicators taking into account
			orthophotos	variability in reflectance for erosion areas, and
				showed high specificity
	Object	NDVI	Infrared	0.5 NDVI often proved as an efficient predictor for
		threshold	orthophotos	the vegetation cover showed the highest scores
				of sensitivity and specificity indicators

Table 3 .

 3 4 -Efficiency of the proposed model

		Sensitivity Specificity Overall	Commission	User	Omission
				accuracy	errors	accuracy	errors
	Global	0.81	0.94	0.90	0.13	0.87	0.19
	Minimum	0.00	0.44	0.46	0.00	0.00	0.01
	Maximum	0.99	1.00	1.00	1.00	1.00	1.00
	Mean	0.74	0.94	0.90	0.33	0.67	0.26
	Median	0.95	0.97	0.94	0.22	0.78	0.04
	Quantile 5%	0.00	0.79	0.72	0.00	0.00	0.01
	Quantile 95%	0.99	1.00	0.99	1.00	1.00	1.00
	Landsat	0.70	0.88	0.82	0.28	0.72	0.31
	model
	Neural	0.73	0.89	0.84	0.25	0.75	0.27
	Network
	Rule-based	0.81	0.93	0.90	0.15	0.85	0.19
	NDVI	0.81	0.94	0.90	0.13	0.87	0.19
	Unweighted	0.91	0.92	0.89	0.18	0.82	0.19
	model
	Without	0.79	0.93	0.88	0.17	0.83	0.21
	NDVI model

  User and producer accuracy and commission and omission error indicators show an improvement of the erosion areas classification compared toYüksel et al. (2008a). Eroglu et al. (2010) paper, dedicated to erosion risks of bare soil areas, developed a slightly better method for the bare soils identification as the User Accuracy is 93.3% and the Producer

	CHAPTER 3. HILLSLOPE EROSION MAPPING FROM MULTI-RESOLUTION AND
	MULTI-SOURCES REMOTE SENSING DATA: APPLICATION IN THE SOUTHERN
	3.5. DISCUSSION																				FRENCH ALPS
	Data source Accuracy, 84.5%, a bit below ours. Finally, Wundram and Löffler (2008) showed very Landsat TM Landsat TM/ETM+ Landsat TM/ETM+ IKONOS high-resolution panchromaticorthopho-tos and Landsat TM aerial Colour Infrared (CIR) photographs panchromatic aerial photographs Kite Aerial Photography ASTER level 1A lower scores for its bedrock / boulder class even this study aimed at analysing mountain
	Location Extent / scale Physiography landscapes. This led us to the conclusion that the mapping efficiency is strongly related to Spanish Pyrenees Central Spanish Pyrenees Philippines NortheasternTurkey North Italy California, USA Israel Norway Turkey Table 3.5 -Scores from literature review Medium (<100 km 2 ) Mountainous; humid and cold Large (>2000km 2 ) Mountainous ; humid and cold Medium (<100 km 2 ) Gently undulating Terrain, tropical climate Medium-Large (<150 km 2 Medium (<100 km 2 ) Small (<5km 2 ) Small (<5km 2 ) Small (<5km 2 ) Medium -Large (<250km 2 ) Mountainous; semi-humid Mountainous; humid-continental foothills of the Santa Cruz Mountains (low the objective of mapping. Classification designed for a particular case of land use / cover ridge); Mediterranean Coastal plain, Mediterranean low alpine belt, continental ) Mountainous, mapping should not be used if only few classes have to be identified, and specific methods Mediterreanean should be developed.
	Efficiency scores	Sensitivity: 0.87	Specificity:0.77	Sensitivity:from 0.47 to 0.77	Specificity:from 0.77 to 0.93	Overall accuracy:0.992	(for bare soils class)	User accuracy: 0.933	Producer accuracy: 0.845	Overall accuracy:0.68	(highest score for bare soils class)	User accuracy:0.33; 0.5;0.67	Producer accuracy:0.88; 0.75;0.75	Sensitivity:from 0.85 to 0.92	Specificity:from 0.98 to 0.99	User accuracy:0.15	(Bedrock boulder class)	Producer accuracy:0.8	(Bedrock boulder class)	User accuracy:0.35	(Bare land class)	Producer accuracy:0.86	(Bare land class)
		Alatorre and Beguería, 2009		Begueria, 2006		De Asis et al., 2008		Eroglu et al., 2010		Geneletti and Gorte, 2003		Lobo et al., 1998		Okeke and Karnieli, 2006		Wundram and Löffler, 2008				Yüksel et al., 2008b

. The overall accuracy of our model is 0.90 which is slightly lower than for De Asis et al. (2008) (0.992) but much more accurate than in Geneletti and Gorte (2003) (0.68 at best).

  HILLSLOPE EROSION MAPPING FROM MULTI-RESOLUTION AND MULTI-SOURCES REMOTE SENSING DATA: APPLICATION IN THE SOUTHERN FRENCH ALPS we proposed could have been likely more efficient if many images of various seasons were used, and if the Landsat 7 ETM+ images chosen were adapted to the landscape units, i.e. spring images for agricultural flat areas (plateaus and terraces) and autumn or summer images for mountainous area also in order to limit the snow coverage which caused less extended erosion patches detection. If we overlay the performance scores with a large scale land use / land cover map (CORINE LAND COVER designed at 1:100 000 scale (General Environment, Nuclear Safety and Civil Protection and European Commission, 1993) in order to identify the global pattern of land use, it confirms that lowest scores are found in alluvial plains, were agricultural practices are intensive. In mountainous area, it seems that the large erosion patches correspond to alpine pastures (not green all the year), or sparse or senescent vegetation. The use of such large scale map could allow, if coupled with relief and geology, to mask areas where erosion patches can never be found. To further explore this, we should again analyse the efficiency indicators within homogeneous landscape units.

	.1)) the model could
	maybe have better discriminate the arable lands from the bare soils because of the plants
	growing. To test this hypothesis, we tried to use an April 2003 Landsat 7 ETM+ image
	(which cover only the left part of the study area) and applied the same model than for
	summer Landsat 7 ETM+ images. This showed better results (Figure 3.10a) on alluvial

fans, terraces or plateaus (two tiles) but on the whole it decreased strongly the scores of efficiency

(Figure 3.10b)

. This is partly in contradiction with what we expected, but we would advise to still further test it, even if the weight given to the model which process the Landsat 7 ETM+ images is quite low and so does its contribution. The final model

CHAPTER 3.

Table des matières -Contents

	CHAPTER 4. GIS APPLICATION OF DEBRIS-FLOW SUSCEPTIBILITY
	ASSESSMENT WITHIN THE SOUTHERN FRENCH ALPS
	Résumé
	L'objectif majeur de ce chapitre est l'évaluation de la susceptibilité torrentielle dans les
	Alpes du Sud. Elle consiste dans un premier temps à évaluer la prédisposition morphomé-
	trique des petits bassins versants de rang inférieur au déclenchement de laves torrentielles,
	lorsque ceux-ci disposent d'une fourniture sédimentaire suffisante (telle que cela a été précisé
	dans le Chapitre 3). L'enjeu est de savoir si des laves torrentielles peuvent se propager
	vers l'aval compte tenu des caractéristiques morphométriques, et de la probabilité de
	déclenchement de laves ou de leur propagation pour les tronçons situés juste en amont. Ce
	chapitre présente la procédure méthodologique permettant l'extraction de ces indicateurs
	à partir d'un Système d'Information Géographique, intégrant une analyse hydrologique
	d'un Modèle Numérique de Terrain, et la prise en compte de la fourniture sédimentaire
	pour caractériser la probabilité d'occurrence spatiale de laves torrentielles à une échelle
	régionale. La méthodologie sert également à déterminer la probabilité de propagation des
	laves torrentielles vers l'aval (approche réseau).
	4.1 Introduction
	4.2 Material and method
	4.2.1 Available data
	4.2.2 General overview of the methodology
	4.2.3 Potential debris-flow triggering in source units
	4.2.3.1 Pre-processing of raw data
	4.2.3.2 Source units definition
	4.2.3.3 Morphometric characterization of the source units
	4.2.3.4 Debris-flow activity according to morphometric properties
	4.2.3.5 Debris-flow susceptibility integrating the sediment availability
	4.2.4 Potential debris-flow propagation through the network
	4.2.4.1 Homogeneous network units definition for debris-flow propagation
	4.2.4.2 Morphometric characterization of HSR
	4.2.4.3 Debris-flow activity according to morphometric properties
	4.2.4.4 Debris-flow susceptibility integrating the sediment availability
	4.2.5 Validation dataset for debris-flow susceptibility assessment
	4.3 Results
	4.3.1 Susceptibility to debris-flow triggering in source units
	4.3.2 Susceptibility to debris-flow propagation through the network
	4.4 Validity of the predicted debris-flow susceptibility
	4.5 Methodological limitations and perspectives
	4.6 Conclusion

Les indicateurs morphométriques utilisés pour caractériser la prédisposition d'un bassin au déclenchement ou à la propagation de laves torrentielles ont déjà été présentés dans le Chapitre 2. Il s'agit de l'indice de Melton et de la pente du chenal. Ces indicateurs viennent alimenter le modèle statistique du Chapitre 2, qui permet d'évaluer la probabilité d'occurrence spatiale de ces processus dans les Alpes du Sud. L'intégration de la fourniture sédimentaire s'appuie sur les résultats du Chapitre 3.

Table (

 (

	CHAPTER 4. GIS APPLICATION OF DEBRIS-FLOW SUSCEPTIBILITY
		ASSESSMENT WITHIN THE SOUTHERN FRENCH ALPS
		Table 4.1 -Raw data used
		Format	Spatial	Extent
		type	resolution / scale
	DEM BD Alti ®	Raster	25 m	3 alpine departments of the
				PACA region
	Hydrographical network BD TOPO ®	Vector	1 : 50 000	3 alpine departments of the PACA region
				4.1).

Table 4

 4

	.2 -Integration of sediment potential and morphometric predisposition for debris
	flow triggering of low order catchments
	Debris-flow susceptibility
	of low order reaches
	according to the
	morphometric
	potential	Null	Low	Intermediate	High
	Debris-flow	P≤0.02	0.02<P≤0.5	0.5<P≤0.75	0.75<P≤1
	susceptibility of low
	order catchments according
	to the sedimentary potential
	Low	Null 1	Low 2	Low 4	Intermediate 6
	High	Null	Intermediate 3	High 5	High 7

Table 4 .

 4 3 -Integration of sediment potential and morphometric predisposition for debris flow propagation along the HSR

	Debris-flow susceptibility of the
	current HSR according to
	the morphometric
	potential
	Highest
	debris-flow	Null	Low	Intermediate	High
	susceptibility class	P≤0.02	0.02<P≤0.5	0.5<P≤0.75	0.75<P≤1
	of the upstream HSR
	according to the
	morphometric and sediment
	potentials (adjusted class)
	Null	Null	Null 3	Null	Null
	P≤ 0.02
	Low	Null 1	Null 4	Low 7	Low 10
	0.02<P≤0.5
	Intermediate	Null 2	Low 5	Intermediate 8	Intermediate 11
	0.5<P≤0.75
	High	Null	Low 6	Intermediate 9	High 12
	0.75 < P ≤ 1

Table 4 .

 4

	4.

Table 4 .

 4 4 -Validation dataset (1 show debris flow activity, and not)

	REF	Sites

Table 4 .

 4 5 -Main characteristics of the low order reaches

		Minimum	Percentile 5%	Median Mean	Percentile 95% Maximum
	Length (m)	26.6	174.9	609.7	488.5	1617.9	6704.4
	Drainage area (km 2 )	3e -3	0.1	0.2	0.3	0.9	21.1
	Melton number	0.0	0.2	0.8	0.8	1.7	6.3
	Channel slope (degree)	0.0	1.1	10.2	12.3	30.1	60.9
	Probability to	0.0	0.1	0.9	0.8	1.0	1.0
	debris-flow activity

Table 4 .

 4 6 -Main characteristics of the HSR having a catchment area lower than 40 km 2

	Minimum	Percentile 5%	Median Mean	Percentile 95%	Maximum
	Length (m)	0.1	50.0	237.6	336.9	977.2	6650
	Drainage area (km 2 )	7e -3	0.3	2.1	5.5	24.7	40.0
	Melton number	0.0	0.1	0.4	0.5	1.1	4.0
	Channel slope (degree)	0.0	0.0	5.7	8.1	23.8	75.1
	Probability to	0.0	0.0	0.8	0.6	1.0	1.0
	debris-flow activity
	Length of HSR under 40 km² (m)

Table 4

 4

	.7 -Prediction scores of the susceptibility approach
	Number of validation individuals	50
	Overall accuracy	0.80
	True positive rate	0.34
	True negative rate	0.46
	False positive rate	0.04
	False negative rate	0.16
	Sensitivity	0.68
	Specificity	0.92

  évaluables à cette échelle, l'amélioration constante de la résolution des MNT (notamment le développement de bases de données Lidar régionalisées) permettra de caractériser la morphométrie de ces zones en érosion afin de prédire leur activité. D'autre part, l'alimentation de la plateforme RHYTMME par des données de précipitations permettra aussi, après superposition, de détecter les secteurs les plus dynamiques.A ce stade, le seul facteur qu'il nous est possible d'explorer est la connectivité qui joue un rôle majeur sur les transferts sédimentaires. L'échelle et la source des données étant très différentes de cellesde Borselli et al. (2008),[START_REF] Cavalli | Geomorphometric assessment of spatial sediment connectivity in small Alpine catchments[END_REF] ou[START_REF] Marchi | GIS morphometric indicators for the analysis of sediment dynamics in mountain basins[END_REF], une démarche exploratoire a été développée dans le but de mettre en évidence l'importance du facteur de connectivité dans le contrôle des apports sédimentaires aux chenaux, en utilisant une résolution de MNT grossière (25 m). L'hypothèse testée est qu'il existe un lien encore plus fort entre la largeur de la bande active et la surface érodée connectée si tant est que l'on appréhende la bonne échelle de connexion.

	5.1. PRÉDISPOSITIONS À LA SUSCEPTIBILITÉ TORRENTIELLE
	Dans les tests effectués, les surfaces en érosion connectées sont calculées à partir de
	différents indicateurs morphométriques (chaque indicateur morphométrique est produit à
	différents niveaux scalaires) calculés en amont. Ces indicateurs sont calculés à partir de
			Pente de la section aval du tronçon
				49.72
	Indice	Description	Références	7.64
	Convergence index	Basé sur l'orientation elle-même définie	Thommeret et al. (2010)
		comme la direction de la pente et correspond
		pour les pixels d'un noyau à l'angle entre
		cette orientation et la direction du centre
		du noyau. Les valeurs positives, négatives
		et nulles représentent respectivement les sur-
	faces divergentes, convergentes et non cour-Figure 5.5 -Relation entre la largeur normalisée de bande active et la proportion de bées surfaces en érosion par bassin versant ; les cercles proportionnels représentent la pente de Terrain Surface Convexity Pourcentage de pixels convexes amont calculé Iwahashi et Pike (2007)
	dans un voisinage. Les valeurs élevées corres-la section aval des tronçons, en degrés pondent aux plaines, aux terrasses alluviales
		et aux cônes de déjections
	tude moyenne des pixels avoisinant, permet-Cette première analyse montre que la surface en érosion ne peut être utilisée seule Topographic Position Index (TPI) Différence entre l'altitude du pixel et l'alti-Wilson et Gallant (2000)
	tant de classer les paysages en unités morpho-comme proxy de l'activité d'érosion sur les versants et qu'à cette échelle régionale d'autres logiques
	Relative Slope Position facteurs contrôlent la dynamique sédimentaire. L'intensité de l'érosion sur les versants Position du pixel sur la pente Böhner et al. (2006) dépend notamment de la nature lithologique (ou plutôt de leur érosivité), de la pente Cross-Sectional curvature
	et de l'intensité des précipitations. L'importance des transferts sédimentaires entre les
	versants et les chenaux dépend aussi de la connectivité hydro-sédimentaire. Ces différents
	facteurs pourraient expliquer la variabilité de la distribution des largeurs de bandes
	actives. Cependant, certains de ces contrôles ne peuvent pas être pris en compte ici par

manque de données à cette échelle. L'intensité de l'érosion sur les surfaces que nous avons identifiées ne pourrait être évaluée qu'à partir de l'érosivité des sols, le degré de fracturation, la pente des surfaces en érosion et l'intensité des précipitations. Si les premiers indicateurs sont intrinsèques à la nature et au degré d'usure des matériaux et sont difficilement l'analyse d'un voisinage de pixel (Figure 4.24a) d'après les équations décrites dans Wilson

[START_REF] Wilson | Terrain Analysis : Principles and Applications[END_REF]

et

[START_REF] Wood | The Geomorphological Characterisation of Digital Elevation Models[END_REF]

. Les différents indicateurs morphométriques testés sont présentés dans le Tableau 5.1).

Tableau 5.1 -Indices morphométriques testés pour évaluer la connectivité hydrosédimentaire

  1, seule la contribution sédimentaire de ces rangs est prise en compte dans le calcul et l'on admettra que la contribution sédimentaire 5.1. PRÉDISPOSITIONS À LA SUSCEPTIBILITÉ TORRENTIELLE des versants situés dans les bassins versants locaux des rangs supérieurs est négligeable. La démarche géomatique d'extraction des indicateurs est présentée dans la Figure 5.6. Les indicateurs de connectivité ont été testés à plusieurs échelles, en faisant varier la taille du voisinage et la distance de calcul autour du pixel d'intérêt. Différentes combinaisons ont été testées mais le détail ne sera pas présenté ici.

		Connectivity indicator
		Classification in 4 classes (quantiles)
		Thresholds
		Binary reclassification
	Erosion areas within low order catchments	Connected areas	Non connected areas
		Multiplication
		Erosion areas within low order catchments and within connected areas	Erosion areas within low order catchments apart from connected areas
		Sum of connected erosion areas to downstream reaches
		Connected erosion areas characterized for each reach

  INFLUENCE DES FACTEURS CLIMATIQUES SUR LE DÉCLENCHEMENT DES LAVES TORRENTIELLES de détermination sont plus faibles. Les seuils de chaque indice (en fonction des valeurs de quantiles) choisis pour restreindre l'étendue des zones connectées impactent de deux manières les coefficients de détermination des relations avec la largeur des bandes actives : excepté pour l'indice de convergence, la pente relative et l'indice de convexité, plus le seuil est élevé, moins l'indice de connectivité est pertinent, et ce quel que soit le niveau scalaire choisi. La tendance inverse, observée pour les autres indices, est une augmentation du coefficient de détermination avec la valeur seuil. Ce cadre d'analyse, intégrant des hypothèses sur la contribution sédimentaire des bassins locaux, démontre que la largeur de la bande active ne peut pas être prédite uniquement à partir de la surface en érosion connectée. Le jeu de tronçons utilisé devrait être filtré afin de ne pas intégrer des tronçons pouvant être contraints latéralement. Une analyse conduite par unité homogène en termes de sensibilité à l'érosion permettrait d'intégrer la variabilité des largeurs de bandes actives.

		0.4
		0.3
	R²	0.2
		0.1
		0.0	3
		Indices topographiques de connectivité
	Figure 5.7 -Coefficients de détermination des relations entre la surface en érosion connectée
	(plusieurs indicateurs et niveaux scalaires) et la largeur des bandes actives, pour des bassins
	torrentiels des Alpes du Sud
	Bien que ces tests soient préliminaires, on peut déjà mettre en évidence quelques pistes
	pour des travaux futurs.
	5.1.3.2 Premiers résultats et recommandations
	A l'échelle régionale, quel que soit l'indicateur topographique de connectivité considéré,
	celui-ci montre toujours un coefficient de détermination plus faible que la taille de bassin
	versant. Le niveau scalaire (le voisinage de calcul) choisi semble légèrement influencer
	les coefficients de détermination : en fait, plus le voisinage de calcul est grand plus les

valeurs des indices sont lissées et plus les zones connectées commencent plus bas dans le bassin versant, c'est-à-dire en contrebas des lignes de crête et montrent des formes plus arrondies. L'indice de convexité, l'indice Topographic Position Index ou encore la courbure maximale montrent qu'en prenant une valeur de voisinage plus grande, les coefficients 5.2.

Tous ces résultats montrent qu'il est nécessaire de poursuivre l'identification d'indicateurs simples rendant compte d'apports sédimentaires. La surface érodée seule n'est pas suffisante car elle ne rend pas compte de manière univoque de la sensibilité à l'érosion et de sa capacité à alimenter les chenaux aval. En zone de haute montagne particulièrement, les conditions topographiques et la présence de gorges rendent la prédictibilité des largeurs « libres » c'est-à-dire qui sont susceptibles de s'ajuster aux conditions de transport très difficiles.

  . A une échelle régionale, la prédiction de l'occurrence de laves torrentielles et donc la caractérisation de l'aléa est problématique car la variabilité des facteurs de déclenchement est importante.La base de données produite pendant le stage de Manon[START_REF] Bajard | Etude bibliographique des conditions de déclenchement des laves torrentielles en montagne[END_REF] synthétise les données d'intensité / durée des précipitations associées à des événements intenses (dont la nature a également été recensée) principalement d'après la base de données de Guzzetti Où I est l'intensité en millimètres par heure et D la durée en heures. Cette base de données nécessiterait un tri préalable afin de comprendre par quel moyen les données de précipitations ont été obtenues (monitoring / observation) puis recensées dans la littérature.Il serait également souhaitable d'évaluer la précision de ces données en fonction par exemple de la position des pluviomètres par rapport à la localisation des événements dans le bassin versant. Enfin, la fiabilité des valeurs serait d'autant plus importante si la nature des

	5.2. INFLUENCE DES FACTEURS CLIMATIQUES SUR LE DÉCLENCHEMENT
	DES LAVES TORRENTIELLES
	Crue
	Inconnu
	Lahar
	Lave torrentielle
	Shallow failure et al. (2008) ainsi que d'après 34 articles parus entre 1980 et 2011, certains ayant eux-mêmes été repris dans Guzzetti et al. (ibid.). La redondance des informations a été évitée le plus Shallow landslide and soil slip
	possible, même s'il peut subsister quelques doublons. Ce rapport recense également toutes les lois statistiques présentes dans ces articles sous la forme : I = aD -b (5.1) Intensité mm/h
	Durée h
	Une des pistes que nous avions envisagée au cours de ce travail était de caractériser les
	seuils d'intensité et la durée des précipitations déclenchant les laves torrentielles à l'image
	de ce qui avait été réalisé en Chapitre 2 par le biais d'analyses statistiques. L'intérêt de ces
	seuils aurait été de pouvoir, sous réserve d'avoir à disposition des données météorologiques
	en temps réel, mettre en évidence les secteurs susceptibles de réagir lors d'événements
	dépassant les conditions requises pour le déclenchement de laves torrentielles. Afin d'acquérir

ces données en temps réel, le projet Rhytmme a permis le déploiement de radar de nouvelle génération (à bande X, plus compacts et moins coûteux) afin de compléter la couverture en zone de montagne et de permettre aux acteurs locaux d'anticiper les événements dangereux et d'améliorer la gestion des risques montagnards. valeurs mesurées était toujours connue (moyenne, maximum). Néanmoins, dans un premier temps, l'ensemble des données est utilisé pour observer la variabilité du couple intensité et durée des précipitations. La Figure 5.8 représente la distribution des valeurs I / D pour tous les événements, quelle que soit la région étudiée ou le processus.

  Tableau 5.2 -Lois intensité / durée référencées à partir de l'étude bibliographique. Les échelles sont classées L : Locale, R : Régionale et G : Globale

	Loi Référence	Echelle Equation	Localisation
	1	Barbero et al. (2004)	L	I = 44.67 * D -0.78	Piedmont, NW Italy
	2	Bolley et Oliaro (1999)a	L	I = 9.52 * D -0.49	Rho Basin, Susa Valley, Piedmont,
					NW Italy
	3	Bolley et Oliaro (1999)b	L	I = 11.69 * D -0.48	Rho Basin, Susa Valley, Piedmont,
					NW Italy
	4	Bolley et Oliaro (1999)c	L	I = 11.00 * D -0.45	Perilleux Basin, Piedmont, NW
					Italy
	5	Bolley et Oliaro (1999)d	L	I = 10.67 * D -0.50	Perilleux Basin, Piedmont, NW
					Italy
	6	Bolley et Oliaro (1999)e	L	I = 12.65 * D -0.53	Champeyron Basin, Piedmont,
					NW Italy
	7	Bolley et Oliaro (1999)f	L	I = 18.68 * D -0.56	Champeyron Basin, Piedmont,
					NW Italy
	8	Cannon et Ellen (1985)a	L	I = 6.90 + 38 * D -1.00	San Francisco Bay Region,
					California
	9	Cannon et Ellen (1985)b	L	I = 2.50 + 300 * D -2.00	San Francisco Bay Region,
					California
	10	Floris et Veneri (2004)	L	I = 18.83 * D -0.59	Valzangona, N Apennines, Italy
	11	Jibson (1989)e	L	I = 41.83 * D -0.58	Hong Kong
	12	Marchi et al. (2002)	L	I = 15.00 * D -0.70	Moscardo Torrent, NE Italy
	13	Montgomery et al. (2000)	L	I = 9.90 * D -0.52	Mettman Ridge, Oregon
	14	Wieczorek (1987)	L	I = 1.70 + 9 * D -1.00	Central Santa Cruz Mountains,
					California
	15	Wieczorek et al. (2000)	L	I = 116.48 * D -0.63	Blue Ridge, Madison County,
					Virginia
	16	Zêzere et al.

  • Bertrand M. et al., Analyse de sensibilité de la réponse écologique à des changements hydrologique et géomorphologique résultant d'actions de restauration dans le bassin de la Drôme. Fête de la Science, Allex, France, 15/10/2011 • Bertrand M., Liébault F. & Piégay H., Debris-flow susceptibility at a regional scale, Southern Alps (France). EGU, Vienne, Autriche, 03-08/04/2011 et Séminaire TR RIVAGE, Aix-en-Provence, 17-18/05/2011 • Bertrand M. et al., Sensitivity analysis of environmental changes associated with riverscape evolutions at a network scale: Application to the Drôme River basin, France. EGU, Vienne, Autriche, 03-08/04/2011 Presentations • IAG, 27-31/08/2013, GIS-based methods to evaluate morphometric characteristics of small catchments within a debris-flow susceptibility assessment approach at a regional scale • Séminaire du projet RHYTMME, 17/12/2012, Susceptibilité aux laves torrentielles dans les Alpes du Sud : Aspects méthodologiques et Premiers livrables • AGU, 03-07/12/2012, Debris-flow susceptibility and hazard assessment at a regional scale from GIS analysis • Séminaire du programme Eaux et Territoires, 06/09/2012, Continuité et connectivité en géomorphologie • Atelier de restitution du projet RiskNat, 06-07/06/2012, Susceptibilité torrentielle dans les Alpes du Sud • Journée des doctorants de l'UMR 5600, 10/11/2011, A nos risques et périls! Les choix méthodologiques pour appréhender les différentes dimensions du risque fluvial • Séminaire du projet RHYTMME, 23/06/2011, Approches régionales de la susceptibilité torrentielle (Alpes du Sud) • Séminaire des doctorants en géomorphologie fluviale, 13/05/2011, Approches régionales de la susceptibilité torrentielle (Alpes du Sud) Article in proceedings • Bertrand M., Liébault F. & Piégay H., 23-26/04/2012, Susceptibility of small upland catchments to debris-flow, Proceedings of Interpraevent, Grenoble Peer-reviewed articles/ book chapters (scientific committee) • Gregory S., Hulse D., Bertrand M. & Oetter D., 2012, The role of remotely sensed data in future scenario analyses at a regional scale, In: Fluvial Remote Sensing for Science and Management, Carbonneau, P.E. & Piégay, H. (eds), Wiley-Blackwell • Bertrand M., Liébault F. & Piégay H., 2013, Debris-flow susceptibility of upland catchments, Natural Hazards, Volume 67, Issue 2, pp 497-511 • Bertrand M. et al., 2013, Sensitivity analysis of environmental changes associated with riverscape evolutions following sediment reintroduction: Geomatic approach on the Drôme River network, France, International Journal of River Basin Management, Volume 11, Issue 1 Synthèse des objectifs et de leur organisation dans le manuscrit 1.2 Alpes du Sud et limite biogéographique avec les Alpes du Nord 1.3 Principales villes du terrain d'étude et leur population 1.4 Altitudes et principaux massifs du terrain d'étude 1.5 Pentes du terrain d'étude, en degrés 1.6 Etendue des zones englacées lors des dernières grandes glaciations, figure modifiée

	Liste des figures / List of figures
	1.1

(a) (b)

Remerciements

El Tahir, M. El Haj et al. (2010). Identification and mapping of soil erosion areas in the Blue Nile, Eastern Sudan using multispectral ASTER and MODIS satellite data and the SRTM elevation model. Hydrology and Earth System Sciences 14 (7), p. 1167-1178. Eroglu, Habip et al. (2010). Using high resolution images and elevation data in classifying erosion risks of bare soil areas in the Hatila Valley Natural Protected Area, Turkey. Stochastic Environmental Research and Risk Assessment 24 (5), p. 699-704. Fannin, R.J. et T. P. Rollerson (1993). Debris flows : some physical characteristics and behaviour. Canadian Geotechnical journal 30 (1), p. 71-81. Floras, Stamatios A. et Ioannis D. Sgouras (1999). Use of geoinformation techniques in identifying and mapping areas of erosion in a hilly landscape of central Greece. International Journal of Applied Earth Observation and Geoinformation 1 (1), p. 68-77. Floris, M. et F. Veneri (2004). Landslide Risk Assessment in Italy : A Case Study in the Umbria-Marche Apennines. In : Lecture notes in Earth Sciences. Springer Berlin / Heidelberg, p. 738-744. Floris, M. et al. (2010). Recent changes in rainfall characteristics and their influence on thresholds for debris flow triggering in the Dolomitic area of Cortina d'Ampezzo, north-eastern Italian Alps. Natural Hazards And Earth System Sciences 10 (3), p. 571-580. Friedl, M.A. et C.E. Brodley (1997). Decision tree classification of land cover from remotely sensed data. Remote Sensing of Environment 61 (3), p. 399-409. Fryirs, K.A. et al. (2007). Catchment-scale (dis)connectivity in sediment flux in the upper Hunter catchment, New South Wales, Australia. Geomorphology 84 (3-4), p. 297-316. Fryirs, Kirstie et Gary Brierley (2000). A Geomorphic Approach to the Identification of River Recovery Potential. Physical Geography 21 (3), p. 244-277. Fuchu, D et al. (1999). Analysis of rainstorminduced slide-debris flows on natural terrain of Lantau Island, Hong Kong. Engineering Geology 51 (4), p. 279-290. Geneletti, D. et B. G. H. Gorte (2003). A method for object-oriented land cover classification combining Landsat TM data and aerial photographs. International Jour-

and propagation have been identified in Chapter 2, i.e. the index Melton and channel slope.

These indicators are used with the statistical model of Chapter 2 to predict processes in the Southern French Alps. Sediment availability is evaluated thanks to the results of the Chapter 3.

Keywords

Susceptibility to debris-flow propagation through the network

Following the definition of the hydrographical units we chosen, 34269 HSR having a catchment area lower than 40 km were identified. They seem to be relevant when overlaid on the topographic maps, some of the discontinuities statistically identified corresponding to dams, roads or abrupt in slope (Figure 4.9).

The main characteristics of these HSR are given in Table 4.6 and their distributions are illustrated in Figure 4.17